Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8,18,Mod(1,8)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 18, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8.1");
S:= CuspForms(chi, 18);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8 = 2^{3} \) |
Weight: | \( k \) | \(=\) | \( 18 \) |
Character orbit: | \([\chi]\) | \(=\) | 8.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: | \(14.6577669876\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{114}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 114 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{7}\cdot 3^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(10.6771\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 18096.0 | 1.59240 | 0.796199 | − | 0.605034i | \(-0.206841\pi\) | ||||
0.796199 | + | 0.605034i | \(0.206841\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.23236e6 | −1.41089 | −0.705445 | − | 0.708765i | \(-0.749253\pi\) | ||||
−0.705445 | + | 0.708765i | \(0.749253\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.89249e7 | −1.89644 | −0.948218 | − | 0.317619i | \(-0.897117\pi\) | ||||
−0.948218 | + | 0.317619i | \(0.897117\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.98325e8 | 1.53573 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.61694e8 | −0.508749 | −0.254375 | − | 0.967106i | \(-0.581870\pi\) | ||||
−0.254375 | + | 0.967106i | \(0.581870\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.37402e8 | −0.216718 | −0.108359 | − | 0.994112i | \(-0.534560\pi\) | ||||
−0.108359 | + | 0.994112i | \(0.534560\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.23008e10 | −2.24670 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −7.41238e9 | −0.257716 | −0.128858 | − | 0.991663i | \(-0.541131\pi\) | ||||
−0.128858 | + | 0.991663i | \(0.541131\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.55981e10 | 0.480863 | 0.240432 | − | 0.970666i | \(-0.422711\pi\) | ||||
0.240432 | + | 0.970666i | \(0.422711\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −5.23425e11 | −3.01988 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.46782e11 | −0.657094 | −0.328547 | − | 0.944488i | \(-0.606559\pi\) | ||||
−0.328547 | + | 0.944488i | \(0.606559\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 7.55776e11 | 0.990610 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.25197e12 | 0.853101 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.56479e12 | 0.580863 | 0.290432 | − | 0.956896i | \(-0.406201\pi\) | ||||
0.290432 | + | 0.956896i | \(0.406201\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.13491e12 | 0.449578 | 0.224789 | − | 0.974407i | \(-0.427831\pi\) | ||||
0.224789 | + | 0.974407i | \(0.427831\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −6.54522e12 | −0.810132 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.56459e13 | 2.67566 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.10238e13 | −1.45205 | −0.726023 | − | 0.687671i | \(-0.758633\pi\) | ||||
−0.726023 | + | 0.687671i | \(0.758633\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.15344e13 | −0.345101 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.09452e13 | −0.409658 | −0.204829 | − | 0.978798i | \(-0.565664\pi\) | ||||
−0.204829 | + | 0.978798i | \(0.565664\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.04137e13 | −1.04918 | −0.524588 | − | 0.851356i | \(-0.675781\pi\) | ||||
−0.524588 | + | 0.851356i | \(0.675781\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.44408e14 | −2.16675 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.25613e14 | 1.38208 | 0.691039 | − | 0.722818i | \(-0.257153\pi\) | ||||
0.691039 | + | 0.722818i | \(0.257153\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.04019e14 | 2.59647 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.34134e14 | −0.410387 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.86376e14 | −1.29369 | −0.646847 | − | 0.762620i | \(-0.723913\pi\) | ||||
−0.646847 | + | 0.762620i | \(0.723913\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.45738e14 | 0.717789 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6.44184e14 | 0.765726 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.67491e14 | 0.503172 | 0.251586 | − | 0.967835i | \(-0.419048\pi\) | ||||
0.251586 | + | 0.967835i | \(0.419048\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.28400e15 | 1.52543 | 0.762714 | − | 0.646736i | \(-0.223866\pi\) | ||||
0.762714 | + | 0.646736i | \(0.223866\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −5.73652e15 | −2.91242 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 7.85509e14 | 0.305765 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.97400e15 | −1.19562 | −0.597808 | − | 0.801639i | \(-0.703962\pi\) | ||||
−0.597808 | + | 0.801639i | \(0.703962\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −4.46577e15 | −1.04635 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.20052e15 | 0.955765 | 0.477882 | − | 0.878424i | \(-0.341405\pi\) | ||||
0.477882 | + | 0.878424i | \(0.341405\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.41800e15 | −0.786311 | −0.393156 | − | 0.919472i | \(-0.628617\pi\) | ||||
−0.393156 | + | 0.919472i | \(0.628617\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.36765e16 | 1.57745 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.04620e16 | 0.964811 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.80248e15 | 0.133672 | 0.0668358 | − | 0.997764i | \(-0.478710\pi\) | ||||
0.0668358 | + | 0.997764i | \(0.478710\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −2.95614e15 | −0.177257 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −6.04601e15 | −0.294649 | −0.147325 | − | 0.989088i | \(-0.547066\pi\) | ||||
−0.147325 | + | 0.989088i | \(0.547066\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 9.13474e15 | 0.363610 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.83165e16 | 0.924966 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.62804e16 | −1.51545 | −0.757726 | − | 0.652573i | \(-0.773690\pi\) | ||||
−0.757726 | + | 0.652573i | \(0.773690\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.84368e16 | 0.410992 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3.86333e16 | 0.715907 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.38698e16 | −0.678445 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.44249e17 | −1.86875 | −0.934377 | − | 0.356287i | \(-0.884043\pi\) | ||||
−0.934377 | + | 0.356287i | \(0.884043\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −7.17330e16 | −0.781303 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −9.49032e16 | −0.872066 | −0.436033 | − | 0.899931i | \(-0.643617\pi\) | ||||
−0.436033 | + | 0.899931i | \(0.643617\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.10941e16 | −0.475207 | −0.237604 | − | 0.971362i | \(-0.576362\pi\) | ||||
−0.237604 | + | 0.971362i | \(0.576362\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 6.45048e17 | 4.26072 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.56499e17 | 1.44319 | 0.721595 | − | 0.692316i | \(-0.243409\pi\) | ||||
0.721595 | + | 0.692316i | \(0.243409\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.02286e16 | −0.337589 | −0.168795 | − | 0.985651i | \(-0.553987\pi\) | ||||
−0.168795 | + | 0.985651i | \(0.553987\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.61406e17 | −2.31224 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.78088e17 | 0.630183 | 0.315092 | − | 0.949061i | \(-0.397965\pi\) | ||||
0.315092 | + | 0.949061i | \(0.397965\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.04125e17 | 0.927087 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.26413e17 | −0.332821 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.14402e17 | 0.488743 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.74624e17 | −0.741174 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.79024e17 | −0.652339 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 8.82838e15 | 0.0132479 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.23676e17 | 0.424404 | 0.212202 | − | 0.977226i | \(-0.431937\pi\) | ||||
0.212202 | + | 0.977226i | \(0.431937\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.45517e18 | −1.67071 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.01569e18 | 1.02318 | 0.511592 | − | 0.859229i | \(-0.329056\pi\) | ||||
0.511592 | + | 0.859229i | \(0.329056\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.02967e18 | −0.911927 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.54287e18 | −1.20363 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.05785e18 | 0.728282 | 0.364141 | − | 0.931344i | \(-0.381363\pi\) | ||||
0.364141 | + | 0.931344i | \(0.381363\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.96765e17 | −0.119763 | −0.0598813 | − | 0.998206i | \(-0.519072\pi\) | ||||
−0.0598813 | + | 0.998206i | \(0.519072\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.08269e18 | 2.20082 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.30545e17 | 0.110255 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.92839e18 | −0.819534 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.09303e19 | 4.13462 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2.50869e18 | −0.845988 | −0.422994 | − | 0.906132i | \(-0.639021\pi\) | ||||
−0.422994 | + | 0.906132i | \(0.639021\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.45687e18 | −1.94410 | −0.972049 | − | 0.234777i | \(-0.924564\pi\) | ||||
−0.972049 | + | 0.234777i | \(0.924564\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.47006e18 | −0.395784 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.63098e18 | −0.634305 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.42616e18 | 0.524533 | 0.262267 | − | 0.964995i | \(-0.415530\pi\) | ||||
0.262267 | + | 0.964995i | \(0.415530\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.06111e19 | −2.06008 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 7.13815e18 | 1.24614 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −7.59735e18 | −1.19417 | −0.597087 | − | 0.802177i | \(-0.703675\pi\) | ||||
−0.597087 | + | 0.802177i | \(0.703675\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 8.06607e18 | 1.14301 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 5.87002e18 | 0.750844 | 0.375422 | − | 0.926854i | \(-0.377498\pi\) | ||||
0.375422 | + | 0.926854i | \(0.377498\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.24414e18 | −0.953033 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 7.06000e18 | 0.738478 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1.46003e19 | −1.38347 | −0.691736 | − | 0.722151i | \(-0.743154\pi\) | ||||
−0.691736 | + | 0.722151i | \(0.743154\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.18607e19 | −1.87863 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.02693e19 | 0.801250 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2.58107e19 | 1.83041 | 0.915205 | − | 0.402988i | \(-0.132028\pi\) | ||||
0.915205 | + | 0.402988i | \(0.132028\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.10436e19 | −0.712597 | −0.356298 | − | 0.934372i | \(-0.615961\pi\) | ||||
−0.356298 | + | 0.934372i | \(0.615961\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.13312e19 | 2.42909 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.82325e19 | 2.04868 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.68102e18 | 0.131113 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −3.62130e19 | −1.61785 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2.90525e19 | −1.18686 | −0.593431 | − | 0.804885i | \(-0.702227\pi\) | ||||
−0.593431 | + | 0.804885i | \(0.702227\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.92782e19 | −0.720826 | −0.360413 | − | 0.932793i | \(-0.617364\pi\) | ||||
−0.360413 | + | 0.932793i | \(0.617364\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.42146e19 | 0.486900 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.85325e19 | 0.896143 | 0.448071 | − | 0.893998i | \(-0.352111\pi\) | ||||
0.448071 | + | 0.893998i | \(0.352111\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −9.19463e18 | −0.265023 | −0.132511 | − | 0.991181i | \(-0.542304\pi\) | ||||
−0.132511 | + | 0.991181i | \(0.542304\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −7.19135e19 | −1.90390 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −4.52615e19 | −1.10157 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.58121e19 | 0.577983 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −4.89430e19 | −1.00912 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.28756e19 | −0.244639 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.65585e19 | 1.16628 | 0.583140 | − | 0.812372i | \(-0.301824\pi\) | ||||
0.583140 | + | 0.812372i | \(0.301824\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 9.41086e19 | 1.52196 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 9.90988e19 | 1.48027 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.17520e19 | −0.852596 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −9.80441e19 | −1.25212 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.72467e18 | 0.0558518 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −8.04446e19 | −0.880857 | −0.440428 | − | 0.897788i | \(-0.645173\pi\) | ||||
−0.440428 | + | 0.897788i | \(0.645173\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.49889e20 | 1.52131 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2.93685e19 | −0.276479 | −0.138240 | − | 0.990399i | \(-0.544144\pi\) | ||||
−0.138240 | + | 0.990399i | \(0.544144\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 7.88248e19 | 0.688749 | 0.344375 | − | 0.938832i | \(-0.388091\pi\) | ||||
0.344375 | + | 0.938832i | \(0.388091\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.89320e20 | 1.53636 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 9.16048e19 | 0.690864 | 0.345432 | − | 0.938444i | \(-0.387732\pi\) | ||||
0.345432 | + | 0.938444i | \(0.387732\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.78037e20 | −1.94996 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3.26176e19 | 0.212859 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.61549e20 | 1.58917 | 0.794586 | − | 0.607152i | \(-0.207688\pi\) | ||||
0.794586 | + | 0.607152i | \(0.207688\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.65469e18 | 0.0206874 | 0.0103437 | − | 0.999947i | \(-0.496707\pi\) | ||||
0.0103437 | + | 0.999947i | \(0.496707\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −2.15173e20 | −1.13536 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −7.44369e20 | −3.66334 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.26903e19 | −0.104212 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.09409e20 | −0.469199 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6.70886e19 | 0.268796 | 0.134398 | − | 0.990927i | \(-0.457090\pi\) | ||||
0.134398 | + | 0.990927i | \(0.457090\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.92597e19 | 0.334296 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.65302e20 | 0.579011 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −4.57087e20 | −1.49819 | −0.749095 | − | 0.662462i | \(-0.769512\pi\) | ||||
−0.749095 | + | 0.662462i | \(0.769512\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.97360e20 | 2.75371 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.10337e20 | 0.892051 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −5.07629e19 | −0.136749 | −0.0683743 | − | 0.997660i | \(-0.521781\pi\) | ||||
−0.0683743 | + | 0.997660i | \(0.521781\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 7.22628e20 | 1.82526 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.01845e21 | −2.41320 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.44913e20 | 0.322265 | 0.161132 | − | 0.986933i | \(-0.448485\pi\) | ||||
0.161132 | + | 0.986933i | \(0.448485\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.80251e19 | 0.0376390 | 0.0188195 | − | 0.999823i | \(-0.494009\pi\) | ||||
0.0188195 | + | 0.999823i | \(0.494009\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3.33632e20 | 0.654463 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.73360e20 | −0.503972 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.22325e20 | −0.212050 | −0.106025 | − | 0.994363i | \(-0.533812\pi\) | ||||
−0.106025 | + | 0.994363i | \(0.533812\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 4.23406e20 | 0.690432 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.19889e20 | 0.183982 | 0.0919910 | − | 0.995760i | \(-0.470677\pi\) | ||||
0.0919910 | + | 0.995760i | \(0.470677\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 9.21025e20 | 1.33072 | 0.665360 | − | 0.746523i | \(-0.268278\pi\) | ||||
0.665360 | + | 0.746523i | \(0.268278\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −7.93867e20 | −1.08036 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.05837e20 | 0.776891 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.72297e20 | −0.933582 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.61032e21 | −2.97580 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.54477e21 | 1.66146 | 0.830729 | − | 0.556677i | \(-0.187924\pi\) | ||||
0.830729 | + | 0.556677i | \(0.187924\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6.99354e20 | −0.709920 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −4.52829e20 | −0.434014 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.57299e20 | 0.142404 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.32596e21 | 1.98970 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1.71737e21 | −1.38868 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.81471e21 | −2.15221 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −7.43532e19 | −0.0537804 | −0.0268902 | − | 0.999638i | \(-0.508560\pi\) | ||||
−0.0268902 | + | 0.999638i | \(0.508560\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.10556e21 | −0.756719 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3.18377e19 | 0.0206290 | 0.0103145 | − | 0.999947i | \(-0.496717\pi\) | ||||
0.0103145 | + | 0.999947i | \(0.496717\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.82416e21 | 1.11927 | 0.559637 | − | 0.828738i | \(-0.310941\pi\) | ||||
0.559637 | + | 0.828738i | \(0.310941\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 7.06947e21 | 4.10910 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3.70538e20 | −0.204093 | −0.102047 | − | 0.994780i | \(-0.532539\pi\) | ||||
−0.102047 | + | 0.994780i | \(0.532539\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5.65977e20 | −0.295514 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4.64160e21 | 2.29813 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.63867e20 | −0.123926 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.81733e20 | −0.214683 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.27086e21 | −0.537577 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −6.52583e21 | −2.62102 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.21102e19 | 0.00843442 | 0.00421721 | − | 0.999991i | \(-0.498658\pi\) | ||||
0.00421721 | + | 0.999991i | \(0.498658\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −6.15279e21 | −2.22995 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 4.89740e21 | 1.68688 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.35669e21 | 1.09915 | 0.549576 | − | 0.835444i | \(-0.314789\pi\) | ||||
0.549576 | + | 0.835444i | \(0.314789\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3.22267e21 | 1.00350 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −7.72184e20 | −0.228722 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.07424e22 | −3.02761 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 5.50344e21 | 1.47629 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.52263e21 | 0.388861 | 0.194431 | − | 0.980916i | \(-0.437714\pi\) | ||||
0.194431 | + | 0.980916i | \(0.437714\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.87454e21 | −0.699121 | −0.349561 | − | 0.936914i | \(-0.613669\pi\) | ||||
−0.349561 | + | 0.936914i | \(0.613669\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −7.98005e20 | −0.184882 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2.36637e21 | 0.522393 | 0.261196 | − | 0.965286i | \(-0.415883\pi\) | ||||
0.261196 | + | 0.965286i | \(0.415883\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6.40892e21 | −1.34848 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3.87982e21 | 0.778274 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2.93438e21 | −0.561324 | −0.280662 | − | 0.959807i | \(-0.590554\pi\) | ||||
−0.280662 | + | 0.959807i | \(0.590554\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.21316e21 | −0.768770 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −6.77920e21 | −1.18024 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6.67693e21 | 1.10940 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.10268e21 | 0.650738 | 0.325369 | − | 0.945587i | \(-0.394512\pi\) | ||||
0.325369 | + | 0.945587i | \(0.394512\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −4.15395e21 | −0.629126 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.69609e22 | 2.45341 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.13317e22 | 1.56592 | 0.782959 | − | 0.622073i | \(-0.213709\pi\) | ||||
0.782959 | + | 0.622073i | \(0.213709\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.59758e20 | 0.0210959 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −9.97402e20 | −0.125883 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.98618e21 | 0.480976 | 0.240488 | − | 0.970652i | \(-0.422692\pi\) | ||||
0.240488 | + | 0.970652i | \(0.422692\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 5.85725e21 | 0.675820 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4.81687e21 | 0.531588 | 0.265794 | − | 0.964030i | \(-0.414366\pi\) | ||||
0.265794 | + | 0.964030i | \(0.414366\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.28929e22 | −1.36124 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.59480e22 | −1.61125 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −6.01398e21 | −0.581555 | −0.290777 | − | 0.956791i | \(-0.593914\pi\) | ||||
−0.290777 | + | 0.956791i | \(0.593914\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.82924e21 | 0.169344 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.83799e22 | 1.62932 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2.22130e21 | −0.188596 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.72178e22 | −1.40042 | −0.700208 | − | 0.713938i | \(-0.746910\pi\) | ||||
−0.700208 | + | 0.713938i | \(0.746910\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.86329e22 | −1.45215 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.12923e22 | −0.843441 | −0.421720 | − | 0.906726i | \(-0.638574\pi\) | ||||
−0.421720 | + | 0.906726i | \(0.638574\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.36079e21 | −0.0974316 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 3.64304e21 | 0.250090 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.12211e22 | 0.738727 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −8.24389e21 | −0.520576 | −0.260288 | − | 0.965531i | \(-0.583817\pi\) | ||||
−0.260288 | + | 0.965531i | \(0.583817\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.91429e22 | 1.15972 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.64146e22 | −0.954234 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7.45087e21 | 0.415717 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3.56065e21 | −0.190710 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.52574e22 | 0.784621 | 0.392311 | − | 0.919833i | \(-0.371676\pi\) | ||||
0.392311 | + | 0.919833i | \(0.371676\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8.43945e21 | 0.416789 | 0.208395 | − | 0.978045i | \(-0.433176\pi\) | ||||
0.208395 | + | 0.978045i | \(0.433176\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 4.47447e22 | 2.12250 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −5.60210e21 | −0.255297 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.60643e22 | −2.89288 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 4.17193e21 | 0.175570 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.88889e22 | 0.764098 | 0.382049 | − | 0.924142i | \(-0.375219\pi\) | ||||
0.382049 | + | 0.924142i | \(0.375219\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.76820e21 | −0.0687676 | −0.0343838 | − | 0.999409i | \(-0.510947\pi\) | ||||
−0.0343838 | + | 0.999409i | \(0.510947\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3.48962e22 | −1.30503 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −8.78499e21 | −0.315972 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.02315e22 | 1.39193 | 0.695965 | − | 0.718076i | \(-0.254977\pi\) | ||||
0.695965 | + | 0.718076i | \(0.254977\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.19792e23 | 3.98749 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2.43504e22 | −0.779963 | −0.389981 | − | 0.920823i | \(-0.627519\pi\) | ||||
−0.389981 | + | 0.920823i | \(0.627519\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6.93578e22 | 2.13814 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −4.53973e22 | −1.34715 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.07884e22 | 0.308221 | 0.154111 | − | 0.988054i | \(-0.450749\pi\) | ||||
0.154111 | + | 0.988054i | \(0.450749\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.57576e21 | 0.208413 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.16844e23 | −3.09578 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.27208e22 | −0.579864 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6.83731e22 | −1.68112 | −0.840558 | − | 0.541722i | \(-0.817773\pi\) | ||||
−0.840558 | + | 0.541722i | \(0.817773\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −9.28005e21 | −0.219858 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.33712e22 | −0.533610 | −0.266805 | − | 0.963751i | \(-0.585968\pi\) | ||||
−0.266805 | + | 0.963751i | \(0.585968\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.28585e22 | −0.503049 | −0.251524 | − | 0.967851i | \(-0.580932\pi\) | ||||
−0.251524 | + | 0.967851i | \(0.580932\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −4.76102e22 | −1.01007 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −5.39107e21 | −0.110276 | −0.0551381 | − | 0.998479i | \(-0.517560\pi\) | ||||
−0.0551381 | + | 0.998479i | \(0.517560\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.14947e23 | 2.26741 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4.39039e22 | 0.835266 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.90852e22 | 0.533767 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.69042e22 | 0.476348 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.16293e23 | −1.98677 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −9.99522e22 | −1.64794 | −0.823968 | − | 0.566636i | \(-0.808245\pi\) | ||||
−0.823968 | + | 0.566636i | \(0.808245\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.97746e22 | 0.314684 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.29172e23 | 1.98435 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.77766e23 | 2.63660 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8.24172e22 | 1.18038 | 0.590190 | − | 0.807265i | \(-0.299053\pi\) | ||||
0.590190 | + | 0.807265i | \(0.299053\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.37482e23 | −1.90160 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.24257e22 | −0.166008 | −0.0830038 | − | 0.996549i | \(-0.526451\pi\) | ||||
−0.0830038 | + | 0.996549i | \(0.526451\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.15988e22 | −0.149698 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 8.84009e22 | 1.10233 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.50425e23 | −1.81255 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.90767e21 | 0.0687957 | 0.0343979 | − | 0.999408i | \(-0.489049\pi\) | ||||
0.0343979 | + | 0.999408i | \(0.489049\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.06224e23 | 1.19564 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −6.76058e22 | −0.735624 | −0.367812 | − | 0.929900i | \(-0.619893\pi\) | ||||
−0.367812 | + | 0.929900i | \(0.619893\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.16955e23 | 1.23039 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.49186e23 | −1.51761 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1.23744e21 | 0.0121737 | 0.00608686 | − | 0.999981i | \(-0.498062\pi\) | ||||
0.00608686 | + | 0.999981i | \(0.498062\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.56715e23 | 1.49119 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 4.45677e22 | 0.410225 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 7.52901e22 | 0.670465 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −8.16030e22 | −0.703131 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2.64207e23 | −2.20304 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3.73793e22 | 0.301655 | 0.150827 | − | 0.988560i | \(-0.451806\pi\) | ||||
0.150827 | + | 0.988560i | \(0.451806\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.13593e23 | 1.66849 | 0.834244 | − | 0.551395i | \(-0.185904\pi\) | ||||
0.834244 | + | 0.551395i | \(0.185904\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −3.95592e23 | −2.99153 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.58248e22 | −0.115864 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −8.01486e22 | −0.568228 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.12547e23 | 0.772738 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.33505e22 | 0.0887802 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3.16099e23 | −2.03618 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 4.67070e23 | 2.91474 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.18470e23 | −1.32095 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.52458e23 | −0.893253 | −0.446626 | − | 0.894721i | \(-0.647375\pi\) | ||||
−0.446626 | + | 0.894721i | \(0.647375\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.99845e23 | −1.13474 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 8.65470e22 | 0.476302 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.00996e23 | −1.07225 | −0.536124 | − | 0.844139i | \(-0.680112\pi\) | ||||
−0.536124 | + | 0.844139i | \(0.680112\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 4.52973e23 | 2.34265 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.57037e22 | 0.279316 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.21364e22 | −0.253500 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 6.91856e23 | 3.26231 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 4.02153e23 | 1.83917 | 0.919586 | − | 0.392888i | \(-0.128524\pi\) | ||||
0.919586 | + | 0.392888i | \(0.128524\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5.12558e22 | 0.227375 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.85157e22 | 0.208784 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.83177e23 | −0.764802 | −0.382401 | − | 0.923996i | \(-0.624903\pi\) | ||||
−0.382401 | + | 0.923996i | \(0.624903\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.19468e23 | −0.889119 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 8.55061e22 | 0.336156 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −2.60456e23 | −0.993758 | −0.496879 | − | 0.867820i | \(-0.665521\pi\) | ||||
−0.496879 | + | 0.867820i | \(0.665521\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.07462e23 | 1.50897 | 0.754484 | − | 0.656319i | \(-0.227887\pi\) | ||||
0.754484 | + | 0.656319i | \(0.227887\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −5.25734e23 | −1.88996 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.86512e23 | −0.650924 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4.27739e23 | −1.44939 | −0.724693 | − | 0.689071i | \(-0.758019\pi\) | ||||
−0.724693 | + | 0.689071i | \(0.758019\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −3.48859e23 | −1.14784 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.74880e23 | 0.558783 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.12089e23 | 0.658166 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.55786e23 | 0.469573 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 2.98640e23 | 0.874427 | 0.437214 | − | 0.899358i | \(-0.355965\pi\) | ||||
0.437214 | + | 0.899358i | \(0.355965\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7.59988e22 | 0.216186 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 5.16324e23 | 1.42702 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −4.06757e23 | −1.09237 | −0.546186 | − | 0.837664i | \(-0.683921\pi\) | ||||
−0.546186 | + | 0.837664i | \(0.683921\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.64221e23 | −0.689562 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.66386e23 | −0.422022 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −8.44514e22 | −0.208199 | −0.104100 | − | 0.994567i | \(-0.533196\pi\) | ||||
−0.104100 | + | 0.994567i | \(0.533196\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.76567e23 | 0.423134 | 0.211567 | − | 0.977364i | \(-0.432143\pi\) | ||||
0.211567 | + | 0.977364i | \(0.432143\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −7.88143e23 | −1.83615 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 4.61673e23 | 1.04572 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −6.46330e23 | −1.42348 | −0.711738 | − | 0.702445i | \(-0.752092\pi\) | ||||
−0.711738 | + | 0.702445i | \(0.752092\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −8.19051e23 | −1.75414 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.43806e23 | −0.299521 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.13581e23 | 0.432662 | 0.216331 | − | 0.976320i | \(-0.430591\pi\) | ||||
0.216331 | + | 0.976320i | \(0.430591\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 4.67095e23 | 0.920379 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 9.85119e23 | 1.88827 | 0.944137 | − | 0.329553i | \(-0.106898\pi\) | ||||
0.944137 | + | 0.329553i | \(0.106898\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.62630e23 | 0.489750 | 0.244875 | − | 0.969555i | \(-0.421253\pi\) | ||||
0.244875 | + | 0.969555i | \(0.421253\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.08963e23 | −0.560567 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.62790e24 | 2.87396 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −5.87491e23 | −1.00930 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.32998e23 | −0.389563 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.29960e23 | 0.374216 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6.27160e23 | −0.993411 | −0.496706 | − | 0.867919i | \(-0.665457\pi\) | ||||
−0.496706 | + | 0.867919i | \(0.665457\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.20444e24 | 1.85718 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −3.98886e23 | −0.598787 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.85002e23 | −0.562702 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.03139e24 | 1.46780 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.72378e23 | 0.377467 | 0.188734 | − | 0.982028i | \(-0.439562\pi\) | ||||
0.188734 | + | 0.982028i | \(0.439562\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4.23545e23 | 0.571619 | 0.285809 | − | 0.958287i | \(-0.407738\pi\) | ||||
0.285809 | + | 0.958287i | \(0.407738\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.79329e24 | 2.35718 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.24483e24 | −1.59376 | −0.796880 | − | 0.604137i | \(-0.793518\pi\) | ||||
−0.796880 | + | 0.604137i | \(0.793518\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.05258e23 | −0.255988 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.11746e24 | −1.35767 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.39998e24 | −1.65715 | −0.828574 | − | 0.559879i | \(-0.810847\pi\) | ||||
−0.828574 | + | 0.559879i | \(0.810847\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.25169e24 | −1.44360 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.07452e24 | −1.20756 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −3.82737e22 | −0.0419154 | −0.0209577 | − | 0.999780i | \(-0.506672\pi\) | ||||
−0.0209577 | + | 0.999780i | \(0.506672\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.88048e23 | 0.307435 | 0.153717 | − | 0.988115i | \(-0.450875\pi\) | ||||
0.153717 | + | 0.988115i | \(0.450875\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 8.54975e22 | 0.0889382 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.26893e24 | 1.28663 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.86163e23 | −0.381682 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.45572e24 | −1.40268 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −8.26108e23 | −0.776060 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.54736e24 | 1.41731 | 0.708654 | − | 0.705556i | \(-0.249303\pi\) | ||||
0.708654 | + | 0.705556i | \(0.249303\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 9.46205e23 | 0.845090 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1.88145e24 | −1.63866 | −0.819331 | − | 0.573321i | \(-0.805655\pi\) | ||||
−0.819331 | + | 0.573321i | \(0.805655\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.17237e24 | 3.54397 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −5.31453e23 | −0.440265 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −2.10444e24 | −1.70044 | −0.850218 | − | 0.526431i | \(-0.823530\pi\) | ||||
−0.850218 | + | 0.526431i | \(0.823530\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.30365e24 | −1.02753 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.42641e24 | 1.09676 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 3.73757e23 | 0.280367 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.36432e23 | −0.612163 | −0.306082 | − | 0.952005i | \(-0.599018\pi\) | ||||
−0.306082 | + | 0.952005i | \(0.599018\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.07487e24 | 1.48169 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2.42485e23 | 0.168972 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.55254e23 | 0.105576 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.65768e24 | 1.10013 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.01169e24 | −0.655307 | −0.327654 | − | 0.944798i | \(-0.606258\pi\) | ||||
−0.327654 | + | 0.944798i | \(0.606258\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.10439e24 | −0.698236 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −5.03135e24 | −3.10511 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2.74506e24 | 1.65382 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.49014e24 | 1.46464 | 0.732320 | − | 0.680961i | \(-0.238438\pi\) | ||||
0.732320 | + | 0.680961i | \(0.238438\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.57476e23 | 0.205284 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −5.26858e23 | −0.295415 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.84114e23 | −0.155558 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 4.73299e24 | 2.53059 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.77673e24 | 0.927739 | 0.463870 | − | 0.885903i | \(-0.346461\pi\) | ||||
0.463870 | + | 0.885903i | \(0.346461\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.76714e24 | 0.901200 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 6.61352e22 | 0.0329426 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.18263e24 | 0.575409 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.45639e24 | −0.692208 | −0.346104 | − | 0.938196i | \(-0.612496\pi\) | ||||
−0.346104 | + | 0.938196i | \(0.612496\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −3.51202e24 | −1.63070 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5.96058e23 | 0.270390 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −3.43336e23 | −0.152172 | −0.0760862 | − | 0.997101i | \(-0.524242\pi\) | ||||
−0.0760862 | + | 0.997101i | \(0.524242\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.34701e25 | −5.83349 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.43737e24 | 0.608269 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.23819e23 | −0.0512048 | −0.0256024 | − | 0.999672i | \(-0.508150\pi\) | ||||
−0.0256024 | + | 0.999672i | \(0.508150\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4.10604e23 | −0.165947 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −8.96803e23 | −0.354236 | −0.177118 | − | 0.984190i | \(-0.556677\pi\) | ||||
−0.177118 | + | 0.984190i | \(0.556677\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.09162e24 | 1.19360 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.19907e24 | −0.452502 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −7.41920e24 | −2.73692 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3.25270e24 | 1.17302 | 0.586508 | − | 0.809943i | \(-0.300502\pi\) | ||||
0.586508 | + | 0.809943i | \(0.300502\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.21404e24 | 0.428030 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 7.95720e24 | 2.74291 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.52863e24 | 0.852258 | 0.426129 | − | 0.904662i | \(-0.359877\pi\) | ||||
0.426129 | + | 0.904662i | \(0.359877\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.61524e24 | 0.532332 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −5.15668e24 | −1.66188 | −0.830942 | − | 0.556359i | \(-0.812198\pi\) | ||||
−0.830942 | + | 0.556359i | \(0.812198\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.03135e24 | 0.640217 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.81165e24 | 0.558407 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −3.61719e23 | −0.109046 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.80944e24 | 0.533543 | 0.266771 | − | 0.963760i | \(-0.414043\pi\) | ||||
0.266771 | + | 0.963760i | \(0.414043\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −8.27144e24 | −2.38572 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −2.10672e24 | −0.594402 | −0.297201 | − | 0.954815i | \(-0.596053\pi\) | ||||
−0.297201 | + | 0.954815i | \(0.596053\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.61351e24 | 0.445357 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.62386e25 | 4.38501 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −7.45610e23 | −0.196990 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.88100e24 | −0.486245 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.95907e24 | 0.495535 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2.98991e24 | −0.740059 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.37159e24 | −0.332229 | −0.166115 | − | 0.986106i | \(-0.553122\pi\) | ||||
−0.166115 | + | 0.986106i | \(0.553122\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −9.18606e23 | −0.217758 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −5.15116e24 | −1.19510 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.45582e24 | −0.330587 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.30767e25 | 2.90654 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 4.84784e24 | 1.05476 | 0.527378 | − | 0.849631i | \(-0.323175\pi\) | ||||
0.527378 | + | 0.849631i | \(0.323175\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.67233e24 | −0.356184 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.11618e25 | −2.32733 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.95966e24 | 0.400035 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −8.79678e24 | −1.75816 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 2.62234e24 | 0.513174 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 3.62003e24 | 0.693665 | 0.346832 | − | 0.937927i | \(-0.387257\pi\) | ||||
0.346832 | + | 0.937927i | \(0.387257\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −5.05588e24 | −0.948680 | −0.474340 | − | 0.880342i | \(-0.657313\pi\) | ||||
−0.474340 | + | 0.880342i | \(0.657313\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 3.26182e23 | 0.0599363 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 9.36268e24 | 1.68485 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.86258e24 | −0.504510 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 3.65647e24 | 0.631174 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.03537e24 | 0.344133 | 0.172067 | − | 0.985085i | \(-0.444956\pi\) | ||||
0.172067 | + | 0.985085i | \(0.444956\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −3.90337e24 | −0.646459 | −0.323229 | − | 0.946321i | \(-0.604769\pi\) | ||||
−0.323229 | + | 0.946321i | \(0.604769\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −4.94672e24 | −0.802525 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −5.68416e24 | −0.903377 | −0.451689 | − | 0.892176i | \(-0.649178\pi\) | ||||
−0.451689 | + | 0.892176i | \(0.649178\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −6.91406e24 | −1.07651 | −0.538257 | − | 0.842781i | \(-0.680917\pi\) | ||||
−0.538257 | + | 0.842781i | \(0.680917\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.21360e24 | −0.337669 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4.47722e24 | −0.669153 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −7.23399e24 | −1.05936 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.67283e24 | 0.383535 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −9.93397e24 | −1.39684 | −0.698419 | − | 0.715689i | \(-0.746113\pi\) | ||||
−0.698419 | + | 0.715689i | \(0.746113\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.80857e24 | −0.662598 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 2.16951e24 | 0.292973 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.01598e25 | 1.34463 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.08360e25 | 1.40559 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.66669e25 | 2.11904 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 7.65612e24 | 0.954130 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 4.07127e24 | 0.497351 | 0.248675 | − | 0.968587i | \(-0.420005\pi\) | ||||
0.248675 | + | 0.968587i | \(0.420005\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −8.70047e24 | −1.04191 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 7.83692e24 | 0.920044 | 0.460022 | − | 0.887907i | \(-0.347841\pi\) | ||||
0.460022 | + | 0.887907i | \(0.347841\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −7.75004e24 | −0.891994 | −0.445997 | − | 0.895034i | \(-0.647151\pi\) | ||||
−0.445997 | + | 0.895034i | \(0.647151\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.09632e25 | 1.23712 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 9.90022e24 | 1.09535 | 0.547675 | − | 0.836691i | \(-0.315513\pi\) | ||||
0.547675 | + | 0.836691i | \(0.315513\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.79929e25 | 1.95193 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1.39755e25 | −1.48664 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −6.51946e23 | −0.0680054 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.53303e24 | 0.259111 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −2.86081e25 | −2.86991 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.55360e23 | −0.0251237 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 9.81741e24 | 0.947328 | 0.473664 | − | 0.880706i | \(-0.342931\pi\) | ||||
0.473664 | + | 0.880706i | \(0.342931\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 2.79542e25 | 2.64570 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.13021e25 | −1.04921 | −0.524607 | − | 0.851345i | \(-0.675788\pi\) | ||||
−0.524607 | + | 0.851345i | \(0.675788\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.05781e25 | −0.963255 | −0.481627 | − | 0.876376i | \(-0.659954\pi\) | ||||
−0.481627 | + | 0.876376i | \(0.659954\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.26555e25 | −1.13048 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1.16661e25 | −1.02230 | −0.511148 | − | 0.859493i | \(-0.670780\pi\) | ||||
−0.511148 | + | 0.859493i | \(0.670780\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −9.36231e24 | −0.804855 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.06922e24 | 0.0901792 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 8.03141e24 | 0.664591 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −3.18081e25 | −2.58251 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.84649e24 | 0.226764 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3.34069e24 | 0.261143 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.34645e24 | 0.333406 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 4.20905e25 | 3.16839 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.36097e25 | 1.00540 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 7.57602e24 | 0.549261 | 0.274631 | − | 0.961550i | \(-0.411444\pi\) | ||||
0.274631 | + | 0.961550i | \(0.411444\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.88217e25 | −1.33926 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.05833e25 | 0.739118 | 0.369559 | − | 0.929207i | \(-0.379509\pi\) | ||||
0.369559 | + | 0.929207i | \(0.379509\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.18681e24 | 0.149903 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −5.09350e25 | −3.42718 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −2.93786e25 | −1.94040 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.44343e25 | 0.935867 | 0.467933 | − | 0.883764i | \(-0.344999\pi\) | ||||
0.467933 | + | 0.883764i | \(0.344999\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.34550e24 | −0.0856398 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −3.31482e24 | −0.207131 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.34470e25 | −1.43841 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.21165e25 | −0.729792 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 2.30190e25 | 1.36130 | 0.680648 | − | 0.732610i | \(-0.261698\pi\) | ||||
0.680648 | + | 0.732610i | \(0.261698\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.15019e25 | 1.24855 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 5.76136e23 | 0.0328496 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −3.30398e24 | −0.184986 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −9.05092e24 | −0.497630 | −0.248815 | − | 0.968551i | \(-0.580041\pi\) | ||||
−0.248815 | + | 0.968551i | \(0.580041\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 3.30100e25 | 1.78233 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.82487e25 | 0.967654 | 0.483827 | − | 0.875164i | \(-0.339246\pi\) | ||||
0.483827 | + | 0.875164i | \(0.339246\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.16890e24 | 0.269184 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 4.46275e25 | 2.28261 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1.28506e25 | −0.645580 | −0.322790 | − | 0.946471i | \(-0.604621\pi\) | ||||
−0.322790 | + | 0.946471i | \(0.604621\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.45344e24 | 0.170408 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −6.70525e24 | −0.324998 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2.06250e25 | −0.981984 | −0.490992 | − | 0.871164i | \(-0.663366\pi\) | ||||
−0.490992 | + | 0.871164i | \(0.663366\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.58032e25 | 1.67453 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1.02419e25 | −0.470576 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −3.05982e25 | −1.38114 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.79923e25 | −0.797880 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 5.08701e25 | 2.21635 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2.37578e25 | 1.01701 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 9.79148e24 | 0.411835 | 0.205918 | − | 0.978569i | \(-0.433982\pi\) | ||||
0.205918 | + | 0.978569i | \(0.433982\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −4.77494e24 | −0.197340 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2.45503e25 | −0.996995 | −0.498498 | − | 0.866891i | \(-0.666115\pi\) | ||||
−0.498498 | + | 0.866891i | \(0.666115\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5.69140e24 | 0.227122 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −8.71743e24 | −0.341861 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 4.70253e24 | 0.181229 | 0.0906145 | − | 0.995886i | \(-0.471117\pi\) | ||||
0.0906145 | + | 0.995886i | \(0.471117\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.03563e25 | 0.770985 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.39281e25 | −0.518447 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −3.79842e25 | −1.38962 | −0.694812 | − | 0.719191i | \(-0.744513\pi\) | ||||
−0.694812 | + | 0.719191i | \(0.744513\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3.51624e25 | −1.26436 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.18091e26 | −4.17371 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.98447e25 | 0.689407 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.78114e24 | −0.0949724 | −0.0474862 | − | 0.998872i | \(-0.515121\pi\) | ||||
−0.0474862 | + | 0.998872i | \(0.515121\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 4.00107e23 | 0.0134310 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.13311e25 | 0.373918 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 5.10311e25 | 1.65549 | 0.827744 | − | 0.561106i | \(-0.189624\pi\) | ||||
0.827744 | + | 0.561106i | \(0.189624\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −3.88407e25 | −1.23874 |
(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 | 8.18.a.b.1.2 | ✓ | 2 | |
3.2 | odd | 2 | 72.18.a.d.1.2 | 2 | |||
4.3 | odd | 2 | 16.18.a.c.1.1 | 2 | |||
8.3 | odd | 2 | 64.18.a.m.1.2 | 2 | |||
8.5 | even | 2 | 64.18.a.f.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8.18.a.b.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial | |
16.18.a.c.1.1 | 2 | 4.3 | odd | 2 | |||
64.18.a.f.1.1 | 2 | 8.5 | even | 2 | |||
64.18.a.m.1.2 | 2 | 8.3 | odd | 2 | |||
72.18.a.d.1.2 | 2 | 3.2 | odd | 2 |