Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [546,8,Mod(1,546)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(546, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("546.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 546.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(170.562223914\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} - 264981x^{4} + 17519669x^{3} + 15113237808x^{2} - 1787613752904x - 21984668630064 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{3}\cdot 3 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(-462.924\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 546.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 8.00000 | 0.707107 | ||||||||
\(3\) | −27.0000 | −0.577350 | ||||||||
\(4\) | 64.0000 | 0.500000 | ||||||||
\(5\) | 496.924 | 1.77785 | 0.888925 | − | 0.458053i | \(-0.151453\pi\) | ||||
0.888925 | + | 0.458053i | \(0.151453\pi\) | |||||||
\(6\) | −216.000 | −0.408248 | ||||||||
\(7\) | −343.000 | −0.377964 | ||||||||
\(8\) | 512.000 | 0.353553 | ||||||||
\(9\) | 729.000 | 0.333333 | ||||||||
\(10\) | 3975.39 | 1.25713 | ||||||||
\(11\) | −3824.74 | −0.866418 | −0.433209 | − | 0.901293i | \(-0.642619\pi\) | ||||
−0.433209 | + | 0.901293i | \(0.642619\pi\) | |||||||
\(12\) | −1728.00 | −0.288675 | ||||||||
\(13\) | 2197.00 | 0.277350 | ||||||||
\(14\) | −2744.00 | −0.267261 | ||||||||
\(15\) | −13417.0 | −1.02644 | ||||||||
\(16\) | 4096.00 | 0.250000 | ||||||||
\(17\) | −2147.73 | −0.106025 | −0.0530126 | − | 0.998594i | \(-0.516882\pi\) | ||||
−0.0530126 | + | 0.998594i | \(0.516882\pi\) | |||||||
\(18\) | 5832.00 | 0.235702 | ||||||||
\(19\) | −18544.8 | −0.620276 | −0.310138 | − | 0.950691i | \(-0.600375\pi\) | ||||
−0.310138 | + | 0.950691i | \(0.600375\pi\) | |||||||
\(20\) | 31803.1 | 0.888925 | ||||||||
\(21\) | 9261.00 | 0.218218 | ||||||||
\(22\) | −30597.9 | −0.612650 | ||||||||
\(23\) | −67563.5 | −1.15788 | −0.578941 | − | 0.815369i | \(-0.696534\pi\) | ||||
−0.578941 | + | 0.815369i | \(0.696534\pi\) | |||||||
\(24\) | −13824.0 | −0.204124 | ||||||||
\(25\) | 168809. | 2.16075 | ||||||||
\(26\) | 17576.0 | 0.196116 | ||||||||
\(27\) | −19683.0 | −0.192450 | ||||||||
\(28\) | −21952.0 | −0.188982 | ||||||||
\(29\) | 58711.4 | 0.447022 | 0.223511 | − | 0.974701i | \(-0.428248\pi\) | ||||
0.223511 | + | 0.974701i | \(0.428248\pi\) | |||||||
\(30\) | −107336. | −0.725804 | ||||||||
\(31\) | 157539. | 0.949781 | 0.474890 | − | 0.880045i | \(-0.342488\pi\) | ||||
0.474890 | + | 0.880045i | \(0.342488\pi\) | |||||||
\(32\) | 32768.0 | 0.176777 | ||||||||
\(33\) | 103268. | 0.500227 | ||||||||
\(34\) | −17181.9 | −0.0749712 | ||||||||
\(35\) | −170445. | −0.671964 | ||||||||
\(36\) | 46656.0 | 0.166667 | ||||||||
\(37\) | 381564. | 1.23840 | 0.619200 | − | 0.785233i | \(-0.287457\pi\) | ||||
0.619200 | + | 0.785233i | \(0.287457\pi\) | |||||||
\(38\) | −148359. | −0.438602 | ||||||||
\(39\) | −59319.0 | −0.160128 | ||||||||
\(40\) | 254425. | 0.628565 | ||||||||
\(41\) | 227136. | 0.514686 | 0.257343 | − | 0.966320i | \(-0.417153\pi\) | ||||
0.257343 | + | 0.966320i | \(0.417153\pi\) | |||||||
\(42\) | 74088.0 | 0.154303 | ||||||||
\(43\) | 532865. | 1.02206 | 0.511031 | − | 0.859562i | \(-0.329264\pi\) | ||||
0.511031 | + | 0.859562i | \(0.329264\pi\) | |||||||
\(44\) | −244783. | −0.433209 | ||||||||
\(45\) | 362258. | 0.592617 | ||||||||
\(46\) | −540508. | −0.818747 | ||||||||
\(47\) | 714364. | 1.00364 | 0.501819 | − | 0.864973i | \(-0.332664\pi\) | ||||
0.501819 | + | 0.864973i | \(0.332664\pi\) | |||||||
\(48\) | −110592. | −0.144338 | ||||||||
\(49\) | 117649. | 0.142857 | ||||||||
\(50\) | 1.35047e6 | 1.52788 | ||||||||
\(51\) | 57988.8 | 0.0612137 | ||||||||
\(52\) | 140608. | 0.138675 | ||||||||
\(53\) | −352284. | −0.325033 | −0.162516 | − | 0.986706i | \(-0.551961\pi\) | ||||
−0.162516 | + | 0.986706i | \(0.551961\pi\) | |||||||
\(54\) | −157464. | −0.136083 | ||||||||
\(55\) | −1.90061e6 | −1.54036 | ||||||||
\(56\) | −175616. | −0.133631 | ||||||||
\(57\) | 500710. | 0.358117 | ||||||||
\(58\) | 469691. | 0.316093 | ||||||||
\(59\) | −534961. | −0.339109 | −0.169555 | − | 0.985521i | \(-0.554233\pi\) | ||||
−0.169555 | + | 0.985521i | \(0.554233\pi\) | |||||||
\(60\) | −858685. | −0.513221 | ||||||||
\(61\) | 947554. | 0.534502 | 0.267251 | − | 0.963627i | \(-0.413885\pi\) | ||||
0.267251 | + | 0.963627i | \(0.413885\pi\) | |||||||
\(62\) | 1.26032e6 | 0.671596 | ||||||||
\(63\) | −250047. | −0.125988 | ||||||||
\(64\) | 262144. | 0.125000 | ||||||||
\(65\) | 1.09174e6 | 0.493087 | ||||||||
\(66\) | 826144. | 0.353714 | ||||||||
\(67\) | 2.20515e6 | 0.895728 | 0.447864 | − | 0.894102i | \(-0.352185\pi\) | ||||
0.447864 | + | 0.894102i | \(0.352185\pi\) | |||||||
\(68\) | −137455. | −0.0530126 | ||||||||
\(69\) | 1.82421e6 | 0.668504 | ||||||||
\(70\) | −1.36356e6 | −0.475150 | ||||||||
\(71\) | −5.03775e6 | −1.67044 | −0.835222 | − | 0.549912i | \(-0.814661\pi\) | ||||
−0.835222 | + | 0.549912i | \(0.814661\pi\) | |||||||
\(72\) | 373248. | 0.117851 | ||||||||
\(73\) | 1.46454e6 | 0.440628 | 0.220314 | − | 0.975429i | \(-0.429292\pi\) | ||||
0.220314 | + | 0.975429i | \(0.429292\pi\) | |||||||
\(74\) | 3.05251e6 | 0.875681 | ||||||||
\(75\) | −4.55783e6 | −1.24751 | ||||||||
\(76\) | −1.18687e6 | −0.310138 | ||||||||
\(77\) | 1.31189e6 | 0.327475 | ||||||||
\(78\) | −474552. | −0.113228 | ||||||||
\(79\) | 8.61725e6 | 1.96641 | 0.983204 | − | 0.182509i | \(-0.0584217\pi\) | ||||
0.983204 | + | 0.182509i | \(0.0584217\pi\) | |||||||
\(80\) | 2.03540e6 | 0.444462 | ||||||||
\(81\) | 531441. | 0.111111 | ||||||||
\(82\) | 1.81709e6 | 0.363938 | ||||||||
\(83\) | −8.80720e6 | −1.69069 | −0.845346 | − | 0.534219i | \(-0.820606\pi\) | ||||
−0.845346 | + | 0.534219i | \(0.820606\pi\) | |||||||
\(84\) | 592704. | 0.109109 | ||||||||
\(85\) | −1.06726e6 | −0.188497 | ||||||||
\(86\) | 4.26292e6 | 0.722707 | ||||||||
\(87\) | −1.58521e6 | −0.258089 | ||||||||
\(88\) | −1.95827e6 | −0.306325 | ||||||||
\(89\) | 3.11870e6 | 0.468930 | 0.234465 | − | 0.972125i | \(-0.424666\pi\) | ||||
0.234465 | + | 0.972125i | \(0.424666\pi\) | |||||||
\(90\) | 2.89806e6 | 0.419043 | ||||||||
\(91\) | −753571. | −0.104828 | ||||||||
\(92\) | −4.32406e6 | −0.578941 | ||||||||
\(93\) | −4.25357e6 | −0.548356 | ||||||||
\(94\) | 5.71491e6 | 0.709679 | ||||||||
\(95\) | −9.21537e6 | −1.10276 | ||||||||
\(96\) | −884736. | −0.102062 | ||||||||
\(97\) | 2.00663e6 | 0.223238 | 0.111619 | − | 0.993751i | \(-0.464396\pi\) | ||||
0.111619 | + | 0.993751i | \(0.464396\pi\) | |||||||
\(98\) | 941192. | 0.101015 | ||||||||
\(99\) | −2.78824e6 | −0.288806 | ||||||||
\(100\) | 1.08037e7 | 1.08037 | ||||||||
\(101\) | 1.91316e7 | 1.84767 | 0.923837 | − | 0.382785i | \(-0.125035\pi\) | ||||
0.923837 | + | 0.382785i | \(0.125035\pi\) | |||||||
\(102\) | 463910. | 0.0432846 | ||||||||
\(103\) | 1.37161e6 | 0.123680 | 0.0618400 | − | 0.998086i | \(-0.480303\pi\) | ||||
0.0618400 | + | 0.998086i | \(0.480303\pi\) | |||||||
\(104\) | 1.12486e6 | 0.0980581 | ||||||||
\(105\) | 4.60201e6 | 0.387959 | ||||||||
\(106\) | −2.81827e6 | −0.229833 | ||||||||
\(107\) | 2.35974e7 | 1.86218 | 0.931088 | − | 0.364795i | \(-0.118861\pi\) | ||||
0.931088 | + | 0.364795i | \(0.118861\pi\) | |||||||
\(108\) | −1.25971e6 | −0.0962250 | ||||||||
\(109\) | 8.39526e6 | 0.620928 | 0.310464 | − | 0.950585i | \(-0.399516\pi\) | ||||
0.310464 | + | 0.950585i | \(0.399516\pi\) | |||||||
\(110\) | −1.52048e7 | −1.08920 | ||||||||
\(111\) | −1.03022e7 | −0.714991 | ||||||||
\(112\) | −1.40493e6 | −0.0944911 | ||||||||
\(113\) | −7.06983e6 | −0.460930 | −0.230465 | − | 0.973081i | \(-0.574025\pi\) | ||||
−0.230465 | + | 0.973081i | \(0.574025\pi\) | |||||||
\(114\) | 4.00568e6 | 0.253227 | ||||||||
\(115\) | −3.35739e7 | −2.05854 | ||||||||
\(116\) | 3.75753e6 | 0.223511 | ||||||||
\(117\) | 1.60161e6 | 0.0924500 | ||||||||
\(118\) | −4.27969e6 | −0.239787 | ||||||||
\(119\) | 736673. | 0.0400738 | ||||||||
\(120\) | −6.86948e6 | −0.362902 | ||||||||
\(121\) | −4.85853e6 | −0.249319 | ||||||||
\(122\) | 7.58043e6 | 0.377950 | ||||||||
\(123\) | −6.13267e6 | −0.297154 | ||||||||
\(124\) | 1.00825e7 | 0.474890 | ||||||||
\(125\) | 4.50629e7 | 2.06364 | ||||||||
\(126\) | −2.00038e6 | −0.0890871 | ||||||||
\(127\) | −985521. | −0.0426926 | −0.0213463 | − | 0.999772i | \(-0.506795\pi\) | ||||
−0.0213463 | + | 0.999772i | \(0.506795\pi\) | |||||||
\(128\) | 2.09715e6 | 0.0883883 | ||||||||
\(129\) | −1.43873e7 | −0.590088 | ||||||||
\(130\) | 8.73394e6 | 0.348665 | ||||||||
\(131\) | −3.54561e7 | −1.37798 | −0.688988 | − | 0.724773i | \(-0.741945\pi\) | ||||
−0.688988 | + | 0.724773i | \(0.741945\pi\) | |||||||
\(132\) | 6.60915e6 | 0.250113 | ||||||||
\(133\) | 6.36088e6 | 0.234442 | ||||||||
\(134\) | 1.76412e7 | 0.633375 | ||||||||
\(135\) | −9.78096e6 | −0.342147 | ||||||||
\(136\) | −1.09964e6 | −0.0374856 | ||||||||
\(137\) | 2.66368e7 | 0.885034 | 0.442517 | − | 0.896760i | \(-0.354086\pi\) | ||||
0.442517 | + | 0.896760i | \(0.354086\pi\) | |||||||
\(138\) | 1.45937e7 | 0.472704 | ||||||||
\(139\) | −5.67858e7 | −1.79345 | −0.896723 | − | 0.442592i | \(-0.854059\pi\) | ||||
−0.896723 | + | 0.442592i | \(0.854059\pi\) | |||||||
\(140\) | −1.09085e7 | −0.335982 | ||||||||
\(141\) | −1.92878e7 | −0.579451 | ||||||||
\(142\) | −4.03020e7 | −1.18118 | ||||||||
\(143\) | −8.40296e6 | −0.240301 | ||||||||
\(144\) | 2.98598e6 | 0.0833333 | ||||||||
\(145\) | 2.91751e7 | 0.794739 | ||||||||
\(146\) | 1.17163e7 | 0.311571 | ||||||||
\(147\) | −3.17652e6 | −0.0824786 | ||||||||
\(148\) | 2.44201e7 | 0.619200 | ||||||||
\(149\) | −7.19892e7 | −1.78285 | −0.891427 | − | 0.453165i | \(-0.850295\pi\) | ||||
−0.891427 | + | 0.453165i | \(0.850295\pi\) | |||||||
\(150\) | −3.64627e7 | −0.882122 | ||||||||
\(151\) | −3.22126e7 | −0.761388 | −0.380694 | − | 0.924701i | \(-0.624315\pi\) | ||||
−0.380694 | + | 0.924701i | \(0.624315\pi\) | |||||||
\(152\) | −9.49495e6 | −0.219301 | ||||||||
\(153\) | −1.56570e6 | −0.0353417 | ||||||||
\(154\) | 1.04951e7 | 0.231560 | ||||||||
\(155\) | 7.82852e7 | 1.68857 | ||||||||
\(156\) | −3.79642e6 | −0.0800641 | ||||||||
\(157\) | −8.76407e7 | −1.80741 | −0.903706 | − | 0.428153i | \(-0.859164\pi\) | ||||
−0.903706 | + | 0.428153i | \(0.859164\pi\) | |||||||
\(158\) | 6.89380e7 | 1.39046 | ||||||||
\(159\) | 9.51167e6 | 0.187658 | ||||||||
\(160\) | 1.62832e7 | 0.314282 | ||||||||
\(161\) | 2.31743e7 | 0.437639 | ||||||||
\(162\) | 4.25153e6 | 0.0785674 | ||||||||
\(163\) | 7.24820e7 | 1.31091 | 0.655456 | − | 0.755233i | \(-0.272476\pi\) | ||||
0.655456 | + | 0.755233i | \(0.272476\pi\) | |||||||
\(164\) | 1.45367e7 | 0.257343 | ||||||||
\(165\) | 5.13164e7 | 0.889328 | ||||||||
\(166\) | −7.04576e7 | −1.19550 | ||||||||
\(167\) | 7.83523e7 | 1.30180 | 0.650900 | − | 0.759163i | \(-0.274392\pi\) | ||||
0.650900 | + | 0.759163i | \(0.274392\pi\) | |||||||
\(168\) | 4.74163e6 | 0.0771517 | ||||||||
\(169\) | 4.82681e6 | 0.0769231 | ||||||||
\(170\) | −8.53808e6 | −0.133287 | ||||||||
\(171\) | −1.35192e7 | −0.206759 | ||||||||
\(172\) | 3.41033e7 | 0.511031 | ||||||||
\(173\) | 2.63684e7 | 0.387189 | 0.193595 | − | 0.981082i | \(-0.437985\pi\) | ||||
0.193595 | + | 0.981082i | \(0.437985\pi\) | |||||||
\(174\) | −1.26817e7 | −0.182496 | ||||||||
\(175\) | −5.79013e7 | −0.816687 | ||||||||
\(176\) | −1.56661e7 | −0.216605 | ||||||||
\(177\) | 1.44439e7 | 0.195785 | ||||||||
\(178\) | 2.49496e7 | 0.331584 | ||||||||
\(179\) | 1.43940e8 | 1.87584 | 0.937920 | − | 0.346852i | \(-0.112749\pi\) | ||||
0.937920 | + | 0.346852i | \(0.112749\pi\) | |||||||
\(180\) | 2.31845e7 | 0.296308 | ||||||||
\(181\) | 7.83164e7 | 0.981698 | 0.490849 | − | 0.871245i | \(-0.336687\pi\) | ||||
0.490849 | + | 0.871245i | \(0.336687\pi\) | |||||||
\(182\) | −6.02857e6 | −0.0741249 | ||||||||
\(183\) | −2.55840e7 | −0.308595 | ||||||||
\(184\) | −3.45925e7 | −0.409373 | ||||||||
\(185\) | 1.89608e8 | 2.20169 | ||||||||
\(186\) | −3.40285e7 | −0.387746 | ||||||||
\(187\) | 8.21452e6 | 0.0918622 | ||||||||
\(188\) | 4.57193e7 | 0.501819 | ||||||||
\(189\) | 6.75127e6 | 0.0727393 | ||||||||
\(190\) | −7.37230e7 | −0.779768 | ||||||||
\(191\) | 6.34840e7 | 0.659246 | 0.329623 | − | 0.944113i | \(-0.393078\pi\) | ||||
0.329623 | + | 0.944113i | \(0.393078\pi\) | |||||||
\(192\) | −7.07789e6 | −0.0721688 | ||||||||
\(193\) | 9.55888e7 | 0.957098 | 0.478549 | − | 0.878061i | \(-0.341163\pi\) | ||||
0.478549 | + | 0.878061i | \(0.341163\pi\) | |||||||
\(194\) | 1.60531e7 | 0.157853 | ||||||||
\(195\) | −2.94770e7 | −0.284684 | ||||||||
\(196\) | 7.52954e6 | 0.0714286 | ||||||||
\(197\) | 8.28275e7 | 0.771867 | 0.385934 | − | 0.922527i | \(-0.373879\pi\) | ||||
0.385934 | + | 0.922527i | \(0.373879\pi\) | |||||||
\(198\) | −2.23059e7 | −0.204217 | ||||||||
\(199\) | −8.13880e7 | −0.732107 | −0.366053 | − | 0.930594i | \(-0.619291\pi\) | ||||
−0.366053 | + | 0.930594i | \(0.619291\pi\) | |||||||
\(200\) | 8.64300e7 | 0.763940 | ||||||||
\(201\) | −5.95390e7 | −0.517149 | ||||||||
\(202\) | 1.53052e8 | 1.30650 | ||||||||
\(203\) | −2.01380e7 | −0.168959 | ||||||||
\(204\) | 3.71128e6 | 0.0306068 | ||||||||
\(205\) | 1.12869e8 | 0.915035 | ||||||||
\(206\) | 1.09729e7 | 0.0874550 | ||||||||
\(207\) | −4.92538e7 | −0.385961 | ||||||||
\(208\) | 8.99891e6 | 0.0693375 | ||||||||
\(209\) | 7.09292e7 | 0.537419 | ||||||||
\(210\) | 3.68161e7 | 0.274328 | ||||||||
\(211\) | 1.89709e8 | 1.39027 | 0.695134 | − | 0.718880i | \(-0.255345\pi\) | ||||
0.695134 | + | 0.718880i | \(0.255345\pi\) | |||||||
\(212\) | −2.25462e7 | −0.162516 | ||||||||
\(213\) | 1.36019e8 | 0.964432 | ||||||||
\(214\) | 1.88779e8 | 1.31676 | ||||||||
\(215\) | 2.64793e8 | 1.81707 | ||||||||
\(216\) | −1.00777e7 | −0.0680414 | ||||||||
\(217\) | −5.40360e7 | −0.358983 | ||||||||
\(218\) | 6.71621e7 | 0.439063 | ||||||||
\(219\) | −3.95426e7 | −0.254396 | ||||||||
\(220\) | −1.21639e8 | −0.770181 | ||||||||
\(221\) | −4.71857e6 | −0.0294061 | ||||||||
\(222\) | −8.24178e7 | −0.505575 | ||||||||
\(223\) | 4.32655e7 | 0.261261 | 0.130630 | − | 0.991431i | \(-0.458300\pi\) | ||||
0.130630 | + | 0.991431i | \(0.458300\pi\) | |||||||
\(224\) | −1.12394e7 | −0.0668153 | ||||||||
\(225\) | 1.23061e8 | 0.720250 | ||||||||
\(226\) | −5.65587e7 | −0.325926 | ||||||||
\(227\) | 1.76524e7 | 0.100164 | 0.0500821 | − | 0.998745i | \(-0.484052\pi\) | ||||
0.0500821 | + | 0.998745i | \(0.484052\pi\) | |||||||
\(228\) | 3.20455e7 | 0.179058 | ||||||||
\(229\) | 2.28130e8 | 1.25533 | 0.627664 | − | 0.778484i | \(-0.284011\pi\) | ||||
0.627664 | + | 0.778484i | \(0.284011\pi\) | |||||||
\(230\) | −2.68591e8 | −1.45561 | ||||||||
\(231\) | −3.54209e7 | −0.189068 | ||||||||
\(232\) | 3.00602e7 | 0.158046 | ||||||||
\(233\) | −9.21660e7 | −0.477337 | −0.238668 | − | 0.971101i | \(-0.576711\pi\) | ||||
−0.238668 | + | 0.971101i | \(0.576711\pi\) | |||||||
\(234\) | 1.28129e7 | 0.0653720 | ||||||||
\(235\) | 3.54985e8 | 1.78432 | ||||||||
\(236\) | −3.42375e7 | −0.169555 | ||||||||
\(237\) | −2.32666e8 | −1.13531 | ||||||||
\(238\) | 5.89338e6 | 0.0283364 | ||||||||
\(239\) | 1.66857e8 | 0.790591 | 0.395296 | − | 0.918554i | \(-0.370642\pi\) | ||||
0.395296 | + | 0.918554i | \(0.370642\pi\) | |||||||
\(240\) | −5.49558e7 | −0.256611 | ||||||||
\(241\) | 2.35779e8 | 1.08504 | 0.542519 | − | 0.840043i | \(-0.317471\pi\) | ||||
0.542519 | + | 0.840043i | \(0.317471\pi\) | |||||||
\(242\) | −3.88682e7 | −0.176295 | ||||||||
\(243\) | −1.43489e7 | −0.0641500 | ||||||||
\(244\) | 6.06435e7 | 0.267251 | ||||||||
\(245\) | 5.84626e7 | 0.253979 | ||||||||
\(246\) | −4.90614e7 | −0.210120 | ||||||||
\(247\) | −4.07430e7 | −0.172034 | ||||||||
\(248\) | 8.06602e7 | 0.335798 | ||||||||
\(249\) | 2.37794e8 | 0.976121 | ||||||||
\(250\) | 3.60503e8 | 1.45921 | ||||||||
\(251\) | −1.87788e8 | −0.749564 | −0.374782 | − | 0.927113i | \(-0.622282\pi\) | ||||
−0.374782 | + | 0.927113i | \(0.622282\pi\) | |||||||
\(252\) | −1.60030e7 | −0.0629941 | ||||||||
\(253\) | 2.58413e8 | 1.00321 | ||||||||
\(254\) | −7.88417e6 | −0.0301883 | ||||||||
\(255\) | 2.88160e7 | 0.108829 | ||||||||
\(256\) | 1.67772e7 | 0.0625000 | ||||||||
\(257\) | 2.09400e8 | 0.769502 | 0.384751 | − | 0.923020i | \(-0.374287\pi\) | ||||
0.384751 | + | 0.923020i | \(0.374287\pi\) | |||||||
\(258\) | −1.15099e8 | −0.417255 | ||||||||
\(259\) | −1.30876e8 | −0.468071 | ||||||||
\(260\) | 6.98715e7 | 0.246543 | ||||||||
\(261\) | 4.28006e7 | 0.149007 | ||||||||
\(262\) | −2.83649e8 | −0.974376 | ||||||||
\(263\) | −3.30860e8 | −1.12150 | −0.560749 | − | 0.827986i | \(-0.689487\pi\) | ||||
−0.560749 | + | 0.827986i | \(0.689487\pi\) | |||||||
\(264\) | 5.28732e7 | 0.176857 | ||||||||
\(265\) | −1.75058e8 | −0.577860 | ||||||||
\(266\) | 5.08870e7 | 0.165776 | ||||||||
\(267\) | −8.42048e7 | −0.270737 | ||||||||
\(268\) | 1.41130e8 | 0.447864 | ||||||||
\(269\) | 3.78010e8 | 1.18405 | 0.592025 | − | 0.805920i | \(-0.298329\pi\) | ||||
0.592025 | + | 0.805920i | \(0.298329\pi\) | |||||||
\(270\) | −7.82477e7 | −0.241935 | ||||||||
\(271\) | 6.09647e6 | 0.0186074 | 0.00930371 | − | 0.999957i | \(-0.497038\pi\) | ||||
0.00930371 | + | 0.999957i | \(0.497038\pi\) | |||||||
\(272\) | −8.79712e6 | −0.0265063 | ||||||||
\(273\) | 2.03464e7 | 0.0605228 | ||||||||
\(274\) | 2.13094e8 | 0.625813 | ||||||||
\(275\) | −6.45649e8 | −1.87211 | ||||||||
\(276\) | 1.16750e8 | 0.334252 | ||||||||
\(277\) | −3.85685e8 | −1.09032 | −0.545159 | − | 0.838333i | \(-0.683531\pi\) | ||||
−0.545159 | + | 0.838333i | \(0.683531\pi\) | |||||||
\(278\) | −4.54287e8 | −1.26816 | ||||||||
\(279\) | 1.14846e8 | 0.316594 | ||||||||
\(280\) | −8.72678e7 | −0.237575 | ||||||||
\(281\) | −6.82120e7 | −0.183396 | −0.0916978 | − | 0.995787i | \(-0.529229\pi\) | ||||
−0.0916978 | + | 0.995787i | \(0.529229\pi\) | |||||||
\(282\) | −1.54303e8 | −0.409733 | ||||||||
\(283\) | −6.19700e7 | −0.162528 | −0.0812642 | − | 0.996693i | \(-0.525896\pi\) | ||||
−0.0812642 | + | 0.996693i | \(0.525896\pi\) | |||||||
\(284\) | −3.22416e8 | −0.835222 | ||||||||
\(285\) | 2.48815e8 | 0.636678 | ||||||||
\(286\) | −6.72236e7 | −0.169919 | ||||||||
\(287\) | −7.79076e7 | −0.194533 | ||||||||
\(288\) | 2.38879e7 | 0.0589256 | ||||||||
\(289\) | −4.05726e8 | −0.988759 | ||||||||
\(290\) | 2.33401e8 | 0.561965 | ||||||||
\(291\) | −5.41791e7 | −0.128886 | ||||||||
\(292\) | 9.37307e7 | 0.220314 | ||||||||
\(293\) | −4.88598e6 | −0.0113479 | −0.00567395 | − | 0.999984i | \(-0.501806\pi\) | ||||
−0.00567395 | + | 0.999984i | \(0.501806\pi\) | |||||||
\(294\) | −2.54122e7 | −0.0583212 | ||||||||
\(295\) | −2.65835e8 | −0.602886 | ||||||||
\(296\) | 1.95361e8 | 0.437841 | ||||||||
\(297\) | 7.52824e7 | 0.166742 | ||||||||
\(298\) | −5.75914e8 | −1.26067 | ||||||||
\(299\) | −1.48437e8 | −0.321139 | ||||||||
\(300\) | −2.91701e8 | −0.623755 | ||||||||
\(301\) | −1.82773e8 | −0.386303 | ||||||||
\(302\) | −2.57701e8 | −0.538383 | ||||||||
\(303\) | −5.16552e8 | −1.06676 | ||||||||
\(304\) | −7.59596e7 | −0.155069 | ||||||||
\(305\) | 4.70862e8 | 0.950265 | ||||||||
\(306\) | −1.25256e7 | −0.0249904 | ||||||||
\(307\) | −2.64128e8 | −0.520992 | −0.260496 | − | 0.965475i | \(-0.583886\pi\) | ||||
−0.260496 | + | 0.965475i | \(0.583886\pi\) | |||||||
\(308\) | 8.39607e7 | 0.163738 | ||||||||
\(309\) | −3.70334e7 | −0.0714067 | ||||||||
\(310\) | 6.26281e8 | 1.19400 | ||||||||
\(311\) | 5.56532e8 | 1.04913 | 0.524564 | − | 0.851371i | \(-0.324228\pi\) | ||||
0.524564 | + | 0.851371i | \(0.324228\pi\) | |||||||
\(312\) | −3.03713e7 | −0.0566139 | ||||||||
\(313\) | −4.42785e8 | −0.816183 | −0.408091 | − | 0.912941i | \(-0.633806\pi\) | ||||
−0.408091 | + | 0.912941i | \(0.633806\pi\) | |||||||
\(314\) | −7.01126e8 | −1.27803 | ||||||||
\(315\) | −1.24254e8 | −0.223988 | ||||||||
\(316\) | 5.51504e8 | 0.983204 | ||||||||
\(317\) | 2.33443e8 | 0.411599 | 0.205799 | − | 0.978594i | \(-0.434021\pi\) | ||||
0.205799 | + | 0.978594i | \(0.434021\pi\) | |||||||
\(318\) | 7.60933e7 | 0.132694 | ||||||||
\(319\) | −2.24556e8 | −0.387308 | ||||||||
\(320\) | 1.30266e8 | 0.222231 | ||||||||
\(321\) | −6.37130e8 | −1.07513 | ||||||||
\(322\) | 1.85394e8 | 0.309457 | ||||||||
\(323\) | 3.98294e7 | 0.0657649 | ||||||||
\(324\) | 3.40122e7 | 0.0555556 | ||||||||
\(325\) | 3.70872e8 | 0.599284 | ||||||||
\(326\) | 5.79856e8 | 0.926955 | ||||||||
\(327\) | −2.26672e8 | −0.358493 | ||||||||
\(328\) | 1.16294e8 | 0.181969 | ||||||||
\(329\) | −2.45027e8 | −0.379339 | ||||||||
\(330\) | 4.10531e8 | 0.628850 | ||||||||
\(331\) | 1.18852e9 | 1.80139 | 0.900693 | − | 0.434455i | \(-0.143059\pi\) | ||||
0.900693 | + | 0.434455i | \(0.143059\pi\) | |||||||
\(332\) | −5.63661e8 | −0.845346 | ||||||||
\(333\) | 2.78160e8 | 0.412800 | ||||||||
\(334\) | 6.26819e8 | 0.920512 | ||||||||
\(335\) | 1.09579e9 | 1.59247 | ||||||||
\(336\) | 3.79331e7 | 0.0545545 | ||||||||
\(337\) | 3.54795e8 | 0.504978 | 0.252489 | − | 0.967600i | \(-0.418751\pi\) | ||||
0.252489 | + | 0.967600i | \(0.418751\pi\) | |||||||
\(338\) | 3.86145e7 | 0.0543928 | ||||||||
\(339\) | 1.90885e8 | 0.266118 | ||||||||
\(340\) | −6.83047e7 | −0.0942485 | ||||||||
\(341\) | −6.02548e8 | −0.822908 | ||||||||
\(342\) | −1.08153e8 | −0.146201 | ||||||||
\(343\) | −4.03536e7 | −0.0539949 | ||||||||
\(344\) | 2.72827e8 | 0.361354 | ||||||||
\(345\) | 9.06496e8 | 1.18850 | ||||||||
\(346\) | 2.10948e8 | 0.273784 | ||||||||
\(347\) | −4.52712e8 | −0.581659 | −0.290830 | − | 0.956775i | \(-0.593931\pi\) | ||||
−0.290830 | + | 0.956775i | \(0.593931\pi\) | |||||||
\(348\) | −1.01453e8 | −0.129044 | ||||||||
\(349\) | 3.15340e8 | 0.397091 | 0.198545 | − | 0.980092i | \(-0.436378\pi\) | ||||
0.198545 | + | 0.980092i | \(0.436378\pi\) | |||||||
\(350\) | −4.63211e8 | −0.577485 | ||||||||
\(351\) | −4.32436e7 | −0.0533761 | ||||||||
\(352\) | −1.25329e8 | −0.153163 | ||||||||
\(353\) | 7.96217e8 | 0.963429 | 0.481715 | − | 0.876328i | \(-0.340014\pi\) | ||||
0.481715 | + | 0.876328i | \(0.340014\pi\) | |||||||
\(354\) | 1.15552e8 | 0.138441 | ||||||||
\(355\) | −2.50338e9 | −2.96980 | ||||||||
\(356\) | 1.99597e8 | 0.234465 | ||||||||
\(357\) | −1.98902e7 | −0.0231366 | ||||||||
\(358\) | 1.15152e9 | 1.32642 | ||||||||
\(359\) | −1.65187e9 | −1.88428 | −0.942142 | − | 0.335214i | \(-0.891191\pi\) | ||||
−0.942142 | + | 0.335214i | \(0.891191\pi\) | |||||||
\(360\) | 1.85476e8 | 0.209522 | ||||||||
\(361\) | −5.49961e8 | −0.615257 | ||||||||
\(362\) | 6.26531e8 | 0.694165 | ||||||||
\(363\) | 1.31180e8 | 0.143945 | ||||||||
\(364\) | −4.82285e7 | −0.0524142 | ||||||||
\(365\) | 7.27766e8 | 0.783370 | ||||||||
\(366\) | −2.04672e8 | −0.218210 | ||||||||
\(367\) | 3.40603e8 | 0.359681 | 0.179840 | − | 0.983696i | \(-0.442442\pi\) | ||||
0.179840 | + | 0.983696i | \(0.442442\pi\) | |||||||
\(368\) | −2.76740e8 | −0.289471 | ||||||||
\(369\) | 1.65582e8 | 0.171562 | ||||||||
\(370\) | 1.51687e9 | 1.55683 | ||||||||
\(371\) | 1.20833e8 | 0.122851 | ||||||||
\(372\) | −2.72228e8 | −0.274178 | ||||||||
\(373\) | −5.88708e8 | −0.587380 | −0.293690 | − | 0.955901i | \(-0.594883\pi\) | ||||
−0.293690 | + | 0.955901i | \(0.594883\pi\) | |||||||
\(374\) | 6.57162e7 | 0.0649564 | ||||||||
\(375\) | −1.21670e9 | −1.19144 | ||||||||
\(376\) | 3.65754e8 | 0.354840 | ||||||||
\(377\) | 1.28989e8 | 0.123982 | ||||||||
\(378\) | 5.40102e7 | 0.0514344 | ||||||||
\(379\) | 8.60219e6 | 0.00811655 | 0.00405828 | − | 0.999992i | \(-0.498708\pi\) | ||||
0.00405828 | + | 0.999992i | \(0.498708\pi\) | |||||||
\(380\) | −5.89784e8 | −0.551379 | ||||||||
\(381\) | 2.66091e7 | 0.0246486 | ||||||||
\(382\) | 5.07872e8 | 0.466157 | ||||||||
\(383\) | −1.84752e9 | −1.68032 | −0.840161 | − | 0.542338i | \(-0.817539\pi\) | ||||
−0.840161 | + | 0.542338i | \(0.817539\pi\) | |||||||
\(384\) | −5.66231e7 | −0.0510310 | ||||||||
\(385\) | 6.51908e8 | 0.582202 | ||||||||
\(386\) | 7.64710e8 | 0.676770 | ||||||||
\(387\) | 3.88458e8 | 0.340687 | ||||||||
\(388\) | 1.28425e8 | 0.111619 | ||||||||
\(389\) | 1.35859e8 | 0.117021 | 0.0585105 | − | 0.998287i | \(-0.481365\pi\) | ||||
0.0585105 | + | 0.998287i | \(0.481365\pi\) | |||||||
\(390\) | −2.35816e8 | −0.201302 | ||||||||
\(391\) | 1.45108e8 | 0.122765 | ||||||||
\(392\) | 6.02363e7 | 0.0505076 | ||||||||
\(393\) | 9.57315e8 | 0.795574 | ||||||||
\(394\) | 6.62620e8 | 0.545793 | ||||||||
\(395\) | 4.28212e9 | 3.49598 | ||||||||
\(396\) | −1.78447e8 | −0.144403 | ||||||||
\(397\) | 6.42588e8 | 0.515425 | 0.257713 | − | 0.966222i | \(-0.417031\pi\) | ||||
0.257713 | + | 0.966222i | \(0.417031\pi\) | |||||||
\(398\) | −6.51104e8 | −0.517678 | ||||||||
\(399\) | −1.71744e8 | −0.135355 | ||||||||
\(400\) | 6.91440e8 | 0.540187 | ||||||||
\(401\) | −2.24032e9 | −1.73502 | −0.867511 | − | 0.497418i | \(-0.834281\pi\) | ||||
−0.867511 | + | 0.497418i | \(0.834281\pi\) | |||||||
\(402\) | −4.76312e8 | −0.365679 | ||||||||
\(403\) | 3.46114e8 | 0.263422 | ||||||||
\(404\) | 1.22442e9 | 0.923837 | ||||||||
\(405\) | 2.64086e8 | 0.197539 | ||||||||
\(406\) | −1.61104e8 | −0.119472 | ||||||||
\(407\) | −1.45938e9 | −1.07297 | ||||||||
\(408\) | 2.96903e7 | 0.0216423 | ||||||||
\(409\) | 7.64379e8 | 0.552430 | 0.276215 | − | 0.961096i | \(-0.410920\pi\) | ||||
0.276215 | + | 0.961096i | \(0.410920\pi\) | |||||||
\(410\) | 9.02955e8 | 0.647027 | ||||||||
\(411\) | −7.19193e8 | −0.510975 | ||||||||
\(412\) | 8.77829e7 | 0.0618400 | ||||||||
\(413\) | 1.83492e8 | 0.128171 | ||||||||
\(414\) | −3.94030e8 | −0.272916 | ||||||||
\(415\) | −4.37651e9 | −3.00580 | ||||||||
\(416\) | 7.19913e7 | 0.0490290 | ||||||||
\(417\) | 1.53322e9 | 1.03545 | ||||||||
\(418\) | 5.67433e8 | 0.380012 | ||||||||
\(419\) | −5.63647e8 | −0.374333 | −0.187166 | − | 0.982328i | \(-0.559930\pi\) | ||||
−0.187166 | + | 0.982328i | \(0.559930\pi\) | |||||||
\(420\) | 2.94529e8 | 0.193979 | ||||||||
\(421\) | −1.67916e8 | −0.109674 | −0.0548371 | − | 0.998495i | \(-0.517464\pi\) | ||||
−0.0548371 | + | 0.998495i | \(0.517464\pi\) | |||||||
\(422\) | 1.51767e9 | 0.983068 | ||||||||
\(423\) | 5.20771e8 | 0.334546 | ||||||||
\(424\) | −1.80369e8 | −0.114917 | ||||||||
\(425\) | −3.62556e8 | −0.229094 | ||||||||
\(426\) | 1.08815e9 | 0.681956 | ||||||||
\(427\) | −3.25011e8 | −0.202023 | ||||||||
\(428\) | 1.51023e9 | 0.931088 | ||||||||
\(429\) | 2.26880e8 | 0.138738 | ||||||||
\(430\) | 2.11835e9 | 1.28486 | ||||||||
\(431\) | 4.07362e8 | 0.245081 | 0.122541 | − | 0.992463i | \(-0.460896\pi\) | ||||
0.122541 | + | 0.992463i | \(0.460896\pi\) | |||||||
\(432\) | −8.06216e7 | −0.0481125 | ||||||||
\(433\) | −1.43524e9 | −0.849604 | −0.424802 | − | 0.905286i | \(-0.639656\pi\) | ||||
−0.424802 | + | 0.905286i | \(0.639656\pi\) | |||||||
\(434\) | −4.32288e8 | −0.253840 | ||||||||
\(435\) | −7.87728e8 | −0.458843 | ||||||||
\(436\) | 5.37297e8 | 0.310464 | ||||||||
\(437\) | 1.25295e9 | 0.718207 | ||||||||
\(438\) | −3.16341e8 | −0.179885 | ||||||||
\(439\) | 8.80200e8 | 0.496541 | 0.248271 | − | 0.968691i | \(-0.420138\pi\) | ||||
0.248271 | + | 0.968691i | \(0.420138\pi\) | |||||||
\(440\) | −9.73110e8 | −0.544600 | ||||||||
\(441\) | 8.57661e7 | 0.0476190 | ||||||||
\(442\) | −3.77486e7 | −0.0207933 | ||||||||
\(443\) | 1.78113e9 | 0.973382 | 0.486691 | − | 0.873574i | \(-0.338204\pi\) | ||||
0.486691 | + | 0.873574i | \(0.338204\pi\) | |||||||
\(444\) | −6.59342e8 | −0.357495 | ||||||||
\(445\) | 1.54976e9 | 0.833687 | ||||||||
\(446\) | 3.46124e8 | 0.184739 | ||||||||
\(447\) | 1.94371e9 | 1.02933 | ||||||||
\(448\) | −8.99154e7 | −0.0472456 | ||||||||
\(449\) | −1.92118e7 | −0.0100162 | −0.00500812 | − | 0.999987i | \(-0.501594\pi\) | ||||
−0.00500812 | + | 0.999987i | \(0.501594\pi\) | |||||||
\(450\) | 9.84492e8 | 0.509294 | ||||||||
\(451\) | −8.68736e8 | −0.445934 | ||||||||
\(452\) | −4.52469e8 | −0.230465 | ||||||||
\(453\) | 8.69740e8 | 0.439588 | ||||||||
\(454\) | 1.41219e8 | 0.0708268 | ||||||||
\(455\) | −3.74468e8 | −0.186369 | ||||||||
\(456\) | 2.56364e8 | 0.126613 | ||||||||
\(457\) | −1.53351e9 | −0.751591 | −0.375795 | − | 0.926703i | \(-0.622630\pi\) | ||||
−0.375795 | + | 0.926703i | \(0.622630\pi\) | |||||||
\(458\) | 1.82504e9 | 0.887651 | ||||||||
\(459\) | 4.22738e7 | 0.0204046 | ||||||||
\(460\) | −2.14873e9 | −1.02927 | ||||||||
\(461\) | −1.15224e9 | −0.547757 | −0.273879 | − | 0.961764i | \(-0.588307\pi\) | ||||
−0.273879 | + | 0.961764i | \(0.588307\pi\) | |||||||
\(462\) | −2.83367e8 | −0.133691 | ||||||||
\(463\) | −9.11439e8 | −0.426770 | −0.213385 | − | 0.976968i | \(-0.568449\pi\) | ||||
−0.213385 | + | 0.976968i | \(0.568449\pi\) | |||||||
\(464\) | 2.40482e8 | 0.111756 | ||||||||
\(465\) | −2.11370e9 | −0.974895 | ||||||||
\(466\) | −7.37328e8 | −0.337528 | ||||||||
\(467\) | −2.27214e9 | −1.03235 | −0.516174 | − | 0.856484i | \(-0.672644\pi\) | ||||
−0.516174 | + | 0.856484i | \(0.672644\pi\) | |||||||
\(468\) | 1.02503e8 | 0.0462250 | ||||||||
\(469\) | −7.56366e8 | −0.338553 | ||||||||
\(470\) | 2.83988e9 | 1.26170 | ||||||||
\(471\) | 2.36630e9 | 1.04351 | ||||||||
\(472\) | −2.73900e8 | −0.119893 | ||||||||
\(473\) | −2.03807e9 | −0.885533 | ||||||||
\(474\) | −1.86133e9 | −0.802783 | ||||||||
\(475\) | −3.13053e9 | −1.34026 | ||||||||
\(476\) | 4.71470e7 | 0.0200369 | ||||||||
\(477\) | −2.56815e8 | −0.108344 | ||||||||
\(478\) | 1.33486e9 | 0.559032 | ||||||||
\(479\) | 6.50250e8 | 0.270337 | 0.135169 | − | 0.990823i | \(-0.456842\pi\) | ||||
0.135169 | + | 0.990823i | \(0.456842\pi\) | |||||||
\(480\) | −4.39647e8 | −0.181451 | ||||||||
\(481\) | 8.38296e8 | 0.343471 | ||||||||
\(482\) | 1.88623e9 | 0.767238 | ||||||||
\(483\) | −6.25705e8 | −0.252671 | ||||||||
\(484\) | −3.10946e8 | −0.124660 | ||||||||
\(485\) | 9.97145e8 | 0.396883 | ||||||||
\(486\) | −1.14791e8 | −0.0453609 | ||||||||
\(487\) | −1.88694e9 | −0.740299 | −0.370150 | − | 0.928972i | \(-0.620694\pi\) | ||||
−0.370150 | + | 0.928972i | \(0.620694\pi\) | |||||||
\(488\) | 4.85148e8 | 0.188975 | ||||||||
\(489\) | −1.95701e9 | −0.756856 | ||||||||
\(490\) | 4.67701e8 | 0.179590 | ||||||||
\(491\) | 1.64654e9 | 0.627750 | 0.313875 | − | 0.949464i | \(-0.398373\pi\) | ||||
0.313875 | + | 0.949464i | \(0.398373\pi\) | |||||||
\(492\) | −3.92491e8 | −0.148577 | ||||||||
\(493\) | −1.26096e8 | −0.0473957 | ||||||||
\(494\) | −3.25944e8 | −0.121646 | ||||||||
\(495\) | −1.38554e9 | −0.513454 | ||||||||
\(496\) | 6.45282e8 | 0.237445 | ||||||||
\(497\) | 1.72795e9 | 0.631369 | ||||||||
\(498\) | 1.90235e9 | 0.690222 | ||||||||
\(499\) | −4.13719e9 | −1.49057 | −0.745287 | − | 0.666744i | \(-0.767687\pi\) | ||||
−0.745287 | + | 0.666744i | \(0.767687\pi\) | |||||||
\(500\) | 2.88402e9 | 1.03182 | ||||||||
\(501\) | −2.11551e9 | −0.751595 | ||||||||
\(502\) | −1.50230e9 | −0.530022 | ||||||||
\(503\) | −2.42528e9 | −0.849717 | −0.424858 | − | 0.905260i | \(-0.639676\pi\) | ||||
−0.424858 | + | 0.905260i | \(0.639676\pi\) | |||||||
\(504\) | −1.28024e8 | −0.0445435 | ||||||||
\(505\) | 9.50693e9 | 3.28489 | ||||||||
\(506\) | 2.06730e9 | 0.709377 | ||||||||
\(507\) | −1.30324e8 | −0.0444116 | ||||||||
\(508\) | −6.30734e7 | −0.0213463 | ||||||||
\(509\) | −1.44039e9 | −0.484135 | −0.242068 | − | 0.970259i | \(-0.577826\pi\) | ||||
−0.242068 | + | 0.970259i | \(0.577826\pi\) | |||||||
\(510\) | 2.30528e8 | 0.0769535 | ||||||||
\(511\) | −5.02338e8 | −0.166542 | ||||||||
\(512\) | 1.34218e8 | 0.0441942 | ||||||||
\(513\) | 3.65018e8 | 0.119372 | ||||||||
\(514\) | 1.67520e9 | 0.544120 | ||||||||
\(515\) | 6.81585e8 | 0.219884 | ||||||||
\(516\) | −9.20790e8 | −0.295044 | ||||||||
\(517\) | −2.73226e9 | −0.869570 | ||||||||
\(518\) | −1.04701e9 | −0.330976 | ||||||||
\(519\) | −7.11948e8 | −0.223544 | ||||||||
\(520\) | 5.58972e8 | 0.174333 | ||||||||
\(521\) | 1.57419e9 | 0.487668 | 0.243834 | − | 0.969817i | \(-0.421595\pi\) | ||||
0.243834 | + | 0.969817i | \(0.421595\pi\) | |||||||
\(522\) | 3.42405e8 | 0.105364 | ||||||||
\(523\) | 3.48172e9 | 1.06424 | 0.532118 | − | 0.846670i | \(-0.321396\pi\) | ||||
0.532118 | + | 0.846670i | \(0.321396\pi\) | |||||||
\(524\) | −2.26919e9 | −0.688988 | ||||||||
\(525\) | 1.56334e9 | 0.471514 | ||||||||
\(526\) | −2.64688e9 | −0.793020 | ||||||||
\(527\) | −3.38353e8 | −0.100701 | ||||||||
\(528\) | 4.22986e8 | 0.125057 | ||||||||
\(529\) | 1.16000e9 | 0.340693 | ||||||||
\(530\) | −1.40047e9 | −0.408609 | ||||||||
\(531\) | −3.89986e8 | −0.113036 | ||||||||
\(532\) | 4.07096e8 | 0.117221 | ||||||||
\(533\) | 4.99018e8 | 0.142748 | ||||||||
\(534\) | −6.73638e8 | −0.191440 | ||||||||
\(535\) | 1.17261e10 | 3.31067 | ||||||||
\(536\) | 1.12904e9 | 0.316688 | ||||||||
\(537\) | −3.88638e9 | −1.08302 | ||||||||
\(538\) | 3.02408e9 | 0.837250 | ||||||||
\(539\) | −4.49977e8 | −0.123774 | ||||||||
\(540\) | −6.25981e8 | −0.171074 | ||||||||
\(541\) | −5.58813e9 | −1.51731 | −0.758657 | − | 0.651490i | \(-0.774144\pi\) | ||||
−0.758657 | + | 0.651490i | \(0.774144\pi\) | |||||||
\(542\) | 4.87718e7 | 0.0131574 | ||||||||
\(543\) | −2.11454e9 | −0.566783 | ||||||||
\(544\) | −7.03769e7 | −0.0187428 | ||||||||
\(545\) | 4.17181e9 | 1.10392 | ||||||||
\(546\) | 1.62771e8 | 0.0427960 | ||||||||
\(547\) | −8.36867e8 | −0.218625 | −0.109313 | − | 0.994007i | \(-0.534865\pi\) | ||||
−0.109313 | + | 0.994007i | \(0.534865\pi\) | |||||||
\(548\) | 1.70475e9 | 0.442517 | ||||||||
\(549\) | 6.90767e8 | 0.178167 | ||||||||
\(550\) | −5.16519e9 | −1.32378 | ||||||||
\(551\) | −1.08879e9 | −0.277277 | ||||||||
\(552\) | 9.33998e8 | 0.236352 | ||||||||
\(553\) | −2.95572e9 | −0.743233 | ||||||||
\(554\) | −3.08548e9 | −0.770971 | ||||||||
\(555\) | −5.11942e9 | −1.27115 | ||||||||
\(556\) | −3.63429e9 | −0.896723 | ||||||||
\(557\) | −2.13091e9 | −0.522483 | −0.261242 | − | 0.965273i | \(-0.584132\pi\) | ||||
−0.261242 | + | 0.965273i | \(0.584132\pi\) | |||||||
\(558\) | 9.18770e8 | 0.223865 | ||||||||
\(559\) | 1.17070e9 | 0.283469 | ||||||||
\(560\) | −6.98143e8 | −0.167991 | ||||||||
\(561\) | −2.21792e8 | −0.0530367 | ||||||||
\(562\) | −5.45696e8 | −0.129680 | ||||||||
\(563\) | −4.67407e9 | −1.10386 | −0.551932 | − | 0.833889i | \(-0.686109\pi\) | ||||
−0.551932 | + | 0.833889i | \(0.686109\pi\) | |||||||
\(564\) | −1.23442e9 | −0.289725 | ||||||||
\(565\) | −3.51317e9 | −0.819464 | ||||||||
\(566\) | −4.95760e8 | −0.114925 | ||||||||
\(567\) | −1.82284e8 | −0.0419961 | ||||||||
\(568\) | −2.57933e9 | −0.590591 | ||||||||
\(569\) | −3.10951e9 | −0.707618 | −0.353809 | − | 0.935318i | \(-0.615114\pi\) | ||||
−0.353809 | + | 0.935318i | \(0.615114\pi\) | |||||||
\(570\) | 1.99052e9 | 0.450199 | ||||||||
\(571\) | 1.90010e9 | 0.427121 | 0.213560 | − | 0.976930i | \(-0.431494\pi\) | ||||
0.213560 | + | 0.976930i | \(0.431494\pi\) | |||||||
\(572\) | −5.37789e8 | −0.120151 | ||||||||
\(573\) | −1.71407e9 | −0.380616 | ||||||||
\(574\) | −6.23261e8 | −0.137556 | ||||||||
\(575\) | −1.14053e10 | −2.50190 | ||||||||
\(576\) | 1.91103e8 | 0.0416667 | ||||||||
\(577\) | 2.04455e8 | 0.0443081 | 0.0221541 | − | 0.999755i | \(-0.492948\pi\) | ||||
0.0221541 | + | 0.999755i | \(0.492948\pi\) | |||||||
\(578\) | −3.24581e9 | −0.699158 | ||||||||
\(579\) | −2.58090e9 | −0.552581 | ||||||||
\(580\) | 1.86721e9 | 0.397369 | ||||||||
\(581\) | 3.02087e9 | 0.639021 | ||||||||
\(582\) | −4.33433e8 | −0.0911363 | ||||||||
\(583\) | 1.34740e9 | 0.281615 | ||||||||
\(584\) | 7.49845e8 | 0.155785 | ||||||||
\(585\) | 7.95880e8 | 0.164362 | ||||||||
\(586\) | −3.90879e7 | −0.00802417 | ||||||||
\(587\) | −2.35979e9 | −0.481548 | −0.240774 | − | 0.970581i | \(-0.577401\pi\) | ||||
−0.240774 | + | 0.970581i | \(0.577401\pi\) | |||||||
\(588\) | −2.03297e8 | −0.0412393 | ||||||||
\(589\) | −2.92154e9 | −0.589127 | ||||||||
\(590\) | −2.12668e9 | −0.426304 | ||||||||
\(591\) | −2.23634e9 | −0.445638 | ||||||||
\(592\) | 1.56289e9 | 0.309600 | ||||||||
\(593\) | 1.48166e9 | 0.291780 | 0.145890 | − | 0.989301i | \(-0.453395\pi\) | ||||
0.145890 | + | 0.989301i | \(0.453395\pi\) | |||||||
\(594\) | 6.02259e8 | 0.117905 | ||||||||
\(595\) | 3.66070e8 | 0.0712451 | ||||||||
\(596\) | −4.60731e9 | −0.891427 | ||||||||
\(597\) | 2.19747e9 | 0.422682 | ||||||||
\(598\) | −1.18750e9 | −0.227080 | ||||||||
\(599\) | −3.55355e9 | −0.675568 | −0.337784 | − | 0.941224i | \(-0.609677\pi\) | ||||
−0.337784 | + | 0.941224i | \(0.609677\pi\) | |||||||
\(600\) | −2.33361e9 | −0.441061 | ||||||||
\(601\) | 5.40134e9 | 1.01494 | 0.507470 | − | 0.861669i | \(-0.330581\pi\) | ||||
0.507470 | + | 0.861669i | \(0.330581\pi\) | |||||||
\(602\) | −1.46218e9 | −0.273158 | ||||||||
\(603\) | 1.60755e9 | 0.298576 | ||||||||
\(604\) | −2.06160e9 | −0.380694 | ||||||||
\(605\) | −2.41432e9 | −0.443252 | ||||||||
\(606\) | −4.13242e9 | −0.754310 | ||||||||
\(607\) | 4.42281e9 | 0.802672 | 0.401336 | − | 0.915931i | \(-0.368546\pi\) | ||||
0.401336 | + | 0.915931i | \(0.368546\pi\) | |||||||
\(608\) | −6.07677e8 | −0.109650 | ||||||||
\(609\) | 5.43726e8 | 0.0975483 | ||||||||
\(610\) | 3.76690e9 | 0.671939 | ||||||||
\(611\) | 1.56946e9 | 0.278359 | ||||||||
\(612\) | −1.00205e8 | −0.0176709 | ||||||||
\(613\) | 4.76865e9 | 0.836149 | 0.418075 | − | 0.908413i | \(-0.362705\pi\) | ||||
0.418075 | + | 0.908413i | \(0.362705\pi\) | |||||||
\(614\) | −2.11303e9 | −0.368397 | ||||||||
\(615\) | −3.04747e9 | −0.528295 | ||||||||
\(616\) | 6.71686e8 | 0.115780 | ||||||||
\(617\) | 1.10275e10 | 1.89008 | 0.945040 | − | 0.326955i | \(-0.106023\pi\) | ||||
0.945040 | + | 0.326955i | \(0.106023\pi\) | |||||||
\(618\) | −2.96267e8 | −0.0504922 | ||||||||
\(619\) | −1.49822e9 | −0.253897 | −0.126949 | − | 0.991909i | \(-0.540518\pi\) | ||||
−0.126949 | + | 0.991909i | \(0.540518\pi\) | |||||||
\(620\) | 5.01025e9 | 0.844284 | ||||||||
\(621\) | 1.32985e9 | 0.222835 | ||||||||
\(622\) | 4.45225e9 | 0.741846 | ||||||||
\(623\) | −1.06971e9 | −0.177239 | ||||||||
\(624\) | −2.42971e8 | −0.0400320 | ||||||||
\(625\) | 9.20465e9 | 1.50809 | ||||||||
\(626\) | −3.54228e9 | −0.577129 | ||||||||
\(627\) | −1.91509e9 | −0.310279 | ||||||||
\(628\) | −5.60901e9 | −0.903706 | ||||||||
\(629\) | −8.19497e8 | −0.131302 | ||||||||
\(630\) | −9.94035e8 | −0.158383 | ||||||||
\(631\) | 6.65589e9 | 1.05464 | 0.527319 | − | 0.849668i | \(-0.323197\pi\) | ||||
0.527319 | + | 0.849668i | \(0.323197\pi\) | |||||||
\(632\) | 4.41203e9 | 0.695230 | ||||||||
\(633\) | −5.12213e9 | −0.802672 | ||||||||
\(634\) | 1.86755e9 | 0.291044 | ||||||||
\(635\) | −4.89729e8 | −0.0759011 | ||||||||
\(636\) | 6.08747e8 | 0.0938289 | ||||||||
\(637\) | 2.58475e8 | 0.0396214 | ||||||||
\(638\) | −1.79645e9 | −0.273868 | ||||||||
\(639\) | −3.67252e9 | −0.556815 | ||||||||
\(640\) | 1.04213e9 | 0.157141 | ||||||||
\(641\) | 6.55404e9 | 0.982892 | 0.491446 | − | 0.870908i | \(-0.336469\pi\) | ||||
0.491446 | + | 0.870908i | \(0.336469\pi\) | |||||||
\(642\) | −5.09704e9 | −0.760230 | ||||||||
\(643\) | −3.63452e9 | −0.539149 | −0.269574 | − | 0.962980i | \(-0.586883\pi\) | ||||
−0.269574 | + | 0.962980i | \(0.586883\pi\) | |||||||
\(644\) | 1.48315e9 | 0.218819 | ||||||||
\(645\) | −7.14942e9 | −1.04909 | ||||||||
\(646\) | 3.18635e8 | 0.0465028 | ||||||||
\(647\) | 8.91495e9 | 1.29406 | 0.647029 | − | 0.762465i | \(-0.276011\pi\) | ||||
0.647029 | + | 0.762465i | \(0.276011\pi\) | |||||||
\(648\) | 2.72098e8 | 0.0392837 | ||||||||
\(649\) | 2.04609e9 | 0.293811 | ||||||||
\(650\) | 2.96698e9 | 0.423758 | ||||||||
\(651\) | 1.45897e9 | 0.207259 | ||||||||
\(652\) | 4.63885e9 | 0.655456 | ||||||||
\(653\) | 3.92610e9 | 0.551779 | 0.275889 | − | 0.961189i | \(-0.411028\pi\) | ||||
0.275889 | + | 0.961189i | \(0.411028\pi\) | |||||||
\(654\) | −1.81338e9 | −0.253493 | ||||||||
\(655\) | −1.76190e10 | −2.44983 | ||||||||
\(656\) | 9.30349e8 | 0.128672 | ||||||||
\(657\) | 1.06765e9 | 0.146876 | ||||||||
\(658\) | −1.96021e9 | −0.268233 | ||||||||
\(659\) | 3.58393e8 | 0.0487822 | 0.0243911 | − | 0.999702i | \(-0.492235\pi\) | ||||
0.0243911 | + | 0.999702i | \(0.492235\pi\) | |||||||
\(660\) | 3.28425e9 | 0.444664 | ||||||||
\(661\) | −1.07820e10 | −1.45210 | −0.726049 | − | 0.687643i | \(-0.758646\pi\) | ||||
−0.726049 | + | 0.687643i | \(0.758646\pi\) | |||||||
\(662\) | 9.50813e9 | 1.27377 | ||||||||
\(663\) | 1.27401e8 | 0.0169776 | ||||||||
\(664\) | −4.50929e9 | −0.597750 | ||||||||
\(665\) | 3.16087e9 | 0.416803 | ||||||||
\(666\) | 2.22528e9 | 0.291894 | ||||||||
\(667\) | −3.96675e9 | −0.517600 | ||||||||
\(668\) | 5.01455e9 | 0.650900 | ||||||||
\(669\) | −1.16817e9 | −0.150839 | ||||||||
\(670\) | 8.76633e9 | 1.12605 | ||||||||
\(671\) | −3.62415e9 | −0.463103 | ||||||||
\(672\) | 3.03464e8 | 0.0385758 | ||||||||
\(673\) | −4.39366e9 | −0.555615 | −0.277808 | − | 0.960637i | \(-0.589608\pi\) | ||||
−0.277808 | + | 0.960637i | \(0.589608\pi\) | |||||||
\(674\) | 2.83836e9 | 0.357073 | ||||||||
\(675\) | −3.32266e9 | −0.415836 | ||||||||
\(676\) | 3.08916e8 | 0.0384615 | ||||||||
\(677\) | 8.11370e9 | 1.00498 | 0.502491 | − | 0.864582i | \(-0.332417\pi\) | ||||
0.502491 | + | 0.864582i | \(0.332417\pi\) | |||||||
\(678\) | 1.52708e9 | 0.188174 | ||||||||
\(679\) | −6.88276e8 | −0.0843758 | ||||||||
\(680\) | −5.46437e8 | −0.0666437 | ||||||||
\(681\) | −4.76614e8 | −0.0578298 | ||||||||
\(682\) | −4.82038e9 | −0.581884 | ||||||||
\(683\) | −1.09490e10 | −1.31493 | −0.657466 | − | 0.753484i | \(-0.728372\pi\) | ||||
−0.657466 | + | 0.753484i | \(0.728372\pi\) | |||||||
\(684\) | −8.65228e8 | −0.103379 | ||||||||
\(685\) | 1.32365e10 | 1.57346 | ||||||||
\(686\) | −3.22829e8 | −0.0381802 | ||||||||
\(687\) | −6.15950e9 | −0.724764 | ||||||||
\(688\) | 2.18261e9 | 0.255516 | ||||||||
\(689\) | −7.73968e8 | −0.0901479 | ||||||||
\(690\) | 7.25197e9 | 0.840396 | ||||||||
\(691\) | −1.34406e9 | −0.154969 | −0.0774844 | − | 0.996994i | \(-0.524689\pi\) | ||||
−0.0774844 | + | 0.996994i | \(0.524689\pi\) | |||||||
\(692\) | 1.68758e9 | 0.193595 | ||||||||
\(693\) | 9.56365e8 | 0.109158 | ||||||||
\(694\) | −3.62169e9 | −0.411295 | ||||||||
\(695\) | −2.82183e10 | −3.18848 | ||||||||
\(696\) | −8.11626e8 | −0.0912481 | ||||||||
\(697\) | −4.87828e8 | −0.0545697 | ||||||||
\(698\) | 2.52272e9 | 0.280786 | ||||||||
\(699\) | 2.48848e9 | 0.275591 | ||||||||
\(700\) | −3.70569e9 | −0.408343 | ||||||||
\(701\) | −1.54593e10 | −1.69503 | −0.847516 | − | 0.530769i | \(-0.821903\pi\) | ||||
−0.847516 | + | 0.530769i | \(0.821903\pi\) | |||||||
\(702\) | −3.45948e8 | −0.0377426 | ||||||||
\(703\) | −7.07604e9 | −0.768151 | ||||||||
\(704\) | −1.00263e9 | −0.108302 | ||||||||
\(705\) | −9.58459e9 | −1.03018 | ||||||||
\(706\) | 6.36973e9 | 0.681247 | ||||||||
\(707\) | −6.56212e9 | −0.698355 | ||||||||
\(708\) | 9.24412e8 | 0.0978924 | ||||||||
\(709\) | −1.07079e10 | −1.12835 | −0.564176 | − | 0.825655i | \(-0.690806\pi\) | ||||
−0.564176 | + | 0.825655i | \(0.690806\pi\) | |||||||
\(710\) | −2.00270e10 | −2.09997 | ||||||||
\(711\) | 6.28197e9 | 0.655470 | ||||||||
\(712\) | 1.59677e9 | 0.165792 | ||||||||
\(713\) | −1.06439e10 | −1.09973 | ||||||||
\(714\) | −1.59121e8 | −0.0163600 | ||||||||
\(715\) | −4.17563e9 | −0.427219 | ||||||||
\(716\) | 9.21216e9 | 0.937920 | ||||||||
\(717\) | −4.50514e9 | −0.456448 | ||||||||
\(718\) | −1.32150e10 | −1.33239 | ||||||||
\(719\) | −1.74028e10 | −1.74610 | −0.873050 | − | 0.487631i | \(-0.837861\pi\) | ||||
−0.873050 | + | 0.487631i | \(0.837861\pi\) | |||||||
\(720\) | 1.48381e9 | 0.148154 | ||||||||
\(721\) | −4.70461e8 | −0.0467466 | ||||||||
\(722\) | −4.39969e9 | −0.435053 | ||||||||
\(723\) | −6.36603e9 | −0.626447 | ||||||||
\(724\) | 5.01225e9 | 0.490849 | ||||||||
\(725\) | 9.91098e9 | 0.965904 | ||||||||
\(726\) | 1.04944e9 | 0.101784 | ||||||||
\(727\) | 1.21160e10 | 1.16947 | 0.584733 | − | 0.811226i | \(-0.301199\pi\) | ||||
0.584733 | + | 0.811226i | \(0.301199\pi\) | |||||||
\(728\) | −3.85828e8 | −0.0370625 | ||||||||
\(729\) | 3.87420e8 | 0.0370370 | ||||||||
\(730\) | 5.82213e9 | 0.553926 | ||||||||
\(731\) | −1.14445e9 | −0.108364 | ||||||||
\(732\) | −1.63737e9 | −0.154298 | ||||||||
\(733\) | 1.12175e10 | 1.05204 | 0.526021 | − | 0.850471i | \(-0.323683\pi\) | ||||
0.526021 | + | 0.850471i | \(0.323683\pi\) | |||||||
\(734\) | 2.72483e9 | 0.254333 | ||||||||
\(735\) | −1.57849e9 | −0.146635 | ||||||||
\(736\) | −2.21392e9 | −0.204687 | ||||||||
\(737\) | −8.43412e9 | −0.776075 | ||||||||
\(738\) | 1.32466e9 | 0.121313 | ||||||||
\(739\) | −9.44143e9 | −0.860562 | −0.430281 | − | 0.902695i | \(-0.641586\pi\) | ||||
−0.430281 | + | 0.902695i | \(0.641586\pi\) | |||||||
\(740\) | 1.21349e10 | 1.10085 | ||||||||
\(741\) | 1.10006e9 | 0.0993237 | ||||||||
\(742\) | 9.66667e8 | 0.0868687 | ||||||||
\(743\) | 1.86509e10 | 1.66817 | 0.834083 | − | 0.551639i | \(-0.185997\pi\) | ||||
0.834083 | + | 0.551639i | \(0.185997\pi\) | |||||||
\(744\) | −2.17783e9 | −0.193873 | ||||||||
\(745\) | −3.57732e10 | −3.16965 | ||||||||
\(746\) | −4.70967e9 | −0.415340 | ||||||||
\(747\) | −6.42045e9 | −0.563564 | ||||||||
\(748\) | 5.25730e8 | 0.0459311 | ||||||||
\(749\) | −8.09390e9 | −0.703836 | ||||||||
\(750\) | −9.73358e9 | −0.842477 | ||||||||
\(751\) | 6.87622e8 | 0.0592394 | 0.0296197 | − | 0.999561i | \(-0.490570\pi\) | ||||
0.0296197 | + | 0.999561i | \(0.490570\pi\) | |||||||
\(752\) | 2.92603e9 | 0.250909 | ||||||||
\(753\) | 5.07026e9 | 0.432761 | ||||||||
\(754\) | 1.03191e9 | 0.0876683 | ||||||||
\(755\) | −1.60072e10 | −1.35363 | ||||||||
\(756\) | 4.32081e8 | 0.0363696 | ||||||||
\(757\) | 6.41867e9 | 0.537786 | 0.268893 | − | 0.963170i | \(-0.413342\pi\) | ||||
0.268893 | + | 0.963170i | \(0.413342\pi\) | |||||||
\(758\) | 6.88175e7 | 0.00573927 | ||||||||
\(759\) | −6.97715e9 | −0.579204 | ||||||||
\(760\) | −4.71827e9 | −0.389884 | ||||||||
\(761\) | −5.67316e9 | −0.466636 | −0.233318 | − | 0.972400i | \(-0.574958\pi\) | ||||
−0.233318 | + | 0.972400i | \(0.574958\pi\) | |||||||
\(762\) | 2.12873e8 | 0.0174292 | ||||||||
\(763\) | −2.87957e9 | −0.234689 | ||||||||
\(764\) | 4.06298e9 | 0.329623 | ||||||||
\(765\) | −7.78033e8 | −0.0628323 | ||||||||
\(766\) | −1.47801e10 | −1.18817 | ||||||||
\(767\) | −1.17531e9 | −0.0940520 | ||||||||
\(768\) | −4.52985e8 | −0.0360844 | ||||||||
\(769\) | 2.70852e9 | 0.214778 | 0.107389 | − | 0.994217i | \(-0.465751\pi\) | ||||
0.107389 | + | 0.994217i | \(0.465751\pi\) | |||||||
\(770\) | 5.21526e9 | 0.411679 | ||||||||
\(771\) | −5.65379e9 | −0.444272 | ||||||||
\(772\) | 6.11768e9 | 0.478549 | ||||||||
\(773\) | 9.88293e8 | 0.0769587 | 0.0384793 | − | 0.999259i | \(-0.487749\pi\) | ||||
0.0384793 | + | 0.999259i | \(0.487749\pi\) | |||||||
\(774\) | 3.10767e9 | 0.240902 | ||||||||
\(775\) | 2.65940e10 | 2.05224 | ||||||||
\(776\) | 1.02740e9 | 0.0789264 | ||||||||
\(777\) | 3.53366e9 | 0.270241 | ||||||||
\(778\) | 1.08687e9 | 0.0827464 | ||||||||
\(779\) | −4.21220e9 | −0.319248 | ||||||||
\(780\) | −1.88653e9 | −0.142342 | ||||||||
\(781\) | 1.92681e10 | 1.44730 | ||||||||
\(782\) | 1.16087e9 | 0.0868078 | ||||||||
\(783\) | −1.15562e9 | −0.0860295 | ||||||||
\(784\) | 4.81890e8 | 0.0357143 | ||||||||
\(785\) | −4.35508e10 | −3.21331 | ||||||||
\(786\) | 7.65852e9 | 0.562556 | ||||||||
\(787\) | 1.24048e10 | 0.907146 | 0.453573 | − | 0.891219i | \(-0.350149\pi\) | ||||
0.453573 | + | 0.891219i | \(0.350149\pi\) | |||||||
\(788\) | 5.30096e9 | 0.385934 | ||||||||
\(789\) | 8.93321e9 | 0.647498 | ||||||||
\(790\) | 3.42569e10 | 2.47203 | ||||||||
\(791\) | 2.42495e9 | 0.174215 | ||||||||
\(792\) | −1.42758e9 | −0.102108 | ||||||||
\(793\) | 2.08178e9 | 0.148244 | ||||||||
\(794\) | 5.14070e9 | 0.364461 | ||||||||
\(795\) | 4.72658e9 | 0.333627 | ||||||||
\(796\) | −5.20883e9 | −0.366053 | ||||||||
\(797\) | −9.25871e9 | −0.647808 | −0.323904 | − | 0.946090i | \(-0.604995\pi\) | ||||
−0.323904 | + | 0.946090i | \(0.604995\pi\) | |||||||
\(798\) | −1.37395e9 | −0.0957107 | ||||||||
\(799\) | −1.53426e9 | −0.106411 | ||||||||
\(800\) | 5.53152e9 | 0.381970 | ||||||||
\(801\) | 2.27353e9 | 0.156310 | ||||||||
\(802\) | −1.79226e10 | −1.22685 | ||||||||
\(803\) | −5.60149e9 | −0.381768 | ||||||||
\(804\) | −3.81050e9 | −0.258574 | ||||||||
\(805\) | 1.15159e10 | 0.778056 | ||||||||
\(806\) | 2.76891e9 | 0.186267 | ||||||||
\(807\) | −1.02063e10 | −0.683611 | ||||||||
\(808\) | 9.79536e9 | 0.653252 | ||||||||
\(809\) | −2.49825e10 | −1.65888 | −0.829441 | − | 0.558595i | \(-0.811341\pi\) | ||||
−0.829441 | + | 0.558595i | \(0.811341\pi\) | |||||||
\(810\) | 2.11269e9 | 0.139681 | ||||||||
\(811\) | 2.50005e10 | 1.64579 | 0.822896 | − | 0.568192i | \(-0.192357\pi\) | ||||
0.822896 | + | 0.568192i | \(0.192357\pi\) | |||||||
\(812\) | −1.28883e9 | −0.0844793 | ||||||||
\(813\) | −1.64605e8 | −0.0107430 | ||||||||
\(814\) | −1.16751e10 | −0.758706 | ||||||||
\(815\) | 3.60181e10 | 2.33061 | ||||||||
\(816\) | 2.37522e8 | 0.0153034 | ||||||||
\(817\) | −9.88188e9 | −0.633961 | ||||||||
\(818\) | 6.11503e9 | 0.390627 | ||||||||
\(819\) | −5.49353e8 | −0.0349428 | ||||||||
\(820\) | 7.22364e9 | 0.457517 | ||||||||
\(821\) | −1.73071e10 | −1.09150 | −0.545749 | − | 0.837949i | \(-0.683755\pi\) | ||||
−0.545749 | + | 0.837949i | \(0.683755\pi\) | |||||||
\(822\) | −5.75355e9 | −0.361314 | ||||||||
\(823\) | 2.31932e10 | 1.45031 | 0.725155 | − | 0.688586i | \(-0.241768\pi\) | ||||
0.725155 | + | 0.688586i | \(0.241768\pi\) | |||||||
\(824\) | 7.02263e8 | 0.0437275 | ||||||||
\(825\) | 1.74325e10 | 1.08087 | ||||||||
\(826\) | 1.46793e9 | 0.0906308 | ||||||||
\(827\) | −2.05547e10 | −1.26369 | −0.631846 | − | 0.775094i | \(-0.717702\pi\) | ||||
−0.631846 | + | 0.775094i | \(0.717702\pi\) | |||||||
\(828\) | −3.15224e9 | −0.192980 | ||||||||
\(829\) | 2.49310e10 | 1.51984 | 0.759921 | − | 0.650015i | \(-0.225237\pi\) | ||||
0.759921 | + | 0.650015i | \(0.225237\pi\) | |||||||
\(830\) | −3.50121e10 | −2.12542 | ||||||||
\(831\) | 1.04135e10 | 0.629495 | ||||||||
\(832\) | 5.75930e8 | 0.0346688 | ||||||||
\(833\) | −2.52679e8 | −0.0151465 | ||||||||
\(834\) | 1.22657e10 | 0.732171 | ||||||||
\(835\) | 3.89352e10 | 2.31441 | ||||||||
\(836\) | 4.53947e9 | 0.268709 | ||||||||
\(837\) | −3.10085e9 | −0.182785 | ||||||||
\(838\) | −4.50918e9 | −0.264693 | ||||||||
\(839\) | 1.12662e10 | 0.658582 | 0.329291 | − | 0.944228i | \(-0.393190\pi\) | ||||
0.329291 | + | 0.944228i | \(0.393190\pi\) | |||||||
\(840\) | 2.35623e9 | 0.137164 | ||||||||
\(841\) | −1.38028e10 | −0.800171 | ||||||||
\(842\) | −1.34333e9 | −0.0775514 | ||||||||
\(843\) | 1.84173e9 | 0.105884 | ||||||||
\(844\) | 1.21414e10 | 0.695134 | ||||||||
\(845\) | 2.39856e9 | 0.136758 | ||||||||
\(846\) | 4.16617e9 | 0.236560 | ||||||||
\(847\) | 1.66647e9 | 0.0942338 | ||||||||
\(848\) | −1.44296e9 | −0.0812582 | ||||||||
\(849\) | 1.67319e9 | 0.0938358 | ||||||||
\(850\) | −2.90045e9 | −0.161994 | ||||||||
\(851\) | −2.57798e10 | −1.43392 | ||||||||
\(852\) | 8.70523e9 | 0.482216 | ||||||||
\(853\) | −1.90222e10 | −1.04940 | −0.524699 | − | 0.851288i | \(-0.675822\pi\) | ||||
−0.524699 | + | 0.851288i | \(0.675822\pi\) | |||||||
\(854\) | −2.60009e9 | −0.142852 | ||||||||
\(855\) | −6.71801e9 | −0.367586 | ||||||||
\(856\) | 1.20819e10 | 0.658379 | ||||||||
\(857\) | 2.03465e10 | 1.10422 | 0.552110 | − | 0.833771i | \(-0.313823\pi\) | ||||
0.552110 | + | 0.833771i | \(0.313823\pi\) | |||||||
\(858\) | 1.81504e9 | 0.0981026 | ||||||||
\(859\) | 2.83480e10 | 1.52597 | 0.762987 | − | 0.646414i | \(-0.223732\pi\) | ||||
0.762987 | + | 0.646414i | \(0.223732\pi\) | |||||||
\(860\) | 1.69468e10 | 0.908537 | ||||||||
\(861\) | 2.10351e9 | 0.112314 | ||||||||
\(862\) | 3.25890e9 | 0.173299 | ||||||||
\(863\) | −2.07145e10 | −1.09708 | −0.548539 | − | 0.836125i | \(-0.684816\pi\) | ||||
−0.548539 | + | 0.836125i | \(0.684816\pi\) | |||||||
\(864\) | −6.44973e8 | −0.0340207 | ||||||||
\(865\) | 1.31031e10 | 0.688364 | ||||||||
\(866\) | −1.14819e10 | −0.600761 | ||||||||
\(867\) | 1.09546e10 | 0.570860 | ||||||||
\(868\) | −3.45831e9 | −0.179492 | ||||||||
\(869\) | −3.29587e10 | −1.70373 | ||||||||
\(870\) | −6.30182e9 | −0.324451 | ||||||||
\(871\) | 4.84471e9 | 0.248430 | ||||||||
\(872\) | 4.29837e9 | 0.219531 | ||||||||
\(873\) | 1.46284e9 | 0.0744125 | ||||||||
\(874\) | 1.00236e10 | 0.507849 | ||||||||
\(875\) | −1.54566e10 | −0.779982 | ||||||||
\(876\) | −2.53073e9 | −0.127198 | ||||||||
\(877\) | −1.44434e10 | −0.723052 | −0.361526 | − | 0.932362i | \(-0.617744\pi\) | ||||
−0.361526 | + | 0.932362i | \(0.617744\pi\) | |||||||
\(878\) | 7.04160e9 | 0.351108 | ||||||||
\(879\) | 1.31922e8 | 0.00655171 | ||||||||
\(880\) | −7.78488e9 | −0.385090 | ||||||||
\(881\) | 6.80586e9 | 0.335326 | 0.167663 | − | 0.985844i | \(-0.446378\pi\) | ||||
0.167663 | + | 0.985844i | \(0.446378\pi\) | |||||||
\(882\) | 6.86129e8 | 0.0336718 | ||||||||
\(883\) | −2.73622e10 | −1.33748 | −0.668741 | − | 0.743495i | \(-0.733167\pi\) | ||||
−0.668741 | + | 0.743495i | \(0.733167\pi\) | |||||||
\(884\) | −3.01989e8 | −0.0147031 | ||||||||
\(885\) | 7.17754e9 | 0.348076 | ||||||||
\(886\) | 1.42491e10 | 0.688285 | ||||||||
\(887\) | 1.70834e10 | 0.821941 | 0.410970 | − | 0.911649i | \(-0.365190\pi\) | ||||
0.410970 | + | 0.911649i | \(0.365190\pi\) | |||||||
\(888\) | −5.27474e9 | −0.252787 | ||||||||
\(889\) | 3.38034e8 | 0.0161363 | ||||||||
\(890\) | 1.23980e10 | 0.589506 | ||||||||
\(891\) | −2.03262e9 | −0.0962687 | ||||||||
\(892\) | 2.76899e9 | 0.130630 | ||||||||
\(893\) | −1.32478e10 | −0.622533 | ||||||||
\(894\) | 1.55497e10 | 0.727847 | ||||||||
\(895\) | 7.15272e10 | 3.33496 | ||||||||
\(896\) | −7.19323e8 | −0.0334077 | ||||||||
\(897\) | 4.00780e9 | 0.185410 | ||||||||
\(898\) | −1.53694e8 | −0.00708255 | ||||||||
\(899\) | 9.24936e9 | 0.424573 | ||||||||
\(900\) | 7.87593e9 | 0.360125 | ||||||||
\(901\) | 7.56612e8 | 0.0344617 | ||||||||
\(902\) | −6.94989e9 | −0.315323 | ||||||||
\(903\) | 4.93486e9 | 0.223032 | ||||||||
\(904\) | −3.61975e9 | −0.162963 | ||||||||
\(905\) | 3.89173e10 | 1.74531 | ||||||||
\(906\) | 6.95792e9 | 0.310835 | ||||||||
\(907\) | −1.38221e10 | −0.615103 | −0.307551 | − | 0.951531i | \(-0.599510\pi\) | ||||
−0.307551 | + | 0.951531i | \(0.599510\pi\) | |||||||
\(908\) | 1.12975e9 | 0.0500821 | ||||||||
\(909\) | 1.39469e10 | 0.615892 | ||||||||
\(910\) | −2.99574e9 | −0.131783 | ||||||||
\(911\) | 2.21664e10 | 0.971360 | 0.485680 | − | 0.874137i | \(-0.338572\pi\) | ||||
0.485680 | + | 0.874137i | \(0.338572\pi\) | |||||||
\(912\) | 2.05091e9 | 0.0895292 | ||||||||
\(913\) | 3.36853e10 | 1.46485 | ||||||||
\(914\) | −1.22681e10 | −0.531455 | ||||||||
\(915\) | −1.27133e10 | −0.548636 | ||||||||
\(916\) | 1.46003e10 | 0.627664 | ||||||||
\(917\) | 1.21614e10 | 0.520826 | ||||||||
\(918\) | 3.38191e8 | 0.0144282 | ||||||||
\(919\) | 1.73285e9 | 0.0736474 | 0.0368237 | − | 0.999322i | \(-0.488276\pi\) | ||||
0.0368237 | + | 0.999322i | \(0.488276\pi\) | |||||||
\(920\) | −1.71898e10 | −0.727804 | ||||||||
\(921\) | 7.13147e9 | 0.300795 | ||||||||
\(922\) | −9.21789e9 | −0.387323 | ||||||||
\(923\) | −1.10679e10 | −0.463298 | ||||||||
\(924\) | −2.26694e9 | −0.0945340 | ||||||||
\(925\) | 6.44112e10 | 2.67587 | ||||||||
\(926\) | −7.29151e9 | −0.301772 | ||||||||
\(927\) | 9.99902e8 | 0.0412267 | ||||||||
\(928\) | 1.92385e9 | 0.0790231 | ||||||||
\(929\) | 4.89668e9 | 0.200377 | 0.100188 | − | 0.994968i | \(-0.468055\pi\) | ||||
0.100188 | + | 0.994968i | \(0.468055\pi\) | |||||||
\(930\) | −1.69096e10 | −0.689355 | ||||||||
\(931\) | −2.18178e9 | −0.0886109 | ||||||||
\(932\) | −5.89862e9 | −0.238668 | ||||||||
\(933\) | −1.50264e10 | −0.605714 | ||||||||
\(934\) | −1.81771e10 | −0.729981 | ||||||||
\(935\) | 4.08200e9 | 0.163317 | ||||||||
\(936\) | 8.20026e8 | 0.0326860 | ||||||||
\(937\) | 8.45195e9 | 0.335636 | 0.167818 | − | 0.985818i | \(-0.446328\pi\) | ||||
0.167818 | + | 0.985818i | \(0.446328\pi\) | |||||||
\(938\) | −6.05093e9 | −0.239393 | ||||||||
\(939\) | 1.19552e10 | 0.471223 | ||||||||
\(940\) | 2.27190e10 | 0.892159 | ||||||||
\(941\) | 3.53018e10 | 1.38113 | 0.690563 | − | 0.723273i | \(-0.257363\pi\) | ||||
0.690563 | + | 0.723273i | \(0.257363\pi\) | |||||||
\(942\) | 1.89304e10 | 0.737873 | ||||||||
\(943\) | −1.53461e10 | −0.595946 | ||||||||
\(944\) | −2.19120e9 | −0.0847773 | ||||||||
\(945\) | 3.35487e9 | 0.129320 | ||||||||
\(946\) | −1.63046e10 | −0.626167 | ||||||||
\(947\) | −1.87980e10 | −0.719263 | −0.359631 | − | 0.933094i | \(-0.617098\pi\) | ||||
−0.359631 | + | 0.933094i | \(0.617098\pi\) | |||||||
\(948\) | −1.48906e10 | −0.567653 | ||||||||
\(949\) | 3.21760e9 | 0.122208 | ||||||||
\(950\) | −2.50442e10 | −0.947708 | ||||||||
\(951\) | −6.30297e9 | −0.237637 | ||||||||
\(952\) | 3.77176e8 | 0.0141682 | ||||||||
\(953\) | −3.46583e10 | −1.29712 | −0.648562 | − | 0.761162i | \(-0.724629\pi\) | ||||
−0.648562 | + | 0.761162i | \(0.724629\pi\) | |||||||
\(954\) | −2.05452e9 | −0.0766110 | ||||||||
\(955\) | 3.15467e10 | 1.17204 | ||||||||
\(956\) | 1.06789e10 | 0.395296 | ||||||||
\(957\) | 6.06301e9 | 0.223613 | ||||||||
\(958\) | 5.20200e9 | 0.191157 | ||||||||
\(959\) | −9.13642e9 | −0.334511 | ||||||||
\(960\) | −3.51717e9 | −0.128305 | ||||||||
\(961\) | −2.69393e9 | −0.0979163 | ||||||||
\(962\) | 6.70637e9 | 0.242870 | ||||||||
\(963\) | 1.72025e10 | 0.620725 | ||||||||
\(964\) | 1.50898e10 | 0.542519 | ||||||||
\(965\) | 4.75004e10 | 1.70158 | ||||||||
\(966\) | −5.00564e9 | −0.178665 | ||||||||
\(967\) | 4.51149e10 | 1.60446 | 0.802228 | − | 0.597018i | \(-0.203648\pi\) | ||||
0.802228 | + | 0.597018i | \(0.203648\pi\) | |||||||
\(968\) | −2.48757e9 | −0.0881477 | ||||||||
\(969\) | −1.07539e9 | −0.0379694 | ||||||||
\(970\) | 7.97716e9 | 0.280638 | ||||||||
\(971\) | 5.39377e10 | 1.89071 | 0.945355 | − | 0.326044i | \(-0.105716\pi\) | ||||
0.945355 | + | 0.326044i | \(0.105716\pi\) | |||||||
\(972\) | −9.18330e8 | −0.0320750 | ||||||||
\(973\) | 1.94775e10 | 0.677859 | ||||||||
\(974\) | −1.50955e10 | −0.523471 | ||||||||
\(975\) | −1.00136e10 | −0.345997 | ||||||||
\(976\) | 3.88118e9 | 0.133626 | ||||||||
\(977\) | −5.29565e9 | −0.181672 | −0.0908360 | − | 0.995866i | \(-0.528954\pi\) | ||||
−0.0908360 | + | 0.995866i | \(0.528954\pi\) | |||||||
\(978\) | −1.56561e10 | −0.535178 | ||||||||
\(979\) | −1.19282e10 | −0.406290 | ||||||||
\(980\) | 3.74161e9 | 0.126989 | ||||||||
\(981\) | 6.12015e9 | 0.206976 | ||||||||
\(982\) | 1.31723e10 | 0.443886 | ||||||||
\(983\) | −3.48690e10 | −1.17085 | −0.585426 | − | 0.810726i | \(-0.699073\pi\) | ||||
−0.585426 | + | 0.810726i | \(0.699073\pi\) | |||||||
\(984\) | −3.13993e9 | −0.105060 | ||||||||
\(985\) | 4.11590e10 | 1.37226 | ||||||||
\(986\) | −1.00877e9 | −0.0335138 | ||||||||
\(987\) | 6.61572e9 | 0.219012 | ||||||||
\(988\) | −2.60755e9 | −0.0860169 | ||||||||
\(989\) | −3.60022e10 | −1.18343 | ||||||||
\(990\) | −1.10843e10 | −0.363067 | ||||||||
\(991\) | −1.20597e10 | −0.393622 | −0.196811 | − | 0.980441i | \(-0.563058\pi\) | ||||
−0.196811 | + | 0.980441i | \(0.563058\pi\) | |||||||
\(992\) | 5.16225e9 | 0.167899 | ||||||||
\(993\) | −3.20899e10 | −1.04003 | ||||||||
\(994\) | 1.38236e10 | 0.446445 | ||||||||
\(995\) | −4.04436e10 | −1.30158 | ||||||||
\(996\) | 1.52188e10 | 0.488061 | ||||||||
\(997\) | −3.70942e10 | −1.18542 | −0.592710 | − | 0.805416i | \(-0.701942\pi\) | ||||
−0.592710 | + | 0.805416i | \(0.701942\pi\) | |||||||
\(998\) | −3.30975e10 | −1.05399 | ||||||||
\(999\) | −7.51032e9 | −0.238330 |
(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 | 546.8.a.r.1.6 | ✓ | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
546.8.a.r.1.6 | ✓ | 6 | 1.1 | even | 1 | trivial |