Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [531,8,Mod(1,531)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(531, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("531.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 531 = 3^{2} \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 531.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: | \(165.876448532\) |
Analytic rank: | \(0\) |
Dimension: | \(17\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{17} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{17} - 2 x^{16} - 1639 x^{15} + 1625 x^{14} + 1070274 x^{13} - 274939 x^{12} - 357079564 x^{11} + \cdots - 58\!\cdots\!76 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | multiple of \( 2^{10}\cdot 3^{5} \) |
Twist minimal: | no (minimal twist has level 177) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.13 | ||
Root | \(-11.3335\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 531.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 13.3335 | 1.17852 | 0.589262 | − | 0.807942i | \(-0.299419\pi\) | ||||
0.589262 | + | 0.807942i | \(0.299419\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 49.7814 | 0.388917 | ||||||||
\(5\) | −152.093 | −0.544144 | −0.272072 | − | 0.962277i | \(-0.587709\pi\) | ||||
−0.272072 | + | 0.962277i | \(0.587709\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1328.47 | −1.46390 | −0.731948 | − | 0.681361i | \(-0.761389\pi\) | ||||
−0.731948 | + | 0.681361i | \(0.761389\pi\) | |||||||
\(8\) | −1042.93 | −0.720176 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −2027.93 | −0.641286 | ||||||||
\(11\) | −5132.02 | −1.16256 | −0.581279 | − | 0.813705i | \(-0.697447\pi\) | ||||
−0.581279 | + | 0.813705i | \(0.697447\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −12251.2 | −1.54660 | −0.773299 | − | 0.634041i | \(-0.781395\pi\) | ||||
−0.773299 | + | 0.634041i | \(0.781395\pi\) | |||||||
\(14\) | −17713.2 | −1.72524 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −20277.8 | −1.23766 | ||||||||
\(17\) | −26601.9 | −1.31323 | −0.656615 | − | 0.754226i | \(-0.728012\pi\) | ||||
−0.656615 | + | 0.754226i | \(0.728012\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 33197.2 | 1.11036 | 0.555181 | − | 0.831730i | \(-0.312649\pi\) | ||||
0.555181 | + | 0.831730i | \(0.312649\pi\) | |||||||
\(20\) | −7571.39 | −0.211627 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −68427.7 | −1.37010 | ||||||||
\(23\) | 97057.0 | 1.66333 | 0.831667 | − | 0.555274i | \(-0.187387\pi\) | ||||
0.831667 | + | 0.555274i | \(0.187387\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −54992.8 | −0.703907 | ||||||||
\(26\) | −163351. | −1.82270 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −66133.3 | −0.569334 | ||||||||
\(29\) | −209269. | −1.59335 | −0.796675 | − | 0.604408i | \(-0.793410\pi\) | ||||
−0.796675 | + | 0.604408i | \(0.793410\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −308874. | −1.86215 | −0.931077 | − | 0.364823i | \(-0.881129\pi\) | ||||
−0.931077 | + | 0.364823i | \(0.881129\pi\) | |||||||
\(32\) | −136879. | −0.738436 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −354695. | −1.54767 | ||||||||
\(35\) | 202052. | 0.796570 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 287842. | 0.934219 | 0.467110 | − | 0.884199i | \(-0.345295\pi\) | ||||
0.467110 | + | 0.884199i | \(0.345295\pi\) | |||||||
\(38\) | 442634. | 1.30859 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 158622. | 0.391879 | ||||||||
\(41\) | −581611. | −1.31792 | −0.658960 | − | 0.752178i | \(-0.729004\pi\) | ||||
−0.658960 | + | 0.752178i | \(0.729004\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 540792. | 1.03727 | 0.518634 | − | 0.854996i | \(-0.326441\pi\) | ||||
0.518634 | + | 0.854996i | \(0.326441\pi\) | |||||||
\(44\) | −255479. | −0.452138 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.29411e6 | 1.96028 | ||||||||
\(47\) | 650609. | 0.914066 | 0.457033 | − | 0.889450i | \(-0.348912\pi\) | ||||
0.457033 | + | 0.889450i | \(0.348912\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 941302. | 1.14299 | ||||||||
\(50\) | −733244. | −0.829571 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −609883. | −0.601499 | ||||||||
\(53\) | 49948.0 | 0.0460843 | 0.0230421 | − | 0.999734i | \(-0.492665\pi\) | ||||
0.0230421 | + | 0.999734i | \(0.492665\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 780544. | 0.632599 | ||||||||
\(56\) | 1.38550e6 | 1.05426 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −2.79028e6 | −1.87780 | ||||||||
\(59\) | 205379. | 0.130189 | ||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −20025.0 | −0.0112958 | −0.00564791 | − | 0.999984i | \(-0.501798\pi\) | ||||
−0.00564791 | + | 0.999984i | \(0.501798\pi\) | |||||||
\(62\) | −4.11836e6 | −2.19459 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 770486. | 0.367396 | ||||||||
\(65\) | 1.86332e6 | 0.841573 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.38680e6 | −0.563314 | −0.281657 | − | 0.959515i | \(-0.590884\pi\) | ||||
−0.281657 | + | 0.959515i | \(0.590884\pi\) | |||||||
\(68\) | −1.32428e6 | −0.510738 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 2.69405e6 | 0.938776 | ||||||||
\(71\) | −1.24373e6 | −0.412403 | −0.206201 | − | 0.978510i | \(-0.566110\pi\) | ||||
−0.206201 | + | 0.978510i | \(0.566110\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.83751e6 | −1.45543 | −0.727716 | − | 0.685879i | \(-0.759418\pi\) | ||||
−0.727716 | + | 0.685879i | \(0.759418\pi\) | |||||||
\(74\) | 3.83794e6 | 1.10100 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.65260e6 | 0.431839 | ||||||||
\(77\) | 6.81777e6 | 1.70186 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.94089e6 | −0.671095 | −0.335547 | − | 0.942023i | \(-0.608921\pi\) | ||||
−0.335547 | + | 0.942023i | \(0.608921\pi\) | |||||||
\(80\) | 3.08411e6 | 0.673466 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −7.75490e6 | −1.55320 | ||||||||
\(83\) | 8.62802e6 | 1.65630 | 0.828148 | − | 0.560510i | \(-0.189395\pi\) | ||||
0.828148 | + | 0.560510i | \(0.189395\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.04595e6 | 0.714586 | ||||||||
\(86\) | 7.21064e6 | 1.22244 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 5.35232e6 | 0.837245 | ||||||||
\(89\) | 879309. | 0.132214 | 0.0661069 | − | 0.997813i | \(-0.478942\pi\) | ||||
0.0661069 | + | 0.997813i | \(0.478942\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.62754e7 | 2.26406 | ||||||||
\(92\) | 4.83163e6 | 0.646899 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 8.67488e6 | 1.07725 | ||||||||
\(95\) | −5.04907e6 | −0.604197 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.62017e7 | −1.80244 | −0.901220 | − | 0.433362i | \(-0.857327\pi\) | ||||
−0.901220 | + | 0.433362i | \(0.857327\pi\) | |||||||
\(98\) | 1.25508e7 | 1.34704 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −2.73761e6 | −0.273761 | ||||||||
\(101\) | −617795. | −0.0596650 | −0.0298325 | − | 0.999555i | \(-0.509497\pi\) | ||||
−0.0298325 | + | 0.999555i | \(0.509497\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.98654e6 | −0.629988 | −0.314994 | − | 0.949094i | \(-0.602002\pi\) | ||||
−0.314994 | + | 0.949094i | \(0.602002\pi\) | |||||||
\(104\) | 1.27771e7 | 1.11382 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 665980. | 0.0543114 | ||||||||
\(107\) | 7.47019e6 | 0.589506 | 0.294753 | − | 0.955573i | \(-0.404763\pi\) | ||||
0.294753 | + | 0.955573i | \(0.404763\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.25015e7 | −1.66425 | −0.832125 | − | 0.554588i | \(-0.812876\pi\) | ||||
−0.832125 | + | 0.554588i | \(0.812876\pi\) | |||||||
\(110\) | 1.04074e7 | 0.745532 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2.69386e7 | 1.81181 | ||||||||
\(113\) | −7.33737e6 | −0.478372 | −0.239186 | − | 0.970974i | \(-0.576881\pi\) | ||||
−0.239186 | + | 0.970974i | \(0.576881\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.47617e7 | −0.905094 | ||||||||
\(116\) | −1.04177e7 | −0.619681 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 2.73841e6 | 0.153431 | ||||||||
\(119\) | 3.53399e7 | 1.92243 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.85051e6 | 0.351539 | ||||||||
\(122\) | −267002. | −0.0133124 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.53762e7 | −0.724223 | ||||||||
\(125\) | 2.02463e7 | 0.927171 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.12559e7 | −0.487605 | −0.243803 | − | 0.969825i | \(-0.578395\pi\) | ||||
−0.243803 | + | 0.969825i | \(0.578395\pi\) | |||||||
\(128\) | 2.77938e7 | 1.17142 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 2.48446e7 | 0.991813 | ||||||||
\(131\) | −4.30156e6 | −0.167177 | −0.0835885 | − | 0.996500i | \(-0.526638\pi\) | ||||
−0.0835885 | + | 0.996500i | \(0.526638\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.41017e7 | −1.62545 | ||||||||
\(134\) | −1.84908e7 | −0.663879 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.77438e7 | 0.945756 | ||||||||
\(137\) | 1.85481e7 | 0.616281 | 0.308140 | − | 0.951341i | \(-0.400293\pi\) | ||||
0.308140 | + | 0.951341i | \(0.400293\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.12956e7 | −1.30422 | −0.652112 | − | 0.758123i | \(-0.726117\pi\) | ||||
−0.652112 | + | 0.758123i | \(0.726117\pi\) | |||||||
\(140\) | 1.00584e7 | 0.309800 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1.65832e7 | −0.486026 | ||||||||
\(143\) | 6.28736e7 | 1.79801 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.18283e7 | 0.867012 | ||||||||
\(146\) | −6.45008e7 | −1.71526 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.43292e7 | 0.363334 | ||||||||
\(149\) | −2.77964e7 | −0.688394 | −0.344197 | − | 0.938897i | \(-0.611849\pi\) | ||||
−0.344197 | + | 0.938897i | \(0.611849\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.05159e7 | 1.19401 | 0.597006 | − | 0.802236i | \(-0.296357\pi\) | ||||
0.597006 | + | 0.802236i | \(0.296357\pi\) | |||||||
\(152\) | −3.46223e7 | −0.799655 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 9.09045e7 | 2.00568 | ||||||||
\(155\) | 4.69775e7 | 1.01328 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.27653e7 | −0.675717 | −0.337858 | − | 0.941197i | \(-0.609703\pi\) | ||||
−0.337858 | + | 0.941197i | \(0.609703\pi\) | |||||||
\(158\) | −3.92122e7 | −0.790901 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 2.08184e7 | 0.401816 | ||||||||
\(161\) | −1.28938e8 | −2.43495 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.27745e7 | 0.592761 | 0.296381 | − | 0.955070i | \(-0.404220\pi\) | ||||
0.296381 | + | 0.955070i | \(0.404220\pi\) | |||||||
\(164\) | −2.89534e7 | −0.512562 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.15041e8 | 1.95198 | ||||||||
\(167\) | 4.91242e7 | 0.816183 | 0.408092 | − | 0.912941i | \(-0.366194\pi\) | ||||
0.408092 | + | 0.912941i | \(0.366194\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 8.73439e7 | 1.39197 | ||||||||
\(170\) | 5.39466e7 | 0.842157 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2.69214e7 | 0.403411 | ||||||||
\(173\) | −2.08181e7 | −0.305688 | −0.152844 | − | 0.988250i | \(-0.548843\pi\) | ||||
−0.152844 | + | 0.988250i | \(0.548843\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 7.30565e7 | 1.03045 | ||||||||
\(176\) | 1.04066e8 | 1.43885 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1.17242e7 | 0.155817 | ||||||||
\(179\) | −8.64093e7 | −1.12609 | −0.563047 | − | 0.826425i | \(-0.690371\pi\) | ||||
−0.563047 | + | 0.826425i | \(0.690371\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.54723e7 | −0.820696 | −0.410348 | − | 0.911929i | \(-0.634593\pi\) | ||||
−0.410348 | + | 0.911929i | \(0.634593\pi\) | |||||||
\(182\) | 2.17008e8 | 2.66825 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1.01223e8 | −1.19789 | ||||||||
\(185\) | −4.37788e7 | −0.508350 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.36521e8 | 1.52671 | ||||||||
\(188\) | 3.23882e7 | 0.355496 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −6.73215e7 | −0.712060 | ||||||||
\(191\) | 8.45503e7 | 0.878007 | 0.439004 | − | 0.898485i | \(-0.355331\pi\) | ||||
0.439004 | + | 0.898485i | \(0.355331\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.04209e7 | −0.204467 | −0.102234 | − | 0.994760i | \(-0.532599\pi\) | ||||
−0.102234 | + | 0.994760i | \(0.532599\pi\) | |||||||
\(194\) | −2.16026e8 | −2.12422 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 4.68593e7 | 0.444529 | ||||||||
\(197\) | −3.23191e7 | −0.301181 | −0.150591 | − | 0.988596i | \(-0.548118\pi\) | ||||
−0.150591 | + | 0.988596i | \(0.548118\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −7.22071e7 | −0.649522 | −0.324761 | − | 0.945796i | \(-0.605284\pi\) | ||||
−0.324761 | + | 0.945796i | \(0.605284\pi\) | |||||||
\(200\) | 5.73534e7 | 0.506937 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −8.23736e6 | −0.0703166 | ||||||||
\(203\) | 2.78008e8 | 2.33250 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 8.84589e7 | 0.717139 | ||||||||
\(206\) | −9.31549e7 | −0.742455 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2.48428e8 | 1.91416 | ||||||||
\(209\) | −1.70369e8 | −1.29086 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.90681e8 | −1.39739 | −0.698696 | − | 0.715419i | \(-0.746236\pi\) | ||||
−0.698696 | + | 0.715419i | \(0.746236\pi\) | |||||||
\(212\) | 2.48648e6 | 0.0179230 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 9.96036e7 | 0.694747 | ||||||||
\(215\) | −8.22507e7 | −0.564423 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.10331e8 | 2.72600 | ||||||||
\(218\) | −3.00023e8 | −1.96136 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 3.88566e7 | 0.246028 | ||||||||
\(221\) | 3.25905e8 | 2.03104 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.03359e8 | 1.22800 | 0.613998 | − | 0.789307i | \(-0.289560\pi\) | ||||
0.613998 | + | 0.789307i | \(0.289560\pi\) | |||||||
\(224\) | 1.81841e8 | 1.08099 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −9.78326e7 | −0.563773 | ||||||||
\(227\) | −3.52165e7 | −0.199828 | −0.0999139 | − | 0.994996i | \(-0.531857\pi\) | ||||
−0.0999139 | + | 0.994996i | \(0.531857\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.50737e8 | −1.93000 | −0.965000 | − | 0.262249i | \(-0.915536\pi\) | ||||
−0.965000 | + | 0.262249i | \(0.915536\pi\) | |||||||
\(230\) | −1.96824e8 | −1.06667 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2.18252e8 | 1.14749 | ||||||||
\(233\) | 2.71870e8 | 1.40804 | 0.704020 | − | 0.710180i | \(-0.251387\pi\) | ||||
0.704020 | + | 0.710180i | \(0.251387\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −9.89530e7 | −0.497384 | ||||||||
\(236\) | 1.02240e7 | 0.0506327 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 4.71203e8 | 2.26563 | ||||||||
\(239\) | 7.12076e7 | 0.337391 | 0.168696 | − | 0.985668i | \(-0.446045\pi\) | ||||
0.168696 | + | 0.985668i | \(0.446045\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.36356e8 | −1.08770 | −0.543848 | − | 0.839184i | \(-0.683033\pi\) | ||||
−0.543848 | + | 0.839184i | \(0.683033\pi\) | |||||||
\(242\) | 9.13410e7 | 0.414297 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −996870. | −0.00439313 | ||||||||
\(245\) | −1.43165e8 | −0.621952 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.06707e8 | −1.71728 | ||||||||
\(248\) | 3.22133e8 | 1.34108 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 2.69953e8 | 1.09269 | ||||||||
\(251\) | −3.04691e7 | −0.121619 | −0.0608094 | − | 0.998149i | \(-0.519368\pi\) | ||||
−0.0608094 | + | 0.998149i | \(0.519368\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.98099e8 | −1.93372 | ||||||||
\(254\) | −1.50081e8 | −0.574654 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 2.71966e8 | 1.01315 | ||||||||
\(257\) | −2.69817e8 | −0.991524 | −0.495762 | − | 0.868458i | \(-0.665111\pi\) | ||||
−0.495762 | + | 0.868458i | \(0.665111\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.82391e8 | −1.36760 | ||||||||
\(260\) | 9.27588e7 | 0.327302 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −5.73548e7 | −0.197022 | ||||||||
\(263\) | 3.30750e8 | 1.12113 | 0.560564 | − | 0.828111i | \(-0.310585\pi\) | ||||
0.560564 | + | 0.828111i | \(0.310585\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −7.59674e6 | −0.0250765 | ||||||||
\(266\) | −5.88029e8 | −1.91564 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −6.90366e7 | −0.219082 | ||||||||
\(269\) | −3.87843e8 | −1.21485 | −0.607426 | − | 0.794377i | \(-0.707798\pi\) | ||||
−0.607426 | + | 0.794377i | \(0.707798\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.62357e8 | 1.10597 | 0.552986 | − | 0.833191i | \(-0.313488\pi\) | ||||
0.552986 | + | 0.833191i | \(0.313488\pi\) | |||||||
\(272\) | 5.39428e8 | 1.62533 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2.47311e8 | 0.726301 | ||||||||
\(275\) | 2.82224e8 | 0.818333 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.92785e8 | 1.11039 | 0.555195 | − | 0.831721i | \(-0.312644\pi\) | ||||
0.555195 | + | 0.831721i | \(0.312644\pi\) | |||||||
\(278\) | −5.50614e8 | −1.53706 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −2.10725e8 | −0.573670 | ||||||||
\(281\) | −2.62473e7 | −0.0705686 | −0.0352843 | − | 0.999377i | \(-0.511234\pi\) | ||||
−0.0352843 | + | 0.999377i | \(0.511234\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3.02721e8 | 0.793945 | 0.396972 | − | 0.917831i | \(-0.370061\pi\) | ||||
0.396972 | + | 0.917831i | \(0.370061\pi\) | |||||||
\(284\) | −6.19146e7 | −0.160390 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 8.38323e8 | 2.11900 | ||||||||
\(287\) | 7.72656e8 | 1.92930 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.97321e8 | 0.724574 | ||||||||
\(290\) | 4.24381e8 | 1.02179 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −2.40818e8 | −0.566042 | ||||||||
\(293\) | −4.44159e8 | −1.03158 | −0.515789 | − | 0.856716i | \(-0.672501\pi\) | ||||
−0.515789 | + | 0.856716i | \(0.672501\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.12367e7 | −0.0708415 | ||||||||
\(296\) | −3.00198e8 | −0.672802 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −3.70623e8 | −0.811288 | ||||||||
\(299\) | −1.18907e9 | −2.57251 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −7.18429e8 | −1.51845 | ||||||||
\(302\) | 6.73552e8 | 1.40717 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −6.73168e8 | −1.37425 | ||||||||
\(305\) | 3.04566e6 | 0.00614655 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −7.17875e8 | −1.41600 | −0.708002 | − | 0.706211i | \(-0.750403\pi\) | ||||
−0.708002 | + | 0.706211i | \(0.750403\pi\) | |||||||
\(308\) | 3.39398e8 | 0.661883 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 6.26374e8 | 1.19417 | ||||||||
\(311\) | 9.91134e8 | 1.86841 | 0.934203 | − | 0.356743i | \(-0.116113\pi\) | ||||
0.934203 | + | 0.356743i | \(0.116113\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.77188e7 | −0.0326610 | −0.0163305 | − | 0.999867i | \(-0.505198\pi\) | ||||
−0.0163305 | + | 0.999867i | \(0.505198\pi\) | |||||||
\(314\) | −4.36875e8 | −0.796348 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.46401e8 | −0.261000 | ||||||||
\(317\) | −6.67310e8 | −1.17658 | −0.588289 | − | 0.808651i | \(-0.700198\pi\) | ||||
−0.588289 | + | 0.808651i | \(0.700198\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.07397e9 | 1.85236 | ||||||||
\(320\) | −1.17185e8 | −0.199917 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −1.71919e9 | −2.86964 | ||||||||
\(323\) | −8.83109e8 | −1.45816 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.73728e8 | 1.08866 | ||||||||
\(326\) | 4.36998e8 | 0.698583 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 6.06577e8 | 0.949134 | ||||||||
\(329\) | −8.64318e8 | −1.33810 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.21309e9 | 1.83863 | 0.919313 | − | 0.393526i | \(-0.128745\pi\) | ||||
0.919313 | + | 0.393526i | \(0.128745\pi\) | |||||||
\(332\) | 4.29515e8 | 0.644161 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 6.54996e8 | 0.961891 | ||||||||
\(335\) | 2.10922e8 | 0.306524 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.03850e8 | 0.574799 | 0.287399 | − | 0.957811i | \(-0.407209\pi\) | ||||
0.287399 | + | 0.957811i | \(0.407209\pi\) | |||||||
\(338\) | 1.16460e9 | 1.64047 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 2.01413e8 | 0.277915 | ||||||||
\(341\) | 1.58515e9 | 2.16486 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.56440e8 | −0.209324 | ||||||||
\(344\) | −5.64006e8 | −0.747015 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −2.77577e8 | −0.360261 | ||||||||
\(347\) | 5.73452e8 | 0.736791 | 0.368395 | − | 0.929669i | \(-0.379907\pi\) | ||||
0.368395 | + | 0.929669i | \(0.379907\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.21244e8 | −0.404525 | −0.202263 | − | 0.979331i | \(-0.564829\pi\) | ||||
−0.202263 | + | 0.979331i | \(0.564829\pi\) | |||||||
\(350\) | 9.74096e8 | 1.21441 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 7.02468e8 | 0.858474 | ||||||||
\(353\) | −3.98442e8 | −0.482118 | −0.241059 | − | 0.970510i | \(-0.577495\pi\) | ||||
−0.241059 | + | 0.970510i | \(0.577495\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.89162e8 | 0.224407 | ||||||||
\(356\) | 4.37732e7 | 0.0514202 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.15214e9 | −1.32713 | ||||||||
\(359\) | −1.40704e9 | −1.60500 | −0.802501 | − | 0.596651i | \(-0.796498\pi\) | ||||
−0.802501 | + | 0.596651i | \(0.796498\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.08186e8 | 0.232903 | ||||||||
\(362\) | −8.72973e8 | −0.967210 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 8.10214e8 | 0.880531 | ||||||||
\(365\) | 7.35751e8 | 0.791965 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −9.65705e8 | −1.01980 | −0.509898 | − | 0.860235i | \(-0.670317\pi\) | ||||
−0.509898 | + | 0.860235i | \(0.670317\pi\) | |||||||
\(368\) | −1.96811e9 | −2.05864 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −5.83723e8 | −0.599102 | ||||||||
\(371\) | −6.63547e7 | −0.0674626 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −6.50998e8 | −0.649529 | −0.324765 | − | 0.945795i | \(-0.605285\pi\) | ||||
−0.324765 | + | 0.945795i | \(0.605285\pi\) | |||||||
\(374\) | 1.82030e9 | 1.79926 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −6.78537e8 | −0.658288 | ||||||||
\(377\) | 2.56380e9 | 2.46427 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.97991e7 | −0.0375522 | −0.0187761 | − | 0.999824i | \(-0.505977\pi\) | ||||
−0.0187761 | + | 0.999824i | \(0.505977\pi\) | |||||||
\(380\) | −2.51349e8 | −0.234982 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 1.12735e9 | 1.03475 | ||||||||
\(383\) | −6.27745e7 | −0.0570936 | −0.0285468 | − | 0.999592i | \(-0.509088\pi\) | ||||
−0.0285468 | + | 0.999592i | \(0.509088\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.03693e9 | −0.926058 | ||||||||
\(386\) | −2.72281e8 | −0.240970 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −8.06545e8 | −0.701000 | ||||||||
\(389\) | 4.14596e8 | 0.357109 | 0.178555 | − | 0.983930i | \(-0.442858\pi\) | ||||
0.178555 | + | 0.983930i | \(0.442858\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.58190e9 | −2.18434 | ||||||||
\(392\) | −9.81708e8 | −0.823154 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −4.30926e8 | −0.354949 | ||||||||
\(395\) | 4.47288e8 | 0.365172 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5.40817e8 | −0.433794 | −0.216897 | − | 0.976194i | \(-0.569594\pi\) | ||||
−0.216897 | + | 0.976194i | \(0.569594\pi\) | |||||||
\(398\) | −9.62771e8 | −0.765477 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.11513e9 | 0.871198 | ||||||||
\(401\) | −1.82362e9 | −1.41231 | −0.706153 | − | 0.708059i | \(-0.749571\pi\) | ||||
−0.706153 | + | 0.708059i | \(0.749571\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.78408e9 | 2.88000 | ||||||||
\(404\) | −3.07547e7 | −0.0232047 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3.70681e9 | 2.74890 | ||||||||
\(407\) | −1.47721e9 | −1.08608 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.97200e9 | 1.42520 | 0.712599 | − | 0.701571i | \(-0.247518\pi\) | ||||
0.712599 | + | 0.701571i | \(0.247518\pi\) | |||||||
\(410\) | 1.17946e9 | 0.845165 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −3.47800e8 | −0.245013 | ||||||||
\(413\) | −2.72841e8 | −0.190583 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.31226e9 | −0.901263 | ||||||||
\(416\) | 1.67694e9 | 1.14206 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −2.27161e9 | −1.52131 | ||||||||
\(419\) | −4.90370e8 | −0.325668 | −0.162834 | − | 0.986653i | \(-0.552064\pi\) | ||||
−0.162834 | + | 0.986653i | \(0.552064\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.72536e8 | −0.112692 | −0.0563459 | − | 0.998411i | \(-0.517945\pi\) | ||||
−0.0563459 | + | 0.998411i | \(0.517945\pi\) | |||||||
\(422\) | −2.54244e9 | −1.64686 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −5.20921e7 | −0.0331888 | ||||||||
\(425\) | 1.46291e9 | 0.924392 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.66027e7 | 0.0165359 | ||||||||
\(428\) | 3.71876e8 | 0.229269 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1.09669e9 | −0.665186 | ||||||||
\(431\) | −1.99685e9 | −1.20136 | −0.600681 | − | 0.799489i | \(-0.705104\pi\) | ||||
−0.600681 | + | 0.799489i | \(0.705104\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6.53171e8 | −0.386651 | −0.193326 | − | 0.981135i | \(-0.561927\pi\) | ||||
−0.193326 | + | 0.981135i | \(0.561927\pi\) | |||||||
\(434\) | 5.47114e9 | 3.21265 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.12015e9 | −0.647255 | ||||||||
\(437\) | 3.22203e9 | 1.84690 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.18962e9 | −1.23521 | −0.617607 | − | 0.786487i | \(-0.711898\pi\) | ||||
−0.617607 | + | 0.786487i | \(0.711898\pi\) | |||||||
\(440\) | −8.14050e8 | −0.455582 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 4.34545e9 | 2.39363 | ||||||||
\(443\) | −2.98274e9 | −1.63006 | −0.815028 | − | 0.579422i | \(-0.803278\pi\) | ||||
−0.815028 | + | 0.579422i | \(0.803278\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.33737e8 | −0.0719433 | ||||||||
\(446\) | 2.71149e9 | 1.44722 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1.02357e9 | −0.537830 | ||||||||
\(449\) | 1.54617e9 | 0.806111 | 0.403055 | − | 0.915176i | \(-0.367948\pi\) | ||||
0.403055 | + | 0.915176i | \(0.367948\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.98484e9 | 1.53216 | ||||||||
\(452\) | −3.65264e8 | −0.186047 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −4.69558e8 | −0.235502 | ||||||||
\(455\) | −2.47538e9 | −1.23197 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7.00396e8 | −0.343271 | −0.171635 | − | 0.985161i | \(-0.554905\pi\) | ||||
−0.171635 | + | 0.985161i | \(0.554905\pi\) | |||||||
\(458\) | −4.67654e9 | −2.27455 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −7.34857e8 | −0.352006 | ||||||||
\(461\) | 2.39080e9 | 1.13655 | 0.568277 | − | 0.822838i | \(-0.307610\pi\) | ||||
0.568277 | + | 0.822838i | \(0.307610\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.71887e9 | 1.27308 | 0.636539 | − | 0.771244i | \(-0.280365\pi\) | ||||
0.636539 | + | 0.771244i | \(0.280365\pi\) | |||||||
\(464\) | 4.24352e9 | 1.97203 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 3.62496e9 | 1.65941 | ||||||||
\(467\) | −3.63245e9 | −1.65041 | −0.825203 | − | 0.564836i | \(-0.808939\pi\) | ||||
−0.825203 | + | 0.564836i | \(0.808939\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.84232e9 | 0.824633 | ||||||||
\(470\) | −1.31939e9 | −0.586178 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −2.14195e8 | −0.0937589 | ||||||||
\(473\) | −2.77536e9 | −1.20588 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.82561e9 | −0.781592 | ||||||||
\(476\) | 1.75927e9 | 0.747666 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 9.49444e8 | 0.397623 | ||||||||
\(479\) | 7.60336e8 | 0.316105 | 0.158053 | − | 0.987431i | \(-0.449478\pi\) | ||||
0.158053 | + | 0.987431i | \(0.449478\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.52642e9 | −1.44486 | ||||||||
\(482\) | −3.15145e9 | −1.28188 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 3.41028e8 | 0.136720 | ||||||||
\(485\) | 2.46417e9 | 0.980787 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3.11666e9 | −1.22275 | −0.611375 | − | 0.791341i | \(-0.709383\pi\) | ||||
−0.611375 | + | 0.791341i | \(0.709383\pi\) | |||||||
\(488\) | 2.08846e7 | 0.00813497 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −1.90889e9 | −0.732984 | ||||||||
\(491\) | 2.02161e9 | 0.770749 | 0.385374 | − | 0.922760i | \(-0.374072\pi\) | ||||
0.385374 | + | 0.922760i | \(0.374072\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5.56694e9 | 2.09244 | ||||||||
\(494\) | −5.42281e9 | −2.02386 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 6.26330e9 | 2.30471 | ||||||||
\(497\) | 1.65226e9 | 0.603715 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.90803e9 | −1.40801 | −0.704006 | − | 0.710194i | \(-0.748607\pi\) | ||||
−0.704006 | + | 0.710194i | \(0.748607\pi\) | |||||||
\(500\) | 1.00789e9 | 0.360593 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −4.06258e8 | −0.143331 | ||||||||
\(503\) | 5.07994e9 | 1.77980 | 0.889899 | − | 0.456158i | \(-0.150775\pi\) | ||||
0.889899 | + | 0.456158i | \(0.150775\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 9.39623e7 | 0.0324664 | ||||||||
\(506\) | −6.64139e9 | −2.27894 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −5.60336e8 | −0.189638 | ||||||||
\(509\) | 2.67138e9 | 0.897892 | 0.448946 | − | 0.893559i | \(-0.351800\pi\) | ||||
0.448946 | + | 0.893559i | \(0.351800\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.42651e9 | 2.13060 | ||||||||
\(512\) | 6.86375e7 | 0.0226004 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −3.59760e9 | −1.16853 | ||||||||
\(515\) | 1.06260e9 | 0.342804 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.33894e9 | −1.06265 | ||||||||
\(518\) | −5.09860e9 | −1.61175 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −1.94331e9 | −0.606080 | ||||||||
\(521\) | −1.52466e9 | −0.472326 | −0.236163 | − | 0.971713i | \(-0.575890\pi\) | ||||
−0.236163 | + | 0.971713i | \(0.575890\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 9.55727e8 | 0.292131 | 0.146066 | − | 0.989275i | \(-0.453339\pi\) | ||||
0.146066 | + | 0.989275i | \(0.453339\pi\) | |||||||
\(524\) | −2.14138e8 | −0.0650180 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 4.41005e9 | 1.32127 | ||||||||
\(527\) | 8.21663e9 | 2.44544 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6.01524e9 | 1.76668 | ||||||||
\(530\) | −1.01291e8 | −0.0295532 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −2.19544e9 | −0.632167 | ||||||||
\(533\) | 7.12545e9 | 2.03829 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.13616e9 | −0.320776 | ||||||||
\(536\) | 1.44632e9 | 0.405685 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −5.17129e9 | −1.43173 | ||||||||
\(539\) | −4.83079e9 | −1.32879 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.12167e9 | 0.304561 | 0.152280 | − | 0.988337i | \(-0.451338\pi\) | ||||
0.152280 | + | 0.988337i | \(0.451338\pi\) | |||||||
\(542\) | 4.83147e9 | 1.30341 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 3.64125e9 | 0.969737 | ||||||||
\(545\) | 3.42232e9 | 0.905591 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.80841e8 | 0.151740 | 0.0758702 | − | 0.997118i | \(-0.475827\pi\) | ||||
0.0758702 | + | 0.997118i | \(0.475827\pi\) | |||||||
\(548\) | 9.23352e8 | 0.239682 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 3.76303e9 | 0.964424 | ||||||||
\(551\) | −6.94715e9 | −1.76920 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.90690e9 | 0.982413 | ||||||||
\(554\) | 5.23718e9 | 1.30862 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −2.05575e9 | −0.507235 | ||||||||
\(557\) | −3.50741e9 | −0.859989 | −0.429994 | − | 0.902832i | \(-0.641484\pi\) | ||||
−0.429994 | + | 0.902832i | \(0.641484\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −6.62537e9 | −1.60424 | ||||||||
\(560\) | −4.09717e9 | −0.985883 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −3.49967e8 | −0.0831668 | ||||||||
\(563\) | −1.57440e9 | −0.371822 | −0.185911 | − | 0.982567i | \(-0.559524\pi\) | ||||
−0.185911 | + | 0.982567i | \(0.559524\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.11596e9 | 0.260303 | ||||||||
\(566\) | 4.03632e9 | 0.935682 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1.29712e9 | 0.297003 | ||||||||
\(569\) | 2.71007e7 | 0.00616719 | 0.00308360 | − | 0.999995i | \(-0.499018\pi\) | ||||
0.00308360 | + | 0.999995i | \(0.499018\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8.12943e9 | −1.82740 | −0.913700 | − | 0.406390i | \(-0.866787\pi\) | ||||
−0.913700 | + | 0.406390i | \(0.866787\pi\) | |||||||
\(572\) | 3.12993e9 | 0.699276 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 1.03022e10 | 2.27372 | ||||||||
\(575\) | −5.33743e9 | −1.17083 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −8.89512e8 | −0.192769 | −0.0963844 | − | 0.995344i | \(-0.530728\pi\) | ||||
−0.0963844 | + | 0.995344i | \(0.530728\pi\) | |||||||
\(578\) | 3.96431e9 | 0.853927 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1.58446e9 | 0.337196 | ||||||||
\(581\) | −1.14621e10 | −2.42464 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.56334e8 | −0.0535756 | ||||||||
\(584\) | 5.04516e9 | 1.04817 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −5.92218e9 | −1.21574 | ||||||||
\(587\) | −8.09762e8 | −0.165243 | −0.0826217 | − | 0.996581i | \(-0.526329\pi\) | ||||
−0.0826217 | + | 0.996581i | \(0.526329\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.02538e10 | −2.06766 | ||||||||
\(590\) | −4.16493e8 | −0.0834884 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −5.83682e9 | −1.15625 | ||||||||
\(593\) | 6.48925e9 | 1.27792 | 0.638959 | − | 0.769241i | \(-0.279365\pi\) | ||||
0.638959 | + | 0.769241i | \(0.279365\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5.37495e9 | −1.04608 | ||||||||
\(596\) | −1.38374e9 | −0.267728 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −1.58544e10 | −3.03176 | ||||||||
\(599\) | −6.51857e8 | −0.123925 | −0.0619624 | − | 0.998078i | \(-0.519736\pi\) | ||||
−0.0619624 | + | 0.998078i | \(0.519736\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.97476e9 | −0.558974 | −0.279487 | − | 0.960150i | \(-0.590164\pi\) | ||||
−0.279487 | + | 0.960150i | \(0.590164\pi\) | |||||||
\(602\) | −9.57915e9 | −1.78953 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 2.51475e9 | 0.464372 | ||||||||
\(605\) | −1.04191e9 | −0.191288 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −4.76572e9 | −0.864905 | −0.432452 | − | 0.901657i | \(-0.642352\pi\) | ||||
−0.432452 | + | 0.901657i | \(0.642352\pi\) | |||||||
\(608\) | −4.54402e9 | −0.819931 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 4.06091e7 | 0.00724385 | ||||||||
\(611\) | −7.97076e9 | −1.41369 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4.10844e9 | 0.720385 | 0.360193 | − | 0.932878i | \(-0.382711\pi\) | ||||
0.360193 | + | 0.932878i | \(0.382711\pi\) | |||||||
\(614\) | −9.57176e9 | −1.66879 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −7.11042e9 | −1.22564 | ||||||||
\(617\) | −8.36433e9 | −1.43362 | −0.716809 | − | 0.697270i | \(-0.754398\pi\) | ||||
−0.716809 | + | 0.697270i | \(0.754398\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.37677e8 | −0.0233315 | −0.0116658 | − | 0.999932i | \(-0.503713\pi\) | ||||
−0.0116658 | + | 0.999932i | \(0.503713\pi\) | |||||||
\(620\) | 2.33861e9 | 0.394082 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 1.32153e10 | 2.20196 | ||||||||
\(623\) | −1.16814e9 | −0.193547 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.21700e9 | 0.199393 | ||||||||
\(626\) | −2.36253e8 | −0.0384917 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −1.63110e9 | −0.262798 | ||||||||
\(629\) | −7.65715e9 | −1.22685 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.86229e9 | −0.295083 | −0.147542 | − | 0.989056i | \(-0.547136\pi\) | ||||
−0.147542 | + | 0.989056i | \(0.547136\pi\) | |||||||
\(632\) | 3.06713e9 | 0.483306 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −8.89756e9 | −1.38662 | ||||||||
\(635\) | 1.71195e9 | 0.265328 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.15321e10 | −1.76775 | ||||||||
\(638\) | 1.43198e10 | 2.18305 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −4.22724e9 | −0.637422 | ||||||||
\(641\) | −1.04508e10 | −1.56727 | −0.783637 | − | 0.621219i | \(-0.786638\pi\) | ||||
−0.783637 | + | 0.621219i | \(0.786638\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.17114e10 | −1.73728 | −0.868642 | − | 0.495440i | \(-0.835007\pi\) | ||||
−0.868642 | + | 0.495440i | \(0.835007\pi\) | |||||||
\(644\) | −6.41870e9 | −0.946993 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.17749e10 | −1.71848 | ||||||||
\(647\) | 2.82698e7 | 0.00410353 | 0.00205176 | − | 0.999998i | \(-0.499347\pi\) | ||||
0.00205176 | + | 0.999998i | \(0.499347\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.05401e9 | −0.151352 | ||||||||
\(650\) | 8.98314e9 | 1.28301 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1.63156e9 | 0.230535 | ||||||||
\(653\) | −1.03288e10 | −1.45163 | −0.725813 | − | 0.687892i | \(-0.758536\pi\) | ||||
−0.725813 | + | 0.687892i | \(0.758536\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6.54237e8 | 0.0909684 | ||||||||
\(656\) | 1.17938e10 | 1.63114 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −1.15244e10 | −1.57698 | ||||||||
\(659\) | 8.85377e9 | 1.20512 | 0.602558 | − | 0.798075i | \(-0.294148\pi\) | ||||
0.602558 | + | 0.798075i | \(0.294148\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.94438e8 | 0.0531219 | 0.0265610 | − | 0.999647i | \(-0.491544\pi\) | ||||
0.0265610 | + | 0.999647i | \(0.491544\pi\) | |||||||
\(662\) | 1.61746e10 | 2.16686 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −8.99838e9 | −1.19282 | ||||||||
\(665\) | 6.70756e9 | 0.884481 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.03110e10 | −2.65027 | ||||||||
\(668\) | 2.44547e9 | 0.317427 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 2.81232e9 | 0.361246 | ||||||||
\(671\) | 1.02769e8 | 0.0131320 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.32239e8 | −0.0420144 | −0.0210072 | − | 0.999779i | \(-0.506687\pi\) | ||||
−0.0210072 | + | 0.999779i | \(0.506687\pi\) | |||||||
\(674\) | 5.38472e9 | 0.677413 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 4.34810e9 | 0.541360 | ||||||||
\(677\) | 7.35957e9 | 0.911574 | 0.455787 | − | 0.890089i | \(-0.349358\pi\) | ||||
0.455787 | + | 0.890089i | \(0.349358\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.15236e10 | 2.63858 | ||||||||
\(680\) | −4.21963e9 | −0.514628 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 2.11355e10 | 2.55134 | ||||||||
\(683\) | 1.53063e10 | 1.83822 | 0.919111 | − | 0.393999i | \(-0.128909\pi\) | ||||
0.919111 | + | 0.393999i | \(0.128909\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.82104e9 | −0.335345 | ||||||||
\(686\) | −2.08589e9 | −0.246693 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1.09661e10 | −1.28379 | ||||||||
\(689\) | −6.11924e8 | −0.0712739 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.49200e10 | −1.72026 | −0.860132 | − | 0.510072i | \(-0.829619\pi\) | ||||
−0.860132 | + | 0.510072i | \(0.829619\pi\) | |||||||
\(692\) | −1.03635e9 | −0.118887 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 7.64611e9 | 0.868325 | ||||||||
\(695\) | 6.28077e9 | 0.709686 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.54719e10 | 1.73073 | ||||||||
\(698\) | −4.28329e9 | −0.476742 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 3.63685e9 | 0.400758 | ||||||||
\(701\) | 6.52424e9 | 0.715347 | 0.357673 | − | 0.933847i | \(-0.383570\pi\) | ||||
0.357673 | + | 0.933847i | \(0.383570\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 9.55558e9 | 1.03732 | ||||||||
\(704\) | −3.95415e9 | −0.427119 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −5.31262e9 | −0.568188 | ||||||||
\(707\) | 8.20726e8 | 0.0873434 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4.55527e9 | 0.480012 | 0.240006 | − | 0.970771i | \(-0.422851\pi\) | ||||
0.240006 | + | 0.970771i | \(0.422851\pi\) | |||||||
\(710\) | 2.52219e9 | 0.264468 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −9.17054e8 | −0.0952171 | ||||||||
\(713\) | −2.99784e10 | −3.09738 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −9.56262e9 | −0.978376 | ||||||||
\(716\) | −4.30157e9 | −0.437957 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −1.87607e10 | −1.89153 | ||||||||
\(719\) | −6.09158e9 | −0.611194 | −0.305597 | − | 0.952161i | \(-0.598856\pi\) | ||||
−0.305597 | + | 0.952161i | \(0.598856\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 9.28145e9 | 0.922236 | ||||||||
\(722\) | 2.77584e9 | 0.274482 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −3.25930e9 | −0.319183 | ||||||||
\(725\) | 1.15083e10 | 1.12157 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.68599e10 | 1.62737 | 0.813684 | − | 0.581308i | \(-0.197459\pi\) | ||||
0.813684 | + | 0.581308i | \(0.197459\pi\) | |||||||
\(728\) | −1.69741e10 | −1.63052 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 9.81011e9 | 0.933349 | ||||||||
\(731\) | −1.43861e10 | −1.36217 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.44578e9 | −0.135593 | −0.0677966 | − | 0.997699i | \(-0.521597\pi\) | ||||
−0.0677966 | + | 0.997699i | \(0.521597\pi\) | |||||||
\(734\) | −1.28762e10 | −1.20185 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.32851e10 | −1.22827 | ||||||||
\(737\) | 7.11707e9 | 0.654885 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8.56684e8 | 0.0780845 | 0.0390423 | − | 0.999238i | \(-0.487569\pi\) | ||||
0.0390423 | + | 0.999238i | \(0.487569\pi\) | |||||||
\(740\) | −2.17937e9 | −0.197706 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −8.84738e8 | −0.0795062 | ||||||||
\(743\) | −1.09080e10 | −0.975630 | −0.487815 | − | 0.872947i | \(-0.662206\pi\) | ||||
−0.487815 | + | 0.872947i | \(0.662206\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4.22764e9 | 0.374585 | ||||||||
\(746\) | −8.68006e9 | −0.765485 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 6.79622e9 | 0.593762 | ||||||||
\(749\) | −9.92396e9 | −0.862976 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −5.27485e9 | −0.454433 | −0.227217 | − | 0.973844i | \(-0.572963\pi\) | ||||
−0.227217 | + | 0.973844i | \(0.572963\pi\) | |||||||
\(752\) | −1.31929e10 | −1.13130 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 3.41843e10 | 2.90420 | ||||||||
\(755\) | −7.68311e9 | −0.649715 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.07054e10 | −1.73479 | −0.867395 | − | 0.497620i | \(-0.834208\pi\) | ||||
−0.867395 | + | 0.497620i | \(0.834208\pi\) | |||||||
\(758\) | −5.30659e8 | −0.0442562 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 5.26580e9 | 0.435128 | ||||||||
\(761\) | −1.35780e10 | −1.11683 | −0.558417 | − | 0.829561i | \(-0.688591\pi\) | ||||
−0.558417 | + | 0.829561i | \(0.688591\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.98927e10 | 2.43629 | ||||||||
\(764\) | 4.20903e9 | 0.341472 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −8.37001e8 | −0.0672861 | ||||||||
\(767\) | −2.51614e9 | −0.201350 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.62978e10 | 1.29237 | 0.646184 | − | 0.763182i | \(-0.276364\pi\) | ||||
0.646184 | + | 0.763182i | \(0.276364\pi\) | |||||||
\(770\) | −1.38259e10 | −1.09138 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −1.01658e9 | −0.0795208 | ||||||||
\(773\) | 2.64697e9 | 0.206120 | 0.103060 | − | 0.994675i | \(-0.467137\pi\) | ||||
0.103060 | + | 0.994675i | \(0.467137\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.69858e10 | 1.31078 | ||||||||
\(776\) | 1.68972e10 | 1.29807 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 5.52800e9 | 0.420862 | ||||||||
\(779\) | −1.93079e10 | −1.46337 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.38285e9 | 0.479442 | ||||||||
\(782\) | −3.44257e10 | −2.57430 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −1.90876e10 | −1.41463 | ||||||||
\(785\) | 4.98336e9 | 0.367687 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −7.25919e9 | −0.530856 | −0.265428 | − | 0.964131i | \(-0.585513\pi\) | ||||
−0.265428 | + | 0.964131i | \(0.585513\pi\) | |||||||
\(788\) | −1.60889e9 | −0.117134 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 5.96390e9 | 0.430364 | ||||||||
\(791\) | 9.74751e9 | 0.700287 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.45330e8 | 0.0174701 | ||||||||
\(794\) | −7.21097e9 | −0.511237 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −3.59457e9 | −0.252610 | ||||||||
\(797\) | 3.67130e9 | 0.256871 | 0.128436 | − | 0.991718i | \(-0.459004\pi\) | ||||
0.128436 | + | 0.991718i | \(0.459004\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.73074e10 | −1.20038 | ||||||||
\(800\) | 7.52737e9 | 0.519791 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −2.43152e10 | −1.66444 | ||||||||
\(803\) | 2.48262e10 | 1.69202 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.96105e10 | 1.32496 | ||||||||
\(806\) | 5.04550e10 | 3.39415 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 6.44315e8 | 0.0429693 | ||||||||
\(809\) | 5.97080e9 | 0.396472 | 0.198236 | − | 0.980154i | \(-0.436479\pi\) | ||||
0.198236 | + | 0.980154i | \(0.436479\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.51680e10 | 1.65682 | 0.828409 | − | 0.560123i | \(-0.189246\pi\) | ||||
0.828409 | + | 0.560123i | \(0.189246\pi\) | |||||||
\(812\) | 1.38396e10 | 0.907148 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −1.96964e10 | −1.27997 | ||||||||
\(815\) | −4.98477e9 | −0.322548 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.79528e10 | 1.15174 | ||||||||
\(818\) | 2.62936e10 | 1.67963 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 4.40361e9 | 0.278907 | ||||||||
\(821\) | −1.74411e10 | −1.09995 | −0.549975 | − | 0.835181i | \(-0.685363\pi\) | ||||
−0.549975 | + | 0.835181i | \(0.685363\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.10753e10 | 0.692557 | 0.346278 | − | 0.938132i | \(-0.387445\pi\) | ||||
0.346278 | + | 0.938132i | \(0.387445\pi\) | |||||||
\(824\) | 7.28644e9 | 0.453702 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −3.63791e9 | −0.224606 | ||||||||
\(827\) | 7.16696e9 | 0.440622 | 0.220311 | − | 0.975430i | \(-0.429293\pi\) | ||||
0.220311 | + | 0.975430i | \(0.429293\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.09285e9 | 0.0666224 | 0.0333112 | − | 0.999445i | \(-0.489395\pi\) | ||||
0.0333112 | + | 0.999445i | \(0.489395\pi\) | |||||||
\(830\) | −1.74970e10 | −1.06216 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −9.43940e9 | −0.568215 | ||||||||
\(833\) | −2.50404e10 | −1.50101 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −7.47144e9 | −0.444121 | ||||||||
\(836\) | −8.48121e9 | −0.502037 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −6.53834e9 | −0.383807 | ||||||||
\(839\) | 2.38628e10 | 1.39494 | 0.697469 | − | 0.716615i | \(-0.254309\pi\) | ||||
0.697469 | + | 0.716615i | \(0.254309\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.65435e10 | 1.53877 | ||||||||
\(842\) | −2.30050e9 | −0.132810 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −9.49235e9 | −0.543469 | ||||||||
\(845\) | −1.32844e10 | −0.757431 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −9.10073e9 | −0.514617 | ||||||||
\(848\) | −1.01284e9 | −0.0570367 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 1.95057e10 | 1.08942 | ||||||||
\(851\) | 2.79371e10 | 1.55392 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.71276e10 | 0.944878 | 0.472439 | − | 0.881363i | \(-0.343374\pi\) | ||||
0.472439 | + | 0.881363i | \(0.343374\pi\) | |||||||
\(854\) | 3.54706e8 | 0.0194879 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −7.79086e9 | −0.424548 | ||||||||
\(857\) | −3.37860e8 | −0.0183360 | −0.00916798 | − | 0.999958i | \(-0.502918\pi\) | ||||
−0.00916798 | + | 0.999958i | \(0.502918\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.39086e9 | 0.182530 | 0.0912649 | − | 0.995827i | \(-0.470909\pi\) | ||||
0.0912649 | + | 0.995827i | \(0.470909\pi\) | |||||||
\(860\) | −4.09455e9 | −0.219514 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −2.66249e10 | −1.41583 | ||||||||
\(863\) | −9.19359e9 | −0.486909 | −0.243454 | − | 0.969912i | \(-0.578281\pi\) | ||||
−0.243454 | + | 0.969912i | \(0.578281\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3.16628e9 | 0.166339 | ||||||||
\(866\) | −8.70904e9 | −0.455678 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 2.04269e10 | 1.06019 | ||||||||
\(869\) | 1.50927e10 | 0.780186 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.69899e10 | 0.871221 | ||||||||
\(872\) | 2.34674e10 | 1.19855 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 4.29608e10 | 2.17662 | ||||||||
\(875\) | −2.68966e10 | −1.35728 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.78531e10 | −0.893747 | −0.446874 | − | 0.894597i | \(-0.647463\pi\) | ||||
−0.446874 | + | 0.894597i | \(0.647463\pi\) | |||||||
\(878\) | −2.91952e10 | −1.45573 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1.58277e10 | −0.782942 | ||||||||
\(881\) | 1.00212e10 | 0.493746 | 0.246873 | − | 0.969048i | \(-0.420597\pi\) | ||||
0.246873 | + | 0.969048i | \(0.420597\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 4.80376e8 | 0.0234811 | 0.0117406 | − | 0.999931i | \(-0.496263\pi\) | ||||
0.0117406 | + | 0.999931i | \(0.496263\pi\) | |||||||
\(884\) | 1.62240e10 | 0.789906 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −3.97703e10 | −1.92106 | ||||||||
\(887\) | 2.86366e9 | 0.137781 | 0.0688903 | − | 0.997624i | \(-0.478054\pi\) | ||||
0.0688903 | + | 0.997624i | \(0.478054\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.49532e10 | 0.713804 | ||||||||
\(890\) | −1.78317e9 | −0.0847869 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 1.01235e10 | 0.477589 | ||||||||
\(893\) | 2.15984e10 | 1.01494 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.31422e10 | 0.612758 | ||||||||
\(896\) | −3.69234e10 | −1.71484 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 2.06158e10 | 0.950020 | ||||||||
\(899\) | 6.46377e10 | 2.96706 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.32871e9 | −0.0605193 | ||||||||
\(902\) | 3.97983e10 | 1.80568 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 7.65233e9 | 0.344512 | ||||||||
\(905\) | 9.95787e9 | 0.446577 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −5.67695e9 | −0.252633 | −0.126316 | − | 0.991990i | \(-0.540315\pi\) | ||||
−0.126316 | + | 0.991990i | \(0.540315\pi\) | |||||||
\(908\) | −1.75313e9 | −0.0777164 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −3.30054e10 | −1.45191 | ||||||||
\(911\) | −2.67566e10 | −1.17251 | −0.586256 | − | 0.810126i | \(-0.699399\pi\) | ||||
−0.586256 | + | 0.810126i | \(0.699399\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.42792e10 | −1.92554 | ||||||||
\(914\) | −9.33871e9 | −0.404553 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1.74602e10 | −0.750610 | ||||||||
\(917\) | 5.71452e9 | 0.244730 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.00200e10 | 0.850862 | 0.425431 | − | 0.904991i | \(-0.360122\pi\) | ||||
0.425431 | + | 0.904991i | \(0.360122\pi\) | |||||||
\(920\) | 1.53953e10 | 0.651826 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 3.18776e10 | 1.33945 | ||||||||
\(923\) | 1.52372e10 | 0.637822 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.58293e10 | −0.657604 | ||||||||
\(926\) | 3.62520e10 | 1.50035 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 2.86446e10 | 1.17659 | ||||||||
\(929\) | −2.42743e10 | −0.993326 | −0.496663 | − | 0.867943i | \(-0.665441\pi\) | ||||
−0.496663 | + | 0.867943i | \(0.665441\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.12486e10 | 1.26913 | ||||||||
\(932\) | 1.35340e10 | 0.547611 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −4.84332e10 | −1.94504 | ||||||||
\(935\) | −2.07639e10 | −0.830748 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.31846e10 | 0.920683 | 0.460342 | − | 0.887742i | \(-0.347727\pi\) | ||||
0.460342 | + | 0.887742i | \(0.347727\pi\) | |||||||
\(938\) | 2.45645e10 | 0.971849 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −4.92602e9 | −0.193441 | ||||||||
\(941\) | 4.82845e10 | 1.88905 | 0.944527 | − | 0.328434i | \(-0.106521\pi\) | ||||
0.944527 | + | 0.328434i | \(0.106521\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −5.64495e10 | −2.19214 | ||||||||
\(944\) | −4.16464e9 | −0.161130 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −3.70052e10 | −1.42116 | ||||||||
\(947\) | 9.48483e9 | 0.362915 | 0.181457 | − | 0.983399i | \(-0.441919\pi\) | ||||
0.181457 | + | 0.983399i | \(0.441919\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5.92654e10 | 2.25097 | ||||||||
\(950\) | −2.43417e10 | −0.921124 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −3.68569e10 | −1.38449 | ||||||||
\(953\) | −3.13620e10 | −1.17376 | −0.586880 | − | 0.809674i | \(-0.699644\pi\) | ||||
−0.586880 | + | 0.809674i | \(0.699644\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.28595e10 | −0.477762 | ||||||||
\(956\) | 3.54481e9 | 0.131217 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 1.01379e10 | 0.372537 | ||||||||
\(959\) | −2.46407e10 | −0.902171 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 6.78906e10 | 2.46762 | ||||||||
\(962\) | −4.70194e10 | −1.70280 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −1.17661e10 | −0.423024 | ||||||||
\(965\) | 3.10587e9 | 0.111260 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −4.56505e10 | −1.62350 | −0.811752 | − | 0.584003i | \(-0.801486\pi\) | ||||
−0.811752 | + | 0.584003i | \(0.801486\pi\) | |||||||
\(968\) | −7.14457e9 | −0.253170 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 3.28559e10 | 1.15588 | ||||||||
\(971\) | 4.75876e10 | 1.66812 | 0.834059 | − | 0.551675i | \(-0.186011\pi\) | ||||
0.834059 | + | 0.551675i | \(0.186011\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5.48602e10 | 1.90925 | ||||||||
\(974\) | −4.15558e10 | −1.44104 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 4.06063e8 | 0.0139804 | ||||||||
\(977\) | 3.64883e10 | 1.25176 | 0.625882 | − | 0.779918i | \(-0.284739\pi\) | ||||
0.625882 | + | 0.779918i | \(0.284739\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4.51264e9 | −0.153706 | ||||||||
\(980\) | −7.12697e9 | −0.241888 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 2.69551e10 | 0.908346 | ||||||||
\(983\) | 2.58715e10 | 0.868729 | 0.434365 | − | 0.900737i | \(-0.356973\pi\) | ||||
0.434365 | + | 0.900737i | \(0.356973\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.91551e9 | 0.163886 | ||||||||
\(986\) | 7.42266e10 | 2.46598 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −2.02464e10 | −0.667881 | ||||||||
\(989\) | 5.24877e10 | 1.72532 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5.08417e10 | 1.65944 | 0.829722 | − | 0.558177i | \(-0.188499\pi\) | ||||
0.829722 | + | 0.558177i | \(0.188499\pi\) | |||||||
\(992\) | 4.22785e10 | 1.37508 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 2.20304e10 | 0.711492 | ||||||||
\(995\) | 1.09822e10 | 0.353434 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −7.59411e9 | −0.242686 | −0.121343 | − | 0.992611i | \(-0.538720\pi\) | ||||
−0.121343 | + | 0.992611i | \(0.538720\pi\) | |||||||
\(998\) | −5.21076e10 | −1.65937 | ||||||||
\(999\) | 0 | 0 |
(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 | 531.8.a.d.1.13 | 17 | ||
3.2 | odd | 2 | 177.8.a.b.1.5 | ✓ | 17 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.8.a.b.1.5 | ✓ | 17 | 3.2 | odd | 2 | ||
531.8.a.d.1.13 | 17 | 1.1 | even | 1 | trivial |