Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,10,Mod(1,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.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: | \(91.1613430010\) |
Analytic rank: | \(1\) |
Dimension: | \(21\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Character | \(\chi\) | \(=\) | 177.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.19317 | −0.141120 | −0.0705598 | − | 0.997508i | \(-0.522479\pi\) | ||||
−0.0705598 | + | 0.997508i | \(0.522479\pi\) | |||||||
\(3\) | 81.0000 | 0.577350 | ||||||||
\(4\) | −501.804 | −0.980085 | ||||||||
\(5\) | −2710.01 | −1.93913 | −0.969564 | − | 0.244838i | \(-0.921265\pi\) | ||||
−0.969564 | + | 0.244838i | \(0.921265\pi\) | |||||||
\(6\) | −258.647 | −0.0814755 | ||||||||
\(7\) | −1841.65 | −0.289911 | −0.144956 | − | 0.989438i | \(-0.546304\pi\) | ||||
−0.144956 | + | 0.989438i | \(0.546304\pi\) | |||||||
\(8\) | 3237.25 | 0.279429 | ||||||||
\(9\) | 6561.00 | 0.333333 | ||||||||
\(10\) | 8653.54 | 0.273649 | ||||||||
\(11\) | 14149.8 | 0.291396 | 0.145698 | − | 0.989329i | \(-0.453457\pi\) | ||||
0.145698 | + | 0.989329i | \(0.453457\pi\) | |||||||
\(12\) | −40646.1 | −0.565852 | ||||||||
\(13\) | 130013. | 1.26253 | 0.631267 | − | 0.775565i | \(-0.282535\pi\) | ||||
0.631267 | + | 0.775565i | \(0.282535\pi\) | |||||||
\(14\) | 5880.69 | 0.0409121 | ||||||||
\(15\) | −219511. | −1.11956 | ||||||||
\(16\) | 246586. | 0.940652 | ||||||||
\(17\) | −550189. | −1.59769 | −0.798844 | − | 0.601539i | \(-0.794555\pi\) | ||||
−0.798844 | + | 0.601539i | \(0.794555\pi\) | |||||||
\(18\) | −20950.4 | −0.0470399 | ||||||||
\(19\) | −76696.3 | −0.135015 | −0.0675077 | − | 0.997719i | \(-0.521505\pi\) | ||||
−0.0675077 | + | 0.997719i | \(0.521505\pi\) | |||||||
\(20\) | 1.35989e6 | 1.90051 | ||||||||
\(21\) | −149173. | −0.167380 | ||||||||
\(22\) | −45182.8 | −0.0411217 | ||||||||
\(23\) | 1.37026e6 | 1.02100 | 0.510501 | − | 0.859877i | \(-0.329460\pi\) | ||||
0.510501 | + | 0.859877i | \(0.329460\pi\) | |||||||
\(24\) | 262217. | 0.161328 | ||||||||
\(25\) | 5.39105e6 | 2.76022 | ||||||||
\(26\) | −415155. | −0.178168 | ||||||||
\(27\) | 531441. | 0.192450 | ||||||||
\(28\) | 924144. | 0.284138 | ||||||||
\(29\) | 1.57961e6 | 0.414725 | 0.207362 | − | 0.978264i | \(-0.433512\pi\) | ||||
0.207362 | + | 0.978264i | \(0.433512\pi\) | |||||||
\(30\) | 700937. | 0.157991 | ||||||||
\(31\) | 2.58891e6 | 0.503489 | 0.251745 | − | 0.967794i | \(-0.418996\pi\) | ||||
0.251745 | + | 0.967794i | \(0.418996\pi\) | |||||||
\(32\) | −2.44486e6 | −0.412173 | ||||||||
\(33\) | 1.14614e6 | 0.168238 | ||||||||
\(34\) | 1.75685e6 | 0.225465 | ||||||||
\(35\) | 4.99088e6 | 0.562175 | ||||||||
\(36\) | −3.29233e6 | −0.326695 | ||||||||
\(37\) | 346183. | 0.0303667 | 0.0151833 | − | 0.999885i | \(-0.495167\pi\) | ||||
0.0151833 | + | 0.999885i | \(0.495167\pi\) | |||||||
\(38\) | 244905. | 0.0190533 | ||||||||
\(39\) | 1.05311e7 | 0.728925 | ||||||||
\(40\) | −8.77299e6 | −0.541848 | ||||||||
\(41\) | −2.25179e7 | −1.24452 | −0.622258 | − | 0.782812i | \(-0.713785\pi\) | ||||
−0.622258 | + | 0.782812i | \(0.713785\pi\) | |||||||
\(42\) | 476336. | 0.0236206 | ||||||||
\(43\) | 3.52017e7 | 1.57020 | 0.785102 | − | 0.619366i | \(-0.212610\pi\) | ||||
0.785102 | + | 0.619366i | \(0.212610\pi\) | |||||||
\(44\) | −7.10043e6 | −0.285593 | ||||||||
\(45\) | −1.77804e7 | −0.646376 | ||||||||
\(46\) | −4.37546e6 | −0.144083 | ||||||||
\(47\) | 3.28211e7 | 0.981099 | 0.490549 | − | 0.871413i | \(-0.336796\pi\) | ||||
0.490549 | + | 0.871413i | \(0.336796\pi\) | |||||||
\(48\) | 1.99735e7 | 0.543086 | ||||||||
\(49\) | −3.69620e7 | −0.915952 | ||||||||
\(50\) | −1.72146e7 | −0.389521 | ||||||||
\(51\) | −4.45653e7 | −0.922425 | ||||||||
\(52\) | −6.52412e7 | −1.23739 | ||||||||
\(53\) | −5.90435e7 | −1.02785 | −0.513926 | − | 0.857835i | \(-0.671809\pi\) | ||||
−0.513926 | + | 0.857835i | \(0.671809\pi\) | |||||||
\(54\) | −1.69698e6 | −0.0271585 | ||||||||
\(55\) | −3.83462e7 | −0.565055 | ||||||||
\(56\) | −5.96187e6 | −0.0810095 | ||||||||
\(57\) | −6.21240e6 | −0.0779512 | ||||||||
\(58\) | −5.04398e6 | −0.0585258 | ||||||||
\(59\) | 1.21174e7 | 0.130189 | ||||||||
\(60\) | 1.10151e8 | 1.09726 | ||||||||
\(61\) | −1.93757e7 | −0.179173 | −0.0895865 | − | 0.995979i | \(-0.528555\pi\) | ||||
−0.0895865 | + | 0.995979i | \(0.528555\pi\) | |||||||
\(62\) | −8.26685e6 | −0.0710522 | ||||||||
\(63\) | −1.20830e7 | −0.0966370 | ||||||||
\(64\) | −1.18445e8 | −0.882487 | ||||||||
\(65\) | −3.52338e8 | −2.44822 | ||||||||
\(66\) | −3.65981e6 | −0.0237416 | ||||||||
\(67\) | −2.82027e8 | −1.70984 | −0.854918 | − | 0.518763i | \(-0.826393\pi\) | ||||
−0.854918 | + | 0.518763i | \(0.826393\pi\) | |||||||
\(68\) | 2.76087e8 | 1.56587 | ||||||||
\(69\) | 1.10991e8 | 0.589475 | ||||||||
\(70\) | −1.59368e7 | −0.0793339 | ||||||||
\(71\) | 6.18639e7 | 0.288918 | 0.144459 | − | 0.989511i | \(-0.453856\pi\) | ||||
0.144459 | + | 0.989511i | \(0.453856\pi\) | |||||||
\(72\) | 2.12396e7 | 0.0931430 | ||||||||
\(73\) | 3.00367e8 | 1.23794 | 0.618970 | − | 0.785414i | \(-0.287550\pi\) | ||||
0.618970 | + | 0.785414i | \(0.287550\pi\) | |||||||
\(74\) | −1.10542e6 | −0.00428534 | ||||||||
\(75\) | 4.36675e8 | 1.59361 | ||||||||
\(76\) | 3.84865e7 | 0.132327 | ||||||||
\(77\) | −2.60589e7 | −0.0844790 | ||||||||
\(78\) | −3.36276e7 | −0.102866 | ||||||||
\(79\) | −2.20861e8 | −0.637964 | −0.318982 | − | 0.947761i | \(-0.603341\pi\) | ||||
−0.318982 | + | 0.947761i | \(0.603341\pi\) | |||||||
\(80\) | −6.68252e8 | −1.82405 | ||||||||
\(81\) | 4.30467e7 | 0.111111 | ||||||||
\(82\) | 7.19035e7 | 0.175626 | ||||||||
\(83\) | −2.37823e8 | −0.550051 | −0.275025 | − | 0.961437i | \(-0.588686\pi\) | ||||
−0.275025 | + | 0.961437i | \(0.588686\pi\) | |||||||
\(84\) | 7.48557e7 | 0.164047 | ||||||||
\(85\) | 1.49102e9 | 3.09812 | ||||||||
\(86\) | −1.12405e8 | −0.221587 | ||||||||
\(87\) | 1.27949e8 | 0.239441 | ||||||||
\(88\) | 4.58065e7 | 0.0814245 | ||||||||
\(89\) | −6.63983e8 | −1.12177 | −0.560883 | − | 0.827895i | \(-0.689538\pi\) | ||||
−0.560883 | + | 0.827895i | \(0.689538\pi\) | |||||||
\(90\) | 5.67759e7 | 0.0912163 | ||||||||
\(91\) | −2.39439e8 | −0.366023 | ||||||||
\(92\) | −6.87599e8 | −1.00067 | ||||||||
\(93\) | 2.09702e8 | 0.290690 | ||||||||
\(94\) | −1.04803e8 | −0.138452 | ||||||||
\(95\) | 2.07848e8 | 0.261812 | ||||||||
\(96\) | −1.98034e8 | −0.237968 | ||||||||
\(97\) | 1.03674e9 | 1.18904 | 0.594520 | − | 0.804081i | \(-0.297342\pi\) | ||||
0.594520 | + | 0.804081i | \(0.297342\pi\) | |||||||
\(98\) | 1.18026e8 | 0.129259 | ||||||||
\(99\) | 9.28370e7 | 0.0971321 | ||||||||
\(100\) | −2.70525e9 | −2.70525 | ||||||||
\(101\) | 1.36477e9 | 1.30501 | 0.652504 | − | 0.757785i | \(-0.273719\pi\) | ||||
0.652504 | + | 0.757785i | \(0.273719\pi\) | |||||||
\(102\) | 1.42305e8 | 0.130172 | ||||||||
\(103\) | 1.23730e9 | 1.08320 | 0.541598 | − | 0.840638i | \(-0.317820\pi\) | ||||
0.541598 | + | 0.840638i | \(0.317820\pi\) | |||||||
\(104\) | 4.20886e8 | 0.352789 | ||||||||
\(105\) | 4.04262e8 | 0.324572 | ||||||||
\(106\) | 1.88536e8 | 0.145050 | ||||||||
\(107\) | −7.61706e8 | −0.561772 | −0.280886 | − | 0.959741i | \(-0.590628\pi\) | ||||
−0.280886 | + | 0.959741i | \(0.590628\pi\) | |||||||
\(108\) | −2.66679e8 | −0.188617 | ||||||||
\(109\) | −6.01385e8 | −0.408069 | −0.204034 | − | 0.978964i | \(-0.565405\pi\) | ||||
−0.204034 | + | 0.978964i | \(0.565405\pi\) | |||||||
\(110\) | 1.22446e8 | 0.0797403 | ||||||||
\(111\) | 2.80408e7 | 0.0175322 | ||||||||
\(112\) | −4.54125e8 | −0.272706 | ||||||||
\(113\) | 3.88144e8 | 0.223944 | 0.111972 | − | 0.993711i | \(-0.464283\pi\) | ||||
0.111972 | + | 0.993711i | \(0.464283\pi\) | |||||||
\(114\) | 1.98373e7 | 0.0110004 | ||||||||
\(115\) | −3.71341e9 | −1.97985 | ||||||||
\(116\) | −7.92656e8 | −0.406465 | ||||||||
\(117\) | 8.53018e8 | 0.420845 | ||||||||
\(118\) | −3.86928e7 | −0.0183722 | ||||||||
\(119\) | 1.01325e9 | 0.463187 | ||||||||
\(120\) | −7.10612e8 | −0.312836 | ||||||||
\(121\) | −2.15773e9 | −0.915088 | ||||||||
\(122\) | 6.18698e7 | 0.0252848 | ||||||||
\(123\) | −1.82395e9 | −0.718522 | ||||||||
\(124\) | −1.29913e9 | −0.493462 | ||||||||
\(125\) | −9.31683e9 | −3.41329 | ||||||||
\(126\) | 3.85832e7 | 0.0136374 | ||||||||
\(127\) | −3.50531e9 | −1.19567 | −0.597833 | − | 0.801621i | \(-0.703971\pi\) | ||||
−0.597833 | + | 0.801621i | \(0.703971\pi\) | |||||||
\(128\) | 1.62999e9 | 0.536710 | ||||||||
\(129\) | 2.85134e9 | 0.906558 | ||||||||
\(130\) | 1.12508e9 | 0.345491 | ||||||||
\(131\) | −1.38898e9 | −0.412073 | −0.206037 | − | 0.978544i | \(-0.566057\pi\) | ||||
−0.206037 | + | 0.978544i | \(0.566057\pi\) | |||||||
\(132\) | −5.75135e8 | −0.164887 | ||||||||
\(133\) | 1.41247e8 | 0.0391425 | ||||||||
\(134\) | 9.00562e8 | 0.241291 | ||||||||
\(135\) | −1.44021e9 | −0.373185 | ||||||||
\(136\) | −1.78110e9 | −0.446440 | ||||||||
\(137\) | −3.63297e9 | −0.881089 | −0.440544 | − | 0.897731i | \(-0.645215\pi\) | ||||
−0.440544 | + | 0.897731i | \(0.645215\pi\) | |||||||
\(138\) | −3.54412e8 | −0.0831865 | ||||||||
\(139\) | −1.45150e9 | −0.329801 | −0.164900 | − | 0.986310i | \(-0.552730\pi\) | ||||
−0.164900 | + | 0.986310i | \(0.552730\pi\) | |||||||
\(140\) | −2.50444e9 | −0.550979 | ||||||||
\(141\) | 2.65851e9 | 0.566438 | ||||||||
\(142\) | −1.97542e8 | −0.0407720 | ||||||||
\(143\) | 1.83967e9 | 0.367898 | ||||||||
\(144\) | 1.61785e9 | 0.313551 | ||||||||
\(145\) | −4.28077e9 | −0.804204 | ||||||||
\(146\) | −9.59125e8 | −0.174698 | ||||||||
\(147\) | −2.99392e9 | −0.528825 | ||||||||
\(148\) | −1.73716e8 | −0.0297619 | ||||||||
\(149\) | 3.34366e9 | 0.555756 | 0.277878 | − | 0.960616i | \(-0.410369\pi\) | ||||
0.277878 | + | 0.960616i | \(0.410369\pi\) | |||||||
\(150\) | −1.39438e9 | −0.224890 | ||||||||
\(151\) | 4.11423e9 | 0.644009 | 0.322005 | − | 0.946738i | \(-0.395643\pi\) | ||||
0.322005 | + | 0.946738i | \(0.395643\pi\) | |||||||
\(152\) | −2.48285e8 | −0.0377272 | ||||||||
\(153\) | −3.60979e9 | −0.532562 | ||||||||
\(154\) | 8.32107e7 | 0.0119216 | ||||||||
\(155\) | −7.01599e9 | −0.976330 | ||||||||
\(156\) | −5.28454e9 | −0.714408 | ||||||||
\(157\) | −1.30658e10 | −1.71627 | −0.858137 | − | 0.513421i | \(-0.828378\pi\) | ||||
−0.858137 | + | 0.513421i | \(0.828378\pi\) | |||||||
\(158\) | 7.05246e8 | 0.0900292 | ||||||||
\(159\) | −4.78252e9 | −0.593431 | ||||||||
\(160\) | 6.62562e9 | 0.799257 | ||||||||
\(161\) | −2.52352e9 | −0.295999 | ||||||||
\(162\) | −1.37456e8 | −0.0156800 | ||||||||
\(163\) | 7.82966e9 | 0.868758 | 0.434379 | − | 0.900730i | \(-0.356968\pi\) | ||||
0.434379 | + | 0.900730i | \(0.356968\pi\) | |||||||
\(164\) | 1.12996e10 | 1.21973 | ||||||||
\(165\) | −3.10604e9 | −0.326234 | ||||||||
\(166\) | 7.59411e8 | 0.0776230 | ||||||||
\(167\) | 1.17540e10 | 1.16939 | 0.584697 | − | 0.811252i | \(-0.301213\pi\) | ||||
0.584697 | + | 0.811252i | \(0.301213\pi\) | |||||||
\(168\) | −4.82911e8 | −0.0467709 | ||||||||
\(169\) | 6.29901e9 | 0.593994 | ||||||||
\(170\) | −4.76108e9 | −0.437206 | ||||||||
\(171\) | −5.03205e8 | −0.0450051 | ||||||||
\(172\) | −1.76644e10 | −1.53893 | ||||||||
\(173\) | 4.88623e9 | 0.414731 | 0.207366 | − | 0.978264i | \(-0.433511\pi\) | ||||
0.207366 | + | 0.978264i | \(0.433511\pi\) | |||||||
\(174\) | −4.08562e8 | −0.0337899 | ||||||||
\(175\) | −9.92840e9 | −0.800218 | ||||||||
\(176\) | 3.48915e9 | 0.274103 | ||||||||
\(177\) | 9.81506e8 | 0.0751646 | ||||||||
\(178\) | 2.12021e9 | 0.158303 | ||||||||
\(179\) | 1.90828e10 | 1.38933 | 0.694664 | − | 0.719335i | \(-0.255553\pi\) | ||||
0.694664 | + | 0.719335i | \(0.255553\pi\) | |||||||
\(180\) | 8.92227e9 | 0.633504 | ||||||||
\(181\) | −1.44737e10 | −1.00237 | −0.501183 | − | 0.865341i | \(-0.667102\pi\) | ||||
−0.501183 | + | 0.865341i | \(0.667102\pi\) | |||||||
\(182\) | 7.64569e8 | 0.0516530 | ||||||||
\(183\) | −1.56943e9 | −0.103446 | ||||||||
\(184\) | 4.43586e9 | 0.285297 | ||||||||
\(185\) | −9.38159e8 | −0.0588849 | ||||||||
\(186\) | −6.69615e8 | −0.0410220 | ||||||||
\(187\) | −7.78508e9 | −0.465560 | ||||||||
\(188\) | −1.64697e10 | −0.961561 | ||||||||
\(189\) | −9.78726e8 | −0.0557934 | ||||||||
\(190\) | −6.63695e8 | −0.0369468 | ||||||||
\(191\) | −8.99432e9 | −0.489010 | −0.244505 | − | 0.969648i | \(-0.578626\pi\) | ||||
−0.244505 | + | 0.969648i | \(0.578626\pi\) | |||||||
\(192\) | −9.59407e9 | −0.509504 | ||||||||
\(193\) | −2.05992e9 | −0.106867 | −0.0534333 | − | 0.998571i | \(-0.517016\pi\) | ||||
−0.0534333 | + | 0.998571i | \(0.517016\pi\) | |||||||
\(194\) | −3.31049e9 | −0.167797 | ||||||||
\(195\) | −2.85394e10 | −1.41348 | ||||||||
\(196\) | 1.85476e10 | 0.897711 | ||||||||
\(197\) | −3.47766e9 | −0.164509 | −0.0822543 | − | 0.996611i | \(-0.526212\pi\) | ||||
−0.0822543 | + | 0.996611i | \(0.526212\pi\) | |||||||
\(198\) | −2.96444e8 | −0.0137072 | ||||||||
\(199\) | −1.91700e10 | −0.866531 | −0.433266 | − | 0.901266i | \(-0.642639\pi\) | ||||
−0.433266 | + | 0.901266i | \(0.642639\pi\) | |||||||
\(200\) | 1.74522e10 | 0.771285 | ||||||||
\(201\) | −2.28442e10 | −0.987174 | ||||||||
\(202\) | −4.35794e9 | −0.184162 | ||||||||
\(203\) | −2.90909e9 | −0.120233 | ||||||||
\(204\) | 2.23630e10 | 0.904055 | ||||||||
\(205\) | 6.10238e10 | 2.41328 | ||||||||
\(206\) | −3.95091e9 | −0.152860 | ||||||||
\(207\) | 8.99024e9 | 0.340334 | ||||||||
\(208\) | 3.20596e10 | 1.18761 | ||||||||
\(209\) | −1.08524e9 | −0.0393430 | ||||||||
\(210\) | −1.29088e9 | −0.0458034 | ||||||||
\(211\) | 3.62374e10 | 1.25859 | 0.629297 | − | 0.777165i | \(-0.283343\pi\) | ||||
0.629297 | + | 0.777165i | \(0.283343\pi\) | |||||||
\(212\) | 2.96282e10 | 1.00738 | ||||||||
\(213\) | 5.01098e9 | 0.166807 | ||||||||
\(214\) | 2.43226e9 | 0.0792771 | ||||||||
\(215\) | −9.53972e10 | −3.04483 | ||||||||
\(216\) | 1.72041e9 | 0.0537761 | ||||||||
\(217\) | −4.76786e9 | −0.145967 | ||||||||
\(218\) | 1.92033e9 | 0.0575865 | ||||||||
\(219\) | 2.43298e10 | 0.714725 | ||||||||
\(220\) | 1.92423e10 | 0.553802 | ||||||||
\(221\) | −7.15320e10 | −2.01714 | ||||||||
\(222\) | −8.95391e7 | −0.00247414 | ||||||||
\(223\) | 3.47716e10 | 0.941570 | 0.470785 | − | 0.882248i | \(-0.343971\pi\) | ||||
0.470785 | + | 0.882248i | \(0.343971\pi\) | |||||||
\(224\) | 4.50257e9 | 0.119494 | ||||||||
\(225\) | 3.53707e10 | 0.920073 | ||||||||
\(226\) | −1.23941e9 | −0.0316029 | ||||||||
\(227\) | −5.98792e9 | −0.149679 | −0.0748393 | − | 0.997196i | \(-0.523844\pi\) | ||||
−0.0748393 | + | 0.997196i | \(0.523844\pi\) | |||||||
\(228\) | 3.11741e9 | 0.0763988 | ||||||||
\(229\) | 6.32536e10 | 1.51994 | 0.759968 | − | 0.649960i | \(-0.225214\pi\) | ||||
0.759968 | + | 0.649960i | \(0.225214\pi\) | |||||||
\(230\) | 1.18576e10 | 0.279396 | ||||||||
\(231\) | −2.11077e9 | −0.0487740 | ||||||||
\(232\) | 5.11360e9 | 0.115886 | ||||||||
\(233\) | −4.49276e9 | −0.0998646 | −0.0499323 | − | 0.998753i | \(-0.515901\pi\) | ||||
−0.0499323 | + | 0.998753i | \(0.515901\pi\) | |||||||
\(234\) | −2.72384e9 | −0.0593895 | ||||||||
\(235\) | −8.89456e10 | −1.90248 | ||||||||
\(236\) | −6.08054e9 | −0.127596 | ||||||||
\(237\) | −1.78897e10 | −0.368329 | ||||||||
\(238\) | −3.23549e9 | −0.0653648 | ||||||||
\(239\) | −4.08140e10 | −0.809131 | −0.404566 | − | 0.914509i | \(-0.632577\pi\) | ||||
−0.404566 | + | 0.914509i | \(0.632577\pi\) | |||||||
\(240\) | −5.41285e10 | −1.05311 | ||||||||
\(241\) | 1.11274e10 | 0.212480 | 0.106240 | − | 0.994341i | \(-0.466119\pi\) | ||||
0.106240 | + | 0.994341i | \(0.466119\pi\) | |||||||
\(242\) | 6.89001e9 | 0.129137 | ||||||||
\(243\) | 3.48678e9 | 0.0641500 | ||||||||
\(244\) | 9.72278e9 | 0.175605 | ||||||||
\(245\) | 1.00167e11 | 1.77615 | ||||||||
\(246\) | 5.82419e9 | 0.101398 | ||||||||
\(247\) | −9.97155e9 | −0.170462 | ||||||||
\(248\) | 8.38096e9 | 0.140689 | ||||||||
\(249\) | −1.92637e10 | −0.317572 | ||||||||
\(250\) | 2.97502e10 | 0.481682 | ||||||||
\(251\) | 2.74625e10 | 0.436725 | 0.218362 | − | 0.975868i | \(-0.429929\pi\) | ||||
0.218362 | + | 0.975868i | \(0.429929\pi\) | |||||||
\(252\) | 6.06331e9 | 0.0947125 | ||||||||
\(253\) | 1.93889e10 | 0.297516 | ||||||||
\(254\) | 1.11931e10 | 0.168732 | ||||||||
\(255\) | 1.20773e11 | 1.78870 | ||||||||
\(256\) | 5.54392e10 | 0.806746 | ||||||||
\(257\) | −8.63869e10 | −1.23523 | −0.617616 | − | 0.786480i | \(-0.711902\pi\) | ||||
−0.617616 | + | 0.786480i | \(0.711902\pi\) | |||||||
\(258\) | −9.10482e9 | −0.127933 | ||||||||
\(259\) | −6.37545e8 | −0.00880364 | ||||||||
\(260\) | 1.76805e11 | 2.39946 | ||||||||
\(261\) | 1.03638e10 | 0.138242 | ||||||||
\(262\) | 4.43525e9 | 0.0581516 | ||||||||
\(263\) | −1.48732e10 | −0.191692 | −0.0958459 | − | 0.995396i | \(-0.530556\pi\) | ||||
−0.0958459 | + | 0.995396i | \(0.530556\pi\) | |||||||
\(264\) | 3.71033e9 | 0.0470105 | ||||||||
\(265\) | 1.60009e11 | 1.99314 | ||||||||
\(266\) | −4.51027e8 | −0.00552377 | ||||||||
\(267\) | −5.37827e10 | −0.647652 | ||||||||
\(268\) | 1.41522e11 | 1.67578 | ||||||||
\(269\) | −1.12574e11 | −1.31085 | −0.655427 | − | 0.755259i | \(-0.727511\pi\) | ||||
−0.655427 | + | 0.755259i | \(0.727511\pi\) | |||||||
\(270\) | 4.59885e9 | 0.0526638 | ||||||||
\(271\) | −1.46802e11 | −1.65337 | −0.826683 | − | 0.562668i | \(-0.809775\pi\) | ||||
−0.826683 | + | 0.562668i | \(0.809775\pi\) | |||||||
\(272\) | −1.35669e11 | −1.50287 | ||||||||
\(273\) | −1.93945e10 | −0.211323 | ||||||||
\(274\) | 1.16007e10 | 0.124339 | ||||||||
\(275\) | 7.62824e10 | 0.804317 | ||||||||
\(276\) | −5.56955e10 | −0.577736 | ||||||||
\(277\) | −1.43398e10 | −0.146347 | −0.0731736 | − | 0.997319i | \(-0.523313\pi\) | ||||
−0.0731736 | + | 0.997319i | \(0.523313\pi\) | |||||||
\(278\) | 4.63490e9 | 0.0465413 | ||||||||
\(279\) | 1.69859e10 | 0.167830 | ||||||||
\(280\) | 1.61567e10 | 0.157088 | ||||||||
\(281\) | −1.86643e11 | −1.78580 | −0.892902 | − | 0.450251i | \(-0.851335\pi\) | ||||
−0.892902 | + | 0.450251i | \(0.851335\pi\) | |||||||
\(282\) | −8.48908e9 | −0.0799355 | ||||||||
\(283\) | 1.15819e11 | 1.07334 | 0.536672 | − | 0.843791i | \(-0.319681\pi\) | ||||
0.536672 | + | 0.843791i | \(0.319681\pi\) | |||||||
\(284\) | −3.10435e10 | −0.283164 | ||||||||
\(285\) | 1.68357e10 | 0.151157 | ||||||||
\(286\) | −5.87438e9 | −0.0519176 | ||||||||
\(287\) | 4.14700e10 | 0.360799 | ||||||||
\(288\) | −1.60408e10 | −0.137391 | ||||||||
\(289\) | 1.84120e11 | 1.55260 | ||||||||
\(290\) | 1.36692e10 | 0.113489 | ||||||||
\(291\) | 8.39759e10 | 0.686493 | ||||||||
\(292\) | −1.50725e11 | −1.21329 | ||||||||
\(293\) | −2.26078e11 | −1.79206 | −0.896032 | − | 0.443990i | \(-0.853563\pi\) | ||||
−0.896032 | + | 0.443990i | \(0.853563\pi\) | |||||||
\(294\) | 9.56010e9 | 0.0746276 | ||||||||
\(295\) | −3.28382e10 | −0.252453 | ||||||||
\(296\) | 1.12068e9 | 0.00848533 | ||||||||
\(297\) | 7.51979e9 | 0.0560792 | ||||||||
\(298\) | −1.06769e10 | −0.0784280 | ||||||||
\(299\) | 1.78152e11 | 1.28905 | ||||||||
\(300\) | −2.19125e11 | −1.56188 | ||||||||
\(301\) | −6.48291e10 | −0.455220 | ||||||||
\(302\) | −1.31374e10 | −0.0908824 | ||||||||
\(303\) | 1.10546e11 | 0.753447 | ||||||||
\(304\) | −1.89123e10 | −0.127003 | ||||||||
\(305\) | 5.25083e10 | 0.347439 | ||||||||
\(306\) | 1.15267e10 | 0.0751550 | ||||||||
\(307\) | −2.72211e10 | −0.174897 | −0.0874487 | − | 0.996169i | \(-0.527871\pi\) | ||||
−0.0874487 | + | 0.996169i | \(0.527871\pi\) | |||||||
\(308\) | 1.30765e10 | 0.0827966 | ||||||||
\(309\) | 1.00221e11 | 0.625383 | ||||||||
\(310\) | 2.24033e10 | 0.137779 | ||||||||
\(311\) | 1.83257e11 | 1.11080 | 0.555402 | − | 0.831582i | \(-0.312564\pi\) | ||||
0.555402 | + | 0.831582i | \(0.312564\pi\) | |||||||
\(312\) | 3.40918e10 | 0.203683 | ||||||||
\(313\) | −1.76321e11 | −1.03837 | −0.519187 | − | 0.854661i | \(-0.673765\pi\) | ||||
−0.519187 | + | 0.854661i | \(0.673765\pi\) | |||||||
\(314\) | 4.17213e10 | 0.242200 | ||||||||
\(315\) | 3.27452e10 | 0.187392 | ||||||||
\(316\) | 1.10829e11 | 0.625259 | ||||||||
\(317\) | −1.66747e11 | −0.927454 | −0.463727 | − | 0.885978i | \(-0.653488\pi\) | ||||
−0.463727 | + | 0.885978i | \(0.653488\pi\) | |||||||
\(318\) | 1.52714e10 | 0.0837447 | ||||||||
\(319\) | 2.23512e10 | 0.120849 | ||||||||
\(320\) | 3.20989e11 | 1.71125 | ||||||||
\(321\) | −6.16982e10 | −0.324339 | ||||||||
\(322\) | 8.05805e9 | 0.0417713 | ||||||||
\(323\) | 4.21975e10 | 0.215712 | ||||||||
\(324\) | −2.16010e10 | −0.108898 | ||||||||
\(325\) | 7.00909e11 | 3.48487 | ||||||||
\(326\) | −2.50015e10 | −0.122599 | ||||||||
\(327\) | −4.87122e10 | −0.235599 | ||||||||
\(328\) | −7.28961e10 | −0.347754 | ||||||||
\(329\) | −6.04448e10 | −0.284431 | ||||||||
\(330\) | 9.91813e9 | 0.0460381 | ||||||||
\(331\) | 2.11596e11 | 0.968906 | 0.484453 | − | 0.874817i | \(-0.339019\pi\) | ||||
0.484453 | + | 0.874817i | \(0.339019\pi\) | |||||||
\(332\) | 1.19341e11 | 0.539097 | ||||||||
\(333\) | 2.27130e9 | 0.0101222 | ||||||||
\(334\) | −3.75325e10 | −0.165024 | ||||||||
\(335\) | 7.64298e11 | 3.31559 | ||||||||
\(336\) | −3.67841e10 | −0.157447 | ||||||||
\(337\) | 2.26484e11 | 0.956538 | 0.478269 | − | 0.878214i | \(-0.341264\pi\) | ||||
0.478269 | + | 0.878214i | \(0.341264\pi\) | |||||||
\(338\) | −2.01138e10 | −0.0838242 | ||||||||
\(339\) | 3.14397e10 | 0.129294 | ||||||||
\(340\) | −7.48199e11 | −3.03642 | ||||||||
\(341\) | 3.66327e10 | 0.146715 | ||||||||
\(342\) | 1.60682e9 | 0.00635111 | ||||||||
\(343\) | 1.42388e11 | 0.555456 | ||||||||
\(344\) | 1.13957e11 | 0.438760 | ||||||||
\(345\) | −3.00786e11 | −1.14307 | ||||||||
\(346\) | −1.56026e10 | −0.0585267 | ||||||||
\(347\) | −3.84748e11 | −1.42460 | −0.712300 | − | 0.701875i | \(-0.752347\pi\) | ||||
−0.712300 | + | 0.701875i | \(0.752347\pi\) | |||||||
\(348\) | −6.42051e10 | −0.234673 | ||||||||
\(349\) | −3.46454e11 | −1.25006 | −0.625031 | − | 0.780600i | \(-0.714914\pi\) | ||||
−0.625031 | + | 0.780600i | \(0.714914\pi\) | |||||||
\(350\) | 3.17031e10 | 0.112926 | ||||||||
\(351\) | 6.90945e10 | 0.242975 | ||||||||
\(352\) | −3.45944e10 | −0.120106 | ||||||||
\(353\) | 1.25860e11 | 0.431421 | 0.215710 | − | 0.976457i | \(-0.430793\pi\) | ||||
0.215710 | + | 0.976457i | \(0.430793\pi\) | |||||||
\(354\) | −3.13412e9 | −0.0106072 | ||||||||
\(355\) | −1.67652e11 | −0.560249 | ||||||||
\(356\) | 3.33189e11 | 1.09943 | ||||||||
\(357\) | 8.20735e10 | 0.267421 | ||||||||
\(358\) | −6.09348e10 | −0.196061 | ||||||||
\(359\) | −1.40320e11 | −0.445855 | −0.222927 | − | 0.974835i | \(-0.571561\pi\) | ||||
−0.222927 | + | 0.974835i | \(0.571561\pi\) | |||||||
\(360\) | −5.75596e10 | −0.180616 | ||||||||
\(361\) | −3.16805e11 | −0.981771 | ||||||||
\(362\) | 4.62171e10 | 0.141454 | ||||||||
\(363\) | −1.74776e11 | −0.528326 | ||||||||
\(364\) | 1.20151e11 | 0.358733 | ||||||||
\(365\) | −8.14000e11 | −2.40053 | ||||||||
\(366\) | 5.01146e9 | 0.0145982 | ||||||||
\(367\) | 5.93748e11 | 1.70846 | 0.854230 | − | 0.519896i | \(-0.174029\pi\) | ||||
0.854230 | + | 0.519896i | \(0.174029\pi\) | |||||||
\(368\) | 3.37886e11 | 0.960407 | ||||||||
\(369\) | −1.47740e11 | −0.414839 | ||||||||
\(370\) | 2.99570e9 | 0.00830981 | ||||||||
\(371\) | 1.08737e11 | 0.297986 | ||||||||
\(372\) | −1.05229e11 | −0.284901 | ||||||||
\(373\) | 5.66466e10 | 0.151525 | 0.0757624 | − | 0.997126i | \(-0.475861\pi\) | ||||
0.0757624 | + | 0.997126i | \(0.475861\pi\) | |||||||
\(374\) | 2.48591e10 | 0.0656996 | ||||||||
\(375\) | −7.54663e11 | −1.97066 | ||||||||
\(376\) | 1.06250e11 | 0.274147 | ||||||||
\(377\) | 2.05371e11 | 0.523604 | ||||||||
\(378\) | 3.12524e9 | 0.00787354 | ||||||||
\(379\) | 7.08119e11 | 1.76291 | 0.881454 | − | 0.472269i | \(-0.156565\pi\) | ||||
0.881454 | + | 0.472269i | \(0.156565\pi\) | |||||||
\(380\) | −1.04299e11 | −0.256598 | ||||||||
\(381\) | −2.83930e11 | −0.690318 | ||||||||
\(382\) | 2.87204e10 | 0.0690090 | ||||||||
\(383\) | −7.14910e11 | −1.69768 | −0.848842 | − | 0.528647i | \(-0.822699\pi\) | ||||
−0.848842 | + | 0.528647i | \(0.822699\pi\) | |||||||
\(384\) | 1.32029e11 | 0.309869 | ||||||||
\(385\) | 7.06201e10 | 0.163816 | ||||||||
\(386\) | 6.57767e9 | 0.0150810 | ||||||||
\(387\) | 2.30959e11 | 0.523401 | ||||||||
\(388\) | −5.20240e11 | −1.16536 | ||||||||
\(389\) | −8.65936e11 | −1.91740 | −0.958700 | − | 0.284421i | \(-0.908199\pi\) | ||||
−0.958700 | + | 0.284421i | \(0.908199\pi\) | |||||||
\(390\) | 9.11312e10 | 0.199470 | ||||||||
\(391\) | −7.53899e11 | −1.63124 | ||||||||
\(392\) | −1.19655e11 | −0.255943 | ||||||||
\(393\) | −1.12507e11 | −0.237911 | ||||||||
\(394\) | 1.11048e10 | 0.0232154 | ||||||||
\(395\) | 5.98535e11 | 1.23709 | ||||||||
\(396\) | −4.65859e10 | −0.0951977 | ||||||||
\(397\) | −6.09151e11 | −1.23074 | −0.615372 | − | 0.788237i | \(-0.710994\pi\) | ||||
−0.615372 | + | 0.788237i | \(0.710994\pi\) | |||||||
\(398\) | 6.12133e10 | 0.122285 | ||||||||
\(399\) | 1.14410e10 | 0.0225989 | ||||||||
\(400\) | 1.32936e12 | 2.59641 | ||||||||
\(401\) | −9.64079e10 | −0.186193 | −0.0930964 | − | 0.995657i | \(-0.529676\pi\) | ||||
−0.0930964 | + | 0.995657i | \(0.529676\pi\) | |||||||
\(402\) | 7.29455e10 | 0.139310 | ||||||||
\(403\) | 3.36594e11 | 0.635672 | ||||||||
\(404\) | −6.84846e11 | −1.27902 | ||||||||
\(405\) | −1.16657e11 | −0.215459 | ||||||||
\(406\) | 9.28922e9 | 0.0169673 | ||||||||
\(407\) | 4.89842e9 | 0.00884874 | ||||||||
\(408\) | −1.44269e11 | −0.257752 | ||||||||
\(409\) | 7.08037e10 | 0.125113 | 0.0625563 | − | 0.998041i | \(-0.480075\pi\) | ||||
0.0625563 | + | 0.998041i | \(0.480075\pi\) | |||||||
\(410\) | −1.94860e11 | −0.340561 | ||||||||
\(411\) | −2.94271e11 | −0.508697 | ||||||||
\(412\) | −6.20881e11 | −1.06162 | ||||||||
\(413\) | −2.23159e10 | −0.0377432 | ||||||||
\(414\) | −2.87074e10 | −0.0480278 | ||||||||
\(415\) | 6.44504e11 | 1.06662 | ||||||||
\(416\) | −3.17865e11 | −0.520383 | ||||||||
\(417\) | −1.17572e11 | −0.190411 | ||||||||
\(418\) | 3.46536e9 | 0.00555207 | ||||||||
\(419\) | −7.01996e11 | −1.11268 | −0.556342 | − | 0.830954i | \(-0.687795\pi\) | ||||
−0.556342 | + | 0.830954i | \(0.687795\pi\) | |||||||
\(420\) | −2.02860e11 | −0.318108 | ||||||||
\(421\) | −2.42037e11 | −0.375503 | −0.187751 | − | 0.982217i | \(-0.560120\pi\) | ||||
−0.187751 | + | 0.982217i | \(0.560120\pi\) | |||||||
\(422\) | −1.15712e11 | −0.177612 | ||||||||
\(423\) | 2.15339e11 | 0.327033 | ||||||||
\(424\) | −1.91138e11 | −0.287211 | ||||||||
\(425\) | −2.96610e12 | −4.40996 | ||||||||
\(426\) | −1.60009e10 | −0.0235397 | ||||||||
\(427\) | 3.56831e10 | 0.0519442 | ||||||||
\(428\) | 3.82227e11 | 0.550585 | ||||||||
\(429\) | 1.49013e11 | 0.212406 | ||||||||
\(430\) | 3.04620e11 | 0.429685 | ||||||||
\(431\) | −3.96082e11 | −0.552888 | −0.276444 | − | 0.961030i | \(-0.589156\pi\) | ||||
−0.276444 | + | 0.961030i | \(0.589156\pi\) | |||||||
\(432\) | 1.31046e11 | 0.181029 | ||||||||
\(433\) | 7.07592e11 | 0.967358 | 0.483679 | − | 0.875245i | \(-0.339300\pi\) | ||||
0.483679 | + | 0.875245i | \(0.339300\pi\) | |||||||
\(434\) | 1.52246e10 | 0.0205988 | ||||||||
\(435\) | −3.46743e11 | −0.464307 | ||||||||
\(436\) | 3.01777e11 | 0.399942 | ||||||||
\(437\) | −1.05094e11 | −0.137851 | ||||||||
\(438\) | −7.76891e10 | −0.100862 | ||||||||
\(439\) | −6.89241e11 | −0.885688 | −0.442844 | − | 0.896599i | \(-0.646030\pi\) | ||||
−0.442844 | + | 0.896599i | \(0.646030\pi\) | |||||||
\(440\) | −1.24136e11 | −0.157893 | ||||||||
\(441\) | −2.42507e11 | −0.305317 | ||||||||
\(442\) | 2.28414e11 | 0.284657 | ||||||||
\(443\) | 1.07328e12 | 1.32403 | 0.662015 | − | 0.749491i | \(-0.269702\pi\) | ||||
0.662015 | + | 0.749491i | \(0.269702\pi\) | |||||||
\(444\) | −1.40710e10 | −0.0171831 | ||||||||
\(445\) | 1.79940e12 | 2.17525 | ||||||||
\(446\) | −1.11032e11 | −0.132874 | ||||||||
\(447\) | 2.70836e11 | 0.320866 | ||||||||
\(448\) | 2.18134e11 | 0.255843 | ||||||||
\(449\) | −6.19979e11 | −0.719894 | −0.359947 | − | 0.932973i | \(-0.617205\pi\) | ||||
−0.359947 | + | 0.932973i | \(0.617205\pi\) | |||||||
\(450\) | −1.12945e11 | −0.129840 | ||||||||
\(451\) | −3.18624e11 | −0.362647 | ||||||||
\(452\) | −1.94772e11 | −0.219485 | ||||||||
\(453\) | 3.33253e11 | 0.371819 | ||||||||
\(454\) | 1.91205e10 | 0.0211226 | ||||||||
\(455\) | 6.48882e11 | 0.709765 | ||||||||
\(456\) | −2.01111e10 | −0.0217818 | ||||||||
\(457\) | 4.70420e10 | 0.0504502 | 0.0252251 | − | 0.999682i | \(-0.491970\pi\) | ||||
0.0252251 | + | 0.999682i | \(0.491970\pi\) | |||||||
\(458\) | −2.01980e11 | −0.214493 | ||||||||
\(459\) | −2.92393e11 | −0.307475 | ||||||||
\(460\) | 1.86340e12 | 1.94042 | ||||||||
\(461\) | 6.86441e11 | 0.707863 | 0.353931 | − | 0.935271i | \(-0.384845\pi\) | ||||
0.353931 | + | 0.935271i | \(0.384845\pi\) | |||||||
\(462\) | 6.74007e9 | 0.00688296 | ||||||||
\(463\) | 9.62356e11 | 0.973243 | 0.486621 | − | 0.873613i | \(-0.338229\pi\) | ||||
0.486621 | + | 0.873613i | \(0.338229\pi\) | |||||||
\(464\) | 3.89511e11 | 0.390112 | ||||||||
\(465\) | −5.68296e11 | −0.563684 | ||||||||
\(466\) | 1.43462e10 | 0.0140929 | ||||||||
\(467\) | 1.04065e11 | 0.101246 | 0.0506230 | − | 0.998718i | \(-0.483879\pi\) | ||||
0.0506230 | + | 0.998718i | \(0.483879\pi\) | |||||||
\(468\) | −4.28048e11 | −0.412464 | ||||||||
\(469\) | 5.19394e11 | 0.495700 | ||||||||
\(470\) | 2.84019e11 | 0.268477 | ||||||||
\(471\) | −1.05833e12 | −0.990891 | ||||||||
\(472\) | 3.92269e10 | 0.0363785 | ||||||||
\(473\) | 4.98098e11 | 0.457551 | ||||||||
\(474\) | 5.71249e10 | 0.0519784 | ||||||||
\(475\) | −4.13474e11 | −0.372672 | ||||||||
\(476\) | −5.08454e11 | −0.453963 | ||||||||
\(477\) | −3.87384e11 | −0.342617 | ||||||||
\(478\) | 1.30326e11 | 0.114184 | ||||||||
\(479\) | −1.00881e12 | −0.875585 | −0.437793 | − | 0.899076i | \(-0.644240\pi\) | ||||
−0.437793 | + | 0.899076i | \(0.644240\pi\) | |||||||
\(480\) | 5.36675e11 | 0.461451 | ||||||||
\(481\) | 4.50084e10 | 0.0383390 | ||||||||
\(482\) | −3.55318e10 | −0.0299851 | ||||||||
\(483\) | −2.04405e11 | −0.170895 | ||||||||
\(484\) | 1.08276e12 | 0.896865 | ||||||||
\(485\) | −2.80958e12 | −2.30570 | ||||||||
\(486\) | −1.11339e10 | −0.00905283 | ||||||||
\(487\) | 1.55674e12 | 1.25411 | 0.627053 | − | 0.778976i | \(-0.284261\pi\) | ||||
0.627053 | + | 0.778976i | \(0.284261\pi\) | |||||||
\(488\) | −6.27239e10 | −0.0500661 | ||||||||
\(489\) | 6.34203e11 | 0.501578 | ||||||||
\(490\) | −3.19852e11 | −0.250649 | ||||||||
\(491\) | 2.06409e12 | 1.60273 | 0.801367 | − | 0.598173i | \(-0.204106\pi\) | ||||
0.801367 | + | 0.598173i | \(0.204106\pi\) | |||||||
\(492\) | 9.15265e11 | 0.704212 | ||||||||
\(493\) | −8.69086e11 | −0.662600 | ||||||||
\(494\) | 3.18409e10 | 0.0240555 | ||||||||
\(495\) | −2.51589e11 | −0.188352 | ||||||||
\(496\) | 6.38391e11 | 0.473608 | ||||||||
\(497\) | −1.13931e11 | −0.0837606 | ||||||||
\(498\) | 6.15123e10 | 0.0448156 | ||||||||
\(499\) | −1.98601e12 | −1.43393 | −0.716966 | − | 0.697108i | \(-0.754470\pi\) | ||||
−0.716966 | + | 0.697108i | \(0.754470\pi\) | |||||||
\(500\) | 4.67522e12 | 3.34531 | ||||||||
\(501\) | 9.52073e11 | 0.675150 | ||||||||
\(502\) | −8.76924e10 | −0.0616304 | ||||||||
\(503\) | −1.09056e12 | −0.759617 | −0.379808 | − | 0.925065i | \(-0.624010\pi\) | ||||
−0.379808 | + | 0.925065i | \(0.624010\pi\) | |||||||
\(504\) | −3.91158e10 | −0.0270032 | ||||||||
\(505\) | −3.69854e12 | −2.53058 | ||||||||
\(506\) | −6.19120e10 | −0.0419853 | ||||||||
\(507\) | 5.10219e11 | 0.342942 | ||||||||
\(508\) | 1.75898e12 | 1.17185 | ||||||||
\(509\) | −2.18830e12 | −1.44503 | −0.722513 | − | 0.691357i | \(-0.757013\pi\) | ||||
−0.722513 | + | 0.691357i | \(0.757013\pi\) | |||||||
\(510\) | −3.85648e11 | −0.252421 | ||||||||
\(511\) | −5.53170e11 | −0.358893 | ||||||||
\(512\) | −1.01158e12 | −0.650557 | ||||||||
\(513\) | −4.07596e10 | −0.0259837 | ||||||||
\(514\) | 2.75848e11 | 0.174316 | ||||||||
\(515\) | −3.35310e12 | −2.10046 | ||||||||
\(516\) | −1.43081e12 | −0.888504 | ||||||||
\(517\) | 4.64413e11 | 0.285888 | ||||||||
\(518\) | 2.03579e9 | 0.00124237 | ||||||||
\(519\) | 3.95785e11 | 0.239445 | ||||||||
\(520\) | −1.14061e12 | −0.684102 | ||||||||
\(521\) | 1.77724e12 | 1.05676 | 0.528379 | − | 0.849008i | \(-0.322800\pi\) | ||||
0.528379 | + | 0.849008i | \(0.322800\pi\) | |||||||
\(522\) | −3.30935e10 | −0.0195086 | ||||||||
\(523\) | −1.31100e12 | −0.766207 | −0.383104 | − | 0.923705i | \(-0.625145\pi\) | ||||
−0.383104 | + | 0.923705i | \(0.625145\pi\) | |||||||
\(524\) | 6.96994e11 | 0.403867 | ||||||||
\(525\) | −8.04201e11 | −0.462006 | ||||||||
\(526\) | 4.74927e10 | 0.0270515 | ||||||||
\(527\) | −1.42439e12 | −0.804418 | ||||||||
\(528\) | 2.82621e11 | 0.158253 | ||||||||
\(529\) | 7.64464e10 | 0.0424431 | ||||||||
\(530\) | −5.10935e11 | −0.281271 | ||||||||
\(531\) | 7.95020e10 | 0.0433963 | ||||||||
\(532\) | −7.08785e10 | −0.0383629 | ||||||||
\(533\) | −2.92763e12 | −1.57124 | ||||||||
\(534\) | 1.71737e11 | 0.0913964 | ||||||||
\(535\) | 2.06423e12 | 1.08935 | ||||||||
\(536\) | −9.12993e11 | −0.477778 | ||||||||
\(537\) | 1.54571e12 | 0.802128 | ||||||||
\(538\) | 3.59469e11 | 0.184987 | ||||||||
\(539\) | −5.23005e11 | −0.266905 | ||||||||
\(540\) | 7.22704e11 | 0.365753 | ||||||||
\(541\) | 2.91894e12 | 1.46500 | 0.732499 | − | 0.680768i | \(-0.238354\pi\) | ||||
0.732499 | + | 0.680768i | \(0.238354\pi\) | |||||||
\(542\) | 4.68763e11 | 0.233322 | ||||||||
\(543\) | −1.17237e12 | −0.578716 | ||||||||
\(544\) | 1.34514e12 | 0.658524 | ||||||||
\(545\) | 1.62976e12 | 0.791298 | ||||||||
\(546\) | 6.19301e10 | 0.0298219 | ||||||||
\(547\) | −6.69857e10 | −0.0319918 | −0.0159959 | − | 0.999872i | \(-0.505092\pi\) | ||||
−0.0159959 | + | 0.999872i | \(0.505092\pi\) | |||||||
\(548\) | 1.82304e12 | 0.863542 | ||||||||
\(549\) | −1.27124e11 | −0.0597243 | ||||||||
\(550\) | −2.43583e11 | −0.113505 | ||||||||
\(551\) | −1.21150e11 | −0.0559942 | ||||||||
\(552\) | 3.59305e11 | 0.164716 | ||||||||
\(553\) | 4.06747e11 | 0.184953 | ||||||||
\(554\) | 4.57895e10 | 0.0206525 | ||||||||
\(555\) | −7.59909e10 | −0.0339972 | ||||||||
\(556\) | 7.28370e11 | 0.323233 | ||||||||
\(557\) | −6.11851e11 | −0.269338 | −0.134669 | − | 0.990891i | \(-0.542997\pi\) | ||||
−0.134669 | + | 0.990891i | \(0.542997\pi\) | |||||||
\(558\) | −5.42388e10 | −0.0236841 | ||||||||
\(559\) | 4.57670e12 | 1.98244 | ||||||||
\(560\) | 1.23068e12 | 0.528811 | ||||||||
\(561\) | −6.30591e11 | −0.268791 | ||||||||
\(562\) | 5.95984e11 | 0.252012 | ||||||||
\(563\) | −3.59339e12 | −1.50736 | −0.753680 | − | 0.657241i | \(-0.771723\pi\) | ||||
−0.753680 | + | 0.657241i | \(0.771723\pi\) | |||||||
\(564\) | −1.33405e12 | −0.555157 | ||||||||
\(565\) | −1.05188e12 | −0.434257 | ||||||||
\(566\) | −3.69829e11 | −0.151470 | ||||||||
\(567\) | −7.92768e10 | −0.0322123 | ||||||||
\(568\) | 2.00269e11 | 0.0807321 | ||||||||
\(569\) | 2.36321e12 | 0.945141 | 0.472571 | − | 0.881293i | \(-0.343326\pi\) | ||||
0.472571 | + | 0.881293i | \(0.343326\pi\) | |||||||
\(570\) | −5.37593e10 | −0.0213313 | ||||||||
\(571\) | 3.97794e11 | 0.156601 | 0.0783007 | − | 0.996930i | \(-0.475051\pi\) | ||||
0.0783007 | + | 0.996930i | \(0.475051\pi\) | |||||||
\(572\) | −9.23152e11 | −0.360571 | ||||||||
\(573\) | −7.28540e11 | −0.282330 | ||||||||
\(574\) | −1.32421e11 | −0.0509158 | ||||||||
\(575\) | 7.38711e12 | 2.81819 | ||||||||
\(576\) | −7.77120e11 | −0.294162 | ||||||||
\(577\) | −3.37457e12 | −1.26744 | −0.633719 | − | 0.773563i | \(-0.718473\pi\) | ||||
−0.633719 | + | 0.773563i | \(0.718473\pi\) | |||||||
\(578\) | −5.87927e11 | −0.219103 | ||||||||
\(579\) | −1.66853e11 | −0.0616995 | ||||||||
\(580\) | 2.14811e12 | 0.788188 | ||||||||
\(581\) | 4.37986e11 | 0.159466 | ||||||||
\(582\) | −2.68149e11 | −0.0968776 | ||||||||
\(583\) | −8.35455e11 | −0.299512 | ||||||||
\(584\) | 9.72364e11 | 0.345916 | ||||||||
\(585\) | −2.31169e12 | −0.816072 | ||||||||
\(586\) | 7.21905e11 | 0.252895 | ||||||||
\(587\) | 3.37780e12 | 1.17425 | 0.587127 | − | 0.809495i | \(-0.300259\pi\) | ||||
0.587127 | + | 0.809495i | \(0.300259\pi\) | |||||||
\(588\) | 1.50236e12 | 0.518293 | ||||||||
\(589\) | −1.98560e11 | −0.0679788 | ||||||||
\(590\) | 1.04858e11 | 0.0356261 | ||||||||
\(591\) | −2.81690e11 | −0.0949791 | ||||||||
\(592\) | 8.53639e10 | 0.0285645 | ||||||||
\(593\) | 3.82059e12 | 1.26877 | 0.634386 | − | 0.773016i | \(-0.281253\pi\) | ||||
0.634386 | + | 0.773016i | \(0.281253\pi\) | |||||||
\(594\) | −2.40120e10 | −0.00791388 | ||||||||
\(595\) | −2.74593e12 | −0.898179 | ||||||||
\(596\) | −1.67786e12 | −0.544688 | ||||||||
\(597\) | −1.55277e12 | −0.500292 | ||||||||
\(598\) | −5.68869e11 | −0.181910 | ||||||||
\(599\) | 5.37586e12 | 1.70619 | 0.853095 | − | 0.521756i | \(-0.174723\pi\) | ||||
0.853095 | + | 0.521756i | \(0.174723\pi\) | |||||||
\(600\) | 1.41363e12 | 0.445301 | ||||||||
\(601\) | −5.38752e12 | −1.68443 | −0.842216 | − | 0.539140i | \(-0.818749\pi\) | ||||
−0.842216 | + | 0.539140i | \(0.818749\pi\) | |||||||
\(602\) | 2.07011e11 | 0.0642404 | ||||||||
\(603\) | −1.85038e12 | −0.569945 | ||||||||
\(604\) | −2.06453e12 | −0.631184 | ||||||||
\(605\) | 5.84748e12 | 1.77447 | ||||||||
\(606\) | −3.52993e11 | −0.106326 | ||||||||
\(607\) | 3.90671e12 | 1.16805 | 0.584026 | − | 0.811735i | \(-0.301477\pi\) | ||||
0.584026 | + | 0.811735i | \(0.301477\pi\) | |||||||
\(608\) | 1.87512e11 | 0.0556498 | ||||||||
\(609\) | −2.35636e11 | −0.0694167 | ||||||||
\(610\) | −1.67668e11 | −0.0490305 | ||||||||
\(611\) | 4.26719e12 | 1.23867 | ||||||||
\(612\) | 1.81141e12 | 0.521957 | ||||||||
\(613\) | −6.06879e12 | −1.73592 | −0.867961 | − | 0.496633i | \(-0.834569\pi\) | ||||
−0.867961 | + | 0.496633i | \(0.834569\pi\) | |||||||
\(614\) | 8.69217e10 | 0.0246815 | ||||||||
\(615\) | 4.94293e12 | 1.39331 | ||||||||
\(616\) | −8.43593e10 | −0.0236059 | ||||||||
\(617\) | −3.25090e12 | −0.903068 | −0.451534 | − | 0.892254i | \(-0.649123\pi\) | ||||
−0.451534 | + | 0.892254i | \(0.649123\pi\) | |||||||
\(618\) | −3.20023e11 | −0.0882539 | ||||||||
\(619\) | −1.92638e12 | −0.527392 | −0.263696 | − | 0.964606i | \(-0.584942\pi\) | ||||
−0.263696 | + | 0.964606i | \(0.584942\pi\) | |||||||
\(620\) | 3.52065e12 | 0.956887 | ||||||||
\(621\) | 7.28210e11 | 0.196492 | ||||||||
\(622\) | −5.85170e11 | −0.156756 | ||||||||
\(623\) | 1.22282e12 | 0.325212 | ||||||||
\(624\) | 2.59682e12 | 0.685665 | ||||||||
\(625\) | 1.47193e13 | 3.85858 | ||||||||
\(626\) | 5.63022e11 | 0.146535 | ||||||||
\(627\) | −8.79044e10 | −0.0227147 | ||||||||
\(628\) | 6.55645e12 | 1.68210 | ||||||||
\(629\) | −1.90466e11 | −0.0485165 | ||||||||
\(630\) | −1.04561e11 | −0.0264446 | ||||||||
\(631\) | −3.10554e12 | −0.779839 | −0.389919 | − | 0.920849i | \(-0.627497\pi\) | ||||
−0.389919 | + | 0.920849i | \(0.627497\pi\) | |||||||
\(632\) | −7.14981e11 | −0.178266 | ||||||||
\(633\) | 2.93523e12 | 0.726650 | ||||||||
\(634\) | 5.32453e11 | 0.130882 | ||||||||
\(635\) | 9.49944e12 | 2.31855 | ||||||||
\(636\) | 2.39989e12 | 0.581613 | ||||||||
\(637\) | −4.80555e12 | −1.15642 | ||||||||
\(638\) | −7.13714e10 | −0.0170542 | ||||||||
\(639\) | 4.05889e11 | 0.0963061 | ||||||||
\(640\) | −4.41729e12 | −1.04075 | ||||||||
\(641\) | −5.08337e12 | −1.18930 | −0.594649 | − | 0.803986i | \(-0.702709\pi\) | ||||
−0.594649 | + | 0.803986i | \(0.702709\pi\) | |||||||
\(642\) | 1.97013e11 | 0.0457706 | ||||||||
\(643\) | 2.93307e12 | 0.676664 | 0.338332 | − | 0.941027i | \(-0.390137\pi\) | ||||
0.338332 | + | 0.941027i | \(0.390137\pi\) | |||||||
\(644\) | 1.26631e12 | 0.290105 | ||||||||
\(645\) | −7.72717e12 | −1.75793 | ||||||||
\(646\) | −1.34744e11 | −0.0304412 | ||||||||
\(647\) | 1.70042e12 | 0.381493 | 0.190746 | − | 0.981639i | \(-0.438909\pi\) | ||||
0.190746 | + | 0.981639i | \(0.438909\pi\) | |||||||
\(648\) | 1.39353e11 | 0.0310477 | ||||||||
\(649\) | 1.71458e11 | 0.0379366 | ||||||||
\(650\) | −2.23812e12 | −0.491784 | ||||||||
\(651\) | −3.86197e11 | −0.0842741 | ||||||||
\(652\) | −3.92895e12 | −0.851457 | ||||||||
\(653\) | −2.02165e12 | −0.435107 | −0.217554 | − | 0.976048i | \(-0.569808\pi\) | ||||
−0.217554 | + | 0.976048i | \(0.569808\pi\) | |||||||
\(654\) | 1.55546e11 | 0.0332476 | ||||||||
\(655\) | 3.76415e12 | 0.799063 | ||||||||
\(656\) | −5.55261e12 | −1.17066 | ||||||||
\(657\) | 1.97071e12 | 0.412647 | ||||||||
\(658\) | 1.93011e11 | 0.0401389 | ||||||||
\(659\) | −5.03004e11 | −0.103893 | −0.0519466 | − | 0.998650i | \(-0.516543\pi\) | ||||
−0.0519466 | + | 0.998650i | \(0.516543\pi\) | |||||||
\(660\) | 1.55862e12 | 0.319738 | ||||||||
\(661\) | −8.54822e12 | −1.74168 | −0.870841 | − | 0.491565i | \(-0.836425\pi\) | ||||
−0.870841 | + | 0.491565i | \(0.836425\pi\) | |||||||
\(662\) | −6.75663e11 | −0.136732 | ||||||||
\(663\) | −5.79409e12 | −1.16459 | ||||||||
\(664\) | −7.69893e11 | −0.153700 | ||||||||
\(665\) | −3.82782e11 | −0.0759022 | ||||||||
\(666\) | −7.25266e9 | −0.00142845 | ||||||||
\(667\) | 2.16447e12 | 0.423434 | ||||||||
\(668\) | −5.89819e12 | −1.14611 | ||||||||
\(669\) | 2.81650e12 | 0.543616 | ||||||||
\(670\) | −2.44053e12 | −0.467895 | ||||||||
\(671\) | −2.74162e11 | −0.0522103 | ||||||||
\(672\) | 3.64708e11 | 0.0689897 | ||||||||
\(673\) | −2.43690e12 | −0.457900 | −0.228950 | − | 0.973438i | \(-0.573529\pi\) | ||||
−0.228950 | + | 0.973438i | \(0.573529\pi\) | |||||||
\(674\) | −7.23201e11 | −0.134986 | ||||||||
\(675\) | 2.86503e12 | 0.531204 | ||||||||
\(676\) | −3.16086e12 | −0.582164 | ||||||||
\(677\) | −9.41571e12 | −1.72268 | −0.861339 | − | 0.508030i | \(-0.830374\pi\) | ||||
−0.861339 | + | 0.508030i | \(0.830374\pi\) | |||||||
\(678\) | −1.00392e11 | −0.0182460 | ||||||||
\(679\) | −1.90931e12 | −0.344716 | ||||||||
\(680\) | 4.82680e12 | 0.865704 | ||||||||
\(681\) | −4.85021e11 | −0.0864170 | ||||||||
\(682\) | −1.16974e11 | −0.0207043 | ||||||||
\(683\) | −7.38882e12 | −1.29922 | −0.649609 | − | 0.760269i | \(-0.725067\pi\) | ||||
−0.649609 | + | 0.760269i | \(0.725067\pi\) | |||||||
\(684\) | 2.52510e11 | 0.0441089 | ||||||||
\(685\) | 9.84541e12 | 1.70854 | ||||||||
\(686\) | −4.54669e11 | −0.0783857 | ||||||||
\(687\) | 5.12354e12 | 0.877536 | ||||||||
\(688\) | 8.68027e12 | 1.47702 | ||||||||
\(689\) | −7.67645e12 | −1.29770 | ||||||||
\(690\) | 9.60462e11 | 0.161309 | ||||||||
\(691\) | −4.29537e12 | −0.716719 | −0.358360 | − | 0.933584i | \(-0.616664\pi\) | ||||
−0.358360 | + | 0.933584i | \(0.616664\pi\) | |||||||
\(692\) | −2.45193e12 | −0.406472 | ||||||||
\(693\) | −1.70973e11 | −0.0281597 | ||||||||
\(694\) | 1.22857e12 | 0.201039 | ||||||||
\(695\) | 3.93360e12 | 0.639526 | ||||||||
\(696\) | 4.14202e11 | 0.0669068 | ||||||||
\(697\) | 1.23891e13 | 1.98835 | ||||||||
\(698\) | 1.10629e12 | 0.176408 | ||||||||
\(699\) | −3.63914e11 | −0.0576569 | ||||||||
\(700\) | 4.98211e12 | 0.784281 | ||||||||
\(701\) | 1.56584e12 | 0.244916 | 0.122458 | − | 0.992474i | \(-0.460922\pi\) | ||||
0.122458 | + | 0.992474i | \(0.460922\pi\) | |||||||
\(702\) | −2.20631e11 | −0.0342885 | ||||||||
\(703\) | −2.65509e10 | −0.00409997 | ||||||||
\(704\) | −1.67598e12 | −0.257153 | ||||||||
\(705\) | −7.20460e12 | −1.09840 | ||||||||
\(706\) | −4.01892e11 | −0.0608819 | ||||||||
\(707\) | −2.51342e12 | −0.378336 | ||||||||
\(708\) | −4.92523e11 | −0.0736677 | ||||||||
\(709\) | −4.53682e12 | −0.674285 | −0.337143 | − | 0.941454i | \(-0.609460\pi\) | ||||
−0.337143 | + | 0.941454i | \(0.609460\pi\) | |||||||
\(710\) | 5.35342e11 | 0.0790622 | ||||||||
\(711\) | −1.44907e12 | −0.212655 | ||||||||
\(712\) | −2.14948e12 | −0.313454 | ||||||||
\(713\) | 3.54747e12 | 0.514063 | ||||||||
\(714\) | −2.62075e11 | −0.0377384 | ||||||||
\(715\) | −4.98552e12 | −0.713401 | ||||||||
\(716\) | −9.57584e12 | −1.36166 | ||||||||
\(717\) | −3.30594e12 | −0.467152 | ||||||||
\(718\) | 4.48065e11 | 0.0629189 | ||||||||
\(719\) | −9.46521e11 | −0.132084 | −0.0660420 | − | 0.997817i | \(-0.521037\pi\) | ||||
−0.0660420 | + | 0.997817i | \(0.521037\pi\) | |||||||
\(720\) | −4.38440e12 | −0.608015 | ||||||||
\(721\) | −2.27866e12 | −0.314030 | ||||||||
\(722\) | 1.01161e12 | 0.138547 | ||||||||
\(723\) | 9.01323e11 | 0.122676 | ||||||||
\(724\) | 7.26296e12 | 0.982404 | ||||||||
\(725\) | 8.51577e12 | 1.14473 | ||||||||
\(726\) | 5.58090e11 | 0.0745572 | ||||||||
\(727\) | −1.17432e13 | −1.55913 | −0.779567 | − | 0.626319i | \(-0.784561\pi\) | ||||
−0.779567 | + | 0.626319i | \(0.784561\pi\) | |||||||
\(728\) | −7.75123e11 | −0.102277 | ||||||||
\(729\) | 2.82430e11 | 0.0370370 | ||||||||
\(730\) | 2.59924e12 | 0.338761 | ||||||||
\(731\) | −1.93676e13 | −2.50870 | ||||||||
\(732\) | 7.87545e11 | 0.101385 | ||||||||
\(733\) | −1.11342e13 | −1.42460 | −0.712299 | − | 0.701876i | \(-0.752346\pi\) | ||||
−0.712299 | + | 0.701876i | \(0.752346\pi\) | |||||||
\(734\) | −1.89594e12 | −0.241097 | ||||||||
\(735\) | 8.11356e12 | 1.02546 | ||||||||
\(736\) | −3.35009e12 | −0.420829 | ||||||||
\(737\) | −3.99063e12 | −0.498240 | ||||||||
\(738\) | 4.71759e11 | 0.0585419 | ||||||||
\(739\) | −1.07908e13 | −1.33092 | −0.665462 | − | 0.746432i | \(-0.731765\pi\) | ||||
−0.665462 | + | 0.746432i | \(0.731765\pi\) | |||||||
\(740\) | 4.70772e11 | 0.0577122 | ||||||||
\(741\) | −8.07696e11 | −0.0984161 | ||||||||
\(742\) | −3.47216e11 | −0.0420516 | ||||||||
\(743\) | 2.76883e12 | 0.333309 | 0.166655 | − | 0.986015i | \(-0.446704\pi\) | ||||
0.166655 | + | 0.986015i | \(0.446704\pi\) | |||||||
\(744\) | 6.78858e11 | 0.0812271 | ||||||||
\(745\) | −9.06137e12 | −1.07768 | ||||||||
\(746\) | −1.80882e11 | −0.0213831 | ||||||||
\(747\) | −1.56036e12 | −0.183350 | ||||||||
\(748\) | 3.90658e12 | 0.456288 | ||||||||
\(749\) | 1.40279e12 | 0.162864 | ||||||||
\(750\) | 2.40977e12 | 0.278099 | ||||||||
\(751\) | 1.09208e13 | 1.25278 | 0.626390 | − | 0.779510i | \(-0.284532\pi\) | ||||
0.626390 | + | 0.779510i | \(0.284532\pi\) | |||||||
\(752\) | 8.09324e12 | 0.922873 | ||||||||
\(753\) | 2.22446e12 | 0.252143 | ||||||||
\(754\) | −6.55785e11 | −0.0738908 | ||||||||
\(755\) | −1.11496e13 | −1.24882 | ||||||||
\(756\) | 4.91128e11 | 0.0546823 | ||||||||
\(757\) | 4.41484e12 | 0.488634 | 0.244317 | − | 0.969695i | \(-0.421436\pi\) | ||||
0.244317 | + | 0.969695i | \(0.421436\pi\) | |||||||
\(758\) | −2.26115e12 | −0.248781 | ||||||||
\(759\) | 1.57050e12 | 0.171771 | ||||||||
\(760\) | 6.72856e11 | 0.0731579 | ||||||||
\(761\) | 5.46578e12 | 0.590774 | 0.295387 | − | 0.955378i | \(-0.404551\pi\) | ||||
0.295387 | + | 0.955378i | \(0.404551\pi\) | |||||||
\(762\) | 9.06638e11 | 0.0974174 | ||||||||
\(763\) | 1.10754e12 | 0.118304 | ||||||||
\(764\) | 4.51338e12 | 0.479272 | ||||||||
\(765\) | 9.78258e12 | 1.03271 | ||||||||
\(766\) | 2.28283e12 | 0.239576 | ||||||||
\(767\) | 1.57542e12 | 0.164368 | ||||||||
\(768\) | 4.49057e12 | 0.465775 | ||||||||
\(769\) | −6.66656e12 | −0.687437 | −0.343719 | − | 0.939073i | \(-0.611687\pi\) | ||||
−0.343719 | + | 0.939073i | \(0.611687\pi\) | |||||||
\(770\) | −2.25502e11 | −0.0231176 | ||||||||
\(771\) | −6.99734e12 | −0.713162 | ||||||||
\(772\) | 1.03367e12 | 0.104738 | ||||||||
\(773\) | −1.37755e13 | −1.38771 | −0.693855 | − | 0.720114i | \(-0.744089\pi\) | ||||
−0.693855 | + | 0.720114i | \(0.744089\pi\) | |||||||
\(774\) | −7.37491e11 | −0.0738622 | ||||||||
\(775\) | 1.39570e13 | 1.38974 | ||||||||
\(776\) | 3.35618e12 | 0.332252 | ||||||||
\(777\) | −5.16412e10 | −0.00508278 | ||||||||
\(778\) | 2.76508e12 | 0.270583 | ||||||||
\(779\) | 1.72704e12 | 0.168029 | ||||||||
\(780\) | 1.43212e13 | 1.38533 | ||||||||
\(781\) | 8.75364e11 | 0.0841897 | ||||||||
\(782\) | 2.40733e12 | 0.230200 | ||||||||
\(783\) | 8.39471e11 | 0.0798138 | ||||||||
\(784\) | −9.11431e12 | −0.861592 | ||||||||
\(785\) | 3.54084e13 | 3.32808 | ||||||||
\(786\) | 3.59255e11 | 0.0335739 | ||||||||
\(787\) | −1.16028e13 | −1.07815 | −0.539074 | − | 0.842259i | \(-0.681226\pi\) | ||||
−0.539074 | + | 0.842259i | \(0.681226\pi\) | |||||||
\(788\) | 1.74510e12 | 0.161232 | ||||||||
\(789\) | −1.20473e12 | −0.110673 | ||||||||
\(790\) | −1.91123e12 | −0.174578 | ||||||||
\(791\) | −7.14824e11 | −0.0649239 | ||||||||
\(792\) | 3.00536e11 | 0.0271415 | ||||||||
\(793\) | −2.51910e12 | −0.226212 | ||||||||
\(794\) | 1.94512e12 | 0.173682 | ||||||||
\(795\) | 1.29607e13 | 1.15074 | ||||||||
\(796\) | 9.61960e12 | 0.849275 | ||||||||
\(797\) | 4.99260e12 | 0.438293 | 0.219147 | − | 0.975692i | \(-0.429673\pi\) | ||||
0.219147 | + | 0.975692i | \(0.429673\pi\) | |||||||
\(798\) | −3.65332e10 | −0.00318915 | ||||||||
\(799\) | −1.80578e13 | −1.56749 | ||||||||
\(800\) | −1.31804e13 | −1.13769 | ||||||||
\(801\) | −4.35639e12 | −0.373922 | ||||||||
\(802\) | 3.07847e11 | 0.0262755 | ||||||||
\(803\) | 4.25014e12 | 0.360731 | ||||||||
\(804\) | 1.14633e13 | 0.967515 | ||||||||
\(805\) | 6.83878e12 | 0.573981 | ||||||||
\(806\) | −1.07480e12 | −0.0897059 | ||||||||
\(807\) | −9.11852e12 | −0.756822 | ||||||||
\(808\) | 4.41810e12 | 0.364657 | ||||||||
\(809\) | −2.00895e13 | −1.64892 | −0.824462 | − | 0.565918i | \(-0.808522\pi\) | ||||
−0.824462 | + | 0.565918i | \(0.808522\pi\) | |||||||
\(810\) | 3.72507e11 | 0.0304054 | ||||||||
\(811\) | −2.34770e13 | −1.90567 | −0.952837 | − | 0.303482i | \(-0.901851\pi\) | ||||
−0.952837 | + | 0.303482i | \(0.901851\pi\) | |||||||
\(812\) | 1.45979e12 | 0.117839 | ||||||||
\(813\) | −1.18909e13 | −0.954571 | ||||||||
\(814\) | −1.56415e10 | −0.00124873 | ||||||||
\(815\) | −2.12185e13 | −1.68463 | ||||||||
\(816\) | −1.09892e13 | −0.867681 | ||||||||
\(817\) | −2.69984e12 | −0.212002 | ||||||||
\(818\) | −2.26088e11 | −0.0176558 | ||||||||
\(819\) | −1.57096e12 | −0.122008 | ||||||||
\(820\) | −3.06220e13 | −2.36522 | ||||||||
\(821\) | −1.67424e13 | −1.28609 | −0.643047 | − | 0.765827i | \(-0.722330\pi\) | ||||
−0.643047 | + | 0.765827i | \(0.722330\pi\) | |||||||
\(822\) | 9.39658e11 | 0.0717871 | ||||||||
\(823\) | 1.40349e13 | 1.06638 | 0.533189 | − | 0.845996i | \(-0.320993\pi\) | ||||
0.533189 | + | 0.845996i | \(0.320993\pi\) | |||||||
\(824\) | 4.00544e12 | 0.302676 | ||||||||
\(825\) | 6.17887e12 | 0.464373 | ||||||||
\(826\) | 7.12585e10 | 0.00532631 | ||||||||
\(827\) | 1.64500e13 | 1.22290 | 0.611450 | − | 0.791283i | \(-0.290587\pi\) | ||||
0.611450 | + | 0.791283i | \(0.290587\pi\) | |||||||
\(828\) | −4.51134e12 | −0.333556 | ||||||||
\(829\) | 7.32077e12 | 0.538346 | 0.269173 | − | 0.963092i | \(-0.413250\pi\) | ||||
0.269173 | + | 0.963092i | \(0.413250\pi\) | |||||||
\(830\) | −2.05801e12 | −0.150521 | ||||||||
\(831\) | −1.16152e12 | −0.0844936 | ||||||||
\(832\) | −1.53995e13 | −1.11417 | ||||||||
\(833\) | 2.03361e13 | 1.46340 | ||||||||
\(834\) | 3.75427e11 | 0.0268707 | ||||||||
\(835\) | −3.18535e13 | −2.26760 | ||||||||
\(836\) | 5.44577e11 | 0.0385595 | ||||||||
\(837\) | 1.37586e12 | 0.0968965 | ||||||||
\(838\) | 2.24159e12 | 0.157021 | ||||||||
\(839\) | −3.76125e12 | −0.262062 | −0.131031 | − | 0.991378i | \(-0.541829\pi\) | ||||
−0.131031 | + | 0.991378i | \(0.541829\pi\) | |||||||
\(840\) | 1.30870e12 | 0.0906947 | ||||||||
\(841\) | −1.20120e13 | −0.828004 | ||||||||
\(842\) | 7.72867e11 | 0.0529908 | ||||||||
\(843\) | −1.51181e13 | −1.03103 | ||||||||
\(844\) | −1.81841e13 | −1.23353 | ||||||||
\(845\) | −1.70704e13 | −1.15183 | ||||||||
\(846\) | −6.87615e11 | −0.0461508 | ||||||||
\(847\) | 3.97377e12 | 0.265294 | ||||||||
\(848\) | −1.45593e13 | −0.966851 | ||||||||
\(849\) | 9.38130e12 | 0.619696 | ||||||||
\(850\) | 9.47126e12 | 0.622333 | ||||||||
\(851\) | 4.74358e11 | 0.0310044 | ||||||||
\(852\) | −2.51453e12 | −0.163485 | ||||||||
\(853\) | 1.07001e13 | 0.692016 | 0.346008 | − | 0.938232i | \(-0.387537\pi\) | ||||
0.346008 | + | 0.938232i | \(0.387537\pi\) | |||||||
\(854\) | −1.13942e11 | −0.00733035 | ||||||||
\(855\) | 1.36369e12 | 0.0872707 | ||||||||
\(856\) | −2.46583e12 | −0.156975 | ||||||||
\(857\) | −1.89336e13 | −1.19900 | −0.599501 | − | 0.800374i | \(-0.704634\pi\) | ||||
−0.599501 | + | 0.800374i | \(0.704634\pi\) | |||||||
\(858\) | −4.75824e11 | −0.0299746 | ||||||||
\(859\) | 3.57770e12 | 0.224199 | 0.112100 | − | 0.993697i | \(-0.464242\pi\) | ||||
0.112100 | + | 0.993697i | \(0.464242\pi\) | |||||||
\(860\) | 4.78707e13 | 2.98419 | ||||||||
\(861\) | 3.35907e12 | 0.208307 | ||||||||
\(862\) | 1.26476e12 | 0.0780234 | ||||||||
\(863\) | 2.26658e13 | 1.39099 | 0.695493 | − | 0.718533i | \(-0.255186\pi\) | ||||
0.695493 | + | 0.718533i | \(0.255186\pi\) | |||||||
\(864\) | −1.29930e12 | −0.0793228 | ||||||||
\(865\) | −1.32418e13 | −0.804217 | ||||||||
\(866\) | −2.25946e12 | −0.136513 | ||||||||
\(867\) | 1.49137e13 | 0.896397 | ||||||||
\(868\) | 2.39253e12 | 0.143060 | ||||||||
\(869\) | −3.12514e12 | −0.185900 | ||||||||
\(870\) | 1.10721e12 | 0.0655229 | ||||||||
\(871\) | −3.66673e13 | −2.15873 | ||||||||
\(872\) | −1.94683e12 | −0.114026 | ||||||||
\(873\) | 6.80205e12 | 0.396347 | ||||||||
\(874\) | 3.35582e11 | 0.0194535 | ||||||||
\(875\) | 1.71583e13 | 0.989550 | ||||||||
\(876\) | −1.22088e13 | −0.700492 | ||||||||
\(877\) | 1.66771e12 | 0.0951969 | 0.0475984 | − | 0.998867i | \(-0.484843\pi\) | ||||
0.0475984 | + | 0.998867i | \(0.484843\pi\) | |||||||
\(878\) | 2.20087e12 | 0.124988 | ||||||||
\(879\) | −1.83123e13 | −1.03465 | ||||||||
\(880\) | −9.45565e12 | −0.531520 | ||||||||
\(881\) | 2.99101e13 | 1.67273 | 0.836365 | − | 0.548172i | \(-0.184676\pi\) | ||||
0.836365 | + | 0.548172i | \(0.184676\pi\) | |||||||
\(882\) | 7.74368e11 | 0.0430862 | ||||||||
\(883\) | 1.23317e13 | 0.682654 | 0.341327 | − | 0.939945i | \(-0.389124\pi\) | ||||
0.341327 | + | 0.939945i | \(0.389124\pi\) | |||||||
\(884\) | 3.58950e13 | 1.97696 | ||||||||
\(885\) | −2.65990e12 | −0.145754 | ||||||||
\(886\) | −3.42718e12 | −0.186847 | ||||||||
\(887\) | 3.44036e12 | 0.186616 | 0.0933078 | − | 0.995637i | \(-0.470256\pi\) | ||||
0.0933078 | + | 0.995637i | \(0.470256\pi\) | |||||||
\(888\) | 9.07750e10 | 0.00489901 | ||||||||
\(889\) | 6.45554e12 | 0.346637 | ||||||||
\(890\) | −5.74581e12 | −0.306970 | ||||||||
\(891\) | 6.09103e11 | 0.0323774 | ||||||||
\(892\) | −1.74485e13 | −0.922819 | ||||||||
\(893\) | −2.51726e12 | −0.132463 | ||||||||
\(894\) | −8.64828e11 | −0.0452804 | ||||||||
\(895\) | −5.17148e13 | −2.69408 | ||||||||
\(896\) | −3.00186e12 | −0.155598 | ||||||||
\(897\) | 1.44303e13 | 0.744233 | ||||||||
\(898\) | 1.97970e12 | 0.101591 | ||||||||
\(899\) | 4.08948e12 | 0.208809 | ||||||||
\(900\) | −1.77491e13 | −0.901750 | ||||||||
\(901\) | 3.24851e13 | 1.64219 | ||||||||
\(902\) | 1.01742e12 | 0.0511766 | ||||||||
\(903\) | −5.25116e12 | −0.262821 | ||||||||
\(904\) | 1.25652e12 | 0.0625765 | ||||||||
\(905\) | 3.92240e13 | 1.94372 | ||||||||
\(906\) | −1.06413e12 | −0.0524710 | ||||||||
\(907\) | 2.75178e13 | 1.35015 | 0.675074 | − | 0.737750i | \(-0.264112\pi\) | ||||
0.675074 | + | 0.737750i | \(0.264112\pi\) | |||||||
\(908\) | 3.00476e12 | 0.146698 | ||||||||
\(909\) | 8.95425e12 | 0.435003 | ||||||||
\(910\) | −2.07199e12 | −0.100162 | ||||||||
\(911\) | −4.63688e12 | −0.223046 | −0.111523 | − | 0.993762i | \(-0.535573\pi\) | ||||
−0.111523 | + | 0.993762i | \(0.535573\pi\) | |||||||
\(912\) | −1.53189e12 | −0.0733250 | ||||||||
\(913\) | −3.36516e12 | −0.160283 | ||||||||
\(914\) | −1.50213e11 | −0.00711952 | ||||||||
\(915\) | 4.25317e12 | 0.200594 | ||||||||
\(916\) | −3.17409e13 | −1.48967 | ||||||||
\(917\) | 2.55800e12 | 0.119465 | ||||||||
\(918\) | 9.33661e11 | 0.0433908 | ||||||||
\(919\) | 9.65278e12 | 0.446409 | 0.223204 | − | 0.974772i | \(-0.428348\pi\) | ||||
0.223204 | + | 0.974772i | \(0.428348\pi\) | |||||||
\(920\) | −1.20212e13 | −0.553228 | ||||||||
\(921\) | −2.20491e12 | −0.100977 | ||||||||
\(922\) | −2.19192e12 | −0.0998933 | ||||||||
\(923\) | 8.04314e12 | 0.364769 | ||||||||
\(924\) | 1.05919e12 | 0.0478026 | ||||||||
\(925\) | 1.86629e12 | 0.0838187 | ||||||||
\(926\) | −3.07297e12 | −0.137344 | ||||||||
\(927\) | 8.11791e12 | 0.361065 | ||||||||
\(928\) | −3.86194e12 | −0.170938 | ||||||||
\(929\) | −1.76404e12 | −0.0777029 | −0.0388515 | − | 0.999245i | \(-0.512370\pi\) | ||||
−0.0388515 | + | 0.999245i | \(0.512370\pi\) | |||||||
\(930\) | 1.81467e12 | 0.0795469 | ||||||||
\(931\) | 2.83485e12 | 0.123668 | ||||||||
\(932\) | 2.25448e12 | 0.0978758 | ||||||||
\(933\) | 1.48438e13 | 0.641323 | ||||||||
\(934\) | −3.32297e11 | −0.0142878 | ||||||||
\(935\) | 2.10977e13 | 0.902780 | ||||||||
\(936\) | 2.76143e12 | 0.117596 | ||||||||
\(937\) | 4.03584e13 | 1.71043 | 0.855217 | − | 0.518270i | \(-0.173424\pi\) | ||||
0.855217 | + | 0.518270i | \(0.173424\pi\) | |||||||
\(938\) | −1.65851e12 | −0.0699530 | ||||||||
\(939\) | −1.42820e13 | −0.599505 | ||||||||
\(940\) | 4.46333e13 | 1.86459 | ||||||||
\(941\) | −4.23441e13 | −1.76051 | −0.880257 | − | 0.474497i | \(-0.842630\pi\) | ||||
−0.880257 | + | 0.474497i | \(0.842630\pi\) | |||||||
\(942\) | 3.37942e12 | 0.139834 | ||||||||
\(943\) | −3.08553e13 | −1.27065 | ||||||||
\(944\) | 2.98798e12 | 0.122463 | ||||||||
\(945\) | 2.65236e12 | 0.108191 | ||||||||
\(946\) | −1.59051e12 | −0.0645695 | ||||||||
\(947\) | 7.00700e12 | 0.283111 | 0.141556 | − | 0.989930i | \(-0.454790\pi\) | ||||
0.141556 | + | 0.989930i | \(0.454790\pi\) | |||||||
\(948\) | 8.97712e12 | 0.360994 | ||||||||
\(949\) | 3.90518e13 | 1.56294 | ||||||||
\(950\) | 1.32029e12 | 0.0525913 | ||||||||
\(951\) | −1.35065e13 | −0.535466 | ||||||||
\(952\) | 3.28015e12 | 0.129428 | ||||||||
\(953\) | 4.88462e13 | 1.91828 | 0.959142 | − | 0.282925i | \(-0.0913046\pi\) | ||||
0.959142 | + | 0.282925i | \(0.0913046\pi\) | |||||||
\(954\) | 1.23698e12 | 0.0483500 | ||||||||
\(955\) | 2.43747e13 | 0.948254 | ||||||||
\(956\) | 2.04806e13 | 0.793018 | ||||||||
\(957\) | 1.81045e12 | 0.0697723 | ||||||||
\(958\) | 3.22130e12 | 0.123562 | ||||||||
\(959\) | 6.69065e12 | 0.255437 | ||||||||
\(960\) | 2.60001e13 | 0.987993 | ||||||||
\(961\) | −1.97371e13 | −0.746499 | ||||||||
\(962\) | −1.43720e11 | −0.00541038 | ||||||||
\(963\) | −4.99755e12 | −0.187257 | ||||||||
\(964\) | −5.58379e12 | −0.208249 | ||||||||
\(965\) | 5.58241e12 | 0.207228 | ||||||||
\(966\) | 6.52702e11 | 0.0241167 | ||||||||
\(967\) | 1.66396e13 | 0.611962 | 0.305981 | − | 0.952038i | \(-0.401016\pi\) | ||||
0.305981 | + | 0.952038i | \(0.401016\pi\) | |||||||
\(968\) | −6.98511e12 | −0.255702 | ||||||||
\(969\) | 3.41800e12 | 0.124542 | ||||||||
\(970\) | 8.97147e12 | 0.325380 | ||||||||
\(971\) | 5.12205e13 | 1.84909 | 0.924543 | − | 0.381078i | \(-0.124447\pi\) | ||||
0.924543 | + | 0.381078i | \(0.124447\pi\) | |||||||
\(972\) | −1.74968e12 | −0.0628725 | ||||||||
\(973\) | 2.67315e12 | 0.0956129 | ||||||||
\(974\) | −4.97093e12 | −0.176979 | ||||||||
\(975\) | 5.67736e13 | 2.01199 | ||||||||
\(976\) | −4.77778e12 | −0.168539 | ||||||||
\(977\) | 1.79228e13 | 0.629333 | 0.314667 | − | 0.949202i | \(-0.398107\pi\) | ||||
0.314667 | + | 0.949202i | \(0.398107\pi\) | |||||||
\(978\) | −2.02512e12 | −0.0707824 | ||||||||
\(979\) | −9.39525e12 | −0.326878 | ||||||||
\(980\) | −5.02644e13 | −1.74078 | ||||||||
\(981\) | −3.94569e12 | −0.136023 | ||||||||
\(982\) | −6.59099e12 | −0.226177 | ||||||||
\(983\) | −2.58483e13 | −0.882961 | −0.441480 | − | 0.897271i | \(-0.645547\pi\) | ||||
−0.441480 | + | 0.897271i | \(0.645547\pi\) | |||||||
\(984\) | −5.90458e12 | −0.200776 | ||||||||
\(985\) | 9.42450e12 | 0.319003 | ||||||||
\(986\) | 2.77514e12 | 0.0935059 | ||||||||
\(987\) | −4.89603e12 | −0.164217 | ||||||||
\(988\) | 5.00376e12 | 0.167067 | ||||||||
\(989\) | 4.82354e13 | 1.60318 | ||||||||
\(990\) | 8.03369e11 | 0.0265801 | ||||||||
\(991\) | −1.55358e13 | −0.511686 | −0.255843 | − | 0.966718i | \(-0.582353\pi\) | ||||
−0.255843 | + | 0.966718i | \(0.582353\pi\) | |||||||
\(992\) | −6.32955e12 | −0.207525 | ||||||||
\(993\) | 1.71393e13 | 0.559398 | ||||||||
\(994\) | 3.63803e11 | 0.0118203 | ||||||||
\(995\) | 5.19511e13 | 1.68032 | ||||||||
\(996\) | 9.66658e12 | 0.311248 | ||||||||
\(997\) | 5.75049e13 | 1.84322 | 0.921609 | − | 0.388120i | \(-0.126875\pi\) | ||||
0.921609 | + | 0.388120i | \(0.126875\pi\) | |||||||
\(998\) | 6.34167e12 | 0.202356 | ||||||||
\(999\) | 1.83976e11 | 0.00584407 |
(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 | 177.10.a.a.1.11 | ✓ | 21 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.10.a.a.1.11 | ✓ | 21 | 1.1 | even | 1 | trivial |