Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [289,10,Mod(1,289)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(289, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("289.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 289 = 17^{2} \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 289.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(148.845356651\) |
Analytic rank: | \(1\) |
Dimension: | \(24\) |
Twist minimal: | no (minimal twist has level 17) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Character | \(\chi\) | \(=\) | 289.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −12.8587 | −0.568279 | −0.284139 | − | 0.958783i | \(-0.591708\pi\) | ||||
−0.284139 | + | 0.958783i | \(0.591708\pi\) | |||||||
\(3\) | −204.729 | −1.45926 | −0.729631 | − | 0.683841i | \(-0.760308\pi\) | ||||
−0.729631 | + | 0.683841i | \(0.760308\pi\) | |||||||
\(4\) | −346.654 | −0.677059 | ||||||||
\(5\) | 120.661 | 0.0863377 | 0.0431688 | − | 0.999068i | \(-0.486255\pi\) | ||||
0.0431688 | + | 0.999068i | \(0.486255\pi\) | |||||||
\(6\) | 2632.54 | 0.829268 | ||||||||
\(7\) | 4525.78 | 0.712446 | 0.356223 | − | 0.934401i | \(-0.384064\pi\) | ||||
0.356223 | + | 0.934401i | \(0.384064\pi\) | |||||||
\(8\) | 11041.2 | 0.953037 | ||||||||
\(9\) | 22230.9 | 1.12945 | ||||||||
\(10\) | −1551.54 | −0.0490639 | ||||||||
\(11\) | −57864.7 | −1.19165 | −0.595823 | − | 0.803116i | \(-0.703174\pi\) | ||||
−0.595823 | + | 0.803116i | \(0.703174\pi\) | |||||||
\(12\) | 70970.1 | 0.988007 | ||||||||
\(13\) | 50786.7 | 0.493179 | 0.246590 | − | 0.969120i | \(-0.420690\pi\) | ||||
0.246590 | + | 0.969120i | \(0.420690\pi\) | |||||||
\(14\) | −58195.5 | −0.404868 | ||||||||
\(15\) | −24702.7 | −0.125989 | ||||||||
\(16\) | 35512.1 | 0.135468 | ||||||||
\(17\) | 0 | 0 | ||||||||
\(18\) | −285861. | −0.641842 | ||||||||
\(19\) | −815845. | −1.43621 | −0.718103 | − | 0.695937i | \(-0.754989\pi\) | ||||
−0.718103 | + | 0.695937i | \(0.754989\pi\) | |||||||
\(20\) | −41827.5 | −0.0584557 | ||||||||
\(21\) | −926557. | −1.03965 | ||||||||
\(22\) | 744065. | 0.677187 | ||||||||
\(23\) | 745187. | 0.555252 | 0.277626 | − | 0.960689i | \(-0.410452\pi\) | ||||
0.277626 | + | 0.960689i | \(0.410452\pi\) | |||||||
\(24\) | −2.26045e6 | −1.39073 | ||||||||
\(25\) | −1.93857e6 | −0.992546 | ||||||||
\(26\) | −653050. | −0.280263 | ||||||||
\(27\) | −521635. | −0.188899 | ||||||||
\(28\) | −1.56888e6 | −0.482368 | ||||||||
\(29\) | 1.01091e6 | 0.265411 | 0.132706 | − | 0.991155i | \(-0.457633\pi\) | ||||
0.132706 | + | 0.991155i | \(0.457633\pi\) | |||||||
\(30\) | 317644. | 0.0715971 | ||||||||
\(31\) | −1.30750e6 | −0.254281 | −0.127140 | − | 0.991885i | \(-0.540580\pi\) | ||||
−0.127140 | + | 0.991885i | \(0.540580\pi\) | |||||||
\(32\) | −6.10972e6 | −1.03002 | ||||||||
\(33\) | 1.18466e7 | 1.73892 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 546083. | 0.0615109 | ||||||||
\(36\) | −7.70645e6 | −0.764703 | ||||||||
\(37\) | −1.57690e7 | −1.38324 | −0.691620 | − | 0.722262i | \(-0.743103\pi\) | ||||
−0.691620 | + | 0.722262i | \(0.743103\pi\) | |||||||
\(38\) | 1.04907e7 | 0.816165 | ||||||||
\(39\) | −1.03975e7 | −0.719678 | ||||||||
\(40\) | 1.33223e6 | 0.0822830 | ||||||||
\(41\) | 4.94296e6 | 0.273187 | 0.136593 | − | 0.990627i | \(-0.456385\pi\) | ||||
0.136593 | + | 0.990627i | \(0.456385\pi\) | |||||||
\(42\) | 1.19143e7 | 0.590809 | ||||||||
\(43\) | −4.64999e6 | −0.207417 | −0.103708 | − | 0.994608i | \(-0.533071\pi\) | ||||
−0.103708 | + | 0.994608i | \(0.533071\pi\) | |||||||
\(44\) | 2.00591e7 | 0.806814 | ||||||||
\(45\) | 2.68240e6 | 0.0975140 | ||||||||
\(46\) | −9.58213e6 | −0.315538 | ||||||||
\(47\) | 3.34810e7 | 1.00082 | 0.500412 | − | 0.865787i | \(-0.333182\pi\) | ||||
0.500412 | + | 0.865787i | \(0.333182\pi\) | |||||||
\(48\) | −7.27035e6 | −0.197683 | ||||||||
\(49\) | −1.98710e7 | −0.492421 | ||||||||
\(50\) | 2.49274e7 | 0.564043 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.76054e7 | −0.333912 | ||||||||
\(53\) | 5.09370e7 | 0.886731 | 0.443366 | − | 0.896341i | \(-0.353784\pi\) | ||||
0.443366 | + | 0.896341i | \(0.353784\pi\) | |||||||
\(54\) | 6.70755e6 | 0.107347 | ||||||||
\(55\) | −6.98199e6 | −0.102884 | ||||||||
\(56\) | 4.99698e7 | 0.678988 | ||||||||
\(57\) | 1.67027e8 | 2.09580 | ||||||||
\(58\) | −1.29989e7 | −0.150828 | ||||||||
\(59\) | 1.72235e8 | 1.85049 | 0.925245 | − | 0.379371i | \(-0.123860\pi\) | ||||
0.925245 | + | 0.379371i | \(0.123860\pi\) | |||||||
\(60\) | 8.56330e6 | 0.0853023 | ||||||||
\(61\) | −4.80961e7 | −0.444760 | −0.222380 | − | 0.974960i | \(-0.571382\pi\) | ||||
−0.222380 | + | 0.974960i | \(0.571382\pi\) | |||||||
\(62\) | 1.68127e7 | 0.144502 | ||||||||
\(63\) | 1.00612e8 | 0.804671 | ||||||||
\(64\) | 6.03807e7 | 0.449871 | ||||||||
\(65\) | 6.12795e6 | 0.0425800 | ||||||||
\(66\) | −1.52332e8 | −0.988194 | ||||||||
\(67\) | 2.00253e8 | 1.21407 | 0.607033 | − | 0.794677i | \(-0.292360\pi\) | ||||
0.607033 | + | 0.794677i | \(0.292360\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.52561e8 | −0.810259 | ||||||||
\(70\) | −7.02191e6 | −0.0349554 | ||||||||
\(71\) | 1.02425e8 | 0.478347 | 0.239174 | − | 0.970977i | \(-0.423124\pi\) | ||||
0.239174 | + | 0.970977i | \(0.423124\pi\) | |||||||
\(72\) | 2.45455e8 | 1.07641 | ||||||||
\(73\) | 4.38332e8 | 1.80655 | 0.903275 | − | 0.429063i | \(-0.141156\pi\) | ||||
0.903275 | + | 0.429063i | \(0.141156\pi\) | |||||||
\(74\) | 2.02769e8 | 0.786066 | ||||||||
\(75\) | 3.96881e8 | 1.44839 | ||||||||
\(76\) | 2.82816e8 | 0.972396 | ||||||||
\(77\) | −2.61883e8 | −0.848983 | ||||||||
\(78\) | 1.33698e8 | 0.408978 | ||||||||
\(79\) | 3.10924e8 | 0.898116 | 0.449058 | − | 0.893502i | \(-0.351760\pi\) | ||||
0.449058 | + | 0.893502i | \(0.351760\pi\) | |||||||
\(80\) | 4.28491e6 | 0.0116960 | ||||||||
\(81\) | −3.30778e8 | −0.853795 | ||||||||
\(82\) | −6.35600e7 | −0.155246 | ||||||||
\(83\) | −8.30705e8 | −1.92130 | −0.960650 | − | 0.277761i | \(-0.910408\pi\) | ||||
−0.960650 | + | 0.277761i | \(0.910408\pi\) | |||||||
\(84\) | 3.21195e8 | 0.703902 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 5.97928e7 | 0.117871 | ||||||||
\(87\) | −2.06962e8 | −0.387305 | ||||||||
\(88\) | −6.38894e8 | −1.13568 | ||||||||
\(89\) | −6.52199e7 | −0.110186 | −0.0550928 | − | 0.998481i | \(-0.517545\pi\) | ||||
−0.0550928 | + | 0.998481i | \(0.517545\pi\) | |||||||
\(90\) | −3.44921e7 | −0.0554151 | ||||||||
\(91\) | 2.29849e8 | 0.351364 | ||||||||
\(92\) | −2.58322e8 | −0.375938 | ||||||||
\(93\) | 2.67683e8 | 0.371063 | ||||||||
\(94\) | −4.30522e8 | −0.568748 | ||||||||
\(95\) | −9.84404e7 | −0.123999 | ||||||||
\(96\) | 1.25084e9 | 1.50307 | ||||||||
\(97\) | 2.25459e8 | 0.258580 | 0.129290 | − | 0.991607i | \(-0.458730\pi\) | ||||
0.129290 | + | 0.991607i | \(0.458730\pi\) | |||||||
\(98\) | 2.55514e8 | 0.279832 | ||||||||
\(99\) | −1.28639e9 | −1.34590 | ||||||||
\(100\) | 6.72012e8 | 0.672012 | ||||||||
\(101\) | 1.79147e9 | 1.71303 | 0.856514 | − | 0.516124i | \(-0.172626\pi\) | ||||
0.856514 | + | 0.516124i | \(0.172626\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.00302e9 | −1.75355 | −0.876773 | − | 0.480904i | \(-0.840308\pi\) | ||||
−0.876773 | + | 0.480904i | \(0.840308\pi\) | |||||||
\(104\) | 5.60744e8 | 0.470018 | ||||||||
\(105\) | −1.11799e8 | −0.0897606 | ||||||||
\(106\) | −6.54983e8 | −0.503911 | ||||||||
\(107\) | −7.80191e8 | −0.575405 | −0.287703 | − | 0.957720i | \(-0.592891\pi\) | ||||
−0.287703 | + | 0.957720i | \(0.592891\pi\) | |||||||
\(108\) | 1.80827e8 | 0.127896 | ||||||||
\(109\) | 2.15583e9 | 1.46284 | 0.731418 | − | 0.681930i | \(-0.238859\pi\) | ||||
0.731418 | + | 0.681930i | \(0.238859\pi\) | |||||||
\(110\) | 8.97793e7 | 0.0584668 | ||||||||
\(111\) | 3.22838e9 | 2.01851 | ||||||||
\(112\) | 1.60720e8 | 0.0965136 | ||||||||
\(113\) | −1.13163e9 | −0.652904 | −0.326452 | − | 0.945214i | \(-0.605853\pi\) | ||||
−0.326452 | + | 0.945214i | \(0.605853\pi\) | |||||||
\(114\) | −2.14775e9 | −1.19100 | ||||||||
\(115\) | 8.99147e7 | 0.0479392 | ||||||||
\(116\) | −3.50435e8 | −0.179699 | ||||||||
\(117\) | 1.12904e9 | 0.557021 | ||||||||
\(118\) | −2.21471e9 | −1.05159 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −2.72747e8 | −0.120073 | ||||||||
\(121\) | 9.90381e8 | 0.420018 | ||||||||
\(122\) | 6.18452e8 | 0.252747 | ||||||||
\(123\) | −1.01197e9 | −0.398651 | ||||||||
\(124\) | 4.53250e8 | 0.172163 | ||||||||
\(125\) | −4.69574e8 | −0.172032 | ||||||||
\(126\) | −1.29374e9 | −0.457278 | ||||||||
\(127\) | −3.66984e9 | −1.25179 | −0.625894 | − | 0.779908i | \(-0.715266\pi\) | ||||
−0.625894 | + | 0.779908i | \(0.715266\pi\) | |||||||
\(128\) | 2.35176e9 | 0.774369 | ||||||||
\(129\) | 9.51988e8 | 0.302676 | ||||||||
\(130\) | −7.87974e7 | −0.0241973 | ||||||||
\(131\) | 1.90644e9 | 0.565591 | 0.282796 | − | 0.959180i | \(-0.408738\pi\) | ||||
0.282796 | + | 0.959180i | \(0.408738\pi\) | |||||||
\(132\) | −4.10667e9 | −1.17735 | ||||||||
\(133\) | −3.69233e9 | −1.02322 | ||||||||
\(134\) | −2.57499e9 | −0.689928 | ||||||||
\(135\) | −6.29408e7 | −0.0163091 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.68382e9 | 0.650895 | 0.325448 | − | 0.945560i | \(-0.394485\pi\) | ||||
0.325448 | + | 0.945560i | \(0.394485\pi\) | |||||||
\(138\) | 1.96174e9 | 0.460453 | ||||||||
\(139\) | 4.34137e9 | 0.986415 | 0.493208 | − | 0.869912i | \(-0.335824\pi\) | ||||
0.493208 | + | 0.869912i | \(0.335824\pi\) | |||||||
\(140\) | −1.89302e8 | −0.0416465 | ||||||||
\(141\) | −6.85453e9 | −1.46047 | ||||||||
\(142\) | −1.31705e9 | −0.271835 | ||||||||
\(143\) | −2.93876e9 | −0.587695 | ||||||||
\(144\) | 7.89467e8 | 0.153004 | ||||||||
\(145\) | 1.21976e8 | 0.0229150 | ||||||||
\(146\) | −5.63637e9 | −1.02662 | ||||||||
\(147\) | 4.06816e9 | 0.718571 | ||||||||
\(148\) | 5.46640e9 | 0.936535 | ||||||||
\(149\) | −7.27303e9 | −1.20886 | −0.604432 | − | 0.796657i | \(-0.706600\pi\) | ||||
−0.604432 | + | 0.796657i | \(0.706600\pi\) | |||||||
\(150\) | −5.10336e9 | −0.823087 | ||||||||
\(151\) | 4.35149e9 | 0.681149 | 0.340574 | − | 0.940218i | \(-0.389379\pi\) | ||||
0.340574 | + | 0.940218i | \(0.389379\pi\) | |||||||
\(152\) | −9.00788e9 | −1.36876 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 3.36747e9 | 0.482459 | ||||||||
\(155\) | −1.57764e8 | −0.0219540 | ||||||||
\(156\) | 3.60434e9 | 0.487265 | ||||||||
\(157\) | −8.25994e9 | −1.08500 | −0.542498 | − | 0.840057i | \(-0.682522\pi\) | ||||
−0.542498 | + | 0.840057i | \(0.682522\pi\) | |||||||
\(158\) | −3.99808e9 | −0.510381 | ||||||||
\(159\) | −1.04283e10 | −1.29397 | ||||||||
\(160\) | −7.37202e8 | −0.0889296 | ||||||||
\(161\) | 3.37255e9 | 0.395587 | ||||||||
\(162\) | 4.25336e9 | 0.485194 | ||||||||
\(163\) | 5.06011e9 | 0.561456 | 0.280728 | − | 0.959787i | \(-0.409424\pi\) | ||||
0.280728 | + | 0.959787i | \(0.409424\pi\) | |||||||
\(164\) | −1.71350e9 | −0.184964 | ||||||||
\(165\) | 1.42942e9 | 0.150135 | ||||||||
\(166\) | 1.06818e10 | 1.09183 | ||||||||
\(167\) | −1.45710e9 | −0.144966 | −0.0724829 | − | 0.997370i | \(-0.523092\pi\) | ||||
−0.0724829 | + | 0.997370i | \(0.523092\pi\) | |||||||
\(168\) | −1.02303e10 | −0.990822 | ||||||||
\(169\) | −8.02521e9 | −0.756774 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.81370e10 | −1.62212 | ||||||||
\(172\) | 1.61194e9 | 0.140433 | ||||||||
\(173\) | 9.29522e9 | 0.788955 | 0.394477 | − | 0.918906i | \(-0.370926\pi\) | ||||
0.394477 | + | 0.918906i | \(0.370926\pi\) | |||||||
\(174\) | 2.66125e9 | 0.220097 | ||||||||
\(175\) | −8.77352e9 | −0.707135 | ||||||||
\(176\) | −2.05490e9 | −0.161430 | ||||||||
\(177\) | −3.52614e10 | −2.70035 | ||||||||
\(178\) | 8.38642e8 | 0.0626162 | ||||||||
\(179\) | 5.29738e9 | 0.385676 | 0.192838 | − | 0.981231i | \(-0.438231\pi\) | ||||
0.192838 | + | 0.981231i | \(0.438231\pi\) | |||||||
\(180\) | −9.29864e8 | −0.0660227 | ||||||||
\(181\) | 2.03955e10 | 1.41248 | 0.706238 | − | 0.707975i | \(-0.250391\pi\) | ||||
0.706238 | + | 0.707975i | \(0.250391\pi\) | |||||||
\(182\) | −2.95556e9 | −0.199673 | ||||||||
\(183\) | 9.84666e9 | 0.649021 | ||||||||
\(184\) | 8.22773e9 | 0.529176 | ||||||||
\(185\) | −1.90270e9 | −0.119426 | ||||||||
\(186\) | −3.44205e9 | −0.210867 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −1.16063e10 | −0.677617 | ||||||||
\(189\) | −2.36081e9 | −0.134580 | ||||||||
\(190\) | 1.26581e9 | 0.0704658 | ||||||||
\(191\) | −1.13020e9 | −0.0614478 | −0.0307239 | − | 0.999528i | \(-0.509781\pi\) | ||||
−0.0307239 | + | 0.999528i | \(0.509781\pi\) | |||||||
\(192\) | −1.23617e10 | −0.656481 | ||||||||
\(193\) | 3.57356e10 | 1.85393 | 0.926966 | − | 0.375146i | \(-0.122408\pi\) | ||||
0.926966 | + | 0.375146i | \(0.122408\pi\) | |||||||
\(194\) | −2.89910e9 | −0.146945 | ||||||||
\(195\) | −1.25457e9 | −0.0621354 | ||||||||
\(196\) | 6.88835e9 | 0.333398 | ||||||||
\(197\) | 3.55928e10 | 1.68370 | 0.841848 | − | 0.539715i | \(-0.181468\pi\) | ||||
0.841848 | + | 0.539715i | \(0.181468\pi\) | |||||||
\(198\) | 1.65412e10 | 0.764848 | ||||||||
\(199\) | −3.12374e10 | −1.41200 | −0.706001 | − | 0.708211i | \(-0.749503\pi\) | ||||
−0.706001 | + | 0.708211i | \(0.749503\pi\) | |||||||
\(200\) | −2.14040e10 | −0.945933 | ||||||||
\(201\) | −4.09976e10 | −1.77164 | ||||||||
\(202\) | −2.30360e10 | −0.973477 | ||||||||
\(203\) | 4.57513e9 | 0.189091 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.96420e8 | 0.0235863 | ||||||||
\(206\) | 2.57562e10 | 0.996503 | ||||||||
\(207\) | 1.65662e10 | 0.627128 | ||||||||
\(208\) | 1.80354e9 | 0.0668100 | ||||||||
\(209\) | 4.72087e10 | 1.71145 | ||||||||
\(210\) | 1.43759e9 | 0.0510091 | ||||||||
\(211\) | 2.89353e10 | 1.00498 | 0.502489 | − | 0.864583i | \(-0.332418\pi\) | ||||
0.502489 | + | 0.864583i | \(0.332418\pi\) | |||||||
\(212\) | −1.76575e10 | −0.600370 | ||||||||
\(213\) | −2.09693e10 | −0.698034 | ||||||||
\(214\) | 1.00322e10 | 0.326991 | ||||||||
\(215\) | −5.61071e8 | −0.0179079 | ||||||||
\(216\) | −5.75946e9 | −0.180028 | ||||||||
\(217\) | −5.91745e9 | −0.181161 | ||||||||
\(218\) | −2.77211e10 | −0.831298 | ||||||||
\(219\) | −8.97391e10 | −2.63623 | ||||||||
\(220\) | 2.42034e9 | 0.0696585 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −4.15127e10 | −1.14708 | ||||||||
\(223\) | −5.45398e10 | −1.47687 | −0.738434 | − | 0.674326i | \(-0.764434\pi\) | ||||
−0.738434 | + | 0.674326i | \(0.764434\pi\) | |||||||
\(224\) | −2.76512e10 | −0.733834 | ||||||||
\(225\) | −4.30961e10 | −1.12103 | ||||||||
\(226\) | 1.45512e10 | 0.371032 | ||||||||
\(227\) | −9.17512e9 | −0.229348 | −0.114674 | − | 0.993403i | \(-0.536582\pi\) | ||||
−0.114674 | + | 0.993403i | \(0.536582\pi\) | |||||||
\(228\) | −5.79006e10 | −1.41898 | ||||||||
\(229\) | 2.94750e10 | 0.708263 | 0.354131 | − | 0.935196i | \(-0.384777\pi\) | ||||
0.354131 | + | 0.935196i | \(0.384777\pi\) | |||||||
\(230\) | −1.15619e9 | −0.0272428 | ||||||||
\(231\) | 5.36150e10 | 1.23889 | ||||||||
\(232\) | 1.11616e10 | 0.252947 | ||||||||
\(233\) | −5.54557e10 | −1.23266 | −0.616332 | − | 0.787487i | \(-0.711382\pi\) | ||||
−0.616332 | + | 0.787487i | \(0.711382\pi\) | |||||||
\(234\) | −1.45179e10 | −0.316543 | ||||||||
\(235\) | 4.03984e9 | 0.0864089 | ||||||||
\(236\) | −5.97059e10 | −1.25289 | ||||||||
\(237\) | −6.36552e10 | −1.31059 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6.16221e10 | −1.22165 | −0.610823 | − | 0.791767i | \(-0.709161\pi\) | ||||
−0.610823 | + | 0.791767i | \(0.709161\pi\) | |||||||
\(240\) | −8.77245e8 | −0.0170675 | ||||||||
\(241\) | 4.49410e10 | 0.858157 | 0.429078 | − | 0.903267i | \(-0.358838\pi\) | ||||
0.429078 | + | 0.903267i | \(0.358838\pi\) | |||||||
\(242\) | −1.27350e10 | −0.238687 | ||||||||
\(243\) | 7.79871e10 | 1.43481 | ||||||||
\(244\) | 1.66727e10 | 0.301128 | ||||||||
\(245\) | −2.39764e9 | −0.0425145 | ||||||||
\(246\) | 1.30126e10 | 0.226545 | ||||||||
\(247\) | −4.14341e10 | −0.708307 | ||||||||
\(248\) | −1.44363e10 | −0.242339 | ||||||||
\(249\) | 1.70069e11 | 2.80368 | ||||||||
\(250\) | 6.03810e9 | 0.0977621 | ||||||||
\(251\) | 3.67666e10 | 0.584685 | 0.292343 | − | 0.956314i | \(-0.405565\pi\) | ||||
0.292343 | + | 0.956314i | \(0.405565\pi\) | |||||||
\(252\) | −3.48777e10 | −0.544810 | ||||||||
\(253\) | −4.31201e10 | −0.661663 | ||||||||
\(254\) | 4.71893e10 | 0.711365 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −6.11554e10 | −0.889929 | ||||||||
\(257\) | 1.06275e11 | 1.51962 | 0.759808 | − | 0.650148i | \(-0.225293\pi\) | ||||
0.759808 | + | 0.650148i | \(0.225293\pi\) | |||||||
\(258\) | −1.22413e10 | −0.172004 | ||||||||
\(259\) | −7.13671e10 | −0.985484 | ||||||||
\(260\) | −2.12428e9 | −0.0288292 | ||||||||
\(261\) | 2.24734e10 | 0.299769 | ||||||||
\(262\) | −2.45143e10 | −0.321414 | ||||||||
\(263\) | −4.15683e10 | −0.535749 | −0.267875 | − | 0.963454i | \(-0.586321\pi\) | ||||
−0.267875 | + | 0.963454i | \(0.586321\pi\) | |||||||
\(264\) | 1.30800e11 | 1.65726 | ||||||||
\(265\) | 6.14609e9 | 0.0765583 | ||||||||
\(266\) | 4.74785e10 | 0.581474 | ||||||||
\(267\) | 1.33524e10 | 0.160790 | ||||||||
\(268\) | −6.94185e10 | −0.821994 | ||||||||
\(269\) | 1.92950e10 | 0.224678 | 0.112339 | − | 0.993670i | \(-0.464166\pi\) | ||||
0.112339 | + | 0.993670i | \(0.464166\pi\) | |||||||
\(270\) | 8.09336e8 | 0.00926813 | ||||||||
\(271\) | −5.51694e10 | −0.621350 | −0.310675 | − | 0.950516i | \(-0.600555\pi\) | ||||
−0.310675 | + | 0.950516i | \(0.600555\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −4.70568e10 | −0.512732 | ||||||||
\(274\) | −3.45104e10 | −0.369890 | ||||||||
\(275\) | 1.12175e11 | 1.18276 | ||||||||
\(276\) | 5.28860e10 | 0.548593 | ||||||||
\(277\) | −1.49538e11 | −1.52613 | −0.763066 | − | 0.646320i | \(-0.776307\pi\) | ||||
−0.763066 | + | 0.646320i | \(0.776307\pi\) | |||||||
\(278\) | −5.58243e10 | −0.560559 | ||||||||
\(279\) | −2.90669e10 | −0.287197 | ||||||||
\(280\) | 6.02939e9 | 0.0586222 | ||||||||
\(281\) | −8.27561e10 | −0.791811 | −0.395906 | − | 0.918291i | \(-0.629569\pi\) | ||||
−0.395906 | + | 0.918291i | \(0.629569\pi\) | |||||||
\(282\) | 8.81402e10 | 0.829952 | ||||||||
\(283\) | 5.14641e10 | 0.476942 | 0.238471 | − | 0.971150i | \(-0.423354\pi\) | ||||
0.238471 | + | 0.971150i | \(0.423354\pi\) | |||||||
\(284\) | −3.55060e10 | −0.323869 | ||||||||
\(285\) | 2.01536e10 | 0.180947 | ||||||||
\(286\) | 3.77886e10 | 0.333975 | ||||||||
\(287\) | 2.23707e10 | 0.194631 | ||||||||
\(288\) | −1.35825e11 | −1.16336 | ||||||||
\(289\) | 0 | 0 | ||||||||
\(290\) | −1.56846e9 | −0.0130221 | ||||||||
\(291\) | −4.61579e10 | −0.377336 | ||||||||
\(292\) | −1.51949e11 | −1.22314 | ||||||||
\(293\) | 1.21927e11 | 0.966484 | 0.483242 | − | 0.875487i | \(-0.339459\pi\) | ||||
0.483242 | + | 0.875487i | \(0.339459\pi\) | |||||||
\(294\) | −5.23112e10 | −0.408349 | ||||||||
\(295\) | 2.07819e10 | 0.159767 | ||||||||
\(296\) | −1.74109e11 | −1.31828 | ||||||||
\(297\) | 3.01843e10 | 0.225101 | ||||||||
\(298\) | 9.35216e10 | 0.686972 | ||||||||
\(299\) | 3.78456e10 | 0.273839 | ||||||||
\(300\) | −1.37580e11 | −0.980642 | ||||||||
\(301\) | −2.10448e10 | −0.147773 | ||||||||
\(302\) | −5.59545e10 | −0.387082 | ||||||||
\(303\) | −3.66766e11 | −2.49976 | ||||||||
\(304\) | −2.89724e10 | −0.194560 | ||||||||
\(305\) | −5.80330e9 | −0.0383995 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9.71611e10 | 0.624266 | 0.312133 | − | 0.950038i | \(-0.398957\pi\) | ||||
0.312133 | + | 0.950038i | \(0.398957\pi\) | |||||||
\(308\) | 9.07828e10 | 0.574811 | ||||||||
\(309\) | 4.10076e11 | 2.55889 | ||||||||
\(310\) | 2.02863e9 | 0.0124760 | ||||||||
\(311\) | −2.23120e11 | −1.35244 | −0.676218 | − | 0.736701i | \(-0.736382\pi\) | ||||
−0.676218 | + | 0.736701i | \(0.736382\pi\) | |||||||
\(312\) | −1.14801e11 | −0.685880 | ||||||||
\(313\) | 1.59734e10 | 0.0940694 | 0.0470347 | − | 0.998893i | \(-0.485023\pi\) | ||||
0.0470347 | + | 0.998893i | \(0.485023\pi\) | |||||||
\(314\) | 1.06212e11 | 0.616581 | ||||||||
\(315\) | 1.21399e10 | 0.0694734 | ||||||||
\(316\) | −1.07783e11 | −0.608078 | ||||||||
\(317\) | −2.02194e11 | −1.12461 | −0.562305 | − | 0.826930i | \(-0.690085\pi\) | ||||
−0.562305 | + | 0.826930i | \(0.690085\pi\) | |||||||
\(318\) | 1.34094e11 | 0.735338 | ||||||||
\(319\) | −5.84958e10 | −0.316276 | ||||||||
\(320\) | 7.28557e9 | 0.0388409 | ||||||||
\(321\) | 1.59728e11 | 0.839667 | ||||||||
\(322\) | −4.33666e10 | −0.224804 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 1.14665e11 | 0.578069 | ||||||||
\(325\) | −9.84534e10 | −0.489503 | ||||||||
\(326\) | −6.50663e10 | −0.319064 | ||||||||
\(327\) | −4.41361e11 | −2.13466 | ||||||||
\(328\) | 5.45760e10 | 0.260357 | ||||||||
\(329\) | 1.51527e11 | 0.713033 | ||||||||
\(330\) | −1.83804e10 | −0.0853184 | ||||||||
\(331\) | −3.68035e11 | −1.68524 | −0.842622 | − | 0.538505i | \(-0.818989\pi\) | ||||
−0.842622 | + | 0.538505i | \(0.818989\pi\) | |||||||
\(332\) | 2.87967e11 | 1.30083 | ||||||||
\(333\) | −3.50560e11 | −1.56230 | ||||||||
\(334\) | 1.87364e10 | 0.0823811 | ||||||||
\(335\) | 2.41626e10 | 0.104820 | ||||||||
\(336\) | −3.29040e10 | −0.140839 | ||||||||
\(337\) | −1.35639e11 | −0.572862 | −0.286431 | − | 0.958101i | \(-0.592469\pi\) | ||||
−0.286431 | + | 0.958101i | \(0.592469\pi\) | |||||||
\(338\) | 1.03194e11 | 0.430059 | ||||||||
\(339\) | 2.31676e11 | 0.952759 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 7.56581e10 | 0.303013 | ||||||||
\(342\) | 2.33218e11 | 0.921817 | ||||||||
\(343\) | −2.72563e11 | −1.06327 | ||||||||
\(344\) | −5.13413e10 | −0.197676 | ||||||||
\(345\) | −1.84081e10 | −0.0699559 | ||||||||
\(346\) | −1.19524e11 | −0.448346 | ||||||||
\(347\) | 1.52215e11 | 0.563603 | 0.281802 | − | 0.959473i | \(-0.409068\pi\) | ||||
0.281802 | + | 0.959473i | \(0.409068\pi\) | |||||||
\(348\) | 7.17441e10 | 0.262228 | ||||||||
\(349\) | 1.78457e11 | 0.643903 | 0.321951 | − | 0.946756i | \(-0.395661\pi\) | ||||
0.321951 | + | 0.946756i | \(0.395661\pi\) | |||||||
\(350\) | 1.12816e11 | 0.401850 | ||||||||
\(351\) | −2.64921e10 | −0.0931612 | ||||||||
\(352\) | 3.53537e11 | 1.22742 | ||||||||
\(353\) | 2.96867e11 | 1.01760 | 0.508798 | − | 0.860886i | \(-0.330090\pi\) | ||||
0.508798 | + | 0.860886i | \(0.330090\pi\) | |||||||
\(354\) | 4.53416e11 | 1.53455 | ||||||||
\(355\) | 1.23587e10 | 0.0412994 | ||||||||
\(356\) | 2.26088e10 | 0.0746022 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −6.81173e10 | −0.219171 | ||||||||
\(359\) | −1.67133e11 | −0.531052 | −0.265526 | − | 0.964104i | \(-0.585546\pi\) | ||||
−0.265526 | + | 0.964104i | \(0.585546\pi\) | |||||||
\(360\) | 2.96168e10 | 0.0929345 | ||||||||
\(361\) | 3.42916e11 | 1.06269 | ||||||||
\(362\) | −2.62259e11 | −0.802680 | ||||||||
\(363\) | −2.02760e11 | −0.612917 | ||||||||
\(364\) | −7.96782e10 | −0.237894 | ||||||||
\(365\) | 5.28893e10 | 0.155973 | ||||||||
\(366\) | −1.26615e11 | −0.368825 | ||||||||
\(367\) | 3.22425e11 | 0.927752 | 0.463876 | − | 0.885900i | \(-0.346458\pi\) | ||||
0.463876 | + | 0.885900i | \(0.346458\pi\) | |||||||
\(368\) | 2.64632e10 | 0.0752188 | ||||||||
\(369\) | 1.09887e11 | 0.308550 | ||||||||
\(370\) | 2.44662e10 | 0.0678671 | ||||||||
\(371\) | 2.30530e11 | 0.631748 | ||||||||
\(372\) | −9.27934e10 | −0.251231 | ||||||||
\(373\) | −3.84623e10 | −0.102883 | −0.0514417 | − | 0.998676i | \(-0.516382\pi\) | ||||
−0.0514417 | + | 0.998676i | \(0.516382\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 9.61353e10 | 0.251040 | ||||||||
\(376\) | 3.69669e11 | 0.953823 | ||||||||
\(377\) | 5.13406e10 | 0.130895 | ||||||||
\(378\) | 3.03569e10 | 0.0764793 | ||||||||
\(379\) | 9.81716e10 | 0.244405 | 0.122202 | − | 0.992505i | \(-0.461004\pi\) | ||||
0.122202 | + | 0.992505i | \(0.461004\pi\) | |||||||
\(380\) | 3.41248e10 | 0.0839544 | ||||||||
\(381\) | 7.51323e11 | 1.82669 | ||||||||
\(382\) | 1.45329e10 | 0.0349195 | ||||||||
\(383\) | −3.91752e11 | −0.930286 | −0.465143 | − | 0.885236i | \(-0.653997\pi\) | ||||
−0.465143 | + | 0.885236i | \(0.653997\pi\) | |||||||
\(384\) | −4.81473e11 | −1.13001 | ||||||||
\(385\) | −3.15989e10 | −0.0732992 | ||||||||
\(386\) | −4.59513e11 | −1.05355 | ||||||||
\(387\) | −1.03374e11 | −0.234267 | ||||||||
\(388\) | −7.81562e10 | −0.175074 | ||||||||
\(389\) | 4.40744e11 | 0.975917 | 0.487959 | − | 0.872867i | \(-0.337742\pi\) | ||||
0.487959 | + | 0.872867i | \(0.337742\pi\) | |||||||
\(390\) | 1.61321e10 | 0.0353102 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −2.19398e11 | −0.469295 | ||||||||
\(393\) | −3.90304e11 | −0.825346 | ||||||||
\(394\) | −4.57676e11 | −0.956809 | ||||||||
\(395\) | 3.75163e10 | 0.0775413 | ||||||||
\(396\) | 4.45932e11 | 0.911255 | ||||||||
\(397\) | 3.38508e11 | 0.683930 | 0.341965 | − | 0.939713i | \(-0.388908\pi\) | ||||
0.341965 | + | 0.939713i | \(0.388908\pi\) | |||||||
\(398\) | 4.01671e11 | 0.802411 | ||||||||
\(399\) | 7.55927e11 | 1.49315 | ||||||||
\(400\) | −6.88426e10 | −0.134458 | ||||||||
\(401\) | 1.71912e11 | 0.332014 | 0.166007 | − | 0.986125i | \(-0.446913\pi\) | ||||
0.166007 | + | 0.986125i | \(0.446913\pi\) | |||||||
\(402\) | 5.27175e11 | 1.00679 | ||||||||
\(403\) | −6.64036e10 | −0.125406 | ||||||||
\(404\) | −6.21022e11 | −1.15982 | ||||||||
\(405\) | −3.99118e10 | −0.0737147 | ||||||||
\(406\) | −5.88302e10 | −0.107457 | ||||||||
\(407\) | 9.12471e11 | 1.64833 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.81166e11 | 0.320126 | 0.160063 | − | 0.987107i | \(-0.448830\pi\) | ||||
0.160063 | + | 0.987107i | \(0.448830\pi\) | |||||||
\(410\) | −7.66918e9 | −0.0134036 | ||||||||
\(411\) | −5.49456e11 | −0.949827 | ||||||||
\(412\) | 6.94354e11 | 1.18725 | ||||||||
\(413\) | 7.79496e11 | 1.31837 | ||||||||
\(414\) | −2.13020e11 | −0.356384 | ||||||||
\(415\) | −1.00233e11 | −0.165881 | ||||||||
\(416\) | −3.10292e11 | −0.507985 | ||||||||
\(417\) | −8.88803e11 | −1.43944 | ||||||||
\(418\) | −6.07041e11 | −0.972579 | ||||||||
\(419\) | −5.34687e11 | −0.847493 | −0.423747 | − | 0.905781i | \(-0.639285\pi\) | ||||
−0.423747 | + | 0.905781i | \(0.639285\pi\) | |||||||
\(420\) | 3.87556e10 | 0.0607732 | ||||||||
\(421\) | −4.75293e10 | −0.0737381 | −0.0368691 | − | 0.999320i | \(-0.511738\pi\) | ||||
−0.0368691 | + | 0.999320i | \(0.511738\pi\) | |||||||
\(422\) | −3.72070e11 | −0.571108 | ||||||||
\(423\) | 7.44314e11 | 1.13038 | ||||||||
\(424\) | 5.62404e11 | 0.845088 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 2.69638e11 | 0.396678 | ||||||||
\(427\) | −2.17672e11 | −0.316867 | ||||||||
\(428\) | 2.70456e11 | 0.389583 | ||||||||
\(429\) | 6.01649e11 | 0.857601 | ||||||||
\(430\) | 7.21463e9 | 0.0101767 | ||||||||
\(431\) | 8.44046e11 | 1.17820 | 0.589099 | − | 0.808061i | \(-0.299483\pi\) | ||||
0.589099 | + | 0.808061i | \(0.299483\pi\) | |||||||
\(432\) | −1.85244e10 | −0.0255898 | ||||||||
\(433\) | −2.09001e10 | −0.0285728 | −0.0142864 | − | 0.999898i | \(-0.504548\pi\) | ||||
−0.0142864 | + | 0.999898i | \(0.504548\pi\) | |||||||
\(434\) | 7.60906e10 | 0.102950 | ||||||||
\(435\) | −2.49721e10 | −0.0334390 | ||||||||
\(436\) | −7.47328e11 | −0.990426 | ||||||||
\(437\) | −6.07957e11 | −0.797456 | ||||||||
\(438\) | 1.15393e12 | 1.49811 | ||||||||
\(439\) | 1.18658e12 | 1.52478 | 0.762389 | − | 0.647119i | \(-0.224026\pi\) | ||||
0.762389 | + | 0.647119i | \(0.224026\pi\) | |||||||
\(440\) | −7.70893e10 | −0.0980522 | ||||||||
\(441\) | −4.41750e11 | −0.556164 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4.19386e11 | 0.517366 | 0.258683 | − | 0.965962i | \(-0.416712\pi\) | ||||
0.258683 | + | 0.965962i | \(0.416712\pi\) | |||||||
\(444\) | −1.11913e12 | −1.36665 | ||||||||
\(445\) | −7.86947e9 | −0.00951318 | ||||||||
\(446\) | 7.01310e11 | 0.839273 | ||||||||
\(447\) | 1.48900e12 | 1.76405 | ||||||||
\(448\) | 2.73270e11 | 0.320509 | ||||||||
\(449\) | 6.83486e11 | 0.793636 | 0.396818 | − | 0.917897i | \(-0.370114\pi\) | ||||
0.396818 | + | 0.917897i | \(0.370114\pi\) | |||||||
\(450\) | 5.54160e11 | 0.637057 | ||||||||
\(451\) | −2.86023e11 | −0.325542 | ||||||||
\(452\) | 3.92283e11 | 0.442055 | ||||||||
\(453\) | −8.90876e11 | −0.993975 | ||||||||
\(454\) | 1.17980e11 | 0.130334 | ||||||||
\(455\) | 2.77337e10 | 0.0303359 | ||||||||
\(456\) | 1.84417e12 | 1.99738 | ||||||||
\(457\) | −1.13726e12 | −1.21966 | −0.609829 | − | 0.792533i | \(-0.708762\pi\) | ||||
−0.609829 | + | 0.792533i | \(0.708762\pi\) | |||||||
\(458\) | −3.79010e11 | −0.402491 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −3.11693e10 | −0.0324577 | ||||||||
\(461\) | 4.01702e11 | 0.414238 | 0.207119 | − | 0.978316i | \(-0.433591\pi\) | ||||
0.207119 | + | 0.978316i | \(0.433591\pi\) | |||||||
\(462\) | −6.89418e11 | −0.704035 | ||||||||
\(463\) | −1.71828e12 | −1.73772 | −0.868859 | − | 0.495059i | \(-0.835146\pi\) | ||||
−0.868859 | + | 0.495059i | \(0.835146\pi\) | |||||||
\(464\) | 3.58994e10 | 0.0359547 | ||||||||
\(465\) | 3.22988e10 | 0.0320367 | ||||||||
\(466\) | 7.13087e11 | 0.700497 | ||||||||
\(467\) | −1.25508e12 | −1.22108 | −0.610542 | − | 0.791984i | \(-0.709048\pi\) | ||||
−0.610542 | + | 0.791984i | \(0.709048\pi\) | |||||||
\(468\) | −3.91385e11 | −0.377136 | ||||||||
\(469\) | 9.06300e11 | 0.864956 | ||||||||
\(470\) | −5.19470e10 | −0.0491044 | ||||||||
\(471\) | 1.69105e12 | 1.58330 | ||||||||
\(472\) | 1.90167e12 | 1.76359 | ||||||||
\(473\) | 2.69071e11 | 0.247167 | ||||||||
\(474\) | 8.18522e11 | 0.744780 | ||||||||
\(475\) | 1.58157e12 | 1.42550 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.13238e12 | 1.00152 | ||||||||
\(478\) | 7.92379e11 | 0.694236 | ||||||||
\(479\) | −1.10403e12 | −0.958235 | −0.479118 | − | 0.877751i | \(-0.659043\pi\) | ||||
−0.479118 | + | 0.877751i | \(0.659043\pi\) | |||||||
\(480\) | 1.50927e11 | 0.129772 | ||||||||
\(481\) | −8.00857e11 | −0.682185 | ||||||||
\(482\) | −5.77883e11 | −0.487672 | ||||||||
\(483\) | −6.90459e11 | −0.577266 | ||||||||
\(484\) | −3.43320e11 | −0.284377 | ||||||||
\(485\) | 2.72040e10 | 0.0223252 | ||||||||
\(486\) | −1.00281e12 | −0.815372 | ||||||||
\(487\) | −1.20949e12 | −0.974370 | −0.487185 | − | 0.873299i | \(-0.661976\pi\) | ||||
−0.487185 | + | 0.873299i | \(0.661976\pi\) | |||||||
\(488\) | −5.31037e11 | −0.423872 | ||||||||
\(489\) | −1.03595e12 | −0.819312 | ||||||||
\(490\) | 3.08305e10 | 0.0241601 | ||||||||
\(491\) | 8.42274e11 | 0.654014 | 0.327007 | − | 0.945022i | \(-0.393960\pi\) | ||||
0.327007 | + | 0.945022i | \(0.393960\pi\) | |||||||
\(492\) | 3.50803e11 | 0.269910 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 5.32788e11 | 0.402516 | ||||||||
\(495\) | −1.55216e11 | −0.116202 | ||||||||
\(496\) | −4.64320e10 | −0.0344469 | ||||||||
\(497\) | 4.63552e11 | 0.340796 | ||||||||
\(498\) | −2.18687e12 | −1.59327 | ||||||||
\(499\) | −1.70715e12 | −1.23259 | −0.616297 | − | 0.787514i | \(-0.711368\pi\) | ||||
−0.616297 | + | 0.787514i | \(0.711368\pi\) | |||||||
\(500\) | 1.62780e11 | 0.116476 | ||||||||
\(501\) | 2.98311e11 | 0.211543 | ||||||||
\(502\) | −4.72771e11 | −0.332264 | ||||||||
\(503\) | −1.31164e12 | −0.913605 | −0.456803 | − | 0.889568i | \(-0.651005\pi\) | ||||
−0.456803 | + | 0.889568i | \(0.651005\pi\) | |||||||
\(504\) | 1.11088e12 | 0.766881 | ||||||||
\(505\) | 2.16160e11 | 0.147899 | ||||||||
\(506\) | 5.54467e11 | 0.376009 | ||||||||
\(507\) | 1.64299e12 | 1.10433 | ||||||||
\(508\) | 1.27217e12 | 0.847534 | ||||||||
\(509\) | −2.27732e12 | −1.50382 | −0.751908 | − | 0.659268i | \(-0.770866\pi\) | ||||
−0.751908 | + | 0.659268i | \(0.770866\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.98379e12 | 1.28707 | ||||||||
\(512\) | −4.17721e11 | −0.268641 | ||||||||
\(513\) | 4.25574e11 | 0.271298 | ||||||||
\(514\) | −1.36656e12 | −0.863566 | ||||||||
\(515\) | −2.41685e11 | −0.151397 | ||||||||
\(516\) | −3.30010e11 | −0.204929 | ||||||||
\(517\) | −1.93737e12 | −1.19263 | ||||||||
\(518\) | 9.17688e11 | 0.560030 | ||||||||
\(519\) | −1.90300e12 | −1.15129 | ||||||||
\(520\) | 6.76597e10 | 0.0405803 | ||||||||
\(521\) | −3.20184e12 | −1.90384 | −0.951919 | − | 0.306351i | \(-0.900892\pi\) | ||||
−0.951919 | + | 0.306351i | \(0.900892\pi\) | |||||||
\(522\) | −2.88978e11 | −0.170352 | ||||||||
\(523\) | 2.74758e11 | 0.160580 | 0.0802902 | − | 0.996772i | \(-0.474415\pi\) | ||||
0.0802902 | + | 0.996772i | \(0.474415\pi\) | |||||||
\(524\) | −6.60876e11 | −0.382939 | ||||||||
\(525\) | 1.79619e12 | 1.03190 | ||||||||
\(526\) | 5.34514e11 | 0.304455 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 4.20697e11 | 0.235568 | ||||||||
\(529\) | −1.24585e12 | −0.691695 | ||||||||
\(530\) | −7.90307e10 | −0.0435065 | ||||||||
\(531\) | 3.82894e12 | 2.09003 | ||||||||
\(532\) | 1.27996e12 | 0.692779 | ||||||||
\(533\) | 2.51037e11 | 0.134730 | ||||||||
\(534\) | −1.71694e11 | −0.0913735 | ||||||||
\(535\) | −9.41383e10 | −0.0496791 | ||||||||
\(536\) | 2.21102e12 | 1.15705 | ||||||||
\(537\) | −1.08453e12 | −0.562802 | ||||||||
\(538\) | −2.48109e11 | −0.127680 | ||||||||
\(539\) | 1.14983e12 | 0.586791 | ||||||||
\(540\) | 2.18187e10 | 0.0110422 | ||||||||
\(541\) | −7.68673e11 | −0.385793 | −0.192896 | − | 0.981219i | \(-0.561788\pi\) | ||||
−0.192896 | + | 0.981219i | \(0.561788\pi\) | |||||||
\(542\) | 7.09406e11 | 0.353100 | ||||||||
\(543\) | −4.17555e12 | −2.06117 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2.60124e11 | 0.126298 | ||||||||
\(546\) | 6.05089e11 | 0.291375 | ||||||||
\(547\) | 3.26534e12 | 1.55950 | 0.779750 | − | 0.626091i | \(-0.215346\pi\) | ||||
0.779750 | + | 0.626091i | \(0.215346\pi\) | |||||||
\(548\) | −9.30358e11 | −0.440694 | ||||||||
\(549\) | −1.06922e12 | −0.502333 | ||||||||
\(550\) | −1.44242e12 | −0.672139 | ||||||||
\(551\) | −8.24742e11 | −0.381185 | ||||||||
\(552\) | −1.68446e12 | −0.772207 | ||||||||
\(553\) | 1.40717e12 | 0.639859 | ||||||||
\(554\) | 1.92286e12 | 0.867269 | ||||||||
\(555\) | 3.89538e11 | 0.174274 | ||||||||
\(556\) | −1.50495e12 | −0.667861 | ||||||||
\(557\) | −1.66914e12 | −0.734760 | −0.367380 | − | 0.930071i | \(-0.619745\pi\) | ||||
−0.367380 | + | 0.930071i | \(0.619745\pi\) | |||||||
\(558\) | 3.73762e11 | 0.163208 | ||||||||
\(559\) | −2.36158e11 | −0.102294 | ||||||||
\(560\) | 1.93926e10 | 0.00833276 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 1.06413e12 | 0.449970 | ||||||||
\(563\) | −1.13172e12 | −0.474734 | −0.237367 | − | 0.971420i | \(-0.576284\pi\) | ||||
−0.237367 | + | 0.971420i | \(0.576284\pi\) | |||||||
\(564\) | 2.37615e12 | 0.988822 | ||||||||
\(565\) | −1.36543e11 | −0.0563703 | ||||||||
\(566\) | −6.61761e11 | −0.271036 | ||||||||
\(567\) | −1.49703e12 | −0.608283 | ||||||||
\(568\) | 1.13089e12 | 0.455883 | ||||||||
\(569\) | −2.09042e12 | −0.836042 | −0.418021 | − | 0.908437i | \(-0.637276\pi\) | ||||
−0.418021 | + | 0.908437i | \(0.637276\pi\) | |||||||
\(570\) | −2.59149e11 | −0.102828 | ||||||||
\(571\) | −6.27130e11 | −0.246885 | −0.123443 | − | 0.992352i | \(-0.539393\pi\) | ||||
−0.123443 | + | 0.992352i | \(0.539393\pi\) | |||||||
\(572\) | 1.01873e12 | 0.397904 | ||||||||
\(573\) | 2.31385e11 | 0.0896685 | ||||||||
\(574\) | −2.87658e11 | −0.110605 | ||||||||
\(575\) | −1.44459e12 | −0.551113 | ||||||||
\(576\) | 1.34232e12 | 0.508106 | ||||||||
\(577\) | 1.42436e12 | 0.534968 | 0.267484 | − | 0.963562i | \(-0.413808\pi\) | ||||
0.267484 | + | 0.963562i | \(0.413808\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −7.31612e12 | −2.70537 | ||||||||
\(580\) | −4.22837e10 | −0.0155148 | ||||||||
\(581\) | −3.75958e12 | −1.36882 | ||||||||
\(582\) | 5.93530e11 | 0.214432 | ||||||||
\(583\) | −2.94746e12 | −1.05667 | ||||||||
\(584\) | 4.83969e12 | 1.72171 | ||||||||
\(585\) | 1.36230e11 | 0.0480919 | ||||||||
\(586\) | −1.56782e12 | −0.549233 | ||||||||
\(587\) | 3.09625e12 | 1.07638 | 0.538189 | − | 0.842824i | \(-0.319109\pi\) | ||||
0.538189 | + | 0.842824i | \(0.319109\pi\) | |||||||
\(588\) | −1.41024e12 | −0.486515 | ||||||||
\(589\) | 1.06672e12 | 0.365200 | ||||||||
\(590\) | −2.67228e11 | −0.0907922 | ||||||||
\(591\) | −7.28687e12 | −2.45695 | ||||||||
\(592\) | −5.59992e11 | −0.187385 | ||||||||
\(593\) | −1.01140e12 | −0.335874 | −0.167937 | − | 0.985798i | \(-0.553711\pi\) | ||||
−0.167937 | + | 0.985798i | \(0.553711\pi\) | |||||||
\(594\) | −3.88130e11 | −0.127920 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 2.52123e12 | 0.818472 | ||||||||
\(597\) | 6.39519e12 | 2.06048 | ||||||||
\(598\) | −4.86645e11 | −0.155617 | ||||||||
\(599\) | −1.80697e12 | −0.573495 | −0.286747 | − | 0.958006i | \(-0.592574\pi\) | ||||
−0.286747 | + | 0.958006i | \(0.592574\pi\) | |||||||
\(600\) | 4.38202e12 | 1.38037 | ||||||||
\(601\) | 1.41403e12 | 0.442102 | 0.221051 | − | 0.975262i | \(-0.429051\pi\) | ||||
0.221051 | + | 0.975262i | \(0.429051\pi\) | |||||||
\(602\) | 2.70609e11 | 0.0839765 | ||||||||
\(603\) | 4.45181e12 | 1.37122 | ||||||||
\(604\) | −1.50846e12 | −0.461178 | ||||||||
\(605\) | 1.19500e11 | 0.0362634 | ||||||||
\(606\) | 4.71613e12 | 1.42056 | ||||||||
\(607\) | 1.19074e12 | 0.356015 | 0.178008 | − | 0.984029i | \(-0.443035\pi\) | ||||
0.178008 | + | 0.984029i | \(0.443035\pi\) | |||||||
\(608\) | 4.98458e12 | 1.47932 | ||||||||
\(609\) | −9.36662e11 | −0.275934 | ||||||||
\(610\) | 7.46228e10 | 0.0218216 | ||||||||
\(611\) | 1.70039e12 | 0.493586 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3.81378e11 | −0.109090 | −0.0545448 | − | 0.998511i | \(-0.517371\pi\) | ||||
−0.0545448 | + | 0.998511i | \(0.517371\pi\) | |||||||
\(614\) | −1.24936e12 | −0.354757 | ||||||||
\(615\) | −1.22104e11 | −0.0344186 | ||||||||
\(616\) | −2.89149e12 | −0.809112 | ||||||||
\(617\) | −2.00413e12 | −0.556727 | −0.278364 | − | 0.960476i | \(-0.589792\pi\) | ||||
−0.278364 | + | 0.960476i | \(0.589792\pi\) | |||||||
\(618\) | −5.27303e12 | −1.45416 | ||||||||
\(619\) | 1.20173e12 | 0.329003 | 0.164501 | − | 0.986377i | \(-0.447399\pi\) | ||||
0.164501 | + | 0.986377i | \(0.447399\pi\) | |||||||
\(620\) | 5.46894e10 | 0.0148642 | ||||||||
\(621\) | −3.88716e11 | −0.104887 | ||||||||
\(622\) | 2.86903e12 | 0.768561 | ||||||||
\(623\) | −2.95171e11 | −0.0785013 | ||||||||
\(624\) | −3.69237e11 | −0.0974933 | ||||||||
\(625\) | 3.72960e12 | 0.977693 | ||||||||
\(626\) | −2.05397e11 | −0.0534576 | ||||||||
\(627\) | −9.66498e12 | −2.49745 | ||||||||
\(628\) | 2.86334e12 | 0.734607 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | −1.56104e11 | −0.0394803 | ||||||||
\(631\) | 9.59070e11 | 0.240834 | 0.120417 | − | 0.992723i | \(-0.461577\pi\) | ||||
0.120417 | + | 0.992723i | \(0.461577\pi\) | |||||||
\(632\) | 3.43297e12 | 0.855939 | ||||||||
\(633\) | −5.92389e12 | −1.46653 | ||||||||
\(634\) | 2.59995e12 | 0.639092 | ||||||||
\(635\) | −4.42805e11 | −0.108076 | ||||||||
\(636\) | 3.61501e12 | 0.876097 | ||||||||
\(637\) | −1.00918e12 | −0.242852 | ||||||||
\(638\) | 7.52179e11 | 0.179733 | ||||||||
\(639\) | 2.27700e12 | 0.540268 | ||||||||
\(640\) | 2.83764e11 | 0.0668572 | ||||||||
\(641\) | −1.76987e12 | −0.414077 | −0.207038 | − | 0.978333i | \(-0.566383\pi\) | ||||
−0.207038 | + | 0.978333i | \(0.566383\pi\) | |||||||
\(642\) | −2.05389e12 | −0.477165 | ||||||||
\(643\) | −7.53766e12 | −1.73895 | −0.869475 | − | 0.493977i | \(-0.835543\pi\) | ||||
−0.869475 | + | 0.493977i | \(0.835543\pi\) | |||||||
\(644\) | −1.16911e12 | −0.267836 | ||||||||
\(645\) | 1.14867e11 | 0.0261323 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −5.30405e12 | −1.18998 | −0.594989 | − | 0.803734i | \(-0.702843\pi\) | ||||
−0.594989 | + | 0.803734i | \(0.702843\pi\) | |||||||
\(648\) | −3.65217e12 | −0.813698 | ||||||||
\(649\) | −9.96632e12 | −2.20513 | ||||||||
\(650\) | 1.26598e12 | 0.278174 | ||||||||
\(651\) | 1.21147e12 | 0.264362 | ||||||||
\(652\) | −1.75411e12 | −0.380139 | ||||||||
\(653\) | 3.41486e11 | 0.0734959 | 0.0367480 | − | 0.999325i | \(-0.488300\pi\) | ||||
0.0367480 | + | 0.999325i | \(0.488300\pi\) | |||||||
\(654\) | 5.67532e12 | 1.21308 | ||||||||
\(655\) | 2.30032e11 | 0.0488318 | ||||||||
\(656\) | 1.75535e11 | 0.0370080 | ||||||||
\(657\) | 9.74452e12 | 2.04040 | ||||||||
\(658\) | −1.94844e12 | −0.405202 | ||||||||
\(659\) | −1.73640e12 | −0.358646 | −0.179323 | − | 0.983790i | \(-0.557391\pi\) | ||||
−0.179323 | + | 0.983790i | \(0.557391\pi\) | |||||||
\(660\) | −4.95513e11 | −0.101650 | ||||||||
\(661\) | −7.10034e12 | −1.44668 | −0.723340 | − | 0.690492i | \(-0.757394\pi\) | ||||
−0.723340 | + | 0.690492i | \(0.757394\pi\) | |||||||
\(662\) | 4.73244e12 | 0.957689 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −9.17195e12 | −1.83107 | ||||||||
\(665\) | −4.45519e11 | −0.0883423 | ||||||||
\(666\) | 4.50775e12 | 0.887821 | ||||||||
\(667\) | 7.53314e11 | 0.147370 | ||||||||
\(668\) | 5.05111e11 | 0.0981505 | ||||||||
\(669\) | 1.11659e13 | 2.15514 | ||||||||
\(670\) | −3.10700e11 | −0.0595668 | ||||||||
\(671\) | 2.78307e12 | 0.529996 | ||||||||
\(672\) | 5.66100e12 | 1.07086 | ||||||||
\(673\) | 8.55362e11 | 0.160725 | 0.0803623 | − | 0.996766i | \(-0.474392\pi\) | ||||
0.0803623 | + | 0.996766i | \(0.474392\pi\) | |||||||
\(674\) | 1.74414e12 | 0.325545 | ||||||||
\(675\) | 1.01122e12 | 0.187491 | ||||||||
\(676\) | 2.78197e12 | 0.512381 | ||||||||
\(677\) | −1.00796e13 | −1.84415 | −0.922073 | − | 0.387017i | \(-0.873506\pi\) | ||||
−0.922073 | + | 0.387017i | \(0.873506\pi\) | |||||||
\(678\) | −2.97905e12 | −0.541433 | ||||||||
\(679\) | 1.02038e12 | 0.184224 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.87841e12 | 0.334679 | ||||||||
\(682\) | −9.72864e11 | −0.172196 | ||||||||
\(683\) | 4.29728e12 | 0.755614 | 0.377807 | − | 0.925884i | \(-0.376678\pi\) | ||||
0.377807 | + | 0.925884i | \(0.376678\pi\) | |||||||
\(684\) | 6.28727e12 | 1.09827 | ||||||||
\(685\) | 3.23831e11 | 0.0561968 | ||||||||
\(686\) | 3.50480e12 | 0.604233 | ||||||||
\(687\) | −6.03439e12 | −1.03354 | ||||||||
\(688\) | −1.65131e11 | −0.0280983 | ||||||||
\(689\) | 2.58692e12 | 0.437318 | ||||||||
\(690\) | 2.36705e11 | 0.0397544 | ||||||||
\(691\) | −7.79682e12 | −1.30097 | −0.650484 | − | 0.759520i | \(-0.725434\pi\) | ||||
−0.650484 | + | 0.759520i | \(0.725434\pi\) | |||||||
\(692\) | −3.22223e12 | −0.534169 | ||||||||
\(693\) | −5.82190e12 | −0.958882 | ||||||||
\(694\) | −1.95728e12 | −0.320284 | ||||||||
\(695\) | 5.23832e11 | 0.0851648 | ||||||||
\(696\) | −2.28510e12 | −0.369116 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | −2.29473e12 | −0.365916 | ||||||||
\(699\) | 1.13534e13 | 1.79878 | ||||||||
\(700\) | 3.04138e12 | 0.478772 | ||||||||
\(701\) | −2.38474e12 | −0.373000 | −0.186500 | − | 0.982455i | \(-0.559714\pi\) | ||||
−0.186500 | + | 0.982455i | \(0.559714\pi\) | |||||||
\(702\) | 3.40654e11 | 0.0529416 | ||||||||
\(703\) | 1.28651e13 | 1.98662 | ||||||||
\(704\) | −3.49391e12 | −0.536087 | ||||||||
\(705\) | −8.27071e11 | −0.126093 | ||||||||
\(706\) | −3.81732e12 | −0.578279 | ||||||||
\(707\) | 8.10781e12 | 1.22044 | ||||||||
\(708\) | 1.22235e13 | 1.82830 | ||||||||
\(709\) | 5.62327e12 | 0.835759 | 0.417880 | − | 0.908502i | \(-0.362773\pi\) | ||||
0.417880 | + | 0.908502i | \(0.362773\pi\) | |||||||
\(710\) | −1.58916e11 | −0.0234696 | ||||||||
\(711\) | 6.91214e12 | 1.01438 | ||||||||
\(712\) | −7.20104e11 | −0.105011 | ||||||||
\(713\) | −9.74332e11 | −0.141190 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.54592e11 | −0.0507402 | ||||||||
\(716\) | −1.83636e12 | −0.261125 | ||||||||
\(717\) | 1.26158e13 | 1.78270 | ||||||||
\(718\) | 2.14911e12 | 0.301786 | ||||||||
\(719\) | 1.53363e12 | 0.214013 | 0.107006 | − | 0.994258i | \(-0.465874\pi\) | ||||
0.107006 | + | 0.994258i | \(0.465874\pi\) | |||||||
\(720\) | 9.52576e10 | 0.0132100 | ||||||||
\(721\) | −9.06521e12 | −1.24931 | ||||||||
\(722\) | −4.40944e12 | −0.603902 | ||||||||
\(723\) | −9.20073e12 | −1.25228 | ||||||||
\(724\) | −7.07019e12 | −0.956329 | ||||||||
\(725\) | −1.95971e12 | −0.263433 | ||||||||
\(726\) | 2.60722e12 | 0.348308 | ||||||||
\(727\) | −1.19798e12 | −0.159054 | −0.0795268 | − | 0.996833i | \(-0.525341\pi\) | ||||
−0.0795268 | + | 0.996833i | \(0.525341\pi\) | |||||||
\(728\) | 2.53780e12 | 0.334863 | ||||||||
\(729\) | −9.45552e12 | −1.23997 | ||||||||
\(730\) | −6.80087e11 | −0.0886364 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −3.41338e12 | −0.439426 | ||||||||
\(733\) | −8.71100e12 | −1.11455 | −0.557276 | − | 0.830328i | \(-0.688153\pi\) | ||||
−0.557276 | + | 0.830328i | \(0.688153\pi\) | |||||||
\(734\) | −4.14597e12 | −0.527222 | ||||||||
\(735\) | 4.90866e11 | 0.0620398 | ||||||||
\(736\) | −4.55288e12 | −0.571921 | ||||||||
\(737\) | −1.15876e13 | −1.44674 | ||||||||
\(738\) | −1.41300e12 | −0.175343 | ||||||||
\(739\) | 1.05005e13 | 1.29512 | 0.647560 | − | 0.762015i | \(-0.275790\pi\) | ||||
0.647560 | + | 0.762015i | \(0.275790\pi\) | |||||||
\(740\) | 6.59580e11 | 0.0808583 | ||||||||
\(741\) | 8.48276e12 | 1.03361 | ||||||||
\(742\) | −2.96431e12 | −0.359009 | ||||||||
\(743\) | −1.33088e13 | −1.60210 | −0.801051 | − | 0.598596i | \(-0.795726\pi\) | ||||
−0.801051 | + | 0.598596i | \(0.795726\pi\) | |||||||
\(744\) | 2.95553e12 | 0.353637 | ||||||||
\(745\) | −8.77568e11 | −0.104370 | ||||||||
\(746\) | 4.94575e11 | 0.0584665 | ||||||||
\(747\) | −1.84673e13 | −2.17001 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −3.53097e12 | −0.409945 | ||||||||
\(750\) | −1.23617e12 | −0.142661 | ||||||||
\(751\) | −9.18538e12 | −1.05370 | −0.526850 | − | 0.849958i | \(-0.676627\pi\) | ||||
−0.526850 | + | 0.849958i | \(0.676627\pi\) | |||||||
\(752\) | 1.18898e12 | 0.135580 | ||||||||
\(753\) | −7.52719e12 | −0.853209 | ||||||||
\(754\) | −6.60172e11 | −0.0743851 | ||||||||
\(755\) | 5.25053e11 | 0.0588088 | ||||||||
\(756\) | 8.18383e11 | 0.0911189 | ||||||||
\(757\) | 1.11837e13 | 1.23781 | 0.618903 | − | 0.785467i | \(-0.287577\pi\) | ||||
0.618903 | + | 0.785467i | \(0.287577\pi\) | |||||||
\(758\) | −1.26236e12 | −0.138890 | ||||||||
\(759\) | 8.82792e12 | 0.965541 | ||||||||
\(760\) | −1.08690e12 | −0.118175 | ||||||||
\(761\) | 4.29799e12 | 0.464553 | 0.232276 | − | 0.972650i | \(-0.425383\pi\) | ||||
0.232276 | + | 0.972650i | \(0.425383\pi\) | |||||||
\(762\) | −9.66102e12 | −1.03807 | ||||||||
\(763\) | 9.75681e12 | 1.04219 | ||||||||
\(764\) | 3.91790e11 | 0.0416038 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 5.03741e12 | 0.528662 | ||||||||
\(767\) | 8.74723e12 | 0.912623 | ||||||||
\(768\) | 1.25203e13 | 1.29864 | ||||||||
\(769\) | −9.88894e12 | −1.01972 | −0.509860 | − | 0.860257i | \(-0.670303\pi\) | ||||
−0.509860 | + | 0.860257i | \(0.670303\pi\) | |||||||
\(770\) | 4.06321e11 | 0.0416544 | ||||||||
\(771\) | −2.17577e13 | −2.21752 | ||||||||
\(772\) | −1.23879e13 | −1.25522 | ||||||||
\(773\) | −1.06695e13 | −1.07482 | −0.537409 | − | 0.843322i | \(-0.680597\pi\) | ||||
−0.537409 | + | 0.843322i | \(0.680597\pi\) | |||||||
\(774\) | 1.32925e12 | 0.133129 | ||||||||
\(775\) | 2.53467e12 | 0.252385 | ||||||||
\(776\) | 2.48933e12 | 0.246436 | ||||||||
\(777\) | 1.46109e13 | 1.43808 | ||||||||
\(778\) | −5.66738e12 | −0.554593 | ||||||||
\(779\) | −4.03269e12 | −0.392352 | ||||||||
\(780\) | 4.34902e11 | 0.0420693 | ||||||||
\(781\) | −5.92679e12 | −0.570020 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −5.27324e11 | −0.0501360 | ||||||||
\(784\) | −7.05659e11 | −0.0667072 | ||||||||
\(785\) | −9.96649e11 | −0.0936761 | ||||||||
\(786\) | 5.01879e12 | 0.469027 | ||||||||
\(787\) | −1.39379e13 | −1.29513 | −0.647563 | − | 0.762012i | \(-0.724212\pi\) | ||||
−0.647563 | + | 0.762012i | \(0.724212\pi\) | |||||||
\(788\) | −1.23384e13 | −1.13996 | ||||||||
\(789\) | 8.51023e12 | 0.781799 | ||||||||
\(790\) | −4.82410e11 | −0.0440651 | ||||||||
\(791\) | −5.12148e12 | −0.465159 | ||||||||
\(792\) | −1.42032e13 | −1.28269 | ||||||||
\(793\) | −2.44264e12 | −0.219346 | ||||||||
\(794\) | −4.35277e12 | −0.388663 | ||||||||
\(795\) | −1.25828e12 | −0.111719 | ||||||||
\(796\) | 1.08286e13 | 0.956009 | ||||||||
\(797\) | 5.24283e11 | 0.0460260 | 0.0230130 | − | 0.999735i | \(-0.492674\pi\) | ||||
0.0230130 | + | 0.999735i | \(0.492674\pi\) | |||||||
\(798\) | −9.72023e12 | −0.848523 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 1.18441e13 | 1.02234 | ||||||||
\(801\) | −1.44990e12 | −0.124449 | ||||||||
\(802\) | −2.21056e12 | −0.188677 | ||||||||
\(803\) | −2.53639e13 | −2.15277 | ||||||||
\(804\) | 1.42120e13 | 1.19951 | ||||||||
\(805\) | 4.06934e11 | 0.0341541 | ||||||||
\(806\) | 8.53863e11 | 0.0712657 | ||||||||
\(807\) | −3.95025e12 | −0.327864 | ||||||||
\(808\) | 1.97800e13 | 1.63258 | ||||||||
\(809\) | 5.77660e12 | 0.474137 | 0.237069 | − | 0.971493i | \(-0.423813\pi\) | ||||
0.237069 | + | 0.971493i | \(0.423813\pi\) | |||||||
\(810\) | 5.13214e11 | 0.0418905 | ||||||||
\(811\) | 4.16550e11 | 0.0338122 | 0.0169061 | − | 0.999857i | \(-0.494618\pi\) | ||||
0.0169061 | + | 0.999857i | \(0.494618\pi\) | |||||||
\(812\) | −1.58599e12 | −0.128026 | ||||||||
\(813\) | 1.12948e13 | 0.906714 | ||||||||
\(814\) | −1.17332e13 | −0.936712 | ||||||||
\(815\) | 6.10556e11 | 0.0484748 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.79367e12 | 0.297893 | ||||||||
\(818\) | −2.32956e12 | −0.181921 | ||||||||
\(819\) | 5.10976e12 | 0.396847 | ||||||||
\(820\) | −2.06752e11 | −0.0159693 | ||||||||
\(821\) | −1.00996e13 | −0.775822 | −0.387911 | − | 0.921697i | \(-0.626803\pi\) | ||||
−0.387911 | + | 0.921697i | \(0.626803\pi\) | |||||||
\(822\) | 7.06528e12 | 0.539767 | ||||||||
\(823\) | −4.79075e12 | −0.364003 | −0.182001 | − | 0.983298i | \(-0.558258\pi\) | ||||
−0.182001 | + | 0.983298i | \(0.558258\pi\) | |||||||
\(824\) | −2.21156e13 | −1.67120 | ||||||||
\(825\) | −2.29654e13 | −1.72596 | ||||||||
\(826\) | −1.00233e13 | −0.749204 | ||||||||
\(827\) | −2.02121e13 | −1.50258 | −0.751288 | − | 0.659975i | \(-0.770567\pi\) | ||||
−0.751288 | + | 0.659975i | \(0.770567\pi\) | |||||||
\(828\) | −5.74275e12 | −0.424603 | ||||||||
\(829\) | 9.90972e12 | 0.728729 | 0.364364 | − | 0.931256i | \(-0.381286\pi\) | ||||
0.364364 | + | 0.931256i | \(0.381286\pi\) | |||||||
\(830\) | 1.28887e12 | 0.0942665 | ||||||||
\(831\) | 3.06147e13 | 2.22703 | ||||||||
\(832\) | 3.06654e12 | 0.221867 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 1.14288e13 | 0.818003 | ||||||||
\(835\) | −1.75815e11 | −0.0125160 | ||||||||
\(836\) | −1.63651e13 | −1.15875 | ||||||||
\(837\) | 6.82038e11 | 0.0480335 | ||||||||
\(838\) | 6.87537e12 | 0.481613 | ||||||||
\(839\) | 8.45160e12 | 0.588857 | 0.294429 | − | 0.955673i | \(-0.404871\pi\) | ||||
0.294429 | + | 0.955673i | \(0.404871\pi\) | |||||||
\(840\) | −1.23439e12 | −0.0855452 | ||||||||
\(841\) | −1.34852e13 | −0.929557 | ||||||||
\(842\) | 6.11165e11 | 0.0419038 | ||||||||
\(843\) | 1.69426e13 | 1.15546 | ||||||||
\(844\) | −1.00305e13 | −0.680430 | ||||||||
\(845\) | −9.68327e11 | −0.0653381 | ||||||||
\(846\) | −9.57090e12 | −0.642371 | ||||||||
\(847\) | 4.48224e12 | 0.299240 | ||||||||
\(848\) | 1.80888e12 | 0.120124 | ||||||||
\(849\) | −1.05362e13 | −0.695984 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.17509e13 | −0.768047 | ||||||||
\(852\) | 7.26911e12 | 0.472610 | ||||||||
\(853\) | 8.99345e12 | 0.581642 | 0.290821 | − | 0.956778i | \(-0.406072\pi\) | ||||
0.290821 | + | 0.956778i | \(0.406072\pi\) | |||||||
\(854\) | 2.79898e12 | 0.180069 | ||||||||
\(855\) | −2.18842e12 | −0.140050 | ||||||||
\(856\) | −8.61421e12 | −0.548383 | ||||||||
\(857\) | −1.72593e12 | −0.109297 | −0.0546486 | − | 0.998506i | \(-0.517404\pi\) | ||||
−0.0546486 | + | 0.998506i | \(0.517404\pi\) | |||||||
\(858\) | −7.73642e12 | −0.487357 | ||||||||
\(859\) | −4.15450e12 | −0.260345 | −0.130173 | − | 0.991491i | \(-0.541553\pi\) | ||||
−0.130173 | + | 0.991491i | \(0.541553\pi\) | |||||||
\(860\) | 1.94497e11 | 0.0121247 | ||||||||
\(861\) | −4.57993e12 | −0.284018 | ||||||||
\(862\) | −1.08533e13 | −0.669545 | ||||||||
\(863\) | −3.76231e11 | −0.0230890 | −0.0115445 | − | 0.999933i | \(-0.503675\pi\) | ||||
−0.0115445 | + | 0.999933i | \(0.503675\pi\) | |||||||
\(864\) | 3.18704e12 | 0.194570 | ||||||||
\(865\) | 1.12157e12 | 0.0681165 | ||||||||
\(866\) | 2.68748e11 | 0.0162373 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 2.05131e12 | 0.122657 | ||||||||
\(869\) | −1.79916e13 | −1.07024 | ||||||||
\(870\) | 3.21109e11 | 0.0190027 | ||||||||
\(871\) | 1.01702e13 | 0.598752 | ||||||||
\(872\) | 2.38029e13 | 1.39414 | ||||||||
\(873\) | 5.01216e12 | 0.292052 | ||||||||
\(874\) | 7.81753e12 | 0.453177 | ||||||||
\(875\) | −2.12519e12 | −0.122563 | ||||||||
\(876\) | 3.11085e13 | 1.78488 | ||||||||
\(877\) | 1.91957e13 | 1.09574 | 0.547869 | − | 0.836564i | \(-0.315439\pi\) | ||||
0.547869 | + | 0.836564i | \(0.315439\pi\) | |||||||
\(878\) | −1.52579e13 | −0.866500 | ||||||||
\(879\) | −2.49619e13 | −1.41035 | ||||||||
\(880\) | −2.47945e11 | −0.0139375 | ||||||||
\(881\) | −1.22362e12 | −0.0684312 | −0.0342156 | − | 0.999414i | \(-0.510893\pi\) | ||||
−0.0342156 | + | 0.999414i | \(0.510893\pi\) | |||||||
\(882\) | 5.68032e12 | 0.316056 | ||||||||
\(883\) | 1.57603e13 | 0.872451 | 0.436225 | − | 0.899837i | \(-0.356315\pi\) | ||||
0.436225 | + | 0.899837i | \(0.356315\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −4.25466e12 | −0.233142 | ||||||||
\(886\) | −5.39276e12 | −0.294008 | ||||||||
\(887\) | 3.84466e12 | 0.208546 | 0.104273 | − | 0.994549i | \(-0.466748\pi\) | ||||
0.104273 | + | 0.994549i | \(0.466748\pi\) | |||||||
\(888\) | 3.56451e13 | 1.92372 | ||||||||
\(889\) | −1.66089e13 | −0.891831 | ||||||||
\(890\) | 1.01191e11 | 0.00540614 | ||||||||
\(891\) | 1.91404e13 | 1.01742 | ||||||||
\(892\) | 1.89064e13 | 0.999926 | ||||||||
\(893\) | −2.73153e13 | −1.43739 | ||||||||
\(894\) | −1.91466e13 | −1.00247 | ||||||||
\(895\) | 6.39185e11 | 0.0332984 | ||||||||
\(896\) | 1.06435e13 | 0.551696 | ||||||||
\(897\) | −7.74809e12 | −0.399603 | ||||||||
\(898\) | −8.78874e12 | −0.451007 | ||||||||
\(899\) | −1.32176e12 | −0.0674891 | ||||||||
\(900\) | 1.49395e13 | 0.759003 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 3.67788e12 | 0.184998 | ||||||||
\(903\) | 4.30848e12 | 0.215640 | ||||||||
\(904\) | −1.24945e13 | −0.622242 | ||||||||
\(905\) | 2.46093e12 | 0.121950 | ||||||||
\(906\) | 1.14555e13 | 0.564855 | ||||||||
\(907\) | 3.00858e13 | 1.47614 | 0.738072 | − | 0.674722i | \(-0.235736\pi\) | ||||
0.738072 | + | 0.674722i | \(0.235736\pi\) | |||||||
\(908\) | 3.18059e12 | 0.155282 | ||||||||
\(909\) | 3.98261e13 | 1.93478 | ||||||||
\(910\) | −3.56620e11 | −0.0172393 | ||||||||
\(911\) | −3.25658e13 | −1.56650 | −0.783249 | − | 0.621709i | \(-0.786439\pi\) | ||||
−0.783249 | + | 0.621709i | \(0.786439\pi\) | |||||||
\(912\) | 5.93148e12 | 0.283914 | ||||||||
\(913\) | 4.80685e13 | 2.28951 | ||||||||
\(914\) | 1.46237e13 | 0.693105 | ||||||||
\(915\) | 1.18810e12 | 0.0560350 | ||||||||
\(916\) | −1.02176e13 | −0.479536 | ||||||||
\(917\) | 8.62813e12 | 0.402953 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.18128e13 | 0.546304 | 0.273152 | − | 0.961971i | \(-0.411934\pi\) | ||||
0.273152 | + | 0.961971i | \(0.411934\pi\) | |||||||
\(920\) | 9.92763e11 | 0.0456878 | ||||||||
\(921\) | −1.98917e13 | −0.910968 | ||||||||
\(922\) | −5.16535e12 | −0.235402 | ||||||||
\(923\) | 5.20182e12 | 0.235911 | ||||||||
\(924\) | −1.85859e13 | −0.838801 | ||||||||
\(925\) | 3.05693e13 | 1.37293 | ||||||||
\(926\) | 2.20948e13 | 0.987509 | ||||||||
\(927\) | −4.45289e13 | −1.98054 | ||||||||
\(928\) | −6.17635e12 | −0.273379 | ||||||||
\(929\) | 3.31944e13 | 1.46216 | 0.731078 | − | 0.682293i | \(-0.239017\pi\) | ||||
0.731078 | + | 0.682293i | \(0.239017\pi\) | |||||||
\(930\) | −4.15320e11 | −0.0182058 | ||||||||
\(931\) | 1.62116e13 | 0.707217 | ||||||||
\(932\) | 1.92239e13 | 0.834586 | ||||||||
\(933\) | 4.56791e13 | 1.97356 | ||||||||
\(934\) | 1.61387e13 | 0.693916 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 1.24659e13 | 0.530862 | ||||||||
\(937\) | −7.61249e12 | −0.322625 | −0.161313 | − | 0.986903i | \(-0.551573\pi\) | ||||
−0.161313 | + | 0.986903i | \(0.551573\pi\) | |||||||
\(938\) | −1.16538e13 | −0.491536 | ||||||||
\(939\) | −3.27022e12 | −0.137272 | ||||||||
\(940\) | −1.40043e12 | −0.0585039 | ||||||||
\(941\) | −8.99657e12 | −0.374045 | −0.187022 | − | 0.982356i | \(-0.559884\pi\) | ||||
−0.187022 | + | 0.982356i | \(0.559884\pi\) | |||||||
\(942\) | −2.17447e13 | −0.899754 | ||||||||
\(943\) | 3.68343e12 | 0.151687 | ||||||||
\(944\) | 6.11642e12 | 0.250682 | ||||||||
\(945\) | −2.84856e11 | −0.0116194 | ||||||||
\(946\) | −3.45989e12 | −0.140460 | ||||||||
\(947\) | −4.12752e12 | −0.166769 | −0.0833843 | − | 0.996517i | \(-0.526573\pi\) | ||||
−0.0833843 | + | 0.996517i | \(0.526573\pi\) | |||||||
\(948\) | 2.20663e13 | 0.887345 | ||||||||
\(949\) | 2.22614e13 | 0.890953 | ||||||||
\(950\) | −2.03369e13 | −0.810081 | ||||||||
\(951\) | 4.13950e13 | 1.64110 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.80381e13 | 0.708389 | 0.354195 | − | 0.935172i | \(-0.384755\pi\) | ||||
0.354195 | + | 0.935172i | \(0.384755\pi\) | |||||||
\(954\) | −1.45609e13 | −0.569141 | ||||||||
\(955\) | −1.36371e11 | −0.00530526 | ||||||||
\(956\) | 2.13615e13 | 0.827127 | ||||||||
\(957\) | 1.19758e13 | 0.461530 | ||||||||
\(958\) | 1.41964e13 | 0.544545 | ||||||||
\(959\) | 1.21464e13 | 0.463728 | ||||||||
\(960\) | −1.49157e12 | −0.0566790 | ||||||||
\(961\) | −2.47301e13 | −0.935341 | ||||||||
\(962\) | 1.02980e13 | 0.387672 | ||||||||
\(963\) | −1.73444e13 | −0.649890 | ||||||||
\(964\) | −1.55790e13 | −0.581023 | ||||||||
\(965\) | 4.31188e12 | 0.160064 | ||||||||
\(966\) | 8.87839e12 | 0.328048 | ||||||||
\(967\) | −3.92827e12 | −0.144472 | −0.0722358 | − | 0.997388i | \(-0.523013\pi\) | ||||
−0.0722358 | + | 0.997388i | \(0.523013\pi\) | |||||||
\(968\) | 1.09350e13 | 0.400293 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −3.49808e11 | −0.0126869 | ||||||||
\(971\) | 3.04563e13 | 1.09949 | 0.549744 | − | 0.835333i | \(-0.314725\pi\) | ||||
0.549744 | + | 0.835333i | \(0.314725\pi\) | |||||||
\(972\) | −2.70346e13 | −0.971451 | ||||||||
\(973\) | 1.96481e13 | 0.702768 | ||||||||
\(974\) | 1.55525e13 | 0.553714 | ||||||||
\(975\) | 2.01563e13 | 0.714314 | ||||||||
\(976\) | −1.70799e12 | −0.0602506 | ||||||||
\(977\) | 1.55251e13 | 0.545140 | 0.272570 | − | 0.962136i | \(-0.412126\pi\) | ||||
0.272570 | + | 0.962136i | \(0.412126\pi\) | |||||||
\(978\) | 1.33210e13 | 0.465598 | ||||||||
\(979\) | 3.77393e12 | 0.131302 | ||||||||
\(980\) | 8.31152e11 | 0.0287848 | ||||||||
\(981\) | 4.79261e13 | 1.65220 | ||||||||
\(982\) | −1.08305e13 | −0.371662 | ||||||||
\(983\) | 4.00675e13 | 1.36868 | 0.684339 | − | 0.729164i | \(-0.260091\pi\) | ||||
0.684339 | + | 0.729164i | \(0.260091\pi\) | |||||||
\(984\) | −1.11733e13 | −0.379930 | ||||||||
\(985\) | 4.29464e12 | 0.145366 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −3.10221e13 | −1.04050 | ||||||||
\(988\) | 1.43633e13 | 0.479566 | ||||||||
\(989\) | −3.46511e12 | −0.115169 | ||||||||
\(990\) | 1.99588e12 | 0.0660352 | ||||||||
\(991\) | 2.48607e12 | 0.0818808 | 0.0409404 | − | 0.999162i | \(-0.486965\pi\) | ||||
0.0409404 | + | 0.999162i | \(0.486965\pi\) | |||||||
\(992\) | 7.98845e12 | 0.261915 | ||||||||
\(993\) | 7.53473e13 | 2.45921 | ||||||||
\(994\) | −5.96067e12 | −0.193667 | ||||||||
\(995\) | −3.76912e12 | −0.121909 | ||||||||
\(996\) | −5.89552e13 | −1.89826 | ||||||||
\(997\) | −2.45995e13 | −0.788494 | −0.394247 | − | 0.919005i | \(-0.628994\pi\) | ||||
−0.394247 | + | 0.919005i | \(0.628994\pi\) | |||||||
\(998\) | 2.19517e13 | 0.700457 | ||||||||
\(999\) | 8.22569e12 | 0.261293 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 289.10.a.f.1.9 | 24 | ||
17.2 | even | 8 | 17.10.c.a.4.5 | ✓ | 24 | ||
17.9 | even | 8 | 17.10.c.a.13.8 | yes | 24 | ||
17.16 | even | 2 | inner | 289.10.a.f.1.10 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
17.10.c.a.4.5 | ✓ | 24 | 17.2 | even | 8 | ||
17.10.c.a.13.8 | yes | 24 | 17.9 | even | 8 | ||
289.10.a.f.1.9 | 24 | 1.1 | even | 1 | trivial | ||
289.10.a.f.1.10 | 24 | 17.16 | even | 2 | inner |