Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [64,24,Mod(1,64)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(64, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 24, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("64.1");
S:= CuspForms(chi, 24);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 64 = 2^{6} \) |
Weight: | \( k \) | \(=\) | \( 24 \) |
Character orbit: | \([\chi]\) | \(=\) | 64.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: | \(214.530583901\) |
Analytic rank: | \(1\) |
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: | \( x^{3} - 166408x - 10560732 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{21}\cdot 3^{3} \) |
Twist minimal: | no (minimal twist has level 8) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(436.575\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 64.1 |
$q$-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 | ||||||||
\(3\) | −574251. | −1.87157 | −0.935787 | − | 0.352565i | \(-0.885309\pi\) | ||||
−0.935787 | + | 0.352565i | \(0.885309\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −8.41392e7 | −0.770625 | −0.385312 | − | 0.922786i | \(-0.625906\pi\) | ||||
−0.385312 | + | 0.922786i | \(0.625906\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 5.95738e9 | 1.13875 | 0.569374 | − | 0.822079i | \(-0.307186\pi\) | ||||
0.569374 | + | 0.822079i | \(0.307186\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.35621e11 | 2.50279 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.24326e12 | 1.31385 | 0.656924 | − | 0.753957i | \(-0.271857\pi\) | ||||
0.656924 | + | 0.753957i | \(0.271857\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −7.21479e12 | −1.11654 | −0.558271 | − | 0.829658i | \(-0.688535\pi\) | ||||
−0.558271 | + | 0.829658i | \(0.688535\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 4.83170e13 | 1.44228 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −6.50936e13 | −0.460655 | −0.230327 | − | 0.973113i | \(-0.573980\pi\) | ||||
−0.230327 | + | 0.973113i | \(0.573980\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.56139e14 | −1.09526 | −0.547629 | − | 0.836721i | \(-0.684470\pi\) | ||||
−0.547629 | + | 0.836721i | \(0.684470\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.42103e15 | −2.13125 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.08126e15 | 0.674307 | 0.337154 | − | 0.941450i | \(-0.390536\pi\) | ||||
0.337154 | + | 0.941450i | \(0.390536\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.84153e15 | −0.406137 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −8.12435e16 | −2.81258 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.69935e16 | 0.715255 | 0.357628 | − | 0.933864i | \(-0.383586\pi\) | ||||
0.357628 | + | 0.933864i | \(0.383586\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.40563e17 | −1.70047 | −0.850234 | − | 0.526405i | \(-0.823540\pi\) | ||||
−0.850234 | + | 0.526405i | \(0.823540\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −7.13941e17 | −2.45896 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −5.01249e17 | −0.877548 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.28193e17 | 0.488059 | 0.244030 | − | 0.969768i | \(-0.421531\pi\) | ||||
0.244030 | + | 0.969768i | \(0.421531\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4.14310e18 | 2.08969 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.59837e18 | 0.453589 | 0.226795 | − | 0.973943i | \(-0.427175\pi\) | ||||
0.226795 | + | 0.973943i | \(0.427175\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.35994e18 | 1.20778 | 0.603889 | − | 0.797068i | \(-0.293617\pi\) | ||||
0.603889 | + | 0.797068i | \(0.293617\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.98249e19 | −1.92871 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.63997e19 | 0.967631 | 0.483815 | − | 0.875170i | \(-0.339251\pi\) | ||||
0.483815 | + | 0.875170i | \(0.339251\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 8.12160e18 | 0.296747 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.73800e19 | 0.862149 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.64089e19 | 0.391361 | 0.195681 | − | 0.980668i | \(-0.437308\pi\) | ||||
0.195681 | + | 0.980668i | \(0.437308\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.04607e20 | −1.01248 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.19363e20 | 2.04986 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.24947e20 | −1.40286 | −0.701429 | − | 0.712739i | \(-0.747454\pi\) | ||||
−0.701429 | + | 0.712739i | \(0.747454\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.22520e20 | 0.948995 | 0.474498 | − | 0.880257i | \(-0.342630\pi\) | ||||
0.474498 | + | 0.880257i | \(0.342630\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.40368e21 | 2.85005 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 6.07047e20 | 0.860436 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.09896e21 | −1.09932 | −0.549658 | − | 0.835390i | \(-0.685242\pi\) | ||||
−0.549658 | + | 0.835390i | \(0.685242\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.76941e21 | −1.26202 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.30177e20 | 0.118193 | 0.0590964 | − | 0.998252i | \(-0.481178\pi\) | ||||
0.0590964 | + | 0.998252i | \(0.481178\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.33706e20 | 0.311028 | 0.155514 | − | 0.987834i | \(-0.450297\pi\) | ||||
0.155514 | + | 0.987834i | \(0.450297\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.78025e21 | 0.760116 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 7.40655e21 | 1.49614 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.59992e21 | −0.391064 | −0.195532 | − | 0.980697i | \(-0.562643\pi\) | ||||
−0.195532 | + | 0.980697i | \(0.562643\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 2.44721e22 | 2.76117 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.05807e22 | −0.901817 | −0.450908 | − | 0.892570i | \(-0.648900\pi\) | ||||
−0.450908 | + | 0.892570i | \(0.648900\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.47692e21 | 0.354992 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.69861e22 | −1.33865 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.07434e22 | 1.55622 | 0.778112 | − | 0.628126i | \(-0.216178\pi\) | ||||
0.778112 | + | 0.628126i | \(0.216178\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.29812e22 | −1.27146 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.38143e23 | 3.18255 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.67930e22 | 0.844034 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9.40029e22 | −1.33434 | −0.667169 | − | 0.744906i | \(-0.732494\pi\) | ||||
−0.667169 | + | 0.744906i | \(0.732494\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.92937e23 | 3.28828 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.31018e23 | 1.16851 | 0.584257 | − | 0.811568i | \(-0.301386\pi\) | ||||
0.584257 | + | 0.811568i | \(0.301386\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.91184e22 | 0.420819 | 0.210409 | − | 0.977613i | \(-0.432520\pi\) | ||||
0.210409 | + | 0.977613i | \(0.432520\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.87842e23 | 1.64240 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −7.78257e22 | −0.357445 | −0.178723 | − | 0.983899i | \(-0.557196\pi\) | ||||
−0.178723 | + | 0.983899i | \(0.557196\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.81626e22 | 0.253012 | 0.126506 | − | 0.991966i | \(-0.459624\pi\) | ||||
0.126506 | + | 0.991966i | \(0.459624\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.03315e23 | −0.913439 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.27400e23 | −1.04817 | −0.524086 | − | 0.851665i | \(-0.675593\pi\) | ||||
−0.524086 | + | 0.851665i | \(0.675593\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.59254e23 | −0.519638 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.69995e24 | −2.79447 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.87787e23 | −0.524570 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.50256e23 | 0.726194 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −9.17865e23 | −0.848926 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.41038e24 | 1.08360 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.80149e23 | 0.435373 | 0.217686 | − | 0.976019i | \(-0.430149\pi\) | ||||
0.217686 | + | 0.976019i | \(0.430149\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −4.22645e24 | −2.26045 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.38677e22 | 0.0286195 | 0.0143097 | − | 0.999898i | \(-0.495445\pi\) | ||||
0.0143097 | + | 0.999898i | \(0.495445\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.31313e24 | −1.24722 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 6.83576e24 | 2.16745 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.16090e24 | 0.846300 | 0.423150 | − | 0.906060i | \(-0.360924\pi\) | ||||
0.423150 | + | 0.906060i | \(0.360924\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.51803e24 | −0.344040 | −0.172020 | − | 0.985093i | \(-0.555029\pi\) | ||||
−0.172020 | + | 0.985093i | \(0.555029\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −9.41752e24 | −1.81099 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −8.96984e24 | −1.46697 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.95400e24 | −0.551194 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −4.66384e24 | −0.555385 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 5.94136e23 | 0.0605680 | 0.0302840 | − | 0.999541i | \(-0.490359\pi\) | ||||
0.0302840 | + | 0.999541i | \(0.490359\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.03677e25 | −0.906664 | −0.453332 | − | 0.891342i | \(-0.649765\pi\) | ||||
−0.453332 | + | 0.891342i | \(0.649765\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.53374e25 | −1.15292 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.02407e25 | 1.31042 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.27647e25 | 0.713125 | 0.356563 | − | 0.934271i | \(-0.383949\pi\) | ||||
0.356563 | + | 0.934271i | \(0.383949\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.51653e25 | −0.732461 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.83562e25 | 0.767866 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.28936e25 | 1.55681 | 0.778404 | − | 0.627764i | \(-0.216030\pi\) | ||||
0.778404 | + | 0.627764i | \(0.216030\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 6.00704e25 | 1.89494 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.74074e25 | 1.85126 | 0.925631 | − | 0.378427i | \(-0.123535\pi\) | ||||
0.925631 | + | 0.378427i | \(0.123535\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.02993e25 | 0.246668 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.31038e26 | −2.74120 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 5.33848e25 | 0.976984 | 0.488492 | − | 0.872569i | \(-0.337547\pi\) | ||||
0.488492 | + | 0.872569i | \(0.337547\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.88428e25 | −0.462488 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.86601e26 | 2.62555 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 5.76759e25 | 0.713156 | 0.356578 | − | 0.934266i | \(-0.383943\pi\) | ||||
0.356578 | + | 0.934266i | \(0.383943\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.31592e26 | 1.43194 | 0.715971 | − | 0.698130i | \(-0.245984\pi\) | ||||
0.715971 | + | 0.698130i | \(0.245984\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.85208e26 | −1.77612 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4.44417e25 | −0.376111 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −8.09280e25 | −0.605230 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −4.83999e26 | −3.20283 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4.07437e25 | −0.238878 | −0.119439 | − | 0.992842i | \(-0.538110\pi\) | ||||
−0.119439 | + | 0.992842i | \(0.538110\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.00984e26 | −1.56543 | −0.782717 | − | 0.622378i | \(-0.786167\pi\) | ||||
−0.782717 | + | 0.622378i | \(0.786167\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −3.48597e26 | −1.61037 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4.17423e25 | 0.171481 | 0.0857403 | − | 0.996318i | \(-0.472674\pi\) | ||||
0.0857403 | + | 0.996318i | \(0.472674\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.13013e25 | 0.114486 | 0.0572430 | − | 0.998360i | \(-0.481769\pi\) | ||||
0.0572430 | + | 0.998360i | \(0.481769\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 6.31080e26 | 2.05745 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.79958e26 | 0.814496 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.34485e26 | −0.349547 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 7.26008e26 | 1.68765 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −6.91423e26 | −1.43900 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.37199e26 | −0.442451 | −0.221226 | − | 0.975223i | \(-0.571006\pi\) | ||||
−0.221226 | + | 0.975223i | \(0.571006\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.32179e26 | −0.221207 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −6.19259e26 | −0.930744 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.43312e27 | −1.93640 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −4.78756e26 | −0.582113 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.69637e26 | 0.514341 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.49431e27 | −1.47549 | −0.737744 | − | 0.675080i | \(-0.764109\pi\) | ||||
−0.737744 | + | 0.675080i | \(0.764109\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.14076e27 | −1.01648 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4.09710e26 | 0.329746 | 0.164873 | − | 0.986315i | \(-0.447279\pi\) | ||||
0.164873 | + | 0.986315i | \(0.447279\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.57268e27 | −1.14428 | −0.572141 | − | 0.820155i | \(-0.693887\pi\) | ||||
−0.572141 | + | 0.820155i | \(0.693887\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −4.25322e27 | −2.80014 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2.46809e27 | 1.47152 | 0.735762 | − | 0.677240i | \(-0.236824\pi\) | ||||
0.735762 | + | 0.677240i | \(0.236824\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.37985e27 | −0.745681 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.49300e27 | 0.731906 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.15361e27 | −0.513432 | −0.256716 | − | 0.966487i | \(-0.582641\pi\) | ||||
−0.256716 | + | 0.966487i | \(0.582641\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.38713e26 | −0.258291 | −0.129146 | − | 0.991626i | \(-0.541223\pi\) | ||||
−0.129146 | + | 0.991626i | \(0.541223\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −6.40458e27 | −2.35515 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −6.83345e26 | −0.228681 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.01243e27 | 1.22290 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 6.07600e27 | 1.68782 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5.85944e26 | 0.148460 | 0.0742298 | − | 0.997241i | \(-0.476350\pi\) | ||||
0.0742298 | + | 0.997241i | \(0.476350\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.83079e27 | 0.885937 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −3.14512e27 | −0.664394 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −5.28864e26 | −0.102121 | −0.0510603 | − | 0.998696i | \(-0.516260\pi\) | ||||
−0.0510603 | + | 0.998696i | \(0.516260\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.14664e27 | 0.555777 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.10726e28 | 1.79013 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −5.59316e27 | −0.828259 | −0.414129 | − | 0.910218i | \(-0.635914\pi\) | ||||
−0.414129 | + | 0.910218i | \(0.635914\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.22202e27 | −0.301593 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.33969e28 | −2.91259 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.11747e28 | −1.27668 | −0.638341 | − | 0.769753i | \(-0.720379\pi\) | ||||
−0.638341 | + | 0.769753i | \(0.720379\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.14584e28 | 1.20220 | 0.601100 | − | 0.799174i | \(-0.294729\pi\) | ||||
0.601100 | + | 0.799174i | \(0.294729\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.46820e28 | 2.37963 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −6.01927e27 | −0.533602 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.04295e28 | 0.850638 | 0.425319 | − | 0.905044i | \(-0.360162\pi\) | ||||
0.425319 | + | 0.905044i | \(0.360162\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −5.66815e28 | −4.25592 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.50359e25 | 0.00657302 | 0.00328651 | − | 0.999995i | \(-0.498954\pi\) | ||||
0.00328651 | + | 0.999995i | \(0.498954\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.19749e28 | −1.40082 | −0.700412 | − | 0.713738i | \(-0.747001\pi\) | ||||
−0.700412 | + | 0.713738i | \(0.747001\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2.68709e28 | −1.57967 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 9.52209e27 | 0.516524 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.57304e28 | −0.787797 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.39812e28 | 2.49731 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2.29758e28 | −0.982410 | −0.491205 | − | 0.871044i | \(-0.663443\pi\) | ||||
−0.491205 | + | 0.871044i | \(0.663443\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.73407e28 | 1.08108 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.01007e29 | −3.69531 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.22306e28 | −0.752893 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.38459e28 | 1.37535 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −7.52370e28 | −2.18696 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.71366e28 | −0.731320 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3.40762e28 | −0.851842 | −0.425921 | − | 0.904760i | \(-0.640050\pi\) | ||||
−0.425921 | + | 0.904760i | \(0.640050\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3.39488e28 | −0.787593 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5.66460e28 | −1.22018 | −0.610091 | − | 0.792331i | \(-0.708867\pi\) | ||||
−0.610091 | + | 0.792331i | \(0.708867\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.78832e28 | 0.758031 | 0.379016 | − | 0.925390i | \(-0.376263\pi\) | ||||
0.379016 | + | 0.925390i | \(0.376263\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.18105e29 | −2.19632 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3.72097e28 | −0.643390 | −0.321695 | − | 0.946843i | \(-0.604253\pi\) | ||||
−0.321695 | + | 0.946843i | \(0.604253\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.84250e28 | 0.939736 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4.46915e28 | 0.668985 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.62010e28 | 0.504536 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.49306e28 | 0.453469 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −3.91424e28 | −0.473531 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 9.76990e28 | 1.10189 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.62405e28 | −0.591599 | −0.295799 | − | 0.955250i | \(-0.595586\pi\) | ||||
−0.295799 | + | 0.955250i | \(0.595586\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.24453e29 | 1.22151 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 9.24657e28 | 0.847160 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9.79219e28 | 0.837792 | 0.418896 | − | 0.908034i | \(-0.362417\pi\) | ||||
0.418896 | + | 0.908034i | \(0.362417\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.45435e29 | 1.96173 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.99081e29 | −2.23416 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.14663e29 | −0.800828 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.48877e29 | 0.972541 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7.68930e28 | 0.470000 | 0.235000 | − | 0.971995i | \(-0.424491\pi\) | ||||
0.235000 | + | 0.971995i | \(0.424491\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.15740e29 | 1.80650 | 0.903249 | − | 0.429116i | \(-0.141175\pi\) | ||||
0.903249 | + | 0.429116i | \(0.141175\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.86155e29 | 3.14037 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2.41820e29 | −1.21362 | −0.606809 | − | 0.794847i | \(-0.707551\pi\) | ||||
−0.606809 | + | 0.794847i | \(0.707551\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.93669e28 | −0.0910824 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.22687e29 | 0.981771 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2.43466e29 | −1.00659 | −0.503294 | − | 0.864115i | \(-0.667879\pi\) | ||||
−0.503294 | + | 0.864115i | \(0.667879\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.14606e28 | 0.199592 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3.73410e29 | −1.35913 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −7.01473e28 | −0.239686 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.79274e29 | 0.896128 | 0.448064 | − | 0.894001i | \(-0.352114\pi\) | ||||
0.448064 | + | 0.894001i | \(0.352114\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3.76609e29 | 1.13524 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.57328e29 | 0.445662 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.37422e29 | 0.365937 | 0.182968 | − | 0.983119i | \(-0.441429\pi\) | ||||
0.182968 | + | 0.983119i | \(0.441429\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −8.09911e29 | −2.02805 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −3.39049e29 | −0.798613 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.24160e29 | 0.275189 | 0.137594 | − | 0.990489i | \(-0.456063\pi\) | ||||
0.137594 | + | 0.990489i | \(0.456063\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3.90576e29 | −0.814832 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.88270e29 | 0.762690 | 0.381345 | − | 0.924433i | \(-0.375461\pi\) | ||||
0.381345 | + | 0.924433i | \(0.375461\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −6.23181e29 | −1.15296 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.73415e30 | 3.02282 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.17387e30 | 1.92841 | 0.964203 | − | 0.265165i | \(-0.0854265\pi\) | ||||
0.964203 | + | 0.265165i | \(0.0854265\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.00570e29 | −0.310623 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −3.66761e28 | −0.0535634 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.18755e29 | 0.301364 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.47771e30 | −1.92087 | −0.960433 | − | 0.278511i | \(-0.910159\pi\) | ||||
−0.960433 | + | 0.278511i | \(0.910159\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.90257e30 | 2.33427 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4.26558e29 | −0.494103 | −0.247052 | − | 0.969002i | \(-0.579462\pi\) | ||||
−0.247052 | + | 0.969002i | \(0.579462\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.73561e30 | 1.89865 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −2.05906e30 | −2.12783 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.56679e29 | 0.641235 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.42830e30 | −1.31826 | −0.659129 | − | 0.752030i | \(-0.729075\pi\) | ||||
−0.659129 | + | 0.752030i | \(0.729075\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.81515e30 | −1.58391 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.93583e30 | −1.59750 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 8.90255e29 | 0.694963 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 8.71728e29 | 0.643897 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1.76509e30 | −1.23397 | −0.616985 | − | 0.786975i | \(-0.711646\pi\) | ||||
−0.616985 | + | 0.786975i | \(0.711646\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.02002e30 | 1.33694 | 0.668471 | − | 0.743739i | \(-0.266949\pi\) | ||||
0.668471 | + | 0.743739i | \(0.266949\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3.86410e30 | 2.42178 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.15153e29 | 0.187089 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.92138e30 | 1.08067 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 5.15094e30 | 2.74554 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.37148e30 | −1.19820 | −0.599102 | − | 0.800673i | \(-0.704476\pi\) | ||||
−0.599102 | + | 0.800673i | \(0.704476\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.23333e30 | 1.06990 | 0.534949 | − | 0.844884i | \(-0.320331\pi\) | ||||
0.534949 | + | 0.844884i | \(0.320331\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.27059e30 | 1.03160 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.71361e30 | −0.738541 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3.90666e30 | −1.59758 | −0.798792 | − | 0.601607i | \(-0.794527\pi\) | ||||
−0.798792 | + | 0.601607i | \(0.794527\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.91362e30 | 0.742697 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −3.27739e30 | −1.20749 | −0.603747 | − | 0.797176i | \(-0.706326\pi\) | ||||
−0.603747 | + | 0.797176i | \(0.706326\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.42811e30 | −1.19927 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −3.41183e29 | −0.113358 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 8.52929e29 | 0.269203 | 0.134602 | − | 0.990900i | \(-0.457025\pi\) | ||||
0.134602 | + | 0.990900i | \(0.457025\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.98718e30 | 0.595947 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 5.95364e30 | 1.69689 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 3.61641e30 | 0.979820 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 7.07801e30 | 1.82337 | 0.911685 | − | 0.410890i | \(-0.134782\pi\) | ||||
0.911685 | + | 0.410890i | \(0.134782\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 5.28843e30 | 1.29563 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5.36478e30 | 1.25023 | 0.625117 | − | 0.780531i | \(-0.285051\pi\) | ||||
0.625117 | + | 0.780531i | \(0.285051\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.58238e30 | 0.572584 | 0.286292 | − | 0.958142i | \(-0.407577\pi\) | ||||
0.286292 | + | 0.958142i | \(0.407577\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.16233e31 | −2.45255 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −3.99016e30 | −0.801394 | −0.400697 | − | 0.916211i | \(-0.631232\pi\) | ||||
−0.400697 | + | 0.916211i | \(0.631232\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6.54693e30 | −1.25184 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −7.33016e30 | −1.33467 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 9.15029e30 | 1.58684 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.69256e30 | 0.444825 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 6.22248e30 | 0.979495 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −5.56629e30 | −0.835041 | −0.417520 | − | 0.908668i | \(-0.637101\pi\) | ||||
−0.417520 | + | 0.908668i | \(0.637101\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.81080e30 | −0.544939 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.05411e31 | −1.43712 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 7.90932e30 | 1.02827 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.57505e30 | 0.443301 | 0.221651 | − | 0.975126i | \(-0.428856\pi\) | ||||
0.221651 | + | 0.975126i | \(0.428856\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2.46317e31 | −2.91368 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6.34262e30 | −0.715865 | −0.357933 | − | 0.933747i | \(-0.616518\pi\) | ||||
−0.357933 | + | 0.933747i | \(0.616518\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.05898e30 | −0.329486 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.46475e31 | −2.53403 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.37125e30 | 0.134592 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.30165e30 | −0.309439 | −0.154720 | − | 0.987958i | \(-0.549447\pi\) | ||||
−0.154720 | + | 0.987958i | \(0.549447\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3.87087e31 | −3.46477 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 2.32758e31 | 1.99009 | 0.995044 | − | 0.0994338i | \(-0.0317031\pi\) | ||||
0.995044 | + | 0.0994338i | \(0.0317031\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.10237e31 | −0.900487 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −5.91440e30 | −0.461657 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −2.41190e31 | −1.79930 | −0.899652 | − | 0.436607i | \(-0.856180\pi\) | ||||
−0.899652 | + | 0.436607i | \(0.856180\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.96670e30 | 0.354183 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 4.51827e31 | 3.08051 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −4.97418e30 | −0.324293 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.03890e31 | 1.27132 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −3.06562e31 | −1.82850 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6.94775e30 | 0.396470 | 0.198235 | − | 0.980155i | \(-0.436479\pi\) | ||||
0.198235 | + | 0.980155i | \(0.436479\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.69454e31 | 1.47135 | 0.735673 | − | 0.677337i | \(-0.236866\pi\) | ||||
0.735673 | + | 0.677337i | \(0.236866\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.65630e31 | 0.865580 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.56591e31 | 0.783328 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.13863e31 | −0.545310 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −7.65641e31 | −3.51106 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.15319e31 | −0.506452 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6.54819e30 | 0.275456 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −3.31204e31 | −1.33472 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.00972e31 | 0.389881 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7.63627e30 | −0.282561 | −0.141281 | − | 0.989970i | \(-0.545122\pi\) | ||||
−0.141281 | + | 0.989970i | \(0.545122\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −7.55667e31 | −2.67999 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −5.73515e30 | −0.194978 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.26514e31 | −0.738312 | −0.369156 | − | 0.929367i | \(-0.620353\pi\) | ||||
−0.369156 | + | 0.929367i | \(0.620353\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 7.59925e31 | 2.37514 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.61349e31 | −0.783390 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.54887e31 | −0.445324 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2.55207e31 | 0.703919 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1.58983e31 | −0.420741 | −0.210371 | − | 0.977622i | \(-0.567467\pi\) | ||||
−0.210371 | + | 0.977622i | \(0.567467\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5.31005e31 | −1.34854 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.64730e31 | 1.13273 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −7.95857e31 | −1.86204 | −0.931019 | − | 0.364972i | \(-0.881079\pi\) | ||||
−0.931019 | + | 0.364972i | \(0.881079\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.59611e31 | 0.807748 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.45789e32 | 3.14428 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 7.26713e31 | 1.50512 | 0.752561 | − | 0.658522i | \(-0.228818\pi\) | ||||
0.752561 | + | 0.658522i | \(0.228818\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.78373e31 | 0.752670 | 0.376335 | − | 0.926484i | \(-0.377184\pi\) | ||||
0.376335 | + | 0.926484i | \(0.377184\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.33971e31 | 0.447078 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.49180e31 | −0.273861 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −6.81473e31 | −1.20206 | −0.601031 | − | 0.799225i | \(-0.705243\pi\) | ||||
−0.601031 | + | 0.799225i | \(0.705243\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.72840e32 | 2.92982 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −6.30335e31 | −1.02694 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.28330e31 | 0.514189 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.43033e32 | 2.15349 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.10842e32 | 1.60459 | 0.802296 | − | 0.596927i | \(-0.203612\pi\) | ||||
0.802296 | + | 0.596927i | \(0.203612\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.33786e32 | 1.86245 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.39706e31 | −0.320939 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.12848e31 | 0.145333 | 0.0726666 | − | 0.997356i | \(-0.476849\pi\) | ||||
0.0726666 | + | 0.997356i | \(0.476849\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.26281e31 | 0.404246 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.79748e31 | −0.214269 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −7.82635e31 | −0.897741 | −0.448870 | − | 0.893597i | \(-0.648174\pi\) | ||||
−0.448870 | + | 0.893597i | \(0.648174\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8.73347e31 | −0.964119 | −0.482059 | − | 0.876139i | \(-0.660111\pi\) | ||||
−0.482059 | + | 0.876139i | \(0.660111\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2.58938e32 | −2.75136 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −5.47120e31 | −0.559623 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 9.31517e31 | 0.917320 | 0.458660 | − | 0.888612i | \(-0.348330\pi\) | ||||
0.458660 | + | 0.888612i | \(0.348330\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.60766e32 | −1.52439 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.18320e32 | −1.08040 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.93566e32 | −1.70229 | −0.851145 | − | 0.524930i | \(-0.824091\pi\) | ||||
−0.851145 | + | 0.524930i | \(0.824091\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 7.72284e31 | 0.654204 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −7.76155e31 | −0.633387 | −0.316694 | − | 0.948528i | \(-0.602573\pi\) | ||||
−0.316694 | + | 0.948528i | \(0.602573\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.48903e32 | −1.17074 | −0.585372 | − | 0.810765i | \(-0.699051\pi\) | ||||
−0.585372 | + | 0.810765i | \(0.699051\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.50332e32 | −1.89655 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.42724e32 | 1.77215 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −6.09526e31 | −0.428916 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 3.97050e32 | 2.69320 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −3.43819e31 | −0.224827 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.00939e31 | −0.126685 | −0.0633426 | − | 0.997992i | \(-0.520176\pi\) | ||||
−0.0633426 | + | 0.997992i | \(0.520176\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.36212e32 | 0.828080 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −5.72271e31 | −0.335509 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5.85957e31 | −0.331331 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 5.42345e31 | 0.295812 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.52315e31 | 0.132762 | 0.0663812 | − | 0.997794i | \(-0.478855\pi\) | ||||
0.0663812 | + | 0.997794i | \(0.478855\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 7.18001e31 | 0.364501 | 0.182251 | − | 0.983252i | \(-0.441662\pi\) | ||||
0.182251 | + | 0.983252i | \(0.441662\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3.55610e32 | 1.74196 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.17766e32 | 0.556700 | 0.278350 | − | 0.960480i | \(-0.410212\pi\) | ||||
0.278350 | + | 0.960480i | \(0.410212\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.03992e32 | −1.84314 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 8.22971e32 | 3.62413 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −2.88510e32 | −1.22648 | −0.613238 | − | 0.789898i | \(-0.710133\pi\) | ||||
−0.613238 | + | 0.789898i | \(0.710133\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5.37377e30 | −0.0220549 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.96438e32 | 0.778439 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.55020e32 | −0.593208 | −0.296604 | − | 0.955001i | \(-0.595854\pi\) | ||||
−0.296604 | + | 0.955001i | \(0.595854\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.65192e32 | 0.980039 | 0.490020 | − | 0.871711i | \(-0.336990\pi\) | ||||
0.490020 | + | 0.871711i | \(0.336990\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2.69689e32 | −0.962627 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.78764e32 | 0.961142 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.44799e32 | 0.482302 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 8.58111e32 | 2.76149 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.00976e32 | 1.24683 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5.25147e32 | 1.57800 | 0.789001 | − | 0.614392i | \(-0.210599\pi\) | ||||
0.789001 | + | 0.614392i | \(0.210599\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3.93343e32 | 1.14229 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −4.13293e32 | −1.16008 | −0.580041 | − | 0.814587i | \(-0.696963\pi\) | ||||
−0.580041 | + | 0.814587i | \(0.696963\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5.60011e32 | −1.51948 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −2.35276e32 | −0.617143 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −5.82971e32 | −1.47846 | −0.739229 | − | 0.673454i | \(-0.764810\pi\) | ||||
−0.739229 | + | 0.673454i | \(0.764810\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.65956e32 | −0.652180 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 9.03114e32 | 2.14161 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.90535e32 | −0.436971 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7.25689e30 | −0.0160973 | −0.00804865 | − | 0.999968i | \(-0.502562\pi\) | ||||
−0.00804865 | + | 0.999968i | \(0.502562\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.74514e33 | 3.74453 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.27725e32 | 0.265126 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.04044e32 | −0.208948 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.41730e33 | −2.75407 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −8.94327e32 | −1.68166 | −0.840832 | − | 0.541297i | \(-0.817934\pi\) | ||||
−0.840832 | + | 0.541297i | \(0.817934\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.93748e32 | −0.534551 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 7.92382e32 | 1.39560 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 7.80522e32 | 1.33064 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.06809e33 | −1.76269 | −0.881346 | − | 0.472472i | \(-0.843362\pi\) | ||||
−0.881346 | + | 0.472472i | \(0.843362\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −6.12594e32 | −0.978752 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −7.41235e32 | −1.14664 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 7.54715e32 | 1.13048 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 6.62461e32 | 0.960927 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.23737e32 | 0.173827 | 0.0869133 | − | 0.996216i | \(-0.472300\pi\) | ||||
0.0869133 | + | 0.996216i | \(0.472300\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.52191e32 | 0.479206 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 3.66781e32 | 0.483411 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.27521e32 | −0.290492 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.92923e32 | −0.238637 | −0.119319 | − | 0.992856i | \(-0.538071\pi\) | ||||
−0.119319 | + | 0.992856i | \(0.538071\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.37396e33 | 1.64667 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4.79085e32 | −0.556368 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −5.14954e31 | −0.0579526 | −0.0289763 | − | 0.999580i | \(-0.509225\pi\) | ||||
−0.0289763 | + | 0.999580i | \(0.509225\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 3.92411e32 | 0.427993 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.36629e33 | −1.44433 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.78518e33 | −1.82924 | −0.914621 | − | 0.404312i | \(-0.867511\pi\) | ||||
−0.914621 | + | 0.404312i | \(0.867511\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.30414e33 | −2.28875 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.03301e32 | −0.0994792 | −0.0497396 | − | 0.998762i | \(-0.515839\pi\) | ||||
−0.0497396 | + | 0.998762i | \(0.515839\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4.99901e31 | −0.0466752 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −2.49304e33 | −2.25706 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −4.63637e32 | −0.407040 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.00354e33 | −1.70584 | −0.852922 | − | 0.522038i | \(-0.825172\pi\) | ||||
−0.852922 | + | 0.522038i | \(0.825172\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −3.36479e32 | −0.277853 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 8.72327e32 | 0.698698 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.90156e32 | −0.225439 | −0.112719 | − | 0.993627i | \(-0.535956\pi\) | ||||
−0.112719 | + | 0.993627i | \(0.535956\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2.19984e33 | −1.65810 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.59845e33 | −1.16889 | −0.584446 | − | 0.811433i | \(-0.698688\pi\) | ||||
−0.584446 | + | 0.811433i | \(0.698688\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.06071e32 | 0.288117 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.29047e33 | 0.888471 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.34442e33 | 1.56635 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −8.79322e32 | −0.570158 | −0.285079 | − | 0.958504i | \(-0.592020\pi\) | ||||
−0.285079 | + | 0.958504i | \(0.592020\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3.03701e32 | 0.191126 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 8.24155e32 | 0.503437 | 0.251718 | − | 0.967801i | \(-0.419004\pi\) | ||||
0.251718 | + | 0.967801i | \(0.419004\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.16469e33 | 0.690623 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.80696e33 | −1.04018 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −8.88915e32 | −0.496798 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.86169e32 | 0.155287 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −3.81792e33 | −2.01172 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.07401e33 | −0.549552 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.89467e31 | −0.00941509 | −0.00470755 | − | 0.999989i | \(-0.501498\pi\) | ||||
−0.00470755 | + | 0.999989i | \(0.501498\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 3.21187e33 | 1.55015 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.54619e33 | −1.19360 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.32692e33 | −1.05959 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.27600e33 | 0.564453 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 5.78084e32 | 0.248439 | 0.124220 | − | 0.992255i | \(-0.460357\pi\) | ||||
0.124220 | + | 0.992255i | \(0.460357\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.06751e33 | −0.445744 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 9.59998e33 | 3.89490 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.03651e33 | 0.408644 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.54448e33 | −0.591737 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 6.41706e33 | 2.38941 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 4.46172e33 | 1.61471 | 0.807355 | − | 0.590066i | \(-0.200898\pi\) | ||||
0.807355 | + | 0.590066i | \(0.200898\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.69737e33 | 0.948857 | 0.474429 | − | 0.880294i | \(-0.342655\pi\) | ||||
0.474429 | + | 0.880294i | \(0.342655\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −6.57999e33 | −2.25001 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3.60903e33 | −1.19971 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4.09315e33 | −1.32283 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.01273e34 | −3.18220 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3.28224e33 | 1.00282 | 0.501412 | − | 0.865209i | \(-0.332814\pi\) | ||||
0.501412 | + | 0.865209i | \(0.332814\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.64872e33 | 0.786933 | 0.393466 | − | 0.919339i | \(-0.371276\pi\) | ||||
0.393466 | + | 0.919339i | \(0.371276\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 3.45657e33 | 0.998676 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.65312e33 | 0.464505 | 0.232253 | − | 0.972655i | \(-0.425390\pi\) | ||||
0.232253 | + | 0.972655i | \(0.425390\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3.48612e33 | −0.952719 | −0.476360 | − | 0.879251i | \(-0.658044\pi\) | ||||
−0.476360 | + | 0.879251i | \(0.658044\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −5.98913e33 | −1.59203 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −5.28664e32 | −0.136698 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −5.67160e33 | −1.42663 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.95442e34 | 4.78271 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −4.22678e33 | −1.00634 | −0.503172 | − | 0.864186i | \(-0.667834\pi\) | ||||
−0.503172 | + | 0.864186i | \(0.667834\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.10833e33 | −0.488410 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −5.45745e31 | −0.0123019 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −8.66577e32 | −0.190088 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.87382e33 | 0.826952 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.26191e34 | 2.62175 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.62750e33 | 0.329102 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −4.60865e33 | −0.907111 | −0.453555 | − | 0.891228i | \(-0.649845\pi\) | ||||
−0.453555 | + | 0.891228i | \(0.649845\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.10254e34 | 2.11244 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.09714e33 | −0.204637 | −0.102318 | − | 0.994752i | \(-0.532626\pi\) | ||||
−0.102318 | + | 0.994752i | \(0.532626\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.95181e33 | 0.536003 | 0.268001 | − | 0.963419i | \(-0.413637\pi\) | ||||
0.268001 | + | 0.963419i | \(0.413637\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −5.46807e33 | −0.966713 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.04670e33 | 0.180177 | 0.0900884 | − | 0.995934i | \(-0.471285\pi\) | ||||
0.0900884 | + | 0.995934i | \(0.471285\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4.49175e33 | −0.752888 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 9.03319e33 | 1.47442 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −3.23237e33 | −0.513799 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7.92878e33 | 1.22743 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −2.21490e34 | −3.33957 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 8.40216e33 | 1.23395 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −3.86117e33 | −0.552362 | −0.276181 | − | 0.961106i | \(-0.589069\pi\) | ||||
−0.276181 | + | 0.961106i | \(0.589069\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.31939e34 | 1.83865 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −7.78654e33 | −1.05711 | −0.528557 | − | 0.848898i | \(-0.677267\pi\) | ||||
−0.528557 | + | 0.848898i | \(0.677267\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −4.55914e33 | −0.603024 | −0.301512 | − | 0.953462i | \(-0.597491\pi\) | ||||
−0.301512 | + | 0.953462i | \(0.597491\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.57004e34 | −2.02332 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −3.58889e32 | −0.0450649 | −0.0225325 | − | 0.999746i | \(-0.507173\pi\) | ||||
−0.0225325 | + | 0.999746i | \(0.507173\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.05190e33 | 0.495780 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.04251e34 | 3.62776 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −9.12049e33 | −1.05981 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −4.85280e33 | −0.549576 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.27660e34 | 1.40909 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.13049e34 | −1.21627 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.71905e33 | −0.180282 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −2.51786e34 | −2.57408 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.10720e34 | −1.10349 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.09184e34 | −1.06090 | −0.530450 | − | 0.847716i | \(-0.677977\pi\) | ||||
−0.530450 | + | 0.847716i | \(0.677977\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 3.08705e34 | 2.92455 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.42933e34 | −1.32029 | −0.660146 | − | 0.751137i | \(-0.729506\pi\) | ||||
−0.660146 | + | 0.751137i | \(0.729506\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.31546e34 | −1.18485 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.55832e34 | 1.36872 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3.80484e32 | 0.0325904 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.15002e34 | 1.79604 | 0.898018 | − | 0.439959i | \(-0.145007\pi\) | ||||
0.898018 | + | 0.439959i | \(0.145007\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.95683e34 | 1.59429 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.66068e33 | −0.131967 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.55726e33 | −0.198219 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.39295e34 | 1.05322 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.53709e34 | −1.13376 | −0.566878 | − | 0.823801i | \(-0.691849\pi\) | ||||
−0.566878 | + | 0.823801i | \(0.691849\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.51674e33 | −0.325015 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 3.25290e34 | 2.28366 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 6.80921e33 | 0.466405 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3.02985e33 | −0.202496 | −0.101248 | − | 0.994861i | \(-0.532284\pi\) | ||||
−0.101248 | + | 0.994861i | \(0.532284\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2.17545e34 | −1.41871 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.40737e34 | −0.895631 | −0.447815 | − | 0.894126i | \(-0.647798\pi\) | ||||
−0.447815 | + | 0.894126i | \(0.647798\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.92499e33 | 0.305859 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 4.07232e34 | 2.46818 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2.84567e34 | 1.68329 | 0.841647 | − | 0.540028i | \(-0.181586\pi\) | ||||
0.841647 | + | 0.540028i | \(0.181586\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −6.01502e33 | −0.347276 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.13677e34 | 1.20415 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −3.91513e33 | −0.215366 | −0.107683 | − | 0.994185i | \(-0.534343\pi\) | ||||
−0.107683 | + | 0.994185i | \(0.534343\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.42814e33 | 0.184085 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −3.35506e34 | −1.75879 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.88307e34 | 0.963723 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3.78570e34 | 1.89159 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.83373e34 | −0.894611 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2.53245e34 | 1.20636 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.18860e34 | 0.552882 | 0.276441 | − | 0.961031i | \(-0.410845\pi\) | ||||
0.276441 | + | 0.961031i | \(0.410845\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2.07885e34 | −0.944277 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2.66114e33 | −0.118045 | −0.0590224 | − | 0.998257i | \(-0.518798\pi\) | ||||
−0.0590224 | + | 0.998257i | \(0.518798\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −9.04346e33 | −0.391775 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2.00589e34 | −0.848702 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.53142e34 | 0.632860 | 0.316430 | − | 0.948616i | \(-0.397516\pi\) | ||||
0.316430 | + | 0.948616i | \(0.397516\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5.06545e34 | 2.04464 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.60605e34 | 0.633237 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1.82163e34 | −0.701610 | −0.350805 | − | 0.936449i | \(-0.614092\pi\) | ||||
−0.350805 | + | 0.936449i | \(0.614092\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3.51217e33 | −0.132147 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −5.61037e34 | −2.06227 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.26779e34 | 0.814413 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.71132e34 | −1.65309 | −0.826543 | − | 0.562874i | \(-0.809696\pi\) | ||||
−0.826543 | + | 0.562874i | \(0.809696\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 3.22961e34 | 1.10722 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2.63367e33 | −0.0882257 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.34856e34 | 0.768791 | 0.384395 | − | 0.923169i | \(-0.374410\pi\) | ||||
0.384395 | + | 0.923169i | \(0.374410\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −4.29122e34 | −1.37271 |
(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 | 64.24.a.h.1.1 | 3 | ||
4.3 | odd | 2 | 64.24.a.k.1.3 | 3 | |||
8.3 | odd | 2 | 8.24.a.a.1.1 | ✓ | 3 | ||
8.5 | even | 2 | 16.24.a.e.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8.24.a.a.1.1 | ✓ | 3 | 8.3 | odd | 2 | ||
16.24.a.e.1.3 | 3 | 8.5 | even | 2 | |||
64.24.a.h.1.1 | 3 | 1.1 | even | 1 | trivial | ||
64.24.a.k.1.3 | 3 | 4.3 | odd | 2 |