Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8,20,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, 20, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8.1");
S:= CuspForms(chi, 20);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8 = 2^{3} \) |
Weight: | \( k \) | \(=\) | \( 20 \) |
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: | \(18.3053357245\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{3} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 2519x + 43659 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{21}\cdot 3^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(37.1696\) 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 | ||||||||
\(3\) | −34307.5 | −1.00632 | −0.503161 | − | 0.864192i | \(-0.667830\pi\) | ||||
−0.503161 | + | 0.864192i | \(0.667830\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.59881e6 | 0.595059 | 0.297529 | − | 0.954713i | \(-0.403837\pi\) | ||||
0.297529 | + | 0.954713i | \(0.403837\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.93114e8 | −1.80877 | −0.904384 | − | 0.426719i | \(-0.859669\pi\) | ||||
−0.904384 | + | 0.426719i | \(0.859669\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.47441e7 | 0.0126857 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 8.32029e8 | 0.106392 | 0.0531958 | − | 0.998584i | \(-0.483059\pi\) | ||||
0.0531958 | + | 0.998584i | \(0.483059\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.50621e10 | 1.17855 | 0.589277 | − | 0.807931i | \(-0.299413\pi\) | ||||
0.589277 | + | 0.807931i | \(0.299413\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −8.91588e10 | −0.598821 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.73062e11 | 0.558467 | 0.279233 | − | 0.960223i | \(-0.409920\pi\) | ||||
0.279233 | + | 0.960223i | \(0.409920\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 9.22463e11 | 0.655828 | 0.327914 | − | 0.944708i | \(-0.393654\pi\) | ||||
0.327914 | + | 0.944708i | \(0.393654\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 6.62527e12 | 1.82020 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.26167e13 | 1.46060 | 0.730299 | − | 0.683128i | \(-0.239381\pi\) | ||||
0.730299 | + | 0.683128i | \(0.239381\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.23197e13 | −0.645905 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.93685e13 | 0.993557 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.27884e14 | 1.63695 | 0.818473 | − | 0.574545i | \(-0.194821\pi\) | ||||
0.818473 | + | 0.574545i | \(0.194821\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.96283e14 | −1.33336 | −0.666679 | − | 0.745345i | \(-0.732285\pi\) | ||||
−0.666679 | + | 0.745345i | \(0.732285\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.85448e13 | −0.107064 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −5.01868e14 | −1.07632 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.60758e14 | −0.962343 | −0.481172 | − | 0.876626i | \(-0.659789\pi\) | ||||
−0.481172 | + | 0.876626i | \(0.659789\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.54597e15 | −1.18601 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.82783e15 | 1.34898 | 0.674492 | − | 0.738282i | \(-0.264363\pi\) | ||||
0.674492 | + | 0.738282i | \(0.264363\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.55031e13 | 0.0289779 | 0.0144890 | − | 0.999895i | \(-0.495388\pi\) | ||||
0.0144890 | + | 0.999895i | \(0.495388\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.83173e13 | 0.00754876 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.05928e15 | −0.529078 | −0.264539 | − | 0.964375i | \(-0.585220\pi\) | ||||
−0.264539 | + | 0.964375i | \(0.585220\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.58942e16 | 2.27164 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −9.36809e15 | −0.561998 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.19955e16 | 1.33189 | 0.665944 | − | 0.746002i | \(-0.268029\pi\) | ||||
0.665944 | + | 0.746002i | \(0.268029\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.16229e15 | 0.0633093 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.16474e16 | −0.659975 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.99553e16 | −0.901019 | −0.450509 | − | 0.892772i | \(-0.648758\pi\) | ||||
−0.450509 | + | 0.892772i | \(0.648758\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.56065e17 | −1.70872 | −0.854361 | − | 0.519679i | \(-0.826051\pi\) | ||||
−0.854361 | + | 0.519679i | \(0.826051\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.84731e15 | −0.0229456 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.17108e17 | 0.701309 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.35957e17 | 0.610506 | 0.305253 | − | 0.952271i | \(-0.401259\pi\) | ||||
0.305253 | + | 0.952271i | \(0.401259\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −4.32847e17 | −1.46983 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.18135e17 | 0.305790 | 0.152895 | − | 0.988242i | \(-0.451140\pi\) | ||||
0.152895 | + | 0.988242i | \(0.451140\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.66518e17 | 1.12628 | 0.563140 | − | 0.826361i | \(-0.309593\pi\) | ||||
0.563140 | + | 0.826361i | \(0.309593\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 4.22657e17 | 0.649989 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.60677e17 | −0.192438 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.38949e18 | 1.30437 | 0.652183 | − | 0.758061i | \(-0.273853\pi\) | ||||
0.652183 | + | 0.758061i | \(0.273853\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.36777e18 | −1.01252 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.99954e18 | 1.17405 | 0.587027 | − | 0.809567i | \(-0.300298\pi\) | ||||
0.587027 | + | 0.809567i | \(0.300298\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 7.09638e17 | 0.332320 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −4.38737e18 | −1.64730 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.16978e18 | −0.959012 | −0.479506 | − | 0.877539i | \(-0.659184\pi\) | ||||
−0.479506 | + | 0.877539i | \(0.659184\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −8.70213e18 | −2.13173 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 6.73399e18 | 1.34179 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.39731e18 | 0.390256 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.60346e18 | 0.214154 | 0.107077 | − | 0.994251i | \(-0.465851\pi\) | ||||
0.107077 | + | 0.994251i | \(0.465851\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.22676e16 | 0.00134966 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.21136e18 | 0.201190 | 0.100595 | − | 0.994927i | \(-0.467925\pi\) | ||||
0.100595 | + | 0.994927i | \(0.467925\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.37696e17 | −0.0708123 | −0.0354061 | − | 0.999373i | \(-0.511272\pi\) | ||||
−0.0354061 | + | 0.999373i | \(0.511272\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.72178e19 | 1.08313 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −4.07453e18 | −0.214256 | −0.107128 | − | 0.994245i | \(-0.534165\pi\) | ||||
−0.107128 | + | 0.994245i | \(0.534165\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.17714e18 | 0.228317 | 0.114159 | − | 0.993463i | \(-0.463583\pi\) | ||||
0.114159 | + | 0.993463i | \(0.463583\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.60997e19 | 0.968428 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.96131e19 | −0.614189 | −0.307094 | − | 0.951679i | \(-0.599357\pi\) | ||||
−0.307094 | + | 0.951679i | \(0.599357\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.27884e19 | 0.869142 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 6.64402e17 | 0.0149508 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −5.27322e19 | −1.01014 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.04668e19 | −0.988681 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −9.70159e19 | −1.35751 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −8.15849e19 | −0.979410 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.26799e20 | 1.30912 | 0.654560 | − | 0.756010i | \(-0.272854\pi\) | ||||
0.654560 | + | 0.756010i | \(0.272854\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −3.27647e18 | −0.0291611 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.28991e20 | 0.991931 | 0.495966 | − | 0.868342i | \(-0.334814\pi\) | ||||
0.495966 | + | 0.868342i | \(0.334814\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.78141e20 | −1.18624 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.02311e20 | 0.591225 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.85432e20 | 1.43436 | 0.717179 | − | 0.696889i | \(-0.245433\pi\) | ||||
0.717179 | + | 0.696889i | \(0.245433\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.44335e19 | −0.0632022 | −0.0316011 | − | 0.999501i | \(-0.510061\pi\) | ||||
−0.0316011 | + | 0.999501i | \(0.510061\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.39264e20 | 0.532423 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.74930e19 | 0.125388 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.32346e20 | 0.974079 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −8.88366e20 | −2.28601 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 4.57287e19 | 0.103495 | 0.0517475 | − | 0.998660i | \(-0.483521\pi\) | ||||
0.0517475 | + | 0.998660i | \(0.483521\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.44110e20 | 1.28434 | 0.642169 | − | 0.766563i | \(-0.278035\pi\) | ||||
0.642169 | + | 0.766563i | \(0.278035\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.02607e18 | 0.00708456 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −5.10103e20 | −0.793427 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.32864e20 | 1.28461 | 0.642306 | − | 0.766449i | \(-0.277978\pi\) | ||||
0.642306 | + | 0.766449i | \(0.277978\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.09768e21 | −1.34031 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.43646e21 | −2.64188 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.50271e20 | −0.434202 | −0.217101 | − | 0.976149i | \(-0.569660\pi\) | ||||
−0.217101 | + | 0.976149i | \(0.569660\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −7.41827e19 | −0.0637096 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.83293e21 | 1.40391 | 0.701954 | − | 0.712223i | \(-0.252311\pi\) | ||||
0.701954 | + | 0.712223i | \(0.252311\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.68672e20 | 0.388990 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.36009e19 | 0.00831966 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 7.77321e20 | 0.425758 | 0.212879 | − | 0.977079i | \(-0.431716\pi\) | ||||
0.212879 | + | 0.977079i | \(0.431716\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.37910e21 | 1.16829 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2.05692e21 | 0.906716 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2.26175e21 | −0.896068 | −0.448034 | − | 0.894016i | \(-0.647876\pi\) | ||||
−0.448034 | + | 0.894016i | \(0.647876\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.20820e20 | −0.221319 | −0.110660 | − | 0.993858i | \(-0.535296\pi\) | ||||
−0.110660 | + | 0.993858i | \(0.535296\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 5.35420e21 | 1.71953 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.97707e21 | −0.572651 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.27196e20 | 0.0594162 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −7.60261e21 | −1.79711 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.01107e21 | 0.216253 | 0.108127 | − | 0.994137i | \(-0.465515\pi\) | ||||
0.108127 | + | 0.994137i | \(0.465515\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.29835e21 | 0.445268 | 0.222634 | − | 0.974902i | \(-0.428535\pi\) | ||||
0.222634 | + | 0.974902i | \(0.428535\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −4.01768e21 | −0.705743 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.67409e21 | 0.266900 | 0.133450 | − | 0.991056i | \(-0.457394\pi\) | ||||
0.133450 | + | 0.991056i | \(0.457394\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.13391e21 | 0.888451 | 0.444225 | − | 0.895915i | \(-0.353479\pi\) | ||||
0.444225 | + | 0.895915i | \(0.353479\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.66434e21 | −0.614366 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.46962e22 | −2.96086 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 7.34901e21 | 0.802725 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.86022e20 | 0.0185288 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 7.67516e20 | 0.0697746 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.82836e21 | 0.733156 | 0.366578 | − | 0.930387i | \(-0.380529\pi\) | ||||
0.366578 | + | 0.930387i | \(0.380529\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −4.05291e21 | −0.307723 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.48195e20 | 0.0172436 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.79051e22 | 2.41174 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.94358e22 | −1.13340 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.23048e22 | 0.658183 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.70960e22 | 0.839456 | 0.419728 | − | 0.907650i | \(-0.362125\pi\) | ||||
0.419728 | + | 0.907650i | \(0.362125\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.81643e20 | −0.00819378 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2.50313e22 | 1.03810 | 0.519049 | − | 0.854745i | \(-0.326286\pi\) | ||||
0.519049 | + | 0.854745i | \(0.326286\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.28082e21 | −0.125183 | −0.0625915 | − | 0.998039i | \(-0.519937\pi\) | ||||
−0.0625915 | + | 0.998039i | \(0.519937\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 5.51241e21 | 0.193655 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −6.12997e22 | −1.98416 | −0.992080 | − | 0.125606i | \(-0.959913\pi\) | ||||
−0.992080 | + | 0.125606i | \(0.959913\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.05493e22 | −0.314833 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −4.76701e22 | −1.31261 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2.05975e22 | −0.523643 | −0.261821 | − | 0.965116i | \(-0.584323\pi\) | ||||
−0.261821 | + | 0.965116i | \(0.584323\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.23955e21 | 0.193527 | 0.0967635 | − | 0.995307i | \(-0.469151\pi\) | ||||
0.0967635 | + | 0.995307i | \(0.469151\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.16837e21 | 0.0253700 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 6.72942e22 | 1.35176 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.15681e22 | 0.772929 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −6.85993e22 | −1.18148 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6.38251e22 | −1.01881 | −0.509403 | − | 0.860528i | \(-0.670134\pi\) | ||||
−0.509403 | + | 0.860528i | \(0.670134\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.04974e22 | 0.155396 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2.43459e22 | −0.334422 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −8.06598e22 | −1.02871 | −0.514354 | − | 0.857578i | \(-0.671968\pi\) | ||||
−0.514354 | + | 0.857578i | \(0.671968\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.46913e23 | 1.74066 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.88554e21 | 0.0207659 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 5.19992e22 | 0.532619 | 0.266310 | − | 0.963888i | \(-0.414196\pi\) | ||||
0.266310 | + | 0.963888i | \(0.414196\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.31502e22 | 0.792551 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.08747e23 | 0.965075 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4.34498e22 | 0.359204 | 0.179602 | − | 0.983739i | \(-0.442519\pi\) | ||||
0.179602 | + | 0.983739i | \(0.442519\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.03032e23 | −1.56443 | −0.782215 | − | 0.623009i | \(-0.785910\pi\) | ||||
−0.782215 | + | 0.623009i | \(0.785910\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.98549e23 | 2.14521 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.02503e22 | −0.0687189 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.84207e23 | −1.15279 | −0.576393 | − | 0.817173i | \(-0.695540\pi\) | ||||
−0.576393 | + | 0.817173i | \(0.695540\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2.89403e21 | −0.0169146 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.59747e23 | 0.872413 | 0.436206 | − | 0.899847i | \(-0.356322\pi\) | ||||
0.436206 | + | 0.899847i | \(0.356322\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5.90709e22 | −0.301580 | −0.150790 | − | 0.988566i | \(-0.548182\pi\) | ||||
−0.150790 | + | 0.988566i | \(0.548182\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −8.22457e22 | −0.392724 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −5.46095e23 | −2.44000 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.64509e23 | −0.688115 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −5.50107e22 | −0.215508 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 9.73152e22 | 0.357222 | 0.178611 | − | 0.983920i | \(-0.442840\pi\) | ||||
0.178611 | + | 0.983920i | \(0.442840\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.55813e23 | −0.536159 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.27557e22 | 0.105706 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 5.68534e23 | 1.72139 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.84430e22 | −0.0524143 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −7.58661e22 | −0.202462 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −4.05583e23 | −1.01679 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.85956e23 | 1.14494 | 0.572470 | − | 0.819926i | \(-0.305985\pi\) | ||||
0.572470 | + | 0.819926i | \(0.305985\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3.21700e22 | 0.0712600 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.66721e23 | 0.972375 | 0.486188 | − | 0.873854i | \(-0.338387\pi\) | ||||
0.486188 | + | 0.873854i | \(0.338387\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3.78777e23 | −0.742526 | −0.371263 | − | 0.928528i | \(-0.621075\pi\) | ||||
−0.371263 | + | 0.928528i | \(0.621075\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −7.39961e21 | −0.0136540 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6.09181e23 | 1.05848 | 0.529241 | − | 0.848472i | \(-0.322477\pi\) | ||||
0.529241 | + | 0.848472i | \(0.322477\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.06403e23 | 0.174157 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.39787e23 | 0.215610 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.51890e23 | 0.366258 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5.55150e23 | −0.761234 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.77615e23 | −0.229761 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 7.83906e23 | 0.956980 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.53458e22 | −0.0292106 | −0.0146053 | − | 0.999893i | \(-0.504649\pi\) | ||||
−0.0146053 | + | 0.999893i | \(0.504649\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.12167e22 | −0.0122080 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.53326e23 | 0.363287 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.23470e24 | −1.19971 | −0.599856 | − | 0.800108i | \(-0.704776\pi\) | ||||
−0.599856 | + | 0.800108i | \(0.704776\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 6.72878e23 | 0.618072 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.63313e23 | −0.141858 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2.79925e24 | −2.30011 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.12489e24 | −0.874637 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2.52463e24 | −1.85809 | −0.929045 | − | 0.369966i | \(-0.879369\pi\) | ||||
−0.929045 | + | 0.369966i | \(0.879369\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5.12360e23 | −0.357054 | −0.178527 | − | 0.983935i | \(-0.557133\pi\) | ||||
−0.178527 | + | 0.983935i | \(0.557133\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.77403e24 | 1.17096 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2.92915e24 | 1.83182 | 0.915909 | − | 0.401387i | \(-0.131472\pi\) | ||||
0.915909 | + | 0.401387i | \(0.131472\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.07010e23 | 0.181963 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.80911e24 | 1.01652 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −6.15112e23 | −0.327761 | −0.163880 | − | 0.986480i | \(-0.552401\pi\) | ||||
−0.163880 | + | 0.986480i | \(0.552401\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.12748e24 | −0.569890 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.07447e24 | 0.994932 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.47227e24 | 0.670203 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.82304e24 | 0.787895 | 0.393947 | − | 0.919133i | \(-0.371109\pi\) | ||||
0.393947 | + | 0.919133i | \(0.371109\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 4.16940e22 | 0.0171129 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −6.17878e24 | −2.40908 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.56558e24 | 0.580018 | 0.290009 | − | 0.957024i | \(-0.406342\pi\) | ||||
0.290009 | + | 0.957024i | \(0.406342\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.79898e24 | 0.985603 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 5.76271e24 | 1.92923 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.92164e23 | −0.0930154 | −0.0465077 | − | 0.998918i | \(-0.514809\pi\) | ||||
−0.0465077 | + | 0.998918i | \(0.514809\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.35015e24 | −1.31740 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 6.56509e23 | 0.189170 | 0.0945850 | − | 0.995517i | \(-0.469848\pi\) | ||||
0.0945850 | + | 0.995517i | \(0.469848\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4.17568e23 | −0.114512 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.40811e21 | 0.000367606 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −7.21370e24 | −1.79323 | −0.896616 | − | 0.442808i | \(-0.853982\pi\) | ||||
−0.896616 | + | 0.442808i | \(0.853982\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.44514e24 | 0.815695 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −4.42535e24 | −0.998203 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3.61104e24 | 0.776175 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.89515e24 | −0.388270 | −0.194135 | − | 0.980975i | \(-0.562190\pi\) | ||||
−0.194135 | + | 0.980975i | \(0.562190\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 6.11157e24 | 1.19374 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.39870e24 | −0.260526 | −0.130263 | − | 0.991479i | \(-0.541582\pi\) | ||||
−0.130263 | + | 0.991479i | \(0.541582\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −8.84493e24 | −1.57144 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −3.55458e24 | −0.602512 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −6.32972e23 | −0.102385 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.64124e24 | −0.870969 | −0.435485 | − | 0.900196i | \(-0.643423\pi\) | ||||
−0.435485 | + | 0.900196i | \(0.643423\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −9.79247e24 | −1.44343 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.15782e25 | 1.62973 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.19643e24 | 0.698632 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4.95179e23 | 0.0636018 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1.48234e24 | −0.181935 | −0.0909674 | − | 0.995854i | \(-0.528996\pi\) | ||||
−0.0909674 | + | 0.995854i | \(0.528996\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.58366e25 | 1.85773 | 0.928863 | − | 0.370424i | \(-0.120788\pi\) | ||||
0.928863 | + | 0.370424i | \(0.120788\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −5.98507e22 | −0.00671175 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.36404e24 | −0.360716 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.01383e25 | 3.09068 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.28629e24 | −0.126181 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.40908e25 | −1.32252 | −0.661259 | − | 0.750157i | \(-0.729978\pi\) | ||||
−0.661259 | + | 0.750157i | \(0.729978\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.35150e24 | 0.390845 | 0.195422 | − | 0.980719i | \(-0.437392\pi\) | ||||
0.195422 | + | 0.980719i | \(0.437392\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.14020e25 | −0.980238 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.16384e25 | 0.957901 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.24030e25 | 0.977493 | 0.488746 | − | 0.872426i | \(-0.337454\pi\) | ||||
0.488746 | + | 0.872426i | \(0.337454\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.81788e23 | 0.0288175 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2.71882e25 | −1.96583 | −0.982914 | − | 0.184064i | \(-0.941075\pi\) | ||||
−0.982914 | + | 0.184064i | \(0.941075\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −8.23766e24 | −0.570668 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.56884e24 | −0.104149 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5.59500e24 | 0.356008 | 0.178004 | − | 0.984030i | \(-0.443036\pi\) | ||||
0.178004 | + | 0.984030i | \(0.443036\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.35284e24 | 0.143521 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −2.20978e25 | −1.29246 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.26152e25 | −1.26851 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.99055e24 | 0.322302 | 0.161151 | − | 0.986930i | \(-0.448479\pi\) | ||||
0.161151 | + | 0.986930i | \(0.448479\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.07500e25 | 0.554868 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.18623e24 | 0.157804 | 0.0789019 | − | 0.996882i | \(-0.474859\pi\) | ||||
0.0789019 | + | 0.996882i | \(0.474859\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9.19655e24 | 0.437125 | 0.218562 | − | 0.975823i | \(-0.429863\pi\) | ||||
0.218562 | + | 0.975823i | \(0.429863\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.75004e25 | 0.798444 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 5.34180e24 | 0.233979 | 0.116990 | − | 0.993133i | \(-0.462676\pi\) | ||||
0.116990 | + | 0.993133i | \(0.462676\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.62552e25 | −1.10426 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.20043e25 | −1.29273 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 7.94613e22 | 0.00308301 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.13644e25 | −0.423602 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.71746e23 | 0.0168960 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5.41606e24 | 0.186422 | 0.0932108 | − | 0.995646i | \(-0.470287\pi\) | ||||
0.0932108 | + | 0.995646i | \(0.470287\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.42813e25 | −1.13417 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 8.35889e25 | 2.65859 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4.16709e24 | 0.127434 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.18277e25 | 0.936010 | 0.468005 | − | 0.883726i | \(-0.344973\pi\) | ||||
0.468005 | + | 0.883726i | \(0.344973\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.54477e25 | 0.436947 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.75069e25 | 0.476360 | 0.238180 | − | 0.971221i | \(-0.423449\pi\) | ||||
0.238180 | + | 0.971221i | \(0.423449\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.49202e25 | 0.914179 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3.18811e22 | 0.000803126 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2.28135e25 | −0.553103 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.62265e25 | 1.31216 | 0.656078 | − | 0.754693i | \(-0.272214\pi\) | ||||
0.656078 | + | 0.754693i | \(0.272214\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6.28831e25 | −1.41278 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −2.26953e25 | −0.490953 | −0.245476 | − | 0.969403i | \(-0.578944\pi\) | ||||
−0.245476 | + | 0.969403i | \(0.578944\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5.74690e24 | 0.119720 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.95097e25 | −0.391449 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 6.77955e25 | 1.31033 | 0.655167 | − | 0.755484i | \(-0.272598\pi\) | ||||
0.655167 | + | 0.755484i | \(0.272598\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.09403e26 | −2.03718 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3.63160e25 | 0.651602 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −2.43690e24 | −0.0421375 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.37744e24 | −0.0562895 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2.66680e25 | −0.428450 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.02376e26 | −1.58576 | −0.792881 | − | 0.609377i | \(-0.791420\pi\) | ||||
−0.792881 | + | 0.609377i | \(0.791420\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4.15135e25 | −0.620045 | −0.310023 | − | 0.950729i | \(-0.600337\pi\) | ||||
−0.310023 | + | 0.950729i | \(0.600337\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −8.16211e25 | −1.17568 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −5.35976e25 | −0.744636 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 8.45652e25 | 1.13335 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −8.83990e23 | −0.0114301 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.27428e26 | 1.58985 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.05889e25 | −0.127495 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 7.75951e25 | 0.901734 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.15447e25 | 0.241684 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.49513e25 | −0.161922 | −0.0809611 | − | 0.996717i | \(-0.525799\pi\) | ||||
−0.0809611 | + | 0.996717i | \(0.525799\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 2.12988e25 | 0.222719 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.34544e25 | 0.135862 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.62975e25 | −0.549047 | −0.274524 | − | 0.961580i | \(-0.588520\pi\) | ||||
−0.274524 | + | 0.961580i | \(0.588520\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2.30104e24 | −0.0216764 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.17968e26 | 1.07355 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.68331e26 | −2.35930 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 6.78282e25 | 0.576272 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 2.39450e26 | 1.96603 | 0.983014 | − | 0.183528i | \(-0.0587519\pi\) | ||||
0.983014 | + | 0.183528i | \(0.0587519\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.30357e24 | 0.0341520 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −7.79452e24 | −0.0597919 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.51707e25 | 0.112506 | 0.0562531 | − | 0.998417i | \(-0.482085\pi\) | ||||
0.0562531 | + | 0.998417i | \(0.482085\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5.09709e25 | −0.365478 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.64136e26 | 1.83142 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.57702e26 | 1.05747 | 0.528737 | − | 0.848786i | \(-0.322666\pi\) | ||||
0.528737 | + | 0.848786i | \(0.322666\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.27956e26 | −0.829882 | −0.414941 | − | 0.909848i | \(-0.636198\pi\) | ||||
−0.414941 | + | 0.909848i | \(0.636198\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −3.46871e25 | −0.217620 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.55433e26 | −0.943408 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.38761e26 | 0.814885 | 0.407442 | − | 0.913231i | \(-0.366421\pi\) | ||||
0.407442 | + | 0.913231i | \(0.366421\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −7.88506e25 | −0.448083 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.86140e26 | −2.12359 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.66211e25 | 0.141702 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.72666e24 | 0.00889663 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.40537e26 | 0.701017 | 0.350509 | − | 0.936560i | \(-0.386009\pi\) | ||||
0.350509 | + | 0.936560i | \(0.386009\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.81064e26 | −0.874454 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −5.74338e25 | −0.268588 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.83090e26 | −0.829171 | −0.414585 | − | 0.910010i | \(-0.636073\pi\) | ||||
−0.414585 | + | 0.910010i | \(0.636073\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.37041e26 | −0.601091 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −2.10439e26 | −0.894068 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.60928e26 | 0.662335 | 0.331167 | − | 0.943572i | \(-0.392558\pi\) | ||||
0.331167 | + | 0.943572i | \(0.392558\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3.63963e26 | −1.45127 | −0.725637 | − | 0.688078i | \(-0.758455\pi\) | ||||
−0.725637 | + | 0.688078i | \(0.758455\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.00457e24 | 0.00774472 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.57142e26 | −0.588323 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5.19977e26 | 1.88665 | 0.943326 | − | 0.331869i | \(-0.107679\pi\) | ||||
0.943326 | + | 0.331869i | \(0.107679\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 8.47264e26 | 2.97958 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.82920e26 | −0.623547 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4.16714e26 | 1.37709 | 0.688547 | − | 0.725192i | \(-0.258249\pi\) | ||||
0.688547 | + | 0.725192i | \(0.258249\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −2.52126e26 | −0.807801 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2.46583e25 | 0.0766045 | 0.0383022 | − | 0.999266i | \(-0.487805\pi\) | ||||
0.0383022 | + | 0.999266i | \(0.487805\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −6.19024e26 | −1.86486 | −0.932430 | − | 0.361351i | \(-0.882316\pi\) | ||||
−0.932430 | + | 0.361351i | \(0.882316\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.96699e26 | 1.45119 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 6.12129e26 | 1.73463 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2.29550e25 | 0.0630982 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.63316e25 | −0.0702158 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2.07734e26 | −0.537436 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6.40082e26 | −1.60678 | −0.803390 | − | 0.595453i | \(-0.796973\pi\) | ||||
−0.803390 | + | 0.595453i | \(0.796973\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −3.02879e26 | −0.737792 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 3.29526e26 | 0.779004 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.16685e27 | 2.67725 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.74180e24 | 0.00387917 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −4.35543e26 | −0.941629 | −0.470815 | − | 0.882232i | \(-0.656040\pi\) | ||||
−0.470815 | + | 0.882232i | \(0.656040\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 8.74903e25 | 0.183635 | 0.0918175 | − | 0.995776i | \(-0.470732\pi\) | ||||
0.0918175 | + | 0.995776i | \(0.470732\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −8.51494e24 | −0.0173526 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 3.17146e26 | 0.627578 | 0.313789 | − | 0.949493i | \(-0.398401\pi\) | ||||
0.313789 | + | 0.949493i | \(0.398401\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.98846e25 | −0.0958609 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.30043e27 | −2.42699 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.61698e26 | −0.293110 | −0.146555 | − | 0.989203i | \(-0.546818\pi\) | ||||
−0.146555 | + | 0.989203i | \(0.546818\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.35223e26 | 0.590257 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 8.35282e24 | 0.0142877 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.45108e26 | −0.241145 | −0.120573 | − | 0.992705i | \(-0.538473\pi\) | ||||
−0.120573 | + | 0.992705i | \(0.538473\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4.52310e26 | −0.730336 | −0.365168 | − | 0.930942i | \(-0.618988\pi\) | ||||
−0.365168 | + | 0.930942i | \(0.618988\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −4.22146e26 | −0.662345 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −4.62954e26 | −0.705883 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.61347e27 | 2.39092 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −5.86521e26 | −0.844764 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.29850e26 | −0.181794 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.55615e26 | 0.620090 | 0.310045 | − | 0.950722i | \(-0.399656\pi\) | ||||
0.310045 | + | 0.950722i | \(0.399656\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4.85006e26 | −0.641743 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1.33349e27 | −1.71553 | −0.857766 | − | 0.514041i | \(-0.828148\pi\) | ||||
−0.857766 | + | 0.514041i | \(0.828148\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.09651e26 | −0.387355 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −8.58763e26 | −1.04466 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 3.13697e26 | 0.371120 | 0.185560 | − | 0.982633i | \(-0.440590\pi\) | ||||
0.185560 | + | 0.982633i | \(0.440590\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 7.41785e26 | 0.853527 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.12557e26 | 0.125974 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.44178e27 | 1.56970 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.07111e27 | 1.13446 | 0.567232 | − | 0.823558i | \(-0.308014\pi\) | ||||
0.567232 | + | 0.823558i | \(0.308014\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2.36904e24 | −0.00244122 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −3.75101e25 | −0.0376090 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 7.72175e26 | 0.753363 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2.10304e27 | 1.99671 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.09656e27 | 1.01324 | 0.506620 | − | 0.862169i | \(-0.330895\pi\) | ||||
0.506620 | + | 0.862169i | \(0.330895\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −7.01771e26 | −0.631131 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 3.61921e26 | 0.316823 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −4.27044e26 | −0.363905 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.04320e27 | −0.865421 | −0.432710 | − | 0.901533i | \(-0.642443\pi\) | ||||
−0.432710 | + | 0.901533i | \(0.642443\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.04869e25 | 0.0165469 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −2.47644e27 | −1.94750 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 9.74372e25 | 0.0746135 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 7.06650e26 | 0.526954 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −9.53130e25 | −0.0692193 | −0.0346097 | − | 0.999401i | \(-0.511019\pi\) | ||||
−0.0346097 | + | 0.999401i | \(0.511019\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.81082e26 | 0.128083 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −2.82678e26 | −0.194751 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.57548e27 | −1.05731 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −8.66622e26 | −0.566569 | −0.283284 | − | 0.959036i | \(-0.591424\pi\) | ||||
−0.283284 | + | 0.959036i | \(0.591424\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.54962e27 | 0.986994 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.60783e25 | 0.0161832 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.89332e27 | 1.14481 | 0.572407 | − | 0.819969i | \(-0.306010\pi\) | ||||
0.572407 | + | 0.819969i | \(0.306010\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −2.30870e27 | −1.36031 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.13120e26 | 0.0649528 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.55052e27 | −0.867673 | −0.433837 | − | 0.900992i | \(-0.642841\pi\) | ||||
−0.433837 | + | 0.900992i | \(0.642841\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.42610e27 | −0.777816 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −3.71515e26 | −0.197507 | −0.0987534 | − | 0.995112i | \(-0.531486\pi\) | ||||
−0.0987534 | + | 0.995112i | \(0.531486\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.18840e26 | 0.0615856 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 2.94815e25 | 0.0148938 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 7.86850e26 | 0.387539 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.51500e27 | −0.727501 | −0.363751 | − | 0.931496i | \(-0.618504\pi\) | ||||
−0.363751 | + | 0.931496i | \(0.618504\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 2.18968e27 | 1.02525 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.67392e27 | 0.764257 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −5.53052e26 | −0.246238 | −0.123119 | − | 0.992392i | \(-0.539290\pi\) | ||||
−0.123119 | + | 0.992392i | \(0.539290\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −3.60141e26 | −0.156378 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.03558e27 | −0.862054 | −0.431027 | − | 0.902339i | \(-0.641849\pi\) | ||||
−0.431027 | + | 0.902339i | \(0.641849\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −9.99780e26 | −0.412973 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.04630e25 | 0.00421573 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −2.70171e27 | −1.06190 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.79338e27 | 1.07110 | 0.535550 | − | 0.844503i | \(-0.320104\pi\) | ||||
0.535550 | + | 0.844503i | \(0.320104\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.76724e27 | 1.03521 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 4.29473e27 | 1.56758 | 0.783791 | − | 0.621025i | \(-0.213283\pi\) | ||||
0.783791 | + | 0.621025i | \(0.213283\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.41814e27 | 0.861223 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −5.04023e27 | −1.75166 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.60857e27 | 0.884702 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 9.82914e25 | 0.0325335 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 5.03459e27 | 1.62640 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.42434e27 | 0.764419 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.18659e27 | 0.672987 | 0.336494 | − | 0.941686i | \(-0.390759\pi\) | ||||
0.336494 | + | 0.941686i | \(0.390759\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.78396e27 | −0.535987 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.78758e27 | 1.11093 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −7.03261e27 | −2.01382 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2.85268e27 | −0.797563 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.65866e27 | 0.452796 | 0.226398 | − | 0.974035i | \(-0.427305\pi\) | ||||
0.226398 | + | 0.974035i | \(0.427305\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.10844e27 | −0.295472 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4.67357e25 | −0.0121658 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 4.71359e26 | 0.119827 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6.33191e27 | −1.57208 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.49066e27 | −0.361475 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −2.56250e27 | −0.606951 | −0.303475 | − | 0.952839i | \(-0.598147\pi\) | ||||
−0.303475 | + | 0.952839i | \(0.598147\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −4.85027e27 | −1.12219 | −0.561096 | − | 0.827751i | \(-0.689620\pi\) | ||||
−0.561096 | + | 0.827751i | \(0.689620\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 6.96552e27 | 1.57432 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.17017e27 | −0.258376 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 8.80981e25 | 0.0190045 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.28306e26 | −0.0270426 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.50335e26 | 0.0515540 | 0.0257770 | − | 0.999668i | \(-0.491794\pi\) | ||||
0.0257770 | + | 0.999668i | \(0.491794\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −5.35775e27 | −1.07816 | −0.539081 | − | 0.842254i | \(-0.681228\pi\) | ||||
−0.539081 | + | 0.842254i | \(0.681228\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 3.51663e26 | 0.0691534 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −8.46014e27 | −1.62583 | −0.812915 | − | 0.582382i | \(-0.802121\pi\) | ||||
−0.812915 | + | 0.582382i | \(0.802121\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −6.64078e27 | −1.24724 | −0.623621 | − | 0.781727i | \(-0.714339\pi\) | ||||
−0.623621 | + | 0.781727i | \(0.714339\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 6.31969e27 | 1.16007 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 7.07074e27 | 1.26864 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.76343e27 | 0.835407 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −7.72737e27 | −1.32477 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 8.48056e27 | 1.42130 | 0.710650 | − | 0.703546i | \(-0.248401\pi\) | ||||
0.710650 | + | 0.703546i | \(0.248401\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.02510e28 | 1.67959 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −5.48052e27 | −0.877929 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.47787e27 | 0.231472 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.16770e28 | 1.78829 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 2.02658e27 | 0.303487 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −9.59824e27 | −1.40560 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −7.67513e27 | −1.09918 | −0.549591 | − | 0.835434i | \(-0.685217\pi\) | ||||
−0.549591 | + | 0.835434i | \(0.685217\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3.53463e25 | 0.00495069 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.77524e27 | 0.243187 | 0.121593 | − | 0.992580i | \(-0.461200\pi\) | ||||
0.121593 | + | 0.992580i | \(0.461200\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −8.09486e27 | −1.08461 | −0.542306 | − | 0.840181i | \(-0.682449\pi\) | ||||
−0.542306 | + | 0.840181i | \(0.682449\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.87352e28 | 2.45543 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1.31037e28 | −1.67993 | −0.839963 | − | 0.542644i | \(-0.817423\pi\) | ||||
−0.839963 | + | 0.542644i | \(0.817423\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.02011e27 | 0.253351 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 5.64391e27 | 0.692466 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.15610e27 | 0.138774 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.12649e27 | 0.719514 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2.36416e25 | 0.00271670 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.57552e28 | 1.77153 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −8.69739e26 | −0.0956958 | −0.0478479 | − | 0.998855i | \(-0.515236\pi\) | ||||
−0.0478479 | + | 0.998855i | \(0.515236\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −3.33864e27 | −0.359481 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 9.28888e27 | 0.978796 | 0.489398 | − | 0.872061i | \(-0.337217\pi\) | ||||
0.489398 | + | 0.872061i | \(0.337217\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −9.02161e27 | −0.930374 | −0.465187 | − | 0.885213i | \(-0.654013\pi\) | ||||
−0.465187 | + | 0.885213i | \(0.654013\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 5.34555e27 | 0.539549 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 6.25902e27 | 0.618346 | 0.309173 | − | 0.951006i | \(-0.399948\pi\) | ||||
0.309173 | + | 0.951006i | \(0.399948\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.44866e28 | −2.36790 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.13802e27 | −0.107724 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −3.74454e27 | −0.346984 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −5.87787e27 | −0.533213 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.95050e28 | −1.73228 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2.51014e28 | −2.18264 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 8.73675e27 | 0.743814 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 6.32734e26 | 0.0527457 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.61340e27 | −0.131698 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.07075e28 | 0.855891 | 0.427946 | − | 0.903804i | \(-0.359237\pi\) | ||||
0.427946 | + | 0.903804i | \(0.359237\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 3.26046e25 | 0.00255224 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 4.49055e27 | 0.344251 | 0.172125 | − | 0.985075i | \(-0.444937\pi\) | ||||
0.172125 | + | 0.985075i | \(0.444937\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.66367e27 | 0.124910 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.39146e28 | 1.02322 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −2.49100e28 | −1.79417 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.03334e27 | 0.0729029 | 0.0364514 | − | 0.999335i | \(-0.488395\pi\) | ||||
0.0364514 | + | 0.999335i | \(0.488395\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.66720e28 | −1.15218 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 5.32340e27 | 0.360390 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9.37228e27 | 0.621582 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.38255e25 | −0.000898306 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 2.40721e28 | 1.53237 | 0.766186 | − | 0.642619i | \(-0.222152\pi\) | ||||
0.766186 | + | 0.642619i | \(0.222152\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.38865e28 | 1.48981 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −1.60120e28 | −0.978523 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 5.90439e26 | 0.0353561 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 9.20092e27 | 0.539890 | 0.269945 | − | 0.962876i | \(-0.412995\pi\) | ||||
0.269945 | + | 0.962876i | \(0.412995\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.29949e28 | 0.747221 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 4.25377e27 | 0.239703 | 0.119851 | − | 0.992792i | \(-0.461758\pi\) | ||||
0.119851 | + | 0.992792i | \(0.461758\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.56779e28 | 1.97032 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.97578e28 | −1.06939 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −3.12257e28 | −1.65649 | −0.828243 | − | 0.560369i | \(-0.810659\pi\) | ||||
−0.828243 | + | 0.560369i | \(0.810659\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.55285e28 | 1.32738 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.08995e28 | −1.06517 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 3.43857e28 | 1.71789 | 0.858945 | − | 0.512068i | \(-0.171120\pi\) | ||||
0.858945 | + | 0.512068i | \(0.171120\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.62757e27 | 0.128683 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −3.65042e27 | −0.175259 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −5.51210e28 | −2.59442 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.68564e28 | 0.777845 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −6.00755e25 | −0.00271799 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 5.97297e27 | 0.264961 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.49897e28 | −0.651990 | −0.325995 | − | 0.945371i | \(-0.605699\pi\) | ||||
−0.325995 | + | 0.945371i | \(0.605699\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −8.64172e27 | −0.368574 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 4.03020e28 | 1.68556 | 0.842780 | − | 0.538258i | \(-0.180917\pi\) | ||||
0.842780 | + | 0.538258i | \(0.180917\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.78732e27 | 0.114318 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.90458e28 | 0.766047 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −2.15857e28 | −0.851468 | −0.425734 | − | 0.904848i | \(-0.639984\pi\) | ||||
−0.425734 | + | 0.904848i | \(0.639984\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.63735e27 | −0.102031 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 7.63326e25 | 0.00289637 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −3.69372e28 | −1.37469 | −0.687346 | − | 0.726330i | \(-0.741225\pi\) | ||||
−0.687346 | + | 0.726330i | \(0.741225\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.35064e27 | 0.158821 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −2.68939e28 | −0.963031 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.20493e27 | 0.0423251 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −9.20845e27 | −0.317312 | −0.158656 | − | 0.987334i | \(-0.550716\pi\) | ||||
−0.158656 | + | 0.987334i | \(0.550716\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 8.69551e26 | 0.0293953 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.59409e28 | 0.528680 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −3.39300e28 | −1.10403 | −0.552013 | − | 0.833835i | \(-0.686140\pi\) | ||||
−0.552013 | + | 0.833835i | \(0.686140\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2.99499e28 | −0.956143 |
(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 | 8.20.a.b.1.1 | ✓ | 3 | |
3.2 | odd | 2 | 72.20.a.f.1.2 | 3 | |||
4.3 | odd | 2 | 16.20.a.f.1.3 | 3 | |||
8.3 | odd | 2 | 64.20.a.m.1.1 | 3 | |||
8.5 | even | 2 | 64.20.a.l.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8.20.a.b.1.1 | ✓ | 3 | 1.1 | even | 1 | trivial | |
16.20.a.f.1.3 | 3 | 4.3 | odd | 2 | |||
64.20.a.l.1.3 | 3 | 8.5 | even | 2 | |||
64.20.a.m.1.1 | 3 | 8.3 | odd | 2 | |||
72.20.a.f.1.2 | 3 | 3.2 | odd | 2 |