Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [289,10,Mod(1,289)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(289, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("289.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 289 = 17^{2} \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 289.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: | \(148.845356651\) |
Analytic rank: | \(1\) |
Dimension: | \(36\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.12 | ||
Character | \(\chi\) | \(=\) | 289.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −20.0534 | −0.886242 | −0.443121 | − | 0.896462i | \(-0.646129\pi\) | ||||
−0.443121 | + | 0.896462i | \(0.646129\pi\) | |||||||
\(3\) | 107.002 | 0.762686 | 0.381343 | − | 0.924434i | \(-0.375462\pi\) | ||||
0.381343 | + | 0.924434i | \(0.375462\pi\) | |||||||
\(4\) | −109.862 | −0.214575 | ||||||||
\(5\) | 2675.64 | 1.91454 | 0.957268 | − | 0.289204i | \(-0.0933905\pi\) | ||||
0.957268 | + | 0.289204i | \(0.0933905\pi\) | |||||||
\(6\) | −2145.75 | −0.675925 | ||||||||
\(7\) | −1982.25 | −0.312045 | −0.156022 | − | 0.987754i | \(-0.549867\pi\) | ||||
−0.156022 | + | 0.987754i | \(0.549867\pi\) | |||||||
\(8\) | 12470.4 | 1.07641 | ||||||||
\(9\) | −8233.60 | −0.418310 | ||||||||
\(10\) | −53655.7 | −1.69674 | ||||||||
\(11\) | −37670.6 | −0.775774 | −0.387887 | − | 0.921707i | \(-0.626795\pi\) | ||||
−0.387887 | + | 0.921707i | \(0.626795\pi\) | |||||||
\(12\) | −11755.5 | −0.163653 | ||||||||
\(13\) | −25139.4 | −0.244124 | −0.122062 | − | 0.992523i | \(-0.538951\pi\) | ||||
−0.122062 | + | 0.992523i | \(0.538951\pi\) | |||||||
\(14\) | 39750.8 | 0.276547 | ||||||||
\(15\) | 286299. | 1.46019 | ||||||||
\(16\) | −193825. | −0.739383 | ||||||||
\(17\) | 0 | 0 | ||||||||
\(18\) | 165111. | 0.370724 | ||||||||
\(19\) | 623741. | 1.09803 | 0.549013 | − | 0.835814i | \(-0.315004\pi\) | ||||
0.549013 | + | 0.835814i | \(0.315004\pi\) | |||||||
\(20\) | −293952. | −0.410810 | ||||||||
\(21\) | −212104. | −0.237992 | ||||||||
\(22\) | 755422. | 0.687523 | ||||||||
\(23\) | 88926.9 | 0.0662610 | 0.0331305 | − | 0.999451i | \(-0.489452\pi\) | ||||
0.0331305 | + | 0.999451i | \(0.489452\pi\) | |||||||
\(24\) | 1.33436e6 | 0.820961 | ||||||||
\(25\) | 5.20595e6 | 2.66544 | ||||||||
\(26\) | 504130. | 0.216353 | ||||||||
\(27\) | −2.98713e6 | −1.08173 | ||||||||
\(28\) | 217774. | 0.0669569 | ||||||||
\(29\) | −116951. | −0.0307053 | −0.0153527 | − | 0.999882i | \(-0.504887\pi\) | ||||
−0.0153527 | + | 0.999882i | \(0.504887\pi\) | |||||||
\(30\) | −5.74126e6 | −1.29408 | ||||||||
\(31\) | −8.85431e6 | −1.72198 | −0.860988 | − | 0.508625i | \(-0.830154\pi\) | ||||
−0.860988 | + | 0.508625i | \(0.830154\pi\) | |||||||
\(32\) | −2.49802e6 | −0.421135 | ||||||||
\(33\) | −4.03082e6 | −0.591672 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −5.30379e6 | −0.597421 | ||||||||
\(36\) | 904560. | 0.0897587 | ||||||||
\(37\) | 1.75902e7 | 1.54299 | 0.771496 | − | 0.636234i | \(-0.219509\pi\) | ||||
0.771496 | + | 0.636234i | \(0.219509\pi\) | |||||||
\(38\) | −1.25081e7 | −0.973118 | ||||||||
\(39\) | −2.68996e6 | −0.186190 | ||||||||
\(40\) | 3.33664e7 | 2.06082 | ||||||||
\(41\) | −2.89173e7 | −1.59820 | −0.799100 | − | 0.601199i | \(-0.794690\pi\) | ||||
−0.799100 | + | 0.601199i | \(0.794690\pi\) | |||||||
\(42\) | 4.25341e6 | 0.210919 | ||||||||
\(43\) | −4.22052e6 | −0.188260 | −0.0941299 | − | 0.995560i | \(-0.530007\pi\) | ||||
−0.0941299 | + | 0.995560i | \(0.530007\pi\) | |||||||
\(44\) | 4.13857e6 | 0.166461 | ||||||||
\(45\) | −2.20302e7 | −0.800869 | ||||||||
\(46\) | −1.78328e6 | −0.0587233 | ||||||||
\(47\) | −3.58857e7 | −1.07271 | −0.536353 | − | 0.843994i | \(-0.680199\pi\) | ||||
−0.536353 | + | 0.843994i | \(0.680199\pi\) | |||||||
\(48\) | −2.07396e7 | −0.563917 | ||||||||
\(49\) | −3.64243e7 | −0.902628 | ||||||||
\(50\) | −1.04397e8 | −2.36223 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.76187e6 | 0.0523827 | ||||||||
\(53\) | −1.03300e7 | −0.179829 | −0.0899147 | − | 0.995949i | \(-0.528659\pi\) | ||||
−0.0899147 | + | 0.995949i | \(0.528659\pi\) | |||||||
\(54\) | 5.99020e7 | 0.958671 | ||||||||
\(55\) | −1.00793e8 | −1.48525 | ||||||||
\(56\) | −2.47195e7 | −0.335887 | ||||||||
\(57\) | 6.67414e7 | 0.837450 | ||||||||
\(58\) | 2.34527e6 | 0.0272124 | ||||||||
\(59\) | 6.28093e7 | 0.674823 | 0.337412 | − | 0.941357i | \(-0.390449\pi\) | ||||
0.337412 | + | 0.941357i | \(0.390449\pi\) | |||||||
\(60\) | −3.14534e7 | −0.313319 | ||||||||
\(61\) | 1.06527e8 | 0.985089 | 0.492545 | − | 0.870287i | \(-0.336067\pi\) | ||||
0.492545 | + | 0.870287i | \(0.336067\pi\) | |||||||
\(62\) | 1.77559e8 | 1.52609 | ||||||||
\(63\) | 1.63210e7 | 0.130531 | ||||||||
\(64\) | 1.49332e8 | 1.11261 | ||||||||
\(65\) | −6.72641e7 | −0.467383 | ||||||||
\(66\) | 8.08316e7 | 0.524365 | ||||||||
\(67\) | −9.64274e7 | −0.584607 | −0.292303 | − | 0.956326i | \(-0.594422\pi\) | ||||
−0.292303 | + | 0.956326i | \(0.594422\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 9.51535e6 | 0.0505363 | ||||||||
\(70\) | 1.06359e8 | 0.529460 | ||||||||
\(71\) | −2.78873e8 | −1.30240 | −0.651199 | − | 0.758907i | \(-0.725734\pi\) | ||||
−0.651199 | + | 0.758907i | \(0.725734\pi\) | |||||||
\(72\) | −1.02677e8 | −0.450272 | ||||||||
\(73\) | 3.95597e8 | 1.63042 | 0.815212 | − | 0.579163i | \(-0.196621\pi\) | ||||
0.815212 | + | 0.579163i | \(0.196621\pi\) | |||||||
\(74\) | −3.52744e8 | −1.36747 | ||||||||
\(75\) | 5.57046e8 | 2.03290 | ||||||||
\(76\) | −6.85255e7 | −0.235609 | ||||||||
\(77\) | 7.46724e7 | 0.242076 | ||||||||
\(78\) | 5.39428e7 | 0.165009 | ||||||||
\(79\) | −5.96898e8 | −1.72416 | −0.862082 | − | 0.506769i | \(-0.830840\pi\) | ||||
−0.862082 | + | 0.506769i | \(0.830840\pi\) | |||||||
\(80\) | −5.18606e8 | −1.41558 | ||||||||
\(81\) | −1.57567e8 | −0.406707 | ||||||||
\(82\) | 5.79890e8 | 1.41639 | ||||||||
\(83\) | −7.90776e8 | −1.82895 | −0.914475 | − | 0.404642i | \(-0.867396\pi\) | ||||
−0.914475 | + | 0.404642i | \(0.867396\pi\) | |||||||
\(84\) | 2.33022e7 | 0.0510671 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 8.46356e7 | 0.166844 | ||||||||
\(87\) | −1.25140e7 | −0.0234185 | ||||||||
\(88\) | −4.69768e8 | −0.835049 | ||||||||
\(89\) | 8.30223e8 | 1.40262 | 0.701309 | − | 0.712857i | \(-0.252599\pi\) | ||||
0.701309 | + | 0.712857i | \(0.252599\pi\) | |||||||
\(90\) | 4.41779e8 | 0.709764 | ||||||||
\(91\) | 4.98325e7 | 0.0761775 | ||||||||
\(92\) | −9.76970e6 | −0.0142179 | ||||||||
\(93\) | −9.47428e8 | −1.31333 | ||||||||
\(94\) | 7.19629e8 | 0.950678 | ||||||||
\(95\) | 1.66891e9 | 2.10221 | ||||||||
\(96\) | −2.67293e8 | −0.321193 | ||||||||
\(97\) | −2.87280e8 | −0.329483 | −0.164741 | − | 0.986337i | \(-0.552679\pi\) | ||||
−0.164741 | + | 0.986337i | \(0.552679\pi\) | |||||||
\(98\) | 7.30430e8 | 0.799947 | ||||||||
\(99\) | 3.10164e8 | 0.324514 | ||||||||
\(100\) | −5.71936e8 | −0.571936 | ||||||||
\(101\) | 3.45867e8 | 0.330721 | 0.165361 | − | 0.986233i | \(-0.447121\pi\) | ||||
0.165361 | + | 0.986233i | \(0.447121\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.59446e8 | −0.577313 | −0.288657 | − | 0.957433i | \(-0.593209\pi\) | ||||
−0.288657 | + | 0.957433i | \(0.593209\pi\) | |||||||
\(104\) | −3.13499e8 | −0.262776 | ||||||||
\(105\) | −5.67516e8 | −0.455644 | ||||||||
\(106\) | 2.07152e8 | 0.159372 | ||||||||
\(107\) | −1.09750e9 | −0.809429 | −0.404715 | − | 0.914443i | \(-0.632629\pi\) | ||||
−0.404715 | + | 0.914443i | \(0.632629\pi\) | |||||||
\(108\) | 3.28172e8 | 0.232111 | ||||||||
\(109\) | 1.47757e9 | 1.00260 | 0.501302 | − | 0.865273i | \(-0.332855\pi\) | ||||
0.501302 | + | 0.865273i | \(0.332855\pi\) | |||||||
\(110\) | 2.02124e9 | 1.31629 | ||||||||
\(111\) | 1.88219e9 | 1.17682 | ||||||||
\(112\) | 3.84209e8 | 0.230721 | ||||||||
\(113\) | −2.63247e8 | −0.151884 | −0.0759418 | − | 0.997112i | \(-0.524196\pi\) | ||||
−0.0759418 | + | 0.997112i | \(0.524196\pi\) | |||||||
\(114\) | −1.33839e9 | −0.742183 | ||||||||
\(115\) | 2.37937e8 | 0.126859 | ||||||||
\(116\) | 1.28485e7 | 0.00658858 | ||||||||
\(117\) | 2.06988e8 | 0.102119 | ||||||||
\(118\) | −1.25954e9 | −0.598057 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 3.57027e9 | 1.57176 | ||||||||
\(121\) | −9.38876e8 | −0.398175 | ||||||||
\(122\) | −2.13623e9 | −0.873028 | ||||||||
\(123\) | −3.09421e9 | −1.21892 | ||||||||
\(124\) | 9.72753e8 | 0.369492 | ||||||||
\(125\) | 8.70339e9 | 3.18855 | ||||||||
\(126\) | −3.27292e8 | −0.115683 | ||||||||
\(127\) | 1.75497e9 | 0.598624 | 0.299312 | − | 0.954155i | \(-0.403243\pi\) | ||||
0.299312 | + | 0.954155i | \(0.403243\pi\) | |||||||
\(128\) | −1.71563e9 | −0.564908 | ||||||||
\(129\) | −4.51603e8 | −0.143583 | ||||||||
\(130\) | 1.34887e9 | 0.414215 | ||||||||
\(131\) | 3.38174e9 | 1.00327 | 0.501637 | − | 0.865078i | \(-0.332731\pi\) | ||||
0.501637 | + | 0.865078i | \(0.332731\pi\) | |||||||
\(132\) | 4.42835e8 | 0.126958 | ||||||||
\(133\) | −1.23641e9 | −0.342634 | ||||||||
\(134\) | 1.93370e9 | 0.518103 | ||||||||
\(135\) | −7.99249e9 | −2.07100 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.32160e9 | 0.320521 | 0.160261 | − | 0.987075i | \(-0.448766\pi\) | ||||
0.160261 | + | 0.987075i | \(0.448766\pi\) | |||||||
\(138\) | −1.90815e8 | −0.0447874 | ||||||||
\(139\) | −2.93386e9 | −0.666612 | −0.333306 | − | 0.942819i | \(-0.608164\pi\) | ||||
−0.333306 | + | 0.942819i | \(0.608164\pi\) | |||||||
\(140\) | 5.82686e8 | 0.128191 | ||||||||
\(141\) | −3.83984e9 | −0.818138 | ||||||||
\(142\) | 5.59234e9 | 1.15424 | ||||||||
\(143\) | 9.47015e8 | 0.189385 | ||||||||
\(144\) | 1.59588e9 | 0.309291 | ||||||||
\(145\) | −3.12920e8 | −0.0587864 | ||||||||
\(146\) | −7.93306e9 | −1.44495 | ||||||||
\(147\) | −3.89747e9 | −0.688422 | ||||||||
\(148\) | −1.93250e9 | −0.331087 | ||||||||
\(149\) | −8.15943e9 | −1.35619 | −0.678097 | − | 0.734972i | \(-0.737195\pi\) | ||||
−0.678097 | + | 0.734972i | \(0.737195\pi\) | |||||||
\(150\) | −1.11707e10 | −1.80164 | ||||||||
\(151\) | −4.41970e9 | −0.691825 | −0.345912 | − | 0.938267i | \(-0.612431\pi\) | ||||
−0.345912 | + | 0.938267i | \(0.612431\pi\) | |||||||
\(152\) | 7.77832e9 | 1.18192 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1.49743e9 | −0.214538 | ||||||||
\(155\) | −2.36910e10 | −3.29678 | ||||||||
\(156\) | 2.95525e8 | 0.0399516 | ||||||||
\(157\) | 1.30118e10 | 1.70918 | 0.854590 | − | 0.519304i | \(-0.173809\pi\) | ||||
0.854590 | + | 0.519304i | \(0.173809\pi\) | |||||||
\(158\) | 1.19698e10 | 1.52803 | ||||||||
\(159\) | −1.10533e9 | −0.137153 | ||||||||
\(160\) | −6.68381e9 | −0.806277 | ||||||||
\(161\) | −1.76275e8 | −0.0206764 | ||||||||
\(162\) | 3.15974e9 | 0.360441 | ||||||||
\(163\) | 3.28470e9 | 0.364461 | 0.182231 | − | 0.983256i | \(-0.441668\pi\) | ||||
0.182231 | + | 0.983256i | \(0.441668\pi\) | |||||||
\(164\) | 3.17692e9 | 0.342933 | ||||||||
\(165\) | −1.07850e10 | −1.13278 | ||||||||
\(166\) | 1.58577e10 | 1.62089 | ||||||||
\(167\) | 2.91128e9 | 0.289641 | 0.144820 | − | 0.989458i | \(-0.453740\pi\) | ||||
0.144820 | + | 0.989458i | \(0.453740\pi\) | |||||||
\(168\) | −2.64503e9 | −0.256177 | ||||||||
\(169\) | −9.97251e9 | −0.940404 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.13563e9 | −0.459316 | ||||||||
\(172\) | 4.63675e8 | 0.0403957 | ||||||||
\(173\) | −5.10510e9 | −0.433308 | −0.216654 | − | 0.976248i | \(-0.569514\pi\) | ||||
−0.216654 | + | 0.976248i | \(0.569514\pi\) | |||||||
\(174\) | 2.50948e8 | 0.0207545 | ||||||||
\(175\) | −1.03195e10 | −0.831738 | ||||||||
\(176\) | 7.30149e9 | 0.573594 | ||||||||
\(177\) | 6.72072e9 | 0.514678 | ||||||||
\(178\) | −1.66488e10 | −1.24306 | ||||||||
\(179\) | 1.56901e10 | 1.14232 | 0.571158 | − | 0.820840i | \(-0.306494\pi\) | ||||
0.571158 | + | 0.820840i | \(0.306494\pi\) | |||||||
\(180\) | 2.42028e9 | 0.171846 | ||||||||
\(181\) | −1.38232e10 | −0.957317 | −0.478659 | − | 0.878001i | \(-0.658877\pi\) | ||||
−0.478659 | + | 0.878001i | \(0.658877\pi\) | |||||||
\(182\) | −9.99310e8 | −0.0675117 | ||||||||
\(183\) | 1.13986e10 | 0.751314 | ||||||||
\(184\) | 1.10896e9 | 0.0713238 | ||||||||
\(185\) | 4.70652e10 | 2.95411 | ||||||||
\(186\) | 1.89991e10 | 1.16393 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 3.94248e9 | 0.230175 | ||||||||
\(189\) | 5.92123e9 | 0.337547 | ||||||||
\(190\) | −3.34672e10 | −1.86307 | ||||||||
\(191\) | 8.25387e9 | 0.448753 | 0.224376 | − | 0.974503i | \(-0.427965\pi\) | ||||
0.224376 | + | 0.974503i | \(0.427965\pi\) | |||||||
\(192\) | 1.59788e10 | 0.848573 | ||||||||
\(193\) | −2.79430e10 | −1.44966 | −0.724828 | − | 0.688929i | \(-0.758081\pi\) | ||||
−0.724828 | + | 0.688929i | \(0.758081\pi\) | |||||||
\(194\) | 5.76093e9 | 0.292001 | ||||||||
\(195\) | −7.19738e9 | −0.356467 | ||||||||
\(196\) | 4.00165e9 | 0.193681 | ||||||||
\(197\) | −3.02715e10 | −1.43198 | −0.715988 | − | 0.698113i | \(-0.754024\pi\) | ||||
−0.715988 | + | 0.698113i | \(0.754024\pi\) | |||||||
\(198\) | −6.21984e9 | −0.287598 | ||||||||
\(199\) | −2.62292e10 | −1.18562 | −0.592810 | − | 0.805342i | \(-0.701982\pi\) | ||||
−0.592810 | + | 0.805342i | \(0.701982\pi\) | |||||||
\(200\) | 6.49204e10 | 2.86910 | ||||||||
\(201\) | −1.03179e10 | −0.445871 | ||||||||
\(202\) | −6.93579e9 | −0.293099 | ||||||||
\(203\) | 2.31826e8 | 0.00958144 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7.73725e10 | −3.05981 | ||||||||
\(206\) | 1.32241e10 | 0.511640 | ||||||||
\(207\) | −7.32188e8 | −0.0277176 | ||||||||
\(208\) | 4.87264e9 | 0.180501 | ||||||||
\(209\) | −2.34967e10 | −0.851820 | ||||||||
\(210\) | 1.13806e10 | 0.403811 | ||||||||
\(211\) | 1.09711e9 | 0.0381048 | 0.0190524 | − | 0.999818i | \(-0.493935\pi\) | ||||
0.0190524 | + | 0.999818i | \(0.493935\pi\) | |||||||
\(212\) | 1.13488e9 | 0.0385868 | ||||||||
\(213\) | −2.98399e10 | −0.993320 | ||||||||
\(214\) | 2.20086e10 | 0.717350 | ||||||||
\(215\) | −1.12926e10 | −0.360430 | ||||||||
\(216\) | −3.72508e10 | −1.16438 | ||||||||
\(217\) | 1.75514e10 | 0.537334 | ||||||||
\(218\) | −2.96303e10 | −0.888549 | ||||||||
\(219\) | 4.23297e10 | 1.24350 | ||||||||
\(220\) | 1.10733e10 | 0.318696 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −3.77442e10 | −1.04295 | ||||||||
\(223\) | −4.13547e10 | −1.11983 | −0.559916 | − | 0.828549i | \(-0.689167\pi\) | ||||
−0.559916 | + | 0.828549i | \(0.689167\pi\) | |||||||
\(224\) | 4.95170e9 | 0.131413 | ||||||||
\(225\) | −4.28637e10 | −1.11498 | ||||||||
\(226\) | 5.27900e9 | 0.134606 | ||||||||
\(227\) | 4.74605e10 | 1.18636 | 0.593180 | − | 0.805070i | \(-0.297872\pi\) | ||||
0.593180 | + | 0.805070i | \(0.297872\pi\) | |||||||
\(228\) | −7.33236e9 | −0.179695 | ||||||||
\(229\) | −2.55438e10 | −0.613799 | −0.306899 | − | 0.951742i | \(-0.599291\pi\) | ||||
−0.306899 | + | 0.951742i | \(0.599291\pi\) | |||||||
\(230\) | −4.77144e9 | −0.112428 | ||||||||
\(231\) | 7.99009e9 | 0.184628 | ||||||||
\(232\) | −1.45843e9 | −0.0330514 | ||||||||
\(233\) | −2.41242e10 | −0.536229 | −0.268115 | − | 0.963387i | \(-0.586401\pi\) | ||||
−0.268115 | + | 0.963387i | \(0.586401\pi\) | |||||||
\(234\) | −4.15080e9 | −0.0905025 | ||||||||
\(235\) | −9.60173e10 | −2.05373 | ||||||||
\(236\) | −6.90037e9 | −0.144800 | ||||||||
\(237\) | −6.38693e10 | −1.31500 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2.43035e10 | −0.481814 | −0.240907 | − | 0.970548i | \(-0.577445\pi\) | ||||
−0.240907 | + | 0.970548i | \(0.577445\pi\) | |||||||
\(240\) | −5.54919e10 | −1.07964 | ||||||||
\(241\) | 3.87672e10 | 0.740266 | 0.370133 | − | 0.928979i | \(-0.379312\pi\) | ||||
0.370133 | + | 0.928979i | \(0.379312\pi\) | |||||||
\(242\) | 1.88276e10 | 0.352880 | ||||||||
\(243\) | 4.19357e10 | 0.771536 | ||||||||
\(244\) | −1.17033e10 | −0.211375 | ||||||||
\(245\) | −9.74585e10 | −1.72811 | ||||||||
\(246\) | 6.20493e10 | 1.08026 | ||||||||
\(247\) | −1.56805e10 | −0.268054 | ||||||||
\(248\) | −1.10417e11 | −1.85355 | ||||||||
\(249\) | −8.46145e10 | −1.39491 | ||||||||
\(250\) | −1.74532e11 | −2.82583 | ||||||||
\(251\) | −2.65809e10 | −0.422705 | −0.211353 | − | 0.977410i | \(-0.567787\pi\) | ||||
−0.211353 | + | 0.977410i | \(0.567787\pi\) | |||||||
\(252\) | −1.79306e9 | −0.0280087 | ||||||||
\(253\) | −3.34993e9 | −0.0514035 | ||||||||
\(254\) | −3.51932e10 | −0.530526 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −4.20539e10 | −0.611965 | ||||||||
\(257\) | −5.92099e10 | −0.846633 | −0.423317 | − | 0.905982i | \(-0.639134\pi\) | ||||
−0.423317 | + | 0.905982i | \(0.639134\pi\) | |||||||
\(258\) | 9.05617e9 | 0.127249 | ||||||||
\(259\) | −3.48682e10 | −0.481483 | ||||||||
\(260\) | 7.38978e9 | 0.100289 | ||||||||
\(261\) | 9.62929e8 | 0.0128443 | ||||||||
\(262\) | −6.78153e10 | −0.889144 | ||||||||
\(263\) | 1.23170e10 | 0.158746 | 0.0793731 | − | 0.996845i | \(-0.474708\pi\) | ||||
0.0793731 | + | 0.996845i | \(0.474708\pi\) | |||||||
\(264\) | −5.02661e10 | −0.636880 | ||||||||
\(265\) | −2.76395e10 | −0.344290 | ||||||||
\(266\) | 2.47942e10 | 0.303656 | ||||||||
\(267\) | 8.88354e10 | 1.06976 | ||||||||
\(268\) | 1.05937e10 | 0.125442 | ||||||||
\(269\) | −1.58343e11 | −1.84379 | −0.921897 | − | 0.387435i | \(-0.873361\pi\) | ||||
−0.921897 | + | 0.387435i | \(0.873361\pi\) | |||||||
\(270\) | 1.60276e11 | 1.83541 | ||||||||
\(271\) | −1.08239e11 | −1.21905 | −0.609524 | − | 0.792767i | \(-0.708640\pi\) | ||||
−0.609524 | + | 0.792767i | \(0.708640\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 5.33218e9 | 0.0580995 | ||||||||
\(274\) | −2.65025e10 | −0.284060 | ||||||||
\(275\) | −1.96111e11 | −2.06778 | ||||||||
\(276\) | −1.04538e9 | −0.0108438 | ||||||||
\(277\) | −5.35501e10 | −0.546515 | −0.273257 | − | 0.961941i | \(-0.588101\pi\) | ||||
−0.273257 | + | 0.961941i | \(0.588101\pi\) | |||||||
\(278\) | 5.88338e10 | 0.590779 | ||||||||
\(279\) | 7.29028e10 | 0.720320 | ||||||||
\(280\) | −6.61406e10 | −0.643068 | ||||||||
\(281\) | 2.49764e10 | 0.238974 | 0.119487 | − | 0.992836i | \(-0.461875\pi\) | ||||
0.119487 | + | 0.992836i | \(0.461875\pi\) | |||||||
\(282\) | 7.70017e10 | 0.725069 | ||||||||
\(283\) | 8.45073e10 | 0.783169 | 0.391585 | − | 0.920142i | \(-0.371927\pi\) | ||||
0.391585 | + | 0.920142i | \(0.371927\pi\) | |||||||
\(284\) | 3.06376e10 | 0.279461 | ||||||||
\(285\) | 1.78576e11 | 1.60333 | ||||||||
\(286\) | −1.89909e10 | −0.167841 | ||||||||
\(287\) | 5.73213e10 | 0.498710 | ||||||||
\(288\) | 2.05677e10 | 0.176165 | ||||||||
\(289\) | 0 | 0 | ||||||||
\(290\) | 6.27510e9 | 0.0520990 | ||||||||
\(291\) | −3.07395e10 | −0.251292 | ||||||||
\(292\) | −4.34612e10 | −0.349847 | ||||||||
\(293\) | −1.26184e11 | −1.00023 | −0.500116 | − | 0.865958i | \(-0.666709\pi\) | ||||
−0.500116 | + | 0.865958i | \(0.666709\pi\) | |||||||
\(294\) | 7.81574e10 | 0.610109 | ||||||||
\(295\) | 1.68055e11 | 1.29197 | ||||||||
\(296\) | 2.19358e11 | 1.66089 | ||||||||
\(297\) | 1.12527e11 | 0.839174 | ||||||||
\(298\) | 1.63624e11 | 1.20192 | ||||||||
\(299\) | −2.23557e9 | −0.0161759 | ||||||||
\(300\) | −6.11983e10 | −0.436208 | ||||||||
\(301\) | 8.36611e9 | 0.0587455 | ||||||||
\(302\) | 8.86298e10 | 0.613124 | ||||||||
\(303\) | 3.70084e10 | 0.252237 | ||||||||
\(304\) | −1.20896e11 | −0.811863 | ||||||||
\(305\) | 2.85028e11 | 1.88599 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3.13729e10 | 0.201573 | 0.100786 | − | 0.994908i | \(-0.467864\pi\) | ||||
0.100786 | + | 0.994908i | \(0.467864\pi\) | |||||||
\(308\) | −8.20367e9 | −0.0519434 | ||||||||
\(309\) | −7.05620e10 | −0.440309 | ||||||||
\(310\) | 4.75084e11 | 2.92175 | ||||||||
\(311\) | 1.11315e11 | 0.674735 | 0.337368 | − | 0.941373i | \(-0.390463\pi\) | ||||
0.337368 | + | 0.941373i | \(0.390463\pi\) | |||||||
\(312\) | −3.35450e10 | −0.200416 | ||||||||
\(313\) | −1.05855e11 | −0.623394 | −0.311697 | − | 0.950181i | \(-0.600897\pi\) | ||||
−0.311697 | + | 0.950181i | \(0.600897\pi\) | |||||||
\(314\) | −2.60930e11 | −1.51475 | ||||||||
\(315\) | 4.36693e10 | 0.249907 | ||||||||
\(316\) | 6.55765e10 | 0.369962 | ||||||||
\(317\) | −1.05802e11 | −0.588474 | −0.294237 | − | 0.955733i | \(-0.595065\pi\) | ||||
−0.294237 | + | 0.955733i | \(0.595065\pi\) | |||||||
\(318\) | 2.21657e10 | 0.121551 | ||||||||
\(319\) | 4.40562e9 | 0.0238204 | ||||||||
\(320\) | 3.99559e11 | 2.13013 | ||||||||
\(321\) | −1.17435e11 | −0.617340 | ||||||||
\(322\) | 3.53491e9 | 0.0183243 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 1.73106e10 | 0.0872689 | ||||||||
\(325\) | −1.30874e11 | −0.650698 | ||||||||
\(326\) | −6.58693e10 | −0.323001 | ||||||||
\(327\) | 1.58103e11 | 0.764671 | ||||||||
\(328\) | −3.60612e11 | −1.72031 | ||||||||
\(329\) | 7.11344e10 | 0.334732 | ||||||||
\(330\) | 2.16277e11 | 1.00391 | ||||||||
\(331\) | −1.63950e11 | −0.750733 | −0.375367 | − | 0.926876i | \(-0.622483\pi\) | ||||
−0.375367 | + | 0.926876i | \(0.622483\pi\) | |||||||
\(332\) | 8.68763e10 | 0.392446 | ||||||||
\(333\) | −1.44831e11 | −0.645449 | ||||||||
\(334\) | −5.83810e10 | −0.256692 | ||||||||
\(335\) | −2.58005e11 | −1.11925 | ||||||||
\(336\) | 4.11111e10 | 0.175967 | ||||||||
\(337\) | 1.50386e11 | 0.635144 | 0.317572 | − | 0.948234i | \(-0.397132\pi\) | ||||
0.317572 | + | 0.948234i | \(0.397132\pi\) | |||||||
\(338\) | 1.99982e11 | 0.833426 | ||||||||
\(339\) | −2.81680e10 | −0.115840 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.33547e11 | 1.33586 | ||||||||
\(342\) | 1.02987e11 | 0.407065 | ||||||||
\(343\) | 1.52193e11 | 0.593705 | ||||||||
\(344\) | −5.26317e10 | −0.202644 | ||||||||
\(345\) | 2.54597e10 | 0.0967536 | ||||||||
\(346\) | 1.02374e11 | 0.384016 | ||||||||
\(347\) | −2.37865e10 | −0.0880741 | −0.0440370 | − | 0.999030i | \(-0.514022\pi\) | ||||
−0.0440370 | + | 0.999030i | \(0.514022\pi\) | |||||||
\(348\) | 1.37482e9 | 0.00502502 | ||||||||
\(349\) | 4.04400e11 | 1.45914 | 0.729570 | − | 0.683907i | \(-0.239720\pi\) | ||||
0.729570 | + | 0.683907i | \(0.239720\pi\) | |||||||
\(350\) | 2.06940e11 | 0.737122 | ||||||||
\(351\) | 7.50946e10 | 0.264075 | ||||||||
\(352\) | 9.41018e10 | 0.326705 | ||||||||
\(353\) | 4.98816e10 | 0.170984 | 0.0854918 | − | 0.996339i | \(-0.472754\pi\) | ||||
0.0854918 | + | 0.996339i | \(0.472754\pi\) | |||||||
\(354\) | −1.34773e11 | −0.456130 | ||||||||
\(355\) | −7.46164e11 | −2.49349 | ||||||||
\(356\) | −9.12100e10 | −0.300966 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −3.14639e11 | −1.01237 | ||||||||
\(359\) | 1.03719e11 | 0.329559 | 0.164779 | − | 0.986330i | \(-0.447309\pi\) | ||||
0.164779 | + | 0.986330i | \(0.447309\pi\) | |||||||
\(360\) | −2.74726e11 | −0.862061 | ||||||||
\(361\) | 6.63648e10 | 0.205663 | ||||||||
\(362\) | 2.77202e11 | 0.848415 | ||||||||
\(363\) | −1.00462e11 | −0.303683 | ||||||||
\(364\) | −5.47471e9 | −0.0163457 | ||||||||
\(365\) | 1.05848e12 | 3.12150 | ||||||||
\(366\) | −2.28580e11 | −0.665846 | ||||||||
\(367\) | 4.35557e10 | 0.125328 | 0.0626640 | − | 0.998035i | \(-0.480040\pi\) | ||||
0.0626640 | + | 0.998035i | \(0.480040\pi\) | |||||||
\(368\) | −1.72362e10 | −0.0489923 | ||||||||
\(369\) | 2.38094e11 | 0.668543 | ||||||||
\(370\) | −9.43816e11 | −2.61806 | ||||||||
\(371\) | 2.04767e10 | 0.0561148 | ||||||||
\(372\) | 1.04086e11 | 0.281806 | ||||||||
\(373\) | −2.49530e11 | −0.667473 | −0.333737 | − | 0.942666i | \(-0.608310\pi\) | ||||
−0.333737 | + | 0.942666i | \(0.608310\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 9.31280e11 | 2.43186 | ||||||||
\(376\) | −4.47510e11 | −1.15467 | ||||||||
\(377\) | 2.94008e9 | 0.00749590 | ||||||||
\(378\) | −1.18741e11 | −0.299148 | ||||||||
\(379\) | 1.02770e11 | 0.255852 | 0.127926 | − | 0.991784i | \(-0.459168\pi\) | ||||
0.127926 | + | 0.991784i | \(0.459168\pi\) | |||||||
\(380\) | −1.83350e11 | −0.451081 | ||||||||
\(381\) | 1.87786e11 | 0.456562 | ||||||||
\(382\) | −1.65518e11 | −0.397704 | ||||||||
\(383\) | 1.80024e10 | 0.0427499 | 0.0213749 | − | 0.999772i | \(-0.493196\pi\) | ||||
0.0213749 | + | 0.999772i | \(0.493196\pi\) | |||||||
\(384\) | −1.83575e11 | −0.430847 | ||||||||
\(385\) | 1.99797e11 | 0.463463 | ||||||||
\(386\) | 5.60352e11 | 1.28475 | ||||||||
\(387\) | 3.47500e10 | 0.0787509 | ||||||||
\(388\) | 3.15612e10 | 0.0706985 | ||||||||
\(389\) | −8.51136e9 | −0.0188463 | −0.00942314 | − | 0.999956i | \(-0.503000\pi\) | ||||
−0.00942314 | + | 0.999956i | \(0.503000\pi\) | |||||||
\(390\) | 1.44332e11 | 0.315916 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −4.54227e11 | −0.971595 | ||||||||
\(393\) | 3.61853e11 | 0.765183 | ||||||||
\(394\) | 6.07046e11 | 1.26908 | ||||||||
\(395\) | −1.59709e12 | −3.30097 | ||||||||
\(396\) | −3.40753e10 | −0.0696324 | ||||||||
\(397\) | 4.11624e11 | 0.831655 | 0.415828 | − | 0.909443i | \(-0.363492\pi\) | ||||
0.415828 | + | 0.909443i | \(0.363492\pi\) | |||||||
\(398\) | 5.25984e11 | 1.05075 | ||||||||
\(399\) | −1.32298e11 | −0.261322 | ||||||||
\(400\) | −1.00904e12 | −1.97079 | ||||||||
\(401\) | 5.74069e11 | 1.10870 | 0.554350 | − | 0.832284i | \(-0.312967\pi\) | ||||
0.554350 | + | 0.832284i | \(0.312967\pi\) | |||||||
\(402\) | 2.06909e11 | 0.395150 | ||||||||
\(403\) | 2.22592e11 | 0.420375 | ||||||||
\(404\) | −3.79976e10 | −0.0709644 | ||||||||
\(405\) | −4.21592e11 | −0.778654 | ||||||||
\(406\) | −4.64890e9 | −0.00849148 | ||||||||
\(407\) | −6.62634e11 | −1.19701 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.72832e11 | 0.658806 | 0.329403 | − | 0.944189i | \(-0.393152\pi\) | ||||
0.329403 | + | 0.944189i | \(0.393152\pi\) | |||||||
\(410\) | 1.55158e12 | 2.71173 | ||||||||
\(411\) | 1.41414e11 | 0.244457 | ||||||||
\(412\) | 7.24481e10 | 0.123877 | ||||||||
\(413\) | −1.24504e11 | −0.210575 | ||||||||
\(414\) | 1.46828e10 | 0.0245645 | ||||||||
\(415\) | −2.11583e12 | −3.50159 | ||||||||
\(416\) | 6.27987e10 | 0.102809 | ||||||||
\(417\) | −3.13929e11 | −0.508415 | ||||||||
\(418\) | 4.71187e11 | 0.754919 | ||||||||
\(419\) | 5.40188e11 | 0.856214 | 0.428107 | − | 0.903728i | \(-0.359181\pi\) | ||||
0.428107 | + | 0.903728i | \(0.359181\pi\) | |||||||
\(420\) | 6.23485e10 | 0.0977697 | ||||||||
\(421\) | −6.79434e11 | −1.05409 | −0.527045 | − | 0.849837i | \(-0.676700\pi\) | ||||
−0.527045 | + | 0.849837i | \(0.676700\pi\) | |||||||
\(422\) | −2.20008e10 | −0.0337701 | ||||||||
\(423\) | 2.95468e11 | 0.448724 | ||||||||
\(424\) | −1.28820e11 | −0.193570 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 5.98391e11 | 0.880323 | ||||||||
\(427\) | −2.11163e11 | −0.307392 | ||||||||
\(428\) | 1.20574e11 | 0.173683 | ||||||||
\(429\) | 1.01332e11 | 0.144441 | ||||||||
\(430\) | 2.26455e11 | 0.319428 | ||||||||
\(431\) | −1.12689e12 | −1.57302 | −0.786511 | − | 0.617577i | \(-0.788114\pi\) | ||||
−0.786511 | + | 0.617577i | \(0.788114\pi\) | |||||||
\(432\) | 5.78980e11 | 0.799810 | ||||||||
\(433\) | −1.10436e12 | −1.50979 | −0.754893 | − | 0.655848i | \(-0.772311\pi\) | ||||
−0.754893 | + | 0.655848i | \(0.772311\pi\) | |||||||
\(434\) | −3.51966e11 | −0.476208 | ||||||||
\(435\) | −3.34830e10 | −0.0448356 | ||||||||
\(436\) | −1.62329e11 | −0.215133 | ||||||||
\(437\) | 5.54673e10 | 0.0727563 | ||||||||
\(438\) | −8.48853e11 | −1.10204 | ||||||||
\(439\) | 1.12796e12 | 1.44945 | 0.724725 | − | 0.689038i | \(-0.241967\pi\) | ||||
0.724725 | + | 0.689038i | \(0.241967\pi\) | |||||||
\(440\) | −1.25693e12 | −1.59873 | ||||||||
\(441\) | 2.99903e11 | 0.377578 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1.35306e12 | −1.66917 | −0.834587 | − | 0.550877i | \(-0.814294\pi\) | ||||
−0.834587 | + | 0.550877i | \(0.814294\pi\) | |||||||
\(444\) | −2.06781e11 | −0.252515 | ||||||||
\(445\) | 2.22138e12 | 2.68536 | ||||||||
\(446\) | 8.29302e11 | 0.992443 | ||||||||
\(447\) | −8.73075e11 | −1.03435 | ||||||||
\(448\) | −2.96013e11 | −0.347184 | ||||||||
\(449\) | 4.41678e11 | 0.512859 | 0.256429 | − | 0.966563i | \(-0.417454\pi\) | ||||
0.256429 | + | 0.966563i | \(0.417454\pi\) | |||||||
\(450\) | 8.59561e11 | 0.988144 | ||||||||
\(451\) | 1.08933e12 | 1.23984 | ||||||||
\(452\) | 2.89209e10 | 0.0325904 | ||||||||
\(453\) | −4.72916e11 | −0.527645 | ||||||||
\(454\) | −9.51744e11 | −1.05140 | ||||||||
\(455\) | 1.33334e11 | 0.145844 | ||||||||
\(456\) | 8.32295e11 | 0.901437 | ||||||||
\(457\) | −5.10055e11 | −0.547008 | −0.273504 | − | 0.961871i | \(-0.588183\pi\) | ||||
−0.273504 | + | 0.961871i | \(0.588183\pi\) | |||||||
\(458\) | 5.12239e11 | 0.543974 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −2.61402e10 | −0.0272207 | ||||||||
\(461\) | 1.40177e12 | 1.44551 | 0.722755 | − | 0.691104i | \(-0.242875\pi\) | ||||
0.722755 | + | 0.691104i | \(0.242875\pi\) | |||||||
\(462\) | −1.60228e11 | −0.163625 | ||||||||
\(463\) | −8.12639e8 | −0.000821832 0 | −0.000410916 | − | 1.00000i | \(-0.500131\pi\) | ||||
−0.000410916 | 1.00000i | \(0.500131\pi\) | ||||||||
\(464\) | 2.26681e10 | 0.0227030 | ||||||||
\(465\) | −2.53498e12 | −2.51441 | ||||||||
\(466\) | 4.83771e11 | 0.475229 | ||||||||
\(467\) | −5.50598e11 | −0.535684 | −0.267842 | − | 0.963463i | \(-0.586311\pi\) | ||||
−0.267842 | + | 0.963463i | \(0.586311\pi\) | |||||||
\(468\) | −2.27401e10 | −0.0219122 | ||||||||
\(469\) | 1.91143e11 | 0.182424 | ||||||||
\(470\) | 1.92547e12 | 1.82011 | ||||||||
\(471\) | 1.39228e12 | 1.30357 | ||||||||
\(472\) | 7.83260e11 | 0.726385 | ||||||||
\(473\) | 1.58989e11 | 0.146047 | ||||||||
\(474\) | 1.28079e12 | 1.16540 | ||||||||
\(475\) | 3.24716e12 | 2.92673 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 8.50534e10 | 0.0752244 | ||||||||
\(478\) | 4.87368e11 | 0.427004 | ||||||||
\(479\) | −4.11777e11 | −0.357398 | −0.178699 | − | 0.983904i | \(-0.557189\pi\) | ||||
−0.178699 | + | 0.983904i | \(0.557189\pi\) | |||||||
\(480\) | −7.15180e11 | −0.614936 | ||||||||
\(481\) | −4.42208e11 | −0.376681 | ||||||||
\(482\) | −7.77413e11 | −0.656055 | ||||||||
\(483\) | −1.88618e10 | −0.0157696 | ||||||||
\(484\) | 1.03147e11 | 0.0854382 | ||||||||
\(485\) | −7.68659e11 | −0.630806 | ||||||||
\(486\) | −8.40953e11 | −0.683768 | ||||||||
\(487\) | −1.25805e12 | −1.01349 | −0.506743 | − | 0.862097i | \(-0.669151\pi\) | ||||
−0.506743 | + | 0.862097i | \(0.669151\pi\) | |||||||
\(488\) | 1.32844e12 | 1.06036 | ||||||||
\(489\) | 3.51469e11 | 0.277969 | ||||||||
\(490\) | 1.95437e12 | 1.53153 | ||||||||
\(491\) | 5.36226e11 | 0.416372 | 0.208186 | − | 0.978089i | \(-0.433244\pi\) | ||||
0.208186 | + | 0.978089i | \(0.433244\pi\) | |||||||
\(492\) | 3.39936e11 | 0.261550 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 3.14446e11 | 0.237561 | ||||||||
\(495\) | 8.29889e11 | 0.621293 | ||||||||
\(496\) | 1.71619e12 | 1.27320 | ||||||||
\(497\) | 5.52795e11 | 0.406406 | ||||||||
\(498\) | 1.69681e12 | 1.23623 | ||||||||
\(499\) | −1.36830e12 | −0.987935 | −0.493967 | − | 0.869480i | \(-0.664454\pi\) | ||||
−0.493967 | + | 0.869480i | \(0.664454\pi\) | |||||||
\(500\) | −9.56173e11 | −0.684182 | ||||||||
\(501\) | 3.11512e11 | 0.220905 | ||||||||
\(502\) | 5.33036e11 | 0.374619 | ||||||||
\(503\) | −2.29853e12 | −1.60101 | −0.800507 | − | 0.599324i | \(-0.795436\pi\) | ||||
−0.800507 | + | 0.599324i | \(0.795436\pi\) | |||||||
\(504\) | 2.03530e11 | 0.140505 | ||||||||
\(505\) | 9.25416e11 | 0.633178 | ||||||||
\(506\) | 6.71773e10 | 0.0455560 | ||||||||
\(507\) | −1.06708e12 | −0.717233 | ||||||||
\(508\) | −1.92805e11 | −0.128449 | ||||||||
\(509\) | −1.11229e11 | −0.0734491 | −0.0367246 | − | 0.999325i | \(-0.511692\pi\) | ||||
−0.0367246 | + | 0.999325i | \(0.511692\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7.84172e11 | −0.508765 | ||||||||
\(512\) | 1.72172e12 | 1.10726 | ||||||||
\(513\) | −1.86319e12 | −1.18776 | ||||||||
\(514\) | 1.18736e12 | 0.750322 | ||||||||
\(515\) | −1.76444e12 | −1.10529 | ||||||||
\(516\) | 4.96141e10 | 0.0308093 | ||||||||
\(517\) | 1.35183e12 | 0.832177 | ||||||||
\(518\) | 6.99225e11 | 0.426710 | ||||||||
\(519\) | −5.46255e11 | −0.330478 | ||||||||
\(520\) | −8.38812e11 | −0.503095 | ||||||||
\(521\) | −2.42441e12 | −1.44157 | −0.720785 | − | 0.693159i | \(-0.756218\pi\) | ||||
−0.720785 | + | 0.693159i | \(0.756218\pi\) | |||||||
\(522\) | −1.93100e10 | −0.0113832 | ||||||||
\(523\) | −2.27833e12 | −1.33156 | −0.665778 | − | 0.746150i | \(-0.731900\pi\) | ||||
−0.665778 | + | 0.746150i | \(0.731900\pi\) | |||||||
\(524\) | −3.71525e11 | −0.215277 | ||||||||
\(525\) | −1.10420e12 | −0.634355 | ||||||||
\(526\) | −2.46997e11 | −0.140688 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 7.81274e11 | 0.437472 | ||||||||
\(529\) | −1.79324e12 | −0.995609 | ||||||||
\(530\) | 5.54266e11 | 0.305124 | ||||||||
\(531\) | −5.17147e11 | −0.282285 | ||||||||
\(532\) | 1.35835e11 | 0.0735204 | ||||||||
\(533\) | 7.26964e11 | 0.390158 | ||||||||
\(534\) | −1.78145e12 | −0.948064 | ||||||||
\(535\) | −2.93653e12 | −1.54968 | ||||||||
\(536\) | −1.20249e12 | −0.629275 | ||||||||
\(537\) | 1.67887e12 | 0.871229 | ||||||||
\(538\) | 3.17530e12 | 1.63405 | ||||||||
\(539\) | 1.37212e12 | 0.700235 | ||||||||
\(540\) | 8.78072e11 | 0.444384 | ||||||||
\(541\) | −4.55216e11 | −0.228470 | −0.114235 | − | 0.993454i | \(-0.536442\pi\) | ||||
−0.114235 | + | 0.993454i | \(0.536442\pi\) | |||||||
\(542\) | 2.17055e12 | 1.08037 | ||||||||
\(543\) | −1.47911e12 | −0.730133 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3.95345e12 | 1.91952 | ||||||||
\(546\) | −1.06928e11 | −0.0514903 | ||||||||
\(547\) | 1.30843e12 | 0.624897 | 0.312449 | − | 0.949935i | \(-0.398851\pi\) | ||||
0.312449 | + | 0.949935i | \(0.398851\pi\) | |||||||
\(548\) | −1.45194e11 | −0.0687757 | ||||||||
\(549\) | −8.77100e11 | −0.412073 | ||||||||
\(550\) | 3.93269e12 | 1.83256 | ||||||||
\(551\) | −7.29472e10 | −0.0337153 | ||||||||
\(552\) | 1.18661e11 | 0.0543977 | ||||||||
\(553\) | 1.18320e12 | 0.538016 | ||||||||
\(554\) | 1.07386e12 | 0.484344 | ||||||||
\(555\) | 5.03607e12 | 2.25306 | ||||||||
\(556\) | 3.22320e11 | 0.143038 | ||||||||
\(557\) | −1.03372e12 | −0.455045 | −0.227523 | − | 0.973773i | \(-0.573063\pi\) | ||||
−0.227523 | + | 0.973773i | \(0.573063\pi\) | |||||||
\(558\) | −1.46195e12 | −0.638378 | ||||||||
\(559\) | 1.06101e11 | 0.0459586 | ||||||||
\(560\) | 1.02801e12 | 0.441723 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −5.00861e11 | −0.211789 | ||||||||
\(563\) | −4.14096e12 | −1.73705 | −0.868526 | − | 0.495643i | \(-0.834932\pi\) | ||||
−0.868526 | + | 0.495643i | \(0.834932\pi\) | |||||||
\(564\) | 4.21853e11 | 0.175552 | ||||||||
\(565\) | −7.04356e11 | −0.290787 | ||||||||
\(566\) | −1.69466e12 | −0.694078 | ||||||||
\(567\) | 3.12336e11 | 0.126911 | ||||||||
\(568\) | −3.47767e12 | −1.40191 | ||||||||
\(569\) | 1.09427e12 | 0.437641 | 0.218821 | − | 0.975765i | \(-0.429779\pi\) | ||||
0.218821 | + | 0.975765i | \(0.429779\pi\) | |||||||
\(570\) | −3.58106e12 | −1.42094 | ||||||||
\(571\) | 9.36336e11 | 0.368612 | 0.184306 | − | 0.982869i | \(-0.440996\pi\) | ||||
0.184306 | + | 0.982869i | \(0.440996\pi\) | |||||||
\(572\) | −1.04041e11 | −0.0406371 | ||||||||
\(573\) | 8.83179e11 | 0.342258 | ||||||||
\(574\) | −1.14949e12 | −0.441978 | ||||||||
\(575\) | 4.62949e11 | 0.176615 | ||||||||
\(576\) | −1.22954e12 | −0.465416 | ||||||||
\(577\) | −3.33902e12 | −1.25409 | −0.627044 | − | 0.778984i | \(-0.715735\pi\) | ||||
−0.627044 | + | 0.778984i | \(0.715735\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −2.98995e12 | −1.10563 | ||||||||
\(580\) | 3.43780e10 | 0.0126141 | ||||||||
\(581\) | 1.56751e12 | 0.570714 | ||||||||
\(582\) | 6.16430e11 | 0.222705 | ||||||||
\(583\) | 3.89138e11 | 0.139507 | ||||||||
\(584\) | 4.93327e12 | 1.75500 | ||||||||
\(585\) | 5.53825e11 | 0.195511 | ||||||||
\(586\) | 2.53042e12 | 0.886448 | ||||||||
\(587\) | 3.96101e12 | 1.37700 | 0.688501 | − | 0.725236i | \(-0.258269\pi\) | ||||
0.688501 | + | 0.725236i | \(0.258269\pi\) | |||||||
\(588\) | 4.28184e11 | 0.147718 | ||||||||
\(589\) | −5.52279e12 | −1.89078 | ||||||||
\(590\) | −3.37008e12 | −1.14500 | ||||||||
\(591\) | −3.23911e12 | −1.09215 | ||||||||
\(592\) | −3.40943e12 | −1.14086 | ||||||||
\(593\) | 3.43524e12 | 1.14080 | 0.570401 | − | 0.821366i | \(-0.306788\pi\) | ||||
0.570401 | + | 0.821366i | \(0.306788\pi\) | |||||||
\(594\) | −2.25654e12 | −0.743712 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 8.96413e11 | 0.291005 | ||||||||
\(597\) | −2.80657e12 | −0.904256 | ||||||||
\(598\) | 4.48307e10 | 0.0143357 | ||||||||
\(599\) | −2.49343e12 | −0.791364 | −0.395682 | − | 0.918388i | \(-0.629492\pi\) | ||||
−0.395682 | + | 0.918388i | \(0.629492\pi\) | |||||||
\(600\) | 6.94661e12 | 2.18823 | ||||||||
\(601\) | −3.17215e12 | −0.991789 | −0.495894 | − | 0.868383i | \(-0.665160\pi\) | ||||
−0.495894 | + | 0.868383i | \(0.665160\pi\) | |||||||
\(602\) | −1.67769e11 | −0.0520627 | ||||||||
\(603\) | 7.93944e11 | 0.244547 | ||||||||
\(604\) | 4.85557e11 | 0.148448 | ||||||||
\(605\) | −2.51210e12 | −0.762320 | ||||||||
\(606\) | −7.42143e11 | −0.223543 | ||||||||
\(607\) | −4.31465e12 | −1.29002 | −0.645010 | − | 0.764174i | \(-0.723147\pi\) | ||||
−0.645010 | + | 0.764174i | \(0.723147\pi\) | |||||||
\(608\) | −1.55812e12 | −0.462417 | ||||||||
\(609\) | 2.48059e10 | 0.00730763 | ||||||||
\(610\) | −5.71578e12 | −1.67144 | ||||||||
\(611\) | 9.02144e11 | 0.261873 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.26850e12 | 0.934924 | 0.467462 | − | 0.884013i | \(-0.345168\pi\) | ||||
0.467462 | + | 0.884013i | \(0.345168\pi\) | |||||||
\(614\) | −6.29132e11 | −0.178642 | ||||||||
\(615\) | −8.27900e12 | −2.33367 | ||||||||
\(616\) | 9.31198e11 | 0.260573 | ||||||||
\(617\) | −5.06880e12 | −1.40806 | −0.704031 | − | 0.710169i | \(-0.748619\pi\) | ||||
−0.704031 | + | 0.710169i | \(0.748619\pi\) | |||||||
\(618\) | 1.41501e12 | 0.390220 | ||||||||
\(619\) | 7.06562e12 | 1.93438 | 0.967191 | − | 0.254049i | \(-0.0817626\pi\) | ||||
0.967191 | + | 0.254049i | \(0.0817626\pi\) | |||||||
\(620\) | 2.60274e12 | 0.707406 | ||||||||
\(621\) | −2.65636e11 | −0.0716762 | ||||||||
\(622\) | −2.23225e12 | −0.597979 | ||||||||
\(623\) | −1.64571e12 | −0.437680 | ||||||||
\(624\) | 5.21382e11 | 0.137666 | ||||||||
\(625\) | 1.31193e13 | 3.43915 | ||||||||
\(626\) | 2.12276e12 | 0.552479 | ||||||||
\(627\) | −2.51419e12 | −0.649671 | ||||||||
\(628\) | −1.42950e12 | −0.366746 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | −8.75716e11 | −0.221478 | ||||||||
\(631\) | 7.16033e12 | 1.79805 | 0.899023 | − | 0.437902i | \(-0.144278\pi\) | ||||
0.899023 | + | 0.437902i | \(0.144278\pi\) | |||||||
\(632\) | −7.44358e12 | −1.85590 | ||||||||
\(633\) | 1.17393e11 | 0.0290620 | ||||||||
\(634\) | 2.12169e12 | 0.521530 | ||||||||
\(635\) | 4.69569e12 | 1.14609 | ||||||||
\(636\) | 1.21434e11 | 0.0294296 | ||||||||
\(637\) | 9.15685e11 | 0.220353 | ||||||||
\(638\) | −8.83475e10 | −0.0211106 | ||||||||
\(639\) | 2.29613e12 | 0.544806 | ||||||||
\(640\) | −4.59040e12 | −1.08154 | ||||||||
\(641\) | −2.36539e11 | −0.0553404 | −0.0276702 | − | 0.999617i | \(-0.508809\pi\) | ||||
−0.0276702 | + | 0.999617i | \(0.508809\pi\) | |||||||
\(642\) | 2.35497e12 | 0.547113 | ||||||||
\(643\) | 2.08306e12 | 0.480566 | 0.240283 | − | 0.970703i | \(-0.422760\pi\) | ||||
0.240283 | + | 0.970703i | \(0.422760\pi\) | |||||||
\(644\) | 1.93660e10 | 0.00443663 | ||||||||
\(645\) | −1.20833e12 | −0.274895 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −2.70502e12 | −0.606877 | −0.303439 | − | 0.952851i | \(-0.598135\pi\) | ||||
−0.303439 | + | 0.952851i | \(0.598135\pi\) | |||||||
\(648\) | −1.96492e12 | −0.437782 | ||||||||
\(649\) | −2.36606e12 | −0.523510 | ||||||||
\(650\) | 2.62447e12 | 0.576676 | ||||||||
\(651\) | 1.87804e12 | 0.409817 | ||||||||
\(652\) | −3.60864e11 | −0.0782040 | ||||||||
\(653\) | 5.39287e12 | 1.16067 | 0.580337 | − | 0.814376i | \(-0.302921\pi\) | ||||
0.580337 | + | 0.814376i | \(0.302921\pi\) | |||||||
\(654\) | −3.17050e12 | −0.677684 | ||||||||
\(655\) | 9.04834e12 | 1.92080 | ||||||||
\(656\) | 5.60490e12 | 1.18168 | ||||||||
\(657\) | −3.25719e12 | −0.682022 | ||||||||
\(658\) | −1.42648e12 | −0.296654 | ||||||||
\(659\) | 1.48113e12 | 0.305921 | 0.152960 | − | 0.988232i | \(-0.451119\pi\) | ||||
0.152960 | + | 0.988232i | \(0.451119\pi\) | |||||||
\(660\) | 1.18487e12 | 0.243065 | ||||||||
\(661\) | 4.29716e12 | 0.875539 | 0.437769 | − | 0.899087i | \(-0.355769\pi\) | ||||
0.437769 | + | 0.899087i | \(0.355769\pi\) | |||||||
\(662\) | 3.28775e12 | 0.665332 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −9.86131e12 | −1.96870 | ||||||||
\(665\) | −3.30819e12 | −0.655984 | ||||||||
\(666\) | 2.90435e12 | 0.572024 | ||||||||
\(667\) | −1.04001e10 | −0.00203457 | ||||||||
\(668\) | −3.19839e11 | −0.0621495 | ||||||||
\(669\) | −4.42503e12 | −0.854081 | ||||||||
\(670\) | 5.17388e12 | 0.991927 | ||||||||
\(671\) | −4.01293e12 | −0.764206 | ||||||||
\(672\) | 5.29841e11 | 0.100227 | ||||||||
\(673\) | 4.96387e12 | 0.932723 | 0.466361 | − | 0.884594i | \(-0.345565\pi\) | ||||
0.466361 | + | 0.884594i | \(0.345565\pi\) | |||||||
\(674\) | −3.01574e12 | −0.562892 | ||||||||
\(675\) | −1.55508e13 | −2.88328 | ||||||||
\(676\) | 1.09560e12 | 0.201787 | ||||||||
\(677\) | −6.78832e12 | −1.24198 | −0.620988 | − | 0.783820i | \(-0.713269\pi\) | ||||
−0.620988 | + | 0.783820i | \(0.713269\pi\) | |||||||
\(678\) | 5.64863e11 | 0.102662 | ||||||||
\(679\) | 5.69460e11 | 0.102813 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 5.07837e12 | 0.904820 | ||||||||
\(682\) | −6.68874e12 | −1.18390 | ||||||||
\(683\) | −2.03815e12 | −0.358379 | −0.179190 | − | 0.983815i | \(-0.557348\pi\) | ||||
−0.179190 | + | 0.983815i | \(0.557348\pi\) | |||||||
\(684\) | 5.64211e11 | 0.0985574 | ||||||||
\(685\) | 3.53613e12 | 0.613650 | ||||||||
\(686\) | −3.05198e12 | −0.526167 | ||||||||
\(687\) | −2.73324e12 | −0.468136 | ||||||||
\(688\) | 8.18041e11 | 0.139196 | ||||||||
\(689\) | 2.59691e11 | 0.0439006 | ||||||||
\(690\) | −5.10553e11 | −0.0857471 | ||||||||
\(691\) | 7.41249e12 | 1.23684 | 0.618419 | − | 0.785848i | \(-0.287773\pi\) | ||||
0.618419 | + | 0.785848i | \(0.287773\pi\) | |||||||
\(692\) | 5.60857e11 | 0.0929769 | ||||||||
\(693\) | −6.14823e11 | −0.101263 | ||||||||
\(694\) | 4.77000e11 | 0.0780550 | ||||||||
\(695\) | −7.84997e12 | −1.27625 | ||||||||
\(696\) | −1.56055e11 | −0.0252079 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | −8.10959e12 | −1.29315 | ||||||||
\(699\) | −2.58133e12 | −0.408975 | ||||||||
\(700\) | 1.13372e12 | 0.178470 | ||||||||
\(701\) | 8.92468e12 | 1.39592 | 0.697962 | − | 0.716135i | \(-0.254090\pi\) | ||||
0.697962 | + | 0.716135i | \(0.254090\pi\) | |||||||
\(702\) | −1.50590e12 | −0.234034 | ||||||||
\(703\) | 1.09717e13 | 1.69425 | ||||||||
\(704\) | −5.62542e12 | −0.863134 | ||||||||
\(705\) | −1.02740e13 | −1.56635 | ||||||||
\(706\) | −1.00030e12 | −0.151533 | ||||||||
\(707\) | −6.85593e11 | −0.103200 | ||||||||
\(708\) | −7.38352e11 | −0.110437 | ||||||||
\(709\) | −4.22575e12 | −0.628053 | −0.314026 | − | 0.949414i | \(-0.601678\pi\) | ||||
−0.314026 | + | 0.949414i | \(0.601678\pi\) | |||||||
\(710\) | 1.49631e13 | 2.20983 | ||||||||
\(711\) | 4.91462e12 | 0.721235 | ||||||||
\(712\) | 1.03532e13 | 1.50979 | ||||||||
\(713\) | −7.87386e11 | −0.114100 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.53388e12 | 0.362584 | ||||||||
\(716\) | −1.72375e12 | −0.245112 | ||||||||
\(717\) | −2.60052e12 | −0.367472 | ||||||||
\(718\) | −2.07991e12 | −0.292069 | ||||||||
\(719\) | 3.96748e12 | 0.553649 | 0.276825 | − | 0.960920i | \(-0.410718\pi\) | ||||
0.276825 | + | 0.960920i | \(0.410718\pi\) | |||||||
\(720\) | 4.27000e12 | 0.592149 | ||||||||
\(721\) | 1.30719e12 | 0.180148 | ||||||||
\(722\) | −1.33084e12 | −0.182267 | ||||||||
\(723\) | 4.14817e12 | 0.564591 | ||||||||
\(724\) | 1.51865e12 | 0.205416 | ||||||||
\(725\) | −6.08842e11 | −0.0818434 | ||||||||
\(726\) | 2.01459e12 | 0.269136 | ||||||||
\(727\) | 4.61627e12 | 0.612895 | 0.306447 | − | 0.951888i | \(-0.400860\pi\) | ||||
0.306447 | + | 0.951888i | \(0.400860\pi\) | |||||||
\(728\) | 6.21433e11 | 0.0819980 | ||||||||
\(729\) | 7.58858e12 | 0.995146 | ||||||||
\(730\) | −2.12260e13 | −2.76641 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −1.25227e12 | −0.161213 | ||||||||
\(733\) | 8.49490e12 | 1.08690 | 0.543451 | − | 0.839441i | \(-0.317117\pi\) | ||||
0.543451 | + | 0.839441i | \(0.317117\pi\) | |||||||
\(734\) | −8.73439e11 | −0.111071 | ||||||||
\(735\) | −1.04282e13 | −1.31801 | ||||||||
\(736\) | −2.22141e11 | −0.0279048 | ||||||||
\(737\) | 3.63247e12 | 0.453523 | ||||||||
\(738\) | −4.77458e12 | −0.592491 | ||||||||
\(739\) | 3.33909e12 | 0.411839 | 0.205920 | − | 0.978569i | \(-0.433981\pi\) | ||||
0.205920 | + | 0.978569i | \(0.433981\pi\) | |||||||
\(740\) | −5.17068e12 | −0.633877 | ||||||||
\(741\) | −1.67784e12 | −0.204441 | ||||||||
\(742\) | −4.10627e11 | −0.0497313 | ||||||||
\(743\) | −5.88526e12 | −0.708461 | −0.354231 | − | 0.935158i | \(-0.615257\pi\) | ||||
−0.354231 | + | 0.935158i | \(0.615257\pi\) | |||||||
\(744\) | −1.18148e13 | −1.41367 | ||||||||
\(745\) | −2.18317e13 | −2.59648 | ||||||||
\(746\) | 5.00393e12 | 0.591543 | ||||||||
\(747\) | 6.51093e12 | 0.765068 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.17552e12 | 0.252578 | ||||||||
\(750\) | −1.86753e13 | −2.15522 | ||||||||
\(751\) | −9.96514e12 | −1.14315 | −0.571576 | − | 0.820549i | \(-0.693668\pi\) | ||||
−0.571576 | + | 0.820549i | \(0.693668\pi\) | |||||||
\(752\) | 6.95554e12 | 0.793141 | ||||||||
\(753\) | −2.84420e12 | −0.322391 | ||||||||
\(754\) | −5.89586e10 | −0.00664318 | ||||||||
\(755\) | −1.18255e13 | −1.32452 | ||||||||
\(756\) | −6.50519e11 | −0.0724289 | ||||||||
\(757\) | −1.18200e13 | −1.30823 | −0.654116 | − | 0.756394i | \(-0.726959\pi\) | ||||
−0.654116 | + | 0.756394i | \(0.726959\pi\) | |||||||
\(758\) | −2.06088e12 | −0.226747 | ||||||||
\(759\) | −3.58449e11 | −0.0392048 | ||||||||
\(760\) | 2.08120e13 | 2.26284 | ||||||||
\(761\) | −5.90382e12 | −0.638120 | −0.319060 | − | 0.947735i | \(-0.603367\pi\) | ||||
−0.319060 | + | 0.947735i | \(0.603367\pi\) | |||||||
\(762\) | −3.76574e12 | −0.404625 | ||||||||
\(763\) | −2.92891e12 | −0.312857 | ||||||||
\(764\) | −9.06788e11 | −0.0962909 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −3.61008e11 | −0.0378868 | ||||||||
\(767\) | −1.57899e12 | −0.164740 | ||||||||
\(768\) | −4.49985e12 | −0.466737 | ||||||||
\(769\) | −1.02640e12 | −0.105839 | −0.0529196 | − | 0.998599i | \(-0.516853\pi\) | ||||
−0.0529196 | + | 0.998599i | \(0.516853\pi\) | |||||||
\(770\) | −4.00660e12 | −0.410741 | ||||||||
\(771\) | −6.33557e12 | −0.645715 | ||||||||
\(772\) | 3.06988e12 | 0.311059 | ||||||||
\(773\) | 9.17802e12 | 0.924573 | 0.462286 | − | 0.886731i | \(-0.347029\pi\) | ||||
0.462286 | + | 0.886731i | \(0.347029\pi\) | |||||||
\(774\) | −6.96855e11 | −0.0697924 | ||||||||
\(775\) | −4.60951e13 | −4.58983 | ||||||||
\(776\) | −3.58250e12 | −0.354657 | ||||||||
\(777\) | −3.73097e12 | −0.367220 | ||||||||
\(778\) | 1.70682e11 | 0.0167024 | ||||||||
\(779\) | −1.80369e13 | −1.75487 | ||||||||
\(780\) | 7.90720e11 | 0.0764887 | ||||||||
\(781\) | 1.05053e13 | 1.01037 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3.49348e11 | 0.0332147 | ||||||||
\(784\) | 7.05994e12 | 0.667388 | ||||||||
\(785\) | 3.48148e13 | 3.27228 | ||||||||
\(786\) | −7.25637e12 | −0.678138 | ||||||||
\(787\) | 4.74889e12 | 0.441271 | 0.220636 | − | 0.975356i | \(-0.429187\pi\) | ||||
0.220636 | + | 0.975356i | \(0.429187\pi\) | |||||||
\(788\) | 3.32569e12 | 0.307266 | ||||||||
\(789\) | 1.31794e12 | 0.121074 | ||||||||
\(790\) | 3.20270e13 | 2.92546 | ||||||||
\(791\) | 5.21822e11 | 0.0473945 | ||||||||
\(792\) | 3.86788e12 | 0.349309 | ||||||||
\(793\) | −2.67803e12 | −0.240484 | ||||||||
\(794\) | −8.25445e12 | −0.737048 | ||||||||
\(795\) | −2.95748e12 | −0.262585 | ||||||||
\(796\) | 2.88159e12 | 0.254404 | ||||||||
\(797\) | 7.41306e12 | 0.650781 | 0.325390 | − | 0.945580i | \(-0.394504\pi\) | ||||
0.325390 | + | 0.945580i | \(0.394504\pi\) | |||||||
\(798\) | 2.65302e12 | 0.231594 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −1.30046e13 | −1.12251 | ||||||||
\(801\) | −6.83572e12 | −0.586729 | ||||||||
\(802\) | −1.15120e13 | −0.982577 | ||||||||
\(803\) | −1.49024e13 | −1.26484 | ||||||||
\(804\) | 1.13355e12 | 0.0956727 | ||||||||
\(805\) | −4.71650e11 | −0.0395857 | ||||||||
\(806\) | −4.46372e12 | −0.372554 | ||||||||
\(807\) | −1.69430e13 | −1.40624 | ||||||||
\(808\) | 4.31311e12 | 0.355991 | ||||||||
\(809\) | 8.29607e12 | 0.680933 | 0.340466 | − | 0.940257i | \(-0.389415\pi\) | ||||
0.340466 | + | 0.940257i | \(0.389415\pi\) | |||||||
\(810\) | 8.45434e12 | 0.690077 | ||||||||
\(811\) | 1.69807e13 | 1.37836 | 0.689178 | − | 0.724592i | \(-0.257972\pi\) | ||||
0.689178 | + | 0.724592i | \(0.257972\pi\) | |||||||
\(812\) | −2.54689e10 | −0.00205593 | ||||||||
\(813\) | −1.15818e13 | −0.929751 | ||||||||
\(814\) | 1.32880e13 | 1.06084 | ||||||||
\(815\) | 8.78868e12 | 0.697773 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.63251e12 | −0.206714 | ||||||||
\(818\) | −7.47653e12 | −0.583862 | ||||||||
\(819\) | −4.10301e11 | −0.0318658 | ||||||||
\(820\) | 8.50031e12 | 0.656557 | ||||||||
\(821\) | −1.43912e13 | −1.10549 | −0.552743 | − | 0.833352i | \(-0.686419\pi\) | ||||
−0.552743 | + | 0.833352i | \(0.686419\pi\) | |||||||
\(822\) | −2.83582e12 | −0.216648 | ||||||||
\(823\) | −2.53247e12 | −0.192418 | −0.0962089 | − | 0.995361i | \(-0.530672\pi\) | ||||
−0.0962089 | + | 0.995361i | \(0.530672\pi\) | |||||||
\(824\) | −8.22358e12 | −0.621424 | ||||||||
\(825\) | −2.09842e13 | −1.57707 | ||||||||
\(826\) | 2.49672e12 | 0.186621 | ||||||||
\(827\) | 3.93590e12 | 0.292597 | 0.146298 | − | 0.989241i | \(-0.453264\pi\) | ||||
0.146298 | + | 0.989241i | \(0.453264\pi\) | |||||||
\(828\) | 8.04398e10 | 0.00594750 | ||||||||
\(829\) | 1.55976e13 | 1.14700 | 0.573500 | − | 0.819205i | \(-0.305585\pi\) | ||||
0.573500 | + | 0.819205i | \(0.305585\pi\) | |||||||
\(830\) | 4.24296e13 | 3.10326 | ||||||||
\(831\) | −5.72997e12 | −0.416819 | ||||||||
\(832\) | −3.75412e12 | −0.271614 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 6.29533e12 | 0.450579 | ||||||||
\(835\) | 7.78955e12 | 0.554527 | ||||||||
\(836\) | 2.58139e12 | 0.182779 | ||||||||
\(837\) | 2.64490e13 | 1.86270 | ||||||||
\(838\) | −1.08326e13 | −0.758813 | ||||||||
\(839\) | 5.06030e12 | 0.352571 | 0.176286 | − | 0.984339i | \(-0.443592\pi\) | ||||
0.176286 | + | 0.984339i | \(0.443592\pi\) | |||||||
\(840\) | −7.07717e12 | −0.490459 | ||||||||
\(841\) | −1.44935e13 | −0.999057 | ||||||||
\(842\) | 1.36249e13 | 0.934180 | ||||||||
\(843\) | 2.67252e12 | 0.182262 | ||||||||
\(844\) | −1.20531e11 | −0.00817631 | ||||||||
\(845\) | −2.66829e13 | −1.80044 | ||||||||
\(846\) | −5.92513e12 | −0.397678 | ||||||||
\(847\) | 1.86109e12 | 0.124248 | ||||||||
\(848\) | 2.00222e12 | 0.132963 | ||||||||
\(849\) | 9.04245e12 | 0.597312 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.56425e12 | 0.102240 | ||||||||
\(852\) | 3.27828e12 | 0.213141 | ||||||||
\(853\) | 1.69134e13 | 1.09386 | 0.546929 | − | 0.837179i | \(-0.315797\pi\) | ||||
0.546929 | + | 0.837179i | \(0.315797\pi\) | |||||||
\(854\) | 4.23453e12 | 0.272424 | ||||||||
\(855\) | −1.37411e13 | −0.879376 | ||||||||
\(856\) | −1.36863e13 | −0.871275 | ||||||||
\(857\) | −4.73778e12 | −0.300028 | −0.150014 | − | 0.988684i | \(-0.547932\pi\) | ||||
−0.150014 | + | 0.988684i | \(0.547932\pi\) | |||||||
\(858\) | −2.03206e12 | −0.128010 | ||||||||
\(859\) | 2.24036e13 | 1.40394 | 0.701969 | − | 0.712208i | \(-0.252305\pi\) | ||||
0.701969 | + | 0.712208i | \(0.252305\pi\) | |||||||
\(860\) | 1.24063e12 | 0.0773391 | ||||||||
\(861\) | 6.13349e12 | 0.380359 | ||||||||
\(862\) | 2.25980e13 | 1.39408 | ||||||||
\(863\) | −2.34169e13 | −1.43708 | −0.718541 | − | 0.695485i | \(-0.755190\pi\) | ||||
−0.718541 | + | 0.695485i | \(0.755190\pi\) | |||||||
\(864\) | 7.46190e12 | 0.455552 | ||||||||
\(865\) | −1.36594e13 | −0.829583 | ||||||||
\(866\) | 2.21461e13 | 1.33804 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −1.92824e12 | −0.115298 | ||||||||
\(869\) | 2.24855e13 | 1.33756 | ||||||||
\(870\) | 6.71447e11 | 0.0397352 | ||||||||
\(871\) | 2.42413e12 | 0.142716 | ||||||||
\(872\) | 1.84259e13 | 1.07921 | ||||||||
\(873\) | 2.36535e12 | 0.137826 | ||||||||
\(874\) | −1.11231e12 | −0.0644798 | ||||||||
\(875\) | −1.72523e13 | −0.994971 | ||||||||
\(876\) | −4.65043e12 | −0.266824 | ||||||||
\(877\) | 2.82044e12 | 0.160997 | 0.0804986 | − | 0.996755i | \(-0.474349\pi\) | ||||
0.0804986 | + | 0.996755i | \(0.474349\pi\) | |||||||
\(878\) | −2.26194e13 | −1.28456 | ||||||||
\(879\) | −1.35020e13 | −0.762863 | ||||||||
\(880\) | 1.95362e13 | 1.09817 | ||||||||
\(881\) | 1.48809e13 | 0.832218 | 0.416109 | − | 0.909315i | \(-0.363394\pi\) | ||||
0.416109 | + | 0.909315i | \(0.363394\pi\) | |||||||
\(882\) | −6.01407e12 | −0.334626 | ||||||||
\(883\) | −2.31573e12 | −0.128193 | −0.0640966 | − | 0.997944i | \(-0.520417\pi\) | ||||
−0.0640966 | + | 0.997944i | \(0.520417\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.79822e13 | 0.985370 | ||||||||
\(886\) | 2.71335e13 | 1.47929 | ||||||||
\(887\) | −9.47146e12 | −0.513760 | −0.256880 | − | 0.966443i | \(-0.582695\pi\) | ||||
−0.256880 | + | 0.966443i | \(0.582695\pi\) | |||||||
\(888\) | 2.34717e13 | 1.26674 | ||||||||
\(889\) | −3.47880e12 | −0.186798 | ||||||||
\(890\) | −4.45462e13 | −2.37988 | ||||||||
\(891\) | 5.93562e12 | 0.315512 | ||||||||
\(892\) | 4.54332e12 | 0.240288 | ||||||||
\(893\) | −2.23834e13 | −1.17786 | ||||||||
\(894\) | 1.75081e13 | 0.916685 | ||||||||
\(895\) | 4.19811e13 | 2.18701 | ||||||||
\(896\) | 3.40080e12 | 0.176277 | ||||||||
\(897\) | −2.39210e11 | −0.0123371 | ||||||||
\(898\) | −8.85714e12 | −0.454517 | ||||||||
\(899\) | 1.03552e12 | 0.0528738 | ||||||||
\(900\) | 4.70909e12 | 0.239247 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | −2.18448e13 | −1.09880 | ||||||||
\(903\) | 8.95190e11 | 0.0448044 | ||||||||
\(904\) | −3.28281e12 | −0.163489 | ||||||||
\(905\) | −3.69860e13 | −1.83282 | ||||||||
\(906\) | 9.48356e12 | 0.467621 | ||||||||
\(907\) | −7.59597e12 | −0.372692 | −0.186346 | − | 0.982484i | \(-0.559665\pi\) | ||||
−0.186346 | + | 0.982484i | \(0.559665\pi\) | |||||||
\(908\) | −5.21412e12 | −0.254563 | ||||||||
\(909\) | −2.84772e12 | −0.138344 | ||||||||
\(910\) | −2.67380e12 | −0.129254 | ||||||||
\(911\) | 2.28116e13 | 1.09729 | 0.548647 | − | 0.836054i | \(-0.315143\pi\) | ||||
0.548647 | + | 0.836054i | \(0.315143\pi\) | |||||||
\(912\) | −1.29362e13 | −0.619196 | ||||||||
\(913\) | 2.97890e13 | 1.41885 | ||||||||
\(914\) | 1.02283e13 | 0.484782 | ||||||||
\(915\) | 3.04986e13 | 1.43842 | ||||||||
\(916\) | 2.80630e12 | 0.131706 | ||||||||
\(917\) | −6.70345e12 | −0.313067 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.37159e13 | 0.634315 | 0.317158 | − | 0.948373i | \(-0.397272\pi\) | ||||
0.317158 | + | 0.948373i | \(0.397272\pi\) | |||||||
\(920\) | 2.96717e12 | 0.136552 | ||||||||
\(921\) | 3.35696e12 | 0.153737 | ||||||||
\(922\) | −2.81101e13 | −1.28107 | ||||||||
\(923\) | 7.01069e12 | 0.317946 | ||||||||
\(924\) | −8.77809e11 | −0.0396165 | ||||||||
\(925\) | 9.15738e13 | 4.11276 | ||||||||
\(926\) | 1.62962e10 | 0.000728342 0 | ||||||||
\(927\) | 5.42961e12 | 0.241496 | ||||||||
\(928\) | 2.92146e11 | 0.0129311 | ||||||||
\(929\) | −3.39205e12 | −0.149414 | −0.0747070 | − | 0.997206i | \(-0.523802\pi\) | ||||
−0.0747070 | + | 0.997206i | \(0.523802\pi\) | |||||||
\(930\) | 5.08349e13 | 2.22838 | ||||||||
\(931\) | −2.27193e13 | −0.991110 | ||||||||
\(932\) | 2.65033e12 | 0.115061 | ||||||||
\(933\) | 1.19110e13 | 0.514611 | ||||||||
\(934\) | 1.10414e13 | 0.474746 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 2.58123e12 | 0.109922 | ||||||||
\(937\) | 3.08488e12 | 0.130740 | 0.0653702 | − | 0.997861i | \(-0.479177\pi\) | ||||
0.0653702 | + | 0.997861i | \(0.479177\pi\) | |||||||
\(938\) | −3.83306e12 | −0.161671 | ||||||||
\(939\) | −1.13267e13 | −0.475454 | ||||||||
\(940\) | 1.05487e13 | 0.440679 | ||||||||
\(941\) | −1.10199e13 | −0.458167 | −0.229084 | − | 0.973407i | \(-0.573573\pi\) | ||||
−0.229084 | + | 0.973407i | \(0.573573\pi\) | |||||||
\(942\) | −2.79200e13 | −1.15528 | ||||||||
\(943\) | −2.57153e12 | −0.105898 | ||||||||
\(944\) | −1.21740e13 | −0.498953 | ||||||||
\(945\) | 1.58431e13 | 0.646245 | ||||||||
\(946\) | −3.18827e12 | −0.129433 | ||||||||
\(947\) | −2.51700e13 | −1.01697 | −0.508485 | − | 0.861071i | \(-0.669794\pi\) | ||||
−0.508485 | + | 0.861071i | \(0.669794\pi\) | |||||||
\(948\) | 7.01681e12 | 0.282165 | ||||||||
\(949\) | −9.94508e12 | −0.398025 | ||||||||
\(950\) | −6.51165e13 | −2.59379 | ||||||||
\(951\) | −1.13210e13 | −0.448821 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 4.52926e13 | 1.77873 | 0.889364 | − | 0.457200i | \(-0.151148\pi\) | ||||
0.889364 | + | 0.457200i | \(0.151148\pi\) | |||||||
\(954\) | −1.70561e12 | −0.0666671 | ||||||||
\(955\) | 2.20844e13 | 0.859153 | ||||||||
\(956\) | 2.67004e12 | 0.103385 | ||||||||
\(957\) | 4.71409e11 | 0.0181675 | ||||||||
\(958\) | 8.25752e12 | 0.316741 | ||||||||
\(959\) | −2.61974e12 | −0.100017 | ||||||||
\(960\) | 4.27536e13 | 1.62462 | ||||||||
\(961\) | 5.19592e13 | 1.96520 | ||||||||
\(962\) | 8.86776e12 | 0.333831 | ||||||||
\(963\) | 9.03640e12 | 0.338592 | ||||||||
\(964\) | −4.25905e12 | −0.158842 | ||||||||
\(965\) | −7.47655e13 | −2.77542 | ||||||||
\(966\) | 3.78242e11 | 0.0139757 | ||||||||
\(967\) | −2.02193e13 | −0.743614 | −0.371807 | − | 0.928310i | \(-0.621262\pi\) | ||||
−0.371807 | + | 0.928310i | \(0.621262\pi\) | |||||||
\(968\) | −1.17082e13 | −0.428599 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 1.54142e13 | 0.559047 | ||||||||
\(971\) | 3.04494e13 | 1.09924 | 0.549620 | − | 0.835415i | \(-0.314772\pi\) | ||||
0.549620 | + | 0.835415i | \(0.314772\pi\) | |||||||
\(972\) | −4.60715e12 | −0.165552 | ||||||||
\(973\) | 5.81564e12 | 0.208013 | ||||||||
\(974\) | 2.52281e13 | 0.898193 | ||||||||
\(975\) | −1.40038e13 | −0.496278 | ||||||||
\(976\) | −2.06476e13 | −0.728358 | ||||||||
\(977\) | 3.69433e13 | 1.29721 | 0.648604 | − | 0.761126i | \(-0.275353\pi\) | ||||
0.648604 | + | 0.761126i | \(0.275353\pi\) | |||||||
\(978\) | −7.04814e12 | −0.246348 | ||||||||
\(979\) | −3.12750e13 | −1.08811 | ||||||||
\(980\) | 1.07070e13 | 0.370809 | ||||||||
\(981\) | −1.21657e13 | −0.419399 | ||||||||
\(982\) | −1.07531e13 | −0.369006 | ||||||||
\(983\) | −5.15287e13 | −1.76018 | −0.880092 | − | 0.474803i | \(-0.842519\pi\) | ||||
−0.880092 | + | 0.474803i | \(0.842519\pi\) | |||||||
\(984\) | −3.85861e13 | −1.31206 | ||||||||
\(985\) | −8.09957e13 | −2.74157 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 7.61151e12 | 0.255296 | ||||||||
\(988\) | 1.72269e12 | 0.0575176 | ||||||||
\(989\) | −3.75317e11 | −0.0124743 | ||||||||
\(990\) | −1.66421e13 | −0.550616 | ||||||||
\(991\) | 2.98474e13 | 0.983049 | 0.491524 | − | 0.870864i | \(-0.336440\pi\) | ||||
0.491524 | + | 0.870864i | \(0.336440\pi\) | |||||||
\(992\) | 2.21182e13 | 0.725184 | ||||||||
\(993\) | −1.75430e13 | −0.572574 | ||||||||
\(994\) | −1.10854e13 | −0.360175 | ||||||||
\(995\) | −7.01799e13 | −2.26991 | ||||||||
\(996\) | 9.29593e12 | 0.299313 | ||||||||
\(997\) | −3.49991e13 | −1.12183 | −0.560917 | − | 0.827872i | \(-0.689551\pi\) | ||||
−0.560917 | + | 0.827872i | \(0.689551\pi\) | |||||||
\(998\) | 2.74390e13 | 0.875550 | ||||||||
\(999\) | −5.25443e13 | −1.66909 |
(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 | 289.10.a.g.1.12 | ✓ | 36 | |
17.16 | even | 2 | 289.10.a.h.1.12 | yes | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
289.10.a.g.1.12 | ✓ | 36 | 1.1 | even | 1 | trivial | |
289.10.a.h.1.12 | yes | 36 | 17.16 | even | 2 |