Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [22,10,Mod(1,22)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(22, 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("22.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 22 = 2 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 22.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: | \(11.3307883956\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{889}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 222 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(15.4081\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 22.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −16.0000 | −0.707107 | ||||||||
\(3\) | −144.672 | −1.03119 | −0.515597 | − | 0.856831i | \(-0.672430\pi\) | ||||
−0.515597 | + | 0.856831i | \(0.672430\pi\) | |||||||
\(4\) | 256.000 | 0.500000 | ||||||||
\(5\) | −1706.58 | −1.22113 | −0.610565 | − | 0.791966i | \(-0.709058\pi\) | ||||
−0.610565 | + | 0.791966i | \(0.709058\pi\) | |||||||
\(6\) | 2314.76 | 0.729164 | ||||||||
\(7\) | −8664.66 | −1.36399 | −0.681993 | − | 0.731358i | \(-0.738887\pi\) | ||||
−0.681993 | + | 0.731358i | \(0.738887\pi\) | |||||||
\(8\) | −4096.00 | −0.353553 | ||||||||
\(9\) | 1247.12 | 0.0633603 | ||||||||
\(10\) | 27305.3 | 0.863469 | ||||||||
\(11\) | 14641.0 | 0.301511 | ||||||||
\(12\) | −37036.2 | −0.515597 | ||||||||
\(13\) | 67852.1 | 0.658898 | 0.329449 | − | 0.944173i | \(-0.393137\pi\) | ||||
0.329449 | + | 0.944173i | \(0.393137\pi\) | |||||||
\(14\) | 138635. | 0.964484 | ||||||||
\(15\) | 246895. | 1.25922 | ||||||||
\(16\) | 65536.0 | 0.250000 | ||||||||
\(17\) | 249646. | 0.724943 | 0.362471 | − | 0.931995i | \(-0.381933\pi\) | ||||
0.362471 | + | 0.931995i | \(0.381933\pi\) | |||||||
\(18\) | −19953.9 | −0.0448025 | ||||||||
\(19\) | −293189. | −0.516127 | −0.258064 | − | 0.966128i | \(-0.583084\pi\) | ||||
−0.258064 | + | 0.966128i | \(0.583084\pi\) | |||||||
\(20\) | −436885. | −0.610565 | ||||||||
\(21\) | 1.25354e6 | 1.40653 | ||||||||
\(22\) | −234256. | −0.213201 | ||||||||
\(23\) | 1.10315e6 | 0.821979 | 0.410990 | − | 0.911640i | \(-0.365183\pi\) | ||||
0.410990 | + | 0.911640i | \(0.365183\pi\) | |||||||
\(24\) | 592578. | 0.364582 | ||||||||
\(25\) | 959294. | 0.491158 | ||||||||
\(26\) | −1.08563e6 | −0.465911 | ||||||||
\(27\) | 2.66716e6 | 0.965857 | ||||||||
\(28\) | −2.21815e6 | −0.681993 | ||||||||
\(29\) | −5.23603e6 | −1.37471 | −0.687354 | − | 0.726322i | \(-0.741228\pi\) | ||||
−0.687354 | + | 0.726322i | \(0.741228\pi\) | |||||||
\(30\) | −3.95032e6 | −0.890404 | ||||||||
\(31\) | −8.38378e6 | −1.63047 | −0.815234 | − | 0.579131i | \(-0.803392\pi\) | ||||
−0.815234 | + | 0.579131i | \(0.803392\pi\) | |||||||
\(32\) | −1.04858e6 | −0.176777 | ||||||||
\(33\) | −2.11815e6 | −0.310917 | ||||||||
\(34\) | −3.99433e6 | −0.512612 | ||||||||
\(35\) | 1.47869e7 | 1.66561 | ||||||||
\(36\) | 319263. | 0.0316802 | ||||||||
\(37\) | 7.34600e6 | 0.644382 | 0.322191 | − | 0.946675i | \(-0.395581\pi\) | ||||
0.322191 | + | 0.946675i | \(0.395581\pi\) | |||||||
\(38\) | 4.69103e6 | 0.364957 | ||||||||
\(39\) | −9.81632e6 | −0.679451 | ||||||||
\(40\) | 6.99016e6 | 0.431735 | ||||||||
\(41\) | 1.01256e7 | 0.559623 | 0.279811 | − | 0.960055i | \(-0.409728\pi\) | ||||
0.279811 | + | 0.960055i | \(0.409728\pi\) | |||||||
\(42\) | −2.00566e7 | −0.994570 | ||||||||
\(43\) | −2.56347e7 | −1.14346 | −0.571730 | − | 0.820442i | \(-0.693727\pi\) | ||||
−0.571730 | + | 0.820442i | \(0.693727\pi\) | |||||||
\(44\) | 3.74810e6 | 0.150756 | ||||||||
\(45\) | −2.12831e6 | −0.0773712 | ||||||||
\(46\) | −1.76505e7 | −0.581227 | ||||||||
\(47\) | 5.88993e7 | 1.76064 | 0.880318 | − | 0.474385i | \(-0.157329\pi\) | ||||
0.880318 | + | 0.474385i | \(0.157329\pi\) | |||||||
\(48\) | −9.48125e6 | −0.257798 | ||||||||
\(49\) | 3.47227e7 | 0.860460 | ||||||||
\(50\) | −1.53487e7 | −0.347301 | ||||||||
\(51\) | −3.61168e7 | −0.747556 | ||||||||
\(52\) | 1.73701e7 | 0.329449 | ||||||||
\(53\) | 8.68723e7 | 1.51231 | 0.756153 | − | 0.654395i | \(-0.227076\pi\) | ||||
0.756153 | + | 0.654395i | \(0.227076\pi\) | |||||||
\(54\) | −4.26746e7 | −0.682964 | ||||||||
\(55\) | −2.49861e7 | −0.368185 | ||||||||
\(56\) | 3.54904e7 | 0.482242 | ||||||||
\(57\) | 4.24164e7 | 0.532227 | ||||||||
\(58\) | 8.37764e7 | 0.972066 | ||||||||
\(59\) | −1.82302e8 | −1.95865 | −0.979326 | − | 0.202289i | \(-0.935162\pi\) | ||||
−0.979326 | + | 0.202289i | \(0.935162\pi\) | |||||||
\(60\) | 6.32052e7 | 0.629611 | ||||||||
\(61\) | 1.22104e8 | 1.12914 | 0.564569 | − | 0.825386i | \(-0.309042\pi\) | ||||
0.564569 | + | 0.825386i | \(0.309042\pi\) | |||||||
\(62\) | 1.34141e8 | 1.15292 | ||||||||
\(63\) | −1.08059e7 | −0.0864227 | ||||||||
\(64\) | 1.67772e7 | 0.125000 | ||||||||
\(65\) | −1.15795e8 | −0.804600 | ||||||||
\(66\) | 3.38904e7 | 0.219851 | ||||||||
\(67\) | −6.80532e7 | −0.412584 | −0.206292 | − | 0.978491i | \(-0.566140\pi\) | ||||
−0.206292 | + | 0.978491i | \(0.566140\pi\) | |||||||
\(68\) | 6.39093e7 | 0.362471 | ||||||||
\(69\) | −1.59596e8 | −0.847620 | ||||||||
\(70\) | −2.36591e8 | −1.17776 | ||||||||
\(71\) | −1.67349e8 | −0.781555 | −0.390777 | − | 0.920485i | \(-0.627794\pi\) | ||||
−0.390777 | + | 0.920485i | \(0.627794\pi\) | |||||||
\(72\) | −5.10821e6 | −0.0224013 | ||||||||
\(73\) | −1.51799e8 | −0.625626 | −0.312813 | − | 0.949815i | \(-0.601271\pi\) | ||||
−0.312813 | + | 0.949815i | \(0.601271\pi\) | |||||||
\(74\) | −1.17536e8 | −0.455647 | ||||||||
\(75\) | −1.38783e8 | −0.506479 | ||||||||
\(76\) | −7.50564e7 | −0.258064 | ||||||||
\(77\) | −1.26859e8 | −0.411258 | ||||||||
\(78\) | 1.57061e8 | 0.480444 | ||||||||
\(79\) | 2.95735e8 | 0.854241 | 0.427120 | − | 0.904195i | \(-0.359528\pi\) | ||||
0.427120 | + | 0.904195i | \(0.359528\pi\) | |||||||
\(80\) | −1.11842e8 | −0.305282 | ||||||||
\(81\) | −4.10412e8 | −1.05935 | ||||||||
\(82\) | −1.62010e8 | −0.395713 | ||||||||
\(83\) | 4.61094e8 | 1.06644 | 0.533222 | − | 0.845975i | \(-0.320981\pi\) | ||||
0.533222 | + | 0.845975i | \(0.320981\pi\) | |||||||
\(84\) | 3.20906e8 | 0.703267 | ||||||||
\(85\) | −4.26040e8 | −0.885249 | ||||||||
\(86\) | 4.10156e8 | 0.808548 | ||||||||
\(87\) | 7.57509e8 | 1.41759 | ||||||||
\(88\) | −5.99695e7 | −0.106600 | ||||||||
\(89\) | 4.63623e8 | 0.783267 | 0.391634 | − | 0.920121i | \(-0.371910\pi\) | ||||
0.391634 | + | 0.920121i | \(0.371910\pi\) | |||||||
\(90\) | 3.40530e7 | 0.0547097 | ||||||||
\(91\) | −5.87915e8 | −0.898728 | ||||||||
\(92\) | 2.82407e8 | 0.410990 | ||||||||
\(93\) | 1.21290e9 | 1.68133 | ||||||||
\(94\) | −9.42388e8 | −1.24496 | ||||||||
\(95\) | 5.00351e8 | 0.630258 | ||||||||
\(96\) | 1.51700e8 | 0.182291 | ||||||||
\(97\) | 1.06866e8 | 0.122565 | 0.0612825 | − | 0.998120i | \(-0.480481\pi\) | ||||
0.0612825 | + | 0.998120i | \(0.480481\pi\) | |||||||
\(98\) | −5.55563e8 | −0.608437 | ||||||||
\(99\) | 1.82591e7 | 0.0191039 | ||||||||
\(100\) | 2.45579e8 | 0.245579 | ||||||||
\(101\) | 1.38561e9 | 1.32494 | 0.662470 | − | 0.749088i | \(-0.269508\pi\) | ||||
0.662470 | + | 0.749088i | \(0.269508\pi\) | |||||||
\(102\) | 5.77869e8 | 0.528602 | ||||||||
\(103\) | −1.45242e9 | −1.27152 | −0.635760 | − | 0.771886i | \(-0.719313\pi\) | ||||
−0.635760 | + | 0.771886i | \(0.719313\pi\) | |||||||
\(104\) | −2.77922e8 | −0.232955 | ||||||||
\(105\) | −2.13926e9 | −1.71756 | ||||||||
\(106\) | −1.38996e9 | −1.06936 | ||||||||
\(107\) | 1.44377e9 | 1.06481 | 0.532405 | − | 0.846490i | \(-0.321288\pi\) | ||||
0.532405 | + | 0.846490i | \(0.321288\pi\) | |||||||
\(108\) | 6.82794e8 | 0.482928 | ||||||||
\(109\) | 2.58675e9 | 1.75524 | 0.877618 | − | 0.479361i | \(-0.159132\pi\) | ||||
0.877618 | + | 0.479361i | \(0.159132\pi\) | |||||||
\(110\) | 3.99777e8 | 0.260346 | ||||||||
\(111\) | −1.06276e9 | −0.664482 | ||||||||
\(112\) | −5.67847e8 | −0.340997 | ||||||||
\(113\) | 1.13601e9 | 0.655433 | 0.327717 | − | 0.944776i | \(-0.393721\pi\) | ||||
0.327717 | + | 0.944776i | \(0.393721\pi\) | |||||||
\(114\) | −6.78662e8 | −0.376341 | ||||||||
\(115\) | −1.88262e9 | −1.00374 | ||||||||
\(116\) | −1.34042e9 | −0.687354 | ||||||||
\(117\) | 8.46198e7 | 0.0417480 | ||||||||
\(118\) | 2.91683e9 | 1.38498 | ||||||||
\(119\) | −2.16309e9 | −0.988812 | ||||||||
\(120\) | −1.01128e9 | −0.445202 | ||||||||
\(121\) | 2.14359e8 | 0.0909091 | ||||||||
\(122\) | −1.95367e9 | −0.798422 | ||||||||
\(123\) | −1.46490e9 | −0.577079 | ||||||||
\(124\) | −2.14625e9 | −0.815234 | ||||||||
\(125\) | 1.69605e9 | 0.621362 | ||||||||
\(126\) | 1.72894e8 | 0.0611101 | ||||||||
\(127\) | −3.27848e9 | −1.11829 | −0.559147 | − | 0.829068i | \(-0.688871\pi\) | ||||
−0.559147 | + | 0.829068i | \(0.688871\pi\) | |||||||
\(128\) | −2.68435e8 | −0.0883883 | ||||||||
\(129\) | 3.70864e9 | 1.17913 | ||||||||
\(130\) | 1.85272e9 | 0.568938 | ||||||||
\(131\) | 1.81056e9 | 0.537146 | 0.268573 | − | 0.963259i | \(-0.413448\pi\) | ||||
0.268573 | + | 0.963259i | \(0.413448\pi\) | |||||||
\(132\) | −5.42246e8 | −0.155458 | ||||||||
\(133\) | 2.54038e9 | 0.703991 | ||||||||
\(134\) | 1.08885e9 | 0.291741 | ||||||||
\(135\) | −4.55173e9 | −1.17944 | ||||||||
\(136\) | −1.02255e9 | −0.256306 | ||||||||
\(137\) | −3.19317e9 | −0.774425 | −0.387213 | − | 0.921990i | \(-0.626562\pi\) | ||||
−0.387213 | + | 0.921990i | \(0.626562\pi\) | |||||||
\(138\) | 2.55354e9 | 0.599358 | ||||||||
\(139\) | −8.30571e8 | −0.188717 | −0.0943583 | − | 0.995538i | \(-0.530080\pi\) | ||||
−0.0943583 | + | 0.995538i | \(0.530080\pi\) | |||||||
\(140\) | 3.78546e9 | 0.832803 | ||||||||
\(141\) | −8.52110e9 | −1.81556 | ||||||||
\(142\) | 2.67758e9 | 0.552643 | ||||||||
\(143\) | 9.93422e8 | 0.198665 | ||||||||
\(144\) | 8.17314e7 | 0.0158401 | ||||||||
\(145\) | 8.93570e9 | 1.67870 | ||||||||
\(146\) | 2.42878e9 | 0.442384 | ||||||||
\(147\) | −5.02341e9 | −0.887301 | ||||||||
\(148\) | 1.88058e9 | 0.322191 | ||||||||
\(149\) | 8.83876e9 | 1.46911 | 0.734553 | − | 0.678551i | \(-0.237392\pi\) | ||||
0.734553 | + | 0.678551i | \(0.237392\pi\) | |||||||
\(150\) | 2.22053e9 | 0.358135 | ||||||||
\(151\) | −6.05461e9 | −0.947742 | −0.473871 | − | 0.880594i | \(-0.657144\pi\) | ||||
−0.473871 | + | 0.880594i | \(0.657144\pi\) | |||||||
\(152\) | 1.20090e9 | 0.182479 | ||||||||
\(153\) | 3.11338e8 | 0.0459326 | ||||||||
\(154\) | 2.02975e9 | 0.290803 | ||||||||
\(155\) | 1.43076e10 | 1.99101 | ||||||||
\(156\) | −2.51298e9 | −0.339726 | ||||||||
\(157\) | −3.21421e9 | −0.422208 | −0.211104 | − | 0.977464i | \(-0.567706\pi\) | ||||
−0.211104 | + | 0.977464i | \(0.567706\pi\) | |||||||
\(158\) | −4.73176e9 | −0.604040 | ||||||||
\(159\) | −1.25680e10 | −1.55948 | ||||||||
\(160\) | 1.78948e9 | 0.215867 | ||||||||
\(161\) | −9.55845e9 | −1.12117 | ||||||||
\(162\) | 6.56660e9 | 0.749071 | ||||||||
\(163\) | 3.35516e9 | 0.372279 | 0.186140 | − | 0.982523i | \(-0.440402\pi\) | ||||
0.186140 | + | 0.982523i | \(0.440402\pi\) | |||||||
\(164\) | 2.59217e9 | 0.279811 | ||||||||
\(165\) | 3.61479e9 | 0.379670 | ||||||||
\(166\) | −7.37750e9 | −0.754090 | ||||||||
\(167\) | 1.13205e10 | 1.12627 | 0.563136 | − | 0.826364i | \(-0.309595\pi\) | ||||
0.563136 | + | 0.826364i | \(0.309595\pi\) | |||||||
\(168\) | −5.13449e9 | −0.497285 | ||||||||
\(169\) | −6.00060e9 | −0.565854 | ||||||||
\(170\) | 6.81665e9 | 0.625966 | ||||||||
\(171\) | −3.65643e8 | −0.0327020 | ||||||||
\(172\) | −6.56249e9 | −0.571730 | ||||||||
\(173\) | 1.24081e10 | 1.05317 | 0.526586 | − | 0.850122i | \(-0.323472\pi\) | ||||
0.526586 | + | 0.850122i | \(0.323472\pi\) | |||||||
\(174\) | −1.21201e10 | −1.00239 | ||||||||
\(175\) | −8.31195e9 | −0.669934 | ||||||||
\(176\) | 9.59513e8 | 0.0753778 | ||||||||
\(177\) | 2.63741e10 | 2.01975 | ||||||||
\(178\) | −7.41797e9 | −0.553854 | ||||||||
\(179\) | −1.78548e10 | −1.29992 | −0.649960 | − | 0.759968i | \(-0.725215\pi\) | ||||
−0.649960 | + | 0.759968i | \(0.725215\pi\) | |||||||
\(180\) | −5.44848e8 | −0.0386856 | ||||||||
\(181\) | 2.69794e10 | 1.86844 | 0.934220 | − | 0.356698i | \(-0.116098\pi\) | ||||
0.934220 | + | 0.356698i | \(0.116098\pi\) | |||||||
\(182\) | 9.40664e9 | 0.635496 | ||||||||
\(183\) | −1.76652e10 | −1.16436 | ||||||||
\(184\) | −4.51852e9 | −0.290614 | ||||||||
\(185\) | −1.25365e10 | −0.786874 | ||||||||
\(186\) | −1.94064e10 | −1.18888 | ||||||||
\(187\) | 3.65506e9 | 0.218578 | ||||||||
\(188\) | 1.50782e10 | 0.880318 | ||||||||
\(189\) | −2.31101e10 | −1.31742 | ||||||||
\(190\) | −8.00562e9 | −0.445660 | ||||||||
\(191\) | −1.88704e10 | −1.02596 | −0.512980 | − | 0.858400i | \(-0.671459\pi\) | ||||
−0.512980 | + | 0.858400i | \(0.671459\pi\) | |||||||
\(192\) | −2.42720e9 | −0.128899 | ||||||||
\(193\) | −1.63769e10 | −0.849618 | −0.424809 | − | 0.905283i | \(-0.639659\pi\) | ||||
−0.424809 | + | 0.905283i | \(0.639659\pi\) | |||||||
\(194\) | −1.70985e9 | −0.0866665 | ||||||||
\(195\) | 1.67524e10 | 0.829698 | ||||||||
\(196\) | 8.88900e9 | 0.430230 | ||||||||
\(197\) | −2.41377e10 | −1.14182 | −0.570909 | − | 0.821013i | \(-0.693409\pi\) | ||||
−0.570909 | + | 0.821013i | \(0.693409\pi\) | |||||||
\(198\) | −2.92146e8 | −0.0135085 | ||||||||
\(199\) | −6.98474e7 | −0.00315727 | −0.00157863 | − | 0.999999i | \(-0.500502\pi\) | ||||
−0.00157863 | + | 0.999999i | \(0.500502\pi\) | |||||||
\(200\) | −3.92927e9 | −0.173651 | ||||||||
\(201\) | 9.84543e9 | 0.425454 | ||||||||
\(202\) | −2.21698e10 | −0.936874 | ||||||||
\(203\) | 4.53684e10 | 1.87508 | ||||||||
\(204\) | −9.24591e9 | −0.373778 | ||||||||
\(205\) | −1.72802e10 | −0.683372 | ||||||||
\(206\) | 2.32387e10 | 0.899101 | ||||||||
\(207\) | 1.37577e9 | 0.0520809 | ||||||||
\(208\) | 4.44675e9 | 0.164724 | ||||||||
\(209\) | −4.29258e9 | −0.155618 | ||||||||
\(210\) | 3.42282e10 | 1.21450 | ||||||||
\(211\) | 3.34436e10 | 1.16156 | 0.580780 | − | 0.814061i | \(-0.302748\pi\) | ||||
0.580780 | + | 0.814061i | \(0.302748\pi\) | |||||||
\(212\) | 2.22393e10 | 0.756153 | ||||||||
\(213\) | 2.42107e10 | 0.805935 | ||||||||
\(214\) | −2.31004e10 | −0.752935 | ||||||||
\(215\) | 4.37478e10 | 1.39631 | ||||||||
\(216\) | −1.09247e10 | −0.341482 | ||||||||
\(217\) | 7.26426e10 | 2.22394 | ||||||||
\(218\) | −4.13880e10 | −1.24114 | ||||||||
\(219\) | 2.19611e10 | 0.645141 | ||||||||
\(220\) | −6.39643e9 | −0.184092 | ||||||||
\(221\) | 1.69390e10 | 0.477663 | ||||||||
\(222\) | 1.70042e10 | 0.469860 | ||||||||
\(223\) | −1.74786e10 | −0.473299 | −0.236650 | − | 0.971595i | \(-0.576049\pi\) | ||||
−0.236650 | + | 0.971595i | \(0.576049\pi\) | |||||||
\(224\) | 9.08555e9 | 0.241121 | ||||||||
\(225\) | 1.19636e9 | 0.0311200 | ||||||||
\(226\) | −1.81761e10 | −0.463461 | ||||||||
\(227\) | −1.99552e10 | −0.498816 | −0.249408 | − | 0.968398i | \(-0.580236\pi\) | ||||
−0.249408 | + | 0.968398i | \(0.580236\pi\) | |||||||
\(228\) | 1.08586e10 | 0.266114 | ||||||||
\(229\) | −7.45741e10 | −1.79196 | −0.895980 | − | 0.444095i | \(-0.853525\pi\) | ||||
−0.895980 | + | 0.444095i | \(0.853525\pi\) | |||||||
\(230\) | 3.01220e10 | 0.709754 | ||||||||
\(231\) | 1.83530e10 | 0.424086 | ||||||||
\(232\) | 2.14468e10 | 0.486033 | ||||||||
\(233\) | −4.84331e10 | −1.07657 | −0.538283 | − | 0.842764i | \(-0.680927\pi\) | ||||
−0.538283 | + | 0.842764i | \(0.680927\pi\) | |||||||
\(234\) | −1.35392e9 | −0.0295203 | ||||||||
\(235\) | −1.00516e11 | −2.14996 | ||||||||
\(236\) | −4.66693e10 | −0.979326 | ||||||||
\(237\) | −4.27847e10 | −0.880888 | ||||||||
\(238\) | 3.46095e10 | 0.699196 | ||||||||
\(239\) | −2.76719e10 | −0.548591 | −0.274295 | − | 0.961645i | \(-0.588445\pi\) | ||||
−0.274295 | + | 0.961645i | \(0.588445\pi\) | |||||||
\(240\) | 1.61805e10 | 0.314805 | ||||||||
\(241\) | 5.23953e10 | 1.00050 | 0.500248 | − | 0.865882i | \(-0.333242\pi\) | ||||
0.500248 | + | 0.865882i | \(0.333242\pi\) | |||||||
\(242\) | −3.42974e9 | −0.0642824 | ||||||||
\(243\) | 6.87757e9 | 0.126534 | ||||||||
\(244\) | 3.12587e10 | 0.564569 | ||||||||
\(245\) | −5.92571e10 | −1.05073 | ||||||||
\(246\) | 2.34384e10 | 0.408057 | ||||||||
\(247\) | −1.98935e10 | −0.340075 | ||||||||
\(248\) | 3.43400e10 | 0.576458 | ||||||||
\(249\) | −6.67076e10 | −1.09971 | ||||||||
\(250\) | −2.71369e10 | −0.439369 | ||||||||
\(251\) | 5.45608e10 | 0.867659 | 0.433829 | − | 0.900995i | \(-0.357162\pi\) | ||||
0.433829 | + | 0.900995i | \(0.357162\pi\) | |||||||
\(252\) | −2.76631e9 | −0.0432113 | ||||||||
\(253\) | 1.61513e10 | 0.247836 | ||||||||
\(254\) | 5.24557e10 | 0.790754 | ||||||||
\(255\) | 6.16363e10 | 0.912863 | ||||||||
\(256\) | 4.29497e9 | 0.0625000 | ||||||||
\(257\) | 1.72020e10 | 0.245969 | 0.122985 | − | 0.992409i | \(-0.460753\pi\) | ||||
0.122985 | + | 0.992409i | \(0.460753\pi\) | |||||||
\(258\) | −5.93383e10 | −0.833770 | ||||||||
\(259\) | −6.36506e10 | −0.878928 | ||||||||
\(260\) | −2.96435e10 | −0.402300 | ||||||||
\(261\) | −6.52996e9 | −0.0871020 | ||||||||
\(262\) | −2.89690e10 | −0.379819 | ||||||||
\(263\) | −2.32552e10 | −0.299722 | −0.149861 | − | 0.988707i | \(-0.547883\pi\) | ||||
−0.149861 | + | 0.988707i | \(0.547883\pi\) | |||||||
\(264\) | 8.67594e9 | 0.109926 | ||||||||
\(265\) | −1.48255e11 | −1.84672 | ||||||||
\(266\) | −4.06461e10 | −0.497797 | ||||||||
\(267\) | −6.70735e10 | −0.807700 | ||||||||
\(268\) | −1.74216e10 | −0.206292 | ||||||||
\(269\) | 2.82157e10 | 0.328554 | 0.164277 | − | 0.986414i | \(-0.447471\pi\) | ||||
0.164277 | + | 0.986414i | \(0.447471\pi\) | |||||||
\(270\) | 7.28277e10 | 0.833988 | ||||||||
\(271\) | 1.37207e11 | 1.54530 | 0.772651 | − | 0.634831i | \(-0.218930\pi\) | ||||
0.772651 | + | 0.634831i | \(0.218930\pi\) | |||||||
\(272\) | 1.63608e10 | 0.181236 | ||||||||
\(273\) | 8.50551e10 | 0.926762 | ||||||||
\(274\) | 5.10907e10 | 0.547601 | ||||||||
\(275\) | 1.40450e10 | 0.148090 | ||||||||
\(276\) | −4.08566e10 | −0.423810 | ||||||||
\(277\) | 1.85402e11 | 1.89215 | 0.946074 | − | 0.323949i | \(-0.105011\pi\) | ||||
0.946074 | + | 0.323949i | \(0.105011\pi\) | |||||||
\(278\) | 1.32891e10 | 0.133443 | ||||||||
\(279\) | −1.04556e10 | −0.103307 | ||||||||
\(280\) | −6.05673e10 | −0.588880 | ||||||||
\(281\) | −5.20765e10 | −0.498268 | −0.249134 | − | 0.968469i | \(-0.580146\pi\) | ||||
−0.249134 | + | 0.968469i | \(0.580146\pi\) | |||||||
\(282\) | 1.36338e11 | 1.28379 | ||||||||
\(283\) | 1.03796e11 | 0.961925 | 0.480963 | − | 0.876741i | \(-0.340287\pi\) | ||||
0.480963 | + | 0.876741i | \(0.340287\pi\) | |||||||
\(284\) | −4.28412e10 | −0.390777 | ||||||||
\(285\) | −7.23870e10 | −0.649918 | ||||||||
\(286\) | −1.58948e10 | −0.140477 | ||||||||
\(287\) | −8.77352e10 | −0.763318 | ||||||||
\(288\) | −1.30770e9 | −0.0112006 | ||||||||
\(289\) | −5.62650e10 | −0.474458 | ||||||||
\(290\) | −1.42971e11 | −1.18702 | ||||||||
\(291\) | −1.54606e10 | −0.126388 | ||||||||
\(292\) | −3.88604e10 | −0.312813 | ||||||||
\(293\) | −8.51536e10 | −0.674992 | −0.337496 | − | 0.941327i | \(-0.609580\pi\) | ||||
−0.337496 | + | 0.941327i | \(0.609580\pi\) | |||||||
\(294\) | 8.03746e10 | 0.627417 | ||||||||
\(295\) | 3.11113e11 | 2.39177 | ||||||||
\(296\) | −3.00892e10 | −0.227823 | ||||||||
\(297\) | 3.90499e10 | 0.291217 | ||||||||
\(298\) | −1.41420e11 | −1.03881 | ||||||||
\(299\) | 7.48513e10 | 0.541600 | ||||||||
\(300\) | −3.55285e10 | −0.253240 | ||||||||
\(301\) | 2.22116e11 | 1.55966 | ||||||||
\(302\) | 9.68738e10 | 0.670155 | ||||||||
\(303\) | −2.00460e11 | −1.36627 | ||||||||
\(304\) | −1.92144e10 | −0.129032 | ||||||||
\(305\) | −2.08381e11 | −1.37882 | ||||||||
\(306\) | −4.98141e9 | −0.0324793 | ||||||||
\(307\) | 2.79447e11 | 1.79547 | 0.897734 | − | 0.440539i | \(-0.145213\pi\) | ||||
0.897734 | + | 0.440539i | \(0.145213\pi\) | |||||||
\(308\) | −3.24760e10 | −0.205629 | ||||||||
\(309\) | 2.10125e11 | 1.31118 | ||||||||
\(310\) | −2.28922e11 | −1.40786 | ||||||||
\(311\) | 2.40111e11 | 1.45543 | 0.727714 | − | 0.685881i | \(-0.240583\pi\) | ||||
0.727714 | + | 0.685881i | \(0.240583\pi\) | |||||||
\(312\) | 4.02077e10 | 0.240222 | ||||||||
\(313\) | 9.68635e10 | 0.570441 | 0.285220 | − | 0.958462i | \(-0.407933\pi\) | ||||
0.285220 | + | 0.958462i | \(0.407933\pi\) | |||||||
\(314\) | 5.14274e10 | 0.298546 | ||||||||
\(315\) | 1.84411e10 | 0.105533 | ||||||||
\(316\) | 7.57081e10 | 0.427120 | ||||||||
\(317\) | −1.70124e11 | −0.946237 | −0.473118 | − | 0.880999i | \(-0.656872\pi\) | ||||
−0.473118 | + | 0.880999i | \(0.656872\pi\) | |||||||
\(318\) | 2.01088e11 | 1.10272 | ||||||||
\(319\) | −7.66606e10 | −0.414490 | ||||||||
\(320\) | −2.86317e10 | −0.152641 | ||||||||
\(321\) | −2.08874e11 | −1.09803 | ||||||||
\(322\) | 1.52935e11 | 0.792786 | ||||||||
\(323\) | −7.31934e10 | −0.374163 | ||||||||
\(324\) | −1.05066e11 | −0.529673 | ||||||||
\(325\) | 6.50900e10 | 0.323623 | ||||||||
\(326\) | −5.36825e10 | −0.263241 | ||||||||
\(327\) | −3.74232e11 | −1.80999 | ||||||||
\(328\) | −4.14746e10 | −0.197857 | ||||||||
\(329\) | −5.10342e11 | −2.40148 | ||||||||
\(330\) | −5.78367e10 | −0.268467 | ||||||||
\(331\) | 2.45318e10 | 0.112332 | 0.0561661 | − | 0.998421i | \(-0.482112\pi\) | ||||
0.0561661 | + | 0.998421i | \(0.482112\pi\) | |||||||
\(332\) | 1.18040e11 | 0.533222 | ||||||||
\(333\) | 9.16136e9 | 0.0408282 | ||||||||
\(334\) | −1.81129e11 | −0.796394 | ||||||||
\(335\) | 1.16138e11 | 0.503818 | ||||||||
\(336\) | 8.21518e10 | 0.351634 | ||||||||
\(337\) | 9.64453e10 | 0.407330 | 0.203665 | − | 0.979041i | \(-0.434715\pi\) | ||||
0.203665 | + | 0.979041i | \(0.434715\pi\) | |||||||
\(338\) | 9.60096e10 | 0.400119 | ||||||||
\(339\) | −1.64349e11 | −0.675879 | ||||||||
\(340\) | −1.09066e11 | −0.442625 | ||||||||
\(341\) | −1.22747e11 | −0.491605 | ||||||||
\(342\) | 5.85028e9 | 0.0231238 | ||||||||
\(343\) | 4.87901e10 | 0.190330 | ||||||||
\(344\) | 1.05000e11 | 0.404274 | ||||||||
\(345\) | 2.72364e11 | 1.03505 | ||||||||
\(346\) | −1.98530e11 | −0.744704 | ||||||||
\(347\) | −1.02569e11 | −0.379783 | −0.189891 | − | 0.981805i | \(-0.560814\pi\) | ||||
−0.189891 | + | 0.981805i | \(0.560814\pi\) | |||||||
\(348\) | 1.93922e11 | 0.708796 | ||||||||
\(349\) | −3.59960e11 | −1.29879 | −0.649397 | − | 0.760450i | \(-0.724979\pi\) | ||||
−0.649397 | + | 0.760450i | \(0.724979\pi\) | |||||||
\(350\) | 1.32991e11 | 0.473715 | ||||||||
\(351\) | 1.80973e11 | 0.636401 | ||||||||
\(352\) | −1.53522e10 | −0.0533002 | ||||||||
\(353\) | −6.23410e10 | −0.213692 | −0.106846 | − | 0.994276i | \(-0.534075\pi\) | ||||
−0.106846 | + | 0.994276i | \(0.534075\pi\) | |||||||
\(354\) | −4.21985e11 | −1.42818 | ||||||||
\(355\) | 2.85594e11 | 0.954380 | ||||||||
\(356\) | 1.18687e11 | 0.391634 | ||||||||
\(357\) | 3.12940e11 | 1.01966 | ||||||||
\(358\) | 2.85677e11 | 0.919183 | ||||||||
\(359\) | −1.12478e11 | −0.357391 | −0.178696 | − | 0.983904i | \(-0.557188\pi\) | ||||
−0.178696 | + | 0.983904i | \(0.557188\pi\) | |||||||
\(360\) | 8.71758e9 | 0.0273549 | ||||||||
\(361\) | −2.36728e11 | −0.733613 | ||||||||
\(362\) | −4.31671e11 | −1.32119 | ||||||||
\(363\) | −3.10118e10 | −0.0937449 | ||||||||
\(364\) | −1.50506e11 | −0.449364 | ||||||||
\(365\) | 2.59056e11 | 0.763970 | ||||||||
\(366\) | 2.82642e11 | 0.823327 | ||||||||
\(367\) | 1.51938e11 | 0.437189 | 0.218594 | − | 0.975816i | \(-0.429853\pi\) | ||||
0.218594 | + | 0.975816i | \(0.429853\pi\) | |||||||
\(368\) | 7.22963e10 | 0.205495 | ||||||||
\(369\) | 1.26279e10 | 0.0354579 | ||||||||
\(370\) | 2.00585e11 | 0.556404 | ||||||||
\(371\) | −7.52719e11 | −2.06277 | ||||||||
\(372\) | 3.10503e11 | 0.840664 | ||||||||
\(373\) | 1.79048e11 | 0.478938 | 0.239469 | − | 0.970904i | \(-0.423027\pi\) | ||||
0.239469 | + | 0.970904i | \(0.423027\pi\) | |||||||
\(374\) | −5.84810e10 | −0.154558 | ||||||||
\(375\) | −2.45372e11 | −0.640744 | ||||||||
\(376\) | −2.41251e11 | −0.622479 | ||||||||
\(377\) | −3.55275e11 | −0.905792 | ||||||||
\(378\) | 3.69761e11 | 0.931554 | ||||||||
\(379\) | 2.31277e11 | 0.575780 | 0.287890 | − | 0.957663i | \(-0.407046\pi\) | ||||
0.287890 | + | 0.957663i | \(0.407046\pi\) | |||||||
\(380\) | 1.28090e11 | 0.315129 | ||||||||
\(381\) | 4.74306e11 | 1.15318 | ||||||||
\(382\) | 3.01926e11 | 0.725463 | ||||||||
\(383\) | 3.53920e11 | 0.840448 | 0.420224 | − | 0.907420i | \(-0.361951\pi\) | ||||
0.420224 | + | 0.907420i | \(0.361951\pi\) | |||||||
\(384\) | 3.88352e10 | 0.0911455 | ||||||||
\(385\) | 2.16496e11 | 0.502199 | ||||||||
\(386\) | 2.62030e11 | 0.600771 | ||||||||
\(387\) | −3.19696e10 | −0.0724500 | ||||||||
\(388\) | 2.73577e10 | 0.0612825 | ||||||||
\(389\) | 4.20470e11 | 0.931027 | 0.465513 | − | 0.885041i | \(-0.345870\pi\) | ||||
0.465513 | + | 0.885041i | \(0.345870\pi\) | |||||||
\(390\) | −2.68038e11 | −0.586685 | ||||||||
\(391\) | 2.75398e11 | 0.595888 | ||||||||
\(392\) | −1.42224e11 | −0.304219 | ||||||||
\(393\) | −2.61938e11 | −0.553901 | ||||||||
\(394\) | 3.86203e11 | 0.807388 | ||||||||
\(395\) | −5.04695e11 | −1.04314 | ||||||||
\(396\) | 4.67433e9 | 0.00955193 | ||||||||
\(397\) | −3.43330e11 | −0.693672 | −0.346836 | − | 0.937926i | \(-0.612744\pi\) | ||||
−0.346836 | + | 0.937926i | \(0.612744\pi\) | |||||||
\(398\) | 1.11756e9 | 0.00223253 | ||||||||
\(399\) | −3.67524e11 | −0.725951 | ||||||||
\(400\) | 6.28683e10 | 0.122790 | ||||||||
\(401\) | 5.15897e11 | 0.996354 | 0.498177 | − | 0.867075i | \(-0.334003\pi\) | ||||
0.498177 | + | 0.867075i | \(0.334003\pi\) | |||||||
\(402\) | −1.57527e11 | −0.300841 | ||||||||
\(403\) | −5.68857e11 | −1.07431 | ||||||||
\(404\) | 3.54717e11 | 0.662470 | ||||||||
\(405\) | 7.00402e11 | 1.29360 | ||||||||
\(406\) | −7.25894e11 | −1.32589 | ||||||||
\(407\) | 1.07553e11 | 0.194288 | ||||||||
\(408\) | 1.47935e11 | 0.264301 | ||||||||
\(409\) | −4.68357e11 | −0.827604 | −0.413802 | − | 0.910367i | \(-0.635799\pi\) | ||||
−0.413802 | + | 0.910367i | \(0.635799\pi\) | |||||||
\(410\) | 2.76484e11 | 0.483217 | ||||||||
\(411\) | 4.61964e11 | 0.798582 | ||||||||
\(412\) | −3.71819e11 | −0.635760 | ||||||||
\(413\) | 1.57958e12 | 2.67158 | ||||||||
\(414\) | −2.20123e10 | −0.0368268 | ||||||||
\(415\) | −7.86894e11 | −1.30227 | ||||||||
\(416\) | −7.11480e10 | −0.116478 | ||||||||
\(417\) | 1.20161e11 | 0.194603 | ||||||||
\(418\) | 6.86813e10 | 0.110039 | ||||||||
\(419\) | −1.15054e12 | −1.82364 | −0.911820 | − | 0.410590i | \(-0.865323\pi\) | ||||
−0.911820 | + | 0.410590i | \(0.865323\pi\) | |||||||
\(420\) | −5.47651e11 | −0.858781 | ||||||||
\(421\) | −2.49749e11 | −0.387467 | −0.193734 | − | 0.981054i | \(-0.562060\pi\) | ||||
−0.193734 | + | 0.981054i | \(0.562060\pi\) | |||||||
\(422\) | −5.35097e11 | −0.821347 | ||||||||
\(423\) | 7.34545e10 | 0.111554 | ||||||||
\(424\) | −3.55829e11 | −0.534681 | ||||||||
\(425\) | 2.39483e11 | 0.356062 | ||||||||
\(426\) | −3.87372e11 | −0.569882 | ||||||||
\(427\) | −1.05799e12 | −1.54013 | ||||||||
\(428\) | 3.69606e11 | 0.532405 | ||||||||
\(429\) | −1.43721e11 | −0.204862 | ||||||||
\(430\) | −6.99964e11 | −0.987342 | ||||||||
\(431\) | 2.80621e11 | 0.391717 | 0.195858 | − | 0.980632i | \(-0.437251\pi\) | ||||
0.195858 | + | 0.980632i | \(0.437251\pi\) | |||||||
\(432\) | 1.74795e11 | 0.241464 | ||||||||
\(433\) | 1.07421e12 | 1.46857 | 0.734285 | − | 0.678841i | \(-0.237518\pi\) | ||||
0.734285 | + | 0.678841i | \(0.237518\pi\) | |||||||
\(434\) | −1.16228e12 | −1.57256 | ||||||||
\(435\) | −1.29275e12 | −1.73106 | ||||||||
\(436\) | 6.62208e11 | 0.877618 | ||||||||
\(437\) | −3.23433e11 | −0.424246 | ||||||||
\(438\) | −3.51377e11 | −0.456184 | ||||||||
\(439\) | 9.45531e11 | 1.21503 | 0.607513 | − | 0.794310i | \(-0.292167\pi\) | ||||
0.607513 | + | 0.794310i | \(0.292167\pi\) | |||||||
\(440\) | 1.02343e11 | 0.130173 | ||||||||
\(441\) | 4.33034e10 | 0.0545191 | ||||||||
\(442\) | −2.71023e11 | −0.337759 | ||||||||
\(443\) | 1.41348e12 | 1.74370 | 0.871852 | − | 0.489769i | \(-0.162919\pi\) | ||||
0.871852 | + | 0.489769i | \(0.162919\pi\) | |||||||
\(444\) | −2.72068e11 | −0.332241 | ||||||||
\(445\) | −7.91210e11 | −0.956471 | ||||||||
\(446\) | 2.79658e11 | 0.334673 | ||||||||
\(447\) | −1.27873e12 | −1.51493 | ||||||||
\(448\) | −1.45369e11 | −0.170498 | ||||||||
\(449\) | 3.24374e11 | 0.376650 | 0.188325 | − | 0.982107i | \(-0.439694\pi\) | ||||
0.188325 | + | 0.982107i | \(0.439694\pi\) | |||||||
\(450\) | −1.91417e10 | −0.0220051 | ||||||||
\(451\) | 1.48250e11 | 0.168733 | ||||||||
\(452\) | 2.90818e11 | 0.327717 | ||||||||
\(453\) | 8.75936e11 | 0.977305 | ||||||||
\(454\) | 3.19284e11 | 0.352716 | ||||||||
\(455\) | 1.00332e12 | 1.09746 | ||||||||
\(456\) | −1.73738e11 | −0.188171 | ||||||||
\(457\) | −1.44780e11 | −0.155269 | −0.0776344 | − | 0.996982i | \(-0.524737\pi\) | ||||
−0.0776344 | + | 0.996982i | \(0.524737\pi\) | |||||||
\(458\) | 1.19319e12 | 1.26711 | ||||||||
\(459\) | 6.65846e11 | 0.700191 | ||||||||
\(460\) | −4.81951e11 | −0.501872 | ||||||||
\(461\) | 2.94094e11 | 0.303271 | 0.151636 | − | 0.988436i | \(-0.451546\pi\) | ||||
0.151636 | + | 0.988436i | \(0.451546\pi\) | |||||||
\(462\) | −2.93649e11 | −0.299874 | ||||||||
\(463\) | 8.78478e11 | 0.888416 | 0.444208 | − | 0.895924i | \(-0.353485\pi\) | ||||
0.444208 | + | 0.895924i | \(0.353485\pi\) | |||||||
\(464\) | −3.43148e11 | −0.343677 | ||||||||
\(465\) | −2.06992e12 | −2.05312 | ||||||||
\(466\) | 7.74930e11 | 0.761247 | ||||||||
\(467\) | 6.31625e11 | 0.614516 | 0.307258 | − | 0.951626i | \(-0.400589\pi\) | ||||
0.307258 | + | 0.951626i | \(0.400589\pi\) | |||||||
\(468\) | 2.16627e10 | 0.0208740 | ||||||||
\(469\) | 5.89658e11 | 0.562759 | ||||||||
\(470\) | 1.60826e12 | 1.52025 | ||||||||
\(471\) | 4.65008e11 | 0.435378 | ||||||||
\(472\) | 7.46709e11 | 0.692488 | ||||||||
\(473\) | −3.75318e11 | −0.344766 | ||||||||
\(474\) | 6.84555e11 | 0.622882 | ||||||||
\(475\) | −2.81255e11 | −0.253500 | ||||||||
\(476\) | −5.53752e11 | −0.494406 | ||||||||
\(477\) | 1.08340e11 | 0.0958203 | ||||||||
\(478\) | 4.42750e11 | 0.387912 | ||||||||
\(479\) | −1.70132e12 | −1.47664 | −0.738321 | − | 0.674449i | \(-0.764381\pi\) | ||||
−0.738321 | + | 0.674449i | \(0.764381\pi\) | |||||||
\(480\) | −2.58888e11 | −0.222601 | ||||||||
\(481\) | 4.98441e11 | 0.424581 | ||||||||
\(482\) | −8.38324e11 | −0.707458 | ||||||||
\(483\) | 1.38284e12 | 1.15614 | ||||||||
\(484\) | 5.48759e10 | 0.0454545 | ||||||||
\(485\) | −1.82375e11 | −0.149668 | ||||||||
\(486\) | −1.10041e11 | −0.0894729 | ||||||||
\(487\) | 2.17815e11 | 0.175472 | 0.0877358 | − | 0.996144i | \(-0.472037\pi\) | ||||
0.0877358 | + | 0.996144i | \(0.472037\pi\) | |||||||
\(488\) | −5.00140e11 | −0.399211 | ||||||||
\(489\) | −4.85399e11 | −0.383892 | ||||||||
\(490\) | 9.48113e11 | 0.742981 | ||||||||
\(491\) | 2.45219e11 | 0.190409 | 0.0952045 | − | 0.995458i | \(-0.469649\pi\) | ||||
0.0952045 | + | 0.995458i | \(0.469649\pi\) | |||||||
\(492\) | −3.75015e11 | −0.288540 | ||||||||
\(493\) | −1.30715e12 | −0.996585 | ||||||||
\(494\) | 3.18296e11 | 0.240469 | ||||||||
\(495\) | −3.11606e10 | −0.0233283 | ||||||||
\(496\) | −5.49440e11 | −0.407617 | ||||||||
\(497\) | 1.45002e12 | 1.06603 | ||||||||
\(498\) | 1.06732e12 | 0.777612 | ||||||||
\(499\) | −2.14365e12 | −1.54775 | −0.773876 | − | 0.633337i | \(-0.781685\pi\) | ||||
−0.773876 | + | 0.633337i | \(0.781685\pi\) | |||||||
\(500\) | 4.34190e11 | 0.310681 | ||||||||
\(501\) | −1.63777e12 | −1.16140 | ||||||||
\(502\) | −8.72973e11 | −0.613528 | ||||||||
\(503\) | 7.47725e11 | 0.520818 | 0.260409 | − | 0.965498i | \(-0.416143\pi\) | ||||
0.260409 | + | 0.965498i | \(0.416143\pi\) | |||||||
\(504\) | 4.42609e10 | 0.0305550 | ||||||||
\(505\) | −2.36466e12 | −1.61792 | ||||||||
\(506\) | −2.58420e11 | −0.175247 | ||||||||
\(507\) | 8.68121e11 | 0.583505 | ||||||||
\(508\) | −8.39292e11 | −0.559147 | ||||||||
\(509\) | 3.60539e11 | 0.238079 | 0.119040 | − | 0.992889i | \(-0.462018\pi\) | ||||
0.119040 | + | 0.992889i | \(0.462018\pi\) | |||||||
\(510\) | −9.86181e11 | −0.645492 | ||||||||
\(511\) | 1.31528e12 | 0.853345 | ||||||||
\(512\) | −6.87195e10 | −0.0441942 | ||||||||
\(513\) | −7.81984e11 | −0.498505 | ||||||||
\(514\) | −2.75232e11 | −0.173926 | ||||||||
\(515\) | 2.47867e12 | 1.55269 | ||||||||
\(516\) | 9.49412e11 | 0.589564 | ||||||||
\(517\) | 8.62344e11 | 0.530852 | ||||||||
\(518\) | 1.01841e12 | 0.621496 | ||||||||
\(519\) | −1.79511e12 | −1.08602 | ||||||||
\(520\) | 4.74296e11 | 0.284469 | ||||||||
\(521\) | −1.98989e12 | −1.18320 | −0.591602 | − | 0.806230i | \(-0.701504\pi\) | ||||
−0.591602 | + | 0.806230i | \(0.701504\pi\) | |||||||
\(522\) | 1.04479e11 | 0.0615904 | ||||||||
\(523\) | 1.26127e12 | 0.737140 | 0.368570 | − | 0.929600i | \(-0.379847\pi\) | ||||
0.368570 | + | 0.929600i | \(0.379847\pi\) | |||||||
\(524\) | 4.63503e11 | 0.268573 | ||||||||
\(525\) | 1.20251e12 | 0.690831 | ||||||||
\(526\) | 3.72083e11 | 0.211936 | ||||||||
\(527\) | −2.09297e12 | −1.18200 | ||||||||
\(528\) | −1.38815e11 | −0.0777291 | ||||||||
\(529\) | −5.84204e11 | −0.324350 | ||||||||
\(530\) | 2.37207e12 | 1.30583 | ||||||||
\(531\) | −2.27353e11 | −0.124101 | ||||||||
\(532\) | 6.50338e11 | 0.351995 | ||||||||
\(533\) | 6.87046e11 | 0.368734 | ||||||||
\(534\) | 1.07318e12 | 0.571130 | ||||||||
\(535\) | −2.46392e12 | −1.30027 | ||||||||
\(536\) | 2.78746e11 | 0.145870 | ||||||||
\(537\) | 2.58310e12 | 1.34047 | ||||||||
\(538\) | −4.51452e11 | −0.232322 | ||||||||
\(539\) | 5.08375e11 | 0.259439 | ||||||||
\(540\) | −1.16524e12 | −0.589718 | ||||||||
\(541\) | 3.48950e12 | 1.75136 | 0.875679 | − | 0.482893i | \(-0.160414\pi\) | ||||
0.875679 | + | 0.482893i | \(0.160414\pi\) | |||||||
\(542\) | −2.19531e12 | −1.09269 | ||||||||
\(543\) | −3.90318e12 | −1.92672 | ||||||||
\(544\) | −2.61772e11 | −0.128153 | ||||||||
\(545\) | −4.41450e12 | −2.14337 | ||||||||
\(546\) | −1.36088e12 | −0.655320 | ||||||||
\(547\) | −2.03037e12 | −0.969687 | −0.484844 | − | 0.874601i | \(-0.661123\pi\) | ||||
−0.484844 | + | 0.874601i | \(0.661123\pi\) | |||||||
\(548\) | −8.17452e11 | −0.387213 | ||||||||
\(549\) | 1.52279e11 | 0.0715426 | ||||||||
\(550\) | −2.24720e11 | −0.104715 | ||||||||
\(551\) | 1.53515e12 | 0.709525 | ||||||||
\(552\) | 6.53705e11 | 0.299679 | ||||||||
\(553\) | −2.56244e12 | −1.16517 | ||||||||
\(554\) | −2.96643e12 | −1.33795 | ||||||||
\(555\) | 1.81369e12 | 0.811419 | ||||||||
\(556\) | −2.12626e11 | −0.0943583 | ||||||||
\(557\) | 2.94692e12 | 1.29724 | 0.648620 | − | 0.761112i | \(-0.275346\pi\) | ||||
0.648620 | + | 0.761112i | \(0.275346\pi\) | |||||||
\(558\) | 1.67290e11 | 0.0730491 | ||||||||
\(559\) | −1.73937e12 | −0.753423 | ||||||||
\(560\) | 9.69077e11 | 0.416401 | ||||||||
\(561\) | −5.28787e11 | −0.225397 | ||||||||
\(562\) | 8.33224e11 | 0.352329 | ||||||||
\(563\) | −7.94805e11 | −0.333405 | −0.166703 | − | 0.986007i | \(-0.553312\pi\) | ||||
−0.166703 | + | 0.986007i | \(0.553312\pi\) | |||||||
\(564\) | −2.18140e12 | −0.907778 | ||||||||
\(565\) | −1.93869e12 | −0.800369 | ||||||||
\(566\) | −1.66073e12 | −0.680184 | ||||||||
\(567\) | 3.55608e12 | 1.44493 | ||||||||
\(568\) | 6.85460e11 | 0.276321 | ||||||||
\(569\) | 1.51857e12 | 0.607338 | 0.303669 | − | 0.952778i | \(-0.401788\pi\) | ||||
0.303669 | + | 0.952778i | \(0.401788\pi\) | |||||||
\(570\) | 1.15819e12 | 0.459562 | ||||||||
\(571\) | −2.97779e11 | −0.117228 | −0.0586140 | − | 0.998281i | \(-0.518668\pi\) | ||||
−0.0586140 | + | 0.998281i | \(0.518668\pi\) | |||||||
\(572\) | 2.54316e11 | 0.0993325 | ||||||||
\(573\) | 2.73002e12 | 1.05796 | ||||||||
\(574\) | 1.40376e12 | 0.539747 | ||||||||
\(575\) | 1.05825e12 | 0.403722 | ||||||||
\(576\) | 2.09232e10 | 0.00792004 | ||||||||
\(577\) | 1.81913e12 | 0.683241 | 0.341620 | − | 0.939838i | \(-0.389024\pi\) | ||||
0.341620 | + | 0.939838i | \(0.389024\pi\) | |||||||
\(578\) | 9.00239e11 | 0.335492 | ||||||||
\(579\) | 2.36929e12 | 0.876121 | ||||||||
\(580\) | 2.28754e12 | 0.839349 | ||||||||
\(581\) | −3.99522e12 | −1.45462 | ||||||||
\(582\) | 2.47369e11 | 0.0893700 | ||||||||
\(583\) | 1.27190e12 | 0.455978 | ||||||||
\(584\) | 6.21767e11 | 0.221192 | ||||||||
\(585\) | −1.44410e11 | −0.0509797 | ||||||||
\(586\) | 1.36246e12 | 0.477292 | ||||||||
\(587\) | 2.78354e12 | 0.967666 | 0.483833 | − | 0.875160i | \(-0.339244\pi\) | ||||
0.483833 | + | 0.875160i | \(0.339244\pi\) | |||||||
\(588\) | −1.28599e12 | −0.443651 | ||||||||
\(589\) | 2.45803e12 | 0.841529 | ||||||||
\(590\) | −4.97781e12 | −1.69124 | ||||||||
\(591\) | 3.49205e12 | 1.17744 | ||||||||
\(592\) | 4.81427e11 | 0.161095 | ||||||||
\(593\) | −5.56438e11 | −0.184787 | −0.0923933 | − | 0.995723i | \(-0.529452\pi\) | ||||
−0.0923933 | + | 0.995723i | \(0.529452\pi\) | |||||||
\(594\) | −6.24799e11 | −0.205921 | ||||||||
\(595\) | 3.69149e12 | 1.20747 | ||||||||
\(596\) | 2.26272e12 | 0.734553 | ||||||||
\(597\) | 1.01050e10 | 0.00325576 | ||||||||
\(598\) | −1.19762e12 | −0.382969 | ||||||||
\(599\) | −5.73449e12 | −1.82001 | −0.910006 | − | 0.414595i | \(-0.863923\pi\) | ||||
−0.910006 | + | 0.414595i | \(0.863923\pi\) | |||||||
\(600\) | 5.68457e11 | 0.179068 | ||||||||
\(601\) | 5.50049e11 | 0.171975 | 0.0859877 | − | 0.996296i | \(-0.472595\pi\) | ||||
0.0859877 | + | 0.996296i | \(0.472595\pi\) | |||||||
\(602\) | −3.55386e12 | −1.10285 | ||||||||
\(603\) | −8.48707e10 | −0.0261415 | ||||||||
\(604\) | −1.54998e12 | −0.473871 | ||||||||
\(605\) | −3.65821e11 | −0.111012 | ||||||||
\(606\) | 3.20736e12 | 0.966099 | ||||||||
\(607\) | 3.73380e12 | 1.11635 | 0.558177 | − | 0.829722i | \(-0.311501\pi\) | ||||
0.558177 | + | 0.829722i | \(0.311501\pi\) | |||||||
\(608\) | 3.07431e11 | 0.0912393 | ||||||||
\(609\) | −6.56355e12 | −1.93358 | ||||||||
\(610\) | 3.33410e12 | 0.974976 | ||||||||
\(611\) | 3.99644e12 | 1.16008 | ||||||||
\(612\) | 7.97026e10 | 0.0229663 | ||||||||
\(613\) | 3.83812e12 | 1.09786 | 0.548929 | − | 0.835869i | \(-0.315036\pi\) | ||||
0.548929 | + | 0.835869i | \(0.315036\pi\) | |||||||
\(614\) | −4.47116e12 | −1.26959 | ||||||||
\(615\) | 2.49997e12 | 0.704689 | ||||||||
\(616\) | 5.19615e11 | 0.145401 | ||||||||
\(617\) | −2.53329e12 | −0.703723 | −0.351861 | − | 0.936052i | \(-0.614451\pi\) | ||||
−0.351861 | + | 0.936052i | \(0.614451\pi\) | |||||||
\(618\) | −3.36199e12 | −0.927147 | ||||||||
\(619\) | 3.23255e12 | 0.884988 | 0.442494 | − | 0.896772i | \(-0.354094\pi\) | ||||
0.442494 | + | 0.896772i | \(0.354094\pi\) | |||||||
\(620\) | 3.66275e12 | 0.995507 | ||||||||
\(621\) | 2.94229e12 | 0.793914 | ||||||||
\(622\) | −3.84178e12 | −1.02914 | ||||||||
\(623\) | −4.01713e12 | −1.06837 | ||||||||
\(624\) | −6.43323e11 | −0.169863 | ||||||||
\(625\) | −4.76807e12 | −1.24992 | ||||||||
\(626\) | −1.54982e12 | −0.403363 | ||||||||
\(627\) | 6.21019e11 | 0.160473 | ||||||||
\(628\) | −8.22838e11 | −0.211104 | ||||||||
\(629\) | 1.83390e12 | 0.467140 | ||||||||
\(630\) | −2.95058e11 | −0.0746233 | ||||||||
\(631\) | 3.95011e11 | 0.0991921 | 0.0495961 | − | 0.998769i | \(-0.484207\pi\) | ||||
0.0495961 | + | 0.998769i | \(0.484207\pi\) | |||||||
\(632\) | −1.21133e12 | −0.302020 | ||||||||
\(633\) | −4.83836e12 | −1.19779 | ||||||||
\(634\) | 2.72199e12 | 0.669090 | ||||||||
\(635\) | 5.59500e12 | 1.36558 | ||||||||
\(636\) | −3.21741e12 | −0.779740 | ||||||||
\(637\) | 2.35600e12 | 0.566955 | ||||||||
\(638\) | 1.22657e12 | 0.293089 | ||||||||
\(639\) | −2.08704e11 | −0.0495196 | ||||||||
\(640\) | 4.58107e11 | 0.107934 | ||||||||
\(641\) | −3.96414e12 | −0.927444 | −0.463722 | − | 0.885981i | \(-0.653486\pi\) | ||||
−0.463722 | + | 0.885981i | \(0.653486\pi\) | |||||||
\(642\) | 3.34199e12 | 0.776422 | ||||||||
\(643\) | −7.33426e12 | −1.69203 | −0.846013 | − | 0.533163i | \(-0.821003\pi\) | ||||
−0.846013 | + | 0.533163i | \(0.821003\pi\) | |||||||
\(644\) | −2.44696e12 | −0.560585 | ||||||||
\(645\) | −6.32910e12 | −1.43987 | ||||||||
\(646\) | 1.17109e12 | 0.264573 | ||||||||
\(647\) | −1.01763e12 | −0.228308 | −0.114154 | − | 0.993463i | \(-0.536416\pi\) | ||||
−0.114154 | + | 0.993463i | \(0.536416\pi\) | |||||||
\(648\) | 1.68105e12 | 0.374535 | ||||||||
\(649\) | −2.66908e12 | −0.590556 | ||||||||
\(650\) | −1.04144e12 | −0.228836 | ||||||||
\(651\) | −1.05094e13 | −2.29331 | ||||||||
\(652\) | 8.58921e11 | 0.186140 | ||||||||
\(653\) | 6.78338e12 | 1.45995 | 0.729973 | − | 0.683476i | \(-0.239533\pi\) | ||||
0.729973 | + | 0.683476i | \(0.239533\pi\) | |||||||
\(654\) | 5.98771e12 | 1.27985 | ||||||||
\(655\) | −3.08987e12 | −0.655925 | ||||||||
\(656\) | 6.63594e11 | 0.139906 | ||||||||
\(657\) | −1.89311e11 | −0.0396399 | ||||||||
\(658\) | 8.16547e12 | 1.69811 | ||||||||
\(659\) | 1.83983e12 | 0.380008 | 0.190004 | − | 0.981783i | \(-0.439150\pi\) | ||||
0.190004 | + | 0.981783i | \(0.439150\pi\) | |||||||
\(660\) | 9.25387e11 | 0.189835 | ||||||||
\(661\) | −3.08220e12 | −0.627992 | −0.313996 | − | 0.949424i | \(-0.601668\pi\) | ||||
−0.313996 | + | 0.949424i | \(0.601668\pi\) | |||||||
\(662\) | −3.92509e11 | −0.0794308 | ||||||||
\(663\) | −2.45060e12 | −0.492563 | ||||||||
\(664\) | −1.88864e12 | −0.377045 | ||||||||
\(665\) | −4.33537e12 | −0.859664 | ||||||||
\(666\) | −1.46582e11 | −0.0288699 | ||||||||
\(667\) | −5.77614e12 | −1.12998 | ||||||||
\(668\) | 2.89806e12 | 0.563136 | ||||||||
\(669\) | 2.52868e12 | 0.488063 | ||||||||
\(670\) | −1.85821e12 | −0.356253 | ||||||||
\(671\) | 1.78773e12 | 0.340448 | ||||||||
\(672\) | −1.31443e12 | −0.248643 | ||||||||
\(673\) | −7.07648e12 | −1.32969 | −0.664844 | − | 0.746983i | \(-0.731502\pi\) | ||||
−0.664844 | + | 0.746983i | \(0.731502\pi\) | |||||||
\(674\) | −1.54313e12 | −0.288026 | ||||||||
\(675\) | 2.55859e12 | 0.474389 | ||||||||
\(676\) | −1.53615e12 | −0.282927 | ||||||||
\(677\) | 1.18522e11 | 0.0216846 | 0.0108423 | − | 0.999941i | \(-0.496549\pi\) | ||||
0.0108423 | + | 0.999941i | \(0.496549\pi\) | |||||||
\(678\) | 2.62959e12 | 0.477918 | ||||||||
\(679\) | −9.25956e11 | −0.167177 | ||||||||
\(680\) | 1.74506e12 | 0.312983 | ||||||||
\(681\) | 2.88697e12 | 0.514376 | ||||||||
\(682\) | 1.96395e12 | 0.347617 | ||||||||
\(683\) | −4.08882e12 | −0.718961 | −0.359480 | − | 0.933153i | \(-0.617046\pi\) | ||||
−0.359480 | + | 0.933153i | \(0.617046\pi\) | |||||||
\(684\) | −9.36045e10 | −0.0163510 | ||||||||
\(685\) | 5.44940e12 | 0.945674 | ||||||||
\(686\) | −7.80642e11 | −0.134584 | ||||||||
\(687\) | 1.07888e13 | 1.84786 | ||||||||
\(688\) | −1.68000e12 | −0.285865 | ||||||||
\(689\) | 5.89446e12 | 0.996455 | ||||||||
\(690\) | −4.35782e12 | −0.731894 | ||||||||
\(691\) | 2.48976e12 | 0.415438 | 0.207719 | − | 0.978189i | \(-0.433396\pi\) | ||||
0.207719 | + | 0.978189i | \(0.433396\pi\) | |||||||
\(692\) | 3.17648e12 | 0.526586 | ||||||||
\(693\) | −1.58209e11 | −0.0260574 | ||||||||
\(694\) | 1.64111e12 | 0.268547 | ||||||||
\(695\) | 1.41744e12 | 0.230447 | ||||||||
\(696\) | −3.10276e12 | −0.501194 | ||||||||
\(697\) | 2.52782e12 | 0.405694 | ||||||||
\(698\) | 5.75936e12 | 0.918386 | ||||||||
\(699\) | 7.00694e12 | 1.11015 | ||||||||
\(700\) | −2.12786e12 | −0.334967 | ||||||||
\(701\) | 6.94398e12 | 1.08612 | 0.543059 | − | 0.839694i | \(-0.317266\pi\) | ||||
0.543059 | + | 0.839694i | \(0.317266\pi\) | |||||||
\(702\) | −2.89556e12 | −0.450003 | ||||||||
\(703\) | −2.15377e12 | −0.332583 | ||||||||
\(704\) | 2.45635e11 | 0.0376889 | ||||||||
\(705\) | 1.45419e13 | 2.21703 | ||||||||
\(706\) | 9.97457e11 | 0.151103 | ||||||||
\(707\) | −1.20059e13 | −1.80720 | ||||||||
\(708\) | 6.75176e12 | 1.00987 | ||||||||
\(709\) | −1.00274e13 | −1.49032 | −0.745159 | − | 0.666887i | \(-0.767626\pi\) | ||||
−0.745159 | + | 0.666887i | \(0.767626\pi\) | |||||||
\(710\) | −4.56950e12 | −0.674849 | ||||||||
\(711\) | 3.68817e11 | 0.0541250 | ||||||||
\(712\) | −1.89900e12 | −0.276927 | ||||||||
\(713\) | −9.24861e12 | −1.34021 | ||||||||
\(714\) | −5.00704e12 | −0.721006 | ||||||||
\(715\) | −1.69535e12 | −0.242596 | ||||||||
\(716\) | −4.57083e12 | −0.649960 | ||||||||
\(717\) | 4.00336e12 | 0.565703 | ||||||||
\(718\) | 1.79965e12 | 0.252714 | ||||||||
\(719\) | 8.41668e12 | 1.17452 | 0.587261 | − | 0.809398i | \(-0.300206\pi\) | ||||
0.587261 | + | 0.809398i | \(0.300206\pi\) | |||||||
\(720\) | −1.39481e11 | −0.0193428 | ||||||||
\(721\) | 1.25847e13 | 1.73434 | ||||||||
\(722\) | 3.78764e12 | 0.518743 | ||||||||
\(723\) | −7.58015e12 | −1.03171 | ||||||||
\(724\) | 6.90673e12 | 0.934220 | ||||||||
\(725\) | −5.02289e12 | −0.675200 | ||||||||
\(726\) | 4.96189e11 | 0.0662876 | ||||||||
\(727\) | −4.69707e10 | −0.00623622 | −0.00311811 | − | 0.999995i | \(-0.500993\pi\) | ||||
−0.00311811 | + | 0.999995i | \(0.500993\pi\) | |||||||
\(728\) | 2.40810e12 | 0.317748 | ||||||||
\(729\) | 7.08315e12 | 0.928865 | ||||||||
\(730\) | −4.14490e12 | −0.540209 | ||||||||
\(731\) | −6.39960e12 | −0.828943 | ||||||||
\(732\) | −4.52228e12 | −0.582180 | ||||||||
\(733\) | 6.70015e12 | 0.857269 | 0.428634 | − | 0.903478i | \(-0.358995\pi\) | ||||
0.428634 | + | 0.903478i | \(0.358995\pi\) | |||||||
\(734\) | −2.43101e12 | −0.309139 | ||||||||
\(735\) | 8.57286e12 | 1.08351 | ||||||||
\(736\) | −1.15674e12 | −0.145307 | ||||||||
\(737\) | −9.96367e11 | −0.124399 | ||||||||
\(738\) | −2.02047e11 | −0.0250725 | ||||||||
\(739\) | −1.71079e11 | −0.0211007 | −0.0105503 | − | 0.999944i | \(-0.503358\pi\) | ||||
−0.0105503 | + | 0.999944i | \(0.503358\pi\) | |||||||
\(740\) | −3.20935e12 | −0.393437 | ||||||||
\(741\) | 2.87804e12 | 0.350683 | ||||||||
\(742\) | 1.20435e13 | 1.45860 | ||||||||
\(743\) | 6.82102e12 | 0.821106 | 0.410553 | − | 0.911837i | \(-0.365336\pi\) | ||||
0.410553 | + | 0.911837i | \(0.365336\pi\) | |||||||
\(744\) | −4.96805e12 | −0.594439 | ||||||||
\(745\) | −1.50841e13 | −1.79397 | ||||||||
\(746\) | −2.86477e12 | −0.338661 | ||||||||
\(747\) | 5.75040e11 | 0.0675702 | ||||||||
\(748\) | 9.35696e11 | 0.109289 | ||||||||
\(749\) | −1.25098e13 | −1.45239 | ||||||||
\(750\) | 3.92596e12 | 0.453075 | ||||||||
\(751\) | 5.72654e12 | 0.656920 | 0.328460 | − | 0.944518i | \(-0.393470\pi\) | ||||
0.328460 | + | 0.944518i | \(0.393470\pi\) | |||||||
\(752\) | 3.86002e12 | 0.440159 | ||||||||
\(753\) | −7.89345e12 | −0.894724 | ||||||||
\(754\) | 5.68440e12 | 0.640492 | ||||||||
\(755\) | 1.03327e13 | 1.15732 | ||||||||
\(756\) | −5.91618e12 | −0.658708 | ||||||||
\(757\) | 2.98205e12 | 0.330052 | 0.165026 | − | 0.986289i | \(-0.447229\pi\) | ||||
0.165026 | + | 0.986289i | \(0.447229\pi\) | |||||||
\(758\) | −3.70044e12 | −0.407138 | ||||||||
\(759\) | −2.33665e12 | −0.255567 | ||||||||
\(760\) | −2.04944e12 | −0.222830 | ||||||||
\(761\) | −8.46525e12 | −0.914974 | −0.457487 | − | 0.889216i | \(-0.651250\pi\) | ||||
−0.457487 | + | 0.889216i | \(0.651250\pi\) | |||||||
\(762\) | −7.58890e12 | −0.815420 | ||||||||
\(763\) | −2.24133e13 | −2.39412 | ||||||||
\(764\) | −4.83082e12 | −0.512980 | ||||||||
\(765\) | −5.31324e11 | −0.0560897 | ||||||||
\(766\) | −5.66273e12 | −0.594287 | ||||||||
\(767\) | −1.23696e13 | −1.29055 | ||||||||
\(768\) | −6.21363e11 | −0.0644496 | ||||||||
\(769\) | 1.77112e13 | 1.82633 | 0.913164 | − | 0.407592i | \(-0.133631\pi\) | ||||
0.913164 | + | 0.407592i | \(0.133631\pi\) | |||||||
\(770\) | −3.46393e12 | −0.355108 | ||||||||
\(771\) | −2.48866e12 | −0.253642 | ||||||||
\(772\) | −4.19249e12 | −0.424809 | ||||||||
\(773\) | 9.83204e12 | 0.990458 | 0.495229 | − | 0.868763i | \(-0.335084\pi\) | ||||
0.495229 | + | 0.868763i | \(0.335084\pi\) | |||||||
\(774\) | 5.11514e11 | 0.0512299 | ||||||||
\(775\) | −8.04251e12 | −0.800818 | ||||||||
\(776\) | −4.37723e11 | −0.0433333 | ||||||||
\(777\) | 9.20848e12 | 0.906345 | ||||||||
\(778\) | −6.72753e12 | −0.658335 | ||||||||
\(779\) | −2.96873e12 | −0.288837 | ||||||||
\(780\) | 4.28860e12 | 0.414849 | ||||||||
\(781\) | −2.45015e12 | −0.235648 | ||||||||
\(782\) | −4.40636e12 | −0.421356 | ||||||||
\(783\) | −1.39653e13 | −1.32777 | ||||||||
\(784\) | 2.27559e12 | 0.215115 | ||||||||
\(785\) | 5.48531e12 | 0.515570 | ||||||||
\(786\) | 4.19101e12 | 0.391667 | ||||||||
\(787\) | −1.78869e12 | −0.166207 | −0.0831036 | − | 0.996541i | \(-0.526483\pi\) | ||||
−0.0831036 | + | 0.996541i | \(0.526483\pi\) | |||||||
\(788\) | −6.17924e12 | −0.570909 | ||||||||
\(789\) | 3.36439e12 | 0.309072 | ||||||||
\(790\) | 8.07512e12 | 0.737611 | ||||||||
\(791\) | −9.84312e12 | −0.894002 | ||||||||
\(792\) | −7.47893e10 | −0.00675424 | ||||||||
\(793\) | 8.28504e12 | 0.743987 | ||||||||
\(794\) | 5.49328e12 | 0.490500 | ||||||||
\(795\) | 2.14484e13 | 1.90433 | ||||||||
\(796\) | −1.78809e10 | −0.00157863 | ||||||||
\(797\) | 1.04170e13 | 0.914496 | 0.457248 | − | 0.889339i | \(-0.348835\pi\) | ||||
0.457248 | + | 0.889339i | \(0.348835\pi\) | |||||||
\(798\) | 5.88038e12 | 0.513325 | ||||||||
\(799\) | 1.47039e13 | 1.27636 | ||||||||
\(800\) | −1.00589e12 | −0.0868254 | ||||||||
\(801\) | 5.78194e11 | 0.0496281 | ||||||||
\(802\) | −8.25436e12 | −0.704529 | ||||||||
\(803\) | −2.22248e12 | −0.188633 | ||||||||
\(804\) | 2.52043e12 | 0.212727 | ||||||||
\(805\) | 1.63123e13 | 1.36909 | ||||||||
\(806\) | 9.10171e12 | 0.759653 | ||||||||
\(807\) | −4.08204e12 | −0.338802 | ||||||||
\(808\) | −5.67548e12 | −0.468437 | ||||||||
\(809\) | −7.91008e10 | −0.00649251 | −0.00324625 | − | 0.999995i | \(-0.501033\pi\) | ||||
−0.00324625 | + | 0.999995i | \(0.501033\pi\) | |||||||
\(810\) | −1.12064e13 | −0.914713 | ||||||||
\(811\) | 7.52015e12 | 0.610425 | 0.305213 | − | 0.952284i | \(-0.401272\pi\) | ||||
0.305213 | + | 0.952284i | \(0.401272\pi\) | |||||||
\(812\) | 1.16143e13 | 0.937542 | ||||||||
\(813\) | −1.98500e13 | −1.59351 | ||||||||
\(814\) | −1.72084e12 | −0.137383 | ||||||||
\(815\) | −5.72585e12 | −0.454601 | ||||||||
\(816\) | −2.36695e12 | −0.186889 | ||||||||
\(817\) | 7.51583e12 | 0.590171 | ||||||||
\(818\) | 7.49372e12 | 0.585204 | ||||||||
\(819\) | −7.33201e11 | −0.0569437 | ||||||||
\(820\) | −4.42374e12 | −0.341686 | ||||||||
\(821\) | 4.67347e12 | 0.359000 | 0.179500 | − | 0.983758i | \(-0.442552\pi\) | ||||
0.179500 | + | 0.983758i | \(0.442552\pi\) | |||||||
\(822\) | −7.39142e12 | −0.564683 | ||||||||
\(823\) | −4.06045e12 | −0.308514 | −0.154257 | − | 0.988031i | \(-0.549298\pi\) | ||||
−0.154257 | + | 0.988031i | \(0.549298\pi\) | |||||||
\(824\) | 5.94910e12 | 0.449551 | ||||||||
\(825\) | −2.03193e12 | −0.152709 | ||||||||
\(826\) | −2.52733e13 | −1.88909 | ||||||||
\(827\) | −2.53074e12 | −0.188136 | −0.0940682 | − | 0.995566i | \(-0.529987\pi\) | ||||
−0.0940682 | + | 0.995566i | \(0.529987\pi\) | |||||||
\(828\) | 3.52196e11 | 0.0260405 | ||||||||
\(829\) | −2.26450e12 | −0.166524 | −0.0832620 | − | 0.996528i | \(-0.526534\pi\) | ||||
−0.0832620 | + | 0.996528i | \(0.526534\pi\) | |||||||
\(830\) | 1.25903e13 | 0.920841 | ||||||||
\(831\) | −2.68226e13 | −1.95117 | ||||||||
\(832\) | 1.13837e12 | 0.0823622 | ||||||||
\(833\) | 8.66836e12 | 0.623784 | ||||||||
\(834\) | −1.92257e12 | −0.137605 | ||||||||
\(835\) | −1.93194e13 | −1.37532 | ||||||||
\(836\) | −1.09890e12 | −0.0778091 | ||||||||
\(837\) | −2.23609e13 | −1.57480 | ||||||||
\(838\) | 1.84087e13 | 1.28951 | ||||||||
\(839\) | 7.42242e12 | 0.517150 | 0.258575 | − | 0.965991i | \(-0.416747\pi\) | ||||
0.258575 | + | 0.965991i | \(0.416747\pi\) | |||||||
\(840\) | 8.76242e12 | 0.607250 | ||||||||
\(841\) | 1.29088e13 | 0.889825 | ||||||||
\(842\) | 3.99599e12 | 0.273981 | ||||||||
\(843\) | 7.53404e12 | 0.513811 | ||||||||
\(844\) | 8.56156e12 | 0.580780 | ||||||||
\(845\) | 1.02405e13 | 0.690981 | ||||||||
\(846\) | −1.17527e12 | −0.0788809 | ||||||||
\(847\) | −1.85735e12 | −0.123999 | ||||||||
\(848\) | 5.69326e12 | 0.378077 | ||||||||
\(849\) | −1.50164e13 | −0.991931 | ||||||||
\(850\) | −3.83173e12 | −0.251774 | ||||||||
\(851\) | 8.10377e12 | 0.529668 | ||||||||
\(852\) | 6.19795e12 | 0.402967 | ||||||||
\(853\) | 1.60812e13 | 1.04004 | 0.520019 | − | 0.854155i | \(-0.325925\pi\) | ||||
0.520019 | + | 0.854155i | \(0.325925\pi\) | |||||||
\(854\) | 1.69279e13 | 1.08904 | ||||||||
\(855\) | 6.23999e11 | 0.0399334 | ||||||||
\(856\) | −5.91370e12 | −0.376467 | ||||||||
\(857\) | 8.68029e11 | 0.0549693 | 0.0274847 | − | 0.999622i | \(-0.491250\pi\) | ||||
0.0274847 | + | 0.999622i | \(0.491250\pi\) | |||||||
\(858\) | 2.29953e12 | 0.144859 | ||||||||
\(859\) | −1.16610e13 | −0.730748 | −0.365374 | − | 0.930861i | \(-0.619059\pi\) | ||||
−0.365374 | + | 0.930861i | \(0.619059\pi\) | |||||||
\(860\) | 1.11994e13 | 0.698156 | ||||||||
\(861\) | 1.26929e13 | 0.787129 | ||||||||
\(862\) | −4.48993e12 | −0.276986 | ||||||||
\(863\) | 2.04030e13 | 1.25212 | 0.626060 | − | 0.779775i | \(-0.284666\pi\) | ||||
0.626060 | + | 0.779775i | \(0.284666\pi\) | |||||||
\(864\) | −2.79672e12 | −0.170741 | ||||||||
\(865\) | −2.11755e13 | −1.28606 | ||||||||
\(866\) | −1.71874e13 | −1.03844 | ||||||||
\(867\) | 8.13999e12 | 0.489258 | ||||||||
\(868\) | 1.85965e13 | 1.11197 | ||||||||
\(869\) | 4.32985e12 | 0.257563 | ||||||||
\(870\) | 2.06840e13 | 1.22405 | ||||||||
\(871\) | −4.61755e12 | −0.271850 | ||||||||
\(872\) | −1.05953e13 | −0.620570 | ||||||||
\(873\) | 1.33275e11 | 0.00776576 | ||||||||
\(874\) | 5.17493e12 | 0.299987 | ||||||||
\(875\) | −1.46957e13 | −0.847529 | ||||||||
\(876\) | 5.62203e12 | 0.322571 | ||||||||
\(877\) | −3.26576e13 | −1.86417 | −0.932085 | − | 0.362239i | \(-0.882012\pi\) | ||||
−0.932085 | + | 0.362239i | \(0.882012\pi\) | |||||||
\(878\) | −1.51285e13 | −0.859153 | ||||||||
\(879\) | 1.23194e13 | 0.696048 | ||||||||
\(880\) | −1.63749e12 | −0.0920461 | ||||||||
\(881\) | 1.89169e13 | 1.05793 | 0.528966 | − | 0.848643i | \(-0.322580\pi\) | ||||
0.528966 | + | 0.848643i | \(0.322580\pi\) | |||||||
\(882\) | −6.92854e11 | −0.0385508 | ||||||||
\(883\) | −4.52036e12 | −0.250236 | −0.125118 | − | 0.992142i | \(-0.539931\pi\) | ||||
−0.125118 | + | 0.992142i | \(0.539931\pi\) | |||||||
\(884\) | 4.33638e12 | 0.238832 | ||||||||
\(885\) | −4.50095e13 | −2.46638 | ||||||||
\(886\) | −2.26157e13 | −1.23299 | ||||||||
\(887\) | 1.67209e13 | 0.906994 | 0.453497 | − | 0.891258i | \(-0.350176\pi\) | ||||
0.453497 | + | 0.891258i | \(0.350176\pi\) | |||||||
\(888\) | 4.35308e12 | 0.234930 | ||||||||
\(889\) | 2.84069e13 | 1.52534 | ||||||||
\(890\) | 1.26594e13 | 0.676327 | ||||||||
\(891\) | −6.00885e12 | −0.319405 | ||||||||
\(892\) | −4.47453e12 | −0.236650 | ||||||||
\(893\) | −1.72686e13 | −0.908712 | ||||||||
\(894\) | 2.04596e13 | 1.07122 | ||||||||
\(895\) | 3.04707e13 | 1.58737 | ||||||||
\(896\) | 2.32590e12 | 0.120561 | ||||||||
\(897\) | −1.08289e13 | −0.558495 | ||||||||
\(898\) | −5.18999e12 | −0.266332 | ||||||||
\(899\) | 4.38977e13 | 2.24142 | ||||||||
\(900\) | 3.06267e11 | 0.0155600 | ||||||||
\(901\) | 2.16873e13 | 1.09634 | ||||||||
\(902\) | −2.37199e12 | −0.119312 | ||||||||
\(903\) | −3.21341e13 | −1.60832 | ||||||||
\(904\) | −4.65309e12 | −0.231731 | ||||||||
\(905\) | −4.60426e13 | −2.28161 | ||||||||
\(906\) | −1.40150e13 | −0.691059 | ||||||||
\(907\) | −2.68525e13 | −1.31751 | −0.658753 | − | 0.752359i | \(-0.728916\pi\) | ||||
−0.658753 | + | 0.752359i | \(0.728916\pi\) | |||||||
\(908\) | −5.10854e12 | −0.249408 | ||||||||
\(909\) | 1.72803e12 | 0.0839487 | ||||||||
\(910\) | −1.60532e13 | −0.776024 | ||||||||
\(911\) | 8.77113e12 | 0.421913 | 0.210957 | − | 0.977495i | \(-0.432342\pi\) | ||||
0.210957 | + | 0.977495i | \(0.432342\pi\) | |||||||
\(912\) | 2.77980e12 | 0.133057 | ||||||||
\(913\) | 6.75088e12 | 0.321545 | ||||||||
\(914\) | 2.31647e12 | 0.109792 | ||||||||
\(915\) | 3.01470e13 | 1.42184 | ||||||||
\(916\) | −1.90910e13 | −0.895980 | ||||||||
\(917\) | −1.56879e13 | −0.732660 | ||||||||
\(918\) | −1.06535e13 | −0.495110 | ||||||||
\(919\) | −8.62159e11 | −0.0398720 | −0.0199360 | − | 0.999801i | \(-0.506346\pi\) | ||||
−0.0199360 | + | 0.999801i | \(0.506346\pi\) | |||||||
\(920\) | 7.71122e12 | 0.354877 | ||||||||
\(921\) | −4.04284e13 | −1.85147 | ||||||||
\(922\) | −4.70550e12 | −0.214445 | ||||||||
\(923\) | −1.13549e13 | −0.514965 | ||||||||
\(924\) | 4.69838e12 | 0.212043 | ||||||||
\(925\) | 7.04697e12 | 0.316493 | ||||||||
\(926\) | −1.40557e13 | −0.628205 | ||||||||
\(927\) | −1.81134e12 | −0.0805640 | ||||||||
\(928\) | 5.49037e12 | 0.243017 | ||||||||
\(929\) | 1.65304e12 | 0.0728138 | 0.0364069 | − | 0.999337i | \(-0.488409\pi\) | ||||
0.0364069 | + | 0.999337i | \(0.488409\pi\) | |||||||
\(930\) | 3.31187e13 | 1.45178 | ||||||||
\(931\) | −1.01803e13 | −0.444107 | ||||||||
\(932\) | −1.23989e13 | −0.538283 | ||||||||
\(933\) | −3.47375e13 | −1.50083 | ||||||||
\(934\) | −1.01060e13 | −0.434529 | ||||||||
\(935\) | −6.23766e12 | −0.266913 | ||||||||
\(936\) | −3.46603e11 | −0.0147601 | ||||||||
\(937\) | −2.41842e13 | −1.02495 | −0.512476 | − | 0.858702i | \(-0.671272\pi\) | ||||
−0.512476 | + | 0.858702i | \(0.671272\pi\) | |||||||
\(938\) | −9.43453e12 | −0.397931 | ||||||||
\(939\) | −1.40135e13 | −0.588235 | ||||||||
\(940\) | −2.57322e13 | −1.07498 | ||||||||
\(941\) | 3.40036e13 | 1.41375 | 0.706874 | − | 0.707340i | \(-0.250105\pi\) | ||||
0.706874 | + | 0.707340i | \(0.250105\pi\) | |||||||
\(942\) | −7.44013e12 | −0.307859 | ||||||||
\(943\) | 1.11701e13 | 0.459998 | ||||||||
\(944\) | −1.19473e13 | −0.489663 | ||||||||
\(945\) | 3.94392e13 | 1.60874 | ||||||||
\(946\) | 6.00509e12 | 0.243786 | ||||||||
\(947\) | 1.65859e13 | 0.670138 | 0.335069 | − | 0.942194i | \(-0.391240\pi\) | ||||
0.335069 | + | 0.942194i | \(0.391240\pi\) | |||||||
\(948\) | −1.09529e13 | −0.440444 | ||||||||
\(949\) | −1.02998e13 | −0.412223 | ||||||||
\(950\) | 4.50007e12 | 0.179252 | ||||||||
\(951\) | 2.46123e13 | 0.975753 | ||||||||
\(952\) | 8.86003e12 | 0.349598 | ||||||||
\(953\) | −2.57430e13 | −1.01098 | −0.505489 | − | 0.862833i | \(-0.668688\pi\) | ||||
−0.505489 | + | 0.862833i | \(0.668688\pi\) | |||||||
\(954\) | −1.73344e12 | −0.0677552 | ||||||||
\(955\) | 3.22038e13 | 1.25283 | ||||||||
\(956\) | −7.08401e12 | −0.274295 | ||||||||
\(957\) | 1.10907e13 | 0.427420 | ||||||||
\(958\) | 2.72211e13 | 1.04414 | ||||||||
\(959\) | 2.76677e13 | 1.05631 | ||||||||
\(960\) | 4.14222e12 | 0.157403 | ||||||||
\(961\) | 4.38482e13 | 1.65843 | ||||||||
\(962\) | −7.97506e12 | −0.300224 | ||||||||
\(963\) | 1.80056e12 | 0.0674668 | ||||||||
\(964\) | 1.34132e13 | 0.500248 | ||||||||
\(965\) | 2.79485e13 | 1.03749 | ||||||||
\(966\) | −2.21255e13 | −0.817516 | ||||||||
\(967\) | 4.94862e12 | 0.181997 | 0.0909986 | − | 0.995851i | \(-0.470994\pi\) | ||||
0.0909986 | + | 0.995851i | \(0.470994\pi\) | |||||||
\(968\) | −8.78014e11 | −0.0321412 | ||||||||
\(969\) | 1.05891e13 | 0.385834 | ||||||||
\(970\) | 2.91801e12 | 0.105831 | ||||||||
\(971\) | 1.45094e13 | 0.523799 | 0.261899 | − | 0.965095i | \(-0.415651\pi\) | ||||
0.261899 | + | 0.965095i | \(0.415651\pi\) | |||||||
\(972\) | 1.76066e12 | 0.0632669 | ||||||||
\(973\) | 7.19661e12 | 0.257407 | ||||||||
\(974\) | −3.48504e12 | −0.124077 | ||||||||
\(975\) | −9.41674e12 | −0.333718 | ||||||||
\(976\) | 8.00224e12 | 0.282285 | ||||||||
\(977\) | −8.00736e12 | −0.281167 | −0.140583 | − | 0.990069i | \(-0.544898\pi\) | ||||
−0.140583 | + | 0.990069i | \(0.544898\pi\) | |||||||
\(978\) | 7.76638e12 | 0.271453 | ||||||||
\(979\) | 6.78790e12 | 0.236164 | ||||||||
\(980\) | −1.51698e13 | −0.525367 | ||||||||
\(981\) | 3.22599e12 | 0.111212 | ||||||||
\(982\) | −3.92351e12 | −0.134640 | ||||||||
\(983\) | −3.29697e13 | −1.12622 | −0.563111 | − | 0.826381i | \(-0.690396\pi\) | ||||
−0.563111 | + | 0.826381i | \(0.690396\pi\) | |||||||
\(984\) | 6.00024e12 | 0.204028 | ||||||||
\(985\) | 4.11929e13 | 1.39431 | ||||||||
\(986\) | 2.09144e13 | 0.704692 | ||||||||
\(987\) | 7.38324e13 | 2.47639 | ||||||||
\(988\) | −5.09273e12 | −0.170037 | ||||||||
\(989\) | −2.82791e13 | −0.939900 | ||||||||
\(990\) | 4.98570e11 | 0.0164956 | ||||||||
\(991\) | 1.22142e12 | 0.0402286 | 0.0201143 | − | 0.999798i | \(-0.493597\pi\) | ||||
0.0201143 | + | 0.999798i | \(0.493597\pi\) | |||||||
\(992\) | 8.79103e12 | 0.288229 | ||||||||
\(993\) | −3.54908e12 | −0.115836 | ||||||||
\(994\) | −2.32003e13 | −0.753798 | ||||||||
\(995\) | 1.19200e11 | 0.00385544 | ||||||||
\(996\) | −1.70771e13 | −0.549855 | ||||||||
\(997\) | −3.27455e13 | −1.04960 | −0.524800 | − | 0.851226i | \(-0.675860\pi\) | ||||
−0.524800 | + | 0.851226i | \(0.675860\pi\) | |||||||
\(998\) | 3.42984e13 | 1.09443 | ||||||||
\(999\) | 1.95930e13 | 0.622380 |
(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 | 22.10.a.d.1.1 | ✓ | 2 | |
3.2 | odd | 2 | 198.10.a.n.1.2 | 2 | |||
4.3 | odd | 2 | 176.10.a.e.1.2 | 2 | |||
11.10 | odd | 2 | 242.10.a.e.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
22.10.a.d.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
176.10.a.e.1.2 | 2 | 4.3 | odd | 2 | |||
198.10.a.n.1.2 | 2 | 3.2 | odd | 2 | |||
242.10.a.e.1.1 | 2 | 11.10 | odd | 2 |