Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [147,8,Mod(1,147)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(147, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("147.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 147 = 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 147.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: | \(45.9205987462\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{4} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 299x^{2} - 1110x + 1890 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{2}\cdot 7 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(1.26815\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 147.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −21.6612 | −1.91460 | −0.957300 | − | 0.289095i | \(-0.906646\pi\) | ||||
−0.957300 | + | 0.289095i | \(0.906646\pi\) | |||||||
\(3\) | 27.0000 | 0.577350 | ||||||||
\(4\) | 341.209 | 2.66570 | ||||||||
\(5\) | 516.937 | 1.84945 | 0.924725 | − | 0.380637i | \(-0.124295\pi\) | ||||
0.924725 | + | 0.380637i | \(0.124295\pi\) | |||||||
\(6\) | −584.853 | −1.10540 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −4618.37 | −3.18914 | ||||||||
\(9\) | 729.000 | 0.333333 | ||||||||
\(10\) | −11197.5 | −3.54096 | ||||||||
\(11\) | 662.581 | 0.150095 | 0.0750473 | − | 0.997180i | \(-0.476089\pi\) | ||||
0.0750473 | + | 0.997180i | \(0.476089\pi\) | |||||||
\(12\) | 9212.65 | 1.53904 | ||||||||
\(13\) | 7851.30 | 0.991151 | 0.495576 | − | 0.868565i | \(-0.334957\pi\) | ||||
0.495576 | + | 0.868565i | \(0.334957\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 13957.3 | 1.06778 | ||||||||
\(16\) | 56364.9 | 3.44024 | ||||||||
\(17\) | 11632.6 | 0.574255 | 0.287127 | − | 0.957892i | \(-0.407300\pi\) | ||||
0.287127 | + | 0.957892i | \(0.407300\pi\) | |||||||
\(18\) | −15791.0 | −0.638200 | ||||||||
\(19\) | 14985.6 | 0.501228 | 0.250614 | − | 0.968087i | \(-0.419367\pi\) | ||||
0.250614 | + | 0.968087i | \(0.419367\pi\) | |||||||
\(20\) | 176384. | 4.93007 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −14352.3 | −0.287371 | ||||||||
\(23\) | −26185.0 | −0.448750 | −0.224375 | − | 0.974503i | \(-0.572034\pi\) | ||||
−0.224375 | + | 0.974503i | \(0.572034\pi\) | |||||||
\(24\) | −124696. | −1.84125 | ||||||||
\(25\) | 189099. | 2.42046 | ||||||||
\(26\) | −170069. | −1.89766 | ||||||||
\(27\) | 19683.0 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 108612. | 0.826959 | 0.413480 | − | 0.910513i | \(-0.364313\pi\) | ||||
0.413480 | + | 0.910513i | \(0.364313\pi\) | |||||||
\(30\) | −302332. | −2.04437 | ||||||||
\(31\) | −195632. | −1.17944 | −0.589719 | − | 0.807609i | \(-0.700761\pi\) | ||||
−0.589719 | + | 0.807609i | \(0.700761\pi\) | |||||||
\(32\) | −629782. | −3.39755 | ||||||||
\(33\) | 17889.7 | 0.0866571 | ||||||||
\(34\) | −251976. | −1.09947 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 248741. | 0.888566 | ||||||||
\(37\) | 326569. | 1.05991 | 0.529955 | − | 0.848026i | \(-0.322209\pi\) | ||||
0.529955 | + | 0.848026i | \(0.322209\pi\) | |||||||
\(38\) | −324606. | −0.959652 | ||||||||
\(39\) | 211985. | 0.572242 | ||||||||
\(40\) | −2.38741e6 | −5.89816 | ||||||||
\(41\) | −79193.0 | −0.179450 | −0.0897249 | − | 0.995967i | \(-0.528599\pi\) | ||||
−0.0897249 | + | 0.995967i | \(0.528599\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 638173. | 1.22405 | 0.612025 | − | 0.790838i | \(-0.290355\pi\) | ||||
0.612025 | + | 0.790838i | \(0.290355\pi\) | |||||||
\(44\) | 226079. | 0.400106 | ||||||||
\(45\) | 376847. | 0.616483 | ||||||||
\(46\) | 567199. | 0.859178 | ||||||||
\(47\) | −776840. | −1.09141 | −0.545707 | − | 0.837976i | \(-0.683739\pi\) | ||||
−0.545707 | + | 0.837976i | \(0.683739\pi\) | |||||||
\(48\) | 1.52185e6 | 1.98622 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −4.09611e6 | −4.63422 | ||||||||
\(51\) | 314079. | 0.331546 | ||||||||
\(52\) | 2.67894e6 | 2.64211 | ||||||||
\(53\) | −928216. | −0.856414 | −0.428207 | − | 0.903681i | \(-0.640855\pi\) | ||||
−0.428207 | + | 0.903681i | \(0.640855\pi\) | |||||||
\(54\) | −426358. | −0.368465 | ||||||||
\(55\) | 342513. | 0.277592 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 404610. | 0.289384 | ||||||||
\(58\) | −2.35267e6 | −1.58330 | ||||||||
\(59\) | −2.29493e6 | −1.45475 | −0.727374 | − | 0.686242i | \(-0.759259\pi\) | ||||
−0.727374 | + | 0.686242i | \(0.759259\pi\) | |||||||
\(60\) | 4.76236e6 | 2.84638 | ||||||||
\(61\) | 2.43649e6 | 1.37439 | 0.687194 | − | 0.726474i | \(-0.258842\pi\) | ||||
0.687194 | + | 0.726474i | \(0.258842\pi\) | |||||||
\(62\) | 4.23764e6 | 2.25815 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 6.42715e6 | 3.06470 | ||||||||
\(65\) | 4.05863e6 | 1.83308 | ||||||||
\(66\) | −387513. | −0.165914 | ||||||||
\(67\) | −1.75090e6 | −0.711213 | −0.355606 | − | 0.934636i | \(-0.615726\pi\) | ||||
−0.355606 | + | 0.934636i | \(0.615726\pi\) | |||||||
\(68\) | 3.96914e6 | 1.53079 | ||||||||
\(69\) | −706995. | −0.259086 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.22315e6 | −0.405581 | −0.202790 | − | 0.979222i | \(-0.565001\pi\) | ||||
−0.202790 | + | 0.979222i | \(0.565001\pi\) | |||||||
\(72\) | −3.36679e6 | −1.06305 | ||||||||
\(73\) | 464159. | 0.139649 | 0.0698244 | − | 0.997559i | \(-0.477756\pi\) | ||||
0.0698244 | + | 0.997559i | \(0.477756\pi\) | |||||||
\(74\) | −7.07389e6 | −2.02930 | ||||||||
\(75\) | 5.10566e6 | 1.39746 | ||||||||
\(76\) | 5.11321e6 | 1.33612 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −4.59186e6 | −1.09561 | ||||||||
\(79\) | 1.73244e6 | 0.395332 | 0.197666 | − | 0.980269i | \(-0.436664\pi\) | ||||
0.197666 | + | 0.980269i | \(0.436664\pi\) | |||||||
\(80\) | 2.91371e7 | 6.36255 | ||||||||
\(81\) | 531441. | 0.111111 | ||||||||
\(82\) | 1.71542e6 | 0.343575 | ||||||||
\(83\) | 3.98160e6 | 0.764337 | 0.382168 | − | 0.924093i | \(-0.375177\pi\) | ||||
0.382168 | + | 0.924093i | \(0.375177\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.01330e6 | 1.06205 | ||||||||
\(86\) | −1.38236e7 | −2.34357 | ||||||||
\(87\) | 2.93252e6 | 0.477445 | ||||||||
\(88\) | −3.06005e6 | −0.478673 | ||||||||
\(89\) | −7.83254e6 | −1.17771 | −0.588854 | − | 0.808240i | \(-0.700421\pi\) | ||||
−0.588854 | + | 0.808240i | \(0.700421\pi\) | |||||||
\(90\) | −8.16297e6 | −1.18032 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −8.93456e6 | −1.19623 | ||||||||
\(93\) | −5.28208e6 | −0.680949 | ||||||||
\(94\) | 1.68273e7 | 2.08962 | ||||||||
\(95\) | 7.74659e6 | 0.926996 | ||||||||
\(96\) | −1.70041e7 | −1.96157 | ||||||||
\(97\) | −4.49108e6 | −0.499632 | −0.249816 | − | 0.968293i | \(-0.580370\pi\) | ||||
−0.249816 | + | 0.968293i | \(0.580370\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 483022. | 0.0500315 | ||||||||
\(100\) | 6.45222e7 | 6.45222 | ||||||||
\(101\) | −1.24245e7 | −1.19993 | −0.599964 | − | 0.800027i | \(-0.704818\pi\) | ||||
−0.599964 | + | 0.800027i | \(0.704818\pi\) | |||||||
\(102\) | −6.80335e6 | −0.634778 | ||||||||
\(103\) | 2.14293e7 | 1.93231 | 0.966157 | − | 0.257955i | \(-0.0830485\pi\) | ||||
0.966157 | + | 0.257955i | \(0.0830485\pi\) | |||||||
\(104\) | −3.62603e7 | −3.16092 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.01063e7 | 1.63969 | ||||||||
\(107\) | −2.22446e7 | −1.75542 | −0.877710 | − | 0.479193i | \(-0.840930\pi\) | ||||
−0.877710 | + | 0.479193i | \(0.840930\pi\) | |||||||
\(108\) | 6.71602e6 | 0.513014 | ||||||||
\(109\) | 9.90130e6 | 0.732318 | 0.366159 | − | 0.930552i | \(-0.380673\pi\) | ||||
0.366159 | + | 0.930552i | \(0.380673\pi\) | |||||||
\(110\) | −7.41925e6 | −0.531478 | ||||||||
\(111\) | 8.81736e6 | 0.611939 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.91928e7 | 1.25130 | 0.625652 | − | 0.780102i | \(-0.284833\pi\) | ||||
0.625652 | + | 0.780102i | \(0.284833\pi\) | |||||||
\(114\) | −8.76436e6 | −0.554055 | ||||||||
\(115\) | −1.35360e7 | −0.829941 | ||||||||
\(116\) | 3.70593e7 | 2.20442 | ||||||||
\(117\) | 5.72360e6 | 0.330384 | ||||||||
\(118\) | 4.97110e7 | 2.78526 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −6.44600e7 | −3.40530 | ||||||||
\(121\) | −1.90482e7 | −0.977472 | ||||||||
\(122\) | −5.27773e7 | −2.63141 | ||||||||
\(123\) | −2.13821e6 | −0.103605 | ||||||||
\(124\) | −6.67516e7 | −3.14402 | ||||||||
\(125\) | 5.73664e7 | 2.62707 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.43563e7 | −0.621912 | −0.310956 | − | 0.950424i | \(-0.600649\pi\) | ||||
−0.310956 | + | 0.950424i | \(0.600649\pi\) | |||||||
\(128\) | −5.86078e7 | −2.47014 | ||||||||
\(129\) | 1.72307e7 | 0.706706 | ||||||||
\(130\) | −8.79149e7 | −3.50963 | ||||||||
\(131\) | 1.82094e7 | 0.707696 | 0.353848 | − | 0.935303i | \(-0.384873\pi\) | ||||
0.353848 | + | 0.935303i | \(0.384873\pi\) | |||||||
\(132\) | 6.10413e6 | 0.231002 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 3.79267e7 | 1.36169 | ||||||||
\(135\) | 1.01749e7 | 0.355927 | ||||||||
\(136\) | −5.37236e7 | −1.83138 | ||||||||
\(137\) | 2.45269e7 | 0.814932 | 0.407466 | − | 0.913220i | \(-0.366413\pi\) | ||||
0.407466 | + | 0.913220i | \(0.366413\pi\) | |||||||
\(138\) | 1.53144e7 | 0.496047 | ||||||||
\(139\) | 1.18402e7 | 0.373946 | 0.186973 | − | 0.982365i | \(-0.440132\pi\) | ||||
0.186973 | + | 0.982365i | \(0.440132\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.09747e7 | −0.630128 | ||||||||
\(142\) | 2.64950e7 | 0.776525 | ||||||||
\(143\) | 5.20213e6 | 0.148766 | ||||||||
\(144\) | 4.10900e7 | 1.14675 | ||||||||
\(145\) | 5.61454e7 | 1.52942 | ||||||||
\(146\) | −1.00543e7 | −0.267372 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.11428e8 | 2.82540 | ||||||||
\(149\) | 5.63211e6 | 0.139482 | 0.0697412 | − | 0.997565i | \(-0.477783\pi\) | ||||
0.0697412 | + | 0.997565i | \(0.477783\pi\) | |||||||
\(150\) | −1.10595e8 | −2.67557 | ||||||||
\(151\) | −6.07958e7 | −1.43699 | −0.718495 | − | 0.695532i | \(-0.755169\pi\) | ||||
−0.718495 | + | 0.695532i | \(0.755169\pi\) | |||||||
\(152\) | −6.92089e7 | −1.59849 | ||||||||
\(153\) | 8.48014e6 | 0.191418 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.01130e8 | −2.18131 | ||||||||
\(156\) | 7.23313e7 | 1.52542 | ||||||||
\(157\) | −5.63347e7 | −1.16179 | −0.580895 | − | 0.813979i | \(-0.697297\pi\) | ||||
−0.580895 | + | 0.813979i | \(0.697297\pi\) | |||||||
\(158\) | −3.75267e7 | −0.756904 | ||||||||
\(159\) | −2.50618e7 | −0.494451 | ||||||||
\(160\) | −3.25557e8 | −6.28359 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −1.15117e7 | −0.212733 | ||||||||
\(163\) | 5.26719e7 | 0.952627 | 0.476313 | − | 0.879276i | \(-0.341973\pi\) | ||||
0.476313 | + | 0.879276i | \(0.341973\pi\) | |||||||
\(164\) | −2.70214e7 | −0.478359 | ||||||||
\(165\) | 9.24784e6 | 0.160268 | ||||||||
\(166\) | −8.62464e7 | −1.46340 | ||||||||
\(167\) | 2.07427e7 | 0.344634 | 0.172317 | − | 0.985042i | \(-0.444875\pi\) | ||||
0.172317 | + | 0.985042i | \(0.444875\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.10556e6 | −0.0176189 | ||||||||
\(170\) | −1.30256e8 | −2.03341 | ||||||||
\(171\) | 1.09245e7 | 0.167076 | ||||||||
\(172\) | 2.17751e8 | 3.26295 | ||||||||
\(173\) | 1.30053e8 | 1.90967 | 0.954834 | − | 0.297140i | \(-0.0960327\pi\) | ||||
0.954834 | + | 0.297140i | \(0.0960327\pi\) | |||||||
\(174\) | −6.35220e7 | −0.914117 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.73463e7 | 0.516361 | ||||||||
\(177\) | −6.19631e7 | −0.839899 | ||||||||
\(178\) | 1.69662e8 | 2.25484 | ||||||||
\(179\) | −1.53454e7 | −0.199983 | −0.0999914 | − | 0.994988i | \(-0.531882\pi\) | ||||
−0.0999914 | + | 0.994988i | \(0.531882\pi\) | |||||||
\(180\) | 1.28584e8 | 1.64336 | ||||||||
\(181\) | 7.02000e7 | 0.879959 | 0.439979 | − | 0.898008i | \(-0.354986\pi\) | ||||
0.439979 | + | 0.898008i | \(0.354986\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 6.57851e7 | 0.793504 | ||||||||
\(184\) | 1.20932e8 | 1.43113 | ||||||||
\(185\) | 1.68815e8 | 1.96025 | ||||||||
\(186\) | 1.14416e8 | 1.30375 | ||||||||
\(187\) | 7.70753e6 | 0.0861925 | ||||||||
\(188\) | −2.65065e8 | −2.90938 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1.67801e8 | −1.77483 | ||||||||
\(191\) | 1.69111e8 | 1.75613 | 0.878063 | − | 0.478545i | \(-0.158836\pi\) | ||||
0.878063 | + | 0.478545i | \(0.158836\pi\) | |||||||
\(192\) | 1.73533e8 | 1.76941 | ||||||||
\(193\) | 9.96399e7 | 0.997660 | 0.498830 | − | 0.866700i | \(-0.333763\pi\) | ||||
0.498830 | + | 0.866700i | \(0.333763\pi\) | |||||||
\(194\) | 9.72824e7 | 0.956595 | ||||||||
\(195\) | 1.09583e8 | 1.05833 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.73109e8 | 1.61319 | 0.806597 | − | 0.591101i | \(-0.201307\pi\) | ||||
0.806597 | + | 0.591101i | \(0.201307\pi\) | |||||||
\(198\) | −1.04629e7 | −0.0957904 | ||||||||
\(199\) | −9.43518e7 | −0.848720 | −0.424360 | − | 0.905494i | \(-0.639501\pi\) | ||||
−0.424360 | + | 0.905494i | \(0.639501\pi\) | |||||||
\(200\) | −8.73328e8 | −7.71921 | ||||||||
\(201\) | −4.72743e7 | −0.410619 | ||||||||
\(202\) | 2.69131e8 | 2.29738 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 1.07167e8 | 0.883801 | ||||||||
\(205\) | −4.09378e7 | −0.331884 | ||||||||
\(206\) | −4.64185e8 | −3.69961 | ||||||||
\(207\) | −1.90889e7 | −0.149583 | ||||||||
\(208\) | 4.42538e8 | 3.40980 | ||||||||
\(209\) | 9.92916e6 | 0.0752316 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.13471e6 | −0.0376294 | −0.0188147 | − | 0.999823i | \(-0.505989\pi\) | ||||
−0.0188147 | + | 0.999823i | \(0.505989\pi\) | |||||||
\(212\) | −3.16716e8 | −2.28294 | ||||||||
\(213\) | −3.30252e7 | −0.234162 | ||||||||
\(214\) | 4.81845e8 | 3.36093 | ||||||||
\(215\) | 3.29895e8 | 2.26382 | ||||||||
\(216\) | −9.09035e7 | −0.613751 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −2.14474e8 | −1.40210 | ||||||||
\(219\) | 1.25323e7 | 0.0806262 | ||||||||
\(220\) | 1.16868e8 | 0.739977 | ||||||||
\(221\) | 9.13308e7 | 0.569173 | ||||||||
\(222\) | −1.90995e8 | −1.17162 | ||||||||
\(223\) | −1.73853e8 | −1.04982 | −0.524909 | − | 0.851158i | \(-0.675901\pi\) | ||||
−0.524909 | + | 0.851158i | \(0.675901\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.37853e8 | 0.806821 | ||||||||
\(226\) | −4.15739e8 | −2.39575 | ||||||||
\(227\) | 1.70253e8 | 0.966063 | 0.483032 | − | 0.875603i | \(-0.339536\pi\) | ||||
0.483032 | + | 0.875603i | \(0.339536\pi\) | |||||||
\(228\) | 1.38057e8 | 0.771411 | ||||||||
\(229\) | 2.47698e8 | 1.36301 | 0.681504 | − | 0.731814i | \(-0.261326\pi\) | ||||
0.681504 | + | 0.731814i | \(0.261326\pi\) | |||||||
\(230\) | 2.93206e8 | 1.58901 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −5.01610e8 | −2.63729 | ||||||||
\(233\) | −1.14411e8 | −0.592548 | −0.296274 | − | 0.955103i | \(-0.595744\pi\) | ||||
−0.296274 | + | 0.955103i | \(0.595744\pi\) | |||||||
\(234\) | −1.23980e8 | −0.632553 | ||||||||
\(235\) | −4.01577e8 | −2.01851 | ||||||||
\(236\) | −7.83051e8 | −3.87791 | ||||||||
\(237\) | 4.67758e7 | 0.228245 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −8.83010e7 | −0.418382 | −0.209191 | − | 0.977875i | \(-0.567083\pi\) | ||||
−0.209191 | + | 0.977875i | \(0.567083\pi\) | |||||||
\(240\) | 7.86702e8 | 3.67342 | ||||||||
\(241\) | −1.55646e8 | −0.716271 | −0.358135 | − | 0.933670i | \(-0.616587\pi\) | ||||
−0.358135 | + | 0.933670i | \(0.616587\pi\) | |||||||
\(242\) | 4.12607e8 | 1.87147 | ||||||||
\(243\) | 1.43489e7 | 0.0641500 | ||||||||
\(244\) | 8.31351e8 | 3.66370 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 4.63163e7 | 0.198363 | ||||||||
\(247\) | 1.17656e8 | 0.496793 | ||||||||
\(248\) | 9.03504e8 | 3.76140 | ||||||||
\(249\) | 1.07503e8 | 0.441290 | ||||||||
\(250\) | −1.24263e9 | −5.02980 | ||||||||
\(251\) | −1.07520e8 | −0.429171 | −0.214585 | − | 0.976705i | \(-0.568840\pi\) | ||||
−0.214585 | + | 0.976705i | \(0.568840\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.73497e7 | −0.0673550 | ||||||||
\(254\) | 3.10975e8 | 1.19071 | ||||||||
\(255\) | 1.62359e8 | 0.613178 | ||||||||
\(256\) | 4.46844e8 | 1.66462 | ||||||||
\(257\) | −4.03178e8 | −1.48160 | −0.740800 | − | 0.671726i | \(-0.765553\pi\) | ||||
−0.740800 | + | 0.671726i | \(0.765553\pi\) | |||||||
\(258\) | −3.73238e8 | −1.35306 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 1.38484e9 | 4.88645 | ||||||||
\(261\) | 7.91780e7 | 0.275653 | ||||||||
\(262\) | −3.94439e8 | −1.35496 | ||||||||
\(263\) | −2.73338e8 | −0.926520 | −0.463260 | − | 0.886223i | \(-0.653320\pi\) | ||||
−0.463260 | + | 0.886223i | \(0.653320\pi\) | |||||||
\(264\) | −8.26213e7 | −0.276362 | ||||||||
\(265\) | −4.79829e8 | −1.58389 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.11478e8 | −0.679950 | ||||||||
\(268\) | −5.97423e8 | −1.89588 | ||||||||
\(269\) | 1.03641e8 | 0.324638 | 0.162319 | − | 0.986738i | \(-0.448103\pi\) | ||||
0.162319 | + | 0.986738i | \(0.448103\pi\) | |||||||
\(270\) | −2.20400e8 | −0.681458 | ||||||||
\(271\) | −1.98124e7 | −0.0604706 | −0.0302353 | − | 0.999543i | \(-0.509626\pi\) | ||||
−0.0302353 | + | 0.999543i | \(0.509626\pi\) | |||||||
\(272\) | 6.55669e8 | 1.97557 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −5.31284e8 | −1.56027 | ||||||||
\(275\) | 1.25293e8 | 0.363298 | ||||||||
\(276\) | −2.41233e8 | −0.690645 | ||||||||
\(277\) | −3.56304e8 | −1.00726 | −0.503630 | − | 0.863919i | \(-0.668003\pi\) | ||||
−0.503630 | + | 0.863919i | \(0.668003\pi\) | |||||||
\(278\) | −2.56474e8 | −0.715957 | ||||||||
\(279\) | −1.42616e8 | −0.393146 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.59268e7 | −0.0428210 | −0.0214105 | − | 0.999771i | \(-0.506816\pi\) | ||||
−0.0214105 | + | 0.999771i | \(0.506816\pi\) | |||||||
\(282\) | 4.54338e8 | 1.20644 | ||||||||
\(283\) | 4.82361e8 | 1.26508 | 0.632542 | − | 0.774526i | \(-0.282011\pi\) | ||||
0.632542 | + | 0.774526i | \(0.282011\pi\) | |||||||
\(284\) | −4.17352e8 | −1.08115 | ||||||||
\(285\) | 2.09158e8 | 0.535202 | ||||||||
\(286\) | −1.12685e8 | −0.284828 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −4.59111e8 | −1.13252 | ||||||||
\(289\) | −2.75022e8 | −0.670232 | ||||||||
\(290\) | −1.21618e9 | −2.92823 | ||||||||
\(291\) | −1.21259e8 | −0.288462 | ||||||||
\(292\) | 1.58375e8 | 0.372261 | ||||||||
\(293\) | −4.43360e8 | −1.02972 | −0.514860 | − | 0.857274i | \(-0.672156\pi\) | ||||
−0.514860 | + | 0.857274i | \(0.672156\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.18633e9 | −2.69048 | ||||||||
\(296\) | −1.50822e9 | −3.38020 | ||||||||
\(297\) | 1.30416e7 | 0.0288857 | ||||||||
\(298\) | −1.21999e8 | −0.267053 | ||||||||
\(299\) | −2.05586e8 | −0.444780 | ||||||||
\(300\) | 1.74210e9 | 3.72519 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 1.31691e9 | 2.75126 | ||||||||
\(303\) | −3.35462e8 | −0.692778 | ||||||||
\(304\) | 8.44660e8 | 1.72435 | ||||||||
\(305\) | 1.25951e9 | 2.54186 | ||||||||
\(306\) | −1.83690e8 | −0.366489 | ||||||||
\(307\) | 7.75755e7 | 0.153017 | 0.0765086 | − | 0.997069i | \(-0.475623\pi\) | ||||
0.0765086 | + | 0.997069i | \(0.475623\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5.78591e8 | 1.11562 | ||||||||
\(310\) | 2.19059e9 | 4.17634 | ||||||||
\(311\) | −4.42636e8 | −0.834421 | −0.417211 | − | 0.908810i | \(-0.636992\pi\) | ||||
−0.417211 | + | 0.908810i | \(0.636992\pi\) | |||||||
\(312\) | −9.79027e8 | −1.82496 | ||||||||
\(313\) | 5.63026e8 | 1.03782 | 0.518912 | − | 0.854828i | \(-0.326337\pi\) | ||||
0.518912 | + | 0.854828i | \(0.326337\pi\) | |||||||
\(314\) | 1.22028e9 | 2.22436 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 5.91123e8 | 1.05384 | ||||||||
\(317\) | −7.63549e8 | −1.34626 | −0.673130 | − | 0.739524i | \(-0.735051\pi\) | ||||
−0.673130 | + | 0.739524i | \(0.735051\pi\) | |||||||
\(318\) | 5.42871e8 | 0.946676 | ||||||||
\(319\) | 7.19642e7 | 0.124122 | ||||||||
\(320\) | 3.32243e9 | 5.66801 | ||||||||
\(321\) | −6.00604e8 | −1.01349 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.74321e8 | 0.287833 | ||||||||
\(324\) | 1.81333e8 | 0.296189 | ||||||||
\(325\) | 1.48467e9 | 2.39905 | ||||||||
\(326\) | −1.14094e9 | −1.82390 | ||||||||
\(327\) | 2.67335e8 | 0.422804 | ||||||||
\(328\) | 3.65743e8 | 0.572292 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −2.00320e8 | −0.306849 | ||||||||
\(331\) | 4.28687e8 | 0.649745 | 0.324872 | − | 0.945758i | \(-0.394679\pi\) | ||||
0.324872 | + | 0.945758i | \(0.394679\pi\) | |||||||
\(332\) | 1.35856e9 | 2.03749 | ||||||||
\(333\) | 2.38069e8 | 0.353303 | ||||||||
\(334\) | −4.49313e8 | −0.659836 | ||||||||
\(335\) | −9.05105e8 | −1.31535 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7.56118e8 | 1.07618 | 0.538090 | − | 0.842887i | \(-0.319146\pi\) | ||||
0.538090 | + | 0.842887i | \(0.319146\pi\) | |||||||
\(338\) | 2.39477e7 | 0.0337331 | ||||||||
\(339\) | 5.18205e8 | 0.722441 | ||||||||
\(340\) | 2.05179e9 | 2.83112 | ||||||||
\(341\) | −1.29622e8 | −0.177027 | ||||||||
\(342\) | −2.36638e8 | −0.319884 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −2.94732e9 | −3.90367 | ||||||||
\(345\) | −3.65472e8 | −0.479167 | ||||||||
\(346\) | −2.81710e9 | −3.65625 | ||||||||
\(347\) | 1.07256e9 | 1.37807 | 0.689033 | − | 0.724730i | \(-0.258035\pi\) | ||||
0.689033 | + | 0.724730i | \(0.258035\pi\) | |||||||
\(348\) | 1.00060e9 | 1.27272 | ||||||||
\(349\) | −8.07851e8 | −1.01728 | −0.508642 | − | 0.860978i | \(-0.669852\pi\) | ||||
−0.508642 | + | 0.860978i | \(0.669852\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.54537e8 | 0.190747 | ||||||||
\(352\) | −4.17282e8 | −0.509953 | ||||||||
\(353\) | 3.52640e8 | 0.426697 | 0.213349 | − | 0.976976i | \(-0.431563\pi\) | ||||
0.213349 | + | 0.976976i | \(0.431563\pi\) | |||||||
\(354\) | 1.34220e9 | 1.60807 | ||||||||
\(355\) | −6.32294e8 | −0.750101 | ||||||||
\(356\) | −2.67253e9 | −3.13941 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 3.32400e8 | 0.382887 | ||||||||
\(359\) | 4.73467e8 | 0.540082 | 0.270041 | − | 0.962849i | \(-0.412963\pi\) | ||||
0.270041 | + | 0.962849i | \(0.412963\pi\) | |||||||
\(360\) | −1.74042e9 | −1.96605 | ||||||||
\(361\) | −6.69305e8 | −0.748770 | ||||||||
\(362\) | −1.52062e9 | −1.68477 | ||||||||
\(363\) | −5.14300e8 | −0.564344 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.39941e8 | 0.258273 | ||||||||
\(366\) | −1.42499e9 | −1.51924 | ||||||||
\(367\) | 9.74512e8 | 1.02910 | 0.514548 | − | 0.857462i | \(-0.327960\pi\) | ||||
0.514548 | + | 0.857462i | \(0.327960\pi\) | |||||||
\(368\) | −1.47591e9 | −1.54381 | ||||||||
\(369\) | −5.77317e7 | −0.0598166 | ||||||||
\(370\) | −3.65675e9 | −3.75309 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −1.80229e9 | −1.81520 | ||||||||
\(373\) | 5.80133e8 | 0.578824 | 0.289412 | − | 0.957205i | \(-0.406540\pi\) | ||||
0.289412 | + | 0.957205i | \(0.406540\pi\) | |||||||
\(374\) | −1.66955e8 | −0.165024 | ||||||||
\(375\) | 1.54889e9 | 1.51674 | ||||||||
\(376\) | 3.58774e9 | 3.48067 | ||||||||
\(377\) | 8.52744e8 | 0.819642 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5.10991e8 | −0.482143 | −0.241072 | − | 0.970507i | \(-0.577499\pi\) | ||||
−0.241072 | + | 0.970507i | \(0.577499\pi\) | |||||||
\(380\) | 2.64321e9 | 2.47109 | ||||||||
\(381\) | −3.87619e8 | −0.359061 | ||||||||
\(382\) | −3.66316e9 | −3.36228 | ||||||||
\(383\) | −2.36881e6 | −0.00215444 | −0.00107722 | − | 0.999999i | \(-0.500343\pi\) | ||||
−0.00107722 | + | 0.999999i | \(0.500343\pi\) | |||||||
\(384\) | −1.58241e9 | −1.42613 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −2.15832e9 | −1.91012 | ||||||||
\(387\) | 4.65228e8 | 0.408017 | ||||||||
\(388\) | −1.53240e9 | −1.33187 | ||||||||
\(389\) | −1.34362e9 | −1.15732 | −0.578660 | − | 0.815569i | \(-0.696424\pi\) | ||||
−0.578660 | + | 0.815569i | \(0.696424\pi\) | |||||||
\(390\) | −2.37370e9 | −2.02628 | ||||||||
\(391\) | −3.04599e8 | −0.257697 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4.91655e8 | 0.408589 | ||||||||
\(394\) | −3.74975e9 | −3.08862 | ||||||||
\(395\) | 8.95560e8 | 0.731147 | ||||||||
\(396\) | 1.64811e8 | 0.133369 | ||||||||
\(397\) | −8.36087e8 | −0.670633 | −0.335317 | − | 0.942106i | \(-0.608843\pi\) | ||||
−0.335317 | + | 0.942106i | \(0.608843\pi\) | |||||||
\(398\) | 2.04378e9 | 1.62496 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.06585e10 | 8.32698 | ||||||||
\(401\) | −2.41709e8 | −0.187192 | −0.0935962 | − | 0.995610i | \(-0.529836\pi\) | ||||
−0.0935962 | + | 0.995610i | \(0.529836\pi\) | |||||||
\(402\) | 1.02402e9 | 0.786171 | ||||||||
\(403\) | −1.53597e9 | −1.16900 | ||||||||
\(404\) | −4.23936e9 | −3.19864 | ||||||||
\(405\) | 2.74721e8 | 0.205494 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.16378e8 | 0.159087 | ||||||||
\(408\) | −1.45054e9 | −1.05735 | ||||||||
\(409\) | 2.67400e8 | 0.193255 | 0.0966273 | − | 0.995321i | \(-0.469194\pi\) | ||||
0.0966273 | + | 0.995321i | \(0.469194\pi\) | |||||||
\(410\) | 8.86763e8 | 0.635424 | ||||||||
\(411\) | 6.62227e8 | 0.470501 | ||||||||
\(412\) | 7.31187e9 | 5.15096 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 4.13488e8 | 0.286393 | ||||||||
\(415\) | 2.05824e9 | 1.41360 | ||||||||
\(416\) | −4.94461e9 | −3.36748 | ||||||||
\(417\) | 3.19687e8 | 0.215898 | ||||||||
\(418\) | −2.15078e8 | −0.144039 | ||||||||
\(419\) | −1.59619e9 | −1.06007 | −0.530036 | − | 0.847975i | \(-0.677822\pi\) | ||||
−0.530036 | + | 0.847975i | \(0.677822\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.89643e9 | −1.23865 | −0.619327 | − | 0.785133i | \(-0.712595\pi\) | ||||
−0.619327 | + | 0.785133i | \(0.712595\pi\) | |||||||
\(422\) | 1.11224e8 | 0.0720454 | ||||||||
\(423\) | −5.66316e8 | −0.363804 | ||||||||
\(424\) | 4.28685e9 | 2.73123 | ||||||||
\(425\) | 2.19970e9 | 1.38996 | ||||||||
\(426\) | 7.15366e8 | 0.448327 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −7.59005e9 | −4.67942 | ||||||||
\(429\) | 1.40457e8 | 0.0858903 | ||||||||
\(430\) | −7.14594e9 | −4.33431 | ||||||||
\(431\) | −4.19921e8 | −0.252637 | −0.126319 | − | 0.991990i | \(-0.540316\pi\) | ||||
−0.126319 | + | 0.991990i | \(0.540316\pi\) | |||||||
\(432\) | 1.10943e9 | 0.662075 | ||||||||
\(433\) | 2.39286e9 | 1.41648 | 0.708238 | − | 0.705974i | \(-0.249491\pi\) | ||||
0.708238 | + | 0.705974i | \(0.249491\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.51593e9 | 0.883010 | ||||||||
\(436\) | 3.37841e9 | 1.95214 | ||||||||
\(437\) | −3.92397e8 | −0.224926 | ||||||||
\(438\) | −2.71465e8 | −0.154367 | ||||||||
\(439\) | −5.68006e8 | −0.320426 | −0.160213 | − | 0.987082i | \(-0.551218\pi\) | ||||
−0.160213 | + | 0.987082i | \(0.551218\pi\) | |||||||
\(440\) | −1.58185e9 | −0.885282 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1.97834e9 | −1.08974 | ||||||||
\(443\) | −2.26339e9 | −1.23693 | −0.618467 | − | 0.785811i | \(-0.712246\pi\) | ||||
−0.618467 | + | 0.785811i | \(0.712246\pi\) | |||||||
\(444\) | 3.00856e9 | 1.63124 | ||||||||
\(445\) | −4.04893e9 | −2.17811 | ||||||||
\(446\) | 3.76586e9 | 2.00998 | ||||||||
\(447\) | 1.52067e8 | 0.0805302 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 7.86592e8 | 0.410098 | 0.205049 | − | 0.978752i | \(-0.434265\pi\) | ||||
0.205049 | + | 0.978752i | \(0.434265\pi\) | |||||||
\(450\) | −2.98607e9 | −1.54474 | ||||||||
\(451\) | −5.24718e7 | −0.0269344 | ||||||||
\(452\) | 6.54875e9 | 3.33560 | ||||||||
\(453\) | −1.64149e9 | −0.829647 | ||||||||
\(454\) | −3.68790e9 | −1.84963 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1.86864e9 | −0.922888 | ||||||||
\(457\) | 1.14935e9 | 0.563310 | 0.281655 | − | 0.959516i | \(-0.409117\pi\) | ||||
0.281655 | + | 0.959516i | \(0.409117\pi\) | |||||||
\(458\) | −5.36545e9 | −2.60962 | ||||||||
\(459\) | 2.28964e8 | 0.110515 | ||||||||
\(460\) | −4.61860e9 | −2.21237 | ||||||||
\(461\) | −7.67125e8 | −0.364681 | −0.182340 | − | 0.983235i | \(-0.558367\pi\) | ||||
−0.182340 | + | 0.983235i | \(0.558367\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.43312e9 | 1.13928 | 0.569640 | − | 0.821894i | \(-0.307082\pi\) | ||||
0.569640 | + | 0.821894i | \(0.307082\pi\) | |||||||
\(464\) | 6.12190e9 | 2.84494 | ||||||||
\(465\) | −2.73050e9 | −1.25938 | ||||||||
\(466\) | 2.47829e9 | 1.13449 | ||||||||
\(467\) | 2.38932e9 | 1.08559 | 0.542794 | − | 0.839866i | \(-0.317366\pi\) | ||||
0.542794 | + | 0.839866i | \(0.317366\pi\) | |||||||
\(468\) | 1.95294e9 | 0.880703 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 8.69866e9 | 3.86465 | ||||||||
\(471\) | −1.52104e9 | −0.670759 | ||||||||
\(472\) | 1.05988e10 | 4.63940 | ||||||||
\(473\) | 4.22842e8 | 0.183723 | ||||||||
\(474\) | −1.01322e9 | −0.436999 | ||||||||
\(475\) | 2.83375e9 | 1.21320 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −6.76670e8 | −0.285471 | ||||||||
\(478\) | 1.91271e9 | 0.801034 | ||||||||
\(479\) | 2.23197e9 | 0.927927 | 0.463964 | − | 0.885854i | \(-0.346427\pi\) | ||||
0.463964 | + | 0.885854i | \(0.346427\pi\) | |||||||
\(480\) | −8.79005e9 | −3.62783 | ||||||||
\(481\) | 2.56399e9 | 1.05053 | ||||||||
\(482\) | 3.37148e9 | 1.37137 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −6.49941e9 | −2.60564 | ||||||||
\(485\) | −2.32161e9 | −0.924043 | ||||||||
\(486\) | −3.10815e8 | −0.122822 | ||||||||
\(487\) | 2.07827e8 | 0.0815361 | 0.0407681 | − | 0.999169i | \(-0.487020\pi\) | ||||
0.0407681 | + | 0.999169i | \(0.487020\pi\) | |||||||
\(488\) | −1.12526e10 | −4.38312 | ||||||||
\(489\) | 1.42214e9 | 0.549999 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.49013e9 | 0.568119 | 0.284060 | − | 0.958807i | \(-0.408319\pi\) | ||||
0.284060 | + | 0.958807i | \(0.408319\pi\) | |||||||
\(492\) | −7.29577e8 | −0.276181 | ||||||||
\(493\) | 1.26343e9 | 0.474885 | ||||||||
\(494\) | −2.54858e9 | −0.951161 | ||||||||
\(495\) | 2.49692e8 | 0.0925307 | ||||||||
\(496\) | −1.10268e10 | −4.05755 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −2.32865e9 | −0.844894 | ||||||||
\(499\) | 1.77157e9 | 0.638274 | 0.319137 | − | 0.947709i | \(-0.396607\pi\) | ||||
0.319137 | + | 0.947709i | \(0.396607\pi\) | |||||||
\(500\) | 1.95739e10 | 7.00298 | ||||||||
\(501\) | 5.60053e8 | 0.198974 | ||||||||
\(502\) | 2.32901e9 | 0.821691 | ||||||||
\(503\) | −2.60286e8 | −0.0911933 | −0.0455966 | − | 0.998960i | \(-0.514519\pi\) | ||||
−0.0455966 | + | 0.998960i | \(0.514519\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.42270e9 | −2.21921 | ||||||||
\(506\) | 3.75816e8 | 0.128958 | ||||||||
\(507\) | −2.98501e7 | −0.0101723 | ||||||||
\(508\) | −4.89849e9 | −1.65783 | ||||||||
\(509\) | 1.21248e9 | 0.407534 | 0.203767 | − | 0.979019i | \(-0.434682\pi\) | ||||
0.203767 | + | 0.979019i | \(0.434682\pi\) | |||||||
\(510\) | −3.51690e9 | −1.17399 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −2.17738e9 | −0.716951 | ||||||||
\(513\) | 2.94961e8 | 0.0964614 | ||||||||
\(514\) | 8.73333e9 | 2.83667 | ||||||||
\(515\) | 1.10776e10 | 3.57372 | ||||||||
\(516\) | 5.87927e9 | 1.88386 | ||||||||
\(517\) | −5.14720e8 | −0.163815 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3.51142e9 | 1.10255 | ||||||||
\(520\) | −1.87443e10 | −5.84597 | ||||||||
\(521\) | −2.57432e9 | −0.797499 | −0.398749 | − | 0.917060i | \(-0.630556\pi\) | ||||
−0.398749 | + | 0.917060i | \(0.630556\pi\) | |||||||
\(522\) | −1.71509e9 | −0.527766 | ||||||||
\(523\) | −2.72268e9 | −0.832226 | −0.416113 | − | 0.909313i | \(-0.636608\pi\) | ||||
−0.416113 | + | 0.909313i | \(0.636608\pi\) | |||||||
\(524\) | 6.21323e9 | 1.88650 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 5.92084e9 | 1.77392 | ||||||||
\(527\) | −2.27571e9 | −0.677298 | ||||||||
\(528\) | 1.00835e9 | 0.298121 | ||||||||
\(529\) | −2.71917e9 | −0.798623 | ||||||||
\(530\) | 1.03937e10 | 3.03253 | ||||||||
\(531\) | −1.67300e9 | −0.484916 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −6.21768e8 | −0.177862 | ||||||||
\(534\) | 4.58089e9 | 1.30183 | ||||||||
\(535\) | −1.14990e10 | −3.24656 | ||||||||
\(536\) | 8.08631e9 | 2.26816 | ||||||||
\(537\) | −4.14326e8 | −0.115460 | ||||||||
\(538\) | −2.24500e9 | −0.621552 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 3.47176e9 | 0.948793 | ||||||||
\(541\) | −1.54196e9 | −0.418681 | −0.209340 | − | 0.977843i | \(-0.567132\pi\) | ||||
−0.209340 | + | 0.977843i | \(0.567132\pi\) | |||||||
\(542\) | 4.29161e8 | 0.115777 | ||||||||
\(543\) | 1.89540e9 | 0.508044 | ||||||||
\(544\) | −7.32598e9 | −1.95106 | ||||||||
\(545\) | 5.11835e9 | 1.35438 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.49200e9 | −1.43475 | −0.717373 | − | 0.696689i | \(-0.754656\pi\) | ||||
−0.717373 | + | 0.696689i | \(0.754656\pi\) | |||||||
\(548\) | 8.36881e9 | 2.17236 | ||||||||
\(549\) | 1.77620e9 | 0.458130 | ||||||||
\(550\) | −2.71401e9 | −0.695571 | ||||||||
\(551\) | 1.62761e9 | 0.414495 | ||||||||
\(552\) | 3.26517e9 | 0.826263 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 7.71799e9 | 1.92850 | ||||||||
\(555\) | 4.55802e9 | 1.13175 | ||||||||
\(556\) | 4.04000e9 | 0.996827 | ||||||||
\(557\) | −6.14019e9 | −1.50553 | −0.752764 | − | 0.658291i | \(-0.771280\pi\) | ||||
−0.752764 | + | 0.658291i | \(0.771280\pi\) | |||||||
\(558\) | 3.08924e9 | 0.752718 | ||||||||
\(559\) | 5.01049e9 | 1.21322 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.08103e8 | 0.0497632 | ||||||||
\(562\) | 3.44994e8 | 0.0819851 | ||||||||
\(563\) | −3.24766e9 | −0.766993 | −0.383497 | − | 0.923542i | \(-0.625280\pi\) | ||||
−0.383497 | + | 0.923542i | \(0.625280\pi\) | |||||||
\(564\) | −7.15675e9 | −1.67973 | ||||||||
\(565\) | 9.92145e9 | 2.31422 | ||||||||
\(566\) | −1.04485e10 | −2.42213 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 5.64899e9 | 1.29346 | ||||||||
\(569\) | 2.01161e9 | 0.457774 | 0.228887 | − | 0.973453i | \(-0.426491\pi\) | ||||
0.228887 | + | 0.973453i | \(0.426491\pi\) | |||||||
\(570\) | −4.53062e9 | −1.02470 | ||||||||
\(571\) | −3.66896e9 | −0.824738 | −0.412369 | − | 0.911017i | \(-0.635299\pi\) | ||||
−0.412369 | + | 0.911017i | \(0.635299\pi\) | |||||||
\(572\) | 1.77501e9 | 0.396566 | ||||||||
\(573\) | 4.56600e9 | 1.01390 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.95155e9 | −1.08618 | ||||||||
\(576\) | 4.68539e9 | 1.02157 | ||||||||
\(577\) | 3.43622e9 | 0.744673 | 0.372337 | − | 0.928098i | \(-0.378557\pi\) | ||||
0.372337 | + | 0.928098i | \(0.378557\pi\) | |||||||
\(578\) | 5.95732e9 | 1.28323 | ||||||||
\(579\) | 2.69028e9 | 0.575999 | ||||||||
\(580\) | 1.91573e10 | 4.07697 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 2.62662e9 | 0.552290 | ||||||||
\(583\) | −6.15019e8 | −0.128543 | ||||||||
\(584\) | −2.14366e9 | −0.445360 | ||||||||
\(585\) | 2.95874e9 | 0.611028 | ||||||||
\(586\) | 9.60372e9 | 1.97150 | ||||||||
\(587\) | 8.47232e9 | 1.72890 | 0.864449 | − | 0.502721i | \(-0.167668\pi\) | ||||
0.864449 | + | 0.502721i | \(0.167668\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.93166e9 | −0.591168 | ||||||||
\(590\) | 2.56975e10 | 5.15120 | ||||||||
\(591\) | 4.67393e9 | 0.931379 | ||||||||
\(592\) | 1.84070e10 | 3.64634 | ||||||||
\(593\) | −9.58929e9 | −1.88840 | −0.944202 | − | 0.329367i | \(-0.893165\pi\) | ||||
−0.944202 | + | 0.329367i | \(0.893165\pi\) | |||||||
\(594\) | −2.82497e8 | −0.0553046 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1.92173e9 | 0.371818 | ||||||||
\(597\) | −2.54750e9 | −0.490009 | ||||||||
\(598\) | 4.45325e9 | 0.851576 | ||||||||
\(599\) | −3.16634e9 | −0.601955 | −0.300978 | − | 0.953631i | \(-0.597313\pi\) | ||||
−0.300978 | + | 0.953631i | \(0.597313\pi\) | |||||||
\(600\) | −2.35799e10 | −4.45669 | ||||||||
\(601\) | −5.32513e9 | −1.00062 | −0.500310 | − | 0.865846i | \(-0.666781\pi\) | ||||
−0.500310 | + | 0.865846i | \(0.666781\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.27641e9 | −0.237071 | ||||||||
\(604\) | −2.07441e10 | −3.83058 | ||||||||
\(605\) | −9.84669e9 | −1.80778 | ||||||||
\(606\) | 7.26653e9 | 1.32639 | ||||||||
\(607\) | −5.32039e9 | −0.965569 | −0.482785 | − | 0.875739i | \(-0.660375\pi\) | ||||
−0.482785 | + | 0.875739i | \(0.660375\pi\) | |||||||
\(608\) | −9.43764e9 | −1.70295 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −2.72825e10 | −4.86665 | ||||||||
\(611\) | −6.09921e9 | −1.08176 | ||||||||
\(612\) | 2.89350e9 | 0.510263 | ||||||||
\(613\) | −6.15195e9 | −1.07870 | −0.539351 | − | 0.842081i | \(-0.681330\pi\) | ||||
−0.539351 | + | 0.842081i | \(0.681330\pi\) | |||||||
\(614\) | −1.68038e9 | −0.292967 | ||||||||
\(615\) | −1.10532e9 | −0.191613 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −4.29619e9 | −0.736352 | −0.368176 | − | 0.929756i | \(-0.620018\pi\) | ||||
−0.368176 | + | 0.929756i | \(0.620018\pi\) | |||||||
\(618\) | −1.25330e10 | −2.13597 | ||||||||
\(619\) | −3.90151e9 | −0.661173 | −0.330587 | − | 0.943776i | \(-0.607247\pi\) | ||||
−0.330587 | + | 0.943776i | \(0.607247\pi\) | |||||||
\(620\) | −3.45064e10 | −5.81471 | ||||||||
\(621\) | −5.15399e8 | −0.0863621 | ||||||||
\(622\) | 9.58804e9 | 1.59758 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 1.19485e10 | 1.96865 | ||||||||
\(625\) | 1.48815e10 | 2.43818 | ||||||||
\(626\) | −1.21958e10 | −1.98702 | ||||||||
\(627\) | 2.68087e8 | 0.0434350 | ||||||||
\(628\) | −1.92219e10 | −3.09698 | ||||||||
\(629\) | 3.79884e9 | 0.608658 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.79183e9 | 0.917726 | 0.458863 | − | 0.888507i | \(-0.348257\pi\) | ||||
0.458863 | + | 0.888507i | \(0.348257\pi\) | |||||||
\(632\) | −8.00104e9 | −1.26077 | ||||||||
\(633\) | −1.38637e8 | −0.0217254 | ||||||||
\(634\) | 1.65394e10 | 2.57755 | ||||||||
\(635\) | −7.42129e9 | −1.15019 | ||||||||
\(636\) | −8.55133e9 | −1.31806 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −1.55883e9 | −0.237644 | ||||||||
\(639\) | −8.91680e8 | −0.135194 | ||||||||
\(640\) | −3.02966e10 | −4.56839 | ||||||||
\(641\) | 3.31891e9 | 0.497729 | 0.248864 | − | 0.968538i | \(-0.419943\pi\) | ||||
0.248864 | + | 0.968538i | \(0.419943\pi\) | |||||||
\(642\) | 1.30098e10 | 1.94043 | ||||||||
\(643\) | −1.23513e10 | −1.83220 | −0.916100 | − | 0.400949i | \(-0.868681\pi\) | ||||
−0.916100 | + | 0.400949i | \(0.868681\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 8.90718e9 | 1.30702 | ||||||||
\(646\) | −3.77600e9 | −0.551085 | ||||||||
\(647\) | 8.67679e9 | 1.25949 | 0.629744 | − | 0.776802i | \(-0.283160\pi\) | ||||
0.629744 | + | 0.776802i | \(0.283160\pi\) | |||||||
\(648\) | −2.45439e9 | −0.354349 | ||||||||
\(649\) | −1.52058e9 | −0.218350 | ||||||||
\(650\) | −3.21598e10 | −4.59321 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1.79722e10 | 2.53941 | ||||||||
\(653\) | −5.08215e9 | −0.714251 | −0.357126 | − | 0.934056i | \(-0.616243\pi\) | ||||
−0.357126 | + | 0.934056i | \(0.616243\pi\) | |||||||
\(654\) | −5.79081e9 | −0.809500 | ||||||||
\(655\) | 9.41313e9 | 1.30885 | ||||||||
\(656\) | −4.46371e9 | −0.617351 | ||||||||
\(657\) | 3.38372e8 | 0.0465496 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 7.83208e9 | 1.06605 | 0.533026 | − | 0.846099i | \(-0.321055\pi\) | ||||
0.533026 | + | 0.846099i | \(0.321055\pi\) | |||||||
\(660\) | 3.15545e9 | 0.427226 | ||||||||
\(661\) | −6.36676e9 | −0.857459 | −0.428729 | − | 0.903433i | \(-0.641039\pi\) | ||||
−0.428729 | + | 0.903433i | \(0.641039\pi\) | |||||||
\(662\) | −9.28590e9 | −1.24400 | ||||||||
\(663\) | 2.46593e9 | 0.328612 | ||||||||
\(664\) | −1.83885e10 | −2.43758 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −5.15686e9 | −0.676434 | ||||||||
\(667\) | −2.84400e9 | −0.371098 | ||||||||
\(668\) | 7.07760e9 | 0.918689 | ||||||||
\(669\) | −4.69402e9 | −0.606113 | ||||||||
\(670\) | 1.96057e10 | 2.51837 | ||||||||
\(671\) | 1.61437e9 | 0.206288 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.11438e10 | 1.40923 | 0.704615 | − | 0.709590i | \(-0.251120\pi\) | ||||
0.704615 | + | 0.709590i | \(0.251120\pi\) | |||||||
\(674\) | −1.63785e10 | −2.06046 | ||||||||
\(675\) | 3.72203e9 | 0.465818 | ||||||||
\(676\) | −3.77226e8 | −0.0469665 | ||||||||
\(677\) | −7.73190e9 | −0.957693 | −0.478846 | − | 0.877899i | \(-0.658945\pi\) | ||||
−0.478846 | + | 0.877899i | \(0.658945\pi\) | |||||||
\(678\) | −1.12250e10 | −1.38319 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −2.77717e10 | −3.38705 | ||||||||
\(681\) | 4.59684e9 | 0.557757 | ||||||||
\(682\) | 2.80778e9 | 0.338936 | ||||||||
\(683\) | 3.26590e9 | 0.392220 | 0.196110 | − | 0.980582i | \(-0.437169\pi\) | ||||
0.196110 | + | 0.980582i | \(0.437169\pi\) | |||||||
\(684\) | 3.72753e9 | 0.445374 | ||||||||
\(685\) | 1.26789e10 | 1.50717 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 6.68785e9 | 0.786933 | ||||||||
\(688\) | 3.59706e10 | 4.21103 | ||||||||
\(689\) | −7.28771e9 | −0.848836 | ||||||||
\(690\) | 7.91657e9 | 0.917413 | ||||||||
\(691\) | −1.44199e10 | −1.66261 | −0.831303 | − | 0.555819i | \(-0.812405\pi\) | ||||
−0.831303 | + | 0.555819i | \(0.812405\pi\) | |||||||
\(692\) | 4.43752e10 | 5.09060 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −2.32331e10 | −2.63845 | ||||||||
\(695\) | 6.12066e9 | 0.691594 | ||||||||
\(696\) | −1.35435e10 | −1.52264 | ||||||||
\(697\) | −9.21218e8 | −0.103050 | ||||||||
\(698\) | 1.74990e10 | 1.94769 | ||||||||
\(699\) | −3.08911e9 | −0.342108 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.37465e9 | 0.150723 | 0.0753615 | − | 0.997156i | \(-0.475989\pi\) | ||||
0.0753615 | + | 0.997156i | \(0.475989\pi\) | |||||||
\(702\) | −3.34747e9 | −0.365205 | ||||||||
\(703\) | 4.89382e9 | 0.531257 | ||||||||
\(704\) | 4.25851e9 | 0.459995 | ||||||||
\(705\) | −1.08426e10 | −1.16539 | ||||||||
\(706\) | −7.63862e9 | −0.816955 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −2.11424e10 | −2.23892 | ||||||||
\(709\) | −1.41543e10 | −1.49151 | −0.745753 | − | 0.666222i | \(-0.767910\pi\) | ||||
−0.745753 | + | 0.666222i | \(0.767910\pi\) | |||||||
\(710\) | 1.36963e10 | 1.43614 | ||||||||
\(711\) | 1.26295e9 | 0.131777 | ||||||||
\(712\) | 3.61736e10 | 3.75588 | ||||||||
\(713\) | 5.12263e9 | 0.529273 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.68917e9 | 0.275136 | ||||||||
\(716\) | −5.23599e9 | −0.533094 | ||||||||
\(717\) | −2.38413e9 | −0.241553 | ||||||||
\(718\) | −1.02559e10 | −1.03404 | ||||||||
\(719\) | −6.64223e9 | −0.666442 | −0.333221 | − | 0.942849i | \(-0.608136\pi\) | ||||
−0.333221 | + | 0.942849i | \(0.608136\pi\) | |||||||
\(720\) | 2.12409e10 | 2.12085 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 1.44980e10 | 1.43360 | ||||||||
\(723\) | −4.20243e9 | −0.413539 | ||||||||
\(724\) | 2.39529e10 | 2.34570 | ||||||||
\(725\) | 2.05383e10 | 2.00162 | ||||||||
\(726\) | 1.11404e10 | 1.08049 | ||||||||
\(727\) | −7.79081e9 | −0.751990 | −0.375995 | − | 0.926622i | \(-0.622699\pi\) | ||||
−0.375995 | + | 0.926622i | \(0.622699\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 3.87420e8 | 0.0370370 | ||||||||
\(730\) | −5.19742e9 | −0.494490 | ||||||||
\(731\) | 7.42360e9 | 0.702916 | ||||||||
\(732\) | 2.24465e10 | 2.11524 | ||||||||
\(733\) | 1.92152e10 | 1.80210 | 0.901052 | − | 0.433711i | \(-0.142796\pi\) | ||||
0.901052 | + | 0.433711i | \(0.142796\pi\) | |||||||
\(734\) | −2.11091e10 | −1.97031 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.64908e10 | 1.52465 | ||||||||
\(737\) | −1.16011e9 | −0.106749 | ||||||||
\(738\) | 1.25054e9 | 0.114525 | ||||||||
\(739\) | −1.13260e10 | −1.03233 | −0.516166 | − | 0.856489i | \(-0.672641\pi\) | ||||
−0.516166 | + | 0.856489i | \(0.672641\pi\) | |||||||
\(740\) | 5.76014e10 | 5.22543 | ||||||||
\(741\) | 3.17672e9 | 0.286824 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −9.10743e9 | −0.814582 | −0.407291 | − | 0.913298i | \(-0.633527\pi\) | ||||
−0.407291 | + | 0.913298i | \(0.633527\pi\) | |||||||
\(744\) | 2.43946e10 | 2.17164 | ||||||||
\(745\) | 2.91145e9 | 0.257966 | ||||||||
\(746\) | −1.25664e10 | −1.10822 | ||||||||
\(747\) | 2.90259e9 | 0.254779 | ||||||||
\(748\) | 2.62988e9 | 0.229763 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −3.35509e10 | −2.90396 | ||||||||
\(751\) | 1.65376e9 | 0.142473 | 0.0712365 | − | 0.997459i | \(-0.477305\pi\) | ||||
0.0712365 | + | 0.997459i | \(0.477305\pi\) | |||||||
\(752\) | −4.37865e10 | −3.75472 | ||||||||
\(753\) | −2.90303e9 | −0.247782 | ||||||||
\(754\) | −1.84715e10 | −1.56929 | ||||||||
\(755\) | −3.14276e10 | −2.65764 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.48318e10 | 1.24268 | 0.621338 | − | 0.783543i | \(-0.286590\pi\) | ||||
0.621338 | + | 0.783543i | \(0.286590\pi\) | |||||||
\(758\) | 1.10687e10 | 0.923111 | ||||||||
\(759\) | −4.68441e8 | −0.0388874 | ||||||||
\(760\) | −3.57767e10 | −2.95632 | ||||||||
\(761\) | 2.80637e9 | 0.230833 | 0.115417 | − | 0.993317i | \(-0.463180\pi\) | ||||
0.115417 | + | 0.993317i | \(0.463180\pi\) | |||||||
\(762\) | 8.39631e9 | 0.687458 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 5.77023e10 | 4.68130 | ||||||||
\(765\) | 4.38370e9 | 0.354018 | ||||||||
\(766\) | 5.13115e7 | 0.00412490 | ||||||||
\(767\) | −1.80182e10 | −1.44187 | ||||||||
\(768\) | 1.20648e10 | 0.961070 | ||||||||
\(769\) | −1.56499e10 | −1.24099 | −0.620496 | − | 0.784210i | \(-0.713068\pi\) | ||||
−0.620496 | + | 0.784210i | \(0.713068\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.08858e10 | −0.855402 | ||||||||
\(772\) | 3.39980e10 | 2.65946 | ||||||||
\(773\) | 4.08905e9 | 0.318416 | 0.159208 | − | 0.987245i | \(-0.449106\pi\) | ||||
0.159208 | + | 0.987245i | \(0.449106\pi\) | |||||||
\(774\) | −1.00774e10 | −0.781189 | ||||||||
\(775\) | −3.69938e10 | −2.85479 | ||||||||
\(776\) | 2.07415e10 | 1.59340 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 2.91045e10 | 2.21580 | ||||||||
\(779\) | −1.18675e9 | −0.0899454 | ||||||||
\(780\) | 3.73907e10 | 2.82119 | ||||||||
\(781\) | −8.10440e8 | −0.0608754 | ||||||||
\(782\) | 6.59798e9 | 0.493387 | ||||||||
\(783\) | 2.13781e9 | 0.159148 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2.91215e10 | −2.14867 | ||||||||
\(786\) | −1.06499e10 | −0.782284 | ||||||||
\(787\) | −2.52055e10 | −1.84325 | −0.921623 | − | 0.388087i | \(-0.873136\pi\) | ||||
−0.921623 | + | 0.388087i | \(0.873136\pi\) | |||||||
\(788\) | 5.90662e10 | 4.30029 | ||||||||
\(789\) | −7.38012e9 | −0.534926 | ||||||||
\(790\) | −1.93989e10 | −1.39986 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −2.23078e9 | −0.159558 | ||||||||
\(793\) | 1.91296e10 | 1.36223 | ||||||||
\(794\) | 1.81107e10 | 1.28399 | ||||||||
\(795\) | −1.29554e10 | −0.914462 | ||||||||
\(796\) | −3.21937e10 | −2.26243 | ||||||||
\(797\) | −6.07194e9 | −0.424838 | −0.212419 | − | 0.977179i | \(-0.568134\pi\) | ||||
−0.212419 | + | 0.977179i | \(0.568134\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −9.03665e9 | −0.626749 | ||||||||
\(800\) | −1.19091e11 | −8.22363 | ||||||||
\(801\) | −5.70992e9 | −0.392569 | ||||||||
\(802\) | 5.23573e9 | 0.358399 | ||||||||
\(803\) | 3.07543e8 | 0.0209605 | ||||||||
\(804\) | −1.61304e10 | −1.09459 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 3.32710e10 | 2.23817 | ||||||||
\(807\) | 2.79831e9 | 0.187430 | ||||||||
\(808\) | 5.73811e10 | 3.82674 | ||||||||
\(809\) | 2.26249e10 | 1.50234 | 0.751168 | − | 0.660111i | \(-0.229491\pi\) | ||||
0.751168 | + | 0.660111i | \(0.229491\pi\) | |||||||
\(810\) | −5.95081e9 | −0.393440 | ||||||||
\(811\) | 1.70292e10 | 1.12104 | 0.560520 | − | 0.828141i | \(-0.310601\pi\) | ||||
0.560520 | + | 0.828141i | \(0.310601\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −5.34935e8 | −0.0349127 | ||||||||
\(814\) | −4.68702e9 | −0.304587 | ||||||||
\(815\) | 2.72281e10 | 1.76184 | ||||||||
\(816\) | 1.77031e10 | 1.14060 | ||||||||
\(817\) | 9.56339e9 | 0.613528 | ||||||||
\(818\) | −5.79222e9 | −0.370006 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.39683e10 | −0.884701 | ||||||||
\(821\) | −2.99513e10 | −1.88893 | −0.944463 | − | 0.328617i | \(-0.893418\pi\) | ||||
−0.944463 | + | 0.328617i | \(0.893418\pi\) | |||||||
\(822\) | −1.43447e10 | −0.900822 | ||||||||
\(823\) | −1.10149e10 | −0.688782 | −0.344391 | − | 0.938826i | \(-0.611915\pi\) | ||||
−0.344391 | + | 0.938826i | \(0.611915\pi\) | |||||||
\(824\) | −9.89685e10 | −6.16243 | ||||||||
\(825\) | 3.38292e9 | 0.209750 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.67625e10 | −1.03055 | −0.515276 | − | 0.857024i | \(-0.672311\pi\) | ||||
−0.515276 | + | 0.857024i | \(0.672311\pi\) | |||||||
\(828\) | −6.51329e9 | −0.398744 | ||||||||
\(829\) | 3.00024e10 | 1.82901 | 0.914504 | − | 0.404577i | \(-0.132581\pi\) | ||||
0.914504 | + | 0.404577i | \(0.132581\pi\) | |||||||
\(830\) | −4.45840e10 | −2.70648 | ||||||||
\(831\) | −9.62022e9 | −0.581542 | ||||||||
\(832\) | 5.04615e10 | 3.03758 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −6.92481e9 | −0.413358 | ||||||||
\(835\) | 1.07227e10 | 0.637383 | ||||||||
\(836\) | 3.38792e9 | 0.200545 | ||||||||
\(837\) | −3.85063e9 | −0.226983 | ||||||||
\(838\) | 3.45754e10 | 2.02961 | ||||||||
\(839\) | −2.30538e10 | −1.34764 | −0.673821 | − | 0.738894i | \(-0.735348\pi\) | ||||
−0.673821 | + | 0.738894i | \(0.735348\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −5.45335e9 | −0.316139 | ||||||||
\(842\) | 4.10791e10 | 2.37153 | ||||||||
\(843\) | −4.30024e8 | −0.0247227 | ||||||||
\(844\) | −1.75201e9 | −0.100309 | ||||||||
\(845\) | −5.71503e8 | −0.0325852 | ||||||||
\(846\) | 1.22671e10 | 0.696540 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −5.23188e10 | −2.94627 | ||||||||
\(849\) | 1.30237e10 | 0.730397 | ||||||||
\(850\) | −4.76483e10 | −2.66122 | ||||||||
\(851\) | −8.55120e9 | −0.475635 | ||||||||
\(852\) | −1.12685e10 | −0.624205 | ||||||||
\(853\) | −5.09026e9 | −0.280814 | −0.140407 | − | 0.990094i | \(-0.544841\pi\) | ||||
−0.140407 | + | 0.990094i | \(0.544841\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 5.64726e9 | 0.308999 | ||||||||
\(856\) | 1.02734e11 | 5.59829 | ||||||||
\(857\) | −1.39679e10 | −0.758052 | −0.379026 | − | 0.925386i | \(-0.623741\pi\) | ||||
−0.379026 | + | 0.925386i | \(0.623741\pi\) | |||||||
\(858\) | −3.04248e9 | −0.164446 | ||||||||
\(859\) | −2.23443e10 | −1.20279 | −0.601396 | − | 0.798951i | \(-0.705389\pi\) | ||||
−0.601396 | + | 0.798951i | \(0.705389\pi\) | |||||||
\(860\) | 1.12563e11 | 6.03465 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 9.09602e9 | 0.483700 | ||||||||
\(863\) | −6.66234e9 | −0.352849 | −0.176425 | − | 0.984314i | \(-0.556453\pi\) | ||||
−0.176425 | + | 0.984314i | \(0.556453\pi\) | |||||||
\(864\) | −1.23960e10 | −0.653858 | ||||||||
\(865\) | 6.72290e10 | 3.53183 | ||||||||
\(866\) | −5.18322e10 | −2.71198 | ||||||||
\(867\) | −7.42559e9 | −0.386958 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.14788e9 | 0.0593372 | ||||||||
\(870\) | −3.28369e10 | −1.69061 | ||||||||
\(871\) | −1.37468e10 | −0.704920 | ||||||||
\(872\) | −4.57279e10 | −2.33547 | ||||||||
\(873\) | −3.27400e9 | −0.166544 | ||||||||
\(874\) | 8.49980e9 | 0.430644 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 4.27614e9 | 0.214925 | ||||||||
\(877\) | −2.98982e10 | −1.49674 | −0.748370 | − | 0.663282i | \(-0.769163\pi\) | ||||
−0.748370 | + | 0.663282i | \(0.769163\pi\) | |||||||
\(878\) | 1.23037e10 | 0.613487 | ||||||||
\(879\) | −1.19707e10 | −0.594510 | ||||||||
\(880\) | 1.93057e10 | 0.954984 | ||||||||
\(881\) | 1.24713e10 | 0.614466 | 0.307233 | − | 0.951634i | \(-0.400597\pi\) | ||||
0.307233 | + | 0.951634i | \(0.400597\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.37548e10 | 0.672345 | 0.336173 | − | 0.941800i | \(-0.390867\pi\) | ||||
0.336173 | + | 0.941800i | \(0.390867\pi\) | |||||||
\(884\) | 3.11629e10 | 1.51724 | ||||||||
\(885\) | −3.20310e10 | −1.55335 | ||||||||
\(886\) | 4.90278e10 | 2.36823 | ||||||||
\(887\) | 3.13536e10 | 1.50853 | 0.754265 | − | 0.656570i | \(-0.227993\pi\) | ||||
0.754265 | + | 0.656570i | \(0.227993\pi\) | |||||||
\(888\) | −4.07219e10 | −1.95156 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 8.77048e10 | 4.17021 | ||||||||
\(891\) | 3.52123e8 | 0.0166772 | ||||||||
\(892\) | −5.93201e10 | −2.79850 | ||||||||
\(893\) | −1.16414e10 | −0.547047 | ||||||||
\(894\) | −3.29396e9 | −0.154183 | ||||||||
\(895\) | −7.93261e9 | −0.369858 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −5.55083e9 | −0.256794 | ||||||||
\(898\) | −1.70386e10 | −0.785174 | ||||||||
\(899\) | −2.12480e10 | −0.975347 | ||||||||
\(900\) | 4.70367e10 | 2.15074 | ||||||||
\(901\) | −1.07975e10 | −0.491800 | ||||||||
\(902\) | 1.13660e9 | 0.0515687 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −8.86394e10 | −3.99059 | ||||||||
\(905\) | 3.62890e10 | 1.62744 | ||||||||
\(906\) | 3.55566e10 | 1.58844 | ||||||||
\(907\) | −1.12062e9 | −0.0498694 | −0.0249347 | − | 0.999689i | \(-0.507938\pi\) | ||||
−0.0249347 | + | 0.999689i | \(0.507938\pi\) | |||||||
\(908\) | 5.80920e10 | 2.57523 | ||||||||
\(909\) | −9.05748e9 | −0.399976 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3.97792e10 | −1.74318 | −0.871589 | − | 0.490238i | \(-0.836910\pi\) | ||||
−0.871589 | + | 0.490238i | \(0.836910\pi\) | |||||||
\(912\) | 2.28058e10 | 0.995552 | ||||||||
\(913\) | 2.63814e9 | 0.114723 | ||||||||
\(914\) | −2.48964e10 | −1.07851 | ||||||||
\(915\) | 3.40068e10 | 1.46754 | ||||||||
\(916\) | 8.45169e10 | 3.63337 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −4.95964e9 | −0.211593 | ||||||||
\(919\) | −1.44290e10 | −0.613244 | −0.306622 | − | 0.951831i | \(-0.599199\pi\) | ||||
−0.306622 | + | 0.951831i | \(0.599199\pi\) | |||||||
\(920\) | 6.25142e10 | 2.64680 | ||||||||
\(921\) | 2.09454e9 | 0.0883446 | ||||||||
\(922\) | 1.66169e10 | 0.698218 | ||||||||
\(923\) | −9.60336e9 | −0.401992 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.17537e10 | 2.56547 | ||||||||
\(926\) | −5.27045e10 | −2.18127 | ||||||||
\(927\) | 1.56220e10 | 0.644105 | ||||||||
\(928\) | −6.84018e10 | −2.80963 | ||||||||
\(929\) | 2.66062e10 | 1.08875 | 0.544374 | − | 0.838842i | \(-0.316767\pi\) | ||||
0.544374 | + | 0.838842i | \(0.316767\pi\) | |||||||
\(930\) | 5.91460e10 | 2.41121 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −3.90382e10 | −1.57955 | ||||||||
\(933\) | −1.19512e10 | −0.481753 | ||||||||
\(934\) | −5.17556e10 | −2.07847 | ||||||||
\(935\) | 3.98430e9 | 0.159409 | ||||||||
\(936\) | −2.64337e10 | −1.05364 | ||||||||
\(937\) | 4.46208e10 | 1.77194 | 0.885970 | − | 0.463742i | \(-0.153494\pi\) | ||||
0.885970 | + | 0.463742i | \(0.153494\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.52017e10 | 0.599188 | ||||||||
\(940\) | −1.37022e11 | −5.38074 | ||||||||
\(941\) | 4.28359e9 | 0.167588 | 0.0837942 | − | 0.996483i | \(-0.473296\pi\) | ||||
0.0837942 | + | 0.996483i | \(0.473296\pi\) | |||||||
\(942\) | 3.29475e10 | 1.28424 | ||||||||
\(943\) | 2.07367e9 | 0.0805282 | ||||||||
\(944\) | −1.29354e11 | −5.00468 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −9.15928e9 | −0.351757 | ||||||||
\(947\) | 1.78755e9 | 0.0683965 | 0.0341982 | − | 0.999415i | \(-0.489112\pi\) | ||||
0.0341982 | + | 0.999415i | \(0.489112\pi\) | |||||||
\(948\) | 1.59603e10 | 0.608433 | ||||||||
\(949\) | 3.64425e9 | 0.138413 | ||||||||
\(950\) | −6.13825e10 | −2.32280 | ||||||||
\(951\) | −2.06158e10 | −0.777264 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.13652e10 | −0.425356 | −0.212678 | − | 0.977122i | \(-0.568219\pi\) | ||||
−0.212678 | + | 0.977122i | \(0.568219\pi\) | |||||||
\(954\) | 1.46575e10 | 0.546564 | ||||||||
\(955\) | 8.74198e10 | 3.24787 | ||||||||
\(956\) | −3.01291e10 | −1.11528 | ||||||||
\(957\) | 1.94303e9 | 0.0716619 | ||||||||
\(958\) | −4.83472e10 | −1.77661 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 8.97056e10 | 3.27243 | ||||||||
\(961\) | 1.07595e10 | 0.391074 | ||||||||
\(962\) | −5.55392e10 | −2.01135 | ||||||||
\(963\) | −1.62163e10 | −0.585140 | ||||||||
\(964\) | −5.31077e10 | −1.90936 | ||||||||
\(965\) | 5.15075e10 | 1.84512 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.31418e10 | 1.53428 | 0.767141 | − | 0.641478i | \(-0.221678\pi\) | ||||
0.767141 | + | 0.641478i | \(0.221678\pi\) | |||||||
\(968\) | 8.79715e10 | 3.11730 | ||||||||
\(969\) | 4.70666e9 | 0.166180 | ||||||||
\(970\) | 5.02888e10 | 1.76917 | ||||||||
\(971\) | −1.88022e10 | −0.659086 | −0.329543 | − | 0.944141i | \(-0.606895\pi\) | ||||
−0.329543 | + | 0.944141i | \(0.606895\pi\) | |||||||
\(972\) | 4.89598e9 | 0.171005 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −4.50179e9 | −0.156109 | ||||||||
\(975\) | 4.00861e10 | 1.38509 | ||||||||
\(976\) | 1.37332e11 | 4.72823 | ||||||||
\(977\) | −2.32046e9 | −0.0796056 | −0.0398028 | − | 0.999208i | \(-0.512673\pi\) | ||||
−0.0398028 | + | 0.999208i | \(0.512673\pi\) | |||||||
\(978\) | −3.08054e10 | −1.05303 | ||||||||
\(979\) | −5.18969e9 | −0.176767 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 7.21805e9 | 0.244106 | ||||||||
\(982\) | −3.22781e10 | −1.08772 | ||||||||
\(983\) | −2.43379e10 | −0.817233 | −0.408616 | − | 0.912706i | \(-0.633989\pi\) | ||||
−0.408616 | + | 0.912706i | \(0.633989\pi\) | |||||||
\(984\) | 9.87506e9 | 0.330413 | ||||||||
\(985\) | 8.94862e10 | 2.98352 | ||||||||
\(986\) | −2.73676e10 | −0.909215 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 4.01454e10 | 1.32430 | ||||||||
\(989\) | −1.67106e10 | −0.549293 | ||||||||
\(990\) | −5.40863e9 | −0.177159 | ||||||||
\(991\) | −2.72855e10 | −0.890582 | −0.445291 | − | 0.895386i | \(-0.646900\pi\) | ||||
−0.445291 | + | 0.895386i | \(0.646900\pi\) | |||||||
\(992\) | 1.23206e11 | 4.00719 | ||||||||
\(993\) | 1.15746e10 | 0.375130 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −4.87739e10 | −1.56966 | ||||||||
\(996\) | 3.66811e10 | 1.17635 | ||||||||
\(997\) | −1.81964e9 | −0.0581503 | −0.0290751 | − | 0.999577i | \(-0.509256\pi\) | ||||
−0.0290751 | + | 0.999577i | \(0.509256\pi\) | |||||||
\(998\) | −3.83744e10 | −1.22204 | ||||||||
\(999\) | 6.42785e9 | 0.203980 |
(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 | 147.8.a.g.1.1 | yes | 4 | |
3.2 | odd | 2 | 441.8.a.u.1.4 | 4 | |||
7.2 | even | 3 | 147.8.e.l.67.4 | 8 | |||
7.3 | odd | 6 | 147.8.e.m.79.4 | 8 | |||
7.4 | even | 3 | 147.8.e.l.79.4 | 8 | |||
7.5 | odd | 6 | 147.8.e.m.67.4 | 8 | |||
7.6 | odd | 2 | 147.8.a.f.1.1 | ✓ | 4 | ||
21.20 | even | 2 | 441.8.a.v.1.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
147.8.a.f.1.1 | ✓ | 4 | 7.6 | odd | 2 | ||
147.8.a.g.1.1 | yes | 4 | 1.1 | even | 1 | trivial | |
147.8.e.l.67.4 | 8 | 7.2 | even | 3 | |||
147.8.e.l.79.4 | 8 | 7.4 | even | 3 | |||
147.8.e.m.67.4 | 8 | 7.5 | odd | 6 | |||
147.8.e.m.79.4 | 8 | 7.3 | odd | 6 | |||
441.8.a.u.1.4 | 4 | 3.2 | odd | 2 | |||
441.8.a.v.1.4 | 4 | 21.20 | even | 2 |