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: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{2} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 618312 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{7}\cdot 3 \) |
Twist minimal: | no (minimal twist has level 4) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-785.828\) 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 | ||||||||
\(3\) | 216690. | 0.706227 | 0.353114 | − | 0.935580i | \(-0.385123\pi\) | ||||
0.353114 | + | 0.935580i | \(0.385123\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.16920e8 | −1.07086 | −0.535431 | − | 0.844579i | \(-0.679851\pi\) | ||||
−0.535431 | + | 0.844579i | \(0.679851\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −5.39865e8 | −0.103195 | −0.0515974 | − | 0.998668i | \(-0.516431\pi\) | ||||
−0.0515974 | + | 0.998668i | \(0.516431\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −4.71886e10 | −0.501243 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.77240e11 | −0.292981 | −0.146491 | − | 0.989212i | \(-0.546798\pi\) | ||||
−0.146491 | + | 0.989212i | \(0.546798\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.06685e13 | 1.65103 | 0.825513 | − | 0.564383i | \(-0.190886\pi\) | ||||
0.825513 | + | 0.564383i | \(0.190886\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.53354e13 | −0.756273 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.32199e14 | −1.64323 | −0.821615 | − | 0.570043i | \(-0.806927\pi\) | ||||
−0.821615 | + | 0.570043i | \(0.806927\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.66455e14 | 0.918635 | 0.459318 | − | 0.888272i | \(-0.348094\pi\) | ||||
0.459318 | + | 0.888272i | \(0.348094\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.16983e14 | −0.0728790 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.60775e15 | 1.44605 | 0.723026 | − | 0.690821i | \(-0.242751\pi\) | ||||
0.723026 | + | 0.690821i | \(0.242751\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.74937e15 | 0.146747 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.06252e16 | −1.06022 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.34130e14 | 0.00660758 | 0.00330379 | − | 0.999995i | \(-0.498948\pi\) | ||||
0.00330379 | + | 0.999995i | \(0.498948\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.65725e17 | −1.87833 | −0.939167 | − | 0.343460i | \(-0.888401\pi\) | ||||
−0.939167 | + | 0.343460i | \(0.888401\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −6.00751e16 | −0.206911 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 6.31211e16 | 0.110507 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.71922e17 | −0.158859 | −0.0794294 | − | 0.996840i | \(-0.525310\pi\) | ||||
−0.0794294 | + | 0.996840i | \(0.525310\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.31175e18 | 1.16600 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.88204e17 | 0.166922 | 0.0834610 | − | 0.996511i | \(-0.473403\pi\) | ||||
0.0834610 | + | 0.996511i | \(0.473403\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.52759e18 | −0.742985 | −0.371492 | − | 0.928436i | \(-0.621154\pi\) | ||||
−0.371492 | + | 0.928436i | \(0.621154\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 5.51729e18 | 0.536762 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.22092e19 | −1.31041 | −0.655205 | − | 0.755451i | \(-0.727418\pi\) | ||||
−0.655205 | + | 0.755451i | \(0.727418\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.70773e19 | −0.989351 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.03153e19 | −1.16049 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.08925e19 | 0.161420 | 0.0807099 | − | 0.996738i | \(-0.474281\pi\) | ||||
0.0807099 | + | 0.996738i | \(0.474281\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.24149e19 | 0.313743 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.01076e20 | 0.648765 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.00557e20 | −1.29756 | −0.648782 | − | 0.760974i | \(-0.724721\pi\) | ||||
−0.648782 | + | 0.760974i | \(0.724721\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.24437e20 | 1.24888 | 0.624440 | − | 0.781073i | \(-0.285327\pi\) | ||||
0.624440 | + | 0.781073i | \(0.285327\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.54755e19 | 0.0517256 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.24736e21 | −1.76802 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.81182e20 | −0.681402 | −0.340701 | − | 0.940172i | \(-0.610664\pi\) | ||||
−0.340701 | + | 0.940172i | \(0.610664\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.43183e21 | 1.02124 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.50119e21 | 1.28433 | 0.642163 | − | 0.766568i | \(-0.278037\pi\) | ||||
0.642163 | + | 0.766568i | \(0.278037\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.31511e21 | 0.863693 | 0.431847 | − | 0.901947i | \(-0.357862\pi\) | ||||
0.431847 | + | 0.901947i | \(0.357862\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 3.79070e20 | 0.103637 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.49672e20 | 0.0302342 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.71022e21 | 0.708483 | 0.354241 | − | 0.935154i | \(-0.384739\pi\) | ||||
0.354241 | + | 0.935154i | \(0.384739\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −2.19369e21 | −0.247513 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.97680e21 | 0.679878 | 0.339939 | − | 0.940448i | \(-0.389594\pi\) | ||||
0.339939 | + | 0.940448i | \(0.389594\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.71488e22 | 1.75967 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 9.40716e19 | 0.00466646 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.30111e22 | 0.878926 | 0.439463 | − | 0.898261i | \(-0.355169\pi\) | ||||
0.439463 | + | 0.898261i | \(0.355169\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.75954e21 | −0.170377 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −5.75800e22 | −1.32653 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −5.45379e22 | −0.983732 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.70590e22 | 1.37772 | 0.688860 | − | 0.724894i | \(-0.258111\pi\) | ||||
0.688860 | + | 0.724894i | \(0.258111\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.30826e22 | 0.146855 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.15267e22 | 0.459554 | 0.229777 | − | 0.973243i | \(-0.426200\pi\) | ||||
0.229777 | + | 0.973243i | \(0.426200\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.07411e23 | −0.764578 | −0.382289 | − | 0.924043i | \(-0.624864\pi\) | ||||
−0.382289 | + | 0.924043i | \(0.624864\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.36777e22 | 0.0780434 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.13016e23 | 0.978359 | 0.489180 | − | 0.872183i | \(-0.337296\pi\) | ||||
0.489180 | + | 0.872183i | \(0.337296\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.91111e22 | 0.108057 | 0.0540286 | − | 0.998539i | \(-0.482794\pi\) | ||||
0.0540286 | + | 0.998539i | \(0.482794\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.72538e22 | −0.112190 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 8.27983e22 | 0.203058 | 0.101529 | − | 0.994833i | \(-0.467627\pi\) | ||||
0.101529 | + | 0.994833i | \(0.467627\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −7.72579e23 | −1.54852 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −5.03431e23 | −0.827565 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.25356e23 | 0.169573 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.18568e23 | −0.914162 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.27458e23 | 0.117885 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.18926e24 | 0.913717 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.61404e24 | 1.03317 | 0.516583 | − | 0.856237i | \(-0.327204\pi\) | ||||
0.516583 | + | 0.856237i | \(0.327204\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −9.81084e23 | −0.524716 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.84884e24 | 1.72468 | 0.862342 | − | 0.506326i | \(-0.168997\pi\) | ||||
0.862342 | + | 0.506326i | \(0.168997\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.51823e23 | −0.0947984 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3.58070e24 | 1.13535 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −3.12427e24 | −0.836492 | −0.418246 | − | 0.908334i | \(-0.637355\pi\) | ||||
−0.418246 | + | 0.908334i | \(0.637355\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7.53219e24 | −1.70707 | −0.853535 | − | 0.521036i | \(-0.825546\pi\) | ||||
−0.853535 | + | 0.521036i | \(0.825546\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.81251e24 | −0.925448 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.95773e24 | −0.483720 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5.07585e22 | −0.00707582 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −5.86738e24 | −0.698707 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 9.61982e24 | 0.980674 | 0.490337 | − | 0.871533i | \(-0.336874\pi\) | ||||
0.490337 | + | 0.871533i | \(0.336874\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.64397e25 | −1.43767 | −0.718835 | − | 0.695180i | \(-0.755324\pi\) | ||||
−0.718835 | + | 0.695180i | \(0.755324\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.09572e25 | 0.823657 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.10686e25 | 2.01144 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.55113e25 | −1.42524 | −0.712619 | − | 0.701551i | \(-0.752491\pi\) | ||||
−0.712619 | + | 0.701551i | \(0.752491\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.36031e24 | 0.113999 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.56730e24 | −0.149225 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −9.60360e24 | −0.348559 | −0.174280 | − | 0.984696i | \(-0.555760\pi\) | ||||
−0.174280 | + | 0.984696i | \(0.555760\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 7.02399e24 | 0.221574 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.23180e25 | 0.338300 | 0.169150 | − | 0.985590i | \(-0.445898\pi\) | ||||
0.169150 | + | 0.985590i | \(0.445898\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.20626e25 | 1.72589 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.20113e25 | −0.460459 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 4.66836e25 | 0.854347 | 0.427174 | − | 0.904170i | \(-0.359509\pi\) | ||||
0.427174 | + | 0.904170i | \(0.359509\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −9.44421e23 | −0.0151436 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −6.51278e25 | −0.916376 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.17980e26 | 1.45881 | 0.729405 | − | 0.684082i | \(-0.239797\pi\) | ||||
0.729405 | + | 0.684082i | \(0.239797\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.32252e25 | 0.361546 | 0.180773 | − | 0.983525i | \(-0.442140\pi\) | ||||
0.180773 | + | 0.983525i | \(0.442140\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 9.19714e25 | 0.881993 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.01011e25 | 0.170116 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.43749e25 | 0.481436 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.65335e25 | 0.109409 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.29936e26 | 1.34810 | 0.674051 | − | 0.738684i | \(-0.264553\pi\) | ||||
0.674051 | + | 0.738684i | \(0.264553\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −8.72143e25 | −0.453606 | −0.226803 | − | 0.973941i | \(-0.572827\pi\) | ||||
−0.226803 | + | 0.973941i | \(0.572827\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2.70290e26 | −1.24863 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1.13225e25 | −0.0465138 | −0.0232569 | − | 0.999730i | \(-0.507404\pi\) | ||||
−0.0232569 | + | 0.999730i | \(0.507404\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.25068e25 | 0.155470 | 0.0777352 | − | 0.996974i | \(-0.475231\pi\) | ||||
0.0777352 | + | 0.996974i | \(0.475231\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.47605e26 | −0.481225 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.34372e23 | −0.000681868 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.87728e25 | −0.178751 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −3.11811e26 | −0.724823 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.29320e26 | −0.269143 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.05293e26 | 1.12906 | 0.564530 | − | 0.825412i | \(-0.309057\pi\) | ||||
0.564530 | + | 0.825412i | \(0.309057\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 5.41982e26 | 0.907026 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 5.29366e26 | 0.795635 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.43456e26 | 0.193834 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 5.01662e26 | 0.609964 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.47721e27 | −2.71302 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.90751e26 | 0.385828 | 0.192914 | − | 0.981216i | \(-0.438206\pi\) | ||||
0.192914 | + | 0.981216i | \(0.438206\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −8.25501e25 | −0.0735561 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 9.06311e26 | 0.729424 | 0.364712 | − | 0.931120i | \(-0.381167\pi\) | ||||
0.364712 | + | 0.931120i | \(0.381167\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.76026e26 | 0.200836 | 0.100418 | − | 0.994945i | \(-0.467982\pi\) | ||||
0.100418 | + | 0.994945i | \(0.467982\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.24325e25 | 0.0213522 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2.39900e27 | 1.43034 | 0.715168 | − | 0.698953i | \(-0.246350\pi\) | ||||
0.715168 | + | 0.698953i | \(0.246350\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.59670e27 | 1.40327 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.02066e27 | 0.500350 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.04793e27 | 0.911465 | 0.455732 | − | 0.890117i | \(-0.349377\pi\) | ||||
0.455732 | + | 0.890117i | \(0.349377\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.44324e27 | −1.39242 | −0.696211 | − | 0.717837i | \(-0.745132\pi\) | ||||
−0.696211 | + | 0.717837i | \(0.745132\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 2.40780e27 | 0.885418 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.16588e27 | 1.05946 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.97636e27 | 1.51669 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.72849e27 | 0.480148 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.69682e27 | 0.429921 | 0.214960 | − | 0.976623i | \(-0.431038\pi\) | ||||
0.214960 | + | 0.976623i | \(0.431038\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.83193e27 | −0.423666 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 5.88287e27 | 1.24273 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2.16634e27 | 0.418308 | 0.209154 | − | 0.977883i | \(-0.432929\pi\) | ||||
0.209154 | + | 0.977883i | \(0.432929\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 9.28146e25 | 0.0163934 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.04860e25 | −0.00331200 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3.76273e27 | 0.557201 | 0.278601 | − | 0.960407i | \(-0.410129\pi\) | ||||
0.278601 | + | 0.960407i | \(0.410129\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.27356e27 | −0.172858 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4.98628e27 | 0.620722 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.38207e28 | 1.57898 | 0.789491 | − | 0.613762i | \(-0.210344\pi\) | ||||
0.789491 | + | 0.613762i | \(0.210344\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.13487e27 | −0.119069 | −0.0595343 | − | 0.998226i | \(-0.518962\pi\) | ||||
−0.0595343 | + | 0.998226i | \(0.518962\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.24804e27 | −0.120325 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −4.84994e26 | −0.0429942 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −9.82908e26 | −0.0801670 | −0.0400835 | − | 0.999196i | \(-0.512762\pi\) | ||||
−0.0400835 | + | 0.999196i | \(0.512762\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.25392e28 | 0.941502 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.82184e28 | −1.26005 | −0.630024 | − | 0.776576i | \(-0.716955\pi\) | ||||
−0.630024 | + | 0.776576i | \(0.716955\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.32526e27 | 0.466960 | 0.233480 | − | 0.972362i | \(-0.424989\pi\) | ||||
0.233480 | + | 0.972362i | \(0.424989\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.18178e28 | −0.694739 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.17551e26 | −0.0172255 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.39490e28 | 1.70021 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.10317e28 | 0.972984 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −3.19438e28 | −1.36587 | −0.682934 | − | 0.730480i | \(-0.739296\pi\) | ||||
−0.682934 | + | 0.730480i | \(0.739296\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.51412e28 | 1.38951 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 8.49053e27 | 0.310624 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 7.04947e28 | 2.38747 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.44429e27 | 0.0766722 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.11653e28 | 0.324550 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −4.96252e28 | −1.33738 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3.20565e28 | 0.801355 | 0.400678 | − | 0.916219i | \(-0.368775\pi\) | ||||
0.400678 | + | 0.916219i | \(0.368775\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.32750e28 | −0.539966 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.76164e27 | 0.0379465 | 0.0189733 | − | 0.999820i | \(-0.493960\pi\) | ||||
0.0189733 | + | 0.999820i | \(0.493960\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5.11434e27 | −0.102336 | −0.0511682 | − | 0.998690i | \(-0.516294\pi\) | ||||
−0.0511682 | + | 0.998690i | \(0.516294\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.97859e27 | −0.0553911 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.90574e28 | 0.502430 | 0.251215 | − | 0.967931i | \(-0.419170\pi\) | ||||
0.251215 | + | 0.967931i | \(0.419170\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.20358e26 | −0.00193590 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4.61584e28 | 0.690944 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.08310e29 | −1.50953 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.86631e28 | 0.242284 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 6.30809e27 | 0.0763130 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.19900e28 | 0.135228 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.94295e28 | −0.204380 | −0.102190 | − | 0.994765i | \(-0.532585\pi\) | ||||
−0.102190 | + | 0.994765i | \(0.532585\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 8.11275e27 | 0.0796268 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 7.96439e28 | 0.729688 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7.14896e28 | −0.611644 | −0.305822 | − | 0.952089i | \(-0.598931\pi\) | ||||
−0.305822 | + | 0.952089i | \(0.598931\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.79416e28 | 0.143405 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 7.36696e28 | 0.550317 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2.93935e28 | 0.205291 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.67410e29 | −1.09361 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6.32031e28 | 0.386322 | 0.193161 | − | 0.981167i | \(-0.438126\pi\) | ||||
0.193161 | + | 0.981167i | \(0.438126\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.65356e29 | 0.946080 | 0.473040 | − | 0.881041i | \(-0.343157\pi\) | ||||
0.473040 | + | 0.881041i | \(0.343157\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.26724e29 | −1.75045 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3.87413e29 | 1.94431 | 0.972153 | − | 0.234346i | \(-0.0752950\pi\) | ||||
0.972153 | + | 0.234346i | \(0.0752950\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.92439e29 | −1.37534 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.71635e28 | 0.119757 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.97727e29 | 0.817484 | 0.408742 | − | 0.912650i | \(-0.365968\pi\) | ||||
0.408742 | + | 0.912650i | \(0.365968\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.02496e28 | −0.156109 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.77376e29 | −0.645606 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.70683e29 | −0.924897 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4.25634e29 | −1.36577 | −0.682883 | − | 0.730528i | \(-0.739274\pi\) | ||||
−0.682883 | + | 0.730528i | \(0.739274\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.77565e28 | −0.0836685 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −5.88050e27 | −0.0166577 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.45786e29 | −0.654495 | −0.327247 | − | 0.944939i | \(-0.606121\pi\) | ||||
−0.327247 | + | 0.944939i | \(0.606121\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.57701e29 | 0.645292 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4.63151e27 | 0.0109093 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5.19016e29 | 1.15035 | 0.575175 | − | 0.818031i | \(-0.304934\pi\) | ||||
0.575175 | + | 0.818031i | \(0.304934\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.49745e29 | 0.729651 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2.42152e29 | −0.475665 | −0.237833 | − | 0.971306i | \(-0.576437\pi\) | ||||
−0.237833 | + | 0.971306i | \(0.576437\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.74997e28 | −0.0323766 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2.13651e29 | 0.372416 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −2.56541e29 | −0.421441 | −0.210721 | − | 0.977546i | \(-0.567581\pi\) | ||||
−0.210721 | + | 0.977546i | \(0.567581\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.53432e30 | −2.37620 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 8.34005e29 | 1.21802 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −5.50719e29 | −0.758688 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −9.53634e29 | −1.23963 | −0.619813 | − | 0.784749i | \(-0.712792\pi\) | ||||
−0.619813 | + | 0.784749i | \(0.712792\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −5.45675e28 | −0.0669492 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.61868e30 | −1.87500 | −0.937501 | − | 0.347982i | \(-0.886867\pi\) | ||||
−0.937501 | + | 0.347982i | \(0.886867\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.83488e30 | −3.10118 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2.56486e29 | 0.265052 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.76636e28 | 0.0465427 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.84424e29 | 0.447103 | 0.223551 | − | 0.974692i | \(-0.428235\pi\) | ||||
0.223551 | + | 0.974692i | \(0.428235\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −6.76998e29 | −0.590754 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.62260e29 | 0.133902 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −9.32648e29 | −0.728056 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1.63215e30 | −1.20558 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.19166e29 | 0.153219 | 0.0766095 | − | 0.997061i | \(-0.475591\pi\) | ||||
0.0766095 | + | 0.997061i | \(0.475591\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.70067e30 | 1.12558 | 0.562789 | − | 0.826600i | \(-0.309728\pi\) | ||||
0.562789 | + | 0.826600i | \(0.309728\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.04802e30 | 0.656834 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −4.06202e29 | −0.241140 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.29139e29 | −0.128878 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −6.40911e29 | −0.341616 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.28932e30 | −1.15669 | −0.578346 | − | 0.815791i | \(-0.696302\pi\) | ||||
−0.578346 | + | 0.815791i | \(0.696302\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.06239e30 | 0.988009 | 0.494004 | − | 0.869459i | \(-0.335533\pi\) | ||||
0.494004 | + | 0.869459i | \(0.335533\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.09989e28 | −0.00499714 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3.08222e30 | 1.32839 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.57142e29 | −0.0642613 | −0.0321306 | − | 0.999484i | \(-0.510229\pi\) | ||||
−0.0321306 | + | 0.999484i | \(0.510229\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.27774e30 | 0.495905 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2.88129e30 | −1.06156 | −0.530779 | − | 0.847511i | \(-0.678100\pi\) | ||||
−0.530779 | + | 0.847511i | \(0.678100\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.69046e30 | −0.941209 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2.08452e30 | 0.692579 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 7.97062e28 | 0.0251570 | 0.0125785 | − | 0.999921i | \(-0.495996\pi\) | ||||
0.0125785 | + | 0.999921i | \(0.495996\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.63074e29 | −0.0489050 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −3.56232e30 | −1.01532 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 6.73406e29 | 0.182451 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2.35544e30 | −0.606786 | −0.303393 | − | 0.952866i | \(-0.598119\pi\) | ||||
−0.303393 | + | 0.952866i | \(0.598119\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 7.11115e30 | 1.74218 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5.69014e30 | 1.32606 | 0.663029 | − | 0.748594i | \(-0.269271\pi\) | ||||
0.663029 | + | 0.748594i | \(0.269271\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.47214e30 | 0.326413 | 0.163206 | − | 0.986592i | \(-0.447816\pi\) | ||||
0.163206 | + | 0.986592i | \(0.447816\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 6.73225e30 | 1.42053 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 6.23957e30 | 1.25317 | 0.626585 | − | 0.779353i | \(-0.284452\pi\) | ||||
0.626585 | + | 0.779353i | \(0.284452\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.67747e29 | 0.0703171 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −5.52806e30 | −1.00654 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.25523e30 | 0.217681 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 8.16000e29 | 0.134807 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −5.14004e29 | −0.0809105 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5.00921e30 | 0.751468 | 0.375734 | − | 0.926727i | \(-0.377391\pi\) | ||||
0.375734 | + | 0.926727i | \(0.377391\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.83415e30 | −0.262280 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −7.72998e29 | −0.105387 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.13481e31 | −1.47535 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3.34402e30 | −0.414654 | −0.207327 | − | 0.978272i | \(-0.566476\pi\) | ||||
−0.207327 | + | 0.978272i | \(0.566476\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2.08101e30 | −0.246162 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.19218e31 | −1.34556 | −0.672782 | − | 0.739841i | \(-0.734901\pi\) | ||||
−0.672782 | + | 0.739841i | \(0.734901\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.00805e29 | −0.0108578 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.52961e30 | −0.157261 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.35030e30 | −0.132536 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.82630e30 | 0.264888 | 0.132444 | − | 0.991190i | \(-0.457718\pi\) | ||||
0.132444 | + | 0.991190i | \(0.457718\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.66919e30 | 0.238916 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 2.24263e31 | 1.91746 | 0.958729 | − | 0.284321i | \(-0.0917680\pi\) | ||||
0.958729 | + | 0.284321i | \(0.0917680\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.02450e30 | −0.492119 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.56152e31 | 1.21887 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 7.05286e30 | 0.526152 | 0.263076 | − | 0.964775i | \(-0.415263\pi\) | ||||
0.263076 | + | 0.964775i | \(0.415263\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.24985e30 | −0.0891286 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.42853e31 | −0.973954 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.25585e31 | 0.818758 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6.15727e30 | 0.383926 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.01159e31 | 0.603363 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.98048e31 | −1.13015 | −0.565075 | − | 0.825040i | \(-0.691153\pi\) | ||||
−0.565075 | + | 0.825040i | \(0.691153\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.73584e30 | −0.0947852 | −0.0473926 | − | 0.998876i | \(-0.515091\pi\) | ||||
−0.0473926 | + | 0.998876i | \(0.515091\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −2.04647e29 | −0.0106948 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 6.17012e31 | 3.08654 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2.27820e31 | 1.09107 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.41829e31 | 0.650395 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 6.27524e30 | 0.275593 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.49058e31 | −1.04769 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2.55651e31 | 1.03025 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 7.50691e30 | 0.289861 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.16112e31 | −0.799669 | −0.399834 | − | 0.916587i | \(-0.630932\pi\) | ||||
−0.399834 | + | 0.916587i | \(0.630932\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 7.19957e30 | 0.255334 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3.40367e30 | −0.115715 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.49009e31 | 0.811634 | 0.405817 | − | 0.913954i | \(-0.366987\pi\) | ||||
0.405817 | + | 0.913954i | \(0.366987\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2.00286e31 | −0.625992 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.02502e29 | 0.00606996 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.54288e30 | −0.0731117 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 4.35571e30 | 0.120141 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 3.55158e31 | 0.939910 | 0.469955 | − | 0.882690i | \(-0.344270\pi\) | ||||
0.469955 | + | 0.882690i | \(0.344270\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4.83025e31 | −1.22669 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.39494e31 | 0.340003 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 3.99841e31 | 0.935493 | 0.467747 | − | 0.883863i | \(-0.345066\pi\) | ||||
0.467747 | + | 0.883863i | \(0.345066\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −9.68077e30 | −0.217447 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.18430e30 | 0.0255420 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1.04446e31 | −0.216323 | −0.108161 | − | 0.994133i | \(-0.534496\pi\) | ||||
−0.108161 | + | 0.994133i | \(0.534496\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.71952e31 | −0.938820 | −0.469410 | − | 0.882980i | \(-0.655533\pi\) | ||||
−0.469410 | + | 0.882980i | \(0.655533\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 4.98248e31 | 0.952067 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.15594e31 | 0.212204 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7.18074e31 | 1.26662 | 0.633312 | − | 0.773897i | \(-0.281695\pi\) | ||||
0.633312 | + | 0.773897i | \(0.281695\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.88985e31 | −0.320349 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.30640e30 | −0.0701598 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3.01985e30 | −0.0472930 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 5.88611e31 | 0.886209 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.52916e31 | −0.221368 | −0.110684 | − | 0.993856i | \(-0.535304\pi\) | ||||
−0.110684 | + | 0.993856i | \(0.535304\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.23949e32 | −1.72550 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.45348e30 | −0.0328493 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.17874e32 | −1.51805 | −0.759027 | − | 0.651059i | \(-0.774325\pi\) | ||||
−0.759027 | + | 0.651059i | \(0.774325\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.46567e31 | −0.181589 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 9.21079e30 | 0.109797 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.02527e32 | −1.17606 | −0.588031 | − | 0.808839i | \(-0.700097\pi\) | ||||
−0.588031 | + | 0.808839i | \(0.700097\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.41324e31 | −0.266406 | −0.133203 | − | 0.991089i | \(-0.542526\pi\) | ||||
−0.133203 | + | 0.991089i | \(0.542526\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3.21440e31 | 0.341548 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 9.57070e31 | 0.978942 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.84578e31 | 0.181765 | 0.0908823 | − | 0.995862i | \(-0.471031\pi\) | ||||
0.0908823 | + | 0.995862i | \(0.471031\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −5.07860e28 | −0.000481554 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.36938e32 | −2.16352 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.88798e32 | 1.66036 | 0.830180 | − | 0.557495i | \(-0.188238\pi\) | ||||
0.830180 | + | 0.557495i | \(0.188238\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.49024e31 | −0.126239 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.33198e32 | −1.08697 | −0.543487 | − | 0.839418i | \(-0.682896\pi\) | ||||
−0.543487 | + | 0.839418i | \(0.682896\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6.61060e30 | 0.0519755 | 0.0259877 | − | 0.999662i | \(-0.491727\pi\) | ||||
0.0259877 | + | 0.999662i | \(0.491727\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.02364e32 | −1.53313 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.24229e31 | −0.0907006 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.59902e32 | −1.12521 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.80223e31 | −0.190076 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3.99202e31 | 0.261042 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.70413e32 | 1.07440 | 0.537198 | − | 0.843456i | \(-0.319483\pi\) | ||||
0.537198 | + | 0.843456i | \(0.319483\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.31161e32 | 0.797373 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.88713e32 | −1.10638 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.88874e32 | −1.63344 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.18027e32 | −0.643759 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.04888e32 | 0.551898 | 0.275949 | − | 0.961172i | \(-0.411008\pi\) | ||||
0.275949 | + | 0.961172i | \(0.411008\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.47552e32 | 1.25673 | 0.628364 | − | 0.777920i | \(-0.283725\pi\) | ||||
0.628364 | + | 0.777920i | \(0.283725\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.14708e32 | 0.561899 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.42958e31 | −0.0675784 | −0.0337892 | − | 0.999429i | \(-0.510757\pi\) | ||||
−0.0337892 | + | 0.999429i | \(0.510757\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 8.33265e31 | 0.380162 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.10854e31 | 0.136891 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.82338e32 | 0.775132 | 0.387566 | − | 0.921842i | \(-0.373316\pi\) | ||||
0.387566 | + | 0.921842i | \(0.373316\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4.50006e32 | −1.84690 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.09247e32 | −0.432920 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −4.48747e32 | −1.71719 | −0.858597 | − | 0.512651i | \(-0.828664\pi\) | ||||
−0.858597 | + | 0.512651i | \(0.828664\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.17730e32 | −0.435082 | −0.217541 | − | 0.976051i | \(-0.569804\pi\) | ||||
−0.217541 | + | 0.976051i | \(0.569804\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −5.36788e32 | −1.91601 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.94431e31 | 0.101516 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.86862e30 | 0.00955491 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 8.46718e31 | 0.272483 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.17671e32 | −0.365898 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.89151e32 | 0.868864 | 0.434432 | − | 0.900705i | \(-0.356949\pi\) | ||||
0.434432 | + | 0.900705i | \(0.356949\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −5.35746e31 | −0.155584 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −4.29377e32 | −1.20523 | −0.602614 | − | 0.798033i | \(-0.705874\pi\) | ||||
−0.602614 | + | 0.798033i | \(0.705874\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5.23988e31 | −0.142174 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.96389e32 | 0.515139 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −3.11964e32 | −0.791164 | −0.395582 | − | 0.918431i | \(-0.629457\pi\) | ||||
−0.395582 | + | 0.918431i | \(0.629457\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.65290e32 | 0.895769 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 5.98121e31 | 0.141836 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.16207e32 | 0.266508 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7.49648e31 | 0.166288 | 0.0831438 | − | 0.996538i | \(-0.473504\pi\) | ||||
0.0831438 | + | 0.996538i | \(0.473504\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −7.06282e30 | −0.0151546 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 8.80664e32 | 1.82804 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.36581e32 | −0.274291 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 5.19840e32 | 1.01014 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.70909e32 | 0.509408 | 0.254704 | − | 0.967019i | \(-0.418022\pi\) | ||||
0.254704 | + | 0.967019i | \(0.418022\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −8.01938e31 | −0.145933 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 5.62679e32 | 0.991028 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −2.78175e31 | −0.0474236 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.59384e32 | 0.263034 | 0.131517 | − | 0.991314i | \(-0.458015\pi\) | ||||
0.131517 | + | 0.991314i | \(0.458015\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.22268e32 | −0.355122 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.75585e33 | −2.71617 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.45818e32 | 0.517998 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 4.43767e32 | 0.643701 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.86352e32 | 0.261789 | 0.130895 | − | 0.991396i | \(-0.458215\pi\) | ||||
0.130895 | + | 0.991396i | \(0.458215\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.79876e31 | 0.0789005 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −7.46115e32 | −0.983367 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 7.59452e29 | 0.000969646 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 6.67960e32 | 0.826237 | 0.413119 | − | 0.910677i | \(-0.364439\pi\) | ||||
0.413119 | + | 0.910677i | \(0.364439\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 7.28268e32 | 0.872820 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.05130e33 | 1.22090 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.40627e33 | −1.58261 | −0.791305 | − | 0.611422i | \(-0.790598\pi\) | ||||
−0.791305 | + | 0.611422i | \(0.790598\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 6.86014e32 | 0.748219 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.88851e32 | 0.199638 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.57416e31 | 0.0161301 | 0.00806506 | − | 0.999967i | \(-0.497433\pi\) | ||||
0.00806506 | + | 0.999967i | \(0.497433\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.07833e33 | 1.07113 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.10884e33 | 1.06782 | 0.533912 | − | 0.845540i | \(-0.320721\pi\) | ||||
0.533912 | + | 0.845540i | \(0.320721\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.12475e33 | −1.05017 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −3.76414e32 | −0.340784 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.15000e32 | −0.100962 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.61832e33 | 1.37786 | 0.688931 | − | 0.724827i | \(-0.258080\pi\) | ||||
0.688931 | + | 0.724827i | \(0.258080\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 3.67685e32 | 0.303622 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.92213e33 | 1.53955 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −3.85513e31 | −0.0299527 | −0.0149764 | − | 0.999888i | \(-0.504767\pi\) | ||||
−0.0149764 | + | 0.999888i | \(0.504767\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −3.96962e32 | −0.299205 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −3.70529e32 | −0.270956 | −0.135478 | − | 0.990780i | \(-0.543257\pi\) | ||||
−0.135478 | + | 0.990780i | \(0.543257\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.57161e31 | −0.0111509 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.28111e33 | −0.882024 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −3.20649e33 | −2.14231 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.16079e33 | −0.752663 | −0.376331 | − | 0.926485i | \(-0.622815\pi\) | ||||
−0.376331 | + | 0.926485i | \(0.622815\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4.69425e32 | 0.295420 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −9.29133e32 | −0.567562 | −0.283781 | − | 0.958889i | \(-0.591589\pi\) | ||||
−0.283781 | + | 0.958889i | \(0.591589\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.64850e32 | −0.275641 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2.01120e31 | 0.0115775 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.74371e32 | 0.153340 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.93429e32 | −0.376283 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.32953e31 | −0.00700548 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.98279e33 | 1.52623 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.04310e33 | 1.01526 | 0.507632 | − | 0.861574i | \(-0.330521\pi\) | ||||
0.507632 | + | 0.861574i | \(0.330521\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 8.15347e32 | 0.393511 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −4.46999e31 | −0.0209545 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.52810e33 | 2.06193 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2.75967e32 | −0.122077 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 8.24304e32 | 0.354255 | 0.177128 | − | 0.984188i | \(-0.443319\pi\) | ||||
0.177128 | + | 0.984188i | \(0.443319\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 5.15696e33 | 2.15331 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.08586e33 | −0.440555 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −6.41842e32 | −0.253046 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4.17088e32 | 0.159800 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 2.99480e33 | 1.11512 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −4.69127e33 | −1.69778 | −0.848892 | − | 0.528567i | \(-0.822730\pi\) | ||||
−0.848892 | + | 0.528567i | \(0.822730\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 5.15175e33 | 1.81224 | 0.906119 | − | 0.423023i | \(-0.139031\pi\) | ||||
0.906119 | + | 0.423023i | \(0.139031\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2.45914e32 | −0.0840896 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.12285e33 | 0.373259 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.11192e33 | −0.682532 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.71785e32 | 0.0854004 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6.68845e32 | 0.204352 | 0.102176 | − | 0.994766i | \(-0.467419\pi\) | ||||
0.102176 | + | 0.994766i | \(0.467419\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.06514e33 | −0.613553 | −0.306776 | − | 0.951782i | \(-0.599250\pi\) | ||||
−0.306776 | + | 0.951782i | \(0.599250\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.05093e32 | −0.0303637 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −2.42837e33 | −0.682341 | −0.341171 | − | 0.940001i | \(-0.610823\pi\) | ||||
−0.341171 | + | 0.940001i | \(0.610823\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.49649e33 | 0.682265 | 0.341133 | − | 0.940015i | \(-0.389189\pi\) | ||||
0.341133 | + | 0.940015i | \(0.389189\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.12986e32 | −0.0566161 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 6.28733e33 | 1.62573 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.44022e33 | −0.362273 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 8.13788e33 | 1.99145 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −3.48206e33 | −0.829035 | −0.414518 | − | 0.910041i | \(-0.636050\pi\) | ||||
−0.414518 | + | 0.910041i | \(0.636050\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.31653e33 | −0.999956 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −3.94774e33 | −0.889880 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −8.42556e33 | −1.84819 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4.41916e32 | 0.0943368 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.58731e33 | 0.329780 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.13602e33 | −0.229718 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.25375e33 | 0.443600 | 0.221800 | − | 0.975092i | \(-0.428807\pi\) | ||||
0.221800 | + | 0.975092i | \(0.428807\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.57357e33 | 0.493089 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 4.25946e33 | 0.794465 | 0.397233 | − | 0.917718i | \(-0.369971\pi\) | ||||
0.397233 | + | 0.917718i | \(0.369971\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.00049e34 | −1.81673 | −0.908363 | − | 0.418183i | \(-0.862667\pi\) | ||||
−0.908363 | + | 0.418183i | \(0.862667\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −6.88101e31 | −0.0121651 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 2.91159e33 | 0.501194 | 0.250597 | − | 0.968092i | \(-0.419373\pi\) | ||||
0.250597 | + | 0.968092i | \(0.419373\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −5.45825e33 | −0.914889 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 7.35641e33 | 1.20073 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.30586e33 | −0.207572 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7.26718e33 | −1.12501 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −4.58008e33 | −0.690572 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −6.42040e32 | −0.0942908 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −7.84349e33 | −1.12205 | −0.561027 | − | 0.827797i | \(-0.689594\pi\) | ||||
−0.561027 | + | 0.827797i | \(0.689594\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −6.92190e33 | −0.964613 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −4.76220e33 | −0.646525 | −0.323262 | − | 0.946309i | \(-0.604780\pi\) | ||||
−0.323262 | + | 0.946309i | \(0.604780\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −4.87573e33 | −0.644899 | −0.322450 | − | 0.946587i | \(-0.604506\pi\) | ||||
−0.322450 | + | 0.946587i | \(0.604506\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 7.61474e33 | 0.981313 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −8.40226e33 | −1.05505 | −0.527527 | − | 0.849538i | \(-0.676881\pi\) | ||||
−0.527527 | + | 0.849538i | \(0.676881\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −8.71362e32 | −0.106617 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 6.08179e32 | 0.0725167 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.03596e34 | −1.20379 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.37942e34 | −1.56219 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.52755e34 | 1.68610 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.15359e32 | −0.0124113 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.52924e33 | −0.265250 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 5.29653e32 | 0.0541480 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −3.88469e33 | −0.387167 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.45779e34 | −1.41648 | −0.708242 | − | 0.705969i | \(-0.750512\pi\) | ||||
−0.708242 | + | 0.705969i | \(0.750512\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −2.43147e33 | −0.230348 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.18817e31 | 0.00202125 | 0.00101063 | − | 0.999999i | \(-0.499678\pi\) | ||||
0.00101063 | + | 0.999999i | \(0.499678\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.21149e33 | −0.199191 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.07533e34 | −0.944494 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −2.07785e33 | −0.177978 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.60404e33 | −0.133995 | −0.0669974 | − | 0.997753i | \(-0.521342\pi\) | ||||
−0.0669974 | + | 0.997753i | \(0.521342\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 6.94633e33 | 0.565939 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2.66839e34 | 2.12046 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.00754e32 | −0.0233121 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 5.06859e33 | 0.383239 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 2.03965e34 | 1.50444 | 0.752219 | − | 0.658913i | \(-0.228984\pi\) | ||||
0.752219 | + | 0.658913i | \(0.228984\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.26303e34 | −0.908852 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 3.81729e32 | 0.0267989 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −7.52672e33 | −0.515552 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.91671e34 | −1.94934 | −0.974670 | − | 0.223649i | \(-0.928203\pi\) | ||||
−0.974670 | + | 0.223649i | \(0.928203\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.10823e33 | −0.0722727 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 7.95391e33 | 0.506174 | 0.253087 | − | 0.967443i | \(-0.418554\pi\) | ||||
0.253087 | + | 0.967443i | \(0.418554\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.88671e33 | 0.241378 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.93309e33 | −0.117162 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2.04508e34 | 1.20972 | 0.604862 | − | 0.796330i | \(-0.293228\pi\) | ||||
0.604862 | + | 0.796330i | \(0.293228\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.46987e34 | 1.42598 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 6.29646e33 | 0.354830 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −3.16254e34 | −1.73967 | −0.869837 | − | 0.493340i | \(-0.835776\pi\) | ||||
−0.869837 | + | 0.493340i | \(0.835776\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.68841e34 | −1.44363 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2.60804e31 | −0.00136718 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.68668e33 | 0.0863217 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.05965e34 | 2.52814 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.00519e34 | −0.490396 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.01971e34 | 0.485750 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.16807e34 | 1.00848 | 0.504242 | − | 0.863562i | \(-0.331772\pi\) | ||||
0.504242 | + | 0.863562i | \(0.331772\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2.34698e34 | −1.06607 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.64733e34 | −0.730734 | −0.365367 | − | 0.930864i | \(-0.619056\pi\) | ||||
−0.365367 | + | 0.930864i | \(0.619056\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4.06637e33 | 0.176161 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 4.04410e33 | 0.171107 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.91054e34 | 0.789529 | 0.394765 | − | 0.918782i | \(-0.370826\pi\) | ||||
0.394765 | + | 0.918782i | \(0.370826\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −6.37960e33 | −0.257509 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.37371e33 | −0.0541629 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −2.04129e34 | −0.786213 | −0.393107 | − | 0.919493i | \(-0.628600\pi\) | ||||
−0.393107 | + | 0.919493i | \(0.628600\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.32383e33 | 0.0498099 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.59811e33 | 0.0955014 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.99172e34 | −1.07439 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.46345e34 | −0.864364 | −0.432182 | − | 0.901786i | \(-0.642256\pi\) | ||||
−0.432182 | + | 0.901786i | \(0.642256\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −4.21017e33 | −0.144339 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −4.96989e33 | −0.166487 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −3.06239e33 | −0.100246 | −0.0501229 | − | 0.998743i | \(-0.515961\pi\) | ||||
−0.0501229 | + | 0.998743i | \(0.515961\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 5.26514e33 | 0.168425 |
(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.e.1.2 | 2 | ||
4.3 | odd | 2 | 64.24.a.f.1.1 | 2 | |||
8.3 | odd | 2 | 16.24.a.c.1.2 | 2 | |||
8.5 | even | 2 | 4.24.a.a.1.1 | ✓ | 2 | ||
24.5 | odd | 2 | 36.24.a.e.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4.24.a.a.1.1 | ✓ | 2 | 8.5 | even | 2 | ||
16.24.a.c.1.2 | 2 | 8.3 | odd | 2 | |||
36.24.a.e.1.1 | 2 | 24.5 | odd | 2 | |||
64.24.a.e.1.2 | 2 | 1.1 | even | 1 | trivial | ||
64.24.a.f.1.1 | 2 | 4.3 | odd | 2 |