Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [289,10,Mod(1,289)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(289, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("289.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 289 = 17^{2} \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 289.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: | \(148.845356651\) |
Analytic rank: | \(1\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 5 x^{11} - 4542 x^{10} + 30079 x^{9} + 7481825 x^{8} - 58373994 x^{7} - 5553197164 x^{6} + \cdots + 245077910606835 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{12}\cdot 3^{5}\cdot 17 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Root | \(25.3822\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 289.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 26.3822 | 1.16594 | 0.582971 | − | 0.812493i | \(-0.301890\pi\) | ||||
0.582971 | + | 0.812493i | \(0.301890\pi\) | |||||||
\(3\) | 66.0249 | 0.470611 | 0.235306 | − | 0.971921i | \(-0.424391\pi\) | ||||
0.235306 | + | 0.971921i | \(0.424391\pi\) | |||||||
\(4\) | 184.023 | 0.359420 | ||||||||
\(5\) | −164.991 | −0.118058 | −0.0590289 | − | 0.998256i | \(-0.518800\pi\) | ||||
−0.0590289 | + | 0.998256i | \(0.518800\pi\) | |||||||
\(6\) | 1741.89 | 0.548705 | ||||||||
\(7\) | 5776.54 | 0.909341 | 0.454670 | − | 0.890660i | \(-0.349757\pi\) | ||||
0.454670 | + | 0.890660i | \(0.349757\pi\) | |||||||
\(8\) | −8652.77 | −0.746879 | ||||||||
\(9\) | −15323.7 | −0.778525 | ||||||||
\(10\) | −4352.83 | −0.137649 | ||||||||
\(11\) | 83760.0 | 1.72492 | 0.862461 | − | 0.506124i | \(-0.168922\pi\) | ||||
0.862461 | + | 0.506124i | \(0.168922\pi\) | |||||||
\(12\) | 12150.1 | 0.169147 | ||||||||
\(13\) | −54843.6 | −0.532575 | −0.266287 | − | 0.963894i | \(-0.585797\pi\) | ||||
−0.266287 | + | 0.963894i | \(0.585797\pi\) | |||||||
\(14\) | 152398. | 1.06024 | ||||||||
\(15\) | −10893.5 | −0.0555593 | ||||||||
\(16\) | −322499. | −1.23024 | ||||||||
\(17\) | 0 | 0 | ||||||||
\(18\) | −404274. | −0.907715 | ||||||||
\(19\) | −415353. | −0.731183 | −0.365592 | − | 0.930775i | \(-0.619133\pi\) | ||||
−0.365592 | + | 0.930775i | \(0.619133\pi\) | |||||||
\(20\) | −30362.1 | −0.0424323 | ||||||||
\(21\) | 381396. | 0.427946 | ||||||||
\(22\) | 2.20978e6 | 2.01116 | ||||||||
\(23\) | −645136. | −0.480702 | −0.240351 | − | 0.970686i | \(-0.577263\pi\) | ||||
−0.240351 | + | 0.970686i | \(0.577263\pi\) | |||||||
\(24\) | −571298. | −0.351490 | ||||||||
\(25\) | −1.92590e6 | −0.986062 | ||||||||
\(26\) | −1.44690e6 | −0.620951 | ||||||||
\(27\) | −2.31132e6 | −0.836994 | ||||||||
\(28\) | 1.06302e6 | 0.326835 | ||||||||
\(29\) | 2.89695e6 | 0.760589 | 0.380294 | − | 0.924866i | \(-0.375823\pi\) | ||||
0.380294 | + | 0.924866i | \(0.375823\pi\) | |||||||
\(30\) | −287395. | −0.0647789 | ||||||||
\(31\) | −3.57166e6 | −0.694613 | −0.347306 | − | 0.937752i | \(-0.612904\pi\) | ||||
−0.347306 | + | 0.937752i | \(0.612904\pi\) | |||||||
\(32\) | −4.07804e6 | −0.687506 | ||||||||
\(33\) | 5.53025e6 | 0.811768 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −953076. | −0.107355 | ||||||||
\(36\) | −2.81992e6 | −0.279817 | ||||||||
\(37\) | 1.64472e7 | 1.44273 | 0.721365 | − | 0.692555i | \(-0.243515\pi\) | ||||
0.721365 | + | 0.692555i | \(0.243515\pi\) | |||||||
\(38\) | −1.09579e7 | −0.852517 | ||||||||
\(39\) | −3.62104e6 | −0.250636 | ||||||||
\(40\) | 1.42763e6 | 0.0881749 | ||||||||
\(41\) | −2.19135e7 | −1.21111 | −0.605557 | − | 0.795802i | \(-0.707050\pi\) | ||||
−0.605557 | + | 0.795802i | \(0.707050\pi\) | |||||||
\(42\) | 1.00621e7 | 0.498960 | ||||||||
\(43\) | 1.63180e7 | 0.727877 | 0.363938 | − | 0.931423i | \(-0.381432\pi\) | ||||
0.363938 | + | 0.931423i | \(0.381432\pi\) | |||||||
\(44\) | 1.54138e7 | 0.619971 | ||||||||
\(45\) | 2.52827e6 | 0.0919110 | ||||||||
\(46\) | −1.70201e7 | −0.560471 | ||||||||
\(47\) | 1.67476e7 | 0.500625 | 0.250313 | − | 0.968165i | \(-0.419467\pi\) | ||||
0.250313 | + | 0.968165i | \(0.419467\pi\) | |||||||
\(48\) | −2.12930e7 | −0.578963 | ||||||||
\(49\) | −6.98519e6 | −0.173100 | ||||||||
\(50\) | −5.08097e7 | −1.14969 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.00925e7 | −0.191418 | ||||||||
\(53\) | −1.54682e7 | −0.269277 | −0.134638 | − | 0.990895i | \(-0.542987\pi\) | ||||
−0.134638 | + | 0.990895i | \(0.542987\pi\) | |||||||
\(54\) | −6.09777e7 | −0.975886 | ||||||||
\(55\) | −1.38196e7 | −0.203640 | ||||||||
\(56\) | −4.99831e7 | −0.679167 | ||||||||
\(57\) | −2.74237e7 | −0.344103 | ||||||||
\(58\) | 7.64280e7 | 0.886802 | ||||||||
\(59\) | −8.58435e7 | −0.922302 | −0.461151 | − | 0.887322i | \(-0.652563\pi\) | ||||
−0.461151 | + | 0.887322i | \(0.652563\pi\) | |||||||
\(60\) | −2.00466e6 | −0.0199691 | ||||||||
\(61\) | −1.58254e8 | −1.46342 | −0.731711 | − | 0.681615i | \(-0.761278\pi\) | ||||
−0.731711 | + | 0.681615i | \(0.761278\pi\) | |||||||
\(62\) | −9.42285e7 | −0.809878 | ||||||||
\(63\) | −8.85180e7 | −0.707945 | ||||||||
\(64\) | 5.75318e7 | 0.428645 | ||||||||
\(65\) | 9.04868e6 | 0.0628746 | ||||||||
\(66\) | 1.45900e8 | 0.946474 | ||||||||
\(67\) | −6.70561e7 | −0.406538 | −0.203269 | − | 0.979123i | \(-0.565157\pi\) | ||||
−0.203269 | + | 0.979123i | \(0.565157\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −4.25951e7 | −0.226224 | ||||||||
\(70\) | −2.51443e7 | −0.125169 | ||||||||
\(71\) | −9.91611e7 | −0.463104 | −0.231552 | − | 0.972823i | \(-0.574380\pi\) | ||||
−0.231552 | + | 0.972823i | \(0.574380\pi\) | |||||||
\(72\) | 1.32593e8 | 0.581464 | ||||||||
\(73\) | 1.78647e8 | 0.736279 | 0.368139 | − | 0.929771i | \(-0.379995\pi\) | ||||
0.368139 | + | 0.929771i | \(0.379995\pi\) | |||||||
\(74\) | 4.33915e8 | 1.68214 | ||||||||
\(75\) | −1.27158e8 | −0.464052 | ||||||||
\(76\) | −7.64345e7 | −0.262802 | ||||||||
\(77\) | 4.83843e8 | 1.56854 | ||||||||
\(78\) | −9.55312e7 | −0.292227 | ||||||||
\(79\) | 3.21915e8 | 0.929865 | 0.464932 | − | 0.885346i | \(-0.346079\pi\) | ||||
0.464932 | + | 0.885346i | \(0.346079\pi\) | |||||||
\(80\) | 5.32094e7 | 0.145239 | ||||||||
\(81\) | 1.49012e8 | 0.384627 | ||||||||
\(82\) | −5.78128e8 | −1.41209 | ||||||||
\(83\) | −7.48591e8 | −1.73138 | −0.865692 | − | 0.500577i | \(-0.833121\pi\) | ||||
−0.865692 | + | 0.500577i | \(0.833121\pi\) | |||||||
\(84\) | 7.01856e7 | 0.153812 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 4.30505e8 | 0.848662 | ||||||||
\(87\) | 1.91271e8 | 0.357942 | ||||||||
\(88\) | −7.24756e8 | −1.28831 | ||||||||
\(89\) | −1.10368e9 | −1.86462 | −0.932309 | − | 0.361662i | \(-0.882209\pi\) | ||||
−0.932309 | + | 0.361662i | \(0.882209\pi\) | |||||||
\(90\) | 6.67015e7 | 0.107163 | ||||||||
\(91\) | −3.16806e8 | −0.484292 | ||||||||
\(92\) | −1.18720e8 | −0.172774 | ||||||||
\(93\) | −2.35819e8 | −0.326893 | ||||||||
\(94\) | 4.41840e8 | 0.583700 | ||||||||
\(95\) | 6.85294e7 | 0.0863219 | ||||||||
\(96\) | −2.69252e8 | −0.323548 | ||||||||
\(97\) | −5.39182e8 | −0.618391 | −0.309195 | − | 0.950999i | \(-0.600060\pi\) | ||||
−0.309195 | + | 0.950999i | \(0.600060\pi\) | |||||||
\(98\) | −1.84285e8 | −0.201824 | ||||||||
\(99\) | −1.28351e9 | −1.34290 | ||||||||
\(100\) | −3.54411e8 | −0.354411 | ||||||||
\(101\) | −7.02632e8 | −0.671865 | −0.335932 | − | 0.941886i | \(-0.609051\pi\) | ||||
−0.335932 | + | 0.941886i | \(0.609051\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.52332e9 | −1.33360 | −0.666799 | − | 0.745238i | \(-0.732336\pi\) | ||||
−0.666799 | + | 0.745238i | \(0.732336\pi\) | |||||||
\(104\) | 4.74549e8 | 0.397769 | ||||||||
\(105\) | −6.29268e7 | −0.0505223 | ||||||||
\(106\) | −4.08086e8 | −0.313961 | ||||||||
\(107\) | 2.26705e9 | 1.67199 | 0.835996 | − | 0.548736i | \(-0.184891\pi\) | ||||
0.835996 | + | 0.548736i | \(0.184891\pi\) | |||||||
\(108\) | −4.25335e8 | −0.300832 | ||||||||
\(109\) | −8.97007e8 | −0.608663 | −0.304331 | − | 0.952566i | \(-0.598433\pi\) | ||||
−0.304331 | + | 0.952566i | \(0.598433\pi\) | |||||||
\(110\) | −3.64593e8 | −0.237433 | ||||||||
\(111\) | 1.08593e9 | 0.678965 | ||||||||
\(112\) | −1.86293e9 | −1.11870 | ||||||||
\(113\) | −2.03489e9 | −1.17405 | −0.587026 | − | 0.809568i | \(-0.699701\pi\) | ||||
−0.587026 | + | 0.809568i | \(0.699701\pi\) | |||||||
\(114\) | −7.23498e8 | −0.401204 | ||||||||
\(115\) | 1.06442e8 | 0.0567506 | ||||||||
\(116\) | 5.33105e8 | 0.273371 | ||||||||
\(117\) | 8.40407e8 | 0.414623 | ||||||||
\(118\) | −2.26474e9 | −1.07535 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 9.42590e7 | 0.0414961 | ||||||||
\(121\) | 4.65779e9 | 1.97536 | ||||||||
\(122\) | −4.17509e9 | −1.70627 | ||||||||
\(123\) | −1.44684e9 | −0.569964 | ||||||||
\(124\) | −6.57268e8 | −0.249658 | ||||||||
\(125\) | 6.40004e8 | 0.234470 | ||||||||
\(126\) | −2.33530e9 | −0.825422 | ||||||||
\(127\) | −5.08437e9 | −1.73429 | −0.867143 | − | 0.498059i | \(-0.834046\pi\) | ||||
−0.867143 | + | 0.498059i | \(0.834046\pi\) | |||||||
\(128\) | 3.60577e9 | 1.18728 | ||||||||
\(129\) | 1.07739e9 | 0.342547 | ||||||||
\(130\) | 2.38725e8 | 0.0733081 | ||||||||
\(131\) | −1.56203e8 | −0.0463413 | −0.0231706 | − | 0.999732i | \(-0.507376\pi\) | ||||
−0.0231706 | + | 0.999732i | \(0.507376\pi\) | |||||||
\(132\) | 1.01769e9 | 0.291765 | ||||||||
\(133\) | −2.39930e9 | −0.664895 | ||||||||
\(134\) | −1.76909e9 | −0.474000 | ||||||||
\(135\) | 3.81346e8 | 0.0988136 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.88812e9 | 0.457918 | 0.228959 | − | 0.973436i | \(-0.426468\pi\) | ||||
0.228959 | + | 0.973436i | \(0.426468\pi\) | |||||||
\(138\) | −1.12375e9 | −0.263764 | ||||||||
\(139\) | −8.04015e9 | −1.82683 | −0.913414 | − | 0.407033i | \(-0.866563\pi\) | ||||
−0.913414 | + | 0.407033i | \(0.866563\pi\) | |||||||
\(140\) | −1.75388e8 | −0.0385854 | ||||||||
\(141\) | 1.10576e9 | 0.235600 | ||||||||
\(142\) | −2.61609e9 | −0.539952 | ||||||||
\(143\) | −4.59370e9 | −0.918650 | ||||||||
\(144\) | 4.94189e9 | 0.957771 | ||||||||
\(145\) | −4.77970e8 | −0.0897934 | ||||||||
\(146\) | 4.71310e9 | 0.858458 | ||||||||
\(147\) | −4.61197e8 | −0.0814626 | ||||||||
\(148\) | 3.02667e9 | 0.518546 | ||||||||
\(149\) | 1.09919e10 | 1.82699 | 0.913495 | − | 0.406850i | \(-0.133373\pi\) | ||||
0.913495 | + | 0.406850i | \(0.133373\pi\) | |||||||
\(150\) | −3.35470e9 | −0.541058 | ||||||||
\(151\) | 1.72635e8 | 0.0270229 | 0.0135114 | − | 0.999909i | \(-0.495699\pi\) | ||||
0.0135114 | + | 0.999909i | \(0.495699\pi\) | |||||||
\(152\) | 3.59396e9 | 0.546105 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1.27649e10 | 1.82883 | ||||||||
\(155\) | 5.89291e8 | 0.0820045 | ||||||||
\(156\) | −6.66355e8 | −0.0900835 | ||||||||
\(157\) | 1.63553e9 | 0.214837 | 0.107418 | − | 0.994214i | \(-0.465742\pi\) | ||||
0.107418 | + | 0.994214i | \(0.465742\pi\) | |||||||
\(158\) | 8.49285e9 | 1.08417 | ||||||||
\(159\) | −1.02129e9 | −0.126725 | ||||||||
\(160\) | 6.72839e8 | 0.0811654 | ||||||||
\(161\) | −3.72665e9 | −0.437122 | ||||||||
\(162\) | 3.93128e9 | 0.448452 | ||||||||
\(163\) | −5.08177e9 | −0.563859 | −0.281930 | − | 0.959435i | \(-0.590974\pi\) | ||||
−0.281930 | + | 0.959435i | \(0.590974\pi\) | |||||||
\(164\) | −4.03259e9 | −0.435298 | ||||||||
\(165\) | −9.12440e8 | −0.0958355 | ||||||||
\(166\) | −1.97495e10 | −2.01869 | ||||||||
\(167\) | −2.55962e9 | −0.254655 | −0.127327 | − | 0.991861i | \(-0.540640\pi\) | ||||
−0.127327 | + | 0.991861i | \(0.540640\pi\) | |||||||
\(168\) | −3.30013e9 | −0.319624 | ||||||||
\(169\) | −7.59668e9 | −0.716364 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.36475e9 | 0.569245 | ||||||||
\(172\) | 3.00288e9 | 0.261614 | ||||||||
\(173\) | −1.27890e9 | −0.108549 | −0.0542747 | − | 0.998526i | \(-0.517285\pi\) | ||||
−0.0542747 | + | 0.998526i | \(0.517285\pi\) | |||||||
\(174\) | 5.04615e9 | 0.417339 | ||||||||
\(175\) | −1.11251e10 | −0.896667 | ||||||||
\(176\) | −2.70125e10 | −2.12206 | ||||||||
\(177\) | −5.66781e9 | −0.434046 | ||||||||
\(178\) | −2.91177e10 | −2.17404 | ||||||||
\(179\) | −1.05831e9 | −0.0770501 | −0.0385250 | − | 0.999258i | \(-0.512266\pi\) | ||||
−0.0385250 | + | 0.999258i | \(0.512266\pi\) | |||||||
\(180\) | 4.65260e8 | 0.0330346 | ||||||||
\(181\) | 3.84880e9 | 0.266546 | 0.133273 | − | 0.991079i | \(-0.457451\pi\) | ||||
0.133273 | + | 0.991079i | \(0.457451\pi\) | |||||||
\(182\) | −8.35806e9 | −0.564656 | ||||||||
\(183\) | −1.04487e10 | −0.688703 | ||||||||
\(184\) | 5.58221e9 | 0.359026 | ||||||||
\(185\) | −2.71364e9 | −0.170326 | ||||||||
\(186\) | −6.22143e9 | −0.381138 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 3.08195e9 | 0.179935 | ||||||||
\(189\) | −1.33514e10 | −0.761112 | ||||||||
\(190\) | 1.80796e9 | 0.100646 | ||||||||
\(191\) | 3.30020e10 | 1.79428 | 0.897139 | − | 0.441749i | \(-0.145642\pi\) | ||||
0.897139 | + | 0.441749i | \(0.145642\pi\) | |||||||
\(192\) | 3.79853e9 | 0.201725 | ||||||||
\(193\) | −2.85018e10 | −1.47865 | −0.739323 | − | 0.673351i | \(-0.764854\pi\) | ||||
−0.739323 | + | 0.673351i | \(0.764854\pi\) | |||||||
\(194\) | −1.42248e10 | −0.721007 | ||||||||
\(195\) | 5.97439e8 | 0.0295895 | ||||||||
\(196\) | −1.28544e9 | −0.0622154 | ||||||||
\(197\) | 3.06795e10 | 1.45128 | 0.725638 | − | 0.688077i | \(-0.241545\pi\) | ||||
0.725638 | + | 0.688077i | \(0.241545\pi\) | |||||||
\(198\) | −3.38620e10 | −1.56574 | ||||||||
\(199\) | 2.76572e10 | 1.25017 | 0.625086 | − | 0.780556i | \(-0.285064\pi\) | ||||
0.625086 | + | 0.780556i | \(0.285064\pi\) | |||||||
\(200\) | 1.66644e10 | 0.736469 | ||||||||
\(201\) | −4.42737e9 | −0.191322 | ||||||||
\(202\) | −1.85370e10 | −0.783355 | ||||||||
\(203\) | 1.67343e10 | 0.691634 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.61553e9 | 0.142981 | ||||||||
\(206\) | −4.01887e10 | −1.55490 | ||||||||
\(207\) | 9.88588e9 | 0.374239 | ||||||||
\(208\) | 1.76870e10 | 0.655193 | ||||||||
\(209\) | −3.47900e10 | −1.26123 | ||||||||
\(210\) | −1.66015e9 | −0.0589061 | ||||||||
\(211\) | 2.15664e10 | 0.749041 | 0.374521 | − | 0.927219i | \(-0.377807\pi\) | ||||
0.374521 | + | 0.927219i | \(0.377807\pi\) | |||||||
\(212\) | −2.84651e9 | −0.0967835 | ||||||||
\(213\) | −6.54710e9 | −0.217942 | ||||||||
\(214\) | 5.98099e10 | 1.94945 | ||||||||
\(215\) | −2.69231e9 | −0.0859316 | ||||||||
\(216\) | 1.99993e10 | 0.625133 | ||||||||
\(217\) | −2.06319e10 | −0.631640 | ||||||||
\(218\) | −2.36651e10 | −0.709665 | ||||||||
\(219\) | 1.17951e10 | 0.346501 | ||||||||
\(220\) | −2.54313e9 | −0.0731925 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 2.86492e10 | 0.791634 | ||||||||
\(223\) | −6.34535e9 | −0.171824 | −0.0859119 | − | 0.996303i | \(-0.527380\pi\) | ||||
−0.0859119 | + | 0.996303i | \(0.527380\pi\) | |||||||
\(224\) | −2.35570e10 | −0.625177 | ||||||||
\(225\) | 2.95120e10 | 0.767674 | ||||||||
\(226\) | −5.36849e10 | −1.36888 | ||||||||
\(227\) | −1.64079e10 | −0.410145 | −0.205073 | − | 0.978747i | \(-0.565743\pi\) | ||||
−0.205073 | + | 0.978747i | \(0.565743\pi\) | |||||||
\(228\) | −5.04658e9 | −0.123678 | ||||||||
\(229\) | −7.28411e10 | −1.75032 | −0.875159 | − | 0.483835i | \(-0.839243\pi\) | ||||
−0.875159 | + | 0.483835i | \(0.839243\pi\) | |||||||
\(230\) | 2.80817e9 | 0.0661679 | ||||||||
\(231\) | 3.19457e10 | 0.738173 | ||||||||
\(232\) | −2.50666e10 | −0.568068 | ||||||||
\(233\) | 5.81677e10 | 1.29295 | 0.646473 | − | 0.762937i | \(-0.276243\pi\) | ||||
0.646473 | + | 0.762937i | \(0.276243\pi\) | |||||||
\(234\) | 2.21718e10 | 0.483426 | ||||||||
\(235\) | −2.76320e9 | −0.0591027 | ||||||||
\(236\) | −1.57972e10 | −0.331494 | ||||||||
\(237\) | 2.12544e10 | 0.437605 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.95985e10 | 0.983281 | 0.491640 | − | 0.870798i | \(-0.336397\pi\) | ||||
0.491640 | + | 0.870798i | \(0.336397\pi\) | |||||||
\(240\) | 3.51315e9 | 0.0683511 | ||||||||
\(241\) | 2.91135e10 | 0.555927 | 0.277963 | − | 0.960592i | \(-0.410341\pi\) | ||||
0.277963 | + | 0.960592i | \(0.410341\pi\) | |||||||
\(242\) | 1.22883e11 | 2.30315 | ||||||||
\(243\) | 5.53321e10 | 1.01800 | ||||||||
\(244\) | −2.91223e10 | −0.525983 | ||||||||
\(245\) | 1.15249e9 | 0.0204357 | ||||||||
\(246\) | −3.81709e10 | −0.664544 | ||||||||
\(247\) | 2.27795e10 | 0.389410 | ||||||||
\(248\) | 3.09048e10 | 0.518792 | ||||||||
\(249\) | −4.94257e10 | −0.814809 | ||||||||
\(250\) | 1.68847e10 | 0.273379 | ||||||||
\(251\) | −1.03901e11 | −1.65229 | −0.826144 | − | 0.563458i | \(-0.809470\pi\) | ||||
−0.826144 | + | 0.563458i | \(0.809470\pi\) | |||||||
\(252\) | −1.62894e10 | −0.254449 | ||||||||
\(253\) | −5.40366e10 | −0.829174 | ||||||||
\(254\) | −1.34137e11 | −2.02208 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 6.56722e10 | 0.955656 | ||||||||
\(257\) | −8.68301e10 | −1.24157 | −0.620785 | − | 0.783981i | \(-0.713186\pi\) | ||||
−0.620785 | + | 0.783981i | \(0.713186\pi\) | |||||||
\(258\) | 2.84240e10 | 0.399390 | ||||||||
\(259\) | 9.50081e10 | 1.31193 | ||||||||
\(260\) | 1.66517e9 | 0.0225984 | ||||||||
\(261\) | −4.43920e10 | −0.592137 | ||||||||
\(262\) | −4.12098e9 | −0.0540312 | ||||||||
\(263\) | 1.65728e10 | 0.213596 | 0.106798 | − | 0.994281i | \(-0.465940\pi\) | ||||
0.106798 | + | 0.994281i | \(0.465940\pi\) | |||||||
\(264\) | −4.78519e10 | −0.606292 | ||||||||
\(265\) | 2.55211e9 | 0.0317902 | ||||||||
\(266\) | −6.32990e10 | −0.775229 | ||||||||
\(267\) | −7.28707e10 | −0.877510 | ||||||||
\(268\) | −1.23399e10 | −0.146118 | ||||||||
\(269\) | 4.82317e10 | 0.561626 | 0.280813 | − | 0.959762i | \(-0.409396\pi\) | ||||
0.280813 | + | 0.959762i | \(0.409396\pi\) | |||||||
\(270\) | 1.00608e10 | 0.115211 | ||||||||
\(271\) | 8.23997e10 | 0.928034 | 0.464017 | − | 0.885826i | \(-0.346408\pi\) | ||||
0.464017 | + | 0.885826i | \(0.346408\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.09171e10 | −0.227913 | ||||||||
\(274\) | 4.98129e10 | 0.533905 | ||||||||
\(275\) | −1.61314e11 | −1.70088 | ||||||||
\(276\) | −7.83847e9 | −0.0813094 | ||||||||
\(277\) | −7.60846e9 | −0.0776493 | −0.0388247 | − | 0.999246i | \(-0.512361\pi\) | ||||
−0.0388247 | + | 0.999246i | \(0.512361\pi\) | |||||||
\(278\) | −2.12117e11 | −2.12997 | ||||||||
\(279\) | 5.47311e10 | 0.540774 | ||||||||
\(280\) | 8.24675e9 | 0.0801810 | ||||||||
\(281\) | −1.09198e10 | −0.104481 | −0.0522405 | − | 0.998635i | \(-0.516636\pi\) | ||||
−0.0522405 | + | 0.998635i | \(0.516636\pi\) | |||||||
\(282\) | 2.91724e10 | 0.274696 | ||||||||
\(283\) | 8.41546e10 | 0.779900 | 0.389950 | − | 0.920836i | \(-0.372492\pi\) | ||||
0.389950 | + | 0.920836i | \(0.372492\pi\) | |||||||
\(284\) | −1.82479e10 | −0.166449 | ||||||||
\(285\) | 4.52465e9 | 0.0406240 | ||||||||
\(286\) | −1.21192e11 | −1.07109 | ||||||||
\(287\) | −1.26584e11 | −1.10131 | ||||||||
\(288\) | 6.24907e10 | 0.535241 | ||||||||
\(289\) | 0 | 0 | ||||||||
\(290\) | −1.26099e10 | −0.104694 | ||||||||
\(291\) | −3.55995e10 | −0.291022 | ||||||||
\(292\) | 3.28751e10 | 0.264633 | ||||||||
\(293\) | −2.03804e11 | −1.61550 | −0.807751 | − | 0.589524i | \(-0.799316\pi\) | ||||
−0.807751 | + | 0.589524i | \(0.799316\pi\) | |||||||
\(294\) | −1.21674e10 | −0.0949806 | ||||||||
\(295\) | 1.41634e10 | 0.108885 | ||||||||
\(296\) | −1.42314e11 | −1.07755 | ||||||||
\(297\) | −1.93596e11 | −1.44375 | ||||||||
\(298\) | 2.89992e11 | 2.13016 | ||||||||
\(299\) | 3.53816e10 | 0.256010 | ||||||||
\(300\) | −2.33999e10 | −0.166790 | ||||||||
\(301\) | 9.42614e10 | 0.661888 | ||||||||
\(302\) | 4.55449e9 | 0.0315071 | ||||||||
\(303\) | −4.63912e10 | −0.316187 | ||||||||
\(304\) | 1.33951e11 | 0.899529 | ||||||||
\(305\) | 2.61104e10 | 0.172768 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.05276e11 | 1.31891 | 0.659455 | − | 0.751744i | \(-0.270787\pi\) | ||||
0.659455 | + | 0.751744i | \(0.270787\pi\) | |||||||
\(308\) | 8.90382e10 | 0.563765 | ||||||||
\(309\) | −1.00577e11 | −0.627606 | ||||||||
\(310\) | 1.55468e10 | 0.0956124 | ||||||||
\(311\) | −6.35962e9 | −0.0385487 | −0.0192743 | − | 0.999814i | \(-0.506136\pi\) | ||||
−0.0192743 | + | 0.999814i | \(0.506136\pi\) | |||||||
\(312\) | 3.13320e10 | 0.187195 | ||||||||
\(313\) | −3.19617e11 | −1.88227 | −0.941133 | − | 0.338037i | \(-0.890237\pi\) | ||||
−0.941133 | + | 0.338037i | \(0.890237\pi\) | |||||||
\(314\) | 4.31488e10 | 0.250487 | ||||||||
\(315\) | 1.46047e10 | 0.0835784 | ||||||||
\(316\) | 5.92398e10 | 0.334212 | ||||||||
\(317\) | −5.43063e10 | −0.302053 | −0.151027 | − | 0.988530i | \(-0.548258\pi\) | ||||
−0.151027 | + | 0.988530i | \(0.548258\pi\) | |||||||
\(318\) | −2.69439e10 | −0.147754 | ||||||||
\(319\) | 2.42648e11 | 1.31196 | ||||||||
\(320\) | −9.49222e9 | −0.0506049 | ||||||||
\(321\) | 1.49682e11 | 0.786858 | ||||||||
\(322\) | −9.83175e10 | −0.509659 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 2.74217e10 | 0.138242 | ||||||||
\(325\) | 1.05623e11 | 0.525152 | ||||||||
\(326\) | −1.34069e11 | −0.657427 | ||||||||
\(327\) | −5.92248e10 | −0.286443 | ||||||||
\(328\) | 1.89613e11 | 0.904555 | ||||||||
\(329\) | 9.67433e10 | 0.455239 | ||||||||
\(330\) | −2.40722e10 | −0.111739 | ||||||||
\(331\) | −1.24105e11 | −0.568283 | −0.284141 | − | 0.958782i | \(-0.591708\pi\) | ||||
−0.284141 | + | 0.958782i | \(0.591708\pi\) | |||||||
\(332\) | −1.37758e11 | −0.622294 | ||||||||
\(333\) | −2.52033e11 | −1.12320 | ||||||||
\(334\) | −6.75286e10 | −0.296913 | ||||||||
\(335\) | 1.10636e10 | 0.0479950 | ||||||||
\(336\) | −1.23000e11 | −0.526475 | ||||||||
\(337\) | 1.12724e11 | 0.476081 | 0.238041 | − | 0.971255i | \(-0.423495\pi\) | ||||
0.238041 | + | 0.971255i | \(0.423495\pi\) | |||||||
\(338\) | −2.00418e11 | −0.835239 | ||||||||
\(339\) | −1.34353e11 | −0.552522 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.99162e11 | −1.19815 | ||||||||
\(342\) | 1.67916e11 | 0.663706 | ||||||||
\(343\) | −2.73454e11 | −1.06675 | ||||||||
\(344\) | −1.41196e11 | −0.543636 | ||||||||
\(345\) | 7.02779e9 | 0.0267075 | ||||||||
\(346\) | −3.37401e10 | −0.126562 | ||||||||
\(347\) | 2.77880e11 | 1.02890 | 0.514452 | − | 0.857519i | \(-0.327995\pi\) | ||||
0.514452 | + | 0.857519i | \(0.327995\pi\) | |||||||
\(348\) | 3.51982e10 | 0.128651 | ||||||||
\(349\) | −2.69627e10 | −0.0972857 | −0.0486429 | − | 0.998816i | \(-0.515490\pi\) | ||||
−0.0486429 | + | 0.998816i | \(0.515490\pi\) | |||||||
\(350\) | −2.93504e11 | −1.04546 | ||||||||
\(351\) | 1.26761e11 | 0.445762 | ||||||||
\(352\) | −3.41576e11 | −1.18589 | ||||||||
\(353\) | 4.08754e11 | 1.40112 | 0.700560 | − | 0.713593i | \(-0.252934\pi\) | ||||
0.700560 | + | 0.713593i | \(0.252934\pi\) | |||||||
\(354\) | −1.49530e11 | −0.506072 | ||||||||
\(355\) | 1.63607e10 | 0.0546731 | ||||||||
\(356\) | −2.03103e11 | −0.670181 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −2.79205e10 | −0.0898359 | ||||||||
\(359\) | 3.75018e11 | 1.19159 | 0.595796 | − | 0.803136i | \(-0.296837\pi\) | ||||
0.595796 | + | 0.803136i | \(0.296837\pi\) | |||||||
\(360\) | −2.18765e10 | −0.0686464 | ||||||||
\(361\) | −1.50169e11 | −0.465371 | ||||||||
\(362\) | 1.01540e11 | 0.310777 | ||||||||
\(363\) | 3.07530e11 | 0.929625 | ||||||||
\(364\) | −5.82996e10 | −0.174064 | ||||||||
\(365\) | −2.94751e10 | −0.0869235 | ||||||||
\(366\) | −2.75660e11 | −0.802987 | ||||||||
\(367\) | −3.22410e11 | −0.927707 | −0.463853 | − | 0.885912i | \(-0.653534\pi\) | ||||
−0.463853 | + | 0.885912i | \(0.653534\pi\) | |||||||
\(368\) | 2.08056e11 | 0.591378 | ||||||||
\(369\) | 3.35797e11 | 0.942882 | ||||||||
\(370\) | −7.15920e10 | −0.198590 | ||||||||
\(371\) | −8.93528e10 | −0.244864 | ||||||||
\(372\) | −4.33961e10 | −0.117492 | ||||||||
\(373\) | −2.11324e11 | −0.565275 | −0.282638 | − | 0.959227i | \(-0.591209\pi\) | ||||
−0.282638 | + | 0.959227i | \(0.591209\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 4.22562e10 | 0.110344 | ||||||||
\(376\) | −1.44913e11 | −0.373906 | ||||||||
\(377\) | −1.58879e11 | −0.405070 | ||||||||
\(378\) | −3.52240e11 | −0.887413 | ||||||||
\(379\) | 4.67354e11 | 1.16351 | 0.581755 | − | 0.813364i | \(-0.302366\pi\) | ||||
0.581755 | + | 0.813364i | \(0.302366\pi\) | |||||||
\(380\) | 1.26110e10 | 0.0310258 | ||||||||
\(381\) | −3.35695e11 | −0.816175 | ||||||||
\(382\) | 8.70666e11 | 2.09202 | ||||||||
\(383\) | 6.63614e11 | 1.57587 | 0.787937 | − | 0.615756i | \(-0.211149\pi\) | ||||
0.787937 | + | 0.615756i | \(0.211149\pi\) | |||||||
\(384\) | 2.38071e11 | 0.558748 | ||||||||
\(385\) | −7.98296e10 | −0.185179 | ||||||||
\(386\) | −7.51942e11 | −1.72402 | ||||||||
\(387\) | −2.50052e11 | −0.566671 | ||||||||
\(388\) | −9.92220e10 | −0.222262 | ||||||||
\(389\) | −1.12068e9 | −0.00248146 | −0.00124073 | − | 0.999999i | \(-0.500395\pi\) | ||||
−0.00124073 | + | 0.999999i | \(0.500395\pi\) | |||||||
\(390\) | 1.57618e10 | 0.0344996 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 6.04412e10 | 0.129284 | ||||||||
\(393\) | −1.03133e10 | −0.0218087 | ||||||||
\(394\) | 8.09393e11 | 1.69210 | ||||||||
\(395\) | −5.31131e10 | −0.109778 | ||||||||
\(396\) | −2.36196e11 | −0.482663 | ||||||||
\(397\) | 5.23692e11 | 1.05808 | 0.529040 | − | 0.848597i | \(-0.322552\pi\) | ||||
0.529040 | + | 0.848597i | \(0.322552\pi\) | |||||||
\(398\) | 7.29659e11 | 1.45763 | ||||||||
\(399\) | −1.58414e11 | −0.312907 | ||||||||
\(400\) | 6.21102e11 | 1.21309 | ||||||||
\(401\) | 4.63692e11 | 0.895529 | 0.447765 | − | 0.894152i | \(-0.352220\pi\) | ||||
0.447765 | + | 0.894152i | \(0.352220\pi\) | |||||||
\(402\) | −1.16804e11 | −0.223070 | ||||||||
\(403\) | 1.95883e11 | 0.369933 | ||||||||
\(404\) | −1.29301e11 | −0.241482 | ||||||||
\(405\) | −2.45856e10 | −0.0454082 | ||||||||
\(406\) | 4.41490e11 | 0.806405 | ||||||||
\(407\) | 1.37762e12 | 2.48860 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −9.57093e11 | −1.69122 | −0.845608 | − | 0.533804i | \(-0.820762\pi\) | ||||
−0.845608 | + | 0.533804i | \(0.820762\pi\) | |||||||
\(410\) | 9.53858e10 | 0.166708 | ||||||||
\(411\) | 1.24663e11 | 0.215501 | ||||||||
\(412\) | −2.80327e11 | −0.479322 | ||||||||
\(413\) | −4.95878e11 | −0.838687 | ||||||||
\(414\) | 2.60812e11 | 0.436341 | ||||||||
\(415\) | 1.23511e11 | 0.204403 | ||||||||
\(416\) | 2.23654e11 | 0.366148 | ||||||||
\(417\) | −5.30850e11 | −0.859725 | ||||||||
\(418\) | −9.17838e11 | −1.47053 | ||||||||
\(419\) | 9.55806e11 | 1.51498 | 0.757490 | − | 0.652847i | \(-0.226426\pi\) | ||||
0.757490 | + | 0.652847i | \(0.226426\pi\) | |||||||
\(420\) | −1.15800e10 | −0.0181587 | ||||||||
\(421\) | −2.81196e11 | −0.436255 | −0.218127 | − | 0.975920i | \(-0.569995\pi\) | ||||
−0.218127 | + | 0.975920i | \(0.569995\pi\) | |||||||
\(422\) | 5.68969e11 | 0.873338 | ||||||||
\(423\) | −2.56636e11 | −0.389749 | ||||||||
\(424\) | 1.33843e11 | 0.201117 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −1.72727e11 | −0.254108 | ||||||||
\(427\) | −9.14159e11 | −1.33075 | ||||||||
\(428\) | 4.17189e11 | 0.600947 | ||||||||
\(429\) | −3.03298e11 | −0.432327 | ||||||||
\(430\) | −7.10293e10 | −0.100191 | ||||||||
\(431\) | 7.09416e11 | 0.990268 | 0.495134 | − | 0.868816i | \(-0.335119\pi\) | ||||
0.495134 | + | 0.868816i | \(0.335119\pi\) | |||||||
\(432\) | 7.45398e11 | 1.02970 | ||||||||
\(433\) | 3.80004e11 | 0.519509 | 0.259754 | − | 0.965675i | \(-0.416358\pi\) | ||||
0.259754 | + | 0.965675i | \(0.416358\pi\) | |||||||
\(434\) | −5.44315e11 | −0.736455 | ||||||||
\(435\) | −3.15579e10 | −0.0422578 | ||||||||
\(436\) | −1.65070e11 | −0.218766 | ||||||||
\(437\) | 2.67959e11 | 0.351481 | ||||||||
\(438\) | 3.11182e11 | 0.404000 | ||||||||
\(439\) | 6.03199e11 | 0.775123 | 0.387561 | − | 0.921844i | \(-0.373317\pi\) | ||||
0.387561 | + | 0.921844i | \(0.373317\pi\) | |||||||
\(440\) | 1.19578e11 | 0.152095 | ||||||||
\(441\) | 1.07039e11 | 0.134762 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1.25487e12 | −1.54804 | −0.774018 | − | 0.633164i | \(-0.781756\pi\) | ||||
−0.774018 | + | 0.633164i | \(0.781756\pi\) | |||||||
\(444\) | 1.99836e11 | 0.244034 | ||||||||
\(445\) | 1.82098e11 | 0.220133 | ||||||||
\(446\) | −1.67405e11 | −0.200337 | ||||||||
\(447\) | 7.25742e11 | 0.859802 | ||||||||
\(448\) | 3.32335e11 | 0.389785 | ||||||||
\(449\) | −3.37996e11 | −0.392467 | −0.196234 | − | 0.980557i | \(-0.562871\pi\) | ||||
−0.196234 | + | 0.980557i | \(0.562871\pi\) | |||||||
\(450\) | 7.78592e11 | 0.895063 | ||||||||
\(451\) | −1.83548e12 | −2.08908 | ||||||||
\(452\) | −3.74466e11 | −0.421978 | ||||||||
\(453\) | 1.13982e10 | 0.0127173 | ||||||||
\(454\) | −4.32878e11 | −0.478206 | ||||||||
\(455\) | 5.22701e10 | 0.0571744 | ||||||||
\(456\) | 2.37291e11 | 0.257003 | ||||||||
\(457\) | 2.71721e11 | 0.291407 | 0.145704 | − | 0.989328i | \(-0.453455\pi\) | ||||
0.145704 | + | 0.989328i | \(0.453455\pi\) | |||||||
\(458\) | −1.92171e12 | −2.04077 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1.95877e10 | 0.0203973 | ||||||||
\(461\) | −1.31496e12 | −1.35600 | −0.677998 | − | 0.735064i | \(-0.737152\pi\) | ||||
−0.677998 | + | 0.735064i | \(0.737152\pi\) | |||||||
\(462\) | 8.42799e11 | 0.860667 | ||||||||
\(463\) | 1.78291e12 | 1.80308 | 0.901539 | − | 0.432698i | \(-0.142439\pi\) | ||||
0.901539 | + | 0.432698i | \(0.142439\pi\) | |||||||
\(464\) | −9.34264e11 | −0.935705 | ||||||||
\(465\) | 3.89079e10 | 0.0385922 | ||||||||
\(466\) | 1.53459e12 | 1.50750 | ||||||||
\(467\) | 1.44519e11 | 0.140605 | 0.0703024 | − | 0.997526i | \(-0.477604\pi\) | ||||
0.0703024 | + | 0.997526i | \(0.477604\pi\) | |||||||
\(468\) | 1.54654e11 | 0.149024 | ||||||||
\(469\) | −3.87352e11 | −0.369682 | ||||||||
\(470\) | −7.28995e10 | −0.0689103 | ||||||||
\(471\) | 1.07985e11 | 0.101105 | ||||||||
\(472\) | 7.42784e11 | 0.688848 | ||||||||
\(473\) | 1.36679e12 | 1.25553 | ||||||||
\(474\) | 5.60740e11 | 0.510222 | ||||||||
\(475\) | 7.99930e11 | 0.720992 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.37031e11 | 0.209639 | ||||||||
\(478\) | 1.30852e12 | 1.14645 | ||||||||
\(479\) | 1.99283e12 | 1.72966 | 0.864829 | − | 0.502067i | \(-0.167427\pi\) | ||||
0.864829 | + | 0.502067i | \(0.167427\pi\) | |||||||
\(480\) | 4.44241e10 | 0.0381974 | ||||||||
\(481\) | −9.02025e11 | −0.768362 | ||||||||
\(482\) | 7.68079e11 | 0.648178 | ||||||||
\(483\) | −2.46052e11 | −0.205715 | ||||||||
\(484\) | 8.57140e11 | 0.709982 | ||||||||
\(485\) | 8.89601e10 | 0.0730058 | ||||||||
\(486\) | 1.45979e12 | 1.18693 | ||||||||
\(487\) | 1.82408e12 | 1.46948 | 0.734740 | − | 0.678349i | \(-0.237304\pi\) | ||||
0.734740 | + | 0.678349i | \(0.237304\pi\) | |||||||
\(488\) | 1.36933e12 | 1.09300 | ||||||||
\(489\) | −3.35523e11 | −0.265359 | ||||||||
\(490\) | 3.04053e10 | 0.0238269 | ||||||||
\(491\) | 1.68204e12 | 1.30608 | 0.653039 | − | 0.757325i | \(-0.273494\pi\) | ||||
0.653039 | + | 0.757325i | \(0.273494\pi\) | |||||||
\(492\) | −2.66252e11 | −0.204856 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 6.00973e11 | 0.454029 | ||||||||
\(495\) | 2.11768e11 | 0.158539 | ||||||||
\(496\) | 1.15186e12 | 0.854539 | ||||||||
\(497\) | −5.72808e11 | −0.421119 | ||||||||
\(498\) | −1.30396e12 | −0.950019 | ||||||||
\(499\) | −2.30279e10 | −0.0166266 | −0.00831328 | − | 0.999965i | \(-0.502646\pi\) | ||||
−0.00831328 | + | 0.999965i | \(0.502646\pi\) | |||||||
\(500\) | 1.17775e11 | 0.0842733 | ||||||||
\(501\) | −1.68999e11 | −0.119843 | ||||||||
\(502\) | −2.74113e12 | −1.92647 | ||||||||
\(503\) | −6.75145e11 | −0.470264 | −0.235132 | − | 0.971963i | \(-0.575552\pi\) | ||||
−0.235132 | + | 0.971963i | \(0.575552\pi\) | |||||||
\(504\) | 7.65926e11 | 0.528749 | ||||||||
\(505\) | 1.15928e11 | 0.0793189 | ||||||||
\(506\) | −1.42561e12 | −0.966768 | ||||||||
\(507\) | −5.01570e11 | −0.337129 | ||||||||
\(508\) | −9.35642e11 | −0.623337 | ||||||||
\(509\) | 2.78050e12 | 1.83609 | 0.918043 | − | 0.396481i | \(-0.129769\pi\) | ||||
0.918043 | + | 0.396481i | \(0.129769\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.03196e12 | 0.669528 | ||||||||
\(512\) | −1.13578e11 | −0.0730429 | ||||||||
\(513\) | 9.60012e11 | 0.611996 | ||||||||
\(514\) | −2.29077e12 | −1.44760 | ||||||||
\(515\) | 2.51334e11 | 0.157442 | ||||||||
\(516\) | 1.98265e11 | 0.123118 | ||||||||
\(517\) | 1.40278e12 | 0.863539 | ||||||||
\(518\) | 2.50653e12 | 1.52964 | ||||||||
\(519\) | −8.44390e10 | −0.0510846 | ||||||||
\(520\) | −7.82962e10 | −0.0469597 | ||||||||
\(521\) | −1.68557e12 | −1.00225 | −0.501126 | − | 0.865374i | \(-0.667081\pi\) | ||||
−0.501126 | + | 0.865374i | \(0.667081\pi\) | |||||||
\(522\) | −1.17116e12 | −0.690398 | ||||||||
\(523\) | 2.39587e12 | 1.40025 | 0.700124 | − | 0.714021i | \(-0.253128\pi\) | ||||
0.700124 | + | 0.714021i | \(0.253128\pi\) | |||||||
\(524\) | −2.87449e10 | −0.0166560 | ||||||||
\(525\) | −7.34531e11 | −0.421981 | ||||||||
\(526\) | 4.37227e11 | 0.249041 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | −1.78350e12 | −0.998667 | ||||||||
\(529\) | −1.38495e12 | −0.768925 | ||||||||
\(530\) | 6.73305e10 | 0.0370655 | ||||||||
\(531\) | 1.31544e12 | 0.718035 | ||||||||
\(532\) | −4.41527e11 | −0.238976 | ||||||||
\(533\) | 1.20182e12 | 0.645009 | ||||||||
\(534\) | −1.92249e12 | −1.02313 | ||||||||
\(535\) | −3.74042e11 | −0.197392 | ||||||||
\(536\) | 5.80221e11 | 0.303635 | ||||||||
\(537\) | −6.98747e10 | −0.0362606 | ||||||||
\(538\) | 1.27246e12 | 0.654824 | ||||||||
\(539\) | −5.85079e11 | −0.298583 | ||||||||
\(540\) | 7.01764e10 | 0.0355156 | ||||||||
\(541\) | 2.02996e12 | 1.01882 | 0.509412 | − | 0.860523i | \(-0.329863\pi\) | ||||
0.509412 | + | 0.860523i | \(0.329863\pi\) | |||||||
\(542\) | 2.17389e12 | 1.08203 | ||||||||
\(543\) | 2.54117e11 | 0.125440 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.47998e11 | 0.0718574 | ||||||||
\(546\) | −5.51840e11 | −0.265734 | ||||||||
\(547\) | −2.99699e12 | −1.43134 | −0.715670 | − | 0.698439i | \(-0.753878\pi\) | ||||
−0.715670 | + | 0.698439i | \(0.753878\pi\) | |||||||
\(548\) | 3.47458e11 | 0.164585 | ||||||||
\(549\) | 2.42503e12 | 1.13931 | ||||||||
\(550\) | −4.25582e12 | −1.98313 | ||||||||
\(551\) | −1.20326e12 | −0.556130 | ||||||||
\(552\) | 3.68565e11 | 0.168962 | ||||||||
\(553\) | 1.85956e12 | 0.845564 | ||||||||
\(554\) | −2.00728e11 | −0.0905346 | ||||||||
\(555\) | −1.79168e11 | −0.0801571 | ||||||||
\(556\) | −1.47957e12 | −0.656598 | ||||||||
\(557\) | −2.35072e12 | −1.03479 | −0.517396 | − | 0.855746i | \(-0.673098\pi\) | ||||
−0.517396 | + | 0.855746i | \(0.673098\pi\) | |||||||
\(558\) | 1.44393e12 | 0.630510 | ||||||||
\(559\) | −8.94936e11 | −0.387649 | ||||||||
\(560\) | 3.07366e11 | 0.132072 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −2.88090e11 | −0.121819 | ||||||||
\(563\) | 1.06843e12 | 0.448186 | 0.224093 | − | 0.974568i | \(-0.428058\pi\) | ||||
0.224093 | + | 0.974568i | \(0.428058\pi\) | |||||||
\(564\) | 2.03485e11 | 0.0846793 | ||||||||
\(565\) | 3.35737e11 | 0.138606 | ||||||||
\(566\) | 2.22019e12 | 0.909318 | ||||||||
\(567\) | 8.60775e11 | 0.349757 | ||||||||
\(568\) | 8.58018e11 | 0.345883 | ||||||||
\(569\) | −6.61622e11 | −0.264609 | −0.132305 | − | 0.991209i | \(-0.542238\pi\) | ||||
−0.132305 | + | 0.991209i | \(0.542238\pi\) | |||||||
\(570\) | 1.19370e11 | 0.0473653 | ||||||||
\(571\) | −1.31584e11 | −0.0518013 | −0.0259007 | − | 0.999665i | \(-0.508245\pi\) | ||||
−0.0259007 | + | 0.999665i | \(0.508245\pi\) | |||||||
\(572\) | −8.45346e11 | −0.330181 | ||||||||
\(573\) | 2.17895e12 | 0.844407 | ||||||||
\(574\) | −3.33958e12 | −1.28407 | ||||||||
\(575\) | 1.24247e12 | 0.474002 | ||||||||
\(576\) | −8.81601e11 | −0.333711 | ||||||||
\(577\) | −3.61547e9 | −0.00135792 | −0.000678959 | − | 1.00000i | \(-0.500216\pi\) | ||||
−0.000678959 | 1.00000i | \(0.500216\pi\) | ||||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.88183e12 | −0.695868 | ||||||||
\(580\) | −8.79575e10 | −0.0322735 | ||||||||
\(581\) | −4.32427e12 | −1.57442 | ||||||||
\(582\) | −9.39194e11 | −0.339314 | ||||||||
\(583\) | −1.29562e12 | −0.464481 | ||||||||
\(584\) | −1.54579e12 | −0.549911 | ||||||||
\(585\) | −1.38659e11 | −0.0489495 | ||||||||
\(586\) | −5.37680e12 | −1.88358 | ||||||||
\(587\) | 1.61905e12 | 0.562846 | 0.281423 | − | 0.959584i | \(-0.409194\pi\) | ||||
0.281423 | + | 0.959584i | \(0.409194\pi\) | |||||||
\(588\) | −8.48708e10 | −0.0292793 | ||||||||
\(589\) | 1.48350e12 | 0.507889 | ||||||||
\(590\) | 3.73662e11 | 0.126953 | ||||||||
\(591\) | 2.02561e12 | 0.682986 | ||||||||
\(592\) | −5.30422e12 | −1.77490 | ||||||||
\(593\) | −6.34063e11 | −0.210565 | −0.105283 | − | 0.994442i | \(-0.533575\pi\) | ||||
−0.105283 | + | 0.994442i | \(0.533575\pi\) | |||||||
\(594\) | −5.10749e12 | −1.68333 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 2.02277e12 | 0.656657 | ||||||||
\(597\) | 1.82606e12 | 0.588344 | ||||||||
\(598\) | 9.33445e11 | 0.298493 | ||||||||
\(599\) | 1.09199e12 | 0.346576 | 0.173288 | − | 0.984871i | \(-0.444561\pi\) | ||||
0.173288 | + | 0.984871i | \(0.444561\pi\) | |||||||
\(600\) | 1.10027e12 | 0.346591 | ||||||||
\(601\) | 4.20600e12 | 1.31502 | 0.657512 | − | 0.753444i | \(-0.271609\pi\) | ||||
0.657512 | + | 0.753444i | \(0.271609\pi\) | |||||||
\(602\) | 2.48683e12 | 0.771723 | ||||||||
\(603\) | 1.02755e12 | 0.316500 | ||||||||
\(604\) | 3.17688e10 | 0.00971257 | ||||||||
\(605\) | −7.68492e11 | −0.233206 | ||||||||
\(606\) | −1.22391e12 | −0.368656 | ||||||||
\(607\) | −6.33595e11 | −0.189436 | −0.0947181 | − | 0.995504i | \(-0.530195\pi\) | ||||
−0.0947181 | + | 0.995504i | \(0.530195\pi\) | |||||||
\(608\) | 1.69383e12 | 0.502693 | ||||||||
\(609\) | 1.10488e12 | 0.325491 | ||||||||
\(610\) | 6.88851e11 | 0.201438 | ||||||||
\(611\) | −9.18499e11 | −0.266620 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4.65062e12 | 1.33027 | 0.665133 | − | 0.746724i | \(-0.268375\pi\) | ||||
0.665133 | + | 0.746724i | \(0.268375\pi\) | |||||||
\(614\) | 5.41564e12 | 1.53777 | ||||||||
\(615\) | 2.38715e11 | 0.0672886 | ||||||||
\(616\) | −4.18658e12 | −1.17151 | ||||||||
\(617\) | 2.62356e12 | 0.728799 | 0.364400 | − | 0.931243i | \(-0.381274\pi\) | ||||
0.364400 | + | 0.931243i | \(0.381274\pi\) | |||||||
\(618\) | −2.65346e12 | −0.731752 | ||||||||
\(619\) | −6.55858e12 | −1.79557 | −0.897784 | − | 0.440437i | \(-0.854824\pi\) | ||||
−0.897784 | + | 0.440437i | \(0.854824\pi\) | |||||||
\(620\) | 1.08443e11 | 0.0294740 | ||||||||
\(621\) | 1.49111e12 | 0.402345 | ||||||||
\(622\) | −1.67781e11 | −0.0449455 | ||||||||
\(623\) | −6.37548e12 | −1.69557 | ||||||||
\(624\) | 1.16778e12 | 0.308341 | ||||||||
\(625\) | 3.65593e12 | 0.958381 | ||||||||
\(626\) | −8.43223e12 | −2.19461 | ||||||||
\(627\) | −2.29700e12 | −0.593551 | ||||||||
\(628\) | 3.00974e11 | 0.0772167 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 3.85304e11 | 0.0974475 | ||||||||
\(631\) | 5.79881e11 | 0.145615 | 0.0728076 | − | 0.997346i | \(-0.476804\pi\) | ||||
0.0728076 | + | 0.997346i | \(0.476804\pi\) | |||||||
\(632\) | −2.78546e12 | −0.694496 | ||||||||
\(633\) | 1.42392e12 | 0.352507 | ||||||||
\(634\) | −1.43272e12 | −0.352177 | ||||||||
\(635\) | 8.38875e11 | 0.204746 | ||||||||
\(636\) | −1.87941e11 | −0.0455474 | ||||||||
\(637\) | 3.83093e11 | 0.0921885 | ||||||||
\(638\) | 6.40161e12 | 1.52966 | ||||||||
\(639\) | 1.51952e12 | 0.360538 | ||||||||
\(640\) | −5.94920e11 | −0.140168 | ||||||||
\(641\) | −5.03353e12 | −1.17764 | −0.588819 | − | 0.808265i | \(-0.700407\pi\) | ||||
−0.588819 | + | 0.808265i | \(0.700407\pi\) | |||||||
\(642\) | 3.94894e12 | 0.917431 | ||||||||
\(643\) | −6.36495e12 | −1.46840 | −0.734202 | − | 0.678931i | \(-0.762444\pi\) | ||||
−0.734202 | + | 0.678931i | \(0.762444\pi\) | |||||||
\(644\) | −6.85790e11 | −0.157110 | ||||||||
\(645\) | −1.77760e11 | −0.0404403 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −3.40666e12 | −0.764292 | −0.382146 | − | 0.924102i | \(-0.624815\pi\) | ||||
−0.382146 | + | 0.924102i | \(0.624815\pi\) | |||||||
\(648\) | −1.28937e12 | −0.287269 | ||||||||
\(649\) | −7.19025e12 | −1.59090 | ||||||||
\(650\) | 2.78658e12 | 0.612297 | ||||||||
\(651\) | −1.36222e12 | −0.297257 | ||||||||
\(652\) | −9.35163e11 | −0.202662 | ||||||||
\(653\) | −2.99407e12 | −0.644397 | −0.322198 | − | 0.946672i | \(-0.604422\pi\) | ||||
−0.322198 | + | 0.946672i | \(0.604422\pi\) | |||||||
\(654\) | −1.56248e12 | −0.333976 | ||||||||
\(655\) | 2.57720e10 | 0.00547095 | ||||||||
\(656\) | 7.06710e12 | 1.48996 | ||||||||
\(657\) | −2.73753e12 | −0.573212 | ||||||||
\(658\) | 2.55231e12 | 0.530782 | ||||||||
\(659\) | −2.03535e12 | −0.420392 | −0.210196 | − | 0.977659i | \(-0.567410\pi\) | ||||
−0.210196 | + | 0.977659i | \(0.567410\pi\) | |||||||
\(660\) | −1.67910e11 | −0.0344452 | ||||||||
\(661\) | −7.04693e12 | −1.43580 | −0.717900 | − | 0.696147i | \(-0.754896\pi\) | ||||
−0.717900 | + | 0.696147i | \(0.754896\pi\) | |||||||
\(662\) | −3.27418e12 | −0.662584 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 6.47739e12 | 1.29313 | ||||||||
\(665\) | 3.95863e11 | 0.0784960 | ||||||||
\(666\) | −6.64919e12 | −1.30959 | ||||||||
\(667\) | −1.86893e12 | −0.365617 | ||||||||
\(668\) | −4.71030e11 | −0.0915281 | ||||||||
\(669\) | −4.18951e11 | −0.0808622 | ||||||||
\(670\) | 2.91884e11 | 0.0559594 | ||||||||
\(671\) | −1.32553e13 | −2.52429 | ||||||||
\(672\) | −1.55535e12 | −0.294215 | ||||||||
\(673\) | −4.04986e12 | −0.760979 | −0.380489 | − | 0.924785i | \(-0.624244\pi\) | ||||
−0.380489 | + | 0.924785i | \(0.624244\pi\) | |||||||
\(674\) | 2.97391e12 | 0.555083 | ||||||||
\(675\) | 4.45137e12 | 0.825328 | ||||||||
\(676\) | −1.39796e12 | −0.257476 | ||||||||
\(677\) | −8.15388e11 | −0.149182 | −0.0745908 | − | 0.997214i | \(-0.523765\pi\) | ||||
−0.0745908 | + | 0.997214i | \(0.523765\pi\) | |||||||
\(678\) | −3.54454e12 | −0.644208 | ||||||||
\(679\) | −3.11461e12 | −0.562328 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.08333e12 | −0.193019 | ||||||||
\(682\) | −7.89258e12 | −1.39698 | ||||||||
\(683\) | 3.55244e12 | 0.624645 | 0.312322 | − | 0.949976i | \(-0.398893\pi\) | ||||
0.312322 | + | 0.949976i | \(0.398893\pi\) | |||||||
\(684\) | 1.17126e12 | 0.204598 | ||||||||
\(685\) | −3.11523e11 | −0.0540607 | ||||||||
\(686\) | −7.21434e12 | −1.24376 | ||||||||
\(687\) | −4.80933e12 | −0.823719 | ||||||||
\(688\) | −5.26253e12 | −0.895461 | ||||||||
\(689\) | 8.48332e11 | 0.143410 | ||||||||
\(690\) | 1.85409e11 | 0.0311394 | ||||||||
\(691\) | 2.88386e11 | 0.0481197 | 0.0240598 | − | 0.999711i | \(-0.492341\pi\) | ||||
0.0240598 | + | 0.999711i | \(0.492341\pi\) | |||||||
\(692\) | −2.35346e11 | −0.0390148 | ||||||||
\(693\) | −7.41427e12 | −1.22115 | ||||||||
\(694\) | 7.33110e12 | 1.19964 | ||||||||
\(695\) | 1.32655e12 | 0.215671 | ||||||||
\(696\) | −1.65502e12 | −0.267339 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | −7.11337e11 | −0.113429 | ||||||||
\(699\) | 3.84052e12 | 0.608474 | ||||||||
\(700\) | −2.04727e12 | −0.322280 | ||||||||
\(701\) | 1.10902e12 | 0.173463 | 0.0867315 | − | 0.996232i | \(-0.472358\pi\) | ||||
0.0867315 | + | 0.996232i | \(0.472358\pi\) | |||||||
\(702\) | 3.34423e12 | 0.519732 | ||||||||
\(703\) | −6.83141e12 | −1.05490 | ||||||||
\(704\) | 4.81886e12 | 0.739380 | ||||||||
\(705\) | −1.82440e11 | −0.0278144 | ||||||||
\(706\) | 1.07838e13 | 1.63362 | ||||||||
\(707\) | −4.05878e12 | −0.610954 | ||||||||
\(708\) | −1.04301e12 | −0.156005 | ||||||||
\(709\) | −7.04264e12 | −1.04671 | −0.523356 | − | 0.852114i | \(-0.675320\pi\) | ||||
−0.523356 | + | 0.852114i | \(0.675320\pi\) | |||||||
\(710\) | 4.31631e11 | 0.0637456 | ||||||||
\(711\) | −4.93294e12 | −0.723923 | ||||||||
\(712\) | 9.54993e12 | 1.39264 | ||||||||
\(713\) | 2.30421e12 | 0.333902 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 7.57918e11 | 0.108454 | ||||||||
\(716\) | −1.94753e11 | −0.0276933 | ||||||||
\(717\) | 3.27473e12 | 0.462743 | ||||||||
\(718\) | 9.89382e12 | 1.38933 | ||||||||
\(719\) | 1.73354e12 | 0.241910 | 0.120955 | − | 0.992658i | \(-0.461404\pi\) | ||||
0.120955 | + | 0.992658i | \(0.461404\pi\) | |||||||
\(720\) | −8.15366e11 | −0.113072 | ||||||||
\(721\) | −8.79954e12 | −1.21269 | ||||||||
\(722\) | −3.96181e12 | −0.542595 | ||||||||
\(723\) | 1.92222e12 | 0.261625 | ||||||||
\(724\) | 7.08269e11 | 0.0958020 | ||||||||
\(725\) | −5.57924e12 | −0.749988 | ||||||||
\(726\) | 8.11333e12 | 1.08389 | ||||||||
\(727\) | 8.60821e11 | 0.114290 | 0.0571450 | − | 0.998366i | \(-0.481800\pi\) | ||||
0.0571450 | + | 0.998366i | \(0.481800\pi\) | |||||||
\(728\) | 2.74125e12 | 0.361707 | ||||||||
\(729\) | 7.20293e11 | 0.0944572 | ||||||||
\(730\) | −7.77619e11 | −0.101348 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −1.92280e12 | −0.247534 | ||||||||
\(733\) | −1.51716e13 | −1.94117 | −0.970583 | − | 0.240766i | \(-0.922602\pi\) | ||||
−0.970583 | + | 0.240766i | \(0.922602\pi\) | |||||||
\(734\) | −8.50589e12 | −1.08165 | ||||||||
\(735\) | 7.60932e10 | 0.00961729 | ||||||||
\(736\) | 2.63089e12 | 0.330486 | ||||||||
\(737\) | −5.61662e12 | −0.701247 | ||||||||
\(738\) | 8.85907e12 | 1.09935 | ||||||||
\(739\) | 4.87991e12 | 0.601882 | 0.300941 | − | 0.953643i | \(-0.402699\pi\) | ||||
0.300941 | + | 0.953643i | \(0.402699\pi\) | |||||||
\(740\) | −4.99373e11 | −0.0612184 | ||||||||
\(741\) | 1.50401e12 | 0.183261 | ||||||||
\(742\) | −2.35733e12 | −0.285498 | ||||||||
\(743\) | −3.76850e12 | −0.453648 | −0.226824 | − | 0.973936i | \(-0.572834\pi\) | ||||
−0.226824 | + | 0.973936i | \(0.572834\pi\) | |||||||
\(744\) | 2.04049e12 | 0.244149 | ||||||||
\(745\) | −1.81357e12 | −0.215690 | ||||||||
\(746\) | −5.57521e12 | −0.659078 | ||||||||
\(747\) | 1.14712e13 | 1.34793 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.30957e13 | 1.52041 | ||||||||
\(750\) | 1.11481e12 | 0.128655 | ||||||||
\(751\) | 6.74548e12 | 0.773808 | 0.386904 | − | 0.922120i | \(-0.373545\pi\) | ||||
0.386904 | + | 0.922120i | \(0.373545\pi\) | |||||||
\(752\) | −5.40110e12 | −0.615888 | ||||||||
\(753\) | −6.86002e12 | −0.777586 | ||||||||
\(754\) | −4.19159e12 | −0.472288 | ||||||||
\(755\) | −2.84831e10 | −0.00319026 | ||||||||
\(756\) | −2.45697e12 | −0.273559 | ||||||||
\(757\) | −1.07821e13 | −1.19336 | −0.596682 | − | 0.802477i | \(-0.703515\pi\) | ||||
−0.596682 | + | 0.802477i | \(0.703515\pi\) | |||||||
\(758\) | 1.23299e13 | 1.35658 | ||||||||
\(759\) | −3.56776e12 | −0.390218 | ||||||||
\(760\) | −5.92969e11 | −0.0644720 | ||||||||
\(761\) | −7.42380e12 | −0.802408 | −0.401204 | − | 0.915989i | \(-0.631408\pi\) | ||||
−0.401204 | + | 0.915989i | \(0.631408\pi\) | |||||||
\(762\) | −8.85640e12 | −0.951612 | ||||||||
\(763\) | −5.18160e12 | −0.553482 | ||||||||
\(764\) | 6.07312e12 | 0.644899 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.75076e13 | 1.83738 | ||||||||
\(767\) | 4.70796e12 | 0.491195 | ||||||||
\(768\) | 4.33600e12 | 0.449742 | ||||||||
\(769\) | 1.65746e13 | 1.70913 | 0.854565 | − | 0.519345i | \(-0.173824\pi\) | ||||
0.854565 | + | 0.519345i | \(0.173824\pi\) | |||||||
\(770\) | −2.10608e12 | −0.215907 | ||||||||
\(771\) | −5.73295e12 | −0.584297 | ||||||||
\(772\) | −5.24499e12 | −0.531455 | ||||||||
\(773\) | 8.48204e12 | 0.854462 | 0.427231 | − | 0.904143i | \(-0.359489\pi\) | ||||
0.427231 | + | 0.904143i | \(0.359489\pi\) | |||||||
\(774\) | −6.59693e12 | −0.660705 | ||||||||
\(775\) | 6.87868e12 | 0.684932 | ||||||||
\(776\) | 4.66542e12 | 0.461863 | ||||||||
\(777\) | 6.27291e12 | 0.617411 | ||||||||
\(778\) | −2.95660e10 | −0.00289324 | ||||||||
\(779\) | 9.10185e12 | 0.885546 | ||||||||
\(780\) | 1.09942e11 | 0.0106351 | ||||||||
\(781\) | −8.30573e12 | −0.798819 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −6.69576e12 | −0.636608 | ||||||||
\(784\) | 2.25272e12 | 0.212953 | ||||||||
\(785\) | −2.69847e11 | −0.0253632 | ||||||||
\(786\) | −2.72087e11 | −0.0254277 | ||||||||
\(787\) | −1.63530e13 | −1.51954 | −0.759768 | − | 0.650195i | \(-0.774687\pi\) | ||||
−0.759768 | + | 0.650195i | \(0.774687\pi\) | |||||||
\(788\) | 5.64573e12 | 0.521617 | ||||||||
\(789\) | 1.09421e12 | 0.100521 | ||||||||
\(790\) | −1.40124e12 | −0.127995 | ||||||||
\(791\) | −1.17546e13 | −1.06761 | ||||||||
\(792\) | 1.11059e13 | 1.00298 | ||||||||
\(793\) | 8.67920e12 | 0.779382 | ||||||||
\(794\) | 1.38162e13 | 1.23366 | ||||||||
\(795\) | 1.68503e11 | 0.0149608 | ||||||||
\(796\) | 5.08956e12 | 0.449336 | ||||||||
\(797\) | −1.73733e13 | −1.52518 | −0.762590 | − | 0.646883i | \(-0.776072\pi\) | ||||
−0.762590 | + | 0.646883i | \(0.776072\pi\) | |||||||
\(798\) | −4.17931e12 | −0.364831 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 7.85391e12 | 0.677924 | ||||||||
\(801\) | 1.69125e13 | 1.45165 | ||||||||
\(802\) | 1.22332e13 | 1.04413 | ||||||||
\(803\) | 1.49635e13 | 1.27002 | ||||||||
\(804\) | −8.14739e11 | −0.0687648 | ||||||||
\(805\) | 6.14864e11 | 0.0516057 | ||||||||
\(806\) | 5.16783e12 | 0.431321 | ||||||||
\(807\) | 3.18450e12 | 0.264308 | ||||||||
\(808\) | 6.07971e12 | 0.501802 | ||||||||
\(809\) | 8.14620e12 | 0.668631 | 0.334316 | − | 0.942461i | \(-0.391495\pi\) | ||||
0.334316 | + | 0.942461i | \(0.391495\pi\) | |||||||
\(810\) | −6.48624e11 | −0.0529433 | ||||||||
\(811\) | −6.41782e12 | −0.520947 | −0.260474 | − | 0.965481i | \(-0.583879\pi\) | ||||
−0.260474 | + | 0.965481i | \(0.583879\pi\) | |||||||
\(812\) | 3.07950e12 | 0.248587 | ||||||||
\(813\) | 5.44043e12 | 0.436743 | ||||||||
\(814\) | 3.63447e13 | 2.90156 | ||||||||
\(815\) | 8.38445e11 | 0.0665680 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −6.77772e12 | −0.532212 | ||||||||
\(818\) | −2.52503e13 | −1.97186 | ||||||||
\(819\) | 4.85464e12 | 0.377033 | ||||||||
\(820\) | 6.65341e11 | 0.0513904 | ||||||||
\(821\) | −6.34823e12 | −0.487650 | −0.243825 | − | 0.969819i | \(-0.578402\pi\) | ||||
−0.243825 | + | 0.969819i | \(0.578402\pi\) | |||||||
\(822\) | 3.28889e12 | 0.251262 | ||||||||
\(823\) | −1.96190e12 | −0.149066 | −0.0745329 | − | 0.997219i | \(-0.523747\pi\) | ||||
−0.0745329 | + | 0.997219i | \(0.523747\pi\) | |||||||
\(824\) | 1.31810e13 | 0.996036 | ||||||||
\(825\) | −1.06507e13 | −0.800453 | ||||||||
\(826\) | −1.30824e13 | −0.977860 | ||||||||
\(827\) | −1.16150e13 | −0.863465 | −0.431732 | − | 0.902002i | \(-0.642098\pi\) | ||||
−0.431732 | + | 0.902002i | \(0.642098\pi\) | |||||||
\(828\) | 1.81923e12 | 0.134509 | ||||||||
\(829\) | 7.30758e12 | 0.537376 | 0.268688 | − | 0.963227i | \(-0.413410\pi\) | ||||
0.268688 | + | 0.963227i | \(0.413410\pi\) | |||||||
\(830\) | 3.25849e12 | 0.238322 | ||||||||
\(831\) | −5.02348e11 | −0.0365426 | ||||||||
\(832\) | −3.15525e12 | −0.228286 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −1.40050e13 | −1.00239 | ||||||||
\(835\) | 4.22314e11 | 0.0300640 | ||||||||
\(836\) | −6.40216e12 | −0.453313 | ||||||||
\(837\) | 8.25524e12 | 0.581387 | ||||||||
\(838\) | 2.52163e13 | 1.76638 | ||||||||
\(839\) | 1.23263e13 | 0.858826 | 0.429413 | − | 0.903108i | \(-0.358720\pi\) | ||||
0.429413 | + | 0.903108i | \(0.358720\pi\) | |||||||
\(840\) | 5.44491e11 | 0.0377341 | ||||||||
\(841\) | −6.11483e12 | −0.421505 | ||||||||
\(842\) | −7.41859e12 | −0.508648 | ||||||||
\(843\) | −7.20981e11 | −0.0491699 | ||||||||
\(844\) | 3.96871e12 | 0.269220 | ||||||||
\(845\) | 1.25338e12 | 0.0845724 | ||||||||
\(846\) | −6.77063e12 | −0.454425 | ||||||||
\(847\) | 2.69059e13 | 1.79627 | ||||||||
\(848\) | 4.98849e12 | 0.331274 | ||||||||
\(849\) | 5.55630e12 | 0.367030 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.06107e13 | −0.693524 | ||||||||
\(852\) | −1.20482e12 | −0.0783327 | ||||||||
\(853\) | 1.80405e13 | 1.16675 | 0.583376 | − | 0.812202i | \(-0.301731\pi\) | ||||
0.583376 | + | 0.812202i | \(0.301731\pi\) | |||||||
\(854\) | −2.41176e13 | −1.55158 | ||||||||
\(855\) | −1.05013e12 | −0.0672038 | ||||||||
\(856\) | −1.96163e13 | −1.24878 | ||||||||
\(857\) | 1.37524e13 | 0.870895 | 0.435448 | − | 0.900214i | \(-0.356590\pi\) | ||||
0.435448 | + | 0.900214i | \(0.356590\pi\) | |||||||
\(858\) | −8.00169e12 | −0.504068 | ||||||||
\(859\) | −9.46970e11 | −0.0593427 | −0.0296713 | − | 0.999560i | \(-0.509446\pi\) | ||||
−0.0296713 | + | 0.999560i | \(0.509446\pi\) | |||||||
\(860\) | −4.95448e11 | −0.0308855 | ||||||||
\(861\) | −8.35772e12 | −0.518291 | ||||||||
\(862\) | 1.87160e13 | 1.15460 | ||||||||
\(863\) | −1.77968e13 | −1.09218 | −0.546088 | − | 0.837728i | \(-0.683884\pi\) | ||||
−0.546088 | + | 0.837728i | \(0.683884\pi\) | |||||||
\(864\) | 9.42563e12 | 0.575438 | ||||||||
\(865\) | 2.11006e11 | 0.0128151 | ||||||||
\(866\) | 1.00254e13 | 0.605717 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −3.79674e12 | −0.227024 | ||||||||
\(869\) | 2.69636e13 | 1.60394 | ||||||||
\(870\) | −8.32569e11 | −0.0492701 | ||||||||
\(871\) | 3.67760e12 | 0.216512 | ||||||||
\(872\) | 7.76160e12 | 0.454597 | ||||||||
\(873\) | 8.26227e12 | 0.481433 | ||||||||
\(874\) | 7.06937e12 | 0.409807 | ||||||||
\(875\) | 3.69701e12 | 0.213213 | ||||||||
\(876\) | 2.17058e12 | 0.124539 | ||||||||
\(877\) | −2.60072e13 | −1.48455 | −0.742276 | − | 0.670095i | \(-0.766253\pi\) | ||||
−0.742276 | + | 0.670095i | \(0.766253\pi\) | |||||||
\(878\) | 1.59138e13 | 0.903748 | ||||||||
\(879\) | −1.34561e13 | −0.760273 | ||||||||
\(880\) | 4.45682e12 | 0.250526 | ||||||||
\(881\) | −2.34952e13 | −1.31398 | −0.656989 | − | 0.753900i | \(-0.728170\pi\) | ||||
−0.656989 | + | 0.753900i | \(0.728170\pi\) | |||||||
\(882\) | 2.82393e12 | 0.157125 | ||||||||
\(883\) | 9.42490e12 | 0.521739 | 0.260870 | − | 0.965374i | \(-0.415991\pi\) | ||||
0.260870 | + | 0.965374i | \(0.415991\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 9.35136e11 | 0.0512425 | ||||||||
\(886\) | −3.31062e13 | −1.80492 | ||||||||
\(887\) | −9.43777e12 | −0.511933 | −0.255966 | − | 0.966686i | \(-0.582394\pi\) | ||||
−0.255966 | + | 0.966686i | \(0.582394\pi\) | |||||||
\(888\) | −9.39628e12 | −0.507105 | ||||||||
\(889\) | −2.93701e13 | −1.57706 | ||||||||
\(890\) | 4.80415e12 | 0.256662 | ||||||||
\(891\) | 1.24813e13 | 0.663451 | ||||||||
\(892\) | −1.16769e12 | −0.0617569 | ||||||||
\(893\) | −6.95618e12 | −0.366049 | ||||||||
\(894\) | 1.91467e13 | 1.00248 | ||||||||
\(895\) | 1.74611e11 | 0.00909636 | ||||||||
\(896\) | 2.08289e13 | 1.07964 | ||||||||
\(897\) | 2.33607e12 | 0.120481 | ||||||||
\(898\) | −8.91711e12 | −0.457594 | ||||||||
\(899\) | −1.03469e13 | −0.528315 | ||||||||
\(900\) | 5.43088e12 | 0.275917 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | −4.84240e13 | −2.43574 | ||||||||
\(903\) | 6.22360e12 | 0.311492 | ||||||||
\(904\) | 1.76074e13 | 0.876874 | ||||||||
\(905\) | −6.35017e11 | −0.0314678 | ||||||||
\(906\) | 3.00710e11 | 0.0148276 | ||||||||
\(907\) | 1.43965e13 | 0.706355 | 0.353178 | − | 0.935556i | \(-0.385101\pi\) | ||||
0.353178 | + | 0.935556i | \(0.385101\pi\) | |||||||
\(908\) | −3.01944e12 | −0.147414 | ||||||||
\(909\) | 1.07669e13 | 0.523064 | ||||||||
\(910\) | 1.37900e12 | 0.0666621 | ||||||||
\(911\) | −8.42261e12 | −0.405148 | −0.202574 | − | 0.979267i | \(-0.564931\pi\) | ||||
−0.202574 | + | 0.979267i | \(0.564931\pi\) | |||||||
\(912\) | 8.84411e12 | 0.423328 | ||||||||
\(913\) | −6.27020e13 | −2.98650 | ||||||||
\(914\) | 7.16861e12 | 0.339764 | ||||||||
\(915\) | 1.72394e12 | 0.0813068 | ||||||||
\(916\) | −1.34044e13 | −0.629099 | ||||||||
\(917\) | −9.02311e11 | −0.0421400 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 4.07249e13 | 1.88339 | 0.941695 | − | 0.336469i | \(-0.109233\pi\) | ||||
0.941695 | + | 0.336469i | \(0.109233\pi\) | |||||||
\(920\) | −9.21014e11 | −0.0423859 | ||||||||
\(921\) | 1.35533e13 | 0.620694 | ||||||||
\(922\) | −3.46916e13 | −1.58101 | ||||||||
\(923\) | 5.43835e12 | 0.246638 | ||||||||
\(924\) | 5.87874e12 | 0.265314 | ||||||||
\(925\) | −3.16758e13 | −1.42262 | ||||||||
\(926\) | 4.70371e13 | 2.10228 | ||||||||
\(927\) | 2.33430e13 | 1.03824 | ||||||||
\(928\) | −1.18139e13 | −0.522909 | ||||||||
\(929\) | 2.48550e13 | 1.09482 | 0.547410 | − | 0.836864i | \(-0.315614\pi\) | ||||
0.547410 | + | 0.836864i | \(0.315614\pi\) | |||||||
\(930\) | 1.02648e12 | 0.0449963 | ||||||||
\(931\) | 2.90132e12 | 0.126568 | ||||||||
\(932\) | 1.07042e13 | 0.464710 | ||||||||
\(933\) | −4.19893e11 | −0.0181414 | ||||||||
\(934\) | 3.81275e12 | 0.163937 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −7.27185e12 | −0.309673 | ||||||||
\(937\) | −1.96674e12 | −0.0833526 | −0.0416763 | − | 0.999131i | \(-0.513270\pi\) | ||||
−0.0416763 | + | 0.999131i | \(0.513270\pi\) | |||||||
\(938\) | −1.02192e13 | −0.431028 | ||||||||
\(939\) | −2.11027e13 | −0.885815 | ||||||||
\(940\) | −5.08493e11 | −0.0212427 | ||||||||
\(941\) | 2.86840e13 | 1.19258 | 0.596288 | − | 0.802770i | \(-0.296642\pi\) | ||||
0.596288 | + | 0.802770i | \(0.296642\pi\) | |||||||
\(942\) | 2.84890e12 | 0.117882 | ||||||||
\(943\) | 1.41372e13 | 0.582185 | ||||||||
\(944\) | 2.76845e13 | 1.13465 | ||||||||
\(945\) | 2.20286e12 | 0.0898553 | ||||||||
\(946\) | 3.60591e13 | 1.46388 | ||||||||
\(947\) | −3.18106e13 | −1.28528 | −0.642640 | − | 0.766169i | \(-0.722161\pi\) | ||||
−0.642640 | + | 0.766169i | \(0.722161\pi\) | |||||||
\(948\) | 3.91131e12 | 0.157284 | ||||||||
\(949\) | −9.79763e12 | −0.392124 | ||||||||
\(950\) | 2.11039e13 | 0.840635 | ||||||||
\(951\) | −3.58557e12 | −0.142150 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2.00740e13 | −0.788343 | −0.394171 | − | 0.919037i | \(-0.628968\pi\) | ||||
−0.394171 | + | 0.919037i | \(0.628968\pi\) | |||||||
\(954\) | 6.25340e12 | 0.244427 | ||||||||
\(955\) | −5.44502e12 | −0.211828 | ||||||||
\(956\) | 9.12726e12 | 0.353411 | ||||||||
\(957\) | 1.60208e13 | 0.617421 | ||||||||
\(958\) | 5.25753e13 | 2.01668 | ||||||||
\(959\) | 1.09068e13 | 0.416403 | ||||||||
\(960\) | −6.26723e11 | −0.0238152 | ||||||||
\(961\) | −1.36828e13 | −0.517513 | ||||||||
\(962\) | −2.37975e13 | −0.895865 | ||||||||
\(963\) | −3.47396e13 | −1.30169 | ||||||||
\(964\) | 5.35755e12 | 0.199811 | ||||||||
\(965\) | 4.70253e12 | 0.174566 | ||||||||
\(966\) | −6.49141e12 | −0.239851 | ||||||||
\(967\) | −9.75077e12 | −0.358608 | −0.179304 | − | 0.983794i | \(-0.557385\pi\) | ||||
−0.179304 | + | 0.983794i | \(0.557385\pi\) | |||||||
\(968\) | −4.03027e13 | −1.47535 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 2.34697e12 | 0.0851205 | ||||||||
\(971\) | 3.82881e13 | 1.38222 | 0.691110 | − | 0.722750i | \(-0.257122\pi\) | ||||
0.691110 | + | 0.722750i | \(0.257122\pi\) | |||||||
\(972\) | 1.01824e13 | 0.365891 | ||||||||
\(973\) | −4.64442e13 | −1.66121 | ||||||||
\(974\) | 4.81233e13 | 1.71333 | ||||||||
\(975\) | 6.97378e12 | 0.247142 | ||||||||
\(976\) | 5.10367e13 | 1.80036 | ||||||||
\(977\) | −7.30921e12 | −0.256652 | −0.128326 | − | 0.991732i | \(-0.540960\pi\) | ||||
−0.128326 | + | 0.991732i | \(0.540960\pi\) | |||||||
\(978\) | −8.85186e12 | −0.309393 | ||||||||
\(979\) | −9.24446e13 | −3.21632 | ||||||||
\(980\) | 2.12085e11 | 0.00734502 | ||||||||
\(981\) | 1.37455e13 | 0.473859 | ||||||||
\(982\) | 4.43759e13 | 1.52281 | ||||||||
\(983\) | −3.14313e13 | −1.07367 | −0.536836 | − | 0.843687i | \(-0.680380\pi\) | ||||
−0.536836 | + | 0.843687i | \(0.680380\pi\) | |||||||
\(984\) | 1.25192e13 | 0.425694 | ||||||||
\(985\) | −5.06183e12 | −0.171334 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 6.38747e12 | 0.214240 | ||||||||
\(988\) | 4.19194e12 | 0.139962 | ||||||||
\(989\) | −1.05273e13 | −0.349892 | ||||||||
\(990\) | 5.58691e12 | 0.184848 | ||||||||
\(991\) | −5.32302e13 | −1.75318 | −0.876590 | − | 0.481238i | \(-0.840187\pi\) | ||||
−0.876590 | + | 0.481238i | \(0.840187\pi\) | |||||||
\(992\) | 1.45654e13 | 0.477551 | ||||||||
\(993\) | −8.19404e12 | −0.267440 | ||||||||
\(994\) | −1.51120e13 | −0.491001 | ||||||||
\(995\) | −4.56318e12 | −0.147592 | ||||||||
\(996\) | −9.09547e12 | −0.292859 | ||||||||
\(997\) | 2.49439e13 | 0.799533 | 0.399767 | − | 0.916617i | \(-0.369091\pi\) | ||||
0.399767 | + | 0.916617i | \(0.369091\pi\) | |||||||
\(998\) | −6.07529e11 | −0.0193856 | ||||||||
\(999\) | −3.80148e13 | −1.20756 |
(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 | 289.10.a.d.1.9 | ✓ | 12 | |
17.16 | even | 2 | 289.10.a.e.1.9 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
289.10.a.d.1.9 | ✓ | 12 | 1.1 | even | 1 | trivial | |
289.10.a.e.1.9 | yes | 12 | 17.16 | even | 2 |