Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [98,10,Mod(1,98)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(98, 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("98.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 98 = 2 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 98.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: | \(50.4735119441\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{2}, \sqrt{4817})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 2411x^{2} + 2412x + 1444802 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2\cdot 3^{2}\cdot 7^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-35.6165\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 98.1 |
$q$-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 | ||||||||
\(3\) | 191.777 | 1.36695 | 0.683473 | − | 0.729976i | \(-0.260469\pi\) | ||||
0.683473 | + | 0.729976i | \(0.260469\pi\) | |||||||
\(4\) | 256.000 | 0.500000 | ||||||||
\(5\) | 33.5898 | 0.0240349 | 0.0120175 | − | 0.999928i | \(-0.496175\pi\) | ||||
0.0120175 | + | 0.999928i | \(0.496175\pi\) | |||||||
\(6\) | −3068.43 | −0.966576 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −4096.00 | −0.353553 | ||||||||
\(9\) | 17095.5 | 0.868540 | ||||||||
\(10\) | −537.437 | −0.0169953 | ||||||||
\(11\) | −51540.4 | −1.06140 | −0.530702 | − | 0.847559i | \(-0.678072\pi\) | ||||
−0.530702 | + | 0.847559i | \(0.678072\pi\) | |||||||
\(12\) | 49094.9 | 0.683473 | ||||||||
\(13\) | 113303. | 1.10026 | 0.550129 | − | 0.835080i | \(-0.314579\pi\) | ||||
0.550129 | + | 0.835080i | \(0.314579\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 6441.76 | 0.0328544 | ||||||||
\(16\) | 65536.0 | 0.250000 | ||||||||
\(17\) | −461667. | −1.34063 | −0.670314 | − | 0.742078i | \(-0.733841\pi\) | ||||
−0.670314 | + | 0.742078i | \(0.733841\pi\) | |||||||
\(18\) | −273528. | −0.614150 | ||||||||
\(19\) | −836657. | −1.47284 | −0.736421 | − | 0.676523i | \(-0.763486\pi\) | ||||
−0.736421 | + | 0.676523i | \(0.763486\pi\) | |||||||
\(20\) | 8598.99 | 0.0120175 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 824646. | 0.750526 | ||||||||
\(23\) | 299404. | 0.223091 | 0.111546 | − | 0.993759i | \(-0.464420\pi\) | ||||
0.111546 | + | 0.993759i | \(0.464420\pi\) | |||||||
\(24\) | −785519. | −0.483288 | ||||||||
\(25\) | −1.95200e6 | −0.999422 | ||||||||
\(26\) | −1.81284e6 | −0.778000 | ||||||||
\(27\) | −496229. | −0.179699 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.58319e6 | 0.678213 | 0.339106 | − | 0.940748i | \(-0.389875\pi\) | ||||
0.339106 | + | 0.940748i | \(0.389875\pi\) | |||||||
\(30\) | −103068. | −0.0232316 | ||||||||
\(31\) | −6.84324e6 | −1.33087 | −0.665433 | − | 0.746458i | \(-0.731753\pi\) | ||||
−0.665433 | + | 0.746458i | \(0.731753\pi\) | |||||||
\(32\) | −1.04858e6 | −0.176777 | ||||||||
\(33\) | −9.88427e6 | −1.45088 | ||||||||
\(34\) | 7.38666e6 | 0.947967 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 4.37644e6 | 0.434270 | ||||||||
\(37\) | 1.39547e7 | 1.22409 | 0.612043 | − | 0.790825i | \(-0.290348\pi\) | ||||
0.612043 | + | 0.790825i | \(0.290348\pi\) | |||||||
\(38\) | 1.33865e7 | 1.04146 | ||||||||
\(39\) | 2.17288e7 | 1.50399 | ||||||||
\(40\) | −137584. | −0.00849763 | ||||||||
\(41\) | 2.22245e7 | 1.22830 | 0.614151 | − | 0.789188i | \(-0.289498\pi\) | ||||
0.614151 | + | 0.789188i | \(0.289498\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.24518e7 | −1.44754 | −0.723770 | − | 0.690042i | \(-0.757592\pi\) | ||||
−0.723770 | + | 0.690042i | \(0.757592\pi\) | |||||||
\(44\) | −1.31943e7 | −0.530702 | ||||||||
\(45\) | 574234. | 0.0208753 | ||||||||
\(46\) | −4.79046e6 | −0.157749 | ||||||||
\(47\) | −3.18053e6 | −0.0950734 | −0.0475367 | − | 0.998869i | \(-0.515137\pi\) | ||||
−0.0475367 | + | 0.998869i | \(0.515137\pi\) | |||||||
\(48\) | 1.25683e7 | 0.341736 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 3.12319e7 | 0.706698 | ||||||||
\(51\) | −8.85371e7 | −1.83257 | ||||||||
\(52\) | 2.90055e7 | 0.550129 | ||||||||
\(53\) | 8.82912e7 | 1.53701 | 0.768504 | − | 0.639845i | \(-0.221001\pi\) | ||||
0.768504 | + | 0.639845i | \(0.221001\pi\) | |||||||
\(54\) | 7.93966e6 | 0.127066 | ||||||||
\(55\) | −1.73123e6 | −0.0255107 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.60452e8 | −2.01330 | ||||||||
\(58\) | −4.13311e7 | −0.479569 | ||||||||
\(59\) | −1.39912e7 | −0.150321 | −0.0751606 | − | 0.997171i | \(-0.523947\pi\) | ||||
−0.0751606 | + | 0.997171i | \(0.523947\pi\) | |||||||
\(60\) | 1.64909e6 | 0.0164272 | ||||||||
\(61\) | −1.13931e8 | −1.05355 | −0.526777 | − | 0.850004i | \(-0.676600\pi\) | ||||
−0.526777 | + | 0.850004i | \(0.676600\pi\) | |||||||
\(62\) | 1.09492e8 | 0.941064 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.67772e7 | 0.125000 | ||||||||
\(65\) | 3.80581e6 | 0.0264446 | ||||||||
\(66\) | 1.58148e8 | 1.02593 | ||||||||
\(67\) | −3.05493e8 | −1.85210 | −0.926050 | − | 0.377400i | \(-0.876818\pi\) | ||||
−0.926050 | + | 0.377400i | \(0.876818\pi\) | |||||||
\(68\) | −1.18187e8 | −0.670314 | ||||||||
\(69\) | 5.74188e7 | 0.304953 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.86664e8 | −1.33878 | −0.669392 | − | 0.742909i | \(-0.733445\pi\) | ||||
−0.669392 | + | 0.742909i | \(0.733445\pi\) | |||||||
\(72\) | −7.00231e7 | −0.307075 | ||||||||
\(73\) | 4.78856e7 | 0.197357 | 0.0986785 | − | 0.995119i | \(-0.468538\pi\) | ||||
0.0986785 | + | 0.995119i | \(0.468538\pi\) | |||||||
\(74\) | −2.23275e8 | −0.865559 | ||||||||
\(75\) | −3.74348e8 | −1.36616 | ||||||||
\(76\) | −2.14184e8 | −0.736421 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −3.47661e8 | −1.06348 | ||||||||
\(79\) | −1.07582e8 | −0.310753 | −0.155377 | − | 0.987855i | \(-0.549659\pi\) | ||||
−0.155377 | + | 0.987855i | \(0.549659\pi\) | |||||||
\(80\) | 2.20134e6 | 0.00600873 | ||||||||
\(81\) | −4.31656e8 | −1.11418 | ||||||||
\(82\) | −3.55593e8 | −0.868541 | ||||||||
\(83\) | 5.67595e7 | 0.131277 | 0.0656383 | − | 0.997843i | \(-0.479092\pi\) | ||||
0.0656383 | + | 0.997843i | \(0.479092\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.55073e7 | −0.0322219 | ||||||||
\(86\) | 5.19228e8 | 1.02356 | ||||||||
\(87\) | 4.95398e8 | 0.927080 | ||||||||
\(88\) | 2.11109e8 | 0.375263 | ||||||||
\(89\) | −8.48669e8 | −1.43378 | −0.716891 | − | 0.697185i | \(-0.754436\pi\) | ||||
−0.716891 | + | 0.697185i | \(0.754436\pi\) | |||||||
\(90\) | −9.18774e6 | −0.0147611 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 7.66474e7 | 0.111546 | ||||||||
\(93\) | −1.31238e9 | −1.81922 | ||||||||
\(94\) | 5.08885e7 | 0.0672270 | ||||||||
\(95\) | −2.81032e7 | −0.0353996 | ||||||||
\(96\) | −2.01093e8 | −0.241644 | ||||||||
\(97\) | 8.99384e8 | 1.03151 | 0.515754 | − | 0.856737i | \(-0.327512\pi\) | ||||
0.515754 | + | 0.856737i | \(0.327512\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −8.81107e8 | −0.921871 | ||||||||
\(100\) | −4.99711e8 | −0.499711 | ||||||||
\(101\) | 6.32202e7 | 0.0604519 | 0.0302259 | − | 0.999543i | \(-0.490377\pi\) | ||||
0.0302259 | + | 0.999543i | \(0.490377\pi\) | |||||||
\(102\) | 1.41659e9 | 1.29582 | ||||||||
\(103\) | 1.21580e9 | 1.06437 | 0.532185 | − | 0.846628i | \(-0.321371\pi\) | ||||
0.532185 | + | 0.846628i | \(0.321371\pi\) | |||||||
\(104\) | −4.64087e8 | −0.389000 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.41266e9 | −1.08683 | ||||||||
\(107\) | −1.28242e9 | −0.945811 | −0.472906 | − | 0.881113i | \(-0.656795\pi\) | ||||
−0.472906 | + | 0.881113i | \(0.656795\pi\) | |||||||
\(108\) | −1.27035e8 | −0.0898494 | ||||||||
\(109\) | −5.06567e8 | −0.343730 | −0.171865 | − | 0.985120i | \(-0.554979\pi\) | ||||
−0.171865 | + | 0.985120i | \(0.554979\pi\) | |||||||
\(110\) | 2.76997e7 | 0.0180388 | ||||||||
\(111\) | 2.67619e9 | 1.67326 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.15512e9 | 0.666462 | 0.333231 | − | 0.942845i | \(-0.391861\pi\) | ||||
0.333231 | + | 0.942845i | \(0.391861\pi\) | |||||||
\(114\) | 2.56723e9 | 1.42361 | ||||||||
\(115\) | 1.00569e7 | 0.00536197 | ||||||||
\(116\) | 6.61298e8 | 0.339106 | ||||||||
\(117\) | 1.93696e9 | 0.955618 | ||||||||
\(118\) | 2.23859e8 | 0.106293 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −2.63854e7 | −0.0116158 | ||||||||
\(121\) | 2.98463e8 | 0.126578 | ||||||||
\(122\) | 1.82289e9 | 0.744975 | ||||||||
\(123\) | 4.26216e9 | 1.67902 | ||||||||
\(124\) | −1.75187e9 | −0.665433 | ||||||||
\(125\) | −1.31172e8 | −0.0480559 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.41280e9 | 1.16411 | 0.582055 | − | 0.813150i | \(-0.302249\pi\) | ||||
0.582055 | + | 0.813150i | \(0.302249\pi\) | |||||||
\(128\) | −2.68435e8 | −0.0883883 | ||||||||
\(129\) | −6.22351e9 | −1.97871 | ||||||||
\(130\) | −6.08930e7 | −0.0186992 | ||||||||
\(131\) | 7.17987e8 | 0.213008 | 0.106504 | − | 0.994312i | \(-0.466034\pi\) | ||||
0.106504 | + | 0.994312i | \(0.466034\pi\) | |||||||
\(132\) | −2.53037e9 | −0.725440 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 4.88789e9 | 1.30963 | ||||||||
\(135\) | −1.66682e7 | −0.00431904 | ||||||||
\(136\) | 1.89099e9 | 0.473984 | ||||||||
\(137\) | −7.31370e9 | −1.77376 | −0.886880 | − | 0.462000i | \(-0.847132\pi\) | ||||
−0.886880 | + | 0.462000i | \(0.847132\pi\) | |||||||
\(138\) | −9.18701e8 | −0.215634 | ||||||||
\(139\) | −4.88666e9 | −1.11031 | −0.555157 | − | 0.831746i | \(-0.687342\pi\) | ||||
−0.555157 | + | 0.831746i | \(0.687342\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.09953e8 | −0.129960 | ||||||||
\(142\) | 4.58662e9 | 0.946663 | ||||||||
\(143\) | −5.83966e9 | −1.16782 | ||||||||
\(144\) | 1.12037e9 | 0.217135 | ||||||||
\(145\) | 8.67690e7 | 0.0163008 | ||||||||
\(146\) | −7.66170e8 | −0.139552 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3.57240e9 | 0.612043 | ||||||||
\(149\) | 6.90289e9 | 1.14734 | 0.573671 | − | 0.819086i | \(-0.305519\pi\) | ||||
0.573671 | + | 0.819086i | \(0.305519\pi\) | |||||||
\(150\) | 5.98957e9 | 0.966018 | ||||||||
\(151\) | −5.65547e9 | −0.885263 | −0.442632 | − | 0.896704i | \(-0.645955\pi\) | ||||
−0.442632 | + | 0.896704i | \(0.645955\pi\) | |||||||
\(152\) | 3.42695e9 | 0.520728 | ||||||||
\(153\) | −7.89241e9 | −1.16439 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.29863e8 | −0.0319872 | ||||||||
\(156\) | 5.56258e9 | 0.751996 | ||||||||
\(157\) | −6.59975e9 | −0.866920 | −0.433460 | − | 0.901173i | \(-0.642707\pi\) | ||||
−0.433460 | + | 0.901173i | \(0.642707\pi\) | |||||||
\(158\) | 1.72130e9 | 0.219736 | ||||||||
\(159\) | 1.69322e10 | 2.10101 | ||||||||
\(160\) | −3.52215e7 | −0.00424881 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 6.90649e9 | 0.787843 | ||||||||
\(163\) | −7.98797e9 | −0.886323 | −0.443162 | − | 0.896442i | \(-0.646143\pi\) | ||||
−0.443162 | + | 0.896442i | \(0.646143\pi\) | |||||||
\(164\) | 5.68948e9 | 0.614151 | ||||||||
\(165\) | −3.32011e8 | −0.0348718 | ||||||||
\(166\) | −9.08152e8 | −0.0928266 | ||||||||
\(167\) | 4.34905e9 | 0.432683 | 0.216342 | − | 0.976318i | \(-0.430588\pi\) | ||||
0.216342 | + | 0.976318i | \(0.430588\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.23297e9 | 0.210568 | ||||||||
\(170\) | 2.48117e8 | 0.0227843 | ||||||||
\(171\) | −1.43030e10 | −1.27922 | ||||||||
\(172\) | −8.30765e9 | −0.723770 | ||||||||
\(173\) | 1.38491e10 | 1.17548 | 0.587739 | − | 0.809051i | \(-0.300018\pi\) | ||||
0.587739 | + | 0.809051i | \(0.300018\pi\) | |||||||
\(174\) | −7.92636e9 | −0.655545 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −3.37775e9 | −0.265351 | ||||||||
\(177\) | −2.68319e9 | −0.205481 | ||||||||
\(178\) | 1.35787e10 | 1.01384 | ||||||||
\(179\) | 1.99542e10 | 1.45277 | 0.726384 | − | 0.687289i | \(-0.241199\pi\) | ||||
0.726384 | + | 0.687289i | \(0.241199\pi\) | |||||||
\(180\) | 1.47004e8 | 0.0104376 | ||||||||
\(181\) | −3.33705e9 | −0.231105 | −0.115552 | − | 0.993301i | \(-0.536864\pi\) | ||||
−0.115552 | + | 0.993301i | \(0.536864\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.18493e10 | −1.44015 | ||||||||
\(184\) | −1.22636e9 | −0.0788746 | ||||||||
\(185\) | 4.68735e8 | 0.0294208 | ||||||||
\(186\) | 2.09980e10 | 1.28638 | ||||||||
\(187\) | 2.37945e10 | 1.42295 | ||||||||
\(188\) | −8.14216e8 | −0.0475367 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 4.49650e8 | 0.0250313 | ||||||||
\(191\) | −2.45891e10 | −1.33688 | −0.668441 | − | 0.743765i | \(-0.733038\pi\) | ||||
−0.668441 | + | 0.743765i | \(0.733038\pi\) | |||||||
\(192\) | 3.21749e9 | 0.170868 | ||||||||
\(193\) | −1.80119e10 | −0.934438 | −0.467219 | − | 0.884142i | \(-0.654744\pi\) | ||||
−0.467219 | + | 0.884142i | \(0.654744\pi\) | |||||||
\(194\) | −1.43901e10 | −0.729386 | ||||||||
\(195\) | 7.29868e8 | 0.0361483 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4.02716e10 | 1.90503 | 0.952514 | − | 0.304496i | \(-0.0984880\pi\) | ||||
0.952514 | + | 0.304496i | \(0.0984880\pi\) | |||||||
\(198\) | 1.40977e10 | 0.651862 | ||||||||
\(199\) | 3.76852e10 | 1.70346 | 0.851730 | − | 0.523981i | \(-0.175554\pi\) | ||||
0.851730 | + | 0.523981i | \(0.175554\pi\) | |||||||
\(200\) | 7.99538e9 | 0.353349 | ||||||||
\(201\) | −5.85866e10 | −2.53172 | ||||||||
\(202\) | −1.01152e9 | −0.0427459 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −2.26655e10 | −0.916283 | ||||||||
\(205\) | 7.46518e8 | 0.0295221 | ||||||||
\(206\) | −1.94527e10 | −0.752624 | ||||||||
\(207\) | 5.11845e9 | 0.193763 | ||||||||
\(208\) | 7.42540e9 | 0.275065 | ||||||||
\(209\) | 4.31216e10 | 1.56328 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.57268e10 | −0.546223 | −0.273111 | − | 0.961982i | \(-0.588053\pi\) | ||||
−0.273111 | + | 0.961982i | \(0.588053\pi\) | |||||||
\(212\) | 2.26026e10 | 0.768504 | ||||||||
\(213\) | −5.49756e10 | −1.83004 | ||||||||
\(214\) | 2.05188e10 | 0.668790 | ||||||||
\(215\) | −1.09005e9 | −0.0347915 | ||||||||
\(216\) | 2.03255e9 | 0.0635331 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 8.10508e9 | 0.243054 | ||||||||
\(219\) | 9.18337e9 | 0.269776 | ||||||||
\(220\) | −4.43195e8 | −0.0127554 | ||||||||
\(221\) | −5.23080e10 | −1.47504 | ||||||||
\(222\) | −4.28190e10 | −1.18317 | ||||||||
\(223\) | 6.29667e10 | 1.70506 | 0.852528 | − | 0.522681i | \(-0.175068\pi\) | ||||
0.852528 | + | 0.522681i | \(0.175068\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.33703e10 | −0.868038 | ||||||||
\(226\) | −1.84820e10 | −0.471260 | ||||||||
\(227\) | 5.48011e10 | 1.36985 | 0.684925 | − | 0.728614i | \(-0.259835\pi\) | ||||
0.684925 | + | 0.728614i | \(0.259835\pi\) | |||||||
\(228\) | −4.10756e10 | −1.00665 | ||||||||
\(229\) | −6.14118e10 | −1.47568 | −0.737840 | − | 0.674976i | \(-0.764154\pi\) | ||||
−0.737840 | + | 0.674976i | \(0.764154\pi\) | |||||||
\(230\) | −1.60911e8 | −0.00379149 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.05808e10 | −0.239784 | ||||||||
\(233\) | −8.42910e9 | −0.187361 | −0.0936806 | − | 0.995602i | \(-0.529863\pi\) | ||||
−0.0936806 | + | 0.995602i | \(0.529863\pi\) | |||||||
\(234\) | −3.09914e10 | −0.675724 | ||||||||
\(235\) | −1.06833e8 | −0.00228508 | ||||||||
\(236\) | −3.58174e9 | −0.0751606 | ||||||||
\(237\) | −2.06317e10 | −0.424783 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3.13951e10 | 0.622402 | 0.311201 | − | 0.950344i | \(-0.399269\pi\) | ||||
0.311201 | + | 0.950344i | \(0.399269\pi\) | |||||||
\(240\) | 4.22167e8 | 0.00821360 | ||||||||
\(241\) | 1.45866e10 | 0.278533 | 0.139267 | − | 0.990255i | \(-0.455525\pi\) | ||||
0.139267 | + | 0.990255i | \(0.455525\pi\) | |||||||
\(242\) | −4.77541e9 | −0.0895039 | ||||||||
\(243\) | −7.30144e10 | −1.34332 | ||||||||
\(244\) | −2.91663e10 | −0.526777 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −6.81945e10 | −1.18725 | ||||||||
\(247\) | −9.47954e10 | −1.62051 | ||||||||
\(248\) | 2.80299e10 | 0.470532 | ||||||||
\(249\) | 1.08852e10 | 0.179448 | ||||||||
\(250\) | 2.09876e9 | 0.0339807 | ||||||||
\(251\) | −3.56389e10 | −0.566752 | −0.283376 | − | 0.959009i | \(-0.591454\pi\) | ||||
−0.283376 | + | 0.959009i | \(0.591454\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.54314e10 | −0.236790 | ||||||||
\(254\) | −5.46048e10 | −0.823150 | ||||||||
\(255\) | −2.97394e9 | −0.0440455 | ||||||||
\(256\) | 4.29497e9 | 0.0625000 | ||||||||
\(257\) | 6.94569e10 | 0.993154 | 0.496577 | − | 0.867993i | \(-0.334590\pi\) | ||||
0.496577 | + | 0.867993i | \(0.334590\pi\) | |||||||
\(258\) | 9.95761e10 | 1.39916 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 9.74288e8 | 0.0132223 | ||||||||
\(261\) | 4.41609e10 | 0.589055 | ||||||||
\(262\) | −1.14878e10 | −0.150619 | ||||||||
\(263\) | 7.23020e10 | 0.931857 | 0.465929 | − | 0.884822i | \(-0.345720\pi\) | ||||
0.465929 | + | 0.884822i | \(0.345720\pi\) | |||||||
\(264\) | 4.04860e10 | 0.512964 | ||||||||
\(265\) | 2.96569e9 | 0.0369419 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.62755e11 | −1.95990 | ||||||||
\(268\) | −7.82062e10 | −0.926050 | ||||||||
\(269\) | 9.03066e10 | 1.05156 | 0.525780 | − | 0.850621i | \(-0.323774\pi\) | ||||
0.525780 | + | 0.850621i | \(0.323774\pi\) | |||||||
\(270\) | 2.66692e8 | 0.00305403 | ||||||||
\(271\) | 4.02229e10 | 0.453014 | 0.226507 | − | 0.974010i | \(-0.427269\pi\) | ||||
0.226507 | + | 0.974010i | \(0.427269\pi\) | |||||||
\(272\) | −3.02558e10 | −0.335157 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.17019e11 | 1.25424 | ||||||||
\(275\) | 1.00607e11 | 1.06079 | ||||||||
\(276\) | 1.46992e10 | 0.152477 | ||||||||
\(277\) | −2.06717e10 | −0.210968 | −0.105484 | − | 0.994421i | \(-0.533639\pi\) | ||||
−0.105484 | + | 0.994421i | \(0.533639\pi\) | |||||||
\(278\) | 7.81866e10 | 0.785110 | ||||||||
\(279\) | −1.16988e11 | −1.15591 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3.46833e10 | −0.331850 | −0.165925 | − | 0.986138i | \(-0.553061\pi\) | ||||
−0.165925 | + | 0.986138i | \(0.553061\pi\) | |||||||
\(282\) | 9.75925e9 | 0.0918957 | ||||||||
\(283\) | 1.04639e11 | 0.969741 | 0.484870 | − | 0.874586i | \(-0.338867\pi\) | ||||
0.484870 | + | 0.874586i | \(0.338867\pi\) | |||||||
\(284\) | −7.33860e10 | −0.669392 | ||||||||
\(285\) | −5.38954e9 | −0.0483894 | ||||||||
\(286\) | 9.34345e10 | 0.825772 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −1.79259e10 | −0.153538 | ||||||||
\(289\) | 9.45481e10 | 0.797283 | ||||||||
\(290\) | −1.38830e9 | −0.0115264 | ||||||||
\(291\) | 1.72481e11 | 1.41001 | ||||||||
\(292\) | 1.22587e10 | 0.0986785 | ||||||||
\(293\) | −1.60760e11 | −1.27431 | −0.637153 | − | 0.770737i | \(-0.719888\pi\) | ||||
−0.637153 | + | 0.770737i | \(0.719888\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.69961e8 | −0.00361296 | ||||||||
\(296\) | −5.71583e10 | −0.432780 | ||||||||
\(297\) | 2.55758e10 | 0.190733 | ||||||||
\(298\) | −1.10446e11 | −0.811293 | ||||||||
\(299\) | 3.39232e10 | 0.245458 | ||||||||
\(300\) | −9.58332e10 | −0.683078 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 9.04875e10 | 0.625976 | ||||||||
\(303\) | 1.21242e10 | 0.0826344 | ||||||||
\(304\) | −5.48312e10 | −0.368211 | ||||||||
\(305\) | −3.82691e9 | −0.0253221 | ||||||||
\(306\) | 1.26279e11 | 0.823347 | ||||||||
\(307\) | 1.45170e11 | 0.932725 | 0.466362 | − | 0.884594i | \(-0.345564\pi\) | ||||
0.466362 | + | 0.884594i | \(0.345564\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.33162e11 | 1.45494 | ||||||||
\(310\) | 3.67781e9 | 0.0226184 | ||||||||
\(311\) | −2.63090e11 | −1.59471 | −0.797356 | − | 0.603510i | \(-0.793768\pi\) | ||||
−0.797356 | + | 0.603510i | \(0.793768\pi\) | |||||||
\(312\) | −8.90013e10 | −0.531742 | ||||||||
\(313\) | −8.38203e10 | −0.493628 | −0.246814 | − | 0.969063i | \(-0.579384\pi\) | ||||
−0.246814 | + | 0.969063i | \(0.579384\pi\) | |||||||
\(314\) | 1.05596e11 | 0.613005 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.75409e10 | −0.155377 | ||||||||
\(317\) | 2.70716e11 | 1.50573 | 0.752865 | − | 0.658175i | \(-0.228671\pi\) | ||||
0.752865 | + | 0.658175i | \(0.228671\pi\) | |||||||
\(318\) | −2.70916e11 | −1.48564 | ||||||||
\(319\) | −1.33139e11 | −0.719858 | ||||||||
\(320\) | 5.63544e8 | 0.00300436 | ||||||||
\(321\) | −2.45940e11 | −1.29287 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.86257e11 | 1.97453 | ||||||||
\(324\) | −1.10504e11 | −0.557089 | ||||||||
\(325\) | −2.21166e11 | −1.09962 | ||||||||
\(326\) | 1.27807e11 | 0.626725 | ||||||||
\(327\) | −9.71480e10 | −0.469861 | ||||||||
\(328\) | −9.10317e10 | −0.434271 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 5.31217e9 | 0.0246581 | ||||||||
\(331\) | 1.93741e11 | 0.887146 | 0.443573 | − | 0.896238i | \(-0.353711\pi\) | ||||
0.443573 | + | 0.896238i | \(0.353711\pi\) | |||||||
\(332\) | 1.45304e10 | 0.0656383 | ||||||||
\(333\) | 2.38562e11 | 1.06317 | ||||||||
\(334\) | −6.95847e10 | −0.305953 | ||||||||
\(335\) | −1.02615e10 | −0.0445151 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.23909e11 | 0.945665 | 0.472832 | − | 0.881152i | \(-0.343232\pi\) | ||||
0.472832 | + | 0.881152i | \(0.343232\pi\) | |||||||
\(338\) | −3.57275e10 | −0.148894 | ||||||||
\(339\) | 2.21526e11 | 0.911017 | ||||||||
\(340\) | −3.96987e9 | −0.0161109 | ||||||||
\(341\) | 3.52703e11 | 1.41259 | ||||||||
\(342\) | 2.28849e11 | 0.904547 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 1.32922e11 | 0.511782 | ||||||||
\(345\) | 1.92869e9 | 0.00732953 | ||||||||
\(346\) | −2.21586e11 | −0.831188 | ||||||||
\(347\) | −2.57729e11 | −0.954289 | −0.477145 | − | 0.878825i | \(-0.658328\pi\) | ||||
−0.477145 | + | 0.878825i | \(0.658328\pi\) | |||||||
\(348\) | 1.26822e11 | 0.463540 | ||||||||
\(349\) | 1.38744e11 | 0.500609 | 0.250304 | − | 0.968167i | \(-0.419469\pi\) | ||||
0.250304 | + | 0.968167i | \(0.419469\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.62240e10 | −0.197715 | ||||||||
\(352\) | 5.40440e10 | 0.187631 | ||||||||
\(353\) | 1.86980e11 | 0.640929 | 0.320464 | − | 0.947261i | \(-0.396161\pi\) | ||||
0.320464 | + | 0.947261i | \(0.396161\pi\) | |||||||
\(354\) | 4.29310e10 | 0.145297 | ||||||||
\(355\) | −9.62899e9 | −0.0321776 | ||||||||
\(356\) | −2.17259e11 | −0.716891 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −3.19268e11 | −1.02726 | ||||||||
\(359\) | 2.07563e11 | 0.659516 | 0.329758 | − | 0.944066i | \(-0.393033\pi\) | ||||
0.329758 | + | 0.944066i | \(0.393033\pi\) | |||||||
\(360\) | −2.35206e9 | −0.00738053 | ||||||||
\(361\) | 3.77307e11 | 1.16926 | ||||||||
\(362\) | 5.33928e10 | 0.163416 | ||||||||
\(363\) | 5.72384e10 | 0.173025 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.60847e9 | 0.00474346 | ||||||||
\(366\) | 3.49589e11 | 1.01834 | ||||||||
\(367\) | 1.79331e11 | 0.516009 | 0.258004 | − | 0.966144i | \(-0.416935\pi\) | ||||
0.258004 | + | 0.966144i | \(0.416935\pi\) | |||||||
\(368\) | 1.96217e10 | 0.0557728 | ||||||||
\(369\) | 3.79939e11 | 1.06683 | ||||||||
\(370\) | −7.49976e9 | −0.0208036 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −3.35968e11 | −0.909610 | ||||||||
\(373\) | −5.44836e11 | −1.45739 | −0.728696 | − | 0.684837i | \(-0.759873\pi\) | ||||
−0.728696 | + | 0.684837i | \(0.759873\pi\) | |||||||
\(374\) | −3.80711e11 | −1.00618 | ||||||||
\(375\) | −2.51559e10 | −0.0656899 | ||||||||
\(376\) | 1.30274e10 | 0.0336135 | ||||||||
\(377\) | 2.92682e11 | 0.746209 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.24662e11 | −0.310353 | −0.155177 | − | 0.987887i | \(-0.549595\pi\) | ||||
−0.155177 | + | 0.987887i | \(0.549595\pi\) | |||||||
\(380\) | −7.19441e9 | −0.0176998 | ||||||||
\(381\) | 6.54497e11 | 1.59127 | ||||||||
\(382\) | 3.93426e11 | 0.945319 | ||||||||
\(383\) | −4.08245e11 | −0.969453 | −0.484726 | − | 0.874666i | \(-0.661081\pi\) | ||||
−0.484726 | + | 0.874666i | \(0.661081\pi\) | |||||||
\(384\) | −5.14798e10 | −0.120822 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 2.88190e11 | 0.660748 | ||||||||
\(387\) | −5.54778e11 | −1.25725 | ||||||||
\(388\) | 2.30242e11 | 0.515754 | ||||||||
\(389\) | 5.13640e11 | 1.13733 | 0.568663 | − | 0.822570i | \(-0.307461\pi\) | ||||
0.568663 | + | 0.822570i | \(0.307461\pi\) | |||||||
\(390\) | −1.16779e10 | −0.0255607 | ||||||||
\(391\) | −1.38225e11 | −0.299082 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.37694e11 | 0.291170 | ||||||||
\(394\) | −6.44346e11 | −1.34706 | ||||||||
\(395\) | −3.61364e9 | −0.00746893 | ||||||||
\(396\) | −2.25563e11 | −0.460936 | ||||||||
\(397\) | 3.60814e11 | 0.728998 | 0.364499 | − | 0.931204i | \(-0.381240\pi\) | ||||
0.364499 | + | 0.931204i | \(0.381240\pi\) | |||||||
\(398\) | −6.02963e11 | −1.20453 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1.27926e11 | −0.249856 | ||||||||
\(401\) | 2.38594e11 | 0.460797 | 0.230399 | − | 0.973096i | \(-0.425997\pi\) | ||||
0.230399 | + | 0.973096i | \(0.425997\pi\) | |||||||
\(402\) | 9.37385e11 | 1.79020 | ||||||||
\(403\) | −7.75356e11 | −1.46430 | ||||||||
\(404\) | 1.61844e10 | 0.0302259 | ||||||||
\(405\) | −1.44992e10 | −0.0267792 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −7.19229e11 | −1.29925 | ||||||||
\(408\) | 3.62648e11 | 0.647910 | ||||||||
\(409\) | −7.74690e11 | −1.36890 | −0.684452 | − | 0.729058i | \(-0.739959\pi\) | ||||
−0.684452 | + | 0.729058i | \(0.739959\pi\) | |||||||
\(410\) | −1.19443e10 | −0.0208753 | ||||||||
\(411\) | −1.40260e12 | −2.42463 | ||||||||
\(412\) | 3.11244e11 | 0.532185 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −8.18952e10 | −0.137011 | ||||||||
\(415\) | 1.90654e9 | 0.00315522 | ||||||||
\(416\) | −1.18806e11 | −0.194500 | ||||||||
\(417\) | −9.37150e11 | −1.51774 | ||||||||
\(418\) | −6.89946e11 | −1.10541 | ||||||||
\(419\) | −5.87231e11 | −0.930777 | −0.465389 | − | 0.885106i | \(-0.654085\pi\) | ||||
−0.465389 | + | 0.885106i | \(0.654085\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.12541e12 | −1.74599 | −0.872993 | − | 0.487733i | \(-0.837824\pi\) | ||||
−0.872993 | + | 0.487733i | \(0.837824\pi\) | |||||||
\(422\) | 2.51629e11 | 0.386238 | ||||||||
\(423\) | −5.43726e10 | −0.0825750 | ||||||||
\(424\) | −3.61641e11 | −0.543414 | ||||||||
\(425\) | 9.01172e11 | 1.33985 | ||||||||
\(426\) | 8.79610e11 | 1.29404 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −3.28300e11 | −0.472906 | ||||||||
\(429\) | −1.11991e12 | −1.59634 | ||||||||
\(430\) | 1.74408e10 | 0.0246013 | ||||||||
\(431\) | −6.77668e11 | −0.945952 | −0.472976 | − | 0.881075i | \(-0.656820\pi\) | ||||
−0.472976 | + | 0.881075i | \(0.656820\pi\) | |||||||
\(432\) | −3.25209e10 | −0.0449247 | ||||||||
\(433\) | 5.66584e11 | 0.774585 | 0.387292 | − | 0.921957i | \(-0.373410\pi\) | ||||
0.387292 | + | 0.921957i | \(0.373410\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.66403e10 | 0.0222823 | ||||||||
\(436\) | −1.29681e11 | −0.171865 | ||||||||
\(437\) | −2.50498e11 | −0.328578 | ||||||||
\(438\) | −1.46934e11 | −0.190761 | ||||||||
\(439\) | −7.41236e11 | −0.952503 | −0.476252 | − | 0.879309i | \(-0.658005\pi\) | ||||
−0.476252 | + | 0.879309i | \(0.658005\pi\) | |||||||
\(440\) | 7.09113e9 | 0.00901941 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 8.36928e11 | 1.04301 | ||||||||
\(443\) | 9.25207e10 | 0.114136 | 0.0570679 | − | 0.998370i | \(-0.481825\pi\) | ||||
0.0570679 | + | 0.998370i | \(0.481825\pi\) | |||||||
\(444\) | 6.85104e11 | 0.836629 | ||||||||
\(445\) | −2.85066e10 | −0.0344608 | ||||||||
\(446\) | −1.00747e12 | −1.20566 | ||||||||
\(447\) | 1.32382e12 | 1.56835 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1.26884e11 | −0.147333 | −0.0736664 | − | 0.997283i | \(-0.523470\pi\) | ||||
−0.0736664 | + | 0.997283i | \(0.523470\pi\) | |||||||
\(450\) | 5.33925e11 | 0.613796 | ||||||||
\(451\) | −1.14546e12 | −1.30372 | ||||||||
\(452\) | 2.95711e11 | 0.333231 | ||||||||
\(453\) | −1.08459e12 | −1.21011 | ||||||||
\(454\) | −8.76817e11 | −0.968630 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 6.57210e11 | 0.711807 | ||||||||
\(457\) | 1.02815e12 | 1.10264 | 0.551321 | − | 0.834293i | \(-0.314124\pi\) | ||||
0.551321 | + | 0.834293i | \(0.314124\pi\) | |||||||
\(458\) | 9.82588e11 | 1.04346 | ||||||||
\(459\) | 2.29092e11 | 0.240909 | ||||||||
\(460\) | 2.57457e9 | 0.00268099 | ||||||||
\(461\) | −8.10233e11 | −0.835518 | −0.417759 | − | 0.908558i | \(-0.637184\pi\) | ||||
−0.417759 | + | 0.908558i | \(0.637184\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.44793e12 | −1.46431 | −0.732155 | − | 0.681139i | \(-0.761485\pi\) | ||||
−0.732155 | + | 0.681139i | \(0.761485\pi\) | |||||||
\(464\) | 1.69292e11 | 0.169553 | ||||||||
\(465\) | −4.40825e10 | −0.0437248 | ||||||||
\(466\) | 1.34866e11 | 0.132484 | ||||||||
\(467\) | −4.47034e11 | −0.434926 | −0.217463 | − | 0.976069i | \(-0.569778\pi\) | ||||
−0.217463 | + | 0.976069i | \(0.569778\pi\) | |||||||
\(468\) | 4.95862e11 | 0.477809 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 1.70933e9 | 0.00161580 | ||||||||
\(471\) | −1.26568e12 | −1.18503 | ||||||||
\(472\) | 5.73079e10 | 0.0531466 | ||||||||
\(473\) | 1.67258e12 | 1.53642 | ||||||||
\(474\) | 3.30107e11 | 0.300367 | ||||||||
\(475\) | 1.63315e12 | 1.47199 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.50938e12 | 1.33495 | ||||||||
\(478\) | −5.02321e11 | −0.440105 | ||||||||
\(479\) | −8.69551e10 | −0.0754719 | −0.0377360 | − | 0.999288i | \(-0.512015\pi\) | ||||
−0.0377360 | + | 0.999288i | \(0.512015\pi\) | |||||||
\(480\) | −6.75467e9 | −0.00580790 | ||||||||
\(481\) | 1.58110e12 | 1.34681 | ||||||||
\(482\) | −2.33386e11 | −0.196953 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 7.64066e10 | 0.0632888 | ||||||||
\(485\) | 3.02101e10 | 0.0247922 | ||||||||
\(486\) | 1.16823e12 | 0.949872 | ||||||||
\(487\) | −4.81935e8 | −0.000388247 0 | −0.000194124 | − | 1.00000i | \(-0.500062\pi\) | ||||
−0.000194124 | 1.00000i | \(0.500062\pi\) | ||||||||
\(488\) | 4.66660e11 | 0.372487 | ||||||||
\(489\) | −1.53191e12 | −1.21156 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5.88640e11 | −0.457070 | −0.228535 | − | 0.973536i | \(-0.573394\pi\) | ||||
−0.228535 | + | 0.973536i | \(0.573394\pi\) | |||||||
\(492\) | 1.09111e12 | 0.839511 | ||||||||
\(493\) | −1.19257e12 | −0.909231 | ||||||||
\(494\) | 1.51673e12 | 1.14587 | ||||||||
\(495\) | −2.95962e10 | −0.0221571 | ||||||||
\(496\) | −4.48478e11 | −0.332716 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −1.74163e11 | −0.126889 | ||||||||
\(499\) | −2.47946e12 | −1.79021 | −0.895107 | − | 0.445852i | \(-0.852901\pi\) | ||||
−0.895107 | + | 0.445852i | \(0.852901\pi\) | |||||||
\(500\) | −3.35801e10 | −0.0240280 | ||||||||
\(501\) | 8.34048e11 | 0.591454 | ||||||||
\(502\) | 5.70223e11 | 0.400754 | ||||||||
\(503\) | 1.35604e12 | 0.944530 | 0.472265 | − | 0.881457i | \(-0.343437\pi\) | ||||
0.472265 | + | 0.881457i | \(0.343437\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.12356e9 | 0.00145296 | ||||||||
\(506\) | 2.46902e11 | 0.167436 | ||||||||
\(507\) | 4.28232e11 | 0.287835 | ||||||||
\(508\) | 8.73676e11 | 0.582055 | ||||||||
\(509\) | 1.68824e12 | 1.11482 | 0.557409 | − | 0.830238i | \(-0.311795\pi\) | ||||
0.557409 | + | 0.830238i | \(0.311795\pi\) | |||||||
\(510\) | 4.75831e10 | 0.0311449 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −6.87195e10 | −0.0441942 | ||||||||
\(513\) | 4.15173e11 | 0.264668 | ||||||||
\(514\) | −1.11131e12 | −0.702266 | ||||||||
\(515\) | 4.08383e10 | 0.0255821 | ||||||||
\(516\) | −1.59322e12 | −0.989354 | ||||||||
\(517\) | 1.63926e11 | 0.100911 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.65594e12 | 1.60681 | ||||||||
\(520\) | −1.55886e10 | −0.00934958 | ||||||||
\(521\) | 9.42135e11 | 0.560200 | 0.280100 | − | 0.959971i | \(-0.409632\pi\) | ||||
0.280100 | + | 0.959971i | \(0.409632\pi\) | |||||||
\(522\) | −7.06575e11 | −0.416525 | ||||||||
\(523\) | 2.44405e12 | 1.42841 | 0.714206 | − | 0.699936i | \(-0.246788\pi\) | ||||
0.714206 | + | 0.699936i | \(0.246788\pi\) | |||||||
\(524\) | 1.83805e11 | 0.106504 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.15683e12 | −0.658923 | ||||||||
\(527\) | 3.15929e12 | 1.78419 | ||||||||
\(528\) | −6.47775e11 | −0.362720 | ||||||||
\(529\) | −1.71151e12 | −0.950230 | ||||||||
\(530\) | −4.74510e10 | −0.0261218 | ||||||||
\(531\) | −2.39186e11 | −0.130560 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.51810e12 | 1.35145 | ||||||||
\(534\) | 2.60408e12 | 1.38586 | ||||||||
\(535\) | −4.30764e10 | −0.0227325 | ||||||||
\(536\) | 1.25130e12 | 0.654816 | ||||||||
\(537\) | 3.82677e12 | 1.98586 | ||||||||
\(538\) | −1.44490e12 | −0.743565 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −4.26707e9 | −0.00215952 | ||||||||
\(541\) | −6.58195e11 | −0.330344 | −0.165172 | − | 0.986265i | \(-0.552818\pi\) | ||||
−0.165172 | + | 0.986265i | \(0.552818\pi\) | |||||||
\(542\) | −6.43566e11 | −0.320329 | ||||||||
\(543\) | −6.39970e11 | −0.315908 | ||||||||
\(544\) | 4.84092e11 | 0.236992 | ||||||||
\(545\) | −1.70155e10 | −0.00826153 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.50775e12 | −1.19768 | −0.598840 | − | 0.800869i | \(-0.704372\pi\) | ||||
−0.598840 | + | 0.800869i | \(0.704372\pi\) | |||||||
\(548\) | −1.87231e12 | −0.886880 | ||||||||
\(549\) | −1.94770e12 | −0.915053 | ||||||||
\(550\) | −1.60971e12 | −0.750092 | ||||||||
\(551\) | −2.16125e12 | −0.998901 | ||||||||
\(552\) | −2.35187e11 | −0.107817 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 3.30747e11 | 0.149177 | ||||||||
\(555\) | 8.98926e10 | 0.0402166 | ||||||||
\(556\) | −1.25099e12 | −0.555157 | ||||||||
\(557\) | −2.60505e12 | −1.14675 | −0.573375 | − | 0.819293i | \(-0.694366\pi\) | ||||
−0.573375 | + | 0.819293i | \(0.694366\pi\) | |||||||
\(558\) | 1.87181e12 | 0.817351 | ||||||||
\(559\) | −3.67687e12 | −1.59267 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.56324e12 | 1.94509 | ||||||||
\(562\) | 5.54933e11 | 0.234654 | ||||||||
\(563\) | 2.59402e11 | 0.108814 | 0.0544071 | − | 0.998519i | \(-0.482673\pi\) | ||||
0.0544071 | + | 0.998519i | \(0.482673\pi\) | |||||||
\(564\) | −1.56148e11 | −0.0649801 | ||||||||
\(565\) | 3.88004e10 | 0.0160183 | ||||||||
\(566\) | −1.67423e12 | −0.685710 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1.17418e12 | 0.473332 | ||||||||
\(569\) | 2.64332e12 | 1.05717 | 0.528585 | − | 0.848880i | \(-0.322723\pi\) | ||||
0.528585 | + | 0.848880i | \(0.322723\pi\) | |||||||
\(570\) | 8.62327e10 | 0.0342165 | ||||||||
\(571\) | −2.06794e12 | −0.814098 | −0.407049 | − | 0.913406i | \(-0.633442\pi\) | ||||
−0.407049 | + | 0.913406i | \(0.633442\pi\) | |||||||
\(572\) | −1.49495e12 | −0.583909 | ||||||||
\(573\) | −4.71564e12 | −1.82745 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −5.84435e11 | −0.222962 | ||||||||
\(576\) | 2.86814e11 | 0.108567 | ||||||||
\(577\) | −2.56500e12 | −0.963377 | −0.481688 | − | 0.876343i | \(-0.659976\pi\) | ||||
−0.481688 | + | 0.876343i | \(0.659976\pi\) | |||||||
\(578\) | −1.51277e12 | −0.563764 | ||||||||
\(579\) | −3.45426e12 | −1.27733 | ||||||||
\(580\) | 2.22129e10 | 0.00815039 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −2.75970e12 | −0.997030 | ||||||||
\(583\) | −4.55056e12 | −1.63139 | ||||||||
\(584\) | −1.96140e11 | −0.0697762 | ||||||||
\(585\) | 6.50621e10 | 0.0229682 | ||||||||
\(586\) | 2.57216e12 | 0.901071 | ||||||||
\(587\) | 1.59591e12 | 0.554800 | 0.277400 | − | 0.960755i | \(-0.410527\pi\) | ||||
0.277400 | + | 0.960755i | \(0.410527\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.72544e12 | 1.96015 | ||||||||
\(590\) | 7.51938e9 | 0.00255475 | ||||||||
\(591\) | 7.72318e12 | 2.60407 | ||||||||
\(592\) | 9.14533e11 | 0.306021 | ||||||||
\(593\) | −1.97116e12 | −0.654600 | −0.327300 | − | 0.944920i | \(-0.606139\pi\) | ||||
−0.327300 | + | 0.944920i | \(0.606139\pi\) | |||||||
\(594\) | −4.09213e11 | −0.134869 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1.76714e12 | 0.573671 | ||||||||
\(597\) | 7.22716e12 | 2.32854 | ||||||||
\(598\) | −5.42771e11 | −0.173565 | ||||||||
\(599\) | 4.97079e12 | 1.57763 | 0.788814 | − | 0.614632i | \(-0.210696\pi\) | ||||
0.788814 | + | 0.614632i | \(0.210696\pi\) | |||||||
\(600\) | 1.53333e12 | 0.483009 | ||||||||
\(601\) | 4.73669e12 | 1.48095 | 0.740475 | − | 0.672084i | \(-0.234601\pi\) | ||||
0.740475 | + | 0.672084i | \(0.234601\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −5.22255e12 | −1.60862 | ||||||||
\(604\) | −1.44780e12 | −0.442632 | ||||||||
\(605\) | 1.00253e10 | 0.00304228 | ||||||||
\(606\) | −1.93987e11 | −0.0584314 | ||||||||
\(607\) | 3.26903e12 | 0.977395 | 0.488697 | − | 0.872453i | \(-0.337472\pi\) | ||||
0.488697 | + | 0.872453i | \(0.337472\pi\) | |||||||
\(608\) | 8.77298e11 | 0.260364 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 6.12306e10 | 0.0179054 | ||||||||
\(611\) | −3.60362e11 | −0.104605 | ||||||||
\(612\) | −2.02046e12 | −0.582194 | ||||||||
\(613\) | −6.53577e11 | −0.186950 | −0.0934748 | − | 0.995622i | \(-0.529797\pi\) | ||||
−0.0934748 | + | 0.995622i | \(0.529797\pi\) | |||||||
\(614\) | −2.32272e12 | −0.659536 | ||||||||
\(615\) | 1.43165e11 | 0.0403552 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −6.63823e12 | −1.84404 | −0.922018 | − | 0.387148i | \(-0.873460\pi\) | ||||
−0.922018 | + | 0.387148i | \(0.873460\pi\) | |||||||
\(618\) | −3.73059e12 | −1.02880 | ||||||||
\(619\) | 7.25374e10 | 0.0198589 | 0.00992943 | − | 0.999951i | \(-0.496839\pi\) | ||||
0.00992943 | + | 0.999951i | \(0.496839\pi\) | |||||||
\(620\) | −5.88450e10 | −0.0159936 | ||||||||
\(621\) | −1.48573e11 | −0.0400892 | ||||||||
\(622\) | 4.20943e12 | 1.12763 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 1.42402e12 | 0.375998 | ||||||||
\(625\) | 3.80809e12 | 0.998267 | ||||||||
\(626\) | 1.34113e12 | 0.349048 | ||||||||
\(627\) | 8.26974e12 | 2.13692 | ||||||||
\(628\) | −1.68954e12 | −0.433460 | ||||||||
\(629\) | −6.44240e12 | −1.64104 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.35325e12 | −0.590930 | −0.295465 | − | 0.955354i | \(-0.595475\pi\) | ||||
−0.295465 | + | 0.955354i | \(0.595475\pi\) | |||||||
\(632\) | 4.40654e11 | 0.109868 | ||||||||
\(633\) | −3.01604e12 | −0.746657 | ||||||||
\(634\) | −4.33145e12 | −1.06471 | ||||||||
\(635\) | 1.14635e11 | 0.0279793 | ||||||||
\(636\) | 4.33465e12 | 1.05050 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 2.13022e12 | 0.509016 | ||||||||
\(639\) | −4.90066e12 | −1.16279 | ||||||||
\(640\) | −9.01670e9 | −0.00212441 | ||||||||
\(641\) | −7.52887e11 | −0.176144 | −0.0880722 | − | 0.996114i | \(-0.528071\pi\) | ||||
−0.0880722 | + | 0.996114i | \(0.528071\pi\) | |||||||
\(642\) | 3.93503e12 | 0.914199 | ||||||||
\(643\) | 4.82355e12 | 1.11280 | 0.556400 | − | 0.830915i | \(-0.312182\pi\) | ||||
0.556400 | + | 0.830915i | \(0.312182\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2.09047e11 | −0.0475581 | ||||||||
\(646\) | −6.18010e12 | −1.39621 | ||||||||
\(647\) | 8.19172e12 | 1.83783 | 0.918916 | − | 0.394454i | \(-0.129066\pi\) | ||||
0.918916 | + | 0.394454i | \(0.129066\pi\) | |||||||
\(648\) | 1.76806e12 | 0.393922 | ||||||||
\(649\) | 7.21111e11 | 0.159552 | ||||||||
\(650\) | 3.53866e12 | 0.777551 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −2.04492e12 | −0.443162 | ||||||||
\(653\) | −5.81217e12 | −1.25092 | −0.625460 | − | 0.780257i | \(-0.715088\pi\) | ||||
−0.625460 | + | 0.780257i | \(0.715088\pi\) | |||||||
\(654\) | 1.55437e12 | 0.332242 | ||||||||
\(655\) | 2.41171e10 | 0.00511963 | ||||||||
\(656\) | 1.45651e12 | 0.307076 | ||||||||
\(657\) | 8.18628e11 | 0.171412 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −3.45418e12 | −0.713446 | −0.356723 | − | 0.934210i | \(-0.616106\pi\) | ||||
−0.356723 | + | 0.934210i | \(0.616106\pi\) | |||||||
\(660\) | −8.49947e10 | −0.0174359 | ||||||||
\(661\) | −5.45581e12 | −1.11161 | −0.555805 | − | 0.831313i | \(-0.687590\pi\) | ||||
−0.555805 | + | 0.831313i | \(0.687590\pi\) | |||||||
\(662\) | −3.09985e12 | −0.627307 | ||||||||
\(663\) | −1.00315e13 | −2.01629 | ||||||||
\(664\) | −2.32487e11 | −0.0464133 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −3.81699e12 | −0.751773 | ||||||||
\(667\) | 7.73418e11 | 0.151303 | ||||||||
\(668\) | 1.11336e12 | 0.216342 | ||||||||
\(669\) | 1.20756e13 | 2.33072 | ||||||||
\(670\) | 1.64183e11 | 0.0314769 | ||||||||
\(671\) | 5.87203e12 | 1.11825 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.93782e12 | 0.927828 | 0.463914 | − | 0.885880i | \(-0.346445\pi\) | ||||
0.463914 | + | 0.885880i | \(0.346445\pi\) | |||||||
\(674\) | −3.58255e12 | −0.668686 | ||||||||
\(675\) | 9.68637e11 | 0.179595 | ||||||||
\(676\) | 5.71639e11 | 0.105284 | ||||||||
\(677\) | −9.07898e12 | −1.66107 | −0.830535 | − | 0.556967i | \(-0.811965\pi\) | ||||
−0.830535 | + | 0.556967i | \(0.811965\pi\) | |||||||
\(678\) | −3.54442e12 | −0.644186 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 6.35179e10 | 0.0113922 | ||||||||
\(681\) | 1.05096e13 | 1.87251 | ||||||||
\(682\) | −5.64325e12 | −0.998848 | ||||||||
\(683\) | −5.09917e12 | −0.896615 | −0.448308 | − | 0.893879i | \(-0.647973\pi\) | ||||
−0.448308 | + | 0.893879i | \(0.647973\pi\) | |||||||
\(684\) | −3.66158e12 | −0.639611 | ||||||||
\(685\) | −2.45666e11 | −0.0426322 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.17774e13 | −2.01717 | ||||||||
\(688\) | −2.12676e12 | −0.361885 | ||||||||
\(689\) | 1.00036e13 | 1.69111 | ||||||||
\(690\) | −3.08590e10 | −0.00518276 | ||||||||
\(691\) | −6.84110e12 | −1.14150 | −0.570748 | − | 0.821125i | \(-0.693347\pi\) | ||||
−0.570748 | + | 0.821125i | \(0.693347\pi\) | |||||||
\(692\) | 3.54537e12 | 0.587739 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 4.12366e12 | 0.674785 | ||||||||
\(695\) | −1.64142e11 | −0.0266863 | ||||||||
\(696\) | −2.02915e12 | −0.327772 | ||||||||
\(697\) | −1.02603e13 | −1.64670 | ||||||||
\(698\) | −2.21990e12 | −0.353984 | ||||||||
\(699\) | −1.61651e12 | −0.256112 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 9.89108e12 | 1.54708 | 0.773539 | − | 0.633748i | \(-0.218484\pi\) | ||||
0.773539 | + | 0.633748i | \(0.218484\pi\) | |||||||
\(702\) | 8.99584e11 | 0.139806 | ||||||||
\(703\) | −1.16753e13 | −1.80289 | ||||||||
\(704\) | −8.64704e11 | −0.132675 | ||||||||
\(705\) | −2.04882e10 | −0.00312358 | ||||||||
\(706\) | −2.99169e12 | −0.453205 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −6.86896e11 | −0.102740 | ||||||||
\(709\) | −1.14431e13 | −1.70074 | −0.850368 | − | 0.526189i | \(-0.823620\pi\) | ||||
−0.850368 | + | 0.526189i | \(0.823620\pi\) | |||||||
\(710\) | 1.54064e11 | 0.0227530 | ||||||||
\(711\) | −1.83916e12 | −0.269902 | ||||||||
\(712\) | 3.47615e12 | 0.506919 | ||||||||
\(713\) | −2.04889e12 | −0.296904 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.96153e11 | −0.0280684 | ||||||||
\(716\) | 5.10828e12 | 0.726384 | ||||||||
\(717\) | 6.02086e12 | 0.850790 | ||||||||
\(718\) | −3.32101e12 | −0.466348 | ||||||||
\(719\) | −7.20450e12 | −1.00537 | −0.502683 | − | 0.864471i | \(-0.667654\pi\) | ||||
−0.502683 | + | 0.864471i | \(0.667654\pi\) | |||||||
\(720\) | 3.76330e10 | 0.00521882 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −6.03692e12 | −0.826795 | ||||||||
\(723\) | 2.79738e12 | 0.380740 | ||||||||
\(724\) | −8.54285e11 | −0.115552 | ||||||||
\(725\) | −5.04239e12 | −0.677821 | ||||||||
\(726\) | −9.15815e11 | −0.122347 | ||||||||
\(727\) | 7.27861e12 | 0.966371 | 0.483185 | − | 0.875518i | \(-0.339480\pi\) | ||||
0.483185 | + | 0.875518i | \(0.339480\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −5.50621e12 | −0.722070 | ||||||||
\(730\) | −2.57355e10 | −0.00335413 | ||||||||
\(731\) | 1.49819e13 | 1.94061 | ||||||||
\(732\) | −5.59342e12 | −0.720075 | ||||||||
\(733\) | 1.36945e13 | 1.75218 | 0.876092 | − | 0.482144i | \(-0.160142\pi\) | ||||
0.876092 | + | 0.482144i | \(0.160142\pi\) | |||||||
\(734\) | −2.86929e12 | −0.364873 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.13948e11 | −0.0394373 | ||||||||
\(737\) | 1.57452e13 | 1.96583 | ||||||||
\(738\) | −6.07902e12 | −0.754363 | ||||||||
\(739\) | −1.65987e12 | −0.204726 | −0.102363 | − | 0.994747i | \(-0.532640\pi\) | ||||
−0.102363 | + | 0.994747i | \(0.532640\pi\) | |||||||
\(740\) | 1.19996e11 | 0.0147104 | ||||||||
\(741\) | −1.81796e13 | −2.21514 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −4.66431e11 | −0.0561484 | −0.0280742 | − | 0.999606i | \(-0.508937\pi\) | ||||
−0.0280742 | + | 0.999606i | \(0.508937\pi\) | |||||||
\(744\) | 5.37550e12 | 0.643191 | ||||||||
\(745\) | 2.31867e11 | 0.0275763 | ||||||||
\(746\) | 8.71738e12 | 1.03053 | ||||||||
\(747\) | 9.70331e11 | 0.114019 | ||||||||
\(748\) | 6.09138e12 | 0.711474 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 4.02494e11 | 0.0464497 | ||||||||
\(751\) | −5.33602e12 | −0.612122 | −0.306061 | − | 0.952012i | \(-0.599011\pi\) | ||||
−0.306061 | + | 0.952012i | \(0.599011\pi\) | |||||||
\(752\) | −2.08439e11 | −0.0237684 | ||||||||
\(753\) | −6.83473e12 | −0.774719 | ||||||||
\(754\) | −4.68292e12 | −0.527650 | ||||||||
\(755\) | −1.89966e11 | −0.0212772 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 8.40938e12 | 0.930748 | 0.465374 | − | 0.885114i | \(-0.345920\pi\) | ||||
0.465374 | + | 0.885114i | \(0.345920\pi\) | |||||||
\(758\) | 1.99458e12 | 0.219453 | ||||||||
\(759\) | −2.95939e12 | −0.323678 | ||||||||
\(760\) | 1.15111e11 | 0.0125157 | ||||||||
\(761\) | 6.16386e12 | 0.666227 | 0.333113 | − | 0.942887i | \(-0.391901\pi\) | ||||
0.333113 | + | 0.942887i | \(0.391901\pi\) | |||||||
\(762\) | −1.04719e13 | −1.12520 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −6.29482e12 | −0.668441 | ||||||||
\(765\) | −2.65104e11 | −0.0279860 | ||||||||
\(766\) | 6.53192e12 | 0.685507 | ||||||||
\(767\) | −1.58524e12 | −0.165392 | ||||||||
\(768\) | 8.23677e11 | 0.0854341 | ||||||||
\(769\) | 9.39193e12 | 0.968470 | 0.484235 | − | 0.874938i | \(-0.339098\pi\) | ||||
0.484235 | + | 0.874938i | \(0.339098\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.33203e13 | 1.35759 | ||||||||
\(772\) | −4.61104e12 | −0.467219 | ||||||||
\(773\) | −4.22637e12 | −0.425755 | −0.212877 | − | 0.977079i | \(-0.568283\pi\) | ||||
−0.212877 | + | 0.977079i | \(0.568283\pi\) | |||||||
\(774\) | 8.87645e12 | 0.889007 | ||||||||
\(775\) | 1.33580e13 | 1.33010 | ||||||||
\(776\) | −3.68388e12 | −0.364693 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −8.21823e12 | −0.804212 | ||||||||
\(779\) | −1.85943e13 | −1.80910 | ||||||||
\(780\) | 1.86846e11 | 0.0180742 | ||||||||
\(781\) | 1.47748e13 | 1.42099 | ||||||||
\(782\) | 2.21160e12 | 0.211483 | ||||||||
\(783\) | −1.28186e12 | −0.121874 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2.21684e11 | −0.0208363 | ||||||||
\(786\) | −2.20310e12 | −0.205889 | ||||||||
\(787\) | −5.89826e11 | −0.0548072 | −0.0274036 | − | 0.999624i | \(-0.508724\pi\) | ||||
−0.0274036 | + | 0.999624i | \(0.508724\pi\) | |||||||
\(788\) | 1.03095e13 | 0.952514 | ||||||||
\(789\) | 1.38659e13 | 1.27380 | ||||||||
\(790\) | 5.78183e10 | 0.00528133 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 3.60901e12 | 0.325931 | ||||||||
\(793\) | −1.29086e13 | −1.15918 | ||||||||
\(794\) | −5.77303e12 | −0.515480 | ||||||||
\(795\) | 5.68751e11 | 0.0504975 | ||||||||
\(796\) | 9.64741e12 | 0.851730 | ||||||||
\(797\) | −2.83029e12 | −0.248467 | −0.124233 | − | 0.992253i | \(-0.539647\pi\) | ||||
−0.124233 | + | 0.992253i | \(0.539647\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.46834e12 | 0.127458 | ||||||||
\(800\) | 2.04682e12 | 0.176675 | ||||||||
\(801\) | −1.45084e13 | −1.24530 | ||||||||
\(802\) | −3.81751e12 | −0.325833 | ||||||||
\(803\) | −2.46804e12 | −0.209475 | ||||||||
\(804\) | −1.49982e13 | −1.26586 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1.24057e13 | 1.03541 | ||||||||
\(807\) | 1.73187e13 | 1.43743 | ||||||||
\(808\) | −2.58950e11 | −0.0213730 | ||||||||
\(809\) | 1.16033e13 | 0.952388 | 0.476194 | − | 0.879340i | \(-0.342016\pi\) | ||||
0.476194 | + | 0.879340i | \(0.342016\pi\) | |||||||
\(810\) | 2.31988e11 | 0.0189357 | ||||||||
\(811\) | −4.13817e12 | −0.335903 | −0.167952 | − | 0.985795i | \(-0.553715\pi\) | ||||
−0.167952 | + | 0.985795i | \(0.553715\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 7.71383e12 | 0.619245 | ||||||||
\(814\) | 1.15077e13 | 0.918708 | ||||||||
\(815\) | −2.68314e11 | −0.0213027 | ||||||||
\(816\) | −5.80237e12 | −0.458141 | ||||||||
\(817\) | 2.71510e13 | 2.13200 | ||||||||
\(818\) | 1.23950e13 | 0.967961 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.91109e11 | 0.0147611 | ||||||||
\(821\) | −1.95703e11 | −0.0150332 | −0.00751662 | − | 0.999972i | \(-0.502393\pi\) | ||||
−0.00751662 | + | 0.999972i | \(0.502393\pi\) | |||||||
\(822\) | 2.24416e13 | 1.71447 | ||||||||
\(823\) | −8.51398e12 | −0.646895 | −0.323447 | − | 0.946246i | \(-0.604842\pi\) | ||||
−0.323447 | + | 0.946246i | \(0.604842\pi\) | |||||||
\(824\) | −4.97990e12 | −0.376312 | ||||||||
\(825\) | 1.92941e13 | 1.45004 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.19931e12 | −0.0891576 | −0.0445788 | − | 0.999006i | \(-0.514195\pi\) | ||||
−0.0445788 | + | 0.999006i | \(0.514195\pi\) | |||||||
\(828\) | 1.31032e12 | 0.0968817 | ||||||||
\(829\) | −1.64084e13 | −1.20662 | −0.603311 | − | 0.797506i | \(-0.706152\pi\) | ||||
−0.603311 | + | 0.797506i | \(0.706152\pi\) | |||||||
\(830\) | −3.05047e10 | −0.00223108 | ||||||||
\(831\) | −3.96436e12 | −0.288382 | ||||||||
\(832\) | 1.90090e12 | 0.137532 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 1.49944e13 | 1.07320 | ||||||||
\(835\) | 1.46084e11 | 0.0103995 | ||||||||
\(836\) | 1.10391e13 | 0.781640 | ||||||||
\(837\) | 3.39581e12 | 0.239155 | ||||||||
\(838\) | 9.39570e12 | 0.658159 | ||||||||
\(839\) | −1.67670e13 | −1.16822 | −0.584111 | − | 0.811674i | \(-0.698557\pi\) | ||||
−0.584111 | + | 0.811674i | \(0.698557\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7.83425e12 | −0.540027 | ||||||||
\(842\) | 1.80065e13 | 1.23460 | ||||||||
\(843\) | −6.65147e12 | −0.453622 | ||||||||
\(844\) | −4.02607e12 | −0.273111 | ||||||||
\(845\) | 7.50049e10 | 0.00506098 | ||||||||
\(846\) | 8.69962e11 | 0.0583894 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 5.78625e12 | 0.384252 | ||||||||
\(849\) | 2.00674e13 | 1.32558 | ||||||||
\(850\) | −1.44187e13 | −0.947419 | ||||||||
\(851\) | 4.17808e12 | 0.273083 | ||||||||
\(852\) | −1.40738e13 | −0.915022 | ||||||||
\(853\) | −6.93277e12 | −0.448370 | −0.224185 | − | 0.974547i | \(-0.571972\pi\) | ||||
−0.224185 | + | 0.974547i | \(0.571972\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −4.80437e11 | −0.0307460 | ||||||||
\(856\) | 5.25281e12 | 0.334395 | ||||||||
\(857\) | −2.60920e11 | −0.0165232 | −0.00826158 | − | 0.999966i | \(-0.502630\pi\) | ||||
−0.00826158 | + | 0.999966i | \(0.502630\pi\) | |||||||
\(858\) | 1.79186e13 | 1.12879 | ||||||||
\(859\) | −2.54206e13 | −1.59300 | −0.796502 | − | 0.604636i | \(-0.793319\pi\) | ||||
−0.796502 | + | 0.604636i | \(0.793319\pi\) | |||||||
\(860\) | −2.79053e11 | −0.0173957 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1.08427e13 | 0.668889 | ||||||||
\(863\) | 7.18619e12 | 0.441012 | 0.220506 | − | 0.975386i | \(-0.429229\pi\) | ||||
0.220506 | + | 0.975386i | \(0.429229\pi\) | |||||||
\(864\) | 5.20334e11 | 0.0317666 | ||||||||
\(865\) | 4.65189e11 | 0.0282525 | ||||||||
\(866\) | −9.06535e12 | −0.547714 | ||||||||
\(867\) | 1.81322e13 | 1.08984 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 5.54479e12 | 0.329835 | ||||||||
\(870\) | −2.66245e11 | −0.0157560 | ||||||||
\(871\) | −3.46131e13 | −2.03779 | ||||||||
\(872\) | 2.07490e12 | 0.121527 | ||||||||
\(873\) | 1.53754e13 | 0.895905 | ||||||||
\(874\) | 4.00797e12 | 0.232340 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 2.35094e12 | 0.134888 | ||||||||
\(877\) | −2.68806e13 | −1.53441 | −0.767205 | − | 0.641402i | \(-0.778353\pi\) | ||||
−0.767205 | + | 0.641402i | \(0.778353\pi\) | |||||||
\(878\) | 1.18598e13 | 0.673521 | ||||||||
\(879\) | −3.08301e13 | −1.74191 | ||||||||
\(880\) | −1.13458e11 | −0.00637769 | ||||||||
\(881\) | 5.33553e11 | 0.0298391 | 0.0149195 | − | 0.999889i | \(-0.495251\pi\) | ||||
0.0149195 | + | 0.999889i | \(0.495251\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 6.42561e12 | 0.355706 | 0.177853 | − | 0.984057i | \(-0.443085\pi\) | ||||
0.177853 | + | 0.984057i | \(0.443085\pi\) | |||||||
\(884\) | −1.33908e13 | −0.737518 | ||||||||
\(885\) | −9.01278e10 | −0.00493872 | ||||||||
\(886\) | −1.48033e12 | −0.0807062 | ||||||||
\(887\) | −2.88437e12 | −0.156457 | −0.0782285 | − | 0.996935i | \(-0.524926\pi\) | ||||
−0.0782285 | + | 0.996935i | \(0.524926\pi\) | |||||||
\(888\) | −1.09617e13 | −0.591586 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 4.56106e11 | 0.0243675 | ||||||||
\(891\) | 2.22477e13 | 1.18259 | ||||||||
\(892\) | 1.61195e13 | 0.852528 | ||||||||
\(893\) | 2.66101e12 | 0.140028 | ||||||||
\(894\) | −2.11811e13 | −1.10899 | ||||||||
\(895\) | 6.70259e11 | 0.0349172 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 6.50570e12 | 0.335527 | ||||||||
\(898\) | 2.03015e12 | 0.104180 | ||||||||
\(899\) | −1.76774e13 | −0.902610 | ||||||||
\(900\) | −8.54280e12 | −0.434019 | ||||||||
\(901\) | −4.07611e13 | −2.06056 | ||||||||
\(902\) | 1.83274e13 | 0.921873 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −4.73138e12 | −0.235630 | ||||||||
\(905\) | −1.12091e11 | −0.00555459 | ||||||||
\(906\) | 1.73534e13 | 0.855675 | ||||||||
\(907\) | −1.74881e13 | −0.858044 | −0.429022 | − | 0.903294i | \(-0.641142\pi\) | ||||
−0.429022 | + | 0.903294i | \(0.641142\pi\) | |||||||
\(908\) | 1.40291e13 | 0.684925 | ||||||||
\(909\) | 1.08078e12 | 0.0525049 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.68088e13 | −0.808543 | −0.404271 | − | 0.914639i | \(-0.632475\pi\) | ||||
−0.404271 | + | 0.914639i | \(0.632475\pi\) | |||||||
\(912\) | −1.05154e13 | −0.503324 | ||||||||
\(913\) | −2.92541e12 | −0.139337 | ||||||||
\(914\) | −1.64504e13 | −0.779686 | ||||||||
\(915\) | −7.33914e11 | −0.0346139 | ||||||||
\(916\) | −1.57214e13 | −0.737840 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −3.66548e12 | −0.170348 | ||||||||
\(919\) | −2.48947e13 | −1.15130 | −0.575648 | − | 0.817698i | \(-0.695250\pi\) | ||||
−0.575648 | + | 0.817698i | \(0.695250\pi\) | |||||||
\(920\) | −4.11931e10 | −0.00189574 | ||||||||
\(921\) | 2.78403e13 | 1.27498 | ||||||||
\(922\) | 1.29637e13 | 0.590800 | ||||||||
\(923\) | −3.24798e13 | −1.47301 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.72395e13 | −1.22338 | ||||||||
\(926\) | 2.31669e13 | 1.03542 | ||||||||
\(927\) | 2.07846e13 | 0.924449 | ||||||||
\(928\) | −2.70868e12 | −0.119892 | ||||||||
\(929\) | 3.84486e13 | 1.69360 | 0.846799 | − | 0.531914i | \(-0.178527\pi\) | ||||
0.846799 | + | 0.531914i | \(0.178527\pi\) | |||||||
\(930\) | 7.05320e11 | 0.0309181 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −2.15785e12 | −0.0936806 | ||||||||
\(933\) | −5.04546e13 | −2.17988 | ||||||||
\(934\) | 7.15255e12 | 0.307539 | ||||||||
\(935\) | 7.99252e11 | 0.0342004 | ||||||||
\(936\) | −7.93379e12 | −0.337862 | ||||||||
\(937\) | −4.89574e11 | −0.0207486 | −0.0103743 | − | 0.999946i | \(-0.503302\pi\) | ||||
−0.0103743 | + | 0.999946i | \(0.503302\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.60748e13 | −0.674763 | ||||||||
\(940\) | −2.73493e10 | −0.00114254 | ||||||||
\(941\) | 2.20721e13 | 0.917679 | 0.458840 | − | 0.888519i | \(-0.348265\pi\) | ||||
0.458840 | + | 0.888519i | \(0.348265\pi\) | |||||||
\(942\) | 2.02509e13 | 0.837944 | ||||||||
\(943\) | 6.65411e12 | 0.274023 | ||||||||
\(944\) | −9.16926e11 | −0.0375803 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2.67612e13 | −1.08642 | ||||||||
\(947\) | 4.86143e11 | 0.0196422 | 0.00982108 | − | 0.999952i | \(-0.496874\pi\) | ||||
0.00982108 | + | 0.999952i | \(0.496874\pi\) | |||||||
\(948\) | −5.28171e12 | −0.212391 | ||||||||
\(949\) | 5.42556e12 | 0.217144 | ||||||||
\(950\) | −2.61304e13 | −1.04086 | ||||||||
\(951\) | 5.19171e13 | 2.05825 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2.77682e13 | −1.09051 | −0.545254 | − | 0.838271i | \(-0.683567\pi\) | ||||
−0.545254 | + | 0.838271i | \(0.683567\pi\) | |||||||
\(954\) | −2.41501e13 | −0.943954 | ||||||||
\(955\) | −8.25945e11 | −0.0321319 | ||||||||
\(956\) | 8.03714e12 | 0.311201 | ||||||||
\(957\) | −2.55330e13 | −0.984006 | ||||||||
\(958\) | 1.39128e12 | 0.0533667 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 1.08075e11 | 0.00410680 | ||||||||
\(961\) | 2.03903e13 | 0.771202 | ||||||||
\(962\) | −2.52976e13 | −0.952339 | ||||||||
\(963\) | −2.19236e13 | −0.821475 | ||||||||
\(964\) | 3.73417e12 | 0.139267 | ||||||||
\(965\) | −6.05015e11 | −0.0224591 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2.53282e12 | −0.0931505 | −0.0465752 | − | 0.998915i | \(-0.514831\pi\) | ||||
−0.0465752 | + | 0.998915i | \(0.514831\pi\) | |||||||
\(968\) | −1.22251e12 | −0.0447519 | ||||||||
\(969\) | 7.40752e13 | 2.69908 | ||||||||
\(970\) | −4.83362e11 | −0.0175307 | ||||||||
\(971\) | 8.52422e12 | 0.307729 | 0.153864 | − | 0.988092i | \(-0.450828\pi\) | ||||
0.153864 | + | 0.988092i | \(0.450828\pi\) | |||||||
\(972\) | −1.86917e13 | −0.671661 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 7.71096e9 | 0.000274532 0 | ||||||||
\(975\) | −4.24146e13 | −1.50312 | ||||||||
\(976\) | −7.46657e12 | −0.263388 | ||||||||
\(977\) | −3.37176e13 | −1.18394 | −0.591972 | − | 0.805958i | \(-0.701651\pi\) | ||||
−0.591972 | + | 0.805958i | \(0.701651\pi\) | |||||||
\(978\) | 2.45106e13 | 0.856699 | ||||||||
\(979\) | 4.37407e13 | 1.52182 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −8.66001e12 | −0.298544 | ||||||||
\(982\) | 9.41824e12 | 0.323197 | ||||||||
\(983\) | 3.27904e12 | 0.112010 | 0.0560049 | − | 0.998430i | \(-0.482164\pi\) | ||||
0.0560049 | + | 0.998430i | \(0.482164\pi\) | |||||||
\(984\) | −1.74578e13 | −0.593624 | ||||||||
\(985\) | 1.35272e12 | 0.0457872 | ||||||||
\(986\) | 1.90812e13 | 0.642923 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −2.42676e13 | −0.810253 | ||||||||
\(989\) | −9.71618e12 | −0.322933 | ||||||||
\(990\) | 4.73540e11 | 0.0156674 | ||||||||
\(991\) | 2.29294e13 | 0.755200 | 0.377600 | − | 0.925969i | \(-0.376749\pi\) | ||||
0.377600 | + | 0.925969i | \(0.376749\pi\) | |||||||
\(992\) | 7.17566e12 | 0.235266 | ||||||||
\(993\) | 3.71550e13 | 1.21268 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.26584e12 | 0.0409425 | ||||||||
\(996\) | 2.78661e12 | 0.0897240 | ||||||||
\(997\) | 1.25509e13 | 0.402297 | 0.201148 | − | 0.979561i | \(-0.435533\pi\) | ||||
0.201148 | + | 0.979561i | \(0.435533\pi\) | |||||||
\(998\) | 3.96714e13 | 1.26587 | ||||||||
\(999\) | −6.92471e12 | −0.219967 |
(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 | 98.10.a.k.1.4 | yes | 4 | |
7.2 | even | 3 | 98.10.c.m.67.1 | 8 | |||
7.3 | odd | 6 | 98.10.c.m.79.4 | 8 | |||
7.4 | even | 3 | 98.10.c.m.79.1 | 8 | |||
7.5 | odd | 6 | 98.10.c.m.67.4 | 8 | |||
7.6 | odd | 2 | inner | 98.10.a.k.1.1 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
98.10.a.k.1.1 | ✓ | 4 | 7.6 | odd | 2 | inner | |
98.10.a.k.1.4 | yes | 4 | 1.1 | even | 1 | trivial | |
98.10.c.m.67.1 | 8 | 7.2 | even | 3 | |||
98.10.c.m.67.4 | 8 | 7.5 | odd | 6 | |||
98.10.c.m.79.1 | 8 | 7.4 | even | 3 | |||
98.10.c.m.79.4 | 8 | 7.3 | odd | 6 |