Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [48,24,Mod(1,48)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(48, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("48.1");
S:= CuspForms(chi, 24);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 48 = 2^{4} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 24 \) |
Character orbit: | \([\chi]\) | \(=\) | 48.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: | \(160.897937926\) |
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: | \( x^{3} - x^{2} - 510971349x - 545907620601 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{21}\cdot 3^{4}\cdot 5 \) |
Twist minimal: | no (minimal twist has level 24) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-22049.7\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 48.1 |
$q$-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 | ||||||||
\(3\) | −177147. | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.66963e7 | −0.244510 | −0.122255 | − | 0.992499i | \(-0.539013\pi\) | ||||
−0.122255 | + | 0.992499i | \(0.539013\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.63708e9 | −0.504075 | −0.252038 | − | 0.967717i | \(-0.581101\pi\) | ||||
−0.252038 | + | 0.967717i | \(0.581101\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.13811e10 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 6.90658e11 | 0.729873 | 0.364936 | − | 0.931032i | \(-0.381091\pi\) | ||||
0.364936 | + | 0.931032i | \(0.381091\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 8.43948e12 | 1.30607 | 0.653036 | − | 0.757327i | \(-0.273495\pi\) | ||||
0.653036 | + | 0.757327i | \(0.273495\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 4.72917e12 | 0.141168 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.75506e13 | 0.124202 | 0.0621012 | − | 0.998070i | \(-0.480220\pi\) | ||||
0.0621012 | + | 0.998070i | \(0.480220\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.46727e14 | 1.07672 | 0.538362 | − | 0.842714i | \(-0.319043\pi\) | ||||
0.538362 | + | 0.842714i | \(0.319043\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.67151e14 | 0.291028 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.16817e15 | −0.912169 | −0.456084 | − | 0.889936i | \(-0.650749\pi\) | ||||
−0.456084 | + | 0.889936i | \(0.650749\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.12082e16 | −0.940215 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.55906e15 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.34605e16 | 1.11809 | 0.559045 | − | 0.829137i | \(-0.311168\pi\) | ||||
0.559045 | + | 0.829137i | \(0.311168\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.44267e17 | −1.01978 | −0.509890 | − | 0.860239i | \(-0.670314\pi\) | ||||
−0.509890 | + | 0.860239i | \(0.670314\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.22348e17 | −0.421392 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 7.04003e16 | 0.123251 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.39423e16 | 0.0406034 | 0.0203017 | − | 0.999794i | \(-0.493537\pi\) | ||||
0.0203017 | + | 0.999794i | \(0.493537\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.49503e18 | −0.754061 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.13798e18 | 0.322938 | 0.161469 | − | 0.986878i | \(-0.448377\pi\) | ||||
0.161469 | + | 0.986878i | \(0.448377\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.65242e18 | 0.599368 | 0.299684 | − | 0.954039i | \(-0.403119\pi\) | ||||
0.299684 | + | 0.954039i | \(0.403119\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −8.37758e17 | −0.0815032 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.31349e18 | −0.0775001 | −0.0387501 | − | 0.999249i | \(-0.512338\pi\) | ||||
−0.0387501 | + | 0.999249i | \(0.512338\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.04146e19 | −0.745908 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.10904e18 | −0.0717083 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.56940e18 | 0.0232575 | 0.0116287 | − | 0.999932i | \(-0.496298\pi\) | ||||
0.0116287 | + | 0.999932i | \(0.496298\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.84380e19 | −0.178461 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −9.68511e19 | −0.621647 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.30965e20 | −0.565403 | −0.282701 | − | 0.959208i | \(-0.591231\pi\) | ||||
−0.282701 | + | 0.959208i | \(0.591231\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.40655e20 | 0.708111 | 0.354056 | − | 0.935224i | \(-0.384802\pi\) | ||||
0.354056 | + | 0.935224i | \(0.384802\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −8.27543e19 | −0.168025 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.25303e20 | −0.319347 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.77336e20 | −0.277425 | −0.138713 | − | 0.990333i | \(-0.544296\pi\) | ||||
−0.138713 | + | 0.990333i | \(0.544296\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 7.38379e20 | 0.526641 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.66742e21 | −1.36968 | −0.684842 | − | 0.728692i | \(-0.740129\pi\) | ||||
−0.684842 | + | 0.728692i | \(0.740129\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.44977e20 | 0.0913929 | 0.0456965 | − | 0.998955i | \(-0.485449\pi\) | ||||
0.0456965 | + | 0.998955i | \(0.485449\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.98551e21 | 0.542833 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.82132e21 | −0.367911 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.73406e21 | −0.712070 | −0.356035 | − | 0.934473i | \(-0.615872\pi\) | ||||
−0.356035 | + | 0.934473i | \(0.615872\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 9.84771e20 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.82639e21 | −0.326130 | −0.163065 | − | 0.986615i | \(-0.552138\pi\) | ||||
−0.163065 | + | 0.986615i | \(0.552138\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.68537e20 | −0.0303687 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.30133e22 | −0.645530 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.93473e22 | 1.50290 | 0.751450 | − | 0.659790i | \(-0.229355\pi\) | ||||
0.751450 | + | 0.659790i | \(0.229355\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.22556e22 | −0.658359 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.55564e22 | 0.588771 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.45956e22 | −0.263269 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.29544e23 | 1.83883 | 0.919415 | − | 0.393290i | \(-0.128663\pi\) | ||||
0.919415 | + | 0.393290i | \(0.128663\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.16736e22 | 0.243291 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.23956e22 | 0.467304 | 0.233652 | − | 0.972320i | \(-0.424932\pi\) | ||||
0.233652 | + | 0.972320i | \(0.424932\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.71005e22 | −0.691184 | −0.345592 | − | 0.938385i | \(-0.612322\pi\) | ||||
−0.345592 | + | 0.938385i | \(0.612322\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.24712e22 | −0.0711592 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.60654e23 | −1.19716 | −0.598579 | − | 0.801064i | \(-0.704268\pi\) | ||||
−0.598579 | + | 0.801064i | \(0.704268\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.69368e23 | 0.628675 | 0.314338 | − | 0.949311i | \(-0.398218\pi\) | ||||
0.314338 | + | 0.949311i | \(0.398218\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −7.78424e21 | −0.0234424 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.71661e23 | 0.420988 | 0.210494 | − | 0.977595i | \(-0.432493\pi\) | ||||
0.210494 | + | 0.977595i | \(0.432493\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.11275e23 | 0.223034 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.64840e23 | 0.435357 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −4.62824e22 | −0.0626074 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.18421e23 | −0.467285 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.01589e23 | −0.186448 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 6.17463e23 | 0.474401 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.61449e24 | −1.03345 | −0.516727 | − | 0.856150i | \(-0.672850\pi\) | ||||
−0.516727 | + | 0.856150i | \(0.672850\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −6.47015e23 | −0.346045 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.87162e24 | 0.838682 | 0.419341 | − | 0.907829i | \(-0.362261\pi\) | ||||
0.419341 | + | 0.907829i | \(0.362261\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.44176e24 | −0.542750 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.48406e23 | 0.0470559 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.89209e24 | 0.506589 | 0.253294 | − | 0.967389i | \(-0.418486\pi\) | ||||
0.253294 | + | 0.967389i | \(0.418486\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.89527e24 | 0.656173 | 0.328086 | − | 0.944648i | \(-0.393596\pi\) | ||||
0.328086 | + | 0.944648i | \(0.393596\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.32681e23 | 0.0447447 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 5.82880e24 | 0.953267 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.96112e24 | −0.273384 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3.61638e24 | 0.430650 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.58742e25 | −1.61827 | −0.809134 | − | 0.587625i | \(-0.800063\pi\) | ||||
−0.809134 | + | 0.587625i | \(0.800063\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.60479e25 | 1.40340 | 0.701702 | − | 0.712471i | \(-0.252424\pi\) | ||||
0.701702 | + | 0.712471i | \(0.252424\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 5.50757e23 | 0.0414008 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.85139e24 | 0.249346 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.83816e24 | 0.437893 | 0.218947 | − | 0.975737i | \(-0.429738\pi\) | ||||
0.218947 | + | 0.975737i | \(0.429738\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.78015e23 | −0.0134277 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.09918e25 | 0.459802 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.53086e25 | 0.918565 | 0.459283 | − | 0.888290i | \(-0.348107\pi\) | ||||
0.459283 | + | 0.888290i | \(0.348107\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3.26624e24 | 0.103035 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3.85481e25 | 1.05868 | 0.529339 | − | 0.848411i | \(-0.322440\pi\) | ||||
0.529339 | + | 0.848411i | \(0.322440\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.94710e25 | 0.705825 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.71569e25 | 0.358908 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 7.85513e25 | 1.43755 | 0.718775 | − | 0.695242i | \(-0.244703\pi\) | ||||
0.718775 | + | 0.695242i | \(0.244703\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.95570e25 | 0.473939 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2.32001e25 | 0.326435 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.00073e26 | −1.23739 | −0.618694 | − | 0.785632i | \(-0.712338\pi\) | ||||
−0.618694 | + | 0.785632i | \(0.712338\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −8.03087e24 | −0.0873894 | −0.0436947 | − | 0.999045i | \(-0.513913\pi\) | ||||
−0.0436947 | + | 0.999045i | \(0.513913\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −4.26313e25 | −0.408828 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.17310e24 | −0.00992793 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.21215e25 | 0.0906520 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.46597e25 | 0.0970094 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.60881e26 | 1.52953 | 0.764767 | − | 0.644307i | \(-0.222854\pi\) | ||||
0.764767 | + | 0.644307i | \(0.222854\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.24177e26 | 1.68606 | 0.843029 | − | 0.537868i | \(-0.180770\pi\) | ||||
0.843029 | + | 0.537868i | \(0.180770\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 3.99118e25 | 0.184375 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3.86517e26 | 1.58784 | 0.793921 | − | 0.608021i | \(-0.208036\pi\) | ||||
0.793921 | + | 0.608021i | \(0.208036\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.51969e26 | −0.555834 | −0.277917 | − | 0.960605i | \(-0.589644\pi\) | ||||
−0.277917 | + | 0.960605i | \(0.589644\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.91292e25 | 0.160171 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.93721e26 | −0.563602 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.03798e25 | −0.0789614 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.30802e26 | −0.304056 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.77602e26 | 0.785872 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.61152e26 | 1.41979 | 0.709894 | − | 0.704309i | \(-0.248743\pi\) | ||||
0.709894 | + | 0.704309i | \(0.248743\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 4.72525e26 | 0.790787 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −9.75061e25 | −0.146551 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.80443e26 | 0.514046 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −4.33970e25 | −0.0527657 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.48118e26 | 0.162217 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.64289e27 | 1.62220 | 0.811098 | − | 0.584910i | \(-0.198870\pi\) | ||||
0.811098 | + | 0.584910i | \(0.198870\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.51726e26 | −0.313405 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.60467e27 | 1.29148 | 0.645742 | − | 0.763556i | \(-0.276548\pi\) | ||||
0.645742 | + | 0.763556i | \(0.276548\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.58626e26 | −0.188176 | −0.0940880 | − | 0.995564i | \(-0.529994\pi\) | ||||
−0.0940880 | + | 0.995564i | \(0.529994\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.22641e26 | 0.212414 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 8.31388e26 | 0.495691 | 0.247845 | − | 0.968800i | \(-0.420278\pi\) | ||||
0.247845 | + | 0.968800i | \(0.420278\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.50654e25 | 0.0189495 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 8.38625e26 | 0.411114 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.57103e27 | 1.14428 | 0.572139 | − | 0.820157i | \(-0.306114\pi\) | ||||
0.572139 | + | 0.820157i | \(0.306114\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.23649e27 | −1.71321 | −0.856605 | − | 0.515973i | \(-0.827430\pi\) | ||||
−0.856605 | + | 0.515973i | \(0.827430\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.74449e26 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 5.44993e26 | 0.182382 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.61409e27 | 1.40628 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 6.77833e26 | 0.188291 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.84249e27 | −0.973566 | −0.486783 | − | 0.873523i | \(-0.661830\pi\) | ||||
−0.486783 | + | 0.873523i | \(0.661830\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.87878e27 | −0.665768 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 8.29999e25 | 0.0175334 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2.26731e27 | −0.437804 | −0.218902 | − | 0.975747i | \(-0.570247\pi\) | ||||
−0.218902 | + | 0.975747i | \(0.570247\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.15879e26 | −0.0204672 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.30527e27 | 0.372697 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −8.92637e27 | −1.32186 | −0.660928 | − | 0.750450i | \(-0.729837\pi\) | ||||
−0.660928 | + | 0.750450i | \(0.729837\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.18973e25 | −0.00568668 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −6.97026e27 | −0.867700 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −6.64561e27 | −0.759248 | −0.379624 | − | 0.925141i | \(-0.623947\pi\) | ||||
−0.379624 | + | 0.925141i | \(0.623947\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.12761e27 | 0.433064 | 0.216532 | − | 0.976276i | \(-0.430525\pi\) | ||||
0.216532 | + | 0.976276i | \(0.430525\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3.94251e27 | 0.380104 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −7.74106e27 | −0.686238 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.21768e28 | −0.993152 | −0.496576 | − | 0.867993i | \(-0.665410\pi\) | ||||
−0.496576 | + | 0.867993i | \(0.665410\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −4.52724e27 | −0.339927 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.78160e28 | 1.23221 | 0.616107 | − | 0.787662i | \(-0.288709\pi\) | ||||
0.616107 | + | 0.787662i | \(0.288709\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6.48624e26 | −0.0413475 | −0.0206737 | − | 0.999786i | \(-0.506581\pi\) | ||||
−0.0206737 | + | 0.999786i | \(0.506581\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2.58557e27 | 0.151999 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.00093e27 | −0.162785 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.96595e28 | −0.984574 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.29483e28 | −1.06165 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.82593e28 | 1.20833 | 0.604163 | − | 0.796861i | \(-0.293508\pi\) | ||||
0.604163 | + | 0.796861i | \(0.293508\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.49629e27 | 0.138246 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.83941e27 | −0.140464 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.51772e28 | −1.19136 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −9.63172e27 | −0.302127 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −9.28173e27 | −0.269798 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −6.42459e27 | −0.173140 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.80973e28 | −0.452401 | −0.226200 | − | 0.974081i | \(-0.572630\pi\) | ||||
−0.226200 | + | 0.974081i | \(0.572630\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.72011e28 | 0.399055 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5.26369e28 | −1.13382 | −0.566912 | − | 0.823778i | \(-0.691862\pi\) | ||||
−0.566912 | + | 0.823778i | \(0.691862\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5.71094e28 | −1.14274 | −0.571370 | − | 0.820693i | \(-0.693588\pi\) | ||||
−0.571370 | + | 0.820693i | \(0.693588\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2.20923e27 | 0.0410838 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −4.58206e28 | −0.792281 | −0.396140 | − | 0.918190i | \(-0.629651\pi\) | ||||
−0.396140 | + | 0.918190i | \(0.629651\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.07361e28 | 0.816064 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4.61741e28 | 0.691180 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 9.59541e27 | 0.133732 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −9.45917e28 | −1.22799 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −3.00030e28 | −0.362966 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3.46378e27 | 0.0390659 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.14307e29 | 1.20240 | 0.601200 | − | 0.799098i | \(-0.294689\pi\) | ||||
0.601200 | + | 0.799098i | \(0.294689\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.37896e27 | 0.0135345 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 7.40384e27 | 0.0678331 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.79475e29 | −1.53553 | −0.767767 | − | 0.640729i | \(-0.778632\pi\) | ||||
−0.767767 | + | 0.640729i | \(0.778632\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −3.04093e28 | −0.243058 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −9.96390e28 | −0.744310 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.26008e29 | 0.880069 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.97120e28 | −0.128769 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −3.77055e28 | −0.230470 | −0.115235 | − | 0.993338i | \(-0.536762\pi\) | ||||
−0.115235 | + | 0.993338i | \(0.536762\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.42646e28 | 0.138829 | 0.0694146 | − | 0.997588i | \(-0.477887\pi\) | ||||
0.0694146 | + | 0.997588i | \(0.477887\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.69156e28 | −0.251354 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2.01961e29 | 1.01358 | 0.506791 | − | 0.862069i | \(-0.330832\pi\) | ||||
0.506791 | + | 0.862069i | \(0.330832\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 7.12102e28 | 0.334901 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 8.19879e27 | 0.0361464 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2.65591e29 | 1.09806 | 0.549032 | − | 0.835801i | \(-0.314996\pi\) | ||||
0.549032 | + | 0.835801i | \(0.314996\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.10810e28 | 0.159334 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 7.41221e28 | 0.269787 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6.53998e27 | −0.0223465 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4.02820e29 | −1.29256 | −0.646281 | − | 0.763100i | \(-0.723676\pi\) | ||||
−0.646281 | + | 0.763100i | \(0.723676\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3.57109e28 | 0.107646 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.13864e27 | −0.0117235 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.34018e29 | 0.623156 | 0.311578 | − | 0.950221i | \(-0.399142\pi\) | ||||
0.311578 | + | 0.950221i | \(0.399142\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.09382e29 | −0.273896 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 6.19969e29 | 1.46031 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7.63581e29 | 1.69241 | 0.846203 | − | 0.532861i | \(-0.178883\pi\) | ||||
0.846203 | + | 0.532861i | \(0.178883\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.86001e29 | 0.596665 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.50832e29 | 0.296283 | 0.148141 | − | 0.988966i | \(-0.452671\pi\) | ||||
0.148141 | + | 0.988966i | \(0.452671\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.86225e28 | 0.0899578 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.14617e29 | 0.199789 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 7.88719e29 | 1.29569 | 0.647846 | − | 0.761771i | \(-0.275670\pi\) | ||||
0.647846 | + | 0.761771i | \(0.275670\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7.31540e28 | −0.113294 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −3.31552e29 | −0.484214 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.26382e29 | 0.174108 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.07099e30 | 1.39218 | 0.696090 | − | 0.717955i | \(-0.254922\pi\) | ||||
0.696090 | + | 0.717955i | \(0.254922\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.55404e29 | 0.313357 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3.53206e29 | −0.409136 | −0.204568 | − | 0.978852i | \(-0.565579\pi\) | ||||
−0.204568 | + | 0.978852i | \(0.565579\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.21754e30 | −1.33191 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −2.62897e28 | −0.0271677 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.03491e28 | 0.0296353 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.43029e30 | 1.32010 | 0.660048 | − | 0.751223i | \(-0.270536\pi\) | ||||
0.660048 | + | 0.751223i | \(0.270536\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3.35178e29 | −0.292479 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3.45365e29 | 0.285006 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.02150e29 | 0.0797420 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −5.12888e29 | −0.378842 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.74971e30 | 1.22322 | 0.611610 | − | 0.791160i | \(-0.290522\pi\) | ||||
0.611610 | + | 0.791160i | \(0.290522\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.48338e30 | −0.981767 | −0.490883 | − | 0.871225i | \(-0.663326\pi\) | ||||
−0.490883 | + | 0.871225i | \(0.663326\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −4.12188e28 | −0.0258334 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.96712e29 | −0.116777 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.34626e29 | −0.356941 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.03255e30 | −0.550369 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.96194e29 | −0.149654 | −0.0748269 | − | 0.997197i | \(-0.523840\pi\) | ||||
−0.0748269 | + | 0.997197i | \(0.523840\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.35179e30 | 1.12665 | 0.563324 | − | 0.826236i | \(-0.309522\pi\) | ||||
0.563324 | + | 0.826236i | \(0.309522\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.47407e29 | 0.157838 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.27885e30 | −0.982154 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.38873e30 | −0.976845 | −0.488422 | − | 0.872607i | \(-0.662427\pi\) | ||||
−0.488422 | + | 0.872607i | \(0.662427\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.40631e29 | −0.248636 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.06602e30 | 1.12962 | 0.564810 | − | 0.825221i | \(-0.308950\pi\) | ||||
0.564810 | + | 0.825221i | \(0.308950\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.05043e30 | −0.367474 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2.81207e30 | 0.934307 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −3.24613e30 | −1.02455 | −0.512274 | − | 0.858822i | \(-0.671197\pi\) | ||||
−0.512274 | + | 0.858822i | \(0.671197\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.85953e29 | 0.235704 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −2.84283e30 | −0.810255 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 5.94142e29 | 0.160975 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.51307e30 | −0.905005 | −0.452502 | − | 0.891763i | \(-0.649469\pi\) | ||||
−0.452502 | + | 0.891763i | \(0.649469\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −9.75650e28 | −0.0239028 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.41936e30 | 0.330774 | 0.165387 | − | 0.986229i | \(-0.447113\pi\) | ||||
0.165387 | + | 0.986229i | \(0.447113\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3.42125e30 | −0.758584 | −0.379292 | − | 0.925277i | \(-0.623832\pi\) | ||||
−0.379292 | + | 0.925277i | \(0.623832\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −6.82262e29 | −0.143960 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 3.68193e30 | 0.739489 | 0.369744 | − | 0.929134i | \(-0.379445\pi\) | ||||
0.369744 | + | 0.929134i | \(0.379445\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 7.31356e29 | 0.139843 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.38851e30 | −0.252818 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.52257e30 | 0.437462 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −6.12785e30 | −1.01235 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.92496e28 | 0.00775249 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2.88655e30 | 0.433033 | 0.216516 | − | 0.976279i | \(-0.430531\pi\) | ||||
0.216516 | + | 0.976279i | \(0.430531\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.70850e29 | 0.0530310 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.94716e30 | −0.265467 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3.45834e30 | −0.449612 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −9.49733e30 | −1.17766 | −0.588828 | − | 0.808259i | \(-0.700410\pi\) | ||||
−0.588828 | + | 0.808259i | \(0.700410\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −4.48334e30 | −0.530334 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.39737e31 | −1.57716 | −0.788580 | − | 0.614932i | \(-0.789183\pi\) | ||||
−0.788580 | + | 0.614932i | \(0.789183\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.28928e30 | 0.138870 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −5.78605e29 | −0.0594870 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 7.03419e30 | 0.690424 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.44217e31 | −1.35164 | −0.675821 | − | 0.737066i | \(-0.736211\pi\) | ||||
−0.675821 | + | 0.737066i | \(0.736211\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6.82868e30 | −0.611228 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.49630e31 | 1.27934 | 0.639671 | − | 0.768649i | \(-0.279071\pi\) | ||||
0.639671 | + | 0.768649i | \(0.279071\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.39877e30 | −0.114260 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −5.22069e30 | −0.407508 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 5.58922e30 | 0.416962 | 0.208481 | − | 0.978026i | \(-0.433148\pi\) | ||||
0.208481 | + | 0.978026i | \(0.433148\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.46024e29 | −0.0460689 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3.03929e30 | −0.207216 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.59223e30 | 0.169001 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −9.07174e29 | −0.0565652 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.39151e31 | −0.829970 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.30155e31 | 0.742726 | 0.371363 | − | 0.928488i | \(-0.378891\pi\) | ||||
0.371363 | + | 0.928488i | \(0.378891\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3.70459e30 | −0.202288 | −0.101144 | − | 0.994872i | \(-0.532250\pi\) | ||||
−0.101144 | + | 0.994872i | \(0.532250\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −5.23593e30 | −0.273629 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2.53197e30 | −0.126659 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.50683e30 | −0.167948 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4.10983e30 | −0.188468 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 9.60393e30 | 0.421780 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6.95851e30 | 0.292717 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.77276e31 | 0.714406 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.40995e31 | −0.544418 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.85046e31 | −1.42477 | −0.712385 | − | 0.701789i | \(-0.752385\pi\) | ||||
−0.712385 | + | 0.701789i | \(0.752385\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.42264e30 | 0.0504543 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4.52150e30 | −0.153717 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.89456e31 | 0.943471 | 0.471736 | − | 0.881740i | \(-0.343628\pi\) | ||||
0.471736 | + | 0.881740i | \(0.343628\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 7.55200e30 | 0.236037 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.01629e31 | 1.20387 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.24841e31 | 0.358937 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2.07811e29 | 0.00573189 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 6.55955e31 | 1.73596 | 0.867979 | − | 0.496601i | \(-0.165419\pi\) | ||||
0.867979 | + | 0.496601i | \(0.165419\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.08245e31 | 0.782818 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.14729e30 | −0.0523380 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 6.24113e31 | 1.46021 | 0.730107 | − | 0.683333i | \(-0.239470\pi\) | ||||
0.730107 | + | 0.683333i | \(0.239470\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4.58272e30 | −0.102936 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.59692e30 | −0.0560084 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 4.79693e31 | 0.993510 | 0.496755 | − | 0.867891i | \(-0.334525\pi\) | ||||
0.496755 | + | 0.867891i | \(0.334525\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7.43230e31 | 1.47845 | 0.739227 | − | 0.673456i | \(-0.235191\pi\) | ||||
0.739227 | + | 0.673456i | \(0.235191\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −4.62143e31 | −0.883076 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.67178e31 | 0.857635 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −7.78263e31 | −1.37279 | −0.686396 | − | 0.727228i | \(-0.740808\pi\) | ||||
−0.686396 | + | 0.727228i | \(0.740808\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −5.74269e31 | −0.973446 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.00905e31 | 0.164394 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.08392e30 | 0.0169750 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −7.07025e30 | −0.106449 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 8.13383e31 | 1.17749 | 0.588744 | − | 0.808319i | \(-0.299623\pi\) | ||||
0.588744 | + | 0.808319i | \(0.299623\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −7.88745e31 | −1.09802 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −6.84704e31 | −0.916741 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.15019e32 | 1.48129 | 0.740644 | − | 0.671898i | \(-0.234521\pi\) | ||||
0.740644 | + | 0.671898i | \(0.234521\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.23557e30 | 0.0153081 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 2.69209e31 | 0.320911 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 2.95748e31 | 0.339244 | 0.169622 | − | 0.985509i | \(-0.445745\pi\) | ||||
0.169622 | + | 0.985509i | \(0.445745\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.33359e31 | 0.147220 | 0.0736099 | − | 0.997287i | \(-0.476548\pi\) | ||||
0.0736099 | + | 0.997287i | \(0.476548\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −8.70309e30 | −0.0924750 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.11703e31 | 0.114256 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8.41625e30 | 0.0828798 | 0.0414399 | − | 0.999141i | \(-0.486805\pi\) | ||||
0.0414399 | + | 0.999141i | \(0.486805\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 3.43171e31 | 0.325396 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.10852e31 | −0.101221 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −6.41255e31 | −0.563943 | −0.281972 | − | 0.959423i | \(-0.590988\pi\) | ||||
−0.281972 | + | 0.959423i | \(0.590988\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 5.38169e30 | 0.0455884 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2.07994e32 | 1.69735 | 0.848675 | − | 0.528915i | \(-0.177401\pi\) | ||||
0.848675 | + | 0.528915i | \(0.177401\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −7.06394e31 | −0.555398 | −0.277699 | − | 0.960668i | \(-0.589572\pi\) | ||||
−0.277699 | + | 0.960668i | \(0.589572\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.31711e31 | 0.175547 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.03762e32 | −0.757575 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.17129e32 | 0.824219 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −6.68910e31 | −0.453723 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 7.71215e29 | 0.00504305 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −7.38793e31 | −0.465785 | −0.232892 | − | 0.972503i | \(-0.574819\pi\) | ||||
−0.232892 | + | 0.972503i | \(0.574819\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.34836e32 | −0.819715 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 4.31008e31 | 0.252690 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.72288e32 | −0.974210 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −8.37064e31 | −0.456561 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.35614e32 | 0.713569 | 0.356785 | − | 0.934187i | \(-0.383873\pi\) | ||||
0.356785 | + | 0.934187i | \(0.383873\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.52991e32 | −0.776677 | −0.388339 | − | 0.921517i | \(-0.626951\pi\) | ||||
−0.388339 | + | 0.921517i | \(0.626951\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.72729e31 | 0.0846114 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −8.82951e31 | −0.417386 | −0.208693 | − | 0.977981i | \(-0.566921\pi\) | ||||
−0.208693 | + | 0.977981i | \(0.566921\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −9.04522e31 | −0.412672 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −6.73943e31 | −0.296785 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 8.08654e31 | 0.343764 | 0.171882 | − | 0.985118i | \(-0.445015\pi\) | ||||
0.171882 | + | 0.985118i | \(0.445015\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4.99653e31 | −0.205066 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 7.68764e30 | 0.0304643 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 3.02900e32 | 1.15909 | 0.579546 | − | 0.814940i | \(-0.303230\pi\) | ||||
0.579546 | + | 0.814940i | \(0.303230\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.69718e32 | −0.627207 | −0.313604 | − | 0.949554i | \(-0.601536\pi\) | ||||
−0.313604 | + | 0.949554i | \(0.601536\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2.62387e31 | −0.0936563 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 3.84897e31 | 0.132708 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.06196e32 | −1.01989 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −2.91034e32 | −0.936575 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.66210e32 | 0.516831 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.59259e32 | 0.779041 | 0.389520 | − | 0.921018i | \(-0.372641\pi\) | ||||
0.389520 | + | 0.921018i | \(0.372641\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 6.23073e31 | 0.180944 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −3.80491e32 | −1.06801 | −0.534004 | − | 0.845482i | \(-0.679313\pi\) | ||||
−0.534004 | + | 0.845482i | \(0.679313\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.41617e32 | −0.926909 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −2.84263e32 | −0.745638 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.34319e32 | 0.340643 | 0.170322 | − | 0.985389i | \(-0.445519\pi\) | ||||
0.170322 | + | 0.985389i | \(0.445519\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −5.05118e31 | −0.123866 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 4.58148e31 | 0.108643 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.32450e31 | 0.0303759 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.79228e32 | 0.619387 | 0.309694 | − | 0.950836i | \(-0.399774\pi\) | ||||
0.309694 | + | 0.950836i | \(0.399774\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −5.71549e31 | −0.122637 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −7.72929e31 | −0.160441 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.99722e31 | 0.0401097 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.47278e32 | −0.286187 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −7.05564e32 | −1.32672 | −0.663360 | − | 0.748301i | \(-0.730870\pi\) | ||||
−0.663360 | + | 0.748301i | \(0.730870\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.40244e31 | 0.0437187 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −6.21173e30 | −0.0109405 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.38171e32 | −0.235556 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −4.54508e32 | −0.750085 | −0.375042 | − | 0.927008i | \(-0.622372\pi\) | ||||
−0.375042 | + | 0.927008i | \(0.622372\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.48560e32 | −0.237357 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 6.01328e32 | 0.930212 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.55607e32 | −0.233083 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −4.55450e32 | −0.660649 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.25674e33 | 1.76548 | 0.882738 | − | 0.469866i | \(-0.155698\pi\) | ||||
0.882738 | + | 0.469866i | \(0.155698\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.56062e32 | 0.348409 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 7.50482e32 | 0.989122 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −8.23363e32 | −1.05125 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.23753e33 | −1.53077 | −0.765384 | − | 0.643574i | \(-0.777451\pi\) | ||||
−0.765384 | + | 0.643574i | \(0.777451\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 3.09032e31 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6.41023e31 | 0.0744429 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −3.07938e32 | −0.346551 | −0.173275 | − | 0.984873i | \(-0.555435\pi\) | ||||
−0.173275 | + | 0.984873i | \(0.555435\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −9.65440e31 | −0.105298 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.91544e32 | −0.202485 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.25293e33 | −1.28386 | −0.641928 | − | 0.766765i | \(-0.721865\pi\) | ||||
−0.641928 | + | 0.766765i | \(0.721865\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −8.17373e32 | −0.811916 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 8.96246e32 | 0.863089 | 0.431545 | − | 0.902092i | \(-0.357969\pi\) | ||||
0.431545 | + | 0.902092i | \(0.357969\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4.23783e32 | 0.395682 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.20076e32 | −0.108710 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 6.87366e32 | 0.603458 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6.16616e32 | 0.524996 | 0.262498 | − | 0.964933i | \(-0.415454\pi\) | ||||
0.262498 | + | 0.964933i | \(0.415454\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 6.80686e32 | 0.562088 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −4.28419e32 | −0.343146 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.99545e33 | 1.55038 | 0.775192 | − | 0.631726i | \(-0.217653\pi\) | ||||
0.775192 | + | 0.631726i | \(0.217653\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 5.09967e32 | 0.384381 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.60859e33 | 1.90757 | 0.953787 | − | 0.300482i | \(-0.0971475\pi\) | ||||
0.953787 | + | 0.300482i | \(0.0971475\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4.46636e32 | −0.316900 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.47032e31 | −0.0101229 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.10528e33 | −0.738457 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.98234e33 | 1.93377 | 0.966884 | − | 0.255216i | \(-0.0821465\pi\) | ||||
0.966884 | + | 0.255216i | \(0.0821465\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4.01647e32 | 0.252766 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 4.86325e32 | 0.297072 | 0.148536 | − | 0.988907i | \(-0.452544\pi\) | ||||
0.148536 | + | 0.988907i | \(0.452544\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.61698e33 | 0.958813 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2.05277e31 | 0.0118167 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 6.22163e32 | 0.347715 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.84227e33 | −0.999695 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −4.08371e32 | −0.215177 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2.09250e32 | −0.107069 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 5.77342e32 | 0.286896 | 0.143448 | − | 0.989658i | \(-0.454181\pi\) | ||||
0.143448 | + | 0.989658i | \(0.454181\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.58128e33 | 0.763173 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −4.52684e32 | −0.212210 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.03100e33 | 0.924844 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 7.42198e30 | 0.00328320 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1.99971e33 | −0.859402 | −0.429701 | − | 0.902971i | \(-0.641381\pi\) | ||||
−0.429701 | + | 0.902971i | \(0.641381\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.30526e31 | −0.00962570 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.23476e33 | 0.500967 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.69195e32 | 0.0667052 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.93440e32 | −0.112426 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.17725e33 | 0.438352 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 2.44035e33 | 0.883169 | 0.441584 | − | 0.897220i | \(-0.354417\pi\) | ||||
0.441584 | + | 0.897220i | \(0.354417\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.28105e33 | 0.802406 | 0.401203 | − | 0.915989i | \(-0.368592\pi\) | ||||
0.401203 | + | 0.915989i | \(0.368592\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −7.31194e32 | −0.250029 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −6.75645e32 | −0.224598 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.99688e33 | 0.645353 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −6.98404e32 | −0.219453 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −5.89474e33 | −1.80102 | −0.900509 | − | 0.434838i | \(-0.856806\pi\) | ||||
−0.900509 | + | 0.434838i | \(0.856806\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 5.31080e33 | 1.57784 | 0.788918 | − | 0.614498i | \(-0.210642\pi\) | ||||
0.788918 | + | 0.614498i | \(0.210642\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.37131e33 | 0.396199 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.64278e33 | −0.461601 | −0.230801 | − | 0.973001i | \(-0.574134\pi\) | ||||
−0.230801 | + | 0.973001i | \(0.574134\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −6.55887e33 | −1.79247 | −0.896235 | − | 0.443579i | \(-0.853708\pi\) | ||||
−0.896235 | + | 0.443579i | \(0.853708\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.15708e33 | 0.573397 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.58289e32 | −0.0926436 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.02909e33 | −0.258857 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 8.01987e32 | 0.196257 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.63564e33 | −0.389426 | −0.194713 | − | 0.980860i | \(-0.562378\pi\) | ||||
−0.194713 | + | 0.980860i | \(0.562378\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.07973e33 | 0.250126 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −3.15604e33 | −0.711419 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −7.86766e32 | −0.172581 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.10341e33 | 0.235547 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.14902e32 | 0.0238720 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.83159e32 | −0.0370372 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −9.05910e33 | −1.78308 | −0.891541 | − | 0.452940i | \(-0.850375\pi\) | ||||
−0.891541 | + | 0.452940i | \(0.850375\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −4.58025e32 | −0.0877565 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 2.55960e33 | 0.477411 | 0.238706 | − | 0.971092i | \(-0.423277\pi\) | ||||
0.238706 | + | 0.971092i | \(0.423277\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 6.48360e33 | 1.17732 | 0.588660 | − | 0.808381i | \(-0.299656\pi\) | ||||
0.588660 | + | 0.808381i | \(0.299656\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 5.31606e32 | 0.0939840 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −5.16834e33 | −0.889666 | −0.444833 | − | 0.895614i | \(-0.646737\pi\) | ||||
−0.444833 | + | 0.895614i | \(0.646737\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.09703e33 | −0.351495 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 3.48263e33 | 0.568444 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −3.26962e33 | −0.519720 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.34057e33 | −0.362337 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 4.06522e33 | 0.612943 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.62830e33 | −0.239134 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.42031e33 | −0.203184 | −0.101592 | − | 0.994826i | \(-0.532394\pi\) | ||||
−0.101592 | + | 0.994826i | \(0.532394\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −5.00606e33 | −0.697628 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.08884e34 | −1.47822 | −0.739111 | − | 0.673584i | \(-0.764754\pi\) | ||||
−0.739111 | + | 0.673584i | \(0.764754\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3.35808e33 | 0.444163 | 0.222082 | − | 0.975028i | \(-0.428715\pi\) | ||||
0.222082 | + | 0.975028i | \(0.428715\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −6.19357e32 | −0.0798166 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −7.80507e33 | −0.980066 | −0.490033 | − | 0.871704i | \(-0.663015\pi\) | ||||
−0.490033 | + | 0.871704i | \(0.663015\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.25752e33 | 0.520939 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 6.80140e32 | 0.0810970 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −7.18122e32 | −0.0834462 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.67157e33 | 0.302553 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 6.23153e33 | 0.687831 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.05979e34 | −1.14021 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.75440e31 | 0.00288863 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.70623e33 | 0.174433 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2.14394e32 | 0.0213676 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.04038e34 | 1.01090 | 0.505449 | − | 0.862856i | \(-0.331327\pi\) | ||||
0.505449 | + | 0.862856i | \(0.331327\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.64423e33 | 0.155768 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −9.34626e33 | −0.863330 | −0.431665 | − | 0.902034i | \(-0.642074\pi\) | ||||
−0.431665 | + | 0.902034i | \(0.642074\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.64273e33 | −0.238034 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.13810e33 | 0.0999625 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −4.93561e33 | −0.422759 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.07362e34 | −0.896854 | −0.448427 | − | 0.893819i | \(-0.648016\pi\) | ||||
−0.448427 | + | 0.893819i | \(0.648016\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 3.20589e33 | 0.261194 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −2.25116e34 | −1.78891 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.92515e32 | −0.0381760 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −3.04712e33 | −0.230395 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 9.90198e33 | 0.730367 | 0.365184 | − | 0.930935i | \(-0.381006\pi\) | ||||
0.365184 | + | 0.930935i | \(0.381006\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.11612e34 | −0.803137 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 9.32447e33 | 0.654614 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −3.23599e32 | −0.0221653 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.21853e34 | 1.48272 | 0.741362 | − | 0.671106i | \(-0.234180\pi\) | ||||
0.741362 | + | 0.671106i | \(0.234180\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.01168e34 | 0.659761 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −2.69613e34 | −1.71578 | −0.857889 | − | 0.513836i | \(-0.828224\pi\) | ||||
−0.857889 | + | 0.513836i | \(0.828224\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −4.74328e33 | −0.294574 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −3.91359e32 | −0.0237197 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.08449e34 | 0.641503 | 0.320752 | − | 0.947163i | \(-0.396064\pi\) | ||||
0.320752 | + | 0.947163i | \(0.396064\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.06748e33 | 0.119366 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 8.11698e33 | 0.457423 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.61511e33 | 0.143854 | 0.0719270 | − | 0.997410i | \(-0.477085\pi\) | ||||
0.0719270 | + | 0.997410i | \(0.477085\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −6.96456e33 | −0.373986 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −8.98775e33 | −0.471155 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −4.98959e33 | −0.255359 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.99577e32 | 0.0399522 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −8.17961e33 | −0.399053 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −8.65432e33 | −0.412258 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.67844e34 | −0.780732 | −0.390366 | − | 0.920660i | \(-0.627652\pi\) | ||||
−0.390366 | + | 0.920660i | \(0.627652\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.69980e33 | −0.0772100 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.05763e33 | 0.0912739 | 0.0456369 | − | 0.998958i | \(-0.485468\pi\) | ||||
0.0456369 | + | 0.998958i | \(0.485468\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −7.63504e33 | −0.330761 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.67566e34 | 0.708980 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.70711e34 | 0.705465 | 0.352732 | − | 0.935724i | \(-0.385253\pi\) | ||||
0.352732 | + | 0.935724i | \(0.385253\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.71755e34 | 1.09693 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5.31494e33 | 0.209558 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 4.02184e34 | 1.54903 | 0.774513 | − | 0.632558i | \(-0.217995\pi\) | ||||
0.774513 | + | 0.632558i | \(0.217995\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.03186e34 | −0.388243 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −6.13599e32 | −0.0225547 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.52239e34 | −0.546725 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.85503e34 | 1.70351 | 0.851756 | − | 0.523939i | \(-0.175538\pi\) | ||||
0.851756 | + | 0.523939i | \(0.175538\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −2.02491e34 | −0.694206 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4.05702e33 | 0.135907 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 3.83432e34 | 1.25515 | 0.627573 | − | 0.778557i | \(-0.284048\pi\) | ||||
0.627573 | + | 0.778557i | \(0.284048\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2.44278e32 | −0.00781413 |
(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 | 48.24.a.k.1.2 | 3 | ||
4.3 | odd | 2 | 24.24.a.d.1.2 | ✓ | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
24.24.a.d.1.2 | ✓ | 3 | 4.3 | odd | 2 | ||
48.24.a.k.1.2 | 3 | 1.1 | even | 1 | trivial |