Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [47,20,Mod(1,47)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(47, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 20, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("47.1");
S:= CuspForms(chi, 20);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 47 \) |
Weight: | \( k \) | \(=\) | \( 20 \) |
Character orbit: | \([\chi]\) | \(=\) | 47.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: | \(107.543847381\) |
Analytic rank: | \(1\) |
Dimension: | \(34\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Character | \(\chi\) | \(=\) | 47.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1322.20 | −1.82605 | −0.913026 | − | 0.407901i | \(-0.866261\pi\) | ||||
−0.913026 | + | 0.407901i | \(0.866261\pi\) | |||||||
\(3\) | −58648.5 | −1.72030 | −0.860152 | − | 0.510037i | \(-0.829632\pi\) | ||||
−0.860152 | + | 0.510037i | \(0.829632\pi\) | |||||||
\(4\) | 1.22393e6 | 2.33447 | ||||||||
\(5\) | −2.69135e6 | −0.616248 | −0.308124 | − | 0.951346i | \(-0.599701\pi\) | ||||
−0.308124 | + | 0.951346i | \(0.599701\pi\) | |||||||
\(6\) | 7.75453e7 | 3.14137 | ||||||||
\(7\) | −1.70403e8 | −1.59605 | −0.798026 | − | 0.602623i | \(-0.794122\pi\) | ||||
−0.798026 | + | 0.602623i | \(0.794122\pi\) | |||||||
\(8\) | −9.25073e8 | −2.43681 | ||||||||
\(9\) | 2.27739e9 | 1.95945 | ||||||||
\(10\) | 3.55852e9 | 1.12530 | ||||||||
\(11\) | 2.84119e9 | 0.363304 | 0.181652 | − | 0.983363i | \(-0.441856\pi\) | ||||
0.181652 | + | 0.983363i | \(0.441856\pi\) | |||||||
\(12\) | −7.17819e10 | −4.01599 | ||||||||
\(13\) | −4.77789e9 | −0.124961 | −0.0624805 | − | 0.998046i | \(-0.519901\pi\) | ||||
−0.0624805 | + | 0.998046i | \(0.519901\pi\) | |||||||
\(14\) | 2.25308e11 | 2.91447 | ||||||||
\(15\) | 1.57844e11 | 1.06013 | ||||||||
\(16\) | 5.81441e11 | 2.11527 | ||||||||
\(17\) | −4.56694e11 | −0.934029 | −0.467014 | − | 0.884250i | \(-0.654670\pi\) | ||||
−0.467014 | + | 0.884250i | \(0.654670\pi\) | |||||||
\(18\) | −3.01117e12 | −3.57805 | ||||||||
\(19\) | −8.99169e11 | −0.639267 | −0.319633 | − | 0.947541i | \(-0.603560\pi\) | ||||
−0.319633 | + | 0.947541i | \(0.603560\pi\) | |||||||
\(20\) | −3.29404e12 | −1.43861 | ||||||||
\(21\) | 9.99391e12 | 2.74569 | ||||||||
\(22\) | −3.75664e12 | −0.663413 | ||||||||
\(23\) | −1.55266e13 | −1.79747 | −0.898737 | − | 0.438488i | \(-0.855514\pi\) | ||||
−0.898737 | + | 0.438488i | \(0.855514\pi\) | |||||||
\(24\) | 5.42542e13 | 4.19205 | ||||||||
\(25\) | −1.18301e13 | −0.620238 | ||||||||
\(26\) | 6.31735e12 | 0.228185 | ||||||||
\(27\) | −6.54007e13 | −1.65054 | ||||||||
\(28\) | −2.08562e14 | −3.72593 | ||||||||
\(29\) | −9.23856e13 | −1.18256 | −0.591280 | − | 0.806466i | \(-0.701377\pi\) | ||||
−0.591280 | + | 0.806466i | \(0.701377\pi\) | |||||||
\(30\) | −2.08702e14 | −1.93586 | ||||||||
\(31\) | −6.23321e13 | −0.423424 | −0.211712 | − | 0.977332i | \(-0.567904\pi\) | ||||
−0.211712 | + | 0.977332i | \(0.567904\pi\) | |||||||
\(32\) | −2.83778e14 | −1.42579 | ||||||||
\(33\) | −1.66632e14 | −0.624994 | ||||||||
\(34\) | 6.03842e14 | 1.70559 | ||||||||
\(35\) | 4.58616e14 | 0.983564 | ||||||||
\(36\) | 2.78737e15 | 4.57427 | ||||||||
\(37\) | 2.05351e14 | 0.259764 | 0.129882 | − | 0.991529i | \(-0.458540\pi\) | ||||
0.129882 | + | 0.991529i | \(0.458540\pi\) | |||||||
\(38\) | 1.18888e15 | 1.16733 | ||||||||
\(39\) | 2.80216e14 | 0.214971 | ||||||||
\(40\) | 2.48970e15 | 1.50168 | ||||||||
\(41\) | 2.83265e15 | 1.35128 | 0.675642 | − | 0.737230i | \(-0.263867\pi\) | ||||
0.675642 | + | 0.737230i | \(0.263867\pi\) | |||||||
\(42\) | −1.32140e16 | −5.01378 | ||||||||
\(43\) | −1.74023e15 | −0.528027 | −0.264013 | − | 0.964519i | \(-0.585046\pi\) | ||||
−0.264013 | + | 0.964519i | \(0.585046\pi\) | |||||||
\(44\) | 3.47743e15 | 0.848122 | ||||||||
\(45\) | −6.12926e15 | −1.20751 | ||||||||
\(46\) | 2.05294e16 | 3.28228 | ||||||||
\(47\) | 1.11913e15 | 0.145865 | ||||||||
\(48\) | −3.41007e16 | −3.63891 | ||||||||
\(49\) | 1.76384e16 | 1.54738 | ||||||||
\(50\) | 1.56418e16 | 1.13259 | ||||||||
\(51\) | 2.67844e16 | 1.60681 | ||||||||
\(52\) | −5.84782e15 | −0.291717 | ||||||||
\(53\) | −1.80802e16 | −0.752631 | −0.376315 | − | 0.926492i | \(-0.622809\pi\) | ||||
−0.376315 | + | 0.926492i | \(0.622809\pi\) | |||||||
\(54\) | 8.64730e16 | 3.01397 | ||||||||
\(55\) | −7.64666e15 | −0.223886 | ||||||||
\(56\) | 1.57636e17 | 3.88927 | ||||||||
\(57\) | 5.27350e16 | 1.09973 | ||||||||
\(58\) | 1.22153e17 | 2.15942 | ||||||||
\(59\) | 6.22662e16 | 0.935746 | 0.467873 | − | 0.883796i | \(-0.345020\pi\) | ||||
0.467873 | + | 0.883796i | \(0.345020\pi\) | |||||||
\(60\) | 1.93190e17 | 2.47485 | ||||||||
\(61\) | −1.45257e17 | −1.59039 | −0.795197 | − | 0.606351i | \(-0.792633\pi\) | ||||
−0.795197 | + | 0.606351i | \(0.792633\pi\) | |||||||
\(62\) | 8.24157e16 | 0.773195 | ||||||||
\(63\) | −3.88075e17 | −3.12738 | ||||||||
\(64\) | 7.03700e16 | 0.488290 | ||||||||
\(65\) | 1.28590e16 | 0.0770070 | ||||||||
\(66\) | 2.20321e17 | 1.14127 | ||||||||
\(67\) | 3.92212e17 | 1.76121 | 0.880603 | − | 0.473855i | \(-0.157138\pi\) | ||||
0.880603 | + | 0.473855i | \(0.157138\pi\) | |||||||
\(68\) | −5.58962e17 | −2.18046 | ||||||||
\(69\) | 9.10614e17 | 3.09220 | ||||||||
\(70\) | −6.06383e17 | −1.79604 | ||||||||
\(71\) | 5.02750e17 | 1.30136 | 0.650681 | − | 0.759352i | \(-0.274484\pi\) | ||||
0.650681 | + | 0.759352i | \(0.274484\pi\) | |||||||
\(72\) | −2.10675e18 | −4.77479 | ||||||||
\(73\) | −9.66948e17 | −1.92237 | −0.961183 | − | 0.275911i | \(-0.911021\pi\) | ||||
−0.961183 | + | 0.275911i | \(0.911021\pi\) | |||||||
\(74\) | −2.71515e17 | −0.474343 | ||||||||
\(75\) | 6.93818e17 | 1.06700 | ||||||||
\(76\) | −1.10052e18 | −1.49235 | ||||||||
\(77\) | −4.84149e17 | −0.579852 | ||||||||
\(78\) | −3.70503e17 | −0.392548 | ||||||||
\(79\) | 1.46449e18 | 1.37476 | 0.687382 | − | 0.726296i | \(-0.258760\pi\) | ||||
0.687382 | + | 0.726296i | \(0.258760\pi\) | |||||||
\(80\) | −1.56486e18 | −1.30353 | ||||||||
\(81\) | 1.18873e18 | 0.879986 | ||||||||
\(82\) | −3.74534e18 | −2.46751 | ||||||||
\(83\) | 5.27599e17 | 0.309786 | 0.154893 | − | 0.987931i | \(-0.450497\pi\) | ||||
0.154893 | + | 0.987931i | \(0.450497\pi\) | |||||||
\(84\) | 1.22319e19 | 6.40973 | ||||||||
\(85\) | 1.22912e18 | 0.575594 | ||||||||
\(86\) | 2.30093e18 | 0.964204 | ||||||||
\(87\) | 5.41828e18 | 2.03436 | ||||||||
\(88\) | −2.62831e18 | −0.885302 | ||||||||
\(89\) | 2.55481e18 | 0.772955 | 0.386477 | − | 0.922299i | \(-0.373692\pi\) | ||||
0.386477 | + | 0.922299i | \(0.373692\pi\) | |||||||
\(90\) | 8.10413e18 | 2.20497 | ||||||||
\(91\) | 8.14169e17 | 0.199444 | ||||||||
\(92\) | −1.90036e19 | −4.19614 | ||||||||
\(93\) | 3.65569e18 | 0.728419 | ||||||||
\(94\) | −1.47972e18 | −0.266357 | ||||||||
\(95\) | 2.41998e18 | 0.393947 | ||||||||
\(96\) | 1.66432e19 | 2.45279 | ||||||||
\(97\) | 1.02912e19 | 1.37447 | 0.687236 | − | 0.726434i | \(-0.258824\pi\) | ||||
0.687236 | + | 0.726434i | \(0.258824\pi\) | |||||||
\(98\) | −2.33216e19 | −2.82560 | ||||||||
\(99\) | 6.47051e18 | 0.711876 | ||||||||
\(100\) | −1.44793e19 | −1.44793 | ||||||||
\(101\) | −1.84934e19 | −1.68253 | −0.841265 | − | 0.540622i | \(-0.818189\pi\) | ||||
−0.841265 | + | 0.540622i | \(0.818189\pi\) | |||||||
\(102\) | −3.54144e19 | −2.93413 | ||||||||
\(103\) | 2.05794e19 | 1.55410 | 0.777052 | − | 0.629436i | \(-0.216714\pi\) | ||||
0.777052 | + | 0.629436i | \(0.216714\pi\) | |||||||
\(104\) | 4.41990e18 | 0.304506 | ||||||||
\(105\) | −2.68972e19 | −1.69203 | ||||||||
\(106\) | 2.39057e19 | 1.37434 | ||||||||
\(107\) | 2.33782e19 | 1.22932 | 0.614660 | − | 0.788792i | \(-0.289293\pi\) | ||||
0.614660 | + | 0.788792i | \(0.289293\pi\) | |||||||
\(108\) | −8.00460e19 | −3.85313 | ||||||||
\(109\) | −5.65107e18 | −0.249218 | −0.124609 | − | 0.992206i | \(-0.539768\pi\) | ||||
−0.124609 | + | 0.992206i | \(0.539768\pi\) | |||||||
\(110\) | 1.01104e19 | 0.408827 | ||||||||
\(111\) | −1.20435e19 | −0.446874 | ||||||||
\(112\) | −9.90795e19 | −3.37608 | ||||||||
\(113\) | −1.30671e19 | −0.409199 | −0.204599 | − | 0.978846i | \(-0.565589\pi\) | ||||
−0.204599 | + | 0.978846i | \(0.565589\pi\) | |||||||
\(114\) | −6.97263e19 | −2.00817 | ||||||||
\(115\) | 4.17876e19 | 1.10769 | ||||||||
\(116\) | −1.13074e20 | −2.76065 | ||||||||
\(117\) | −1.08811e19 | −0.244855 | ||||||||
\(118\) | −8.23285e19 | −1.70872 | ||||||||
\(119\) | 7.78222e19 | 1.49076 | ||||||||
\(120\) | −1.46017e20 | −2.58334 | ||||||||
\(121\) | −5.30867e19 | −0.868010 | ||||||||
\(122\) | 1.92060e20 | 2.90414 | ||||||||
\(123\) | −1.66131e20 | −2.32462 | ||||||||
\(124\) | −7.62904e19 | −0.988470 | ||||||||
\(125\) | 8.31725e19 | 0.998469 | ||||||||
\(126\) | 5.13114e20 | 5.71076 | ||||||||
\(127\) | −4.94029e19 | −0.510055 | −0.255028 | − | 0.966934i | \(-0.582085\pi\) | ||||
−0.255028 | + | 0.966934i | \(0.582085\pi\) | |||||||
\(128\) | 5.57381e19 | 0.534143 | ||||||||
\(129\) | 1.02062e20 | 0.908366 | ||||||||
\(130\) | −1.70022e19 | −0.140619 | ||||||||
\(131\) | −4.90716e19 | −0.377357 | −0.188679 | − | 0.982039i | \(-0.560420\pi\) | ||||
−0.188679 | + | 0.982039i | \(0.560420\pi\) | |||||||
\(132\) | −2.03946e20 | −1.45903 | ||||||||
\(133\) | 1.53221e20 | 1.02030 | ||||||||
\(134\) | −5.18584e20 | −3.21605 | ||||||||
\(135\) | 1.76016e20 | 1.01714 | ||||||||
\(136\) | 4.22475e20 | 2.27605 | ||||||||
\(137\) | 7.58339e19 | 0.381081 | 0.190541 | − | 0.981679i | \(-0.438976\pi\) | ||||
0.190541 | + | 0.981679i | \(0.438976\pi\) | |||||||
\(138\) | −1.20402e21 | −5.64652 | ||||||||
\(139\) | −3.12924e20 | −1.37024 | −0.685122 | − | 0.728429i | \(-0.740251\pi\) | ||||
−0.685122 | + | 0.728429i | \(0.740251\pi\) | |||||||
\(140\) | 5.61315e20 | 2.29610 | ||||||||
\(141\) | −6.56354e19 | −0.250932 | ||||||||
\(142\) | −6.64738e20 | −2.37635 | ||||||||
\(143\) | −1.35749e19 | −0.0453989 | ||||||||
\(144\) | 1.32417e21 | 4.14476 | ||||||||
\(145\) | 2.48642e20 | 0.728751 | ||||||||
\(146\) | 1.27850e21 | 3.51034 | ||||||||
\(147\) | −1.03447e21 | −2.66197 | ||||||||
\(148\) | 2.51335e20 | 0.606411 | ||||||||
\(149\) | 3.98820e19 | 0.0902625 | 0.0451312 | − | 0.998981i | \(-0.485629\pi\) | ||||
0.0451312 | + | 0.998981i | \(0.485629\pi\) | |||||||
\(150\) | −9.17369e20 | −1.94839 | ||||||||
\(151\) | −3.53199e20 | −0.704268 | −0.352134 | − | 0.935950i | \(-0.614544\pi\) | ||||
−0.352134 | + | 0.935950i | \(0.614544\pi\) | |||||||
\(152\) | 8.31797e20 | 1.55777 | ||||||||
\(153\) | −1.04007e21 | −1.83018 | ||||||||
\(154\) | 6.40144e20 | 1.05884 | ||||||||
\(155\) | 1.67758e20 | 0.260935 | ||||||||
\(156\) | 3.42966e20 | 0.501843 | ||||||||
\(157\) | 7.79631e20 | 1.07360 | 0.536800 | − | 0.843710i | \(-0.319633\pi\) | ||||
0.536800 | + | 0.843710i | \(0.319633\pi\) | |||||||
\(158\) | −1.93635e21 | −2.51039 | ||||||||
\(159\) | 1.06038e21 | 1.29475 | ||||||||
\(160\) | 7.63747e20 | 0.878638 | ||||||||
\(161\) | 2.64579e21 | 2.86886 | ||||||||
\(162\) | −1.57174e21 | −1.60690 | ||||||||
\(163\) | 4.08379e20 | 0.393805 | 0.196902 | − | 0.980423i | \(-0.436912\pi\) | ||||
0.196902 | + | 0.980423i | \(0.436912\pi\) | |||||||
\(164\) | 3.46698e21 | 3.15453 | ||||||||
\(165\) | 4.48465e20 | 0.385151 | ||||||||
\(166\) | −6.97593e20 | −0.565686 | ||||||||
\(167\) | −6.36067e20 | −0.487188 | −0.243594 | − | 0.969877i | \(-0.578326\pi\) | ||||
−0.243594 | + | 0.969877i | \(0.578326\pi\) | |||||||
\(168\) | −9.24510e21 | −6.69073 | ||||||||
\(169\) | −1.43909e21 | −0.984385 | ||||||||
\(170\) | −1.62515e21 | −1.05106 | ||||||||
\(171\) | −2.04776e21 | −1.25261 | ||||||||
\(172\) | −2.12992e21 | −1.23266 | ||||||||
\(173\) | 3.54433e21 | 1.94132 | 0.970659 | − | 0.240461i | \(-0.0772987\pi\) | ||||
0.970659 | + | 0.240461i | \(0.0772987\pi\) | |||||||
\(174\) | −7.16407e21 | −3.71485 | ||||||||
\(175\) | 2.01589e21 | 0.989932 | ||||||||
\(176\) | 1.65199e21 | 0.768486 | ||||||||
\(177\) | −3.65182e21 | −1.60977 | ||||||||
\(178\) | −3.37798e21 | −1.41146 | ||||||||
\(179\) | −4.67429e19 | −0.0185188 | −0.00925938 | − | 0.999957i | \(-0.502947\pi\) | ||||
−0.00925938 | + | 0.999957i | \(0.502947\pi\) | |||||||
\(180\) | −7.50181e21 | −2.81888 | ||||||||
\(181\) | 2.13871e21 | 0.762439 | 0.381219 | − | 0.924485i | \(-0.375504\pi\) | ||||
0.381219 | + | 0.924485i | \(0.375504\pi\) | |||||||
\(182\) | −1.07650e21 | −0.364196 | ||||||||
\(183\) | 8.51913e21 | 2.73596 | ||||||||
\(184\) | 1.43633e22 | 4.38010 | ||||||||
\(185\) | −5.52671e20 | −0.160079 | ||||||||
\(186\) | −4.83356e21 | −1.33013 | ||||||||
\(187\) | −1.29756e21 | −0.339337 | ||||||||
\(188\) | 1.36974e21 | 0.340517 | ||||||||
\(189\) | 1.11445e22 | 2.63435 | ||||||||
\(190\) | −3.19971e21 | −0.719368 | ||||||||
\(191\) | 1.01335e21 | 0.216743 | 0.108371 | − | 0.994110i | \(-0.465436\pi\) | ||||
0.108371 | + | 0.994110i | \(0.465436\pi\) | |||||||
\(192\) | −4.12710e21 | −0.840007 | ||||||||
\(193\) | −7.21040e21 | −1.39690 | −0.698449 | − | 0.715660i | \(-0.746126\pi\) | ||||
−0.698449 | + | 0.715660i | \(0.746126\pi\) | |||||||
\(194\) | −1.36071e22 | −2.50986 | ||||||||
\(195\) | −7.54162e20 | −0.132476 | ||||||||
\(196\) | 2.15883e22 | 3.61231 | ||||||||
\(197\) | 3.23089e21 | 0.515102 | 0.257551 | − | 0.966265i | \(-0.417085\pi\) | ||||
0.257551 | + | 0.966265i | \(0.417085\pi\) | |||||||
\(198\) | −8.55533e21 | −1.29992 | ||||||||
\(199\) | 8.80627e21 | 1.27552 | 0.637761 | − | 0.770235i | \(-0.279861\pi\) | ||||
0.637761 | + | 0.770235i | \(0.279861\pi\) | |||||||
\(200\) | 1.09437e22 | 1.51140 | ||||||||
\(201\) | −2.30027e22 | −3.02981 | ||||||||
\(202\) | 2.44520e22 | 3.07239 | ||||||||
\(203\) | 1.57428e22 | 1.88743 | ||||||||
\(204\) | 3.27823e22 | 3.75105 | ||||||||
\(205\) | −7.62367e21 | −0.832726 | ||||||||
\(206\) | −2.72102e22 | −2.83788 | ||||||||
\(207\) | −3.53602e22 | −3.52206 | ||||||||
\(208\) | −2.77806e21 | −0.264326 | ||||||||
\(209\) | −2.55471e21 | −0.232248 | ||||||||
\(210\) | 3.55635e22 | 3.08973 | ||||||||
\(211\) | 6.06241e21 | 0.503456 | 0.251728 | − | 0.967798i | \(-0.419001\pi\) | ||||
0.251728 | + | 0.967798i | \(0.419001\pi\) | |||||||
\(212\) | −2.21289e22 | −1.75699 | ||||||||
\(213\) | −2.94856e22 | −2.23874 | ||||||||
\(214\) | −3.09107e22 | −2.24480 | ||||||||
\(215\) | 4.68357e21 | 0.325395 | ||||||||
\(216\) | 6.05004e22 | 4.02205 | ||||||||
\(217\) | 1.06216e22 | 0.675807 | ||||||||
\(218\) | 7.47186e21 | 0.455084 | ||||||||
\(219\) | 5.67101e22 | 3.30706 | ||||||||
\(220\) | −9.35900e21 | −0.522654 | ||||||||
\(221\) | 2.18203e21 | 0.116717 | ||||||||
\(222\) | 1.59240e22 | 0.816015 | ||||||||
\(223\) | −3.15141e22 | −1.54742 | −0.773710 | − | 0.633540i | \(-0.781601\pi\) | ||||
−0.773710 | + | 0.633540i | \(0.781601\pi\) | |||||||
\(224\) | 4.83568e22 | 2.27563 | ||||||||
\(225\) | −2.69418e22 | −1.21532 | ||||||||
\(226\) | 1.72774e22 | 0.747219 | ||||||||
\(227\) | 1.20611e22 | 0.500197 | 0.250098 | − | 0.968220i | \(-0.419537\pi\) | ||||
0.250098 | + | 0.968220i | \(0.419537\pi\) | |||||||
\(228\) | 6.45440e22 | 2.56729 | ||||||||
\(229\) | 2.72200e22 | 1.03860 | 0.519302 | − | 0.854591i | \(-0.326192\pi\) | ||||
0.519302 | + | 0.854591i | \(0.326192\pi\) | |||||||
\(230\) | −5.52517e22 | −2.02270 | ||||||||
\(231\) | 2.83946e22 | 0.997523 | ||||||||
\(232\) | 8.54634e22 | 2.88167 | ||||||||
\(233\) | −2.37504e21 | −0.0768758 | −0.0384379 | − | 0.999261i | \(-0.512238\pi\) | ||||
−0.0384379 | + | 0.999261i | \(0.512238\pi\) | |||||||
\(234\) | 1.43871e22 | 0.447117 | ||||||||
\(235\) | −3.01198e21 | −0.0898890 | ||||||||
\(236\) | 7.62096e22 | 2.18447 | ||||||||
\(237\) | −8.58901e22 | −2.36501 | ||||||||
\(238\) | −1.02897e23 | −2.72220 | ||||||||
\(239\) | 6.11619e22 | 1.55489 | 0.777447 | − | 0.628949i | \(-0.216515\pi\) | ||||
0.777447 | + | 0.628949i | \(0.216515\pi\) | |||||||
\(240\) | 9.17769e22 | 2.24247 | ||||||||
\(241\) | −6.69064e21 | −0.157147 | −0.0785735 | − | 0.996908i | \(-0.525037\pi\) | ||||
−0.0785735 | + | 0.996908i | \(0.525037\pi\) | |||||||
\(242\) | 7.01914e22 | 1.58503 | ||||||||
\(243\) | 6.29533e21 | 0.136697 | ||||||||
\(244\) | −1.77785e23 | −3.71272 | ||||||||
\(245\) | −4.74713e22 | −0.953571 | ||||||||
\(246\) | 2.19659e23 | 4.24488 | ||||||||
\(247\) | 4.29613e21 | 0.0798834 | ||||||||
\(248\) | 5.76618e22 | 1.03180 | ||||||||
\(249\) | −3.09429e22 | −0.532927 | ||||||||
\(250\) | −1.09971e23 | −1.82326 | ||||||||
\(251\) | −2.38196e22 | −0.380219 | −0.190109 | − | 0.981763i | \(-0.560884\pi\) | ||||
−0.190109 | + | 0.981763i | \(0.560884\pi\) | |||||||
\(252\) | −4.74978e23 | −7.30076 | ||||||||
\(253\) | −4.41142e22 | −0.653030 | ||||||||
\(254\) | 6.53207e22 | 0.931388 | ||||||||
\(255\) | −7.20863e22 | −0.990196 | ||||||||
\(256\) | −1.10591e23 | −1.46366 | ||||||||
\(257\) | −4.69045e21 | −0.0598205 | −0.0299102 | − | 0.999553i | \(-0.509522\pi\) | ||||
−0.0299102 | + | 0.999553i | \(0.509522\pi\) | |||||||
\(258\) | −1.34946e23 | −1.65872 | ||||||||
\(259\) | −3.49924e22 | −0.414597 | ||||||||
\(260\) | 1.57386e22 | 0.179770 | ||||||||
\(261\) | −2.10398e23 | −2.31716 | ||||||||
\(262\) | 6.48826e22 | 0.689074 | ||||||||
\(263\) | 1.60562e23 | 1.64461 | 0.822303 | − | 0.569049i | \(-0.192689\pi\) | ||||
0.822303 | + | 0.569049i | \(0.192689\pi\) | |||||||
\(264\) | 1.54147e23 | 1.52299 | ||||||||
\(265\) | 4.86601e22 | 0.463807 | ||||||||
\(266\) | −2.02590e23 | −1.86313 | ||||||||
\(267\) | −1.49836e23 | −1.32972 | ||||||||
\(268\) | 4.80041e23 | 4.11148 | ||||||||
\(269\) | −4.37427e22 | −0.361626 | −0.180813 | − | 0.983518i | \(-0.557873\pi\) | ||||
−0.180813 | + | 0.983518i | \(0.557873\pi\) | |||||||
\(270\) | −2.32729e23 | −1.85736 | ||||||||
\(271\) | −2.05602e22 | −0.158423 | −0.0792117 | − | 0.996858i | \(-0.525240\pi\) | ||||
−0.0792117 | + | 0.996858i | \(0.525240\pi\) | |||||||
\(272\) | −2.65540e23 | −1.97572 | ||||||||
\(273\) | −4.77498e22 | −0.343105 | ||||||||
\(274\) | −1.00268e23 | −0.695875 | ||||||||
\(275\) | −3.36116e22 | −0.225335 | ||||||||
\(276\) | 1.11453e24 | 7.21865 | ||||||||
\(277\) | −2.73950e23 | −1.71440 | −0.857202 | − | 0.514980i | \(-0.827799\pi\) | ||||
−0.857202 | + | 0.514980i | \(0.827799\pi\) | |||||||
\(278\) | 4.13749e23 | 2.50214 | ||||||||
\(279\) | −1.41955e23 | −0.829678 | ||||||||
\(280\) | −4.24253e23 | −2.39676 | ||||||||
\(281\) | 1.26702e23 | 0.691947 | 0.345973 | − | 0.938244i | \(-0.387549\pi\) | ||||
0.345973 | + | 0.938244i | \(0.387549\pi\) | |||||||
\(282\) | 8.67833e22 | 0.458215 | ||||||||
\(283\) | 1.68047e23 | 0.857948 | 0.428974 | − | 0.903317i | \(-0.358875\pi\) | ||||
0.428974 | + | 0.903317i | \(0.358875\pi\) | |||||||
\(284\) | 6.15332e23 | 3.03798 | ||||||||
\(285\) | −1.41928e23 | −0.677709 | ||||||||
\(286\) | 1.79488e22 | 0.0829007 | ||||||||
\(287\) | −4.82694e23 | −2.15672 | ||||||||
\(288\) | −6.46274e23 | −2.79375 | ||||||||
\(289\) | −3.05033e22 | −0.127590 | ||||||||
\(290\) | −3.28756e23 | −1.33074 | ||||||||
\(291\) | −6.03566e23 | −2.36451 | ||||||||
\(292\) | −1.18348e24 | −4.48770 | ||||||||
\(293\) | 2.99058e22 | 0.109778 | 0.0548888 | − | 0.998492i | \(-0.482520\pi\) | ||||
0.0548888 | + | 0.998492i | \(0.482520\pi\) | |||||||
\(294\) | 1.36778e24 | 4.86089 | ||||||||
\(295\) | −1.67580e23 | −0.576652 | ||||||||
\(296\) | −1.89964e23 | −0.632996 | ||||||||
\(297\) | −1.85816e23 | −0.599649 | ||||||||
\(298\) | −5.27321e22 | −0.164824 | ||||||||
\(299\) | 7.41846e22 | 0.224614 | ||||||||
\(300\) | 8.49187e23 | 2.49087 | ||||||||
\(301\) | 2.96541e23 | 0.842758 | ||||||||
\(302\) | 4.67000e23 | 1.28603 | ||||||||
\(303\) | 1.08461e24 | 2.89447 | ||||||||
\(304\) | −5.22814e23 | −1.35222 | ||||||||
\(305\) | 3.90939e23 | 0.980077 | ||||||||
\(306\) | 1.37518e24 | 3.34200 | ||||||||
\(307\) | −4.63550e23 | −1.09215 | −0.546074 | − | 0.837737i | \(-0.683878\pi\) | ||||
−0.546074 | + | 0.837737i | \(0.683878\pi\) | |||||||
\(308\) | −5.92566e23 | −1.35365 | ||||||||
\(309\) | −1.20695e24 | −2.67353 | ||||||||
\(310\) | −2.21810e23 | −0.476480 | ||||||||
\(311\) | 8.89663e23 | 1.85354 | 0.926770 | − | 0.375630i | \(-0.122574\pi\) | ||||
0.926770 | + | 0.375630i | \(0.122574\pi\) | |||||||
\(312\) | −2.59221e23 | −0.523843 | ||||||||
\(313\) | −3.71088e23 | −0.727454 | −0.363727 | − | 0.931506i | \(-0.618496\pi\) | ||||
−0.363727 | + | 0.931506i | \(0.618496\pi\) | |||||||
\(314\) | −1.03083e24 | −1.96045 | ||||||||
\(315\) | 1.04445e24 | 1.92724 | ||||||||
\(316\) | 1.79244e24 | 3.20934 | ||||||||
\(317\) | 3.52777e23 | 0.612967 | 0.306483 | − | 0.951876i | \(-0.400848\pi\) | ||||
0.306483 | + | 0.951876i | \(0.400848\pi\) | |||||||
\(318\) | −1.40203e24 | −2.36429 | ||||||||
\(319\) | −2.62485e23 | −0.429629 | ||||||||
\(320\) | −1.89391e23 | −0.300908 | ||||||||
\(321\) | −1.37110e24 | −2.11480 | ||||||||
\(322\) | −3.49827e24 | −5.23869 | ||||||||
\(323\) | 4.10645e23 | 0.597094 | ||||||||
\(324\) | 1.45493e24 | 2.05430 | ||||||||
\(325\) | 5.65230e22 | 0.0775056 | ||||||||
\(326\) | −5.39960e23 | −0.719108 | ||||||||
\(327\) | 3.31427e23 | 0.428730 | ||||||||
\(328\) | −2.62041e24 | −3.29282 | ||||||||
\(329\) | −1.90704e23 | −0.232808 | ||||||||
\(330\) | −5.92962e23 | −0.703307 | ||||||||
\(331\) | −1.28705e24 | −1.48330 | −0.741650 | − | 0.670787i | \(-0.765957\pi\) | ||||
−0.741650 | + | 0.670787i | \(0.765957\pi\) | |||||||
\(332\) | 6.45746e23 | 0.723186 | ||||||||
\(333\) | 4.67663e23 | 0.508995 | ||||||||
\(334\) | 8.41010e23 | 0.889631 | ||||||||
\(335\) | −1.05558e24 | −1.08534 | ||||||||
\(336\) | 5.81087e24 | 5.80788 | ||||||||
\(337\) | 1.61437e24 | 1.56862 | 0.784311 | − | 0.620368i | \(-0.213017\pi\) | ||||
0.784311 | + | 0.620368i | \(0.213017\pi\) | |||||||
\(338\) | 1.90277e24 | 1.79754 | ||||||||
\(339\) | 7.66367e23 | 0.703947 | ||||||||
\(340\) | 1.50437e24 | 1.34370 | ||||||||
\(341\) | −1.77098e23 | −0.153832 | ||||||||
\(342\) | 2.70755e24 | 2.28733 | ||||||||
\(343\) | −1.06324e24 | −0.873648 | ||||||||
\(344\) | 1.60984e24 | 1.28670 | ||||||||
\(345\) | −2.45078e24 | −1.90556 | ||||||||
\(346\) | −4.68633e24 | −3.54495 | ||||||||
\(347\) | −2.17772e23 | −0.160277 | −0.0801387 | − | 0.996784i | \(-0.525536\pi\) | ||||
−0.0801387 | + | 0.996784i | \(0.525536\pi\) | |||||||
\(348\) | 6.63161e24 | 4.74915 | ||||||||
\(349\) | −2.32960e24 | −1.62345 | −0.811727 | − | 0.584037i | \(-0.801472\pi\) | ||||
−0.811727 | + | 0.584037i | \(0.801472\pi\) | |||||||
\(350\) | −2.66542e24 | −1.80767 | ||||||||
\(351\) | 3.12477e23 | 0.206253 | ||||||||
\(352\) | −8.06269e23 | −0.517994 | ||||||||
\(353\) | 5.69515e23 | 0.356160 | 0.178080 | − | 0.984016i | \(-0.443011\pi\) | ||||
0.178080 | + | 0.984016i | \(0.443011\pi\) | |||||||
\(354\) | 4.82845e24 | 2.93952 | ||||||||
\(355\) | −1.35308e24 | −0.801961 | ||||||||
\(356\) | 3.12692e24 | 1.80444 | ||||||||
\(357\) | −4.56416e24 | −2.56456 | ||||||||
\(358\) | 6.18036e22 | 0.0338162 | ||||||||
\(359\) | 1.74335e23 | 0.0928937 | 0.0464469 | − | 0.998921i | \(-0.485210\pi\) | ||||
0.0464469 | + | 0.998921i | \(0.485210\pi\) | |||||||
\(360\) | 5.67001e24 | 2.94246 | ||||||||
\(361\) | −1.16991e24 | −0.591338 | ||||||||
\(362\) | −2.82781e24 | −1.39225 | ||||||||
\(363\) | 3.11346e24 | 1.49324 | ||||||||
\(364\) | 9.96489e23 | 0.465596 | ||||||||
\(365\) | 2.60240e24 | 1.18465 | ||||||||
\(366\) | −1.12640e25 | −4.99601 | ||||||||
\(367\) | 1.48756e24 | 0.642907 | 0.321454 | − | 0.946925i | \(-0.395829\pi\) | ||||
0.321454 | + | 0.946925i | \(0.395829\pi\) | |||||||
\(368\) | −9.02781e24 | −3.80214 | ||||||||
\(369\) | 6.45105e24 | 2.64777 | ||||||||
\(370\) | 7.30743e23 | 0.292313 | ||||||||
\(371\) | 3.08092e24 | 1.20124 | ||||||||
\(372\) | 4.47432e24 | 1.70047 | ||||||||
\(373\) | −2.27107e24 | −0.841390 | −0.420695 | − | 0.907202i | \(-0.638214\pi\) | ||||
−0.420695 | + | 0.907202i | \(0.638214\pi\) | |||||||
\(374\) | 1.71563e24 | 0.619646 | ||||||||
\(375\) | −4.87794e24 | −1.71767 | ||||||||
\(376\) | −1.03528e24 | −0.355445 | ||||||||
\(377\) | 4.41408e23 | 0.147774 | ||||||||
\(378\) | −1.47353e25 | −4.81046 | ||||||||
\(379\) | 1.06621e24 | 0.339445 | 0.169723 | − | 0.985492i | \(-0.445713\pi\) | ||||
0.169723 | + | 0.985492i | \(0.445713\pi\) | |||||||
\(380\) | 2.96190e24 | 0.919656 | ||||||||
\(381\) | 2.89741e24 | 0.877450 | ||||||||
\(382\) | −1.33986e24 | −0.395783 | ||||||||
\(383\) | −1.11067e24 | −0.320034 | −0.160017 | − | 0.987114i | \(-0.551155\pi\) | ||||
−0.160017 | + | 0.987114i | \(0.551155\pi\) | |||||||
\(384\) | −3.26896e24 | −0.918888 | ||||||||
\(385\) | 1.30302e24 | 0.357333 | ||||||||
\(386\) | 9.53361e24 | 2.55081 | ||||||||
\(387\) | −3.96318e24 | −1.03464 | ||||||||
\(388\) | 1.25958e25 | 3.20866 | ||||||||
\(389\) | 3.99560e24 | 0.993255 | 0.496627 | − | 0.867964i | \(-0.334572\pi\) | ||||
0.496627 | + | 0.867964i | \(0.334572\pi\) | |||||||
\(390\) | 9.97155e23 | 0.241907 | ||||||||
\(391\) | 7.09091e24 | 1.67889 | ||||||||
\(392\) | −1.63168e25 | −3.77067 | ||||||||
\(393\) | 2.87798e24 | 0.649169 | ||||||||
\(394\) | −4.27189e24 | −0.940602 | ||||||||
\(395\) | −3.94145e24 | −0.847196 | ||||||||
\(396\) | 7.91947e24 | 1.66185 | ||||||||
\(397\) | 7.01228e24 | 1.43664 | 0.718322 | − | 0.695711i | \(-0.244910\pi\) | ||||
0.718322 | + | 0.695711i | \(0.244910\pi\) | |||||||
\(398\) | −1.16437e25 | −2.32917 | ||||||||
\(399\) | −8.98622e24 | −1.75523 | ||||||||
\(400\) | −6.87850e24 | −1.31197 | ||||||||
\(401\) | 3.42848e24 | 0.638602 | 0.319301 | − | 0.947653i | \(-0.396552\pi\) | ||||
0.319301 | + | 0.947653i | \(0.396552\pi\) | |||||||
\(402\) | 3.04142e25 | 5.53259 | ||||||||
\(403\) | 2.97816e23 | 0.0529116 | ||||||||
\(404\) | −2.26346e25 | −3.92781 | ||||||||
\(405\) | −3.19930e24 | −0.542290 | ||||||||
\(406\) | −2.08152e25 | −3.44654 | ||||||||
\(407\) | 5.83441e23 | 0.0943735 | ||||||||
\(408\) | −2.47775e25 | −3.91549 | ||||||||
\(409\) | 7.94943e24 | 1.22734 | 0.613670 | − | 0.789563i | \(-0.289693\pi\) | ||||
0.613670 | + | 0.789563i | \(0.289693\pi\) | |||||||
\(410\) | 1.00800e25 | 1.52060 | ||||||||
\(411\) | −4.44755e24 | −0.655576 | ||||||||
\(412\) | 2.51879e25 | 3.62800 | ||||||||
\(413\) | −1.06104e25 | −1.49350 | ||||||||
\(414\) | 4.67533e25 | 6.43146 | ||||||||
\(415\) | −1.41996e24 | −0.190905 | ||||||||
\(416\) | 1.35586e24 | 0.178168 | ||||||||
\(417\) | 1.83525e25 | 2.35724 | ||||||||
\(418\) | 3.37785e24 | 0.424098 | ||||||||
\(419\) | 4.64557e24 | 0.570171 | 0.285086 | − | 0.958502i | \(-0.407978\pi\) | ||||
0.285086 | + | 0.958502i | \(0.407978\pi\) | |||||||
\(420\) | −3.29203e25 | −3.94999 | ||||||||
\(421\) | −1.17976e25 | −1.38393 | −0.691965 | − | 0.721931i | \(-0.743255\pi\) | ||||
−0.691965 | + | 0.721931i | \(0.743255\pi\) | |||||||
\(422\) | −8.01573e24 | −0.919337 | ||||||||
\(423\) | 2.54870e24 | 0.285815 | ||||||||
\(424\) | 1.67255e25 | 1.83402 | ||||||||
\(425\) | 5.40273e24 | 0.579320 | ||||||||
\(426\) | 3.89859e25 | 4.08805 | ||||||||
\(427\) | 2.47524e25 | 2.53835 | ||||||||
\(428\) | 2.86133e25 | 2.86981 | ||||||||
\(429\) | 7.96150e23 | 0.0780999 | ||||||||
\(430\) | −6.19263e24 | −0.594189 | ||||||||
\(431\) | 8.47412e24 | 0.795354 | 0.397677 | − | 0.917525i | \(-0.369816\pi\) | ||||
0.397677 | + | 0.917525i | \(0.369816\pi\) | |||||||
\(432\) | −3.80266e25 | −3.49134 | ||||||||
\(433\) | −8.51618e24 | −0.764909 | −0.382455 | − | 0.923974i | \(-0.624921\pi\) | ||||
−0.382455 | + | 0.923974i | \(0.624921\pi\) | |||||||
\(434\) | −1.40439e25 | −1.23406 | ||||||||
\(435\) | −1.45825e25 | −1.25367 | ||||||||
\(436\) | −6.91653e24 | −0.581790 | ||||||||
\(437\) | 1.39611e25 | 1.14907 | ||||||||
\(438\) | −7.49823e25 | −6.03886 | ||||||||
\(439\) | −6.00148e24 | −0.472983 | −0.236492 | − | 0.971634i | \(-0.575998\pi\) | ||||
−0.236492 | + | 0.971634i | \(0.575998\pi\) | |||||||
\(440\) | 7.07372e24 | 0.545566 | ||||||||
\(441\) | 4.01696e25 | 3.03201 | ||||||||
\(442\) | −2.88509e24 | −0.213132 | ||||||||
\(443\) | −1.75866e25 | −1.27159 | −0.635795 | − | 0.771858i | \(-0.719328\pi\) | ||||
−0.635795 | + | 0.771858i | \(0.719328\pi\) | |||||||
\(444\) | −1.47405e25 | −1.04321 | ||||||||
\(445\) | −6.87590e24 | −0.476332 | ||||||||
\(446\) | 4.16680e25 | 2.82567 | ||||||||
\(447\) | −2.33902e24 | −0.155279 | ||||||||
\(448\) | −1.19913e25 | −0.779336 | ||||||||
\(449\) | 1.04881e25 | 0.667352 | 0.333676 | − | 0.942688i | \(-0.391711\pi\) | ||||
0.333676 | + | 0.942688i | \(0.391711\pi\) | |||||||
\(450\) | 3.56225e25 | 2.21924 | ||||||||
\(451\) | 8.04811e24 | 0.490927 | ||||||||
\(452\) | −1.59933e25 | −0.955261 | ||||||||
\(453\) | 2.07146e25 | 1.21156 | ||||||||
\(454\) | −1.59472e25 | −0.913385 | ||||||||
\(455\) | −2.19122e24 | −0.122907 | ||||||||
\(456\) | −4.87837e25 | −2.67984 | ||||||||
\(457\) | −1.92079e25 | −1.03342 | −0.516710 | − | 0.856161i | \(-0.672843\pi\) | ||||
−0.516710 | + | 0.856161i | \(0.672843\pi\) | |||||||
\(458\) | −3.59903e25 | −1.89655 | ||||||||
\(459\) | 2.98681e25 | 1.54165 | ||||||||
\(460\) | 5.11453e25 | 2.58587 | ||||||||
\(461\) | 3.39478e22 | 0.00168133 | 0.000840666 | − | 1.00000i | \(-0.499732\pi\) | ||||
0.000840666 | 1.00000i | \(0.499732\pi\) | ||||||||
\(462\) | −3.75435e25 | −1.82153 | ||||||||
\(463\) | −4.51089e24 | −0.214409 | −0.107205 | − | 0.994237i | \(-0.534190\pi\) | ||||
−0.107205 | + | 0.994237i | \(0.534190\pi\) | |||||||
\(464\) | −5.37167e25 | −2.50143 | ||||||||
\(465\) | −9.83875e24 | −0.448887 | ||||||||
\(466\) | 3.14029e24 | 0.140379 | ||||||||
\(467\) | −2.71051e25 | −1.18725 | −0.593623 | − | 0.804743i | \(-0.702303\pi\) | ||||
−0.593623 | + | 0.804743i | \(0.702303\pi\) | |||||||
\(468\) | −1.33178e25 | −0.571605 | ||||||||
\(469\) | −6.68343e25 | −2.81098 | ||||||||
\(470\) | 3.98244e24 | 0.164142 | ||||||||
\(471\) | −4.57242e25 | −1.84692 | ||||||||
\(472\) | −5.76008e25 | −2.28023 | ||||||||
\(473\) | −4.94433e24 | −0.191834 | ||||||||
\(474\) | 1.13564e26 | 4.31864 | ||||||||
\(475\) | 1.06373e25 | 0.396498 | ||||||||
\(476\) | 9.52491e25 | 3.48013 | ||||||||
\(477\) | −4.11756e25 | −1.47474 | ||||||||
\(478\) | −8.08684e25 | −2.83932 | ||||||||
\(479\) | 6.93873e23 | 0.0238832 | 0.0119416 | − | 0.999929i | \(-0.496199\pi\) | ||||
0.0119416 | + | 0.999929i | \(0.496199\pi\) | |||||||
\(480\) | −4.47927e25 | −1.51152 | ||||||||
\(481\) | −9.81143e23 | −0.0324604 | ||||||||
\(482\) | 8.84639e24 | 0.286959 | ||||||||
\(483\) | −1.55172e26 | −4.93532 | ||||||||
\(484\) | −6.49746e25 | −2.02634 | ||||||||
\(485\) | −2.76974e25 | −0.847016 | ||||||||
\(486\) | −8.32371e24 | −0.249616 | ||||||||
\(487\) | 2.07702e25 | 0.610823 | 0.305412 | − | 0.952220i | \(-0.401206\pi\) | ||||
0.305412 | + | 0.952220i | \(0.401206\pi\) | |||||||
\(488\) | 1.34374e26 | 3.87548 | ||||||||
\(489\) | −2.39508e25 | −0.677464 | ||||||||
\(490\) | 6.27666e25 | 1.74127 | ||||||||
\(491\) | 6.25793e24 | 0.170277 | 0.0851386 | − | 0.996369i | \(-0.472867\pi\) | ||||
0.0851386 | + | 0.996369i | \(0.472867\pi\) | |||||||
\(492\) | −2.03333e26 | −5.42675 | ||||||||
\(493\) | 4.21919e25 | 1.10455 | ||||||||
\(494\) | −5.68036e24 | −0.145871 | ||||||||
\(495\) | −1.74144e25 | −0.438692 | ||||||||
\(496\) | −3.62424e25 | −0.895657 | ||||||||
\(497\) | −8.56703e25 | −2.07704 | ||||||||
\(498\) | 4.09128e25 | 0.973152 | ||||||||
\(499\) | 5.68771e25 | 1.32734 | 0.663670 | − | 0.748025i | \(-0.268998\pi\) | ||||
0.663670 | + | 0.748025i | \(0.268998\pi\) | |||||||
\(500\) | 1.01798e26 | 2.33089 | ||||||||
\(501\) | 3.73044e25 | 0.838111 | ||||||||
\(502\) | 3.14943e25 | 0.694299 | ||||||||
\(503\) | 3.93303e25 | 0.850808 | 0.425404 | − | 0.905003i | \(-0.360132\pi\) | ||||
0.425404 | + | 0.905003i | \(0.360132\pi\) | |||||||
\(504\) | 3.58998e26 | 7.62082 | ||||||||
\(505\) | 4.97722e25 | 1.03686 | ||||||||
\(506\) | 5.83279e25 | 1.19247 | ||||||||
\(507\) | 8.44006e25 | 1.69344 | ||||||||
\(508\) | −6.04659e25 | −1.19071 | ||||||||
\(509\) | −4.33876e25 | −0.838585 | −0.419292 | − | 0.907851i | \(-0.637722\pi\) | ||||
−0.419292 | + | 0.907851i | \(0.637722\pi\) | |||||||
\(510\) | 9.53128e25 | 1.80815 | ||||||||
\(511\) | 1.64771e26 | 3.06820 | ||||||||
\(512\) | 1.17001e26 | 2.13858 | ||||||||
\(513\) | 5.88063e25 | 1.05514 | ||||||||
\(514\) | 6.20173e24 | 0.109235 | ||||||||
\(515\) | −5.53866e25 | −0.957714 | ||||||||
\(516\) | 1.24917e26 | 2.12055 | ||||||||
\(517\) | 3.17967e24 | 0.0529934 | ||||||||
\(518\) | 4.62671e25 | 0.757076 | ||||||||
\(519\) | −2.07870e26 | −3.33966 | ||||||||
\(520\) | −1.18955e25 | −0.187651 | ||||||||
\(521\) | −8.39328e25 | −1.30009 | −0.650045 | − | 0.759896i | \(-0.725250\pi\) | ||||
−0.650045 | + | 0.759896i | \(0.725250\pi\) | |||||||
\(522\) | 2.78189e26 | 4.23126 | ||||||||
\(523\) | 4.20105e25 | 0.627468 | 0.313734 | − | 0.949511i | \(-0.398420\pi\) | ||||
0.313734 | + | 0.949511i | \(0.398420\pi\) | |||||||
\(524\) | −6.00603e25 | −0.880928 | ||||||||
\(525\) | −1.18229e26 | −1.70298 | ||||||||
\(526\) | −2.12295e26 | −3.00314 | ||||||||
\(527\) | 2.84667e25 | 0.395491 | ||||||||
\(528\) | −9.68866e25 | −1.32203 | ||||||||
\(529\) | 1.66461e26 | 2.23091 | ||||||||
\(530\) | −6.43386e25 | −0.846936 | ||||||||
\(531\) | 1.41804e26 | 1.83355 | ||||||||
\(532\) | 1.87533e26 | 2.38186 | ||||||||
\(533\) | −1.35341e25 | −0.168858 | ||||||||
\(534\) | 1.98114e26 | 2.42813 | ||||||||
\(535\) | −6.29189e25 | −0.757566 | ||||||||
\(536\) | −3.62825e26 | −4.29172 | ||||||||
\(537\) | 2.74140e24 | 0.0318579 | ||||||||
\(538\) | 5.78368e25 | 0.660348 | ||||||||
\(539\) | 5.01142e25 | 0.562170 | ||||||||
\(540\) | 2.15432e26 | 2.37449 | ||||||||
\(541\) | 2.48081e25 | 0.268670 | 0.134335 | − | 0.990936i | \(-0.457110\pi\) | ||||
0.134335 | + | 0.990936i | \(0.457110\pi\) | |||||||
\(542\) | 2.71848e25 | 0.289290 | ||||||||
\(543\) | −1.25432e26 | −1.31163 | ||||||||
\(544\) | 1.29600e26 | 1.33172 | ||||||||
\(545\) | 1.52090e25 | 0.153580 | ||||||||
\(546\) | 6.31350e25 | 0.626527 | ||||||||
\(547\) | −1.72124e26 | −1.67865 | −0.839327 | − | 0.543626i | \(-0.817051\pi\) | ||||
−0.839327 | + | 0.543626i | \(0.817051\pi\) | |||||||
\(548\) | 9.28156e25 | 0.889622 | ||||||||
\(549\) | −3.30808e26 | −3.11629 | ||||||||
\(550\) | 4.44414e25 | 0.411474 | ||||||||
\(551\) | 8.30703e25 | 0.755971 | ||||||||
\(552\) | −8.42384e26 | −7.53510 | ||||||||
\(553\) | −2.49554e26 | −2.19420 | ||||||||
\(554\) | 3.62217e26 | 3.13059 | ||||||||
\(555\) | 3.24134e25 | 0.275385 | ||||||||
\(556\) | −3.82998e26 | −3.19879 | ||||||||
\(557\) | 1.17024e26 | 0.960843 | 0.480421 | − | 0.877038i | \(-0.340484\pi\) | ||||
0.480421 | + | 0.877038i | \(0.340484\pi\) | |||||||
\(558\) | 1.87693e26 | 1.51504 | ||||||||
\(559\) | 8.31462e24 | 0.0659827 | ||||||||
\(560\) | 2.66658e26 | 2.08050 | ||||||||
\(561\) | 7.60997e25 | 0.583762 | ||||||||
\(562\) | −1.67525e26 | −1.26353 | ||||||||
\(563\) | −2.68438e26 | −1.99074 | −0.995368 | − | 0.0961344i | \(-0.969352\pi\) | ||||
−0.995368 | + | 0.0961344i | \(0.969352\pi\) | |||||||
\(564\) | −8.03333e25 | −0.585793 | ||||||||
\(565\) | 3.51682e25 | 0.252168 | ||||||||
\(566\) | −2.22193e26 | −1.56666 | ||||||||
\(567\) | −2.02564e26 | −1.40450 | ||||||||
\(568\) | −4.65080e26 | −3.17117 | ||||||||
\(569\) | −1.61116e25 | −0.108037 | −0.0540184 | − | 0.998540i | \(-0.517203\pi\) | ||||
−0.0540184 | + | 0.998540i | \(0.517203\pi\) | |||||||
\(570\) | 1.87658e26 | 1.23753 | ||||||||
\(571\) | −2.06594e26 | −1.33991 | −0.669953 | − | 0.742403i | \(-0.733686\pi\) | ||||
−0.669953 | + | 0.742403i | \(0.733686\pi\) | |||||||
\(572\) | −1.66148e25 | −0.105982 | ||||||||
\(573\) | −5.94317e25 | −0.372863 | ||||||||
\(574\) | 6.38219e26 | 3.93828 | ||||||||
\(575\) | 1.83682e26 | 1.11486 | ||||||||
\(576\) | 1.60260e26 | 0.956778 | ||||||||
\(577\) | 9.57142e25 | 0.562090 | 0.281045 | − | 0.959695i | \(-0.409319\pi\) | ||||
0.281045 | + | 0.959695i | \(0.409319\pi\) | |||||||
\(578\) | 4.03316e25 | 0.232987 | ||||||||
\(579\) | 4.22879e26 | 2.40309 | ||||||||
\(580\) | 3.04322e26 | 1.70124 | ||||||||
\(581\) | −8.99047e25 | −0.494435 | ||||||||
\(582\) | 7.98037e26 | 4.31772 | ||||||||
\(583\) | −5.13693e25 | −0.273434 | ||||||||
\(584\) | 8.94498e26 | 4.68444 | ||||||||
\(585\) | 2.92850e25 | 0.150891 | ||||||||
\(586\) | −3.95416e25 | −0.200460 | ||||||||
\(587\) | 3.14607e25 | 0.156930 | 0.0784651 | − | 0.996917i | \(-0.474998\pi\) | ||||
0.0784651 | + | 0.996917i | \(0.474998\pi\) | |||||||
\(588\) | −1.26612e27 | −6.21427 | ||||||||
\(589\) | 5.60471e25 | 0.270681 | ||||||||
\(590\) | 2.21575e26 | 1.05300 | ||||||||
\(591\) | −1.89487e26 | −0.886132 | ||||||||
\(592\) | 1.19399e26 | 0.549472 | ||||||||
\(593\) | −6.01991e25 | −0.272628 | −0.136314 | − | 0.990666i | \(-0.543526\pi\) | ||||
−0.136314 | + | 0.990666i | \(0.543526\pi\) | |||||||
\(594\) | 2.45687e26 | 1.09499 | ||||||||
\(595\) | −2.09447e26 | −0.918677 | ||||||||
\(596\) | 4.88129e25 | 0.210715 | ||||||||
\(597\) | −5.16475e26 | −2.19428 | ||||||||
\(598\) | −9.80871e25 | −0.410157 | ||||||||
\(599\) | −3.12461e26 | −1.28600 | −0.643000 | − | 0.765866i | \(-0.722310\pi\) | ||||
−0.643000 | + | 0.765866i | \(0.722310\pi\) | |||||||
\(600\) | −6.41832e26 | −2.60007 | ||||||||
\(601\) | 9.39020e24 | 0.0374427 | 0.0187214 | − | 0.999825i | \(-0.494040\pi\) | ||||
0.0187214 | + | 0.999825i | \(0.494040\pi\) | |||||||
\(602\) | −3.92087e26 | −1.53892 | ||||||||
\(603\) | 8.93220e26 | 3.45099 | ||||||||
\(604\) | −4.32291e26 | −1.64409 | ||||||||
\(605\) | 1.42875e26 | 0.534910 | ||||||||
\(606\) | −1.43407e27 | −5.28544 | ||||||||
\(607\) | 4.26351e26 | 1.54695 | 0.773473 | − | 0.633830i | \(-0.218518\pi\) | ||||
0.773473 | + | 0.633830i | \(0.218518\pi\) | |||||||
\(608\) | 2.55165e26 | 0.911457 | ||||||||
\(609\) | −9.23293e26 | −3.24695 | ||||||||
\(610\) | −5.16901e26 | −1.78967 | ||||||||
\(611\) | −5.34709e24 | −0.0182274 | ||||||||
\(612\) | −1.27298e27 | −4.27249 | ||||||||
\(613\) | −4.29268e26 | −1.41858 | −0.709291 | − | 0.704916i | \(-0.750985\pi\) | ||||
−0.709291 | + | 0.704916i | \(0.750985\pi\) | |||||||
\(614\) | 6.12907e26 | 1.99432 | ||||||||
\(615\) | 4.47117e26 | 1.43254 | ||||||||
\(616\) | 4.47873e26 | 1.41299 | ||||||||
\(617\) | −2.23620e26 | −0.694706 | −0.347353 | − | 0.937735i | \(-0.612919\pi\) | ||||
−0.347353 | + | 0.937735i | \(0.612919\pi\) | |||||||
\(618\) | 1.59584e27 | 4.88201 | ||||||||
\(619\) | −4.50989e26 | −1.35864 | −0.679321 | − | 0.733841i | \(-0.737726\pi\) | ||||
−0.679321 | + | 0.733841i | \(0.737726\pi\) | |||||||
\(620\) | 2.05324e26 | 0.609143 | ||||||||
\(621\) | 1.01545e27 | 2.96681 | ||||||||
\(622\) | −1.17631e27 | −3.38466 | ||||||||
\(623\) | −4.35349e26 | −1.23368 | ||||||||
\(624\) | 1.62929e26 | 0.454722 | ||||||||
\(625\) | 1.79474e24 | 0.00493335 | ||||||||
\(626\) | 4.90653e26 | 1.32837 | ||||||||
\(627\) | 1.49830e26 | 0.399538 | ||||||||
\(628\) | 9.54216e26 | 2.50628 | ||||||||
\(629\) | −9.37823e25 | −0.242627 | ||||||||
\(630\) | −1.38097e27 | −3.51924 | ||||||||
\(631\) | −1.55016e26 | −0.389133 | −0.194566 | − | 0.980889i | \(-0.562330\pi\) | ||||
−0.194566 | + | 0.980889i | \(0.562330\pi\) | |||||||
\(632\) | −1.35476e27 | −3.35004 | ||||||||
\(633\) | −3.55551e26 | −0.866098 | ||||||||
\(634\) | −4.66443e26 | −1.11931 | ||||||||
\(635\) | 1.32961e26 | 0.314321 | ||||||||
\(636\) | 1.29783e27 | 3.02256 | ||||||||
\(637\) | −8.42745e25 | −0.193362 | ||||||||
\(638\) | 3.47059e26 | 0.784525 | ||||||||
\(639\) | 1.14496e27 | 2.54995 | ||||||||
\(640\) | −1.50011e26 | −0.329164 | ||||||||
\(641\) | −5.61369e26 | −1.21366 | −0.606830 | − | 0.794832i | \(-0.707559\pi\) | ||||
−0.606830 | + | 0.794832i | \(0.707559\pi\) | |||||||
\(642\) | 1.81287e27 | 3.86174 | ||||||||
\(643\) | 4.02825e26 | 0.845496 | 0.422748 | − | 0.906247i | \(-0.361065\pi\) | ||||
0.422748 | + | 0.906247i | \(0.361065\pi\) | |||||||
\(644\) | 3.23827e27 | 6.69726 | ||||||||
\(645\) | −2.74684e26 | −0.559779 | ||||||||
\(646\) | −5.42956e26 | −1.09032 | ||||||||
\(647\) | −5.60723e26 | −1.10958 | −0.554789 | − | 0.831991i | \(-0.687201\pi\) | ||||
−0.554789 | + | 0.831991i | \(0.687201\pi\) | |||||||
\(648\) | −1.09966e27 | −2.14436 | ||||||||
\(649\) | 1.76910e26 | 0.339961 | ||||||||
\(650\) | −7.47348e25 | −0.141529 | ||||||||
\(651\) | −6.22942e26 | −1.16259 | ||||||||
\(652\) | 4.99828e26 | 0.919324 | ||||||||
\(653\) | 4.04392e26 | 0.733039 | 0.366520 | − | 0.930410i | \(-0.380549\pi\) | ||||
0.366520 | + | 0.930410i | \(0.380549\pi\) | |||||||
\(654\) | −4.38214e26 | −0.782884 | ||||||||
\(655\) | 1.32069e26 | 0.232546 | ||||||||
\(656\) | 1.64702e27 | 2.85833 | ||||||||
\(657\) | −2.20212e27 | −3.76678 | ||||||||
\(658\) | 2.52149e26 | 0.425120 | ||||||||
\(659\) | 1.30756e26 | 0.217294 | 0.108647 | − | 0.994080i | \(-0.465348\pi\) | ||||
0.108647 | + | 0.994080i | \(0.465348\pi\) | |||||||
\(660\) | 5.48892e26 | 0.899123 | ||||||||
\(661\) | 3.84863e26 | 0.621430 | 0.310715 | − | 0.950503i | \(-0.399432\pi\) | ||||
0.310715 | + | 0.950503i | \(0.399432\pi\) | |||||||
\(662\) | 1.70174e27 | 2.70858 | ||||||||
\(663\) | −1.27973e26 | −0.200789 | ||||||||
\(664\) | −4.88067e26 | −0.754889 | ||||||||
\(665\) | −4.12373e26 | −0.628760 | ||||||||
\(666\) | −6.18346e26 | −0.929451 | ||||||||
\(667\) | 1.43444e27 | 2.12562 | ||||||||
\(668\) | −7.78504e26 | −1.13732 | ||||||||
\(669\) | 1.84825e27 | 2.66203 | ||||||||
\(670\) | 1.39569e27 | 1.98189 | ||||||||
\(671\) | −4.12704e26 | −0.577797 | ||||||||
\(672\) | −2.83605e27 | −3.91477 | ||||||||
\(673\) | 2.55951e26 | 0.348348 | 0.174174 | − | 0.984715i | \(-0.444274\pi\) | ||||
0.174174 | + | 0.984715i | \(0.444274\pi\) | |||||||
\(674\) | −2.13452e27 | −2.86439 | ||||||||
\(675\) | 7.73697e26 | 1.02373 | ||||||||
\(676\) | −1.76135e27 | −2.29801 | ||||||||
\(677\) | 1.04099e27 | 1.33923 | 0.669615 | − | 0.742708i | \(-0.266459\pi\) | ||||
0.669615 | + | 0.742708i | \(0.266459\pi\) | |||||||
\(678\) | −1.01329e27 | −1.28544 | ||||||||
\(679\) | −1.75366e27 | −2.19373 | ||||||||
\(680\) | −1.13703e27 | −1.40261 | ||||||||
\(681\) | −7.07365e26 | −0.860490 | ||||||||
\(682\) | 2.34159e26 | 0.280905 | ||||||||
\(683\) | 1.44567e26 | 0.171030 | 0.0855148 | − | 0.996337i | \(-0.472747\pi\) | ||||
0.0855148 | + | 0.996337i | \(0.472747\pi\) | |||||||
\(684\) | −2.50632e27 | −2.92418 | ||||||||
\(685\) | −2.04096e26 | −0.234841 | ||||||||
\(686\) | 1.40582e27 | 1.59533 | ||||||||
\(687\) | −1.59641e27 | −1.78672 | ||||||||
\(688\) | −1.01184e27 | −1.11692 | ||||||||
\(689\) | 8.63851e25 | 0.0940495 | ||||||||
\(690\) | 3.24043e27 | 3.47966 | ||||||||
\(691\) | −6.53138e26 | −0.691773 | −0.345887 | − | 0.938276i | \(-0.612422\pi\) | ||||
−0.345887 | + | 0.938276i | \(0.612422\pi\) | |||||||
\(692\) | 4.33803e27 | 4.53194 | ||||||||
\(693\) | −1.10260e27 | −1.13619 | ||||||||
\(694\) | 2.87939e26 | 0.292675 | ||||||||
\(695\) | 8.42188e26 | 0.844410 | ||||||||
\(696\) | −5.01230e27 | −4.95735 | ||||||||
\(697\) | −1.29365e27 | −1.26214 | ||||||||
\(698\) | 3.08021e27 | 2.96451 | ||||||||
\(699\) | 1.39293e26 | 0.132250 | ||||||||
\(700\) | 2.46731e27 | 2.31096 | ||||||||
\(701\) | 3.41306e26 | 0.315372 | 0.157686 | − | 0.987489i | \(-0.449597\pi\) | ||||
0.157686 | + | 0.987489i | \(0.449597\pi\) | |||||||
\(702\) | −4.13159e26 | −0.376629 | ||||||||
\(703\) | −1.84645e26 | −0.166059 | ||||||||
\(704\) | 1.99935e26 | 0.177398 | ||||||||
\(705\) | 1.76648e26 | 0.154637 | ||||||||
\(706\) | −7.53014e26 | −0.650367 | ||||||||
\(707\) | 3.15133e27 | 2.68541 | ||||||||
\(708\) | −4.46958e27 | −3.75795 | ||||||||
\(709\) | 1.57710e27 | 1.30834 | 0.654168 | − | 0.756350i | \(-0.273019\pi\) | ||||
0.654168 | + | 0.756350i | \(0.273019\pi\) | |||||||
\(710\) | 1.78904e27 | 1.46442 | ||||||||
\(711\) | 3.33521e27 | 2.69378 | ||||||||
\(712\) | −2.36339e27 | −1.88354 | ||||||||
\(713\) | 9.67808e26 | 0.761095 | ||||||||
\(714\) | 6.03474e27 | 4.68302 | ||||||||
\(715\) | 3.65349e25 | 0.0279770 | ||||||||
\(716\) | −5.72102e25 | −0.0432314 | ||||||||
\(717\) | −3.58705e27 | −2.67489 | ||||||||
\(718\) | −2.30506e26 | −0.169629 | ||||||||
\(719\) | −1.89429e26 | −0.137569 | −0.0687846 | − | 0.997632i | \(-0.521912\pi\) | ||||
−0.0687846 | + | 0.997632i | \(0.521912\pi\) | |||||||
\(720\) | −3.56380e27 | −2.55420 | ||||||||
\(721\) | −3.50681e27 | −2.48043 | ||||||||
\(722\) | 1.54686e27 | 1.07981 | ||||||||
\(723\) | 3.92396e26 | 0.270341 | ||||||||
\(724\) | 2.61763e27 | 1.77989 | ||||||||
\(725\) | 1.09293e27 | 0.733469 | ||||||||
\(726\) | −4.11662e27 | −2.72674 | ||||||||
\(727\) | 8.93095e25 | 0.0583876 | 0.0291938 | − | 0.999574i | \(-0.490706\pi\) | ||||
0.0291938 | + | 0.999574i | \(0.490706\pi\) | |||||||
\(728\) | −7.53166e26 | −0.486007 | ||||||||
\(729\) | −1.75083e27 | −1.11515 | ||||||||
\(730\) | −3.44090e27 | −2.16324 | ||||||||
\(731\) | 7.94751e26 | 0.493192 | ||||||||
\(732\) | 1.04268e28 | 6.38701 | ||||||||
\(733\) | −2.78862e26 | −0.168617 | −0.0843084 | − | 0.996440i | \(-0.526868\pi\) | ||||
−0.0843084 | + | 0.996440i | \(0.526868\pi\) | |||||||
\(734\) | −1.96686e27 | −1.17398 | ||||||||
\(735\) | 2.78412e27 | 1.64043 | ||||||||
\(736\) | 4.40612e27 | 2.56281 | ||||||||
\(737\) | 1.11435e27 | 0.639854 | ||||||||
\(738\) | −8.52960e27 | −4.83497 | ||||||||
\(739\) | −1.85137e27 | −1.03603 | −0.518014 | − | 0.855372i | \(-0.673328\pi\) | ||||
−0.518014 | + | 0.855372i | \(0.673328\pi\) | |||||||
\(740\) | −6.76432e26 | −0.373700 | ||||||||
\(741\) | −2.51962e26 | −0.137424 | ||||||||
\(742\) | −4.07361e27 | −2.19352 | ||||||||
\(743\) | 1.53671e27 | 0.816953 | 0.408476 | − | 0.912769i | \(-0.366060\pi\) | ||||
0.408476 | + | 0.912769i | \(0.366060\pi\) | |||||||
\(744\) | −3.38178e27 | −1.77502 | ||||||||
\(745\) | −1.07337e26 | −0.0556241 | ||||||||
\(746\) | 3.00282e27 | 1.53642 | ||||||||
\(747\) | 1.20155e27 | 0.607010 | ||||||||
\(748\) | −1.58812e27 | −0.792170 | ||||||||
\(749\) | −3.98372e27 | −1.96206 | ||||||||
\(750\) | 6.44963e27 | 3.13656 | ||||||||
\(751\) | 7.02555e26 | 0.337366 | 0.168683 | − | 0.985670i | \(-0.446049\pi\) | ||||
0.168683 | + | 0.985670i | \(0.446049\pi\) | |||||||
\(752\) | 6.50708e26 | 0.308544 | ||||||||
\(753\) | 1.39698e27 | 0.654092 | ||||||||
\(754\) | −5.83632e26 | −0.269843 | ||||||||
\(755\) | 9.50582e26 | 0.434004 | ||||||||
\(756\) | 1.36401e28 | 6.14980 | ||||||||
\(757\) | 7.72841e25 | 0.0344096 | 0.0172048 | − | 0.999852i | \(-0.494523\pi\) | ||||
0.0172048 | + | 0.999852i | \(0.494523\pi\) | |||||||
\(758\) | −1.40975e27 | −0.619845 | ||||||||
\(759\) | 2.58723e27 | 1.12341 | ||||||||
\(760\) | −2.23866e27 | −0.959973 | ||||||||
\(761\) | 8.14043e26 | 0.344741 | 0.172371 | − | 0.985032i | \(-0.444857\pi\) | ||||
0.172371 | + | 0.985032i | \(0.444857\pi\) | |||||||
\(762\) | −3.83096e27 | −1.60227 | ||||||||
\(763\) | 9.62961e26 | 0.397764 | ||||||||
\(764\) | 1.24028e27 | 0.505978 | ||||||||
\(765\) | 2.79920e27 | 1.12785 | ||||||||
\(766\) | 1.46853e27 | 0.584400 | ||||||||
\(767\) | −2.97501e26 | −0.116932 | ||||||||
\(768\) | 6.48601e27 | 2.51794 | ||||||||
\(769\) | −2.37838e27 | −0.911972 | −0.455986 | − | 0.889987i | \(-0.650713\pi\) | ||||
−0.455986 | + | 0.889987i | \(0.650713\pi\) | |||||||
\(770\) | −1.72285e27 | −0.652509 | ||||||||
\(771\) | 2.75088e26 | 0.102909 | ||||||||
\(772\) | −8.82504e27 | −3.26101 | ||||||||
\(773\) | 2.34964e27 | 0.857622 | 0.428811 | − | 0.903394i | \(-0.358933\pi\) | ||||
0.428811 | + | 0.903394i | \(0.358933\pi\) | |||||||
\(774\) | 5.24013e27 | 1.88931 | ||||||||
\(775\) | 7.37396e26 | 0.262624 | ||||||||
\(776\) | −9.52014e27 | −3.34932 | ||||||||
\(777\) | 2.05226e27 | 0.713234 | ||||||||
\(778\) | −5.28299e27 | −1.81374 | ||||||||
\(779\) | −2.54703e27 | −0.863831 | ||||||||
\(780\) | −9.23043e26 | −0.309260 | ||||||||
\(781\) | 1.42841e27 | 0.472790 | ||||||||
\(782\) | −9.37563e27 | −3.06575 | ||||||||
\(783\) | 6.04208e27 | 1.95186 | ||||||||
\(784\) | 1.02557e28 | 3.27313 | ||||||||
\(785\) | −2.09826e27 | −0.661604 | ||||||||
\(786\) | −3.80527e27 | −1.18542 | ||||||||
\(787\) | 2.38408e27 | 0.733773 | 0.366886 | − | 0.930266i | \(-0.380424\pi\) | ||||
0.366886 | + | 0.930266i | \(0.380424\pi\) | |||||||
\(788\) | 3.95439e27 | 1.20249 | ||||||||
\(789\) | −9.41670e27 | −2.82922 | ||||||||
\(790\) | 5.21140e27 | 1.54703 | ||||||||
\(791\) | 2.22668e27 | 0.653103 | ||||||||
\(792\) | −5.98569e27 | −1.73470 | ||||||||
\(793\) | 6.94024e26 | 0.198737 | ||||||||
\(794\) | −9.27165e27 | −2.62339 | ||||||||
\(795\) | −2.85385e27 | −0.797890 | ||||||||
\(796\) | 1.07783e28 | 2.97766 | ||||||||
\(797\) | −4.01027e27 | −1.09476 | −0.547381 | − | 0.836884i | \(-0.684375\pi\) | ||||
−0.547381 | + | 0.836884i | \(0.684375\pi\) | |||||||
\(798\) | 1.18816e28 | 3.20514 | ||||||||
\(799\) | −5.11100e26 | −0.136242 | ||||||||
\(800\) | 3.35713e27 | 0.884327 | ||||||||
\(801\) | 5.81831e27 | 1.51456 | ||||||||
\(802\) | −4.53315e27 | −1.16612 | ||||||||
\(803\) | −2.74729e27 | −0.698404 | ||||||||
\(804\) | −2.81537e28 | −7.07299 | ||||||||
\(805\) | −7.12076e27 | −1.76793 | ||||||||
\(806\) | −3.93774e26 | −0.0966193 | ||||||||
\(807\) | 2.56545e27 | 0.622106 | ||||||||
\(808\) | 1.71077e28 | 4.10000 | ||||||||
\(809\) | −7.49296e27 | −1.77477 | −0.887386 | − | 0.461027i | \(-0.847481\pi\) | ||||
−0.887386 | + | 0.461027i | \(0.847481\pi\) | |||||||
\(810\) | 4.23012e27 | 0.990250 | ||||||||
\(811\) | 2.22585e27 | 0.514988 | 0.257494 | − | 0.966280i | \(-0.417103\pi\) | ||||
0.257494 | + | 0.966280i | \(0.417103\pi\) | |||||||
\(812\) | 1.92682e28 | 4.40614 | ||||||||
\(813\) | 1.20583e27 | 0.272537 | ||||||||
\(814\) | −7.71428e26 | −0.172331 | ||||||||
\(815\) | −1.09909e27 | −0.242681 | ||||||||
\(816\) | 1.55736e28 | 3.39884 | ||||||||
\(817\) | 1.56476e27 | 0.337550 | ||||||||
\(818\) | −1.05108e28 | −2.24119 | ||||||||
\(819\) | 1.85418e27 | 0.390801 | ||||||||
\(820\) | −9.33086e27 | −1.94397 | ||||||||
\(821\) | 5.23686e27 | 1.07848 | 0.539238 | − | 0.842153i | \(-0.318712\pi\) | ||||
0.539238 | + | 0.842153i | \(0.318712\pi\) | |||||||
\(822\) | 5.88056e27 | 1.19712 | ||||||||
\(823\) | 5.49200e27 | 1.10518 | 0.552589 | − | 0.833454i | \(-0.313640\pi\) | ||||
0.552589 | + | 0.833454i | \(0.313640\pi\) | |||||||
\(824\) | −1.90375e28 | −3.78705 | ||||||||
\(825\) | 1.97127e27 | 0.387645 | ||||||||
\(826\) | 1.40291e28 | 2.72721 | ||||||||
\(827\) | −6.15200e27 | −1.18226 | −0.591131 | − | 0.806576i | \(-0.701318\pi\) | ||||
−0.591131 | + | 0.806576i | \(0.701318\pi\) | |||||||
\(828\) | −4.32785e28 | −8.22212 | ||||||||
\(829\) | −2.25398e27 | −0.423334 | −0.211667 | − | 0.977342i | \(-0.567889\pi\) | ||||
−0.211667 | + | 0.977342i | \(0.567889\pi\) | |||||||
\(830\) | 1.87747e27 | 0.348603 | ||||||||
\(831\) | 1.60668e28 | 2.94930 | ||||||||
\(832\) | −3.36220e26 | −0.0610172 | ||||||||
\(833\) | −8.05536e27 | −1.44530 | ||||||||
\(834\) | −2.42658e28 | −4.30444 | ||||||||
\(835\) | 1.71188e27 | 0.300229 | ||||||||
\(836\) | −3.12680e27 | −0.542176 | ||||||||
\(837\) | 4.07656e27 | 0.698880 | ||||||||
\(838\) | −6.14238e27 | −1.04116 | ||||||||
\(839\) | 1.59602e27 | 0.267485 | 0.133742 | − | 0.991016i | \(-0.457301\pi\) | ||||
0.133742 | + | 0.991016i | \(0.457301\pi\) | |||||||
\(840\) | 2.48818e28 | 4.12315 | ||||||||
\(841\) | 2.43184e27 | 0.398449 | ||||||||
\(842\) | 1.55988e28 | 2.52713 | ||||||||
\(843\) | −7.43088e27 | −1.19036 | ||||||||
\(844\) | 7.41998e27 | 1.17530 | ||||||||
\(845\) | 3.87311e27 | 0.606625 | ||||||||
\(846\) | −3.36989e27 | −0.521913 | ||||||||
\(847\) | 9.04616e27 | 1.38539 | ||||||||
\(848\) | −1.05126e28 | −1.59202 | ||||||||
\(849\) | −9.85574e27 | −1.47593 | ||||||||
\(850\) | −7.14351e27 | −1.05787 | ||||||||
\(851\) | −3.18840e27 | −0.466920 | ||||||||
\(852\) | −3.60883e28 | −5.22626 | ||||||||
\(853\) | 5.16929e27 | 0.740312 | 0.370156 | − | 0.928970i | \(-0.379304\pi\) | ||||
0.370156 | + | 0.928970i | \(0.379304\pi\) | |||||||
\(854\) | −3.27276e28 | −4.63516 | ||||||||
\(855\) | 5.51124e27 | 0.771918 | ||||||||
\(856\) | −2.16265e28 | −2.99561 | ||||||||
\(857\) | −6.83211e27 | −0.935916 | −0.467958 | − | 0.883751i | \(-0.655010\pi\) | ||||
−0.467958 | + | 0.883751i | \(0.655010\pi\) | |||||||
\(858\) | −1.05267e27 | −0.142614 | ||||||||
\(859\) | −3.84485e27 | −0.515162 | −0.257581 | − | 0.966257i | \(-0.582925\pi\) | ||||
−0.257581 | + | 0.966257i | \(0.582925\pi\) | |||||||
\(860\) | 5.73237e27 | 0.759625 | ||||||||
\(861\) | 2.83093e28 | 3.71021 | ||||||||
\(862\) | −1.12045e28 | −1.45236 | ||||||||
\(863\) | −3.97127e27 | −0.509128 | −0.254564 | − | 0.967056i | \(-0.581932\pi\) | ||||
−0.254564 | + | 0.967056i | \(0.581932\pi\) | |||||||
\(864\) | 1.85593e28 | 2.35332 | ||||||||
\(865\) | −9.53905e27 | −1.19633 | ||||||||
\(866\) | 1.12601e28 | 1.39676 | ||||||||
\(867\) | 1.78898e27 | 0.219494 | ||||||||
\(868\) | 1.30001e28 | 1.57765 | ||||||||
\(869\) | 4.16090e27 | 0.499458 | ||||||||
\(870\) | 1.92810e28 | 2.28927 | ||||||||
\(871\) | −1.87395e27 | −0.220082 | ||||||||
\(872\) | 5.22765e27 | 0.607295 | ||||||||
\(873\) | 2.34372e28 | 2.69321 | ||||||||
\(874\) | −1.84594e28 | −2.09825 | ||||||||
\(875\) | −1.41729e28 | −1.59361 | ||||||||
\(876\) | 6.94094e28 | 7.72021 | ||||||||
\(877\) | 1.36071e28 | 1.49716 | 0.748581 | − | 0.663044i | \(-0.230736\pi\) | ||||
0.748581 | + | 0.663044i | \(0.230736\pi\) | |||||||
\(878\) | 7.93518e27 | 0.863692 | ||||||||
\(879\) | −1.75393e27 | −0.188851 | ||||||||
\(880\) | −4.44608e27 | −0.473578 | ||||||||
\(881\) | 3.37587e27 | 0.355725 | 0.177863 | − | 0.984055i | \(-0.443082\pi\) | ||||
0.177863 | + | 0.984055i | \(0.443082\pi\) | |||||||
\(882\) | −5.31124e28 | −5.53661 | ||||||||
\(883\) | −7.60060e27 | −0.783829 | −0.391915 | − | 0.920002i | \(-0.628187\pi\) | ||||
−0.391915 | + | 0.920002i | \(0.628187\pi\) | |||||||
\(884\) | 2.67066e27 | 0.272472 | ||||||||
\(885\) | 9.82834e27 | 0.992017 | ||||||||
\(886\) | 2.32531e28 | 2.32199 | ||||||||
\(887\) | −5.06677e26 | −0.0500560 | −0.0250280 | − | 0.999687i | \(-0.507967\pi\) | ||||
−0.0250280 | + | 0.999687i | \(0.507967\pi\) | |||||||
\(888\) | 1.11411e28 | 1.08895 | ||||||||
\(889\) | 8.41843e27 | 0.814075 | ||||||||
\(890\) | 9.09134e27 | 0.869807 | ||||||||
\(891\) | 3.37742e27 | 0.319703 | ||||||||
\(892\) | −3.85711e28 | −3.61240 | ||||||||
\(893\) | −1.00629e27 | −0.0932466 | ||||||||
\(894\) | 3.09266e27 | 0.283548 | ||||||||
\(895\) | 1.25802e26 | 0.0114122 | ||||||||
\(896\) | −9.49796e27 | −0.852519 | ||||||||
\(897\) | −4.35082e27 | −0.386405 | ||||||||
\(898\) | −1.38673e28 | −1.21862 | ||||||||
\(899\) | 5.75859e27 | 0.500725 | ||||||||
\(900\) | −3.29749e28 | −2.83713 | ||||||||
\(901\) | 8.25710e27 | 0.702979 | ||||||||
\(902\) | −1.06412e28 | −0.896459 | ||||||||
\(903\) | −1.73917e28 | −1.44980 | ||||||||
\(904\) | 1.20880e28 | 0.997138 | ||||||||
\(905\) | −5.75602e27 | −0.469851 | ||||||||
\(906\) | −2.73889e28 | −2.21236 | ||||||||
\(907\) | 9.96747e26 | 0.0796739 | 0.0398369 | − | 0.999206i | \(-0.487316\pi\) | ||||
0.0398369 | + | 0.999206i | \(0.487316\pi\) | |||||||
\(908\) | 1.47620e28 | 1.16769 | ||||||||
\(909\) | −4.21166e28 | −3.29683 | ||||||||
\(910\) | 2.89723e27 | 0.224435 | ||||||||
\(911\) | 1.76029e28 | 1.34946 | 0.674729 | − | 0.738066i | \(-0.264261\pi\) | ||||
0.674729 | + | 0.738066i | \(0.264261\pi\) | |||||||
\(912\) | 3.06623e28 | 2.32623 | ||||||||
\(913\) | 1.49901e27 | 0.112547 | ||||||||
\(914\) | 2.53968e28 | 1.88708 | ||||||||
\(915\) | −2.29280e28 | −1.68603 | ||||||||
\(916\) | 3.33154e28 | 2.42459 | ||||||||
\(917\) | 8.36196e27 | 0.602282 | ||||||||
\(918\) | −3.94917e28 | −2.81514 | ||||||||
\(919\) | −7.68415e27 | −0.542123 | −0.271062 | − | 0.962562i | \(-0.587375\pi\) | ||||
−0.271062 | + | 0.962562i | \(0.587375\pi\) | |||||||
\(920\) | −3.86566e28 | −2.69923 | ||||||||
\(921\) | 2.71865e28 | 1.87883 | ||||||||
\(922\) | −4.48860e25 | −0.00307020 | ||||||||
\(923\) | −2.40209e27 | −0.162619 | ||||||||
\(924\) | 3.47532e28 | 2.32868 | ||||||||
\(925\) | −2.42932e27 | −0.161116 | ||||||||
\(926\) | 5.96432e27 | 0.391522 | ||||||||
\(927\) | 4.68674e28 | 3.04518 | ||||||||
\(928\) | 2.62170e28 | 1.68608 | ||||||||
\(929\) | −1.66489e28 | −1.05983 | −0.529914 | − | 0.848052i | \(-0.677776\pi\) | ||||
−0.529914 | + | 0.848052i | \(0.677776\pi\) | |||||||
\(930\) | 1.30088e28 | 0.819691 | ||||||||
\(931\) | −1.58599e28 | −0.989189 | ||||||||
\(932\) | −2.90689e27 | −0.179464 | ||||||||
\(933\) | −5.21774e28 | −3.18865 | ||||||||
\(934\) | 3.58385e28 | 2.16797 | ||||||||
\(935\) | 3.49218e27 | 0.209116 | ||||||||
\(936\) | 1.00658e28 | 0.596663 | ||||||||
\(937\) | 1.50489e27 | 0.0883035 | 0.0441517 | − | 0.999025i | \(-0.485941\pi\) | ||||
0.0441517 | + | 0.999025i | \(0.485941\pi\) | |||||||
\(938\) | 8.83685e28 | 5.13299 | ||||||||
\(939\) | 2.17638e28 | 1.25144 | ||||||||
\(940\) | −3.68646e27 | −0.209843 | ||||||||
\(941\) | −2.86653e28 | −1.61531 | −0.807654 | − | 0.589657i | \(-0.799263\pi\) | ||||
−0.807654 | + | 0.589657i | \(0.799263\pi\) | |||||||
\(942\) | 6.04567e28 | 3.37257 | ||||||||
\(943\) | −4.39815e28 | −2.42890 | ||||||||
\(944\) | 3.62041e28 | 1.97936 | ||||||||
\(945\) | −2.99938e28 | −1.62341 | ||||||||
\(946\) | 6.53740e27 | 0.350299 | ||||||||
\(947\) | −1.33710e28 | −0.709317 | −0.354659 | − | 0.934996i | \(-0.615403\pi\) | ||||
−0.354659 | + | 0.934996i | \(0.615403\pi\) | |||||||
\(948\) | −1.05124e29 | −5.52105 | ||||||||
\(949\) | 4.61998e27 | 0.240221 | ||||||||
\(950\) | −1.40646e28 | −0.724025 | ||||||||
\(951\) | −2.06898e28 | −1.05449 | ||||||||
\(952\) | −7.19912e28 | −3.63269 | ||||||||
\(953\) | −1.17054e27 | −0.0584794 | −0.0292397 | − | 0.999572i | \(-0.509309\pi\) | ||||
−0.0292397 | + | 0.999572i | \(0.509309\pi\) | |||||||
\(954\) | 5.44425e28 | 2.69295 | ||||||||
\(955\) | −2.72729e27 | −0.133567 | ||||||||
\(956\) | 7.48580e28 | 3.62985 | ||||||||
\(957\) | 1.53944e28 | 0.739093 | ||||||||
\(958\) | −9.17442e26 | −0.0436120 | ||||||||
\(959\) | −1.29224e28 | −0.608226 | ||||||||
\(960\) | 1.11075e28 | 0.517653 | ||||||||
\(961\) | −1.77854e28 | −0.820712 | ||||||||
\(962\) | 1.29727e27 | 0.0592744 | ||||||||
\(963\) | 5.32412e28 | 2.40879 | ||||||||
\(964\) | −8.18890e27 | −0.366854 | ||||||||
\(965\) | 1.94057e28 | 0.860836 | ||||||||
\(966\) | 2.05169e29 | 9.01214 | ||||||||
\(967\) | −6.76607e27 | −0.294297 | −0.147148 | − | 0.989114i | \(-0.547009\pi\) | ||||
−0.147148 | + | 0.989114i | \(0.547009\pi\) | |||||||
\(968\) | 4.91091e28 | 2.11517 | ||||||||
\(969\) | −2.40837e28 | −1.02718 | ||||||||
\(970\) | 3.66215e28 | 1.54670 | ||||||||
\(971\) | 1.02807e28 | 0.429972 | 0.214986 | − | 0.976617i | \(-0.431029\pi\) | ||||
0.214986 | + | 0.976617i | \(0.431029\pi\) | |||||||
\(972\) | 7.70506e27 | 0.319115 | ||||||||
\(973\) | 5.33233e28 | 2.18698 | ||||||||
\(974\) | −2.74624e28 | −1.11540 | ||||||||
\(975\) | −3.31499e27 | −0.133333 | ||||||||
\(976\) | −8.44585e28 | −3.36411 | ||||||||
\(977\) | −4.10318e28 | −1.61854 | −0.809268 | − | 0.587440i | \(-0.800136\pi\) | ||||
−0.809268 | + | 0.587440i | \(0.800136\pi\) | |||||||
\(978\) | 3.16678e28 | 1.23708 | ||||||||
\(979\) | 7.25872e27 | 0.280818 | ||||||||
\(980\) | −5.81016e28 | −2.22608 | ||||||||
\(981\) | −1.28697e28 | −0.488329 | ||||||||
\(982\) | −8.27425e27 | −0.310935 | ||||||||
\(983\) | −3.47207e28 | −1.29220 | −0.646101 | − | 0.763252i | \(-0.723601\pi\) | ||||
−0.646101 | + | 0.763252i | \(0.723601\pi\) | |||||||
\(984\) | 1.53683e29 | 5.66465 | ||||||||
\(985\) | −8.69546e27 | −0.317430 | ||||||||
\(986\) | −5.57863e28 | −2.01696 | ||||||||
\(987\) | 1.11845e28 | 0.400501 | ||||||||
\(988\) | 5.25818e27 | 0.186485 | ||||||||
\(989\) | 2.70199e28 | 0.949114 | ||||||||
\(990\) | 2.30254e28 | 0.801075 | ||||||||
\(991\) | −4.12923e28 | −1.42288 | −0.711442 | − | 0.702745i | \(-0.751957\pi\) | ||||
−0.711442 | + | 0.702745i | \(0.751957\pi\) | |||||||
\(992\) | 1.76885e28 | 0.603713 | ||||||||
\(993\) | 7.54836e28 | 2.55173 | ||||||||
\(994\) | 1.13274e29 | 3.79278 | ||||||||
\(995\) | −2.37008e28 | −0.786038 | ||||||||
\(996\) | −3.78720e28 | −1.24410 | ||||||||
\(997\) | −3.41785e28 | −1.11211 | −0.556057 | − | 0.831144i | \(-0.687686\pi\) | ||||
−0.556057 | + | 0.831144i | \(0.687686\pi\) | |||||||
\(998\) | −7.52031e28 | −2.42379 | ||||||||
\(999\) | −1.34301e28 | −0.428752 |
(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 | 47.20.a.a.1.3 | ✓ | 34 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
47.20.a.a.1.3 | ✓ | 34 | 1.1 | even | 1 | trivial |