Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [75,10,Mod(1,75)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(75, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("75.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 75 = 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 75.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: | \(38.6276877123\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{79}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 79 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(8.88819\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 75.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 35.7764 | 1.58111 | 0.790554 | − | 0.612392i | \(-0.209793\pi\) | ||||
0.790554 | + | 0.612392i | \(0.209793\pi\) | |||||||
\(3\) | −81.0000 | −0.577350 | ||||||||
\(4\) | 767.950 | 1.49990 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −2897.89 | −0.912853 | ||||||||
\(7\) | −3898.82 | −0.613751 | −0.306876 | − | 0.951750i | \(-0.599284\pi\) | ||||
−0.306876 | + | 0.951750i | \(0.599284\pi\) | |||||||
\(8\) | 9156.97 | 0.790400 | ||||||||
\(9\) | 6561.00 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −23047.7 | −0.474636 | −0.237318 | − | 0.971432i | \(-0.576268\pi\) | ||||
−0.237318 | + | 0.971432i | \(0.576268\pi\) | |||||||
\(12\) | −62203.9 | −0.865969 | ||||||||
\(13\) | 113302. | 1.10025 | 0.550125 | − | 0.835082i | \(-0.314580\pi\) | ||||
0.550125 | + | 0.835082i | \(0.314580\pi\) | |||||||
\(14\) | −139486. | −0.970407 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −65587.2 | −0.250195 | ||||||||
\(17\) | −369116. | −1.07187 | −0.535936 | − | 0.844259i | \(-0.680041\pi\) | ||||
−0.535936 | + | 0.844259i | \(0.680041\pi\) | |||||||
\(18\) | 234729. | 0.527036 | ||||||||
\(19\) | −1.10031e6 | −1.93697 | −0.968487 | − | 0.249064i | \(-0.919877\pi\) | ||||
−0.968487 | + | 0.249064i | \(0.919877\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 315805. | 0.354350 | ||||||||
\(22\) | −824563. | −0.750450 | ||||||||
\(23\) | −1.32065e6 | −0.984041 | −0.492020 | − | 0.870584i | \(-0.663741\pi\) | ||||
−0.492020 | + | 0.870584i | \(0.663741\pi\) | |||||||
\(24\) | −741714. | −0.456337 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 4.05353e6 | 1.73961 | ||||||||
\(27\) | −531441. | −0.192450 | ||||||||
\(28\) | −2.99410e6 | −0.920567 | ||||||||
\(29\) | 66845.9 | 0.0175503 | 0.00877513 | − | 0.999961i | \(-0.497207\pi\) | ||||
0.00877513 | + | 0.999961i | \(0.497207\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.78077e6 | 1.31872 | 0.659358 | − | 0.751829i | \(-0.270828\pi\) | ||||
0.659358 | + | 0.751829i | \(0.270828\pi\) | |||||||
\(32\) | −7.03484e6 | −1.18599 | ||||||||
\(33\) | 1.86686e6 | 0.274031 | ||||||||
\(34\) | −1.32056e7 | −1.69475 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 5.03852e6 | 0.499967 | ||||||||
\(37\) | −9.94470e6 | −0.872336 | −0.436168 | − | 0.899865i | \(-0.643665\pi\) | ||||
−0.436168 | + | 0.899865i | \(0.643665\pi\) | |||||||
\(38\) | −3.93651e7 | −3.06256 | ||||||||
\(39\) | −9.17744e6 | −0.635230 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.50042e7 | −1.93461 | −0.967303 | − | 0.253625i | \(-0.918377\pi\) | ||||
−0.967303 | + | 0.253625i | \(0.918377\pi\) | |||||||
\(42\) | 1.12984e7 | 0.560265 | ||||||||
\(43\) | 2.55307e7 | 1.13882 | 0.569410 | − | 0.822054i | \(-0.307172\pi\) | ||||
0.569410 | + | 0.822054i | \(0.307172\pi\) | |||||||
\(44\) | −1.76995e7 | −0.711907 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.72481e7 | −1.55587 | ||||||||
\(47\) | 1.54853e7 | 0.462891 | 0.231445 | − | 0.972848i | \(-0.425655\pi\) | ||||
0.231445 | + | 0.972848i | \(0.425655\pi\) | |||||||
\(48\) | 5.31256e6 | 0.144450 | ||||||||
\(49\) | −2.51528e7 | −0.623309 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.98984e7 | 0.618846 | ||||||||
\(52\) | 8.70100e7 | 1.65027 | ||||||||
\(53\) | −1.54895e7 | −0.269647 | −0.134824 | − | 0.990870i | \(-0.543047\pi\) | ||||
−0.134824 | + | 0.990870i | \(0.543047\pi\) | |||||||
\(54\) | −1.90130e7 | −0.304284 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −3.57014e7 | −0.485109 | ||||||||
\(57\) | 8.91251e7 | 1.11831 | ||||||||
\(58\) | 2.39150e6 | 0.0277489 | ||||||||
\(59\) | 6.45979e7 | 0.694039 | 0.347020 | − | 0.937858i | \(-0.387194\pi\) | ||||
0.347020 | + | 0.937858i | \(0.387194\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.07375e8 | −0.992928 | −0.496464 | − | 0.868057i | \(-0.665369\pi\) | ||||
−0.496464 | + | 0.868057i | \(0.665369\pi\) | |||||||
\(62\) | 2.42591e8 | 2.08503 | ||||||||
\(63\) | −2.55802e7 | −0.204584 | ||||||||
\(64\) | −2.18101e8 | −1.62498 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 6.67896e7 | 0.433273 | ||||||||
\(67\) | 1.29631e8 | 0.785911 | 0.392956 | − | 0.919557i | \(-0.371453\pi\) | ||||
0.392956 | + | 0.919557i | \(0.371453\pi\) | |||||||
\(68\) | −2.83463e8 | −1.60770 | ||||||||
\(69\) | 1.06973e8 | 0.568136 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.25343e8 | 1.05240 | 0.526201 | − | 0.850360i | \(-0.323616\pi\) | ||||
0.526201 | + | 0.850360i | \(0.323616\pi\) | |||||||
\(72\) | 6.00789e7 | 0.263467 | ||||||||
\(73\) | 1.72446e8 | 0.710723 | 0.355362 | − | 0.934729i | \(-0.384358\pi\) | ||||
0.355362 | + | 0.934729i | \(0.384358\pi\) | |||||||
\(74\) | −3.55785e8 | −1.37926 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −8.44983e8 | −2.90527 | ||||||||
\(77\) | 8.98589e7 | 0.291308 | ||||||||
\(78\) | −3.28336e8 | −1.00437 | ||||||||
\(79\) | −3.14962e8 | −0.909779 | −0.454890 | − | 0.890548i | \(-0.650321\pi\) | ||||
−0.454890 | + | 0.890548i | \(0.650321\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.30467e7 | 0.111111 | ||||||||
\(82\) | −1.25232e9 | −3.05882 | ||||||||
\(83\) | 4.03289e8 | 0.932748 | 0.466374 | − | 0.884588i | \(-0.345560\pi\) | ||||
0.466374 | + | 0.884588i | \(0.345560\pi\) | |||||||
\(84\) | 2.42522e8 | 0.531490 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 9.13397e8 | 1.80060 | ||||||||
\(87\) | −5.41452e6 | −0.0101327 | ||||||||
\(88\) | −2.11047e8 | −0.375152 | ||||||||
\(89\) | −5.72362e8 | −0.966975 | −0.483488 | − | 0.875351i | \(-0.660630\pi\) | ||||
−0.483488 | + | 0.875351i | \(0.660630\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.41743e8 | −0.675280 | ||||||||
\(92\) | −1.01419e9 | −1.47596 | ||||||||
\(93\) | −5.49242e8 | −0.761361 | ||||||||
\(94\) | 5.54007e8 | 0.731881 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 5.69822e8 | 0.684729 | ||||||||
\(97\) | −5.62737e8 | −0.645406 | −0.322703 | − | 0.946500i | \(-0.604591\pi\) | ||||
−0.322703 | + | 0.946500i | \(0.604591\pi\) | |||||||
\(98\) | −8.99875e8 | −0.985519 | ||||||||
\(99\) | −1.51216e8 | −0.158212 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.92891e9 | 1.84445 | 0.922224 | − | 0.386655i | \(-0.126370\pi\) | ||||
0.922224 | + | 0.386655i | \(0.126370\pi\) | |||||||
\(102\) | 1.06966e9 | 0.978462 | ||||||||
\(103\) | 1.90431e9 | 1.66713 | 0.833566 | − | 0.552420i | \(-0.186296\pi\) | ||||
0.833566 | + | 0.552420i | \(0.186296\pi\) | |||||||
\(104\) | 1.03750e9 | 0.869637 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −5.54159e8 | −0.426342 | ||||||||
\(107\) | 1.05533e9 | 0.778323 | 0.389162 | − | 0.921170i | \(-0.372765\pi\) | ||||
0.389162 | + | 0.921170i | \(0.372765\pi\) | |||||||
\(108\) | −4.08120e8 | −0.288656 | ||||||||
\(109\) | −5.12411e8 | −0.347696 | −0.173848 | − | 0.984773i | \(-0.555620\pi\) | ||||
−0.173848 | + | 0.984773i | \(0.555620\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.05521e8 | 0.503644 | ||||||||
\(112\) | 2.55713e8 | 0.153558 | ||||||||
\(113\) | 2.18469e9 | 1.26048 | 0.630242 | − | 0.776399i | \(-0.282956\pi\) | ||||
0.630242 | + | 0.776399i | \(0.282956\pi\) | |||||||
\(114\) | 3.18857e9 | 1.76817 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 5.13343e7 | 0.0263237 | ||||||||
\(117\) | 7.43372e8 | 0.366750 | ||||||||
\(118\) | 2.31108e9 | 1.09735 | ||||||||
\(119\) | 1.43912e9 | 0.657863 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.82675e9 | −0.774721 | ||||||||
\(122\) | −3.84148e9 | −1.56993 | ||||||||
\(123\) | 2.83534e9 | 1.11694 | ||||||||
\(124\) | 5.20729e9 | 1.97794 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −9.15167e8 | −0.323469 | ||||||||
\(127\) | 1.18646e9 | 0.404702 | 0.202351 | − | 0.979313i | \(-0.435142\pi\) | ||||
0.202351 | + | 0.979313i | \(0.435142\pi\) | |||||||
\(128\) | −4.20101e9 | −1.38328 | ||||||||
\(129\) | −2.06799e9 | −0.657498 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.71076e9 | −1.10089 | −0.550443 | − | 0.834873i | \(-0.685541\pi\) | ||||
−0.550443 | + | 0.834873i | \(0.685541\pi\) | |||||||
\(132\) | 1.43366e9 | 0.411020 | ||||||||
\(133\) | 4.28992e9 | 1.18882 | ||||||||
\(134\) | 4.63774e9 | 1.24261 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.37999e9 | −0.847207 | ||||||||
\(137\) | −3.20066e9 | −0.776241 | −0.388120 | − | 0.921609i | \(-0.626876\pi\) | ||||
−0.388120 | + | 0.921609i | \(0.626876\pi\) | |||||||
\(138\) | 3.82710e9 | 0.898285 | ||||||||
\(139\) | −2.18950e9 | −0.497483 | −0.248742 | − | 0.968570i | \(-0.580017\pi\) | ||||
−0.248742 | + | 0.968570i | \(0.580017\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.25431e9 | −0.267250 | ||||||||
\(142\) | 8.06197e9 | 1.66396 | ||||||||
\(143\) | −2.61134e9 | −0.522218 | ||||||||
\(144\) | −4.30318e8 | −0.0833984 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 6.16950e9 | 1.12373 | ||||||||
\(147\) | 2.03737e9 | 0.359868 | ||||||||
\(148\) | −7.63703e9 | −1.30842 | ||||||||
\(149\) | −6.64377e9 | −1.10427 | −0.552137 | − | 0.833754i | \(-0.686187\pi\) | ||||
−0.552137 | + | 0.833754i | \(0.686187\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.18641e10 | 1.85711 | 0.928556 | − | 0.371193i | \(-0.121051\pi\) | ||||
0.928556 | + | 0.371193i | \(0.121051\pi\) | |||||||
\(152\) | −1.00755e10 | −1.53098 | ||||||||
\(153\) | −2.42177e9 | −0.357291 | ||||||||
\(154\) | 3.21483e9 | 0.460590 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −7.04781e9 | −0.952782 | ||||||||
\(157\) | −3.30825e9 | −0.434560 | −0.217280 | − | 0.976109i | \(-0.569718\pi\) | ||||
−0.217280 | + | 0.976109i | \(0.569718\pi\) | |||||||
\(158\) | −1.12682e10 | −1.43846 | ||||||||
\(159\) | 1.25465e9 | 0.155681 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5.14899e9 | 0.603956 | ||||||||
\(162\) | 1.54006e9 | 0.175679 | ||||||||
\(163\) | −3.84635e9 | −0.426781 | −0.213390 | − | 0.976967i | \(-0.568451\pi\) | ||||
−0.213390 | + | 0.976967i | \(0.568451\pi\) | |||||||
\(164\) | −2.68814e10 | −2.90172 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.44282e10 | 1.47478 | ||||||||
\(167\) | −1.21105e10 | −1.20486 | −0.602431 | − | 0.798171i | \(-0.705801\pi\) | ||||
−0.602431 | + | 0.798171i | \(0.705801\pi\) | |||||||
\(168\) | 2.89181e9 | 0.280078 | ||||||||
\(169\) | 2.23278e9 | 0.210550 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −7.21913e9 | −0.645658 | ||||||||
\(172\) | 1.96063e10 | 1.70812 | ||||||||
\(173\) | 1.36229e10 | 1.15628 | 0.578138 | − | 0.815939i | \(-0.303780\pi\) | ||||
0.578138 | + | 0.815939i | \(0.303780\pi\) | |||||||
\(174\) | −1.93712e8 | −0.0160208 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.51163e9 | 0.118752 | ||||||||
\(177\) | −5.23243e9 | −0.400704 | ||||||||
\(178\) | −2.04770e10 | −1.52889 | ||||||||
\(179\) | −2.50779e10 | −1.82580 | −0.912898 | − | 0.408188i | \(-0.866161\pi\) | ||||
−0.912898 | + | 0.408188i | \(0.866161\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.53748e9 | −0.383494 | −0.191747 | − | 0.981444i | \(-0.561415\pi\) | ||||
−0.191747 | + | 0.981444i | \(0.561415\pi\) | |||||||
\(182\) | −1.58040e10 | −1.06769 | ||||||||
\(183\) | 8.69735e9 | 0.573267 | ||||||||
\(184\) | −1.20932e10 | −0.777785 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −1.96499e10 | −1.20379 | ||||||||
\(187\) | 8.50728e9 | 0.508749 | ||||||||
\(188\) | 1.18919e10 | 0.694291 | ||||||||
\(189\) | 2.07200e9 | 0.118117 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2.74204e10 | −1.49081 | −0.745406 | − | 0.666611i | \(-0.767744\pi\) | ||||
−0.745406 | + | 0.666611i | \(0.767744\pi\) | |||||||
\(192\) | 1.76661e10 | 0.938180 | ||||||||
\(193\) | −1.47069e10 | −0.762978 | −0.381489 | − | 0.924373i | \(-0.624589\pi\) | ||||
−0.381489 | + | 0.924373i | \(0.624589\pi\) | |||||||
\(194\) | −2.01327e10 | −1.02046 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.93161e10 | −0.934903 | ||||||||
\(197\) | 6.27835e9 | 0.296994 | 0.148497 | − | 0.988913i | \(-0.452556\pi\) | ||||
0.148497 | + | 0.988913i | \(0.452556\pi\) | |||||||
\(198\) | −5.40996e9 | −0.250150 | ||||||||
\(199\) | 2.30488e10 | 1.04186 | 0.520930 | − | 0.853599i | \(-0.325585\pi\) | ||||
0.520930 | + | 0.853599i | \(0.325585\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.05001e10 | −0.453746 | ||||||||
\(202\) | 6.90096e10 | 2.91627 | ||||||||
\(203\) | −2.60620e8 | −0.0107715 | ||||||||
\(204\) | 2.29605e10 | 0.928208 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 6.81293e10 | 2.63592 | ||||||||
\(207\) | −8.66480e9 | −0.328014 | ||||||||
\(208\) | −7.43114e9 | −0.275277 | ||||||||
\(209\) | 2.53596e10 | 0.919357 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.61916e10 | −0.909684 | −0.454842 | − | 0.890572i | \(-0.650304\pi\) | ||||
−0.454842 | + | 0.890572i | \(0.650304\pi\) | |||||||
\(212\) | −1.18952e10 | −0.404445 | ||||||||
\(213\) | −1.82528e10 | −0.607605 | ||||||||
\(214\) | 3.77558e10 | 1.23061 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −4.86639e9 | −0.152112 | ||||||||
\(217\) | −2.64370e10 | −0.809364 | ||||||||
\(218\) | −1.83322e10 | −0.549744 | ||||||||
\(219\) | −1.39681e10 | −0.410336 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.18215e10 | −1.17933 | ||||||||
\(222\) | 2.88186e10 | 0.796315 | ||||||||
\(223\) | 6.95437e10 | 1.88316 | 0.941578 | − | 0.336796i | \(-0.109343\pi\) | ||||
0.941578 | + | 0.336796i | \(0.109343\pi\) | |||||||
\(224\) | 2.74276e10 | 0.727900 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 7.81604e10 | 1.99296 | ||||||||
\(227\) | 6.83035e9 | 0.170737 | 0.0853684 | − | 0.996349i | \(-0.472793\pi\) | ||||
0.0853684 | + | 0.996349i | \(0.472793\pi\) | |||||||
\(228\) | 6.84436e10 | 1.67736 | ||||||||
\(229\) | 2.43923e10 | 0.586129 | 0.293065 | − | 0.956093i | \(-0.405325\pi\) | ||||
0.293065 | + | 0.956093i | \(0.405325\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −7.27857e9 | −0.168187 | ||||||||
\(232\) | 6.12106e8 | 0.0138717 | ||||||||
\(233\) | −8.36542e10 | −1.85946 | −0.929729 | − | 0.368245i | \(-0.879959\pi\) | ||||
−0.929729 | + | 0.368245i | \(0.879959\pi\) | |||||||
\(234\) | 2.65952e10 | 0.579871 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 4.96079e10 | 1.04099 | ||||||||
\(237\) | 2.55119e10 | 0.525261 | ||||||||
\(238\) | 5.14865e10 | 1.04015 | ||||||||
\(239\) | −1.66318e10 | −0.329723 | −0.164862 | − | 0.986317i | \(-0.552718\pi\) | ||||
−0.164862 | + | 0.986317i | \(0.552718\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −9.26682e10 | −1.76951 | −0.884757 | − | 0.466053i | \(-0.845676\pi\) | ||||
−0.884757 | + | 0.466053i | \(0.845676\pi\) | |||||||
\(242\) | −6.53546e10 | −1.22492 | ||||||||
\(243\) | −3.48678e9 | −0.0641500 | ||||||||
\(244\) | −8.24584e10 | −1.48930 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 1.01438e11 | 1.76601 | ||||||||
\(247\) | −1.24667e11 | −2.13116 | ||||||||
\(248\) | 6.20913e10 | 1.04231 | ||||||||
\(249\) | −3.26664e10 | −0.538523 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.99958e10 | −0.317985 | −0.158993 | − | 0.987280i | \(-0.550825\pi\) | ||||
−0.158993 | + | 0.987280i | \(0.550825\pi\) | |||||||
\(252\) | −1.96443e10 | −0.306856 | ||||||||
\(253\) | 3.04380e10 | 0.467061 | ||||||||
\(254\) | 4.24472e10 | 0.639878 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −3.86295e10 | −0.562134 | ||||||||
\(257\) | −1.27910e11 | −1.82897 | −0.914483 | − | 0.404624i | \(-0.867402\pi\) | ||||
−0.914483 | + | 0.404624i | \(0.867402\pi\) | |||||||
\(258\) | −7.39852e10 | −1.03958 | ||||||||
\(259\) | 3.87726e10 | 0.535398 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.38576e8 | 0.00585009 | ||||||||
\(262\) | −1.32758e11 | −1.74062 | ||||||||
\(263\) | −2.76120e10 | −0.355875 | −0.177938 | − | 0.984042i | \(-0.556943\pi\) | ||||
−0.177938 | + | 0.984042i | \(0.556943\pi\) | |||||||
\(264\) | 1.70948e10 | 0.216594 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 1.53478e11 | 1.87965 | ||||||||
\(267\) | 4.63613e10 | 0.558284 | ||||||||
\(268\) | 9.95504e10 | 1.17879 | ||||||||
\(269\) | 4.03173e10 | 0.469468 | 0.234734 | − | 0.972060i | \(-0.424578\pi\) | ||||
0.234734 | + | 0.972060i | \(0.424578\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.36744e10 | 0.491886 | 0.245943 | − | 0.969284i | \(-0.420902\pi\) | ||||
0.245943 | + | 0.969284i | \(0.420902\pi\) | |||||||
\(272\) | 2.42093e10 | 0.268177 | ||||||||
\(273\) | 3.57812e10 | 0.389873 | ||||||||
\(274\) | −1.14508e11 | −1.22732 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 8.21498e10 | 0.852149 | ||||||||
\(277\) | 4.35371e10 | 0.444324 | 0.222162 | − | 0.975010i | \(-0.428689\pi\) | ||||
0.222162 | + | 0.975010i | \(0.428689\pi\) | |||||||
\(278\) | −7.83325e10 | −0.786575 | ||||||||
\(279\) | 4.44886e10 | 0.439572 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.86443e10 | −0.274069 | −0.137035 | − | 0.990566i | \(-0.543757\pi\) | ||||
−0.137035 | + | 0.990566i | \(0.543757\pi\) | |||||||
\(282\) | −4.48746e10 | −0.422551 | ||||||||
\(283\) | −2.31306e10 | −0.214362 | −0.107181 | − | 0.994240i | \(-0.534182\pi\) | ||||
−0.107181 | + | 0.994240i | \(0.534182\pi\) | |||||||
\(284\) | 1.73052e11 | 1.57850 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −9.34244e10 | −0.825683 | ||||||||
\(287\) | 1.36475e11 | 1.18737 | ||||||||
\(288\) | −4.61556e10 | −0.395328 | ||||||||
\(289\) | 1.76589e10 | 0.148910 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4.55817e10 | 0.372625 | ||||||||
\(292\) | 1.32430e11 | 1.06602 | ||||||||
\(293\) | 4.76003e10 | 0.377316 | 0.188658 | − | 0.982043i | \(-0.439586\pi\) | ||||
0.188658 | + | 0.982043i | \(0.439586\pi\) | |||||||
\(294\) | 7.28899e10 | 0.568990 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −9.10633e10 | −0.689494 | ||||||||
\(297\) | 1.22485e10 | 0.0913437 | ||||||||
\(298\) | −2.37690e11 | −1.74598 | ||||||||
\(299\) | −1.49632e11 | −1.08269 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −9.95398e10 | −0.698953 | ||||||||
\(302\) | 4.24454e11 | 2.93629 | ||||||||
\(303\) | −1.56242e11 | −1.06489 | ||||||||
\(304\) | 7.21662e10 | 0.484622 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −8.66422e10 | −0.564915 | ||||||||
\(307\) | −2.45646e11 | −1.57829 | −0.789145 | − | 0.614207i | \(-0.789476\pi\) | ||||
−0.789145 | + | 0.614207i | \(0.789476\pi\) | |||||||
\(308\) | 6.90072e10 | 0.436934 | ||||||||
\(309\) | −1.54249e11 | −0.962519 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.62977e10 | −0.159403 | −0.0797015 | − | 0.996819i | \(-0.525397\pi\) | ||||
−0.0797015 | + | 0.996819i | \(0.525397\pi\) | |||||||
\(312\) | −8.40375e10 | −0.502085 | ||||||||
\(313\) | 2.18427e11 | 1.28635 | 0.643173 | − | 0.765721i | \(-0.277618\pi\) | ||||
0.643173 | + | 0.765721i | \(0.277618\pi\) | |||||||
\(314\) | −1.18357e11 | −0.687086 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.41875e11 | −1.36458 | ||||||||
\(317\) | 1.97173e11 | 1.09668 | 0.548341 | − | 0.836255i | \(-0.315260\pi\) | ||||
0.548341 | + | 0.836255i | \(0.315260\pi\) | |||||||
\(318\) | 4.48869e10 | 0.246149 | ||||||||
\(319\) | −1.54064e9 | −0.00832998 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −8.54815e10 | −0.449365 | ||||||||
\(322\) | 1.84212e11 | 0.954920 | ||||||||
\(323\) | 4.06142e11 | 2.07619 | ||||||||
\(324\) | 3.30577e10 | 0.166656 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −1.37609e11 | −0.674787 | ||||||||
\(327\) | 4.15053e10 | 0.200742 | ||||||||
\(328\) | −3.20532e11 | −1.52911 | ||||||||
\(329\) | −6.03744e10 | −0.284100 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7.19139e10 | 0.329296 | 0.164648 | − | 0.986352i | \(-0.447351\pi\) | ||||
0.164648 | + | 0.986352i | \(0.447351\pi\) | |||||||
\(332\) | 3.09705e11 | 1.39903 | ||||||||
\(333\) | −6.52472e10 | −0.290779 | ||||||||
\(334\) | −4.33269e11 | −1.90502 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −2.07128e10 | −0.0886566 | ||||||||
\(337\) | −9.49224e10 | −0.400898 | −0.200449 | − | 0.979704i | \(-0.564240\pi\) | ||||
−0.200449 | + | 0.979704i | \(0.564240\pi\) | |||||||
\(338\) | 7.98807e10 | 0.332902 | ||||||||
\(339\) | −1.76960e11 | −0.727741 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.56281e11 | −0.625910 | ||||||||
\(342\) | −2.58274e11 | −1.02085 | ||||||||
\(343\) | 2.55398e11 | 0.996308 | ||||||||
\(344\) | 2.33784e11 | 0.900123 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 4.87377e11 | 1.82820 | ||||||||
\(347\) | −2.17424e11 | −0.805054 | −0.402527 | − | 0.915408i | \(-0.631868\pi\) | ||||
−0.402527 | + | 0.915408i | \(0.631868\pi\) | |||||||
\(348\) | −4.15808e9 | −0.0151980 | ||||||||
\(349\) | 2.50076e11 | 0.902315 | 0.451157 | − | 0.892444i | \(-0.351011\pi\) | ||||
0.451157 | + | 0.892444i | \(0.351011\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −6.02132e10 | −0.211743 | ||||||||
\(352\) | 1.62137e11 | 0.562911 | ||||||||
\(353\) | −4.64191e11 | −1.59115 | −0.795573 | − | 0.605857i | \(-0.792830\pi\) | ||||
−0.795573 | + | 0.605857i | \(0.792830\pi\) | |||||||
\(354\) | −1.87197e11 | −0.633556 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −4.39545e11 | −1.45037 | ||||||||
\(357\) | −1.16569e11 | −0.379817 | ||||||||
\(358\) | −8.97196e11 | −2.88678 | ||||||||
\(359\) | −2.17323e11 | −0.690526 | −0.345263 | − | 0.938506i | \(-0.612210\pi\) | ||||
−0.345263 | + | 0.938506i | \(0.612210\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8.87994e11 | 2.75187 | ||||||||
\(362\) | −1.98111e11 | −0.606345 | ||||||||
\(363\) | 1.47967e11 | 0.447285 | ||||||||
\(364\) | −3.39237e11 | −1.01285 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 3.11160e11 | 0.906398 | ||||||||
\(367\) | 5.69129e11 | 1.63762 | 0.818811 | − | 0.574063i | \(-0.194634\pi\) | ||||
0.818811 | + | 0.574063i | \(0.194634\pi\) | |||||||
\(368\) | 8.66178e10 | 0.246202 | ||||||||
\(369\) | −2.29662e11 | −0.644868 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.03909e10 | 0.165497 | ||||||||
\(372\) | −4.21791e11 | −1.14197 | ||||||||
\(373\) | −2.82198e10 | −0.0754856 | −0.0377428 | − | 0.999287i | \(-0.512017\pi\) | ||||
−0.0377428 | + | 0.999287i | \(0.512017\pi\) | |||||||
\(374\) | 3.04360e11 | 0.804387 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.41798e11 | 0.365869 | ||||||||
\(377\) | 7.57375e9 | 0.0193097 | ||||||||
\(378\) | 7.41285e10 | 0.186755 | ||||||||
\(379\) | 1.30996e10 | 0.0326124 | 0.0163062 | − | 0.999867i | \(-0.494809\pi\) | ||||
0.0163062 | + | 0.999867i | \(0.494809\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −9.61031e10 | −0.233655 | ||||||||
\(382\) | −9.81001e11 | −2.35714 | ||||||||
\(383\) | −2.80400e11 | −0.665861 | −0.332931 | − | 0.942951i | \(-0.608038\pi\) | ||||
−0.332931 | + | 0.942951i | \(0.608038\pi\) | |||||||
\(384\) | 3.40282e11 | 0.798635 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −5.26158e11 | −1.20635 | ||||||||
\(387\) | 1.67507e11 | 0.379607 | ||||||||
\(388\) | −4.32154e11 | −0.968046 | ||||||||
\(389\) | −3.02952e11 | −0.670811 | −0.335405 | − | 0.942074i | \(-0.608873\pi\) | ||||
−0.335405 | + | 0.942074i | \(0.608873\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.87474e11 | 1.05477 | ||||||||
\(392\) | −2.30323e11 | −0.492663 | ||||||||
\(393\) | 3.00572e11 | 0.635597 | ||||||||
\(394\) | 2.24617e11 | 0.469580 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −1.16126e11 | −0.237302 | ||||||||
\(397\) | −7.31203e11 | −1.47734 | −0.738670 | − | 0.674067i | \(-0.764546\pi\) | ||||
−0.738670 | + | 0.674067i | \(0.764546\pi\) | |||||||
\(398\) | 8.24603e11 | 1.64729 | ||||||||
\(399\) | −3.47483e11 | −0.686366 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3.27396e9 | −0.00632301 | −0.00316150 | − | 0.999995i | \(-0.501006\pi\) | ||||
−0.00316150 | + | 0.999995i | \(0.501006\pi\) | |||||||
\(402\) | −3.75657e11 | −0.717422 | ||||||||
\(403\) | 7.68272e11 | 1.45092 | ||||||||
\(404\) | 1.48131e12 | 2.76649 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −9.32406e9 | −0.0170309 | ||||||||
\(407\) | 2.29202e11 | 0.414042 | ||||||||
\(408\) | 2.73779e11 | 0.489135 | ||||||||
\(409\) | 6.73551e11 | 1.19019 | 0.595094 | − | 0.803656i | \(-0.297115\pi\) | ||||
0.595094 | + | 0.803656i | \(0.297115\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.59253e11 | 0.448163 | ||||||||
\(412\) | 1.46241e12 | 2.50053 | ||||||||
\(413\) | −2.51856e11 | −0.425968 | ||||||||
\(414\) | −3.09995e11 | −0.518625 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −7.97059e11 | −1.30488 | ||||||||
\(417\) | 1.77350e11 | 0.287222 | ||||||||
\(418\) | 9.07275e11 | 1.45360 | ||||||||
\(419\) | 9.58213e11 | 1.51879 | 0.759397 | − | 0.650628i | \(-0.225494\pi\) | ||||
0.759397 | + | 0.650628i | \(0.225494\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.79406e11 | −0.433477 | −0.216739 | − | 0.976230i | \(-0.569542\pi\) | ||||
−0.216739 | + | 0.976230i | \(0.569542\pi\) | |||||||
\(422\) | −9.37040e11 | −1.43831 | ||||||||
\(423\) | 1.01599e11 | 0.154297 | ||||||||
\(424\) | −1.41837e11 | −0.213129 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −6.53019e11 | −0.960689 | ||||||||
\(427\) | 4.18635e11 | 0.609411 | ||||||||
\(428\) | 8.10438e11 | 1.16741 | ||||||||
\(429\) | 2.11519e11 | 0.301503 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.85936e11 | −0.259546 | −0.129773 | − | 0.991544i | \(-0.541425\pi\) | ||||
−0.129773 | + | 0.991544i | \(0.541425\pi\) | |||||||
\(432\) | 3.48557e10 | 0.0481501 | ||||||||
\(433\) | −2.36668e11 | −0.323551 | −0.161776 | − | 0.986828i | \(-0.551722\pi\) | ||||
−0.161776 | + | 0.986828i | \(0.551722\pi\) | |||||||
\(434\) | −9.45821e11 | −1.27969 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −3.93506e11 | −0.521509 | ||||||||
\(437\) | 1.45313e12 | 1.90606 | ||||||||
\(438\) | −4.99730e11 | −0.648786 | ||||||||
\(439\) | 1.10414e12 | 1.41885 | 0.709423 | − | 0.704783i | \(-0.248956\pi\) | ||||
0.709423 | + | 0.704783i | \(0.248956\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.65027e11 | −0.207770 | ||||||||
\(442\) | −1.49622e12 | −1.86464 | ||||||||
\(443\) | −2.82238e11 | −0.348175 | −0.174088 | − | 0.984730i | \(-0.555698\pi\) | ||||
−0.174088 | + | 0.984730i | \(0.555698\pi\) | |||||||
\(444\) | 6.18600e11 | 0.755416 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 2.48802e12 | 2.97747 | ||||||||
\(447\) | 5.38146e11 | 0.637553 | ||||||||
\(448\) | 8.50336e11 | 0.997331 | ||||||||
\(449\) | −5.99349e11 | −0.695939 | −0.347970 | − | 0.937506i | \(-0.613129\pi\) | ||||
−0.347970 | + | 0.937506i | \(0.613129\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8.06765e11 | 0.918233 | ||||||||
\(452\) | 1.67773e12 | 1.89060 | ||||||||
\(453\) | −9.60991e11 | −1.07220 | ||||||||
\(454\) | 2.44365e11 | 0.269953 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 8.16115e11 | 0.883914 | ||||||||
\(457\) | 4.94163e11 | 0.529965 | 0.264983 | − | 0.964253i | \(-0.414634\pi\) | ||||
0.264983 | + | 0.964253i | \(0.414634\pi\) | |||||||
\(458\) | 8.72669e11 | 0.926734 | ||||||||
\(459\) | 1.96164e11 | 0.206282 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6.25704e11 | 0.645230 | 0.322615 | − | 0.946530i | \(-0.395438\pi\) | ||||
0.322615 | + | 0.946530i | \(0.395438\pi\) | |||||||
\(462\) | −2.60401e11 | −0.265922 | ||||||||
\(463\) | −8.05319e11 | −0.814429 | −0.407215 | − | 0.913332i | \(-0.633500\pi\) | ||||
−0.407215 | + | 0.913332i | \(0.633500\pi\) | |||||||
\(464\) | −4.38423e9 | −0.00439099 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −2.99285e12 | −2.94000 | ||||||||
\(467\) | −2.95042e11 | −0.287050 | −0.143525 | − | 0.989647i | \(-0.545844\pi\) | ||||
−0.143525 | + | 0.989647i | \(0.545844\pi\) | |||||||
\(468\) | 5.70873e11 | 0.550089 | ||||||||
\(469\) | −5.05410e11 | −0.482354 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.67968e11 | 0.250893 | ||||||||
\(472\) | 5.91520e11 | 0.548568 | ||||||||
\(473\) | −5.88424e11 | −0.540525 | ||||||||
\(474\) | 9.12724e11 | 0.830495 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 1.10517e12 | 0.986730 | ||||||||
\(477\) | −1.01627e11 | −0.0898825 | ||||||||
\(478\) | −5.95027e11 | −0.521328 | ||||||||
\(479\) | 4.71656e11 | 0.409369 | 0.204685 | − | 0.978828i | \(-0.434383\pi\) | ||||
0.204685 | + | 0.978828i | \(0.434383\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.12675e12 | −0.959788 | ||||||||
\(482\) | −3.31533e12 | −2.79779 | ||||||||
\(483\) | −4.17068e11 | −0.348694 | ||||||||
\(484\) | −1.40285e12 | −1.16201 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −1.24745e11 | −0.101428 | ||||||||
\(487\) | −2.13496e12 | −1.71993 | −0.859964 | − | 0.510355i | \(-0.829514\pi\) | ||||
−0.859964 | + | 0.510355i | \(0.829514\pi\) | |||||||
\(488\) | −9.83227e11 | −0.784810 | ||||||||
\(489\) | 3.11555e11 | 0.246402 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.15317e12 | −0.895418 | −0.447709 | − | 0.894179i | \(-0.647760\pi\) | ||||
−0.447709 | + | 0.894179i | \(0.647760\pi\) | |||||||
\(492\) | 2.17740e12 | 1.67531 | ||||||||
\(493\) | −2.46739e10 | −0.0188116 | ||||||||
\(494\) | −4.46013e12 | −3.36959 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −4.44732e11 | −0.329937 | ||||||||
\(497\) | −8.78574e11 | −0.645914 | ||||||||
\(498\) | −1.16868e12 | −0.851462 | ||||||||
\(499\) | −9.44785e10 | −0.0682151 | −0.0341075 | − | 0.999418i | \(-0.510859\pi\) | ||||
−0.0341075 | + | 0.999418i | \(0.510859\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 9.80949e11 | 0.695627 | ||||||||
\(502\) | −7.15377e11 | −0.502769 | ||||||||
\(503\) | −1.99443e12 | −1.38920 | −0.694598 | − | 0.719398i | \(-0.744418\pi\) | ||||
−0.694598 | + | 0.719398i | \(0.744418\pi\) | |||||||
\(504\) | −2.34237e11 | −0.161703 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 1.08896e12 | 0.738474 | ||||||||
\(507\) | −1.80855e11 | −0.121561 | ||||||||
\(508\) | 9.11141e11 | 0.607014 | ||||||||
\(509\) | 1.29001e12 | 0.851847 | 0.425923 | − | 0.904759i | \(-0.359949\pi\) | ||||
0.425923 | + | 0.904759i | \(0.359949\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.72337e11 | −0.436208 | ||||||||
\(512\) | 7.68892e11 | 0.494482 | ||||||||
\(513\) | 5.84750e11 | 0.372771 | ||||||||
\(514\) | −4.57616e12 | −2.89179 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −1.58811e12 | −0.986183 | ||||||||
\(517\) | −3.56900e11 | −0.219705 | ||||||||
\(518\) | 1.38715e12 | 0.846522 | ||||||||
\(519\) | −1.10345e12 | −0.667576 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.19407e12 | 0.710003 | 0.355001 | − | 0.934866i | \(-0.384480\pi\) | ||||
0.355001 | + | 0.934866i | \(0.384480\pi\) | |||||||
\(522\) | 1.56907e10 | 0.00924962 | ||||||||
\(523\) | −8.52995e9 | −0.00498527 | −0.00249264 | − | 0.999997i | \(-0.500793\pi\) | ||||
−0.00249264 | + | 0.999997i | \(0.500793\pi\) | |||||||
\(524\) | −2.84968e12 | −1.65122 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −9.87859e11 | −0.562677 | ||||||||
\(527\) | −2.50289e12 | −1.41349 | ||||||||
\(528\) | −1.22442e11 | −0.0685613 | ||||||||
\(529\) | −5.70317e10 | −0.0316640 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.23827e11 | 0.231346 | ||||||||
\(532\) | 3.29444e12 | 1.78311 | ||||||||
\(533\) | −3.96603e12 | −2.12855 | ||||||||
\(534\) | 1.65864e12 | 0.882707 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 1.18703e12 | 0.621184 | ||||||||
\(537\) | 2.03131e12 | 1.05412 | ||||||||
\(538\) | 1.44241e12 | 0.742280 | ||||||||
\(539\) | 5.79713e11 | 0.295845 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.03592e11 | 0.102182 | 0.0510908 | − | 0.998694i | \(-0.483730\pi\) | ||||
0.0510908 | + | 0.998694i | \(0.483730\pi\) | |||||||
\(542\) | 1.56251e12 | 0.777726 | ||||||||
\(543\) | 4.48536e11 | 0.221410 | ||||||||
\(544\) | 2.59667e12 | 1.27122 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 1.28012e12 | 0.616431 | ||||||||
\(547\) | 2.64470e12 | 1.26309 | 0.631545 | − | 0.775339i | \(-0.282421\pi\) | ||||
0.631545 | + | 0.775339i | \(0.282421\pi\) | |||||||
\(548\) | −2.45794e12 | −1.16429 | ||||||||
\(549\) | −7.04486e11 | −0.330976 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7.35512e10 | −0.0339944 | ||||||||
\(552\) | 9.79546e11 | 0.449055 | ||||||||
\(553\) | 1.22798e12 | 0.558378 | ||||||||
\(554\) | 1.55760e12 | 0.702525 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.68143e12 | −0.746177 | ||||||||
\(557\) | 1.68698e12 | 0.742613 | 0.371307 | − | 0.928510i | \(-0.378910\pi\) | ||||
0.371307 | + | 0.928510i | \(0.378910\pi\) | |||||||
\(558\) | 1.59164e12 | 0.695011 | ||||||||
\(559\) | 2.89267e12 | 1.25299 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −6.89090e11 | −0.293726 | ||||||||
\(562\) | −1.02479e12 | −0.433333 | ||||||||
\(563\) | −5.77046e11 | −0.242060 | −0.121030 | − | 0.992649i | \(-0.538620\pi\) | ||||
−0.121030 | + | 0.992649i | \(0.538620\pi\) | |||||||
\(564\) | −9.63246e11 | −0.400849 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −8.27531e11 | −0.338930 | ||||||||
\(567\) | −1.67832e11 | −0.0681946 | ||||||||
\(568\) | 2.06346e12 | 0.831819 | ||||||||
\(569\) | −5.33359e11 | −0.213311 | −0.106656 | − | 0.994296i | \(-0.534014\pi\) | ||||
−0.106656 | + | 0.994296i | \(0.534014\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.56331e12 | 1.00911 | 0.504556 | − | 0.863379i | \(-0.331656\pi\) | ||||
0.504556 | + | 0.863379i | \(0.331656\pi\) | |||||||
\(572\) | −2.00538e12 | −0.783276 | ||||||||
\(573\) | 2.22105e12 | 0.860721 | ||||||||
\(574\) | 4.88259e12 | 1.87736 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −1.43096e12 | −0.541659 | ||||||||
\(577\) | 4.17162e12 | 1.56680 | 0.783400 | − | 0.621518i | \(-0.213484\pi\) | ||||
0.783400 | + | 0.621518i | \(0.213484\pi\) | |||||||
\(578\) | 6.31772e11 | 0.235443 | ||||||||
\(579\) | 1.19126e12 | 0.440505 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.57235e12 | −0.572476 | ||||||||
\(582\) | 1.63075e12 | 0.589161 | ||||||||
\(583\) | 3.56998e11 | 0.127984 | ||||||||
\(584\) | 1.57908e12 | 0.561755 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.70297e12 | 0.596577 | ||||||||
\(587\) | −1.53800e12 | −0.534668 | −0.267334 | − | 0.963604i | \(-0.586143\pi\) | ||||
−0.267334 | + | 0.963604i | \(0.586143\pi\) | |||||||
\(588\) | 1.56460e12 | 0.539766 | ||||||||
\(589\) | −7.46094e12 | −2.55432 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −5.08546e11 | −0.171470 | ||||||||
\(592\) | 6.52245e11 | 0.218254 | ||||||||
\(593\) | 8.68139e11 | 0.288299 | 0.144150 | − | 0.989556i | \(-0.453955\pi\) | ||||
0.144150 | + | 0.989556i | \(0.453955\pi\) | |||||||
\(594\) | 4.38207e11 | 0.144424 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −5.10209e12 | −1.65630 | ||||||||
\(597\) | −1.86695e12 | −0.601519 | ||||||||
\(598\) | −5.35330e12 | −1.71185 | ||||||||
\(599\) | 4.89825e12 | 1.55461 | 0.777303 | − | 0.629127i | \(-0.216587\pi\) | ||||
0.777303 | + | 0.629127i | \(0.216587\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.06839e12 | 0.334036 | 0.167018 | − | 0.985954i | \(-0.446586\pi\) | ||||
0.167018 | + | 0.985954i | \(0.446586\pi\) | |||||||
\(602\) | −3.56118e12 | −1.10512 | ||||||||
\(603\) | 8.50511e11 | 0.261970 | ||||||||
\(604\) | 9.11103e12 | 2.78549 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −5.58977e12 | −1.68371 | ||||||||
\(607\) | 3.11476e11 | 0.0931268 | 0.0465634 | − | 0.998915i | \(-0.485173\pi\) | ||||
0.0465634 | + | 0.998915i | \(0.485173\pi\) | |||||||
\(608\) | 7.74050e12 | 2.29722 | ||||||||
\(609\) | 2.11103e10 | 0.00621893 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.75451e12 | 0.509296 | ||||||||
\(612\) | −1.85980e12 | −0.535901 | ||||||||
\(613\) | 3.17050e10 | 0.00906891 | 0.00453445 | − | 0.999990i | \(-0.498557\pi\) | ||||
0.00453445 | + | 0.999990i | \(0.498557\pi\) | |||||||
\(614\) | −8.78832e12 | −2.49545 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 8.22835e11 | 0.230250 | ||||||||
\(617\) | −4.71027e12 | −1.30847 | −0.654233 | − | 0.756293i | \(-0.727008\pi\) | ||||
−0.654233 | + | 0.756293i | \(0.727008\pi\) | |||||||
\(618\) | −5.51847e12 | −1.52185 | ||||||||
\(619\) | −4.40729e12 | −1.20660 | −0.603301 | − | 0.797513i | \(-0.706148\pi\) | ||||
−0.603301 | + | 0.797513i | \(0.706148\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 7.01848e11 | 0.189379 | ||||||||
\(622\) | −9.40837e11 | −0.252033 | ||||||||
\(623\) | 2.23154e12 | 0.593483 | ||||||||
\(624\) | 6.01922e11 | 0.158931 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 7.81454e12 | 2.03385 | ||||||||
\(627\) | −2.05413e12 | −0.530791 | ||||||||
\(628\) | −2.54057e12 | −0.651798 | ||||||||
\(629\) | 3.67075e12 | 0.935033 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.28716e12 | −0.323221 | −0.161610 | − | 0.986855i | \(-0.551669\pi\) | ||||
−0.161610 | + | 0.986855i | \(0.551669\pi\) | |||||||
\(632\) | −2.88410e12 | −0.719089 | ||||||||
\(633\) | 2.12152e12 | 0.525206 | ||||||||
\(634\) | 7.05414e12 | 1.73397 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 9.63509e11 | 0.233506 | ||||||||
\(637\) | −2.84985e12 | −0.685796 | ||||||||
\(638\) | −5.51187e10 | −0.0131706 | ||||||||
\(639\) | 1.47848e12 | 0.350801 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −5.95493e12 | −1.39321 | −0.696603 | − | 0.717457i | \(-0.745306\pi\) | ||||
−0.696603 | + | 0.717457i | \(0.745306\pi\) | |||||||
\(642\) | −3.05822e12 | −0.710495 | ||||||||
\(643\) | −1.38447e12 | −0.319399 | −0.159700 | − | 0.987166i | \(-0.551053\pi\) | ||||
−0.159700 | + | 0.987166i | \(0.551053\pi\) | |||||||
\(644\) | 3.95417e12 | 0.905876 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.45303e13 | 3.28268 | ||||||||
\(647\) | 1.41737e12 | 0.317991 | 0.158996 | − | 0.987279i | \(-0.449174\pi\) | ||||
0.158996 | + | 0.987279i | \(0.449174\pi\) | |||||||
\(648\) | 3.94177e11 | 0.0878222 | ||||||||
\(649\) | −1.48883e12 | −0.329416 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.14140e12 | 0.467286 | ||||||||
\(652\) | −2.95381e12 | −0.640130 | ||||||||
\(653\) | 7.68868e12 | 1.65479 | 0.827394 | − | 0.561621i | \(-0.189822\pi\) | ||||
0.827394 | + | 0.561621i | \(0.189822\pi\) | |||||||
\(654\) | 1.48491e12 | 0.317395 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 2.29583e12 | 0.484029 | ||||||||
\(657\) | 1.13142e12 | 0.236908 | ||||||||
\(658\) | −2.15998e12 | −0.449193 | ||||||||
\(659\) | −8.26006e12 | −1.70608 | −0.853039 | − | 0.521847i | \(-0.825243\pi\) | ||||
−0.853039 | + | 0.521847i | \(0.825243\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.87919e12 | 0.994126 | 0.497063 | − | 0.867714i | \(-0.334412\pi\) | ||||
0.497063 | + | 0.867714i | \(0.334412\pi\) | |||||||
\(662\) | 2.57282e12 | 0.520653 | ||||||||
\(663\) | 3.38754e12 | 0.680885 | ||||||||
\(664\) | 3.69290e12 | 0.737244 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −2.33431e12 | −0.459753 | ||||||||
\(667\) | −8.82801e10 | −0.0172702 | ||||||||
\(668\) | −9.30024e12 | −1.80718 | ||||||||
\(669\) | −5.63304e12 | −1.08724 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.47474e12 | 0.471279 | ||||||||
\(672\) | −2.22164e12 | −0.420253 | ||||||||
\(673\) | −3.86510e12 | −0.726261 | −0.363130 | − | 0.931738i | \(-0.618292\pi\) | ||||
−0.363130 | + | 0.931738i | \(0.618292\pi\) | |||||||
\(674\) | −3.39598e12 | −0.633863 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.71466e12 | 0.315804 | ||||||||
\(677\) | 2.05208e12 | 0.375444 | 0.187722 | − | 0.982222i | \(-0.439890\pi\) | ||||
0.187722 | + | 0.982222i | \(0.439890\pi\) | |||||||
\(678\) | −6.33099e12 | −1.15064 | ||||||||
\(679\) | 2.19401e12 | 0.396119 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −5.53259e11 | −0.0985749 | ||||||||
\(682\) | −5.59117e12 | −0.989631 | ||||||||
\(683\) | 4.25955e12 | 0.748981 | 0.374490 | − | 0.927231i | \(-0.377818\pi\) | ||||
0.374490 | + | 0.927231i | \(0.377818\pi\) | |||||||
\(684\) | −5.54393e12 | −0.968424 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 9.13721e12 | 1.57527 | ||||||||
\(687\) | −1.97578e12 | −0.338402 | ||||||||
\(688\) | −1.67449e12 | −0.284927 | ||||||||
\(689\) | −1.75499e12 | −0.296680 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3.86518e12 | −0.644938 | −0.322469 | − | 0.946580i | \(-0.604513\pi\) | ||||
−0.322469 | + | 0.946580i | \(0.604513\pi\) | |||||||
\(692\) | 1.04617e13 | 1.73430 | ||||||||
\(693\) | 5.89564e11 | 0.0971028 | ||||||||
\(694\) | −7.77865e12 | −1.27288 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −4.95806e10 | −0.00800884 | ||||||||
\(697\) | 1.29206e13 | 2.07365 | ||||||||
\(698\) | 8.94683e12 | 1.42666 | ||||||||
\(699\) | 6.77599e12 | 1.07356 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.03789e13 | −1.62338 | −0.811692 | − | 0.584086i | \(-0.801453\pi\) | ||||
−0.811692 | + | 0.584086i | \(0.801453\pi\) | |||||||
\(702\) | −2.15421e12 | −0.334789 | ||||||||
\(703\) | 1.09423e13 | 1.68969 | ||||||||
\(704\) | 5.02671e12 | 0.771272 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1.66071e13 | −2.51577 | ||||||||
\(707\) | −7.52050e12 | −1.13203 | ||||||||
\(708\) | −4.01824e12 | −0.601017 | ||||||||
\(709\) | −8.16100e12 | −1.21293 | −0.606465 | − | 0.795110i | \(-0.707413\pi\) | ||||
−0.606465 | + | 0.795110i | \(0.707413\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.06646e12 | −0.303260 | ||||||||
\(712\) | −5.24110e12 | −0.764297 | ||||||||
\(713\) | −8.95503e12 | −1.29767 | ||||||||
\(714\) | −4.17041e12 | −0.600532 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −1.92586e13 | −2.73851 | ||||||||
\(717\) | 1.34718e12 | 0.190366 | ||||||||
\(718\) | −7.77502e12 | −1.09180 | ||||||||
\(719\) | 9.74567e12 | 1.35998 | 0.679989 | − | 0.733223i | \(-0.261985\pi\) | ||||
0.679989 | + | 0.733223i | \(0.261985\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7.42457e12 | −1.02320 | ||||||||
\(722\) | 3.17692e13 | 4.35100 | ||||||||
\(723\) | 7.50612e12 | 1.02163 | ||||||||
\(724\) | −4.25250e12 | −0.575203 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 5.29372e12 | 0.707206 | ||||||||
\(727\) | −9.02097e12 | −1.19770 | −0.598850 | − | 0.800861i | \(-0.704376\pi\) | ||||
−0.598850 | + | 0.800861i | \(0.704376\pi\) | |||||||
\(728\) | −4.04503e12 | −0.533741 | ||||||||
\(729\) | 2.82430e11 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −9.42381e12 | −1.22067 | ||||||||
\(732\) | 6.67913e12 | 0.859845 | ||||||||
\(733\) | 9.01918e12 | 1.15398 | 0.576991 | − | 0.816750i | \(-0.304227\pi\) | ||||
0.576991 | + | 0.816750i | \(0.304227\pi\) | |||||||
\(734\) | 2.03614e13 | 2.58926 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 9.29057e12 | 1.16706 | ||||||||
\(737\) | −2.98770e12 | −0.373022 | ||||||||
\(738\) | −8.21649e12 | −1.01961 | ||||||||
\(739\) | −6.50657e12 | −0.802513 | −0.401257 | − | 0.915966i | \(-0.631426\pi\) | ||||
−0.401257 | + | 0.915966i | \(0.631426\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.00980e13 | 1.23042 | ||||||||
\(742\) | 2.16057e12 | 0.261668 | ||||||||
\(743\) | −9.86689e12 | −1.18777 | −0.593883 | − | 0.804552i | \(-0.702406\pi\) | ||||
−0.593883 | + | 0.804552i | \(0.702406\pi\) | |||||||
\(744\) | −5.02939e12 | −0.601779 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −1.00960e12 | −0.119351 | ||||||||
\(747\) | 2.64598e12 | 0.310916 | ||||||||
\(748\) | 6.53317e12 | 0.763074 | ||||||||
\(749\) | −4.11453e12 | −0.477697 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −9.02486e12 | −1.03529 | −0.517644 | − | 0.855596i | \(-0.673191\pi\) | ||||
−0.517644 | + | 0.855596i | \(0.673191\pi\) | |||||||
\(752\) | −1.01564e12 | −0.115813 | ||||||||
\(753\) | 1.61966e12 | 0.183589 | ||||||||
\(754\) | 2.70962e11 | 0.0305307 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 1.59119e12 | 0.177163 | ||||||||
\(757\) | 1.47517e13 | 1.63271 | 0.816356 | − | 0.577549i | \(-0.195991\pi\) | ||||
0.816356 | + | 0.577549i | \(0.195991\pi\) | |||||||
\(758\) | 4.68657e11 | 0.0515637 | ||||||||
\(759\) | −2.46548e12 | −0.269658 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.39852e13 | 1.51160 | 0.755802 | − | 0.654800i | \(-0.227247\pi\) | ||||
0.755802 | + | 0.654800i | \(0.227247\pi\) | |||||||
\(762\) | −3.43822e12 | −0.369434 | ||||||||
\(763\) | 1.99780e12 | 0.213399 | ||||||||
\(764\) | −2.10575e13 | −2.23607 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.00317e13 | −1.05280 | ||||||||
\(767\) | 7.31905e12 | 0.763617 | ||||||||
\(768\) | 3.12899e12 | 0.324548 | ||||||||
\(769\) | −1.52150e13 | −1.56893 | −0.784464 | − | 0.620175i | \(-0.787062\pi\) | ||||
−0.784464 | + | 0.620175i | \(0.787062\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.03607e13 | 1.05595 | ||||||||
\(772\) | −1.12941e13 | −1.14439 | ||||||||
\(773\) | −1.35332e13 | −1.36330 | −0.681652 | − | 0.731677i | \(-0.738738\pi\) | ||||
−0.681652 | + | 0.731677i | \(0.738738\pi\) | |||||||
\(774\) | 5.99280e12 | 0.600199 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −5.15297e12 | −0.510129 | ||||||||
\(777\) | −3.14058e12 | −0.309112 | ||||||||
\(778\) | −1.08385e13 | −1.06062 | ||||||||
\(779\) | 3.85154e13 | 3.74728 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5.19364e12 | −0.499508 | ||||||||
\(782\) | 1.74401e13 | 1.66770 | ||||||||
\(783\) | −3.55246e10 | −0.00337755 | ||||||||
\(784\) | 1.64970e12 | 0.155949 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 1.07534e13 | 1.00495 | ||||||||
\(787\) | −9.11709e12 | −0.847169 | −0.423585 | − | 0.905857i | \(-0.639228\pi\) | ||||
−0.423585 | + | 0.905857i | \(0.639228\pi\) | |||||||
\(788\) | 4.82146e12 | 0.445462 | ||||||||
\(789\) | 2.23658e12 | 0.205465 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −8.51773e12 | −0.773624 | ||||||||
\(792\) | −1.38468e12 | −0.125051 | ||||||||
\(793\) | −1.21657e13 | −1.09247 | ||||||||
\(794\) | −2.61598e13 | −2.33584 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.77003e13 | 1.56269 | ||||||||
\(797\) | −6.45668e12 | −0.566822 | −0.283411 | − | 0.958999i | \(-0.591466\pi\) | ||||
−0.283411 | + | 0.958999i | \(0.591466\pi\) | |||||||
\(798\) | −1.24317e13 | −1.08522 | ||||||||
\(799\) | −5.71587e12 | −0.496160 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.75526e12 | −0.322325 | ||||||||
\(802\) | −1.17130e11 | −0.00999736 | ||||||||
\(803\) | −3.97449e12 | −0.337335 | ||||||||
\(804\) | −8.06358e12 | −0.680575 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 2.74860e13 | 2.29406 | ||||||||
\(807\) | −3.26570e12 | −0.271048 | ||||||||
\(808\) | 1.76630e13 | 1.45785 | ||||||||
\(809\) | −1.53222e13 | −1.25763 | −0.628815 | − | 0.777555i | \(-0.716460\pi\) | ||||
−0.628815 | + | 0.777555i | \(0.716460\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 7.37601e12 | 0.598725 | 0.299363 | − | 0.954139i | \(-0.403226\pi\) | ||||
0.299363 | + | 0.954139i | \(0.403226\pi\) | |||||||
\(812\) | −2.00143e11 | −0.0161562 | ||||||||
\(813\) | −3.53762e12 | −0.283991 | ||||||||
\(814\) | 8.20004e12 | 0.654645 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −1.96095e12 | −0.154832 | ||||||||
\(817\) | −2.80917e13 | −2.20586 | ||||||||
\(818\) | 2.40972e13 | 1.88182 | ||||||||
\(819\) | −2.89828e12 | −0.225093 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.51211e13 | −1.16156 | −0.580779 | − | 0.814062i | \(-0.697252\pi\) | ||||
−0.580779 | + | 0.814062i | \(0.697252\pi\) | |||||||
\(822\) | 9.27514e12 | 0.708594 | ||||||||
\(823\) | 4.00688e12 | 0.304444 | 0.152222 | − | 0.988346i | \(-0.451357\pi\) | ||||
0.152222 | + | 0.988346i | \(0.451357\pi\) | |||||||
\(824\) | 1.74377e13 | 1.31770 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −9.01049e12 | −0.673501 | ||||||||
\(827\) | −1.91371e13 | −1.42266 | −0.711331 | − | 0.702858i | \(-0.751907\pi\) | ||||
−0.711331 | + | 0.702858i | \(0.751907\pi\) | |||||||
\(828\) | −6.65413e12 | −0.491988 | ||||||||
\(829\) | −9.83691e11 | −0.0723375 | −0.0361687 | − | 0.999346i | \(-0.511515\pi\) | ||||
−0.0361687 | + | 0.999346i | \(0.511515\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −3.52650e12 | −0.256531 | ||||||||
\(832\) | −2.47112e13 | −1.78788 | ||||||||
\(833\) | 9.28430e12 | 0.668108 | ||||||||
\(834\) | 6.34493e12 | 0.454129 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 1.94749e13 | 1.37895 | ||||||||
\(837\) | −3.60358e12 | −0.253787 | ||||||||
\(838\) | 3.42814e13 | 2.40138 | ||||||||
\(839\) | 2.22885e12 | 0.155293 | 0.0776464 | − | 0.996981i | \(-0.475259\pi\) | ||||
0.0776464 | + | 0.996981i | \(0.475259\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.45027e13 | −0.999692 | ||||||||
\(842\) | −9.99614e12 | −0.685374 | ||||||||
\(843\) | 2.32019e12 | 0.158234 | ||||||||
\(844\) | −2.01138e13 | −1.36444 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 3.63484e12 | 0.243960 | ||||||||
\(847\) | 7.12218e12 | 0.475486 | ||||||||
\(848\) | 1.01591e12 | 0.0674645 | ||||||||
\(849\) | 1.87358e12 | 0.123762 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.31335e13 | 0.858414 | ||||||||
\(852\) | −1.40172e13 | −0.911348 | ||||||||
\(853\) | −2.18337e13 | −1.41207 | −0.706036 | − | 0.708176i | \(-0.749518\pi\) | ||||
−0.706036 | + | 0.708176i | \(0.749518\pi\) | |||||||
\(854\) | 1.49773e13 | 0.963545 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 9.66359e12 | 0.615186 | ||||||||
\(857\) | 9.68361e12 | 0.613230 | 0.306615 | − | 0.951834i | \(-0.400804\pi\) | ||||
0.306615 | + | 0.951834i | \(0.400804\pi\) | |||||||
\(858\) | 7.56738e12 | 0.476708 | ||||||||
\(859\) | 2.42005e13 | 1.51654 | 0.758271 | − | 0.651940i | \(-0.226044\pi\) | ||||
0.758271 | + | 0.651940i | \(0.226044\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.10545e13 | −0.685527 | ||||||||
\(862\) | −6.65210e12 | −0.410371 | ||||||||
\(863\) | −8.31922e12 | −0.510545 | −0.255272 | − | 0.966869i | \(-0.582165\pi\) | ||||
−0.255272 | + | 0.966869i | \(0.582165\pi\) | |||||||
\(864\) | 3.73860e12 | 0.228243 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −8.46711e12 | −0.511570 | ||||||||
\(867\) | −1.43037e12 | −0.0859732 | ||||||||
\(868\) | −2.03023e13 | −1.21397 | ||||||||
\(869\) | 7.25915e12 | 0.431814 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.46875e13 | 0.864699 | ||||||||
\(872\) | −4.69213e12 | −0.274818 | ||||||||
\(873\) | −3.69212e12 | −0.215135 | ||||||||
\(874\) | 5.19876e13 | 3.01369 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −1.07268e13 | −0.615464 | ||||||||
\(877\) | 5.75721e12 | 0.328635 | 0.164317 | − | 0.986408i | \(-0.447458\pi\) | ||||
0.164317 | + | 0.986408i | \(0.447458\pi\) | |||||||
\(878\) | 3.95023e13 | 2.24335 | ||||||||
\(879\) | −3.85562e12 | −0.217843 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.44674e13 | −0.809093 | −0.404546 | − | 0.914517i | \(-0.632571\pi\) | ||||
−0.404546 | + | 0.914517i | \(0.632571\pi\) | |||||||
\(882\) | −5.90408e12 | −0.328506 | ||||||||
\(883\) | −2.35593e12 | −0.130418 | −0.0652092 | − | 0.997872i | \(-0.520771\pi\) | ||||
−0.0652092 | + | 0.997872i | \(0.520771\pi\) | |||||||
\(884\) | −3.21168e13 | −1.76888 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1.00974e13 | −0.550503 | ||||||||
\(887\) | −8.46394e12 | −0.459110 | −0.229555 | − | 0.973296i | \(-0.573727\pi\) | ||||
−0.229555 | + | 0.973296i | \(0.573727\pi\) | |||||||
\(888\) | 7.37613e12 | 0.398080 | ||||||||
\(889\) | −4.62579e12 | −0.248387 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −9.92128e11 | −0.0527373 | ||||||||
\(892\) | 5.34061e13 | 2.82455 | ||||||||
\(893\) | −1.70386e13 | −0.896608 | ||||||||
\(894\) | 1.92529e13 | 1.00804 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 1.63790e13 | 0.848988 | ||||||||
\(897\) | 1.21202e13 | 0.625092 | ||||||||
\(898\) | −2.14426e13 | −1.10036 | ||||||||
\(899\) | 4.53266e11 | 0.0231438 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.71743e12 | 0.289028 | ||||||||
\(902\) | 2.88632e13 | 1.45183 | ||||||||
\(903\) | 8.06273e12 | 0.403540 | ||||||||
\(904\) | 2.00052e13 | 0.996286 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −3.43808e13 | −1.69527 | ||||||||
\(907\) | 1.03461e13 | 0.507627 | 0.253813 | − | 0.967253i | \(-0.418315\pi\) | ||||
0.253813 | + | 0.967253i | \(0.418315\pi\) | |||||||
\(908\) | 5.24537e12 | 0.256088 | ||||||||
\(909\) | 1.26556e13 | 0.614816 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.71086e13 | 0.822967 | 0.411484 | − | 0.911417i | \(-0.365011\pi\) | ||||
0.411484 | + | 0.911417i | \(0.365011\pi\) | |||||||
\(912\) | −5.84546e12 | −0.279797 | ||||||||
\(913\) | −9.29487e12 | −0.442716 | ||||||||
\(914\) | 1.76794e13 | 0.837933 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.87321e13 | 0.879137 | ||||||||
\(917\) | 1.44676e13 | 0.675670 | ||||||||
\(918\) | 7.01802e12 | 0.326154 | ||||||||
\(919\) | 1.22871e13 | 0.568239 | 0.284120 | − | 0.958789i | \(-0.408299\pi\) | ||||
0.284120 | + | 0.958789i | \(0.408299\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.98973e13 | 0.911226 | ||||||||
\(922\) | 2.23854e13 | 1.02018 | ||||||||
\(923\) | 2.55318e13 | 1.15791 | ||||||||
\(924\) | −5.58958e12 | −0.252264 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −2.88114e13 | −1.28770 | ||||||||
\(927\) | 1.24942e13 | 0.555711 | ||||||||
\(928\) | −4.70250e11 | −0.0208144 | ||||||||
\(929\) | −2.64336e11 | −0.0116436 | −0.00582178 | − | 0.999983i | \(-0.501853\pi\) | ||||
−0.00582178 | + | 0.999983i | \(0.501853\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.76758e13 | 1.20733 | ||||||||
\(932\) | −6.42423e13 | −2.78900 | ||||||||
\(933\) | 2.13011e12 | 0.0920313 | ||||||||
\(934\) | −1.05555e13 | −0.453857 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 6.80704e12 | 0.289879 | ||||||||
\(937\) | 4.09385e13 | 1.73502 | 0.867508 | − | 0.497424i | \(-0.165721\pi\) | ||||
0.867508 | + | 0.497424i | \(0.165721\pi\) | |||||||
\(938\) | −1.80817e13 | −0.762654 | ||||||||
\(939\) | −1.76926e13 | −0.742672 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3.12966e13 | −1.30120 | −0.650601 | − | 0.759420i | \(-0.725483\pi\) | ||||
−0.650601 | + | 0.759420i | \(0.725483\pi\) | |||||||
\(942\) | 9.58694e12 | 0.396690 | ||||||||
\(943\) | 4.62283e13 | 1.90373 | ||||||||
\(944\) | −4.23679e12 | −0.173645 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2.10517e13 | −0.854628 | ||||||||
\(947\) | −2.81260e13 | −1.13641 | −0.568203 | − | 0.822889i | \(-0.692361\pi\) | ||||
−0.568203 | + | 0.822889i | \(0.692361\pi\) | |||||||
\(948\) | 1.95919e13 | 0.787841 | ||||||||
\(949\) | 1.95384e13 | 0.781973 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.59710e13 | −0.633170 | ||||||||
\(952\) | 1.31780e13 | 0.519975 | ||||||||
\(953\) | −4.17759e13 | −1.64062 | −0.820309 | − | 0.571920i | \(-0.806199\pi\) | ||||
−0.820309 | + | 0.571920i | \(0.806199\pi\) | |||||||
\(954\) | −3.63584e12 | −0.142114 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −1.27724e13 | −0.494553 | ||||||||
\(957\) | 1.24792e11 | 0.00480932 | ||||||||
\(958\) | 1.68741e13 | 0.647257 | ||||||||
\(959\) | 1.24788e13 | 0.476419 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.95392e13 | 0.739011 | ||||||||
\(962\) | −4.03111e13 | −1.51753 | ||||||||
\(963\) | 6.92400e12 | 0.259441 | ||||||||
\(964\) | −7.11645e13 | −2.65410 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −1.49212e13 | −0.551323 | ||||||||
\(967\) | −6.22122e12 | −0.228800 | −0.114400 | − | 0.993435i | \(-0.536495\pi\) | ||||
−0.114400 | + | 0.993435i | \(0.536495\pi\) | |||||||
\(968\) | −1.67275e13 | −0.612339 | ||||||||
\(969\) | −3.28975e13 | −1.19869 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 4.60161e12 | 0.166120 | 0.0830602 | − | 0.996545i | \(-0.473531\pi\) | ||||
0.0830602 | + | 0.996545i | \(0.473531\pi\) | |||||||
\(972\) | −2.67768e12 | −0.0962188 | ||||||||
\(973\) | 8.53648e12 | 0.305331 | ||||||||
\(974\) | −7.63813e13 | −2.71939 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 7.04241e12 | 0.248426 | ||||||||
\(977\) | 1.25975e13 | 0.442344 | 0.221172 | − | 0.975235i | \(-0.429012\pi\) | ||||
0.221172 | + | 0.975235i | \(0.429012\pi\) | |||||||
\(978\) | 1.11463e13 | 0.389588 | ||||||||
\(979\) | 1.31916e13 | 0.458961 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.36193e12 | −0.115899 | ||||||||
\(982\) | −4.12562e13 | −1.41575 | ||||||||
\(983\) | −5.00583e12 | −0.170996 | −0.0854978 | − | 0.996338i | \(-0.527248\pi\) | ||||
−0.0854978 | + | 0.996338i | \(0.527248\pi\) | |||||||
\(984\) | 2.59631e13 | 0.882833 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −8.82743e11 | −0.0297432 | ||||||||
\(987\) | 4.89033e12 | 0.164025 | ||||||||
\(988\) | −9.57380e13 | −3.19652 | ||||||||
\(989\) | −3.37172e13 | −1.12065 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.38829e13 | 1.44532 | 0.722660 | − | 0.691204i | \(-0.242919\pi\) | ||||
0.722660 | + | 0.691204i | \(0.242919\pi\) | |||||||
\(992\) | −4.77016e13 | −1.56398 | ||||||||
\(993\) | −5.82503e12 | −0.190119 | ||||||||
\(994\) | −3.14322e13 | −1.02126 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −2.50861e13 | −0.807731 | ||||||||
\(997\) | 2.53017e13 | 0.811000 | 0.405500 | − | 0.914095i | \(-0.367097\pi\) | ||||
0.405500 | + | 0.914095i | \(0.367097\pi\) | |||||||
\(998\) | −3.38010e12 | −0.107855 | ||||||||
\(999\) | 5.28502e12 | 0.167881 |
(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 | 75.10.a.h.1.2 | yes | 2 | |
3.2 | odd | 2 | 225.10.a.g.1.1 | 2 | |||
5.2 | odd | 4 | 75.10.b.g.49.4 | 4 | |||
5.3 | odd | 4 | 75.10.b.g.49.1 | 4 | |||
5.4 | even | 2 | 75.10.a.e.1.1 | ✓ | 2 | ||
15.2 | even | 4 | 225.10.b.j.199.1 | 4 | |||
15.8 | even | 4 | 225.10.b.j.199.4 | 4 | |||
15.14 | odd | 2 | 225.10.a.l.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
75.10.a.e.1.1 | ✓ | 2 | 5.4 | even | 2 | ||
75.10.a.h.1.2 | yes | 2 | 1.1 | even | 1 | trivial | |
75.10.b.g.49.1 | 4 | 5.3 | odd | 4 | |||
75.10.b.g.49.4 | 4 | 5.2 | odd | 4 | |||
225.10.a.g.1.1 | 2 | 3.2 | odd | 2 | |||
225.10.a.l.1.2 | 2 | 15.14 | odd | 2 | |||
225.10.b.j.199.1 | 4 | 15.2 | even | 4 | |||
225.10.b.j.199.4 | 4 | 15.8 | even | 4 |