Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [289,10,Mod(1,289)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(289, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("289.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 289 = 17^{2} \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 289.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(148.845356651\) |
Analytic rank: | \(1\) |
Dimension: | \(36\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.28 | ||
Character | \(\chi\) | \(=\) | 289.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 28.5023 | 1.25963 | 0.629817 | − | 0.776743i | \(-0.283130\pi\) | ||||
0.629817 | + | 0.776743i | \(0.283130\pi\) | |||||||
\(3\) | 173.222 | 1.23469 | 0.617343 | − | 0.786694i | \(-0.288209\pi\) | ||||
0.617343 | + | 0.786694i | \(0.288209\pi\) | |||||||
\(4\) | 300.380 | 0.586679 | ||||||||
\(5\) | −1462.89 | −1.04676 | −0.523378 | − | 0.852101i | \(-0.675328\pi\) | ||||
−0.523378 | + | 0.852101i | \(0.675328\pi\) | |||||||
\(6\) | 4937.21 | 1.55525 | ||||||||
\(7\) | 2705.62 | 0.425917 | 0.212959 | − | 0.977061i | \(-0.431690\pi\) | ||||
0.212959 | + | 0.977061i | \(0.431690\pi\) | |||||||
\(8\) | −6031.66 | −0.520633 | ||||||||
\(9\) | 10322.7 | 0.524448 | ||||||||
\(10\) | −41695.6 | −1.31853 | ||||||||
\(11\) | 45163.0 | 0.930069 | 0.465035 | − | 0.885292i | \(-0.346042\pi\) | ||||
0.465035 | + | 0.885292i | \(0.346042\pi\) | |||||||
\(12\) | 52032.2 | 0.724364 | ||||||||
\(13\) | −57896.3 | −0.562219 | −0.281110 | − | 0.959676i | \(-0.590702\pi\) | ||||
−0.281110 | + | 0.959676i | \(0.590702\pi\) | |||||||
\(14\) | 77116.3 | 0.536500 | ||||||||
\(15\) | −253403. | −1.29241 | ||||||||
\(16\) | −325710. | −1.24249 | ||||||||
\(17\) | 0 | 0 | ||||||||
\(18\) | 294221. | 0.660613 | ||||||||
\(19\) | 323804. | 0.570021 | 0.285010 | − | 0.958524i | \(-0.408003\pi\) | ||||
0.285010 | + | 0.958524i | \(0.408003\pi\) | |||||||
\(20\) | −439421. | −0.614109 | ||||||||
\(21\) | 468671. | 0.525874 | ||||||||
\(22\) | 1.28725e6 | 1.17155 | ||||||||
\(23\) | 2.17545e6 | 1.62097 | 0.810483 | − | 0.585763i | \(-0.199205\pi\) | ||||
0.810483 | + | 0.585763i | \(0.199205\pi\) | |||||||
\(24\) | −1.04481e6 | −0.642819 | ||||||||
\(25\) | 186908. | 0.0956967 | ||||||||
\(26\) | −1.65018e6 | −0.708190 | ||||||||
\(27\) | −1.62140e6 | −0.587157 | ||||||||
\(28\) | 812712. | 0.249877 | ||||||||
\(29\) | −2.98380e6 | −0.783392 | −0.391696 | − | 0.920095i | \(-0.628112\pi\) | ||||
−0.391696 | + | 0.920095i | \(0.628112\pi\) | |||||||
\(30\) | −7.22257e6 | −1.62797 | ||||||||
\(31\) | −9.05752e6 | −1.76150 | −0.880748 | − | 0.473584i | \(-0.842960\pi\) | ||||
−0.880748 | + | 0.473584i | \(0.842960\pi\) | |||||||
\(32\) | −6.19528e6 | −1.04445 | ||||||||
\(33\) | 7.82320e6 | 1.14834 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.95801e6 | −0.445831 | ||||||||
\(36\) | 3.10073e6 | 0.307683 | ||||||||
\(37\) | −1.28689e7 | −1.12885 | −0.564423 | − | 0.825486i | \(-0.690901\pi\) | ||||
−0.564423 | + | 0.825486i | \(0.690901\pi\) | |||||||
\(38\) | 9.22914e6 | 0.718018 | ||||||||
\(39\) | −1.00289e7 | −0.694164 | ||||||||
\(40\) | 8.82363e6 | 0.544976 | ||||||||
\(41\) | 2.91740e7 | 1.61239 | 0.806194 | − | 0.591652i | \(-0.201524\pi\) | ||||
0.806194 | + | 0.591652i | \(0.201524\pi\) | |||||||
\(42\) | 1.33582e7 | 0.662409 | ||||||||
\(43\) | −2.54101e7 | −1.13344 | −0.566719 | − | 0.823911i | \(-0.691788\pi\) | ||||
−0.566719 | + | 0.823911i | \(0.691788\pi\) | |||||||
\(44\) | 1.35660e7 | 0.545652 | ||||||||
\(45\) | −1.51009e7 | −0.548969 | ||||||||
\(46\) | 6.20053e7 | 2.04182 | ||||||||
\(47\) | −2.66571e7 | −0.796842 | −0.398421 | − | 0.917203i | \(-0.630442\pi\) | ||||
−0.398421 | + | 0.917203i | \(0.630442\pi\) | |||||||
\(48\) | −5.64201e7 | −1.53408 | ||||||||
\(49\) | −3.30332e7 | −0.818594 | ||||||||
\(50\) | 5.32729e6 | 0.120543 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.73909e7 | −0.329842 | ||||||||
\(53\) | −1.32615e7 | −0.230861 | −0.115430 | − | 0.993316i | \(-0.536825\pi\) | ||||
−0.115430 | + | 0.993316i | \(0.536825\pi\) | |||||||
\(54\) | −4.62137e7 | −0.739603 | ||||||||
\(55\) | −6.60682e7 | −0.973555 | ||||||||
\(56\) | −1.63194e7 | −0.221747 | ||||||||
\(57\) | 5.60898e7 | 0.703796 | ||||||||
\(58\) | −8.50452e7 | −0.986788 | ||||||||
\(59\) | 5.04039e7 | 0.541539 | 0.270770 | − | 0.962644i | \(-0.412722\pi\) | ||||
0.270770 | + | 0.962644i | \(0.412722\pi\) | |||||||
\(60\) | −7.61172e7 | −0.758232 | ||||||||
\(61\) | −1.10036e8 | −1.01754 | −0.508768 | − | 0.860904i | \(-0.669899\pi\) | ||||
−0.508768 | + | 0.860904i | \(0.669899\pi\) | |||||||
\(62\) | −2.58160e8 | −2.21884 | ||||||||
\(63\) | 2.79293e7 | 0.223372 | ||||||||
\(64\) | −9.81574e6 | −0.0731330 | ||||||||
\(65\) | 8.46956e7 | 0.588506 | ||||||||
\(66\) | 2.22979e8 | 1.44649 | ||||||||
\(67\) | −1.13093e8 | −0.685646 | −0.342823 | − | 0.939400i | \(-0.611383\pi\) | ||||
−0.342823 | + | 0.939400i | \(0.611383\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.76835e8 | 2.00138 | ||||||||
\(70\) | −1.12812e8 | −0.561584 | ||||||||
\(71\) | −3.38574e8 | −1.58121 | −0.790607 | − | 0.612324i | \(-0.790235\pi\) | ||||
−0.790607 | + | 0.612324i | \(0.790235\pi\) | |||||||
\(72\) | −6.22631e7 | −0.273045 | ||||||||
\(73\) | 2.36539e8 | 0.974877 | 0.487438 | − | 0.873157i | \(-0.337931\pi\) | ||||
0.487438 | + | 0.873157i | \(0.337931\pi\) | |||||||
\(74\) | −3.66794e8 | −1.42193 | ||||||||
\(75\) | 3.23764e7 | 0.118155 | ||||||||
\(76\) | 9.72640e7 | 0.334419 | ||||||||
\(77\) | 1.22194e8 | 0.396133 | ||||||||
\(78\) | −2.85846e8 | −0.874393 | ||||||||
\(79\) | −5.61145e8 | −1.62089 | −0.810444 | − | 0.585816i | \(-0.800774\pi\) | ||||
−0.810444 | + | 0.585816i | \(0.800774\pi\) | |||||||
\(80\) | 4.76477e8 | 1.30058 | ||||||||
\(81\) | −4.84044e8 | −1.24940 | ||||||||
\(82\) | 8.31527e8 | 2.03102 | ||||||||
\(83\) | 2.95912e8 | 0.684403 | 0.342201 | − | 0.939627i | \(-0.388827\pi\) | ||||
0.342201 | + | 0.939627i | \(0.388827\pi\) | |||||||
\(84\) | 1.40779e8 | 0.308519 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −7.24245e8 | −1.42772 | ||||||||
\(87\) | −5.16859e8 | −0.967243 | ||||||||
\(88\) | −2.72408e8 | −0.484225 | ||||||||
\(89\) | −1.78872e8 | −0.302195 | −0.151098 | − | 0.988519i | \(-0.548281\pi\) | ||||
−0.151098 | + | 0.988519i | \(0.548281\pi\) | |||||||
\(90\) | −4.30411e8 | −0.691500 | ||||||||
\(91\) | −1.56645e8 | −0.239459 | ||||||||
\(92\) | 6.53461e8 | 0.950986 | ||||||||
\(93\) | −1.56896e9 | −2.17489 | ||||||||
\(94\) | −7.59787e8 | −1.00373 | ||||||||
\(95\) | −4.73687e8 | −0.596672 | ||||||||
\(96\) | −1.07316e9 | −1.28956 | ||||||||
\(97\) | −9.76224e7 | −0.111964 | −0.0559818 | − | 0.998432i | \(-0.517829\pi\) | ||||
−0.0559818 | + | 0.998432i | \(0.517829\pi\) | |||||||
\(98\) | −9.41522e8 | −1.03113 | ||||||||
\(99\) | 4.66204e8 | 0.487773 | ||||||||
\(100\) | 5.61433e7 | 0.0561433 | ||||||||
\(101\) | 7.74498e8 | 0.740583 | 0.370292 | − | 0.928916i | \(-0.379258\pi\) | ||||
0.370292 | + | 0.928916i | \(0.379258\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.22734e9 | 1.07448 | 0.537240 | − | 0.843429i | \(-0.319467\pi\) | ||||
0.537240 | + | 0.843429i | \(0.319467\pi\) | |||||||
\(104\) | 3.49211e8 | 0.292710 | ||||||||
\(105\) | −6.85612e8 | −0.550461 | ||||||||
\(106\) | −3.77982e8 | −0.290800 | ||||||||
\(107\) | −2.30141e9 | −1.69733 | −0.848665 | − | 0.528930i | \(-0.822593\pi\) | ||||
−0.848665 | + | 0.528930i | \(0.822593\pi\) | |||||||
\(108\) | −4.87037e8 | −0.344473 | ||||||||
\(109\) | −2.60083e9 | −1.76479 | −0.882393 | − | 0.470513i | \(-0.844069\pi\) | ||||
−0.882393 | + | 0.470513i | \(0.844069\pi\) | |||||||
\(110\) | −1.88309e9 | −1.22632 | ||||||||
\(111\) | −2.22918e9 | −1.39377 | ||||||||
\(112\) | −8.81248e8 | −0.529197 | ||||||||
\(113\) | 1.75376e9 | 1.01185 | 0.505925 | − | 0.862577i | \(-0.331151\pi\) | ||||
0.505925 | + | 0.862577i | \(0.331151\pi\) | |||||||
\(114\) | 1.59869e9 | 0.886526 | ||||||||
\(115\) | −3.18243e9 | −1.69675 | ||||||||
\(116\) | −8.96274e8 | −0.459600 | ||||||||
\(117\) | −5.97647e8 | −0.294855 | ||||||||
\(118\) | 1.43662e9 | 0.682141 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 1.52844e9 | 0.672874 | ||||||||
\(121\) | −3.18255e8 | −0.134971 | ||||||||
\(122\) | −3.13627e9 | −1.28172 | ||||||||
\(123\) | 5.05357e9 | 1.99079 | ||||||||
\(124\) | −2.72070e9 | −1.03343 | ||||||||
\(125\) | 2.58377e9 | 0.946584 | ||||||||
\(126\) | 7.96049e8 | 0.281367 | ||||||||
\(127\) | −1.62086e9 | −0.552877 | −0.276438 | − | 0.961032i | \(-0.589154\pi\) | ||||
−0.276438 | + | 0.961032i | \(0.589154\pi\) | |||||||
\(128\) | 2.89221e9 | 0.952325 | ||||||||
\(129\) | −4.40158e9 | −1.39944 | ||||||||
\(130\) | 2.41402e9 | 0.741302 | ||||||||
\(131\) | 1.04453e9 | 0.309884 | 0.154942 | − | 0.987924i | \(-0.450481\pi\) | ||||
0.154942 | + | 0.987924i | \(0.450481\pi\) | |||||||
\(132\) | 2.34993e9 | 0.673709 | ||||||||
\(133\) | 8.76089e8 | 0.242782 | ||||||||
\(134\) | −3.22342e9 | −0.863664 | ||||||||
\(135\) | 2.37193e9 | 0.614610 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.19321e9 | 1.50201 | 0.751005 | − | 0.660296i | \(-0.229569\pi\) | ||||
0.751005 | + | 0.660296i | \(0.229569\pi\) | |||||||
\(138\) | 1.07406e10 | 2.52101 | ||||||||
\(139\) | −2.59074e9 | −0.588649 | −0.294325 | − | 0.955706i | \(-0.595095\pi\) | ||||
−0.294325 | + | 0.955706i | \(0.595095\pi\) | |||||||
\(140\) | −1.18890e9 | −0.261560 | ||||||||
\(141\) | −4.61758e9 | −0.983849 | ||||||||
\(142\) | −9.65012e9 | −1.99175 | ||||||||
\(143\) | −2.61477e9 | −0.522903 | ||||||||
\(144\) | −3.36222e9 | −0.651620 | ||||||||
\(145\) | 4.36496e9 | 0.820020 | ||||||||
\(146\) | 6.74190e9 | 1.22799 | ||||||||
\(147\) | −5.72207e9 | −1.01071 | ||||||||
\(148\) | −3.86556e9 | −0.662270 | ||||||||
\(149\) | 4.82673e9 | 0.802259 | 0.401130 | − | 0.916021i | \(-0.368618\pi\) | ||||
0.401130 | + | 0.916021i | \(0.368618\pi\) | |||||||
\(150\) | 9.22802e8 | 0.148833 | ||||||||
\(151\) | 6.24839e9 | 0.978075 | 0.489037 | − | 0.872263i | \(-0.337348\pi\) | ||||
0.489037 | + | 0.872263i | \(0.337348\pi\) | |||||||
\(152\) | −1.95307e9 | −0.296772 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 3.48280e9 | 0.498982 | ||||||||
\(155\) | 1.32501e10 | 1.84386 | ||||||||
\(156\) | −3.01247e9 | −0.407251 | ||||||||
\(157\) | −3.18687e9 | −0.418616 | −0.209308 | − | 0.977850i | \(-0.567121\pi\) | ||||
−0.209308 | + | 0.977850i | \(0.567121\pi\) | |||||||
\(158\) | −1.59939e10 | −2.04173 | ||||||||
\(159\) | −2.29717e9 | −0.285040 | ||||||||
\(160\) | 9.06298e9 | 1.09328 | ||||||||
\(161\) | 5.88593e9 | 0.690397 | ||||||||
\(162\) | −1.37964e10 | −1.57379 | ||||||||
\(163\) | −1.22687e10 | −1.36130 | −0.680650 | − | 0.732609i | \(-0.738302\pi\) | ||||
−0.680650 | + | 0.732609i | \(0.738302\pi\) | |||||||
\(164\) | 8.76329e9 | 0.945954 | ||||||||
\(165\) | −1.14444e10 | −1.20203 | ||||||||
\(166\) | 8.43418e9 | 0.862097 | ||||||||
\(167\) | 6.15276e9 | 0.612133 | 0.306066 | − | 0.952010i | \(-0.400987\pi\) | ||||
0.306066 | + | 0.952010i | \(0.400987\pi\) | |||||||
\(168\) | −2.82687e9 | −0.273788 | ||||||||
\(169\) | −7.25252e9 | −0.683910 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.34253e9 | 0.298946 | ||||||||
\(172\) | −7.63267e9 | −0.664965 | ||||||||
\(173\) | 1.18129e10 | 1.00265 | 0.501323 | − | 0.865260i | \(-0.332847\pi\) | ||||
0.501323 | + | 0.865260i | \(0.332847\pi\) | |||||||
\(174\) | −1.47317e10 | −1.21837 | ||||||||
\(175\) | 5.05701e8 | 0.0407589 | ||||||||
\(176\) | −1.47100e10 | −1.15560 | ||||||||
\(177\) | 8.73104e9 | 0.668630 | ||||||||
\(178\) | −5.09826e9 | −0.380655 | ||||||||
\(179\) | 2.62945e10 | 1.91437 | 0.957184 | − | 0.289479i | \(-0.0934822\pi\) | ||||
0.957184 | + | 0.289479i | \(0.0934822\pi\) | |||||||
\(180\) | −4.53602e9 | −0.322069 | ||||||||
\(181\) | 1.32577e10 | 0.918154 | 0.459077 | − | 0.888397i | \(-0.348180\pi\) | ||||
0.459077 | + | 0.888397i | \(0.348180\pi\) | |||||||
\(182\) | −4.46474e9 | −0.301631 | ||||||||
\(183\) | −1.90606e10 | −1.25634 | ||||||||
\(184\) | −1.31216e10 | −0.843929 | ||||||||
\(185\) | 1.88258e10 | 1.18163 | ||||||||
\(186\) | −4.47189e10 | −2.73957 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −8.00724e9 | −0.467490 | ||||||||
\(189\) | −4.38690e9 | −0.250080 | ||||||||
\(190\) | −1.35012e10 | −0.751589 | ||||||||
\(191\) | 1.65717e10 | 0.900983 | 0.450492 | − | 0.892781i | \(-0.351249\pi\) | ||||
0.450492 | + | 0.892781i | \(0.351249\pi\) | |||||||
\(192\) | −1.70030e9 | −0.0902962 | ||||||||
\(193\) | 1.44377e10 | 0.749016 | 0.374508 | − | 0.927224i | \(-0.377812\pi\) | ||||
0.374508 | + | 0.927224i | \(0.377812\pi\) | |||||||
\(194\) | −2.78246e9 | −0.141033 | ||||||||
\(195\) | 1.46711e10 | 0.726620 | ||||||||
\(196\) | −9.92251e9 | −0.480252 | ||||||||
\(197\) | −2.61363e10 | −1.23636 | −0.618181 | − | 0.786036i | \(-0.712130\pi\) | ||||
−0.618181 | + | 0.786036i | \(0.712130\pi\) | |||||||
\(198\) | 1.32879e10 | 0.614416 | ||||||||
\(199\) | −6.06022e8 | −0.0273936 | −0.0136968 | − | 0.999906i | \(-0.504360\pi\) | ||||
−0.0136968 | + | 0.999906i | \(0.504360\pi\) | |||||||
\(200\) | −1.12736e9 | −0.0498229 | ||||||||
\(201\) | −1.95902e10 | −0.846558 | ||||||||
\(202\) | 2.20749e10 | 0.932864 | ||||||||
\(203\) | −8.07303e9 | −0.333660 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.26783e10 | −1.68777 | ||||||||
\(206\) | 3.49821e10 | 1.35345 | ||||||||
\(207\) | 2.24565e10 | 0.850112 | ||||||||
\(208\) | 1.88574e10 | 0.698550 | ||||||||
\(209\) | 1.46239e10 | 0.530159 | ||||||||
\(210\) | −1.95415e10 | −0.693380 | ||||||||
\(211\) | 2.06432e10 | 0.716979 | 0.358490 | − | 0.933534i | \(-0.383292\pi\) | ||||
0.358490 | + | 0.933534i | \(0.383292\pi\) | |||||||
\(212\) | −3.98347e9 | −0.135441 | ||||||||
\(213\) | −5.86482e10 | −1.95230 | ||||||||
\(214\) | −6.55953e10 | −2.13802 | ||||||||
\(215\) | 3.71720e10 | 1.18643 | ||||||||
\(216\) | 9.77976e9 | 0.305693 | ||||||||
\(217\) | −2.45062e10 | −0.750252 | ||||||||
\(218\) | −7.41294e10 | −2.22298 | ||||||||
\(219\) | 4.09736e10 | 1.20367 | ||||||||
\(220\) | −1.98455e10 | −0.571164 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −6.35366e10 | −1.75564 | ||||||||
\(223\) | −4.43950e10 | −1.20216 | −0.601080 | − | 0.799189i | \(-0.705263\pi\) | ||||
−0.601080 | + | 0.799189i | \(0.705263\pi\) | |||||||
\(224\) | −1.67621e10 | −0.444847 | ||||||||
\(225\) | 1.92939e9 | 0.0501880 | ||||||||
\(226\) | 4.99860e10 | 1.27456 | ||||||||
\(227\) | −3.23612e10 | −0.808924 | −0.404462 | − | 0.914555i | \(-0.632541\pi\) | ||||
−0.404462 | + | 0.914555i | \(0.632541\pi\) | |||||||
\(228\) | 1.68482e10 | 0.412902 | ||||||||
\(229\) | 5.05693e10 | 1.21514 | 0.607571 | − | 0.794265i | \(-0.292144\pi\) | ||||
0.607571 | + | 0.794265i | \(0.292144\pi\) | |||||||
\(230\) | −9.07066e10 | −2.13729 | ||||||||
\(231\) | 2.11666e10 | 0.489099 | ||||||||
\(232\) | 1.79973e10 | 0.407860 | ||||||||
\(233\) | −1.71501e10 | −0.381211 | −0.190606 | − | 0.981667i | \(-0.561045\pi\) | ||||
−0.190606 | + | 0.981667i | \(0.561045\pi\) | |||||||
\(234\) | −1.70343e10 | −0.371409 | ||||||||
\(235\) | 3.89962e10 | 0.834098 | ||||||||
\(236\) | 1.51403e10 | 0.317710 | ||||||||
\(237\) | −9.72024e10 | −2.00129 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.56762e10 | −0.310779 | −0.155389 | − | 0.987853i | \(-0.549663\pi\) | ||||
−0.155389 | + | 0.987853i | \(0.549663\pi\) | |||||||
\(240\) | 8.25361e10 | 1.60581 | ||||||||
\(241\) | 7.80137e9 | 0.148968 | 0.0744842 | − | 0.997222i | \(-0.476269\pi\) | ||||
0.0744842 | + | 0.997222i | \(0.476269\pi\) | |||||||
\(242\) | −9.07099e9 | −0.170014 | ||||||||
\(243\) | −5.19328e10 | −0.955462 | ||||||||
\(244\) | −3.30525e10 | −0.596967 | ||||||||
\(245\) | 4.83238e10 | 0.856868 | ||||||||
\(246\) | 1.44038e11 | 2.50767 | ||||||||
\(247\) | −1.87470e10 | −0.320476 | ||||||||
\(248\) | 5.46319e10 | 0.917094 | ||||||||
\(249\) | 5.12584e10 | 0.845022 | ||||||||
\(250\) | 7.36434e10 | 1.19235 | ||||||||
\(251\) | 9.23115e10 | 1.46799 | 0.733996 | − | 0.679153i | \(-0.237653\pi\) | ||||
0.733996 | + | 0.679153i | \(0.237653\pi\) | |||||||
\(252\) | 8.38940e9 | 0.131047 | ||||||||
\(253\) | 9.82497e10 | 1.50761 | ||||||||
\(254\) | −4.61982e10 | −0.696423 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 8.74603e10 | 1.27271 | ||||||||
\(257\) | −9.75670e9 | −0.139510 | −0.0697548 | − | 0.997564i | \(-0.522222\pi\) | ||||
−0.0697548 | + | 0.997564i | \(0.522222\pi\) | |||||||
\(258\) | −1.25455e11 | −1.76278 | ||||||||
\(259\) | −3.48184e10 | −0.480795 | ||||||||
\(260\) | 2.54408e10 | 0.345264 | ||||||||
\(261\) | −3.08010e10 | −0.410849 | ||||||||
\(262\) | 2.97714e10 | 0.390340 | ||||||||
\(263\) | −1.15838e11 | −1.49296 | −0.746482 | − | 0.665406i | \(-0.768259\pi\) | ||||
−0.746482 | + | 0.665406i | \(0.768259\pi\) | |||||||
\(264\) | −4.71869e10 | −0.597866 | ||||||||
\(265\) | 1.94000e10 | 0.241654 | ||||||||
\(266\) | 2.49705e10 | 0.305816 | ||||||||
\(267\) | −3.09845e10 | −0.373116 | ||||||||
\(268\) | −3.39709e10 | −0.402254 | ||||||||
\(269\) | −5.41725e10 | −0.630802 | −0.315401 | − | 0.948958i | \(-0.602139\pi\) | ||||
−0.315401 | + | 0.948958i | \(0.602139\pi\) | |||||||
\(270\) | 6.76053e10 | 0.774183 | ||||||||
\(271\) | −1.20057e11 | −1.35215 | −0.676073 | − | 0.736834i | \(-0.736320\pi\) | ||||
−0.676073 | + | 0.736834i | \(0.736320\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.71343e10 | −0.295656 | ||||||||
\(274\) | 1.76520e11 | 1.89198 | ||||||||
\(275\) | 8.44130e9 | 0.0890046 | ||||||||
\(276\) | 1.13193e11 | 1.17417 | ||||||||
\(277\) | 2.71263e10 | 0.276842 | 0.138421 | − | 0.990373i | \(-0.455797\pi\) | ||||
0.138421 | + | 0.990373i | \(0.455797\pi\) | |||||||
\(278\) | −7.38418e10 | −0.741483 | ||||||||
\(279\) | −9.34982e10 | −0.923814 | ||||||||
\(280\) | 2.38734e10 | 0.232115 | ||||||||
\(281\) | 7.42502e10 | 0.710427 | 0.355213 | − | 0.934785i | \(-0.384408\pi\) | ||||
0.355213 | + | 0.934785i | \(0.384408\pi\) | |||||||
\(282\) | −1.31612e11 | −1.23929 | ||||||||
\(283\) | −5.06373e10 | −0.469279 | −0.234640 | − | 0.972082i | \(-0.575391\pi\) | ||||
−0.234640 | + | 0.972082i | \(0.575391\pi\) | |||||||
\(284\) | −1.01701e11 | −0.927664 | ||||||||
\(285\) | −8.20529e10 | −0.736702 | ||||||||
\(286\) | −7.45268e10 | −0.658666 | ||||||||
\(287\) | 7.89338e10 | 0.686744 | ||||||||
\(288\) | −6.39521e10 | −0.547758 | ||||||||
\(289\) | 0 | 0 | ||||||||
\(290\) | 1.24411e11 | 1.03293 | ||||||||
\(291\) | −1.69103e10 | −0.138240 | ||||||||
\(292\) | 7.10515e10 | 0.571940 | ||||||||
\(293\) | −1.70721e11 | −1.35326 | −0.676632 | − | 0.736321i | \(-0.736561\pi\) | ||||
−0.676632 | + | 0.736321i | \(0.736561\pi\) | |||||||
\(294\) | −1.63092e11 | −1.27312 | ||||||||
\(295\) | −7.37351e10 | −0.566859 | ||||||||
\(296\) | 7.76210e10 | 0.587715 | ||||||||
\(297\) | −7.32274e10 | −0.546097 | ||||||||
\(298\) | 1.37573e11 | 1.01055 | ||||||||
\(299\) | −1.25950e11 | −0.911338 | ||||||||
\(300\) | 9.72522e9 | 0.0693193 | ||||||||
\(301\) | −6.87500e10 | −0.482751 | ||||||||
\(302\) | 1.78093e11 | 1.23202 | ||||||||
\(303\) | 1.34160e11 | 0.914387 | ||||||||
\(304\) | −1.05466e11 | −0.708243 | ||||||||
\(305\) | 1.60970e11 | 1.06511 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.23971e11 | 0.796522 | 0.398261 | − | 0.917272i | \(-0.369614\pi\) | ||||
0.398261 | + | 0.917272i | \(0.369614\pi\) | |||||||
\(308\) | 3.67045e10 | 0.232403 | ||||||||
\(309\) | 2.12602e11 | 1.32665 | ||||||||
\(310\) | 3.77658e11 | 2.32258 | ||||||||
\(311\) | −3.00821e11 | −1.82342 | −0.911709 | − | 0.410836i | \(-0.865237\pi\) | ||||
−0.911709 | + | 0.410836i | \(0.865237\pi\) | |||||||
\(312\) | 6.04908e10 | 0.361405 | ||||||||
\(313\) | 1.54699e11 | 0.911040 | 0.455520 | − | 0.890225i | \(-0.349453\pi\) | ||||
0.455520 | + | 0.890225i | \(0.349453\pi\) | |||||||
\(314\) | −9.08330e10 | −0.527303 | ||||||||
\(315\) | −4.08574e10 | −0.233815 | ||||||||
\(316\) | −1.68556e11 | −0.950941 | ||||||||
\(317\) | 5.39434e10 | 0.300035 | 0.150017 | − | 0.988683i | \(-0.452067\pi\) | ||||
0.150017 | + | 0.988683i | \(0.452067\pi\) | |||||||
\(318\) | −6.54746e10 | −0.359046 | ||||||||
\(319\) | −1.34757e11 | −0.728609 | ||||||||
\(320\) | 1.43593e10 | 0.0765523 | ||||||||
\(321\) | −3.98653e11 | −2.09567 | ||||||||
\(322\) | 1.67763e11 | 0.869648 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −1.45397e11 | −0.732998 | ||||||||
\(325\) | −1.08213e10 | −0.0538025 | ||||||||
\(326\) | −3.49685e11 | −1.71474 | ||||||||
\(327\) | −4.50519e11 | −2.17896 | ||||||||
\(328\) | −1.75968e11 | −0.839463 | ||||||||
\(329\) | −7.21238e10 | −0.339389 | ||||||||
\(330\) | −3.26193e11 | −1.51412 | ||||||||
\(331\) | −3.15316e11 | −1.44384 | −0.721921 | − | 0.691975i | \(-0.756741\pi\) | ||||
−0.721921 | + | 0.691975i | \(0.756741\pi\) | |||||||
\(332\) | 8.88861e10 | 0.401525 | ||||||||
\(333\) | −1.32842e11 | −0.592021 | ||||||||
\(334\) | 1.75368e11 | 0.771064 | ||||||||
\(335\) | 1.65442e11 | 0.717704 | ||||||||
\(336\) | −1.52651e11 | −0.653391 | ||||||||
\(337\) | 1.09713e10 | 0.0463367 | 0.0231684 | − | 0.999732i | \(-0.492625\pi\) | ||||
0.0231684 | + | 0.999732i | \(0.492625\pi\) | |||||||
\(338\) | −2.06713e11 | −0.861476 | ||||||||
\(339\) | 3.03788e11 | 1.24932 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.09065e11 | −1.63831 | ||||||||
\(342\) | 9.52698e10 | 0.376563 | ||||||||
\(343\) | −1.98557e11 | −0.774571 | ||||||||
\(344\) | 1.53265e11 | 0.590106 | ||||||||
\(345\) | −5.51266e11 | −2.09496 | ||||||||
\(346\) | 3.36693e11 | 1.26297 | ||||||||
\(347\) | 7.01283e10 | 0.259663 | 0.129832 | − | 0.991536i | \(-0.458556\pi\) | ||||
0.129832 | + | 0.991536i | \(0.458556\pi\) | |||||||
\(348\) | −1.55254e11 | −0.567461 | ||||||||
\(349\) | 3.76499e11 | 1.35847 | 0.679234 | − | 0.733922i | \(-0.262312\pi\) | ||||
0.679234 | + | 0.733922i | \(0.262312\pi\) | |||||||
\(350\) | 1.44136e10 | 0.0513413 | ||||||||
\(351\) | 9.38732e10 | 0.330111 | ||||||||
\(352\) | −2.79797e11 | −0.971407 | ||||||||
\(353\) | −3.15575e11 | −1.08172 | −0.540862 | − | 0.841112i | \(-0.681902\pi\) | ||||
−0.540862 | + | 0.841112i | \(0.681902\pi\) | |||||||
\(354\) | 2.48854e11 | 0.842230 | ||||||||
\(355\) | 4.95294e11 | 1.65514 | ||||||||
\(356\) | −5.37295e10 | −0.177292 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 7.49452e11 | 2.41140 | ||||||||
\(359\) | −2.05111e11 | −0.651723 | −0.325861 | − | 0.945418i | \(-0.605654\pi\) | ||||
−0.325861 | + | 0.945418i | \(0.605654\pi\) | |||||||
\(360\) | 9.10838e10 | 0.285812 | ||||||||
\(361\) | −2.17839e11 | −0.675077 | ||||||||
\(362\) | 3.77875e11 | 1.15654 | ||||||||
\(363\) | −5.51286e10 | −0.166647 | ||||||||
\(364\) | −4.70530e10 | −0.140485 | ||||||||
\(365\) | −3.46029e11 | −1.02046 | ||||||||
\(366\) | −5.43270e11 | −1.58252 | ||||||||
\(367\) | 1.30843e11 | 0.376489 | 0.188245 | − | 0.982122i | \(-0.439720\pi\) | ||||
0.188245 | + | 0.982122i | \(0.439720\pi\) | |||||||
\(368\) | −7.08567e11 | −2.01403 | ||||||||
\(369\) | 3.01155e11 | 0.845614 | ||||||||
\(370\) | 5.36577e11 | 1.48842 | ||||||||
\(371\) | −3.58804e10 | −0.0983275 | ||||||||
\(372\) | −4.71283e11 | −1.27596 | ||||||||
\(373\) | 4.08317e11 | 1.09221 | 0.546107 | − | 0.837715i | \(-0.316109\pi\) | ||||
0.546107 | + | 0.837715i | \(0.316109\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 4.47565e11 | 1.16873 | ||||||||
\(376\) | 1.60786e11 | 0.414862 | ||||||||
\(377\) | 1.72751e11 | 0.440438 | ||||||||
\(378\) | −1.25037e11 | −0.315010 | ||||||||
\(379\) | 6.78686e11 | 1.68963 | 0.844817 | − | 0.535055i | \(-0.179709\pi\) | ||||
0.844817 | + | 0.535055i | \(0.179709\pi\) | |||||||
\(380\) | −1.42286e11 | −0.350055 | ||||||||
\(381\) | −2.80768e11 | −0.682629 | ||||||||
\(382\) | 4.72331e11 | 1.13491 | ||||||||
\(383\) | 3.43718e11 | 0.816221 | 0.408111 | − | 0.912932i | \(-0.366188\pi\) | ||||
0.408111 | + | 0.912932i | \(0.366188\pi\) | |||||||
\(384\) | 5.00993e11 | 1.17582 | ||||||||
\(385\) | −1.78755e11 | −0.414654 | ||||||||
\(386\) | 4.11508e11 | 0.943487 | ||||||||
\(387\) | −2.62301e11 | −0.594430 | ||||||||
\(388\) | −2.93238e10 | −0.0656867 | ||||||||
\(389\) | 3.94284e11 | 0.873044 | 0.436522 | − | 0.899694i | \(-0.356210\pi\) | ||||
0.436522 | + | 0.899694i | \(0.356210\pi\) | |||||||
\(390\) | 4.18160e11 | 0.915275 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 1.99245e11 | 0.426188 | ||||||||
\(393\) | 1.80935e11 | 0.382609 | ||||||||
\(394\) | −7.44943e11 | −1.55736 | ||||||||
\(395\) | 8.20890e11 | 1.69667 | ||||||||
\(396\) | 1.40038e11 | 0.286166 | ||||||||
\(397\) | −2.30296e9 | −0.00465295 | −0.00232648 | − | 0.999997i | \(-0.500741\pi\) | ||||
−0.00232648 | + | 0.999997i | \(0.500741\pi\) | |||||||
\(398\) | −1.72730e10 | −0.0345059 | ||||||||
\(399\) | 1.51757e11 | 0.299759 | ||||||||
\(400\) | −6.08778e10 | −0.118902 | ||||||||
\(401\) | 5.69424e11 | 1.09973 | 0.549865 | − | 0.835253i | \(-0.314679\pi\) | ||||
0.549865 | + | 0.835253i | \(0.314679\pi\) | |||||||
\(402\) | −5.58365e11 | −1.06635 | ||||||||
\(403\) | 5.24397e11 | 0.990347 | ||||||||
\(404\) | 2.32643e11 | 0.434485 | ||||||||
\(405\) | 7.08101e11 | 1.30782 | ||||||||
\(406\) | −2.30100e11 | −0.420290 | ||||||||
\(407\) | −5.81199e11 | −1.04990 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.66217e11 | 0.647118 | 0.323559 | − | 0.946208i | \(-0.395121\pi\) | ||||
0.323559 | + | 0.946208i | \(0.395121\pi\) | |||||||
\(410\) | −1.21643e12 | −2.12598 | ||||||||
\(411\) | 1.07280e12 | 1.85451 | ||||||||
\(412\) | 3.68669e11 | 0.630375 | ||||||||
\(413\) | 1.36374e11 | 0.230651 | ||||||||
\(414\) | 6.40063e11 | 1.07083 | ||||||||
\(415\) | −4.32886e11 | −0.716402 | ||||||||
\(416\) | 3.58683e11 | 0.587207 | ||||||||
\(417\) | −4.48771e11 | −0.726796 | ||||||||
\(418\) | 4.16815e11 | 0.667806 | ||||||||
\(419\) | −6.26394e11 | −0.992852 | −0.496426 | − | 0.868079i | \(-0.665355\pi\) | ||||
−0.496426 | + | 0.868079i | \(0.665355\pi\) | |||||||
\(420\) | −2.05944e11 | −0.322944 | ||||||||
\(421\) | −5.86511e11 | −0.909927 | −0.454963 | − | 0.890510i | \(-0.650348\pi\) | ||||
−0.454963 | + | 0.890510i | \(0.650348\pi\) | |||||||
\(422\) | 5.88379e11 | 0.903132 | ||||||||
\(423\) | −2.75173e11 | −0.417902 | ||||||||
\(424\) | 7.99886e10 | 0.120194 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −1.67161e12 | −2.45919 | ||||||||
\(427\) | −2.97715e11 | −0.433386 | ||||||||
\(428\) | −6.91296e11 | −0.995788 | ||||||||
\(429\) | −4.52934e11 | −0.645620 | ||||||||
\(430\) | 1.05949e12 | 1.49447 | ||||||||
\(431\) | −1.97901e11 | −0.276249 | −0.138125 | − | 0.990415i | \(-0.544107\pi\) | ||||
−0.138125 | + | 0.990415i | \(0.544107\pi\) | |||||||
\(432\) | 5.28108e11 | 0.729535 | ||||||||
\(433\) | 1.60613e11 | 0.219576 | 0.109788 | − | 0.993955i | \(-0.464983\pi\) | ||||
0.109788 | + | 0.993955i | \(0.464983\pi\) | |||||||
\(434\) | −6.98482e11 | −0.945043 | ||||||||
\(435\) | 7.56106e11 | 1.01247 | ||||||||
\(436\) | −7.81235e11 | −1.03536 | ||||||||
\(437\) | 7.04418e11 | 0.923984 | ||||||||
\(438\) | 1.16784e12 | 1.51618 | ||||||||
\(439\) | −1.14252e12 | −1.46816 | −0.734078 | − | 0.679065i | \(-0.762385\pi\) | ||||
−0.734078 | + | 0.679065i | \(0.762385\pi\) | |||||||
\(440\) | 3.98501e11 | 0.506865 | ||||||||
\(441\) | −3.40993e11 | −0.429310 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −5.38672e11 | −0.664520 | −0.332260 | − | 0.943188i | \(-0.607811\pi\) | ||||
−0.332260 | + | 0.943188i | \(0.607811\pi\) | |||||||
\(444\) | −6.69599e11 | −0.817695 | ||||||||
\(445\) | 2.61669e11 | 0.316324 | ||||||||
\(446\) | −1.26536e12 | −1.51428 | ||||||||
\(447\) | 8.36094e11 | 0.990538 | ||||||||
\(448\) | −2.65576e10 | −0.0311486 | ||||||||
\(449\) | −3.13597e11 | −0.364136 | −0.182068 | − | 0.983286i | \(-0.558279\pi\) | ||||
−0.182068 | + | 0.983286i | \(0.558279\pi\) | |||||||
\(450\) | 5.49921e10 | 0.0632185 | ||||||||
\(451\) | 1.31759e12 | 1.49963 | ||||||||
\(452\) | 5.26793e11 | 0.593631 | ||||||||
\(453\) | 1.08236e12 | 1.20761 | ||||||||
\(454\) | −9.22367e11 | −1.01895 | ||||||||
\(455\) | 2.29154e11 | 0.250655 | ||||||||
\(456\) | −3.38315e11 | −0.366420 | ||||||||
\(457\) | −2.44031e11 | −0.261711 | −0.130856 | − | 0.991401i | \(-0.541772\pi\) | ||||
−0.130856 | + | 0.991401i | \(0.541772\pi\) | |||||||
\(458\) | 1.44134e12 | 1.53064 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −9.55938e11 | −0.995450 | ||||||||
\(461\) | −1.41045e12 | −1.45447 | −0.727235 | − | 0.686388i | \(-0.759195\pi\) | ||||
−0.727235 | + | 0.686388i | \(0.759195\pi\) | |||||||
\(462\) | 6.03296e11 | 0.616086 | ||||||||
\(463\) | −6.57436e11 | −0.664873 | −0.332437 | − | 0.943126i | \(-0.607871\pi\) | ||||
−0.332437 | + | 0.943126i | \(0.607871\pi\) | |||||||
\(464\) | 9.71856e11 | 0.973355 | ||||||||
\(465\) | 2.29521e12 | 2.27658 | ||||||||
\(466\) | −4.88817e11 | −0.480187 | ||||||||
\(467\) | 7.29178e11 | 0.709427 | 0.354714 | − | 0.934975i | \(-0.384578\pi\) | ||||
0.354714 | + | 0.934975i | \(0.384578\pi\) | |||||||
\(468\) | −1.79521e11 | −0.172985 | ||||||||
\(469\) | −3.05987e11 | −0.292029 | ||||||||
\(470\) | 1.11148e12 | 1.05066 | ||||||||
\(471\) | −5.52034e11 | −0.516859 | ||||||||
\(472\) | −3.04019e11 | −0.281943 | ||||||||
\(473\) | −1.14759e12 | −1.05418 | ||||||||
\(474\) | −2.77049e12 | −2.52089 | ||||||||
\(475\) | 6.05214e10 | 0.0545491 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.36894e11 | −0.121074 | ||||||||
\(478\) | −4.46808e11 | −0.391467 | ||||||||
\(479\) | 1.63616e12 | 1.42009 | 0.710044 | − | 0.704157i | \(-0.248675\pi\) | ||||
0.710044 | + | 0.704157i | \(0.248675\pi\) | |||||||
\(480\) | 1.56990e12 | 1.34986 | ||||||||
\(481\) | 7.45063e11 | 0.634659 | ||||||||
\(482\) | 2.22357e11 | 0.187646 | ||||||||
\(483\) | 1.01957e12 | 0.852423 | ||||||||
\(484\) | −9.55973e10 | −0.0791847 | ||||||||
\(485\) | 1.42810e11 | 0.117198 | ||||||||
\(486\) | −1.48020e12 | −1.20353 | ||||||||
\(487\) | 6.40767e11 | 0.516202 | 0.258101 | − | 0.966118i | \(-0.416903\pi\) | ||||
0.258101 | + | 0.966118i | \(0.416903\pi\) | |||||||
\(488\) | 6.63699e11 | 0.529763 | ||||||||
\(489\) | −2.12520e12 | −1.68078 | ||||||||
\(490\) | 1.37734e12 | 1.07934 | ||||||||
\(491\) | 1.71959e12 | 1.33523 | 0.667617 | − | 0.744505i | \(-0.267314\pi\) | ||||
0.667617 | + | 0.744505i | \(0.267314\pi\) | |||||||
\(492\) | 1.51799e12 | 1.16796 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | −5.34333e11 | −0.403683 | ||||||||
\(495\) | −6.82003e11 | −0.510579 | ||||||||
\(496\) | 2.95013e12 | 2.18864 | ||||||||
\(497\) | −9.16051e11 | −0.673466 | ||||||||
\(498\) | 1.46098e12 | 1.06442 | ||||||||
\(499\) | 2.47929e12 | 1.79009 | 0.895045 | − | 0.445975i | \(-0.147143\pi\) | ||||
0.895045 | + | 0.445975i | \(0.147143\pi\) | |||||||
\(500\) | 7.76113e11 | 0.555341 | ||||||||
\(501\) | 1.06579e12 | 0.755792 | ||||||||
\(502\) | 2.63109e12 | 1.84913 | ||||||||
\(503\) | 1.47785e12 | 1.02938 | 0.514689 | − | 0.857377i | \(-0.327907\pi\) | ||||
0.514689 | + | 0.857377i | \(0.327907\pi\) | |||||||
\(504\) | −1.68460e11 | −0.116295 | ||||||||
\(505\) | −1.13300e12 | −0.775210 | ||||||||
\(506\) | 2.80034e12 | 1.89904 | ||||||||
\(507\) | −1.25629e12 | −0.844413 | ||||||||
\(508\) | −4.86873e11 | −0.324361 | ||||||||
\(509\) | −1.05268e12 | −0.695127 | −0.347564 | − | 0.937656i | \(-0.612991\pi\) | ||||
−0.347564 | + | 0.937656i | \(0.612991\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.39984e11 | 0.415217 | ||||||||
\(512\) | 1.01200e12 | 0.650830 | ||||||||
\(513\) | −5.25016e11 | −0.334691 | ||||||||
\(514\) | −2.78088e11 | −0.175731 | ||||||||
\(515\) | −1.79546e12 | −1.12472 | ||||||||
\(516\) | −1.32214e12 | −0.821022 | ||||||||
\(517\) | −1.20391e12 | −0.741118 | ||||||||
\(518\) | −9.92404e11 | −0.605626 | ||||||||
\(519\) | 2.04624e12 | 1.23795 | ||||||||
\(520\) | −5.10855e11 | −0.306396 | ||||||||
\(521\) | −3.56580e11 | −0.212025 | −0.106013 | − | 0.994365i | \(-0.533808\pi\) | ||||
−0.106013 | + | 0.994365i | \(0.533808\pi\) | |||||||
\(522\) | −8.77897e11 | −0.517519 | ||||||||
\(523\) | 1.08984e12 | 0.636951 | 0.318476 | − | 0.947931i | \(-0.396829\pi\) | ||||
0.318476 | + | 0.947931i | \(0.396829\pi\) | |||||||
\(524\) | 3.13755e11 | 0.181802 | ||||||||
\(525\) | 8.75983e10 | 0.0503244 | ||||||||
\(526\) | −3.30164e12 | −1.88059 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | −2.54810e12 | −1.42680 | ||||||||
\(529\) | 2.93143e12 | 1.62753 | ||||||||
\(530\) | 5.52944e11 | 0.304396 | ||||||||
\(531\) | 5.20305e11 | 0.284009 | ||||||||
\(532\) | 2.63159e11 | 0.142435 | ||||||||
\(533\) | −1.68907e12 | −0.906515 | ||||||||
\(534\) | −8.83129e11 | −0.469990 | ||||||||
\(535\) | 3.36669e12 | 1.77669 | ||||||||
\(536\) | 6.82140e11 | 0.356970 | ||||||||
\(537\) | 4.55477e12 | 2.36364 | ||||||||
\(538\) | −1.54404e12 | −0.794580 | ||||||||
\(539\) | −1.49188e12 | −0.761350 | ||||||||
\(540\) | 7.12478e11 | 0.360578 | ||||||||
\(541\) | 1.83215e12 | 0.919546 | 0.459773 | − | 0.888036i | \(-0.347931\pi\) | ||||
0.459773 | + | 0.888036i | \(0.347931\pi\) | |||||||
\(542\) | −3.42188e12 | −1.70321 | ||||||||
\(543\) | 2.29652e12 | 1.13363 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3.80471e12 | 1.84730 | ||||||||
\(546\) | −7.73390e11 | −0.372419 | ||||||||
\(547\) | −1.24502e12 | −0.594609 | −0.297305 | − | 0.954783i | \(-0.596088\pi\) | ||||
−0.297305 | + | 0.954783i | \(0.596088\pi\) | |||||||
\(548\) | 1.86031e12 | 0.881198 | ||||||||
\(549\) | −1.13587e12 | −0.533645 | ||||||||
\(550\) | 2.40596e11 | 0.112113 | ||||||||
\(551\) | −9.66167e11 | −0.446550 | ||||||||
\(552\) | −2.27294e12 | −1.04199 | ||||||||
\(553\) | −1.51824e12 | −0.690364 | ||||||||
\(554\) | 7.73161e11 | 0.348719 | ||||||||
\(555\) | 3.26103e12 | 1.45894 | ||||||||
\(556\) | −7.78204e11 | −0.345348 | ||||||||
\(557\) | 3.48794e12 | 1.53540 | 0.767698 | − | 0.640812i | \(-0.221402\pi\) | ||||
0.767698 | + | 0.640812i | \(0.221402\pi\) | |||||||
\(558\) | −2.66491e12 | −1.16367 | ||||||||
\(559\) | 1.47115e12 | 0.637241 | ||||||||
\(560\) | 1.28916e12 | 0.553939 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 2.11630e12 | 0.894878 | ||||||||
\(563\) | −3.26487e11 | −0.136955 | −0.0684775 | − | 0.997653i | \(-0.521814\pi\) | ||||
−0.0684775 | + | 0.997653i | \(0.521814\pi\) | |||||||
\(564\) | −1.38703e12 | −0.577203 | ||||||||
\(565\) | −2.56554e12 | −1.05916 | ||||||||
\(566\) | −1.44328e12 | −0.591120 | ||||||||
\(567\) | −1.30964e12 | −0.532142 | ||||||||
\(568\) | 2.04216e12 | 0.823233 | ||||||||
\(569\) | −4.62696e11 | −0.185051 | −0.0925254 | − | 0.995710i | \(-0.529494\pi\) | ||||
−0.0925254 | + | 0.995710i | \(0.529494\pi\) | |||||||
\(570\) | −2.33869e12 | −0.927976 | ||||||||
\(571\) | 1.24733e11 | 0.0491044 | 0.0245522 | − | 0.999699i | \(-0.492184\pi\) | ||||
0.0245522 | + | 0.999699i | \(0.492184\pi\) | |||||||
\(572\) | −7.85423e11 | −0.306776 | ||||||||
\(573\) | 2.87057e12 | 1.11243 | ||||||||
\(574\) | 2.24979e12 | 0.865046 | ||||||||
\(575\) | 4.06608e11 | 0.155121 | ||||||||
\(576\) | −1.01325e11 | −0.0383545 | ||||||||
\(577\) | 6.12818e11 | 0.230166 | 0.115083 | − | 0.993356i | \(-0.463287\pi\) | ||||
0.115083 | + | 0.993356i | \(0.463287\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 2.50093e12 | 0.924800 | ||||||||
\(580\) | 1.31115e12 | 0.481089 | ||||||||
\(581\) | 8.00626e11 | 0.291499 | ||||||||
\(582\) | −4.81982e11 | −0.174132 | ||||||||
\(583\) | −5.98926e11 | −0.214716 | ||||||||
\(584\) | −1.42672e12 | −0.507553 | ||||||||
\(585\) | 8.74289e11 | 0.308641 | ||||||||
\(586\) | −4.86594e12 | −1.70462 | ||||||||
\(587\) | −1.18091e12 | −0.410529 | −0.205264 | − | 0.978707i | \(-0.565805\pi\) | ||||
−0.205264 | + | 0.978707i | \(0.565805\pi\) | |||||||
\(588\) | −1.71879e12 | −0.592960 | ||||||||
\(589\) | −2.93286e12 | −1.00409 | ||||||||
\(590\) | −2.10162e12 | −0.714035 | ||||||||
\(591\) | −4.52737e12 | −1.52652 | ||||||||
\(592\) | 4.19154e12 | 1.40258 | ||||||||
\(593\) | −3.63746e10 | −0.0120796 | −0.00603979 | − | 0.999982i | \(-0.501923\pi\) | ||||
−0.00603979 | + | 0.999982i | \(0.501923\pi\) | |||||||
\(594\) | −2.08715e12 | −0.687882 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1.44985e12 | 0.470669 | ||||||||
\(597\) | −1.04976e11 | −0.0338225 | ||||||||
\(598\) | −3.58987e12 | −1.14795 | ||||||||
\(599\) | 4.00830e12 | 1.27215 | 0.636077 | − | 0.771625i | \(-0.280556\pi\) | ||||
0.636077 | + | 0.771625i | \(0.280556\pi\) | |||||||
\(600\) | −1.95284e11 | −0.0615156 | ||||||||
\(601\) | −4.29519e12 | −1.34291 | −0.671456 | − | 0.741044i | \(-0.734331\pi\) | ||||
−0.671456 | + | 0.741044i | \(0.734331\pi\) | |||||||
\(602\) | −1.95953e12 | −0.608090 | ||||||||
\(603\) | −1.16743e12 | −0.359586 | ||||||||
\(604\) | 1.87689e12 | 0.573816 | ||||||||
\(605\) | 4.65570e11 | 0.141282 | ||||||||
\(606\) | 3.82386e12 | 1.15179 | ||||||||
\(607\) | 4.27985e12 | 1.27961 | 0.639807 | − | 0.768535i | \(-0.279014\pi\) | ||||
0.639807 | + | 0.768535i | \(0.279014\pi\) | |||||||
\(608\) | −2.00605e12 | −0.595355 | ||||||||
\(609\) | −1.39842e12 | −0.411966 | ||||||||
\(610\) | 4.58800e12 | 1.34165 | ||||||||
\(611\) | 1.54335e12 | 0.448000 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.59171e12 | −0.455293 | −0.227647 | − | 0.973744i | \(-0.573103\pi\) | ||||
−0.227647 | + | 0.973744i | \(0.573103\pi\) | |||||||
\(614\) | 3.53346e12 | 1.00333 | ||||||||
\(615\) | −7.39280e12 | −2.08387 | ||||||||
\(616\) | −7.37031e11 | −0.206240 | ||||||||
\(617\) | −5.66989e12 | −1.57504 | −0.787519 | − | 0.616290i | \(-0.788635\pi\) | ||||
−0.787519 | + | 0.616290i | \(0.788635\pi\) | |||||||
\(618\) | 6.05965e12 | 1.67109 | ||||||||
\(619\) | 6.99348e11 | 0.191463 | 0.0957316 | − | 0.995407i | \(-0.469481\pi\) | ||||
0.0957316 | + | 0.995407i | \(0.469481\pi\) | |||||||
\(620\) | 3.98007e12 | 1.08175 | ||||||||
\(621\) | −3.52728e12 | −0.951761 | ||||||||
\(622\) | −8.57408e12 | −2.29684 | ||||||||
\(623\) | −4.83959e11 | −0.128710 | ||||||||
\(624\) | 3.26651e12 | 0.862489 | ||||||||
\(625\) | −4.14482e12 | −1.08654 | ||||||||
\(626\) | 4.40927e12 | 1.14758 | ||||||||
\(627\) | 2.53318e12 | 0.654579 | ||||||||
\(628\) | −9.57270e11 | −0.245593 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | −1.16453e12 | −0.294522 | ||||||||
\(631\) | 1.12865e12 | 0.283417 | 0.141708 | − | 0.989908i | \(-0.454740\pi\) | ||||
0.141708 | + | 0.989908i | \(0.454740\pi\) | |||||||
\(632\) | 3.38463e12 | 0.843888 | ||||||||
\(633\) | 3.57585e12 | 0.885244 | ||||||||
\(634\) | 1.53751e12 | 0.377934 | ||||||||
\(635\) | 2.37113e12 | 0.578727 | ||||||||
\(636\) | −6.90023e11 | −0.167227 | ||||||||
\(637\) | 1.91250e12 | 0.460229 | ||||||||
\(638\) | −3.84089e12 | −0.917781 | ||||||||
\(639\) | −3.49500e12 | −0.829265 | ||||||||
\(640\) | −4.23097e12 | −0.996851 | ||||||||
\(641\) | 1.79395e12 | 0.419711 | 0.209855 | − | 0.977732i | \(-0.432701\pi\) | ||||
0.209855 | + | 0.977732i | \(0.432701\pi\) | |||||||
\(642\) | −1.13625e13 | −2.63978 | ||||||||
\(643\) | −5.27160e12 | −1.21617 | −0.608083 | − | 0.793873i | \(-0.708061\pi\) | ||||
−0.608083 | + | 0.793873i | \(0.708061\pi\) | |||||||
\(644\) | 1.76801e12 | 0.405041 | ||||||||
\(645\) | 6.43900e12 | 1.46487 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.48582e12 | −0.333347 | −0.166674 | − | 0.986012i | \(-0.553303\pi\) | ||||
−0.166674 | + | 0.986012i | \(0.553303\pi\) | |||||||
\(648\) | 2.91959e12 | 0.650481 | ||||||||
\(649\) | 2.27639e12 | 0.503669 | ||||||||
\(650\) | −3.08431e11 | −0.0677715 | ||||||||
\(651\) | −4.24500e12 | −0.926325 | ||||||||
\(652\) | −3.68526e12 | −0.798646 | ||||||||
\(653\) | −5.84380e12 | −1.25773 | −0.628863 | − | 0.777516i | \(-0.716479\pi\) | ||||
−0.628863 | + | 0.777516i | \(0.716479\pi\) | |||||||
\(654\) | −1.28408e13 | −2.74469 | ||||||||
\(655\) | −1.52802e12 | −0.324373 | ||||||||
\(656\) | −9.50229e12 | −2.00337 | ||||||||
\(657\) | 2.44172e12 | 0.511272 | ||||||||
\(658\) | −2.05569e12 | −0.427506 | ||||||||
\(659\) | −3.45631e12 | −0.713885 | −0.356943 | − | 0.934126i | \(-0.616181\pi\) | ||||
−0.356943 | + | 0.934126i | \(0.616181\pi\) | |||||||
\(660\) | −3.43768e12 | −0.705208 | ||||||||
\(661\) | −6.00332e12 | −1.22316 | −0.611582 | − | 0.791181i | \(-0.709467\pi\) | ||||
−0.611582 | + | 0.791181i | \(0.709467\pi\) | |||||||
\(662\) | −8.98722e12 | −1.81871 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −1.78484e12 | −0.356323 | ||||||||
\(665\) | −1.28162e12 | −0.254133 | ||||||||
\(666\) | −3.78631e12 | −0.745730 | ||||||||
\(667\) | −6.49111e12 | −1.26985 | ||||||||
\(668\) | 1.84816e12 | 0.359125 | ||||||||
\(669\) | −7.69017e12 | −1.48429 | ||||||||
\(670\) | 4.71549e12 | 0.904045 | ||||||||
\(671\) | −4.96954e12 | −0.946379 | ||||||||
\(672\) | −2.90355e12 | −0.549247 | ||||||||
\(673\) | 4.90600e12 | 0.921849 | 0.460925 | − | 0.887439i | \(-0.347518\pi\) | ||||
0.460925 | + | 0.887439i | \(0.347518\pi\) | |||||||
\(674\) | 3.12708e11 | 0.0583673 | ||||||||
\(675\) | −3.03053e11 | −0.0561890 | ||||||||
\(676\) | −2.17851e12 | −0.401235 | ||||||||
\(677\) | 6.76575e12 | 1.23785 | 0.618923 | − | 0.785451i | \(-0.287569\pi\) | ||||
0.618923 | + | 0.785451i | \(0.287569\pi\) | |||||||
\(678\) | 8.65866e12 | 1.57368 | ||||||||
\(679\) | −2.64129e11 | −0.0476872 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −5.60565e12 | −0.998767 | ||||||||
\(682\) | −1.16593e13 | −2.06368 | ||||||||
\(683\) | −9.99306e12 | −1.75714 | −0.878568 | − | 0.477618i | \(-0.841500\pi\) | ||||
−0.878568 | + | 0.477618i | \(0.841500\pi\) | |||||||
\(684\) | 1.00403e12 | 0.175385 | ||||||||
\(685\) | −9.05995e12 | −1.57224 | ||||||||
\(686\) | −5.65932e12 | −0.975676 | ||||||||
\(687\) | 8.75969e12 | 1.50032 | ||||||||
\(688\) | 8.27633e12 | 1.40828 | ||||||||
\(689\) | 7.67789e11 | 0.129794 | ||||||||
\(690\) | −1.57123e13 | −2.63888 | ||||||||
\(691\) | −7.48255e12 | −1.24853 | −0.624264 | − | 0.781213i | \(-0.714601\pi\) | ||||
−0.624264 | + | 0.781213i | \(0.714601\pi\) | |||||||
\(692\) | 3.54834e12 | 0.588231 | ||||||||
\(693\) | 1.26137e12 | 0.207751 | ||||||||
\(694\) | 1.99882e12 | 0.327081 | ||||||||
\(695\) | 3.78995e12 | 0.616172 | ||||||||
\(696\) | 3.11752e12 | 0.503579 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 1.07311e13 | 1.71117 | ||||||||
\(699\) | −2.97077e12 | −0.470676 | ||||||||
\(700\) | 1.51902e11 | 0.0239124 | ||||||||
\(701\) | −2.73381e12 | −0.427599 | −0.213800 | − | 0.976878i | \(-0.568584\pi\) | ||||
−0.213800 | + | 0.976878i | \(0.568584\pi\) | |||||||
\(702\) | 2.67560e12 | 0.415819 | ||||||||
\(703\) | −4.16701e12 | −0.643465 | ||||||||
\(704\) | −4.43308e11 | −0.0680187 | ||||||||
\(705\) | 6.75499e12 | 1.02985 | ||||||||
\(706\) | −8.99460e12 | −1.36258 | ||||||||
\(707\) | 2.09549e12 | 0.315427 | ||||||||
\(708\) | 2.62263e12 | 0.392271 | ||||||||
\(709\) | −4.63155e12 | −0.688364 | −0.344182 | − | 0.938903i | \(-0.611844\pi\) | ||||
−0.344182 | + | 0.938903i | \(0.611844\pi\) | |||||||
\(710\) | 1.41170e13 | 2.08488 | ||||||||
\(711\) | −5.79254e12 | −0.850072 | ||||||||
\(712\) | 1.07890e12 | 0.157333 | ||||||||
\(713\) | −1.97042e13 | −2.85533 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.82510e12 | 0.547351 | ||||||||
\(716\) | 7.89832e12 | 1.12312 | ||||||||
\(717\) | −2.71546e12 | −0.383714 | ||||||||
\(718\) | −5.84612e12 | −0.820932 | ||||||||
\(719\) | −8.31957e10 | −0.0116097 | −0.00580485 | − | 0.999983i | \(-0.501848\pi\) | ||||
−0.00580485 | + | 0.999983i | \(0.501848\pi\) | |||||||
\(720\) | 4.91854e12 | 0.682087 | ||||||||
\(721\) | 3.32072e12 | 0.457640 | ||||||||
\(722\) | −6.20890e12 | −0.850350 | ||||||||
\(723\) | 1.35137e12 | 0.183929 | ||||||||
\(724\) | 3.98235e12 | 0.538662 | ||||||||
\(725\) | −5.57696e11 | −0.0749681 | ||||||||
\(726\) | −1.57129e12 | −0.209914 | ||||||||
\(727\) | 6.97498e10 | 0.00926058 | 0.00463029 | − | 0.999989i | \(-0.498526\pi\) | ||||
0.00463029 | + | 0.999989i | \(0.498526\pi\) | |||||||
\(728\) | 9.44831e11 | 0.124670 | ||||||||
\(729\) | 5.31559e11 | 0.0697072 | ||||||||
\(730\) | −9.86262e12 | −1.28540 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −5.72541e12 | −0.737066 | ||||||||
\(733\) | 1.35099e13 | 1.72856 | 0.864278 | − | 0.503014i | \(-0.167776\pi\) | ||||
0.864278 | + | 0.503014i | \(0.167776\pi\) | |||||||
\(734\) | 3.72932e12 | 0.474239 | ||||||||
\(735\) | 8.37073e12 | 1.05796 | ||||||||
\(736\) | −1.34775e13 | −1.69301 | ||||||||
\(737\) | −5.10763e12 | −0.637699 | ||||||||
\(738\) | 8.58361e12 | 1.06516 | ||||||||
\(739\) | 8.62113e12 | 1.06332 | 0.531660 | − | 0.846958i | \(-0.321568\pi\) | ||||
0.531660 | + | 0.846958i | \(0.321568\pi\) | |||||||
\(740\) | 5.65487e12 | 0.693235 | ||||||||
\(741\) | −3.24739e12 | −0.395688 | ||||||||
\(742\) | −1.02267e12 | −0.123857 | ||||||||
\(743\) | −6.08624e12 | −0.732654 | −0.366327 | − | 0.930486i | \(-0.619385\pi\) | ||||
−0.366327 | + | 0.930486i | \(0.619385\pi\) | |||||||
\(744\) | 9.46343e12 | 1.13232 | ||||||||
\(745\) | −7.06095e12 | −0.839769 | ||||||||
\(746\) | 1.16380e13 | 1.37579 | ||||||||
\(747\) | 3.05462e12 | 0.358934 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −6.22673e12 | −0.722922 | ||||||||
\(750\) | 1.27566e13 | 1.47218 | ||||||||
\(751\) | −4.96208e12 | −0.569225 | −0.284613 | − | 0.958643i | \(-0.591865\pi\) | ||||
−0.284613 | + | 0.958643i | \(0.591865\pi\) | |||||||
\(752\) | 8.68249e12 | 0.990065 | ||||||||
\(753\) | 1.59903e13 | 1.81251 | ||||||||
\(754\) | 4.92380e12 | 0.554791 | ||||||||
\(755\) | −9.14068e12 | −1.02381 | ||||||||
\(756\) | −1.31773e12 | −0.146717 | ||||||||
\(757\) | 1.25361e13 | 1.38749 | 0.693746 | − | 0.720219i | \(-0.255959\pi\) | ||||
0.693746 | + | 0.720219i | \(0.255959\pi\) | |||||||
\(758\) | 1.93441e13 | 2.12832 | ||||||||
\(759\) | 1.70190e13 | 1.86142 | ||||||||
\(760\) | 2.85712e12 | 0.310647 | ||||||||
\(761\) | −1.38427e13 | −1.49620 | −0.748102 | − | 0.663584i | \(-0.769035\pi\) | ||||
−0.748102 | + | 0.663584i | \(0.769035\pi\) | |||||||
\(762\) | −8.00252e12 | −0.859863 | ||||||||
\(763\) | −7.03684e12 | −0.751653 | ||||||||
\(764\) | 4.97780e12 | 0.528588 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 9.79675e12 | 1.02814 | ||||||||
\(767\) | −2.91820e12 | −0.304464 | ||||||||
\(768\) | 1.51500e13 | 1.57140 | ||||||||
\(769\) | −1.11058e13 | −1.14520 | −0.572598 | − | 0.819837i | \(-0.694064\pi\) | ||||
−0.572598 | + | 0.819837i | \(0.694064\pi\) | |||||||
\(770\) | −5.09493e12 | −0.522312 | ||||||||
\(771\) | −1.69007e12 | −0.172250 | ||||||||
\(772\) | 4.33680e12 | 0.439432 | ||||||||
\(773\) | 9.23656e12 | 0.930470 | 0.465235 | − | 0.885187i | \(-0.345970\pi\) | ||||
0.465235 | + | 0.885187i | \(0.345970\pi\) | |||||||
\(774\) | −7.47618e12 | −0.748765 | ||||||||
\(775\) | −1.69292e12 | −0.168570 | ||||||||
\(776\) | 5.88825e11 | 0.0582920 | ||||||||
\(777\) | −6.03130e12 | −0.593630 | ||||||||
\(778\) | 1.12380e13 | 1.09972 | ||||||||
\(779\) | 9.44666e12 | 0.919094 | ||||||||
\(780\) | 4.40690e12 | 0.426292 | ||||||||
\(781\) | −1.52910e13 | −1.47064 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 4.83795e12 | 0.459974 | ||||||||
\(784\) | 1.07593e13 | 1.01709 | ||||||||
\(785\) | 4.66202e12 | 0.438188 | ||||||||
\(786\) | 5.15705e12 | 0.481948 | ||||||||
\(787\) | 9.46933e12 | 0.879900 | 0.439950 | − | 0.898022i | \(-0.354996\pi\) | ||||
0.439950 | + | 0.898022i | \(0.354996\pi\) | |||||||
\(788\) | −7.85080e12 | −0.725347 | ||||||||
\(789\) | −2.00656e13 | −1.84334 | ||||||||
\(790\) | 2.33972e13 | 2.13719 | ||||||||
\(791\) | 4.74499e12 | 0.430964 | ||||||||
\(792\) | −2.81199e12 | −0.253951 | ||||||||
\(793\) | 6.37066e12 | 0.572078 | ||||||||
\(794\) | −6.56395e10 | −0.00586102 | ||||||||
\(795\) | 3.36049e12 | 0.298367 | ||||||||
\(796\) | −1.82037e11 | −0.0160713 | ||||||||
\(797\) | −5.94914e12 | −0.522266 | −0.261133 | − | 0.965303i | \(-0.584096\pi\) | ||||
−0.261133 | + | 0.965303i | \(0.584096\pi\) | |||||||
\(798\) | 4.32543e12 | 0.377587 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −1.15795e12 | −0.0999500 | ||||||||
\(801\) | −1.84645e12 | −0.158486 | ||||||||
\(802\) | 1.62299e13 | 1.38526 | ||||||||
\(803\) | 1.06828e13 | 0.906703 | ||||||||
\(804\) | −5.88449e12 | −0.496657 | ||||||||
\(805\) | −8.61045e12 | −0.722677 | ||||||||
\(806\) | 1.49465e13 | 1.24748 | ||||||||
\(807\) | −9.38384e12 | −0.778843 | ||||||||
\(808\) | −4.67151e12 | −0.385572 | ||||||||
\(809\) | −2.92616e12 | −0.240176 | −0.120088 | − | 0.992763i | \(-0.538318\pi\) | ||||
−0.120088 | + | 0.992763i | \(0.538318\pi\) | |||||||
\(810\) | 2.01825e13 | 1.64737 | ||||||||
\(811\) | −1.70693e13 | −1.38555 | −0.692774 | − | 0.721155i | \(-0.743612\pi\) | ||||
−0.692774 | + | 0.721155i | \(0.743612\pi\) | |||||||
\(812\) | −2.42497e12 | −0.195751 | ||||||||
\(813\) | −2.07964e13 | −1.66948 | ||||||||
\(814\) | −1.65655e13 | −1.32250 | ||||||||
\(815\) | 1.79477e13 | 1.42495 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8.22788e12 | −0.646083 | ||||||||
\(818\) | 1.04380e13 | 0.815132 | ||||||||
\(819\) | −1.61700e12 | −0.125584 | ||||||||
\(820\) | −1.28197e13 | −0.990182 | ||||||||
\(821\) | 2.36190e13 | 1.81433 | 0.907166 | − | 0.420772i | \(-0.138241\pi\) | ||||
0.907166 | + | 0.420772i | \(0.138241\pi\) | |||||||
\(822\) | 3.05771e13 | 2.33601 | ||||||||
\(823\) | 8.07533e12 | 0.613566 | 0.306783 | − | 0.951779i | \(-0.400747\pi\) | ||||
0.306783 | + | 0.951779i | \(0.400747\pi\) | |||||||
\(824\) | −7.40292e12 | −0.559410 | ||||||||
\(825\) | 1.46222e12 | 0.109893 | ||||||||
\(826\) | 3.88696e12 | 0.290536 | ||||||||
\(827\) | 2.36419e13 | 1.75755 | 0.878774 | − | 0.477239i | \(-0.158362\pi\) | ||||
0.878774 | + | 0.477239i | \(0.158362\pi\) | |||||||
\(828\) | 6.74549e12 | 0.498743 | ||||||||
\(829\) | 1.99403e13 | 1.46635 | 0.733173 | − | 0.680042i | \(-0.238038\pi\) | ||||
0.733173 | + | 0.680042i | \(0.238038\pi\) | |||||||
\(830\) | −1.23382e13 | −0.902405 | ||||||||
\(831\) | 4.69886e12 | 0.341812 | ||||||||
\(832\) | 5.68295e11 | 0.0411167 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −1.27910e13 | −0.915498 | ||||||||
\(835\) | −9.00078e12 | −0.640753 | ||||||||
\(836\) | 4.39273e12 | 0.311033 | ||||||||
\(837\) | 1.46859e13 | 1.03427 | ||||||||
\(838\) | −1.78537e13 | −1.25063 | ||||||||
\(839\) | −5.03307e11 | −0.0350675 | −0.0175337 | − | 0.999846i | \(-0.505581\pi\) | ||||
−0.0175337 | + | 0.999846i | \(0.505581\pi\) | |||||||
\(840\) | 4.13538e12 | 0.286589 | ||||||||
\(841\) | −5.60406e12 | −0.386296 | ||||||||
\(842\) | −1.67169e13 | −1.14617 | ||||||||
\(843\) | 1.28617e13 | 0.877154 | ||||||||
\(844\) | 6.20081e12 | 0.420637 | ||||||||
\(845\) | 1.06096e13 | 0.715886 | ||||||||
\(846\) | −7.84307e12 | −0.526404 | ||||||||
\(847\) | −8.61076e11 | −0.0574866 | ||||||||
\(848\) | 4.31939e12 | 0.286841 | ||||||||
\(849\) | −8.77147e12 | −0.579412 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.79957e13 | −1.82982 | ||||||||
\(852\) | −1.76167e13 | −1.14537 | ||||||||
\(853\) | −1.68280e13 | −1.08833 | −0.544167 | − | 0.838977i | \(-0.683154\pi\) | ||||
−0.544167 | + | 0.838977i | \(0.683154\pi\) | |||||||
\(854\) | −8.48555e12 | −0.545908 | ||||||||
\(855\) | −4.88974e12 | −0.312924 | ||||||||
\(856\) | 1.38813e13 | 0.883687 | ||||||||
\(857\) | −2.00682e13 | −1.27085 | −0.635425 | − | 0.772163i | \(-0.719175\pi\) | ||||
−0.635425 | + | 0.772163i | \(0.719175\pi\) | |||||||
\(858\) | −1.29097e13 | −0.813246 | ||||||||
\(859\) | 2.05798e13 | 1.28965 | 0.644826 | − | 0.764329i | \(-0.276930\pi\) | ||||
0.644826 | + | 0.764329i | \(0.276930\pi\) | |||||||
\(860\) | 1.11657e13 | 0.696055 | ||||||||
\(861\) | 1.36730e13 | 0.847912 | ||||||||
\(862\) | −5.64064e12 | −0.347973 | ||||||||
\(863\) | −5.58574e11 | −0.0342793 | −0.0171397 | − | 0.999853i | \(-0.505456\pi\) | ||||
−0.0171397 | + | 0.999853i | \(0.505456\pi\) | |||||||
\(864\) | 1.00450e13 | 0.613253 | ||||||||
\(865\) | −1.72808e13 | −1.04952 | ||||||||
\(866\) | 4.57783e12 | 0.276585 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −7.36116e12 | −0.440157 | ||||||||
\(869\) | −2.53430e13 | −1.50754 | ||||||||
\(870\) | 2.15507e13 | 1.27534 | ||||||||
\(871\) | 6.54768e12 | 0.385483 | ||||||||
\(872\) | 1.56873e13 | 0.918806 | ||||||||
\(873\) | −1.00773e12 | −0.0587191 | ||||||||
\(874\) | 2.00775e13 | 1.16388 | ||||||||
\(875\) | 6.99070e12 | 0.403167 | ||||||||
\(876\) | 1.23076e13 | 0.706166 | ||||||||
\(877\) | −1.61009e13 | −0.919076 | −0.459538 | − | 0.888158i | \(-0.651985\pi\) | ||||
−0.459538 | + | 0.888158i | \(0.651985\pi\) | |||||||
\(878\) | −3.25643e13 | −1.84934 | ||||||||
\(879\) | −2.95726e13 | −1.67086 | ||||||||
\(880\) | 2.15191e13 | 1.20963 | ||||||||
\(881\) | 3.38486e13 | 1.89299 | 0.946496 | − | 0.322715i | \(-0.104596\pi\) | ||||
0.946496 | + | 0.322715i | \(0.104596\pi\) | |||||||
\(882\) | −9.71907e12 | −0.540774 | ||||||||
\(883\) | 6.37789e12 | 0.353064 | 0.176532 | − | 0.984295i | \(-0.443512\pi\) | ||||
0.176532 | + | 0.984295i | \(0.443512\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.27725e13 | −0.699892 | ||||||||
\(886\) | −1.53534e13 | −0.837052 | ||||||||
\(887\) | 1.11778e13 | 0.606315 | 0.303158 | − | 0.952940i | \(-0.401959\pi\) | ||||
0.303158 | + | 0.952940i | \(0.401959\pi\) | |||||||
\(888\) | 1.34456e13 | 0.725643 | ||||||||
\(889\) | −4.38542e12 | −0.235480 | ||||||||
\(890\) | 7.45817e12 | 0.398453 | ||||||||
\(891\) | −2.18609e13 | −1.16203 | ||||||||
\(892\) | −1.33354e13 | −0.705282 | ||||||||
\(893\) | −8.63166e12 | −0.454216 | ||||||||
\(894\) | 2.38306e13 | 1.24772 | ||||||||
\(895\) | −3.84658e13 | −2.00388 | ||||||||
\(896\) | 7.82522e12 | 0.405612 | ||||||||
\(897\) | −2.18173e13 | −1.12522 | ||||||||
\(898\) | −8.93824e12 | −0.458678 | ||||||||
\(899\) | 2.70259e13 | 1.37994 | ||||||||
\(900\) | 5.79551e11 | 0.0294442 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 3.75542e13 | 1.88899 | ||||||||
\(903\) | −1.19090e13 | −0.596046 | ||||||||
\(904\) | −1.05781e13 | −0.526803 | ||||||||
\(905\) | −1.93945e13 | −0.961082 | ||||||||
\(906\) | 3.08496e13 | 1.52115 | ||||||||
\(907\) | −1.99609e13 | −0.979373 | −0.489686 | − | 0.871899i | \(-0.662889\pi\) | ||||
−0.489686 | + | 0.871899i | \(0.662889\pi\) | |||||||
\(908\) | −9.72064e12 | −0.474579 | ||||||||
\(909\) | 7.99492e12 | 0.388398 | ||||||||
\(910\) | 6.53141e12 | 0.315733 | ||||||||
\(911\) | −2.62947e13 | −1.26484 | −0.632420 | − | 0.774626i | \(-0.717938\pi\) | ||||
−0.632420 | + | 0.774626i | \(0.717938\pi\) | |||||||
\(912\) | −1.82690e13 | −0.874457 | ||||||||
\(913\) | 1.33643e13 | 0.636542 | ||||||||
\(914\) | −6.95544e12 | −0.329660 | ||||||||
\(915\) | 2.78834e13 | 1.31508 | ||||||||
\(916\) | 1.51900e13 | 0.712898 | ||||||||
\(917\) | 2.82609e12 | 0.131985 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.48727e13 | 0.687812 | 0.343906 | − | 0.939004i | \(-0.388250\pi\) | ||||
0.343906 | + | 0.939004i | \(0.388250\pi\) | |||||||
\(920\) | 1.91954e13 | 0.883387 | ||||||||
\(921\) | 2.14745e13 | 0.983454 | ||||||||
\(922\) | −4.02012e13 | −1.83210 | ||||||||
\(923\) | 1.96021e13 | 0.888988 | ||||||||
\(924\) | 6.35801e12 | 0.286944 | ||||||||
\(925\) | −2.40530e12 | −0.108027 | ||||||||
\(926\) | −1.87384e13 | −0.837497 | ||||||||
\(927\) | 1.26695e13 | 0.563509 | ||||||||
\(928\) | 1.84855e13 | 0.818211 | ||||||||
\(929\) | −3.16348e13 | −1.39346 | −0.696730 | − | 0.717333i | \(-0.745362\pi\) | ||||
−0.696730 | + | 0.717333i | \(0.745362\pi\) | |||||||
\(930\) | 6.54186e13 | 2.86766 | ||||||||
\(931\) | −1.06963e13 | −0.466616 | ||||||||
\(932\) | −5.15155e12 | −0.223649 | ||||||||
\(933\) | −5.21087e13 | −2.25135 | ||||||||
\(934\) | 2.07832e13 | 0.893619 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 3.60480e12 | 0.153511 | ||||||||
\(937\) | −2.25664e13 | −0.956390 | −0.478195 | − | 0.878254i | \(-0.658709\pi\) | ||||
−0.478195 | + | 0.878254i | \(0.658709\pi\) | |||||||
\(938\) | −8.72133e12 | −0.367849 | ||||||||
\(939\) | 2.67972e13 | 1.12485 | ||||||||
\(940\) | 1.17137e13 | 0.489348 | ||||||||
\(941\) | −2.88841e13 | −1.20090 | −0.600448 | − | 0.799664i | \(-0.705011\pi\) | ||||
−0.600448 | + | 0.799664i | \(0.705011\pi\) | |||||||
\(942\) | −1.57342e13 | −0.651053 | ||||||||
\(943\) | 6.34667e13 | 2.61362 | ||||||||
\(944\) | −1.64171e13 | −0.672855 | ||||||||
\(945\) | 6.41753e12 | 0.261773 | ||||||||
\(946\) | −3.27091e13 | −1.32788 | ||||||||
\(947\) | −1.70699e13 | −0.689695 | −0.344847 | − | 0.938659i | \(-0.612069\pi\) | ||||
−0.344847 | + | 0.938659i | \(0.612069\pi\) | |||||||
\(948\) | −2.91976e13 | −1.17411 | ||||||||
\(949\) | −1.36947e13 | −0.548094 | ||||||||
\(950\) | 1.72500e12 | 0.0687119 | ||||||||
\(951\) | 9.34416e12 | 0.370449 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 4.06332e13 | 1.59574 | 0.797872 | − | 0.602827i | \(-0.205959\pi\) | ||||
0.797872 | + | 0.602827i | \(0.205959\pi\) | |||||||
\(954\) | −3.90180e12 | −0.152509 | ||||||||
\(955\) | −2.42425e13 | −0.943109 | ||||||||
\(956\) | −4.70882e12 | −0.182327 | ||||||||
\(957\) | −2.33429e13 | −0.899603 | ||||||||
\(958\) | 4.66342e13 | 1.78879 | ||||||||
\(959\) | 1.67564e13 | 0.639732 | ||||||||
\(960\) | 2.48734e12 | 0.0945180 | ||||||||
\(961\) | 5.55991e13 | 2.10287 | ||||||||
\(962\) | 2.12360e13 | 0.799438 | ||||||||
\(963\) | −2.37568e13 | −0.890162 | ||||||||
\(964\) | 2.34337e12 | 0.0873966 | ||||||||
\(965\) | −2.11208e13 | −0.784037 | ||||||||
\(966\) | 2.90601e13 | 1.07374 | ||||||||
\(967\) | 3.75260e13 | 1.38011 | 0.690055 | − | 0.723757i | \(-0.257586\pi\) | ||||
0.690055 | + | 0.723757i | \(0.257586\pi\) | |||||||
\(968\) | 1.91961e12 | 0.0702705 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 4.07042e12 | 0.147627 | ||||||||
\(971\) | −2.63924e13 | −0.952778 | −0.476389 | − | 0.879235i | \(-0.658055\pi\) | ||||
−0.476389 | + | 0.879235i | \(0.658055\pi\) | |||||||
\(972\) | −1.55996e13 | −0.560549 | ||||||||
\(973\) | −7.00954e12 | −0.250716 | ||||||||
\(974\) | 1.82633e13 | 0.650226 | ||||||||
\(975\) | −1.87448e12 | −0.0664292 | ||||||||
\(976\) | 3.58398e13 | 1.26427 | ||||||||
\(977\) | −4.44812e13 | −1.56189 | −0.780947 | − | 0.624598i | \(-0.785263\pi\) | ||||
−0.780947 | + | 0.624598i | \(0.785263\pi\) | |||||||
\(978\) | −6.05731e13 | −2.11716 | ||||||||
\(979\) | −8.07839e12 | −0.281062 | ||||||||
\(980\) | 1.45155e13 | 0.502706 | ||||||||
\(981\) | −2.68476e13 | −0.925539 | ||||||||
\(982\) | 4.90121e13 | 1.68191 | ||||||||
\(983\) | 3.61778e13 | 1.23581 | 0.617904 | − | 0.786254i | \(-0.287982\pi\) | ||||
0.617904 | + | 0.786254i | \(0.287982\pi\) | |||||||
\(984\) | −3.04815e13 | −1.03647 | ||||||||
\(985\) | 3.82344e13 | 1.29417 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.24934e13 | −0.419038 | ||||||||
\(988\) | −5.63122e12 | −0.188017 | ||||||||
\(989\) | −5.52784e13 | −1.83727 | ||||||||
\(990\) | −1.94386e13 | −0.643143 | ||||||||
\(991\) | −1.90887e13 | −0.628701 | −0.314351 | − | 0.949307i | \(-0.601787\pi\) | ||||
−0.314351 | + | 0.949307i | \(0.601787\pi\) | |||||||
\(992\) | 5.61139e13 | 1.83979 | ||||||||
\(993\) | −5.46195e13 | −1.78269 | ||||||||
\(994\) | −2.61095e13 | −0.848321 | ||||||||
\(995\) | 8.86540e11 | 0.0286744 | ||||||||
\(996\) | 1.53970e13 | 0.495757 | ||||||||
\(997\) | −5.48487e13 | −1.75808 | −0.879039 | − | 0.476749i | \(-0.841815\pi\) | ||||
−0.879039 | + | 0.476749i | \(0.841815\pi\) | |||||||
\(998\) | 7.06654e13 | 2.25486 | ||||||||
\(999\) | 2.08657e13 | 0.662809 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 289.10.a.g.1.28 | ✓ | 36 | |
17.16 | even | 2 | 289.10.a.h.1.28 | yes | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
289.10.a.g.1.28 | ✓ | 36 | 1.1 | even | 1 | trivial | |
289.10.a.h.1.28 | yes | 36 | 17.16 | even | 2 |