Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [197,14,Mod(1,197)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(197, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 14, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("197.1");
S:= CuspForms(chi, 14);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 197 \) |
Weight: | \( k \) | \(=\) | \( 14 \) |
Character orbit: | \([\chi]\) | \(=\) | 197.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: | \(211.244930035\) |
Analytic rank: | \(1\) |
Dimension: | \(104\) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.18 | ||
Character | \(\chi\) | \(=\) | 197.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −135.981 | −1.50240 | −0.751198 | − | 0.660077i | \(-0.770523\pi\) | ||||
−0.751198 | + | 0.660077i | \(0.770523\pi\) | |||||||
\(3\) | 2210.13 | 1.75037 | 0.875185 | − | 0.483788i | \(-0.160739\pi\) | ||||
0.875185 | + | 0.483788i | \(0.160739\pi\) | |||||||
\(4\) | 10298.9 | 1.25719 | ||||||||
\(5\) | 24727.3 | 0.707736 | 0.353868 | − | 0.935295i | \(-0.384866\pi\) | ||||
0.353868 | + | 0.935295i | \(0.384866\pi\) | |||||||
\(6\) | −300537. | −2.62975 | ||||||||
\(7\) | −333758. | −1.07225 | −0.536123 | − | 0.844140i | \(-0.680112\pi\) | ||||
−0.536123 | + | 0.844140i | \(0.680112\pi\) | |||||||
\(8\) | −286501. | −0.386404 | ||||||||
\(9\) | 3.29036e6 | 2.06380 | ||||||||
\(10\) | −3.36245e6 | −1.06330 | ||||||||
\(11\) | 2.42731e6 | 0.413117 | 0.206558 | − | 0.978434i | \(-0.433774\pi\) | ||||
0.206558 | + | 0.978434i | \(0.433774\pi\) | |||||||
\(12\) | 2.27620e7 | 2.20055 | ||||||||
\(13\) | 1.74555e7 | 1.00300 | 0.501501 | − | 0.865157i | \(-0.332781\pi\) | ||||
0.501501 | + | 0.865157i | \(0.332781\pi\) | |||||||
\(14\) | 4.53848e7 | 1.61094 | ||||||||
\(15\) | 5.46505e7 | 1.23880 | ||||||||
\(16\) | −4.54099e7 | −0.676661 | ||||||||
\(17\) | −5.12193e6 | −0.0514654 | −0.0257327 | − | 0.999669i | \(-0.508192\pi\) | ||||
−0.0257327 | + | 0.999669i | \(0.508192\pi\) | |||||||
\(18\) | −4.47427e8 | −3.10064 | ||||||||
\(19\) | −2.76788e8 | −1.34974 | −0.674868 | − | 0.737939i | \(-0.735799\pi\) | ||||
−0.674868 | + | 0.737939i | \(0.735799\pi\) | |||||||
\(20\) | 2.54664e8 | 0.889760 | ||||||||
\(21\) | −7.37649e8 | −1.87683 | ||||||||
\(22\) | −3.30069e8 | −0.620664 | ||||||||
\(23\) | 3.30732e8 | 0.465849 | 0.232925 | − | 0.972495i | \(-0.425170\pi\) | ||||
0.232925 | + | 0.972495i | \(0.425170\pi\) | |||||||
\(24\) | −6.33205e8 | −0.676349 | ||||||||
\(25\) | −6.09265e8 | −0.499110 | ||||||||
\(26\) | −2.37363e9 | −1.50690 | ||||||||
\(27\) | 3.74846e9 | 1.86204 | ||||||||
\(28\) | −3.43734e9 | −1.34802 | ||||||||
\(29\) | −1.77627e9 | −0.554527 | −0.277264 | − | 0.960794i | \(-0.589428\pi\) | ||||
−0.277264 | + | 0.960794i | \(0.589428\pi\) | |||||||
\(30\) | −7.43145e9 | −1.86117 | ||||||||
\(31\) | −4.02156e9 | −0.813848 | −0.406924 | − | 0.913462i | \(-0.633399\pi\) | ||||
−0.406924 | + | 0.913462i | \(0.633399\pi\) | |||||||
\(32\) | 8.52192e9 | 1.40302 | ||||||||
\(33\) | 5.36467e9 | 0.723107 | ||||||||
\(34\) | 6.96487e8 | 0.0773214 | ||||||||
\(35\) | −8.25292e9 | −0.758866 | ||||||||
\(36\) | 3.38871e10 | 2.59459 | ||||||||
\(37\) | 7.48195e9 | 0.479406 | 0.239703 | − | 0.970846i | \(-0.422950\pi\) | ||||
0.239703 | + | 0.970846i | \(0.422950\pi\) | |||||||
\(38\) | 3.76380e10 | 2.02784 | ||||||||
\(39\) | 3.85790e10 | 1.75562 | ||||||||
\(40\) | −7.08439e9 | −0.273472 | ||||||||
\(41\) | −2.60082e10 | −0.855098 | −0.427549 | − | 0.903992i | \(-0.640623\pi\) | ||||
−0.427549 | + | 0.903992i | \(0.640623\pi\) | |||||||
\(42\) | 1.00306e11 | 2.81973 | ||||||||
\(43\) | 3.17109e10 | 0.765005 | 0.382502 | − | 0.923954i | \(-0.375062\pi\) | ||||
0.382502 | + | 0.923954i | \(0.375062\pi\) | |||||||
\(44\) | 2.49986e10 | 0.519367 | ||||||||
\(45\) | 8.13616e10 | 1.46062 | ||||||||
\(46\) | −4.49734e10 | −0.699890 | ||||||||
\(47\) | −9.22642e10 | −1.24853 | −0.624263 | − | 0.781215i | \(-0.714600\pi\) | ||||
−0.624263 | + | 0.781215i | \(0.714600\pi\) | |||||||
\(48\) | −1.00362e11 | −1.18441 | ||||||||
\(49\) | 1.45052e10 | 0.149710 | ||||||||
\(50\) | 8.28487e10 | 0.749861 | ||||||||
\(51\) | −1.13201e10 | −0.0900836 | ||||||||
\(52\) | 1.79773e11 | 1.26096 | ||||||||
\(53\) | −1.70900e11 | −1.05913 | −0.529564 | − | 0.848270i | \(-0.677644\pi\) | ||||
−0.529564 | + | 0.848270i | \(0.677644\pi\) | |||||||
\(54\) | −5.09720e11 | −2.79752 | ||||||||
\(55\) | 6.00207e10 | 0.292377 | ||||||||
\(56\) | 9.56219e10 | 0.414319 | ||||||||
\(57\) | −6.11737e11 | −2.36254 | ||||||||
\(58\) | 2.41540e11 | 0.833119 | ||||||||
\(59\) | −3.65076e10 | −0.112680 | −0.0563399 | − | 0.998412i | \(-0.517943\pi\) | ||||
−0.0563399 | + | 0.998412i | \(0.517943\pi\) | |||||||
\(60\) | 5.62841e11 | 1.55741 | ||||||||
\(61\) | 3.48182e11 | 0.865291 | 0.432645 | − | 0.901564i | \(-0.357580\pi\) | ||||
0.432645 | + | 0.901564i | \(0.357580\pi\) | |||||||
\(62\) | 5.46857e11 | 1.22272 | ||||||||
\(63\) | −1.09818e12 | −2.21290 | ||||||||
\(64\) | −7.86823e11 | −1.43122 | ||||||||
\(65\) | 4.31628e11 | 0.709860 | ||||||||
\(66\) | −7.29495e11 | −1.08639 | ||||||||
\(67\) | −5.00394e11 | −0.675811 | −0.337906 | − | 0.941180i | \(-0.609718\pi\) | ||||
−0.337906 | + | 0.941180i | \(0.609718\pi\) | |||||||
\(68\) | −5.27503e10 | −0.0647019 | ||||||||
\(69\) | 7.30961e11 | 0.815408 | ||||||||
\(70\) | 1.12224e12 | 1.14012 | ||||||||
\(71\) | −2.58712e11 | −0.239683 | −0.119842 | − | 0.992793i | \(-0.538239\pi\) | ||||
−0.119842 | + | 0.992793i | \(0.538239\pi\) | |||||||
\(72\) | −9.42690e11 | −0.797458 | ||||||||
\(73\) | −3.41103e11 | −0.263808 | −0.131904 | − | 0.991263i | \(-0.542109\pi\) | ||||
−0.131904 | + | 0.991263i | \(0.542109\pi\) | |||||||
\(74\) | −1.01741e12 | −0.720257 | ||||||||
\(75\) | −1.34656e12 | −0.873627 | ||||||||
\(76\) | −2.85061e12 | −1.69688 | ||||||||
\(77\) | −8.10133e11 | −0.442962 | ||||||||
\(78\) | −5.24603e12 | −2.63764 | ||||||||
\(79\) | 4.33087e11 | 0.200447 | 0.100223 | − | 0.994965i | \(-0.468044\pi\) | ||||
0.100223 | + | 0.994965i | \(0.468044\pi\) | |||||||
\(80\) | −1.12286e12 | −0.478897 | ||||||||
\(81\) | 3.03869e12 | 1.19546 | ||||||||
\(82\) | 3.53664e12 | 1.28470 | ||||||||
\(83\) | −3.93626e12 | −1.32153 | −0.660763 | − | 0.750594i | \(-0.729767\pi\) | ||||
−0.660763 | + | 0.750594i | \(0.729767\pi\) | |||||||
\(84\) | −7.59698e12 | −2.35953 | ||||||||
\(85\) | −1.26651e11 | −0.0364239 | ||||||||
\(86\) | −4.31209e12 | −1.14934 | ||||||||
\(87\) | −3.92580e12 | −0.970628 | ||||||||
\(88\) | −6.95426e11 | −0.159630 | ||||||||
\(89\) | −5.61964e12 | −1.19860 | −0.599299 | − | 0.800525i | \(-0.704554\pi\) | ||||
−0.599299 | + | 0.800525i | \(0.704554\pi\) | |||||||
\(90\) | −1.10637e13 | −2.19443 | ||||||||
\(91\) | −5.82592e12 | −1.07546 | ||||||||
\(92\) | 3.40618e12 | 0.585662 | ||||||||
\(93\) | −8.88817e12 | −1.42454 | ||||||||
\(94\) | 1.25462e13 | 1.87578 | ||||||||
\(95\) | −6.84421e12 | −0.955256 | ||||||||
\(96\) | 1.88346e13 | 2.45580 | ||||||||
\(97\) | 9.80267e11 | 0.119489 | 0.0597445 | − | 0.998214i | \(-0.480971\pi\) | ||||
0.0597445 | + | 0.998214i | \(0.480971\pi\) | |||||||
\(98\) | −1.97244e12 | −0.224923 | ||||||||
\(99\) | 7.98672e12 | 0.852588 | ||||||||
\(100\) | −6.27477e12 | −0.627477 | ||||||||
\(101\) | −1.80524e13 | −1.69217 | −0.846087 | − | 0.533044i | \(-0.821048\pi\) | ||||
−0.846087 | + | 0.533044i | \(0.821048\pi\) | |||||||
\(102\) | 1.53933e12 | 0.135341 | ||||||||
\(103\) | 1.05325e13 | 0.869137 | 0.434568 | − | 0.900639i | \(-0.356901\pi\) | ||||
0.434568 | + | 0.900639i | \(0.356901\pi\) | |||||||
\(104\) | −5.00103e12 | −0.387563 | ||||||||
\(105\) | −1.82400e13 | −1.32830 | ||||||||
\(106\) | 2.32392e13 | 1.59123 | ||||||||
\(107\) | 2.62913e13 | 1.69363 | 0.846814 | − | 0.531889i | \(-0.178518\pi\) | ||||
0.846814 | + | 0.531889i | \(0.178518\pi\) | |||||||
\(108\) | 3.86051e13 | 2.34094 | ||||||||
\(109\) | −1.71710e13 | −0.980669 | −0.490335 | − | 0.871534i | \(-0.663125\pi\) | ||||
−0.490335 | + | 0.871534i | \(0.663125\pi\) | |||||||
\(110\) | −8.16170e12 | −0.439266 | ||||||||
\(111\) | 1.65361e13 | 0.839138 | ||||||||
\(112\) | 1.51559e13 | 0.725546 | ||||||||
\(113\) | 5.46644e12 | 0.246999 | 0.123499 | − | 0.992345i | \(-0.460588\pi\) | ||||
0.123499 | + | 0.992345i | \(0.460588\pi\) | |||||||
\(114\) | 8.31849e13 | 3.54946 | ||||||||
\(115\) | 8.17810e12 | 0.329698 | ||||||||
\(116\) | −1.82937e13 | −0.697147 | ||||||||
\(117\) | 5.74350e13 | 2.06999 | ||||||||
\(118\) | 4.96436e12 | 0.169289 | ||||||||
\(119\) | 1.70948e12 | 0.0551836 | ||||||||
\(120\) | −1.56574e13 | −0.478677 | ||||||||
\(121\) | −2.86309e13 | −0.829335 | ||||||||
\(122\) | −4.73462e13 | −1.30001 | ||||||||
\(123\) | −5.74816e13 | −1.49674 | ||||||||
\(124\) | −4.14177e13 | −1.02316 | ||||||||
\(125\) | −4.52501e13 | −1.06097 | ||||||||
\(126\) | 1.49332e14 | 3.32464 | ||||||||
\(127\) | 3.53962e13 | 0.748570 | 0.374285 | − | 0.927314i | \(-0.377888\pi\) | ||||
0.374285 | + | 0.927314i | \(0.377888\pi\) | |||||||
\(128\) | 3.71817e13 | 0.747247 | ||||||||
\(129\) | 7.00853e13 | 1.33904 | ||||||||
\(130\) | −5.86933e13 | −1.06649 | ||||||||
\(131\) | −1.42234e12 | −0.0245889 | −0.0122944 | − | 0.999924i | \(-0.503914\pi\) | ||||
−0.0122944 | + | 0.999924i | \(0.503914\pi\) | |||||||
\(132\) | 5.52503e13 | 0.909084 | ||||||||
\(133\) | 9.23801e13 | 1.44725 | ||||||||
\(134\) | 6.80442e13 | 1.01534 | ||||||||
\(135\) | 9.26892e13 | 1.31783 | ||||||||
\(136\) | 1.46744e12 | 0.0198864 | ||||||||
\(137\) | 5.44544e13 | 0.703638 | 0.351819 | − | 0.936068i | \(-0.385563\pi\) | ||||
0.351819 | + | 0.936068i | \(0.385563\pi\) | |||||||
\(138\) | −9.93970e13 | −1.22507 | ||||||||
\(139\) | 5.74325e13 | 0.675401 | 0.337700 | − | 0.941254i | \(-0.390351\pi\) | ||||
0.337700 | + | 0.941254i | \(0.390351\pi\) | |||||||
\(140\) | −8.49961e13 | −0.954040 | ||||||||
\(141\) | −2.03916e14 | −2.18538 | ||||||||
\(142\) | 3.51800e13 | 0.360099 | ||||||||
\(143\) | 4.23700e13 | 0.414356 | ||||||||
\(144\) | −1.49415e14 | −1.39649 | ||||||||
\(145\) | −4.39224e13 | −0.392459 | ||||||||
\(146\) | 4.63837e13 | 0.396344 | ||||||||
\(147\) | 3.20585e13 | 0.262048 | ||||||||
\(148\) | 7.70559e13 | 0.602705 | ||||||||
\(149\) | −9.62237e13 | −0.720396 | −0.360198 | − | 0.932876i | \(-0.617291\pi\) | ||||
−0.360198 | + | 0.932876i | \(0.617291\pi\) | |||||||
\(150\) | 1.83106e14 | 1.31253 | ||||||||
\(151\) | −1.04732e14 | −0.719003 | −0.359501 | − | 0.933145i | \(-0.617053\pi\) | ||||
−0.359501 | + | 0.933145i | \(0.617053\pi\) | |||||||
\(152\) | 7.93000e13 | 0.521542 | ||||||||
\(153\) | −1.68530e13 | −0.106214 | ||||||||
\(154\) | 1.10163e14 | 0.665504 | ||||||||
\(155\) | −9.94421e13 | −0.575989 | ||||||||
\(156\) | 3.97322e14 | 2.20716 | ||||||||
\(157\) | 1.79282e14 | 0.955410 | 0.477705 | − | 0.878520i | \(-0.341469\pi\) | ||||
0.477705 | + | 0.878520i | \(0.341469\pi\) | |||||||
\(158\) | −5.88918e13 | −0.301151 | ||||||||
\(159\) | −3.77711e14 | −1.85386 | ||||||||
\(160\) | 2.10724e14 | 0.992964 | ||||||||
\(161\) | −1.10384e14 | −0.499505 | ||||||||
\(162\) | −4.13206e14 | −1.79605 | ||||||||
\(163\) | 3.97441e13 | 0.165979 | 0.0829895 | − | 0.996550i | \(-0.473553\pi\) | ||||
0.0829895 | + | 0.996550i | \(0.473553\pi\) | |||||||
\(164\) | −2.67857e14 | −1.07502 | ||||||||
\(165\) | 1.32654e14 | 0.511769 | ||||||||
\(166\) | 5.35257e14 | 1.98546 | ||||||||
\(167\) | 9.71509e13 | 0.346569 | 0.173284 | − | 0.984872i | \(-0.444562\pi\) | ||||
0.173284 | + | 0.984872i | \(0.444562\pi\) | |||||||
\(168\) | 2.11337e14 | 0.725212 | ||||||||
\(169\) | 1.82074e12 | 0.00601153 | ||||||||
\(170\) | 1.72222e13 | 0.0547231 | ||||||||
\(171\) | −9.10731e14 | −2.78558 | ||||||||
\(172\) | 3.26588e14 | 0.961758 | ||||||||
\(173\) | 6.78768e13 | 0.192496 | 0.0962479 | − | 0.995357i | \(-0.469316\pi\) | ||||
0.0962479 | + | 0.995357i | \(0.469316\pi\) | |||||||
\(174\) | 5.33835e14 | 1.45827 | ||||||||
\(175\) | 2.03347e14 | 0.535168 | ||||||||
\(176\) | −1.10224e14 | −0.279540 | ||||||||
\(177\) | −8.06867e13 | −0.197231 | ||||||||
\(178\) | 7.64166e14 | 1.80077 | ||||||||
\(179\) | 6.18015e14 | 1.40428 | 0.702141 | − | 0.712038i | \(-0.252228\pi\) | ||||
0.702141 | + | 0.712038i | \(0.252228\pi\) | |||||||
\(180\) | 8.37936e14 | 1.83628 | ||||||||
\(181\) | −4.00598e14 | −0.846834 | −0.423417 | − | 0.905935i | \(-0.639169\pi\) | ||||
−0.423417 | + | 0.905935i | \(0.639169\pi\) | |||||||
\(182\) | 7.92216e14 | 1.61577 | ||||||||
\(183\) | 7.69528e14 | 1.51458 | ||||||||
\(184\) | −9.47550e13 | −0.180006 | ||||||||
\(185\) | 1.85008e14 | 0.339293 | ||||||||
\(186\) | 1.20862e15 | 2.14021 | ||||||||
\(187\) | −1.24325e13 | −0.0212612 | ||||||||
\(188\) | −9.50221e14 | −1.56964 | ||||||||
\(189\) | −1.25108e15 | −1.99656 | ||||||||
\(190\) | 9.30684e14 | 1.43517 | ||||||||
\(191\) | 8.51707e12 | 0.0126933 | 0.00634663 | − | 0.999980i | \(-0.497980\pi\) | ||||
0.00634663 | + | 0.999980i | \(0.497980\pi\) | |||||||
\(192\) | −1.73898e15 | −2.50517 | ||||||||
\(193\) | −5.88423e14 | −0.819534 | −0.409767 | − | 0.912190i | \(-0.634390\pi\) | ||||
−0.409767 | + | 0.912190i | \(0.634390\pi\) | |||||||
\(194\) | −1.33298e14 | −0.179520 | ||||||||
\(195\) | 9.53954e14 | 1.24252 | ||||||||
\(196\) | 1.49388e14 | 0.188214 | ||||||||
\(197\) | −5.84517e13 | −0.0712470 | ||||||||
\(198\) | −1.08604e15 | −1.28092 | ||||||||
\(199\) | −1.37423e15 | −1.56861 | −0.784306 | − | 0.620374i | \(-0.786981\pi\) | ||||
−0.784306 | + | 0.620374i | \(0.786981\pi\) | |||||||
\(200\) | 1.74555e14 | 0.192858 | ||||||||
\(201\) | −1.10594e15 | −1.18292 | ||||||||
\(202\) | 2.45478e15 | 2.54232 | ||||||||
\(203\) | 5.92845e14 | 0.594589 | ||||||||
\(204\) | −1.16585e14 | −0.113252 | ||||||||
\(205\) | −6.43113e14 | −0.605184 | ||||||||
\(206\) | −1.43222e15 | −1.30579 | ||||||||
\(207\) | 1.08823e15 | 0.961418 | ||||||||
\(208\) | −7.92655e14 | −0.678692 | ||||||||
\(209\) | −6.71850e14 | −0.557598 | ||||||||
\(210\) | 2.48030e15 | 1.99563 | ||||||||
\(211\) | 6.02454e14 | 0.469989 | 0.234995 | − | 0.971997i | \(-0.424493\pi\) | ||||
0.234995 | + | 0.971997i | \(0.424493\pi\) | |||||||
\(212\) | −1.76008e15 | −1.33153 | ||||||||
\(213\) | −5.71788e14 | −0.419535 | ||||||||
\(214\) | −3.57513e15 | −2.54450 | ||||||||
\(215\) | 7.84125e14 | 0.541421 | ||||||||
\(216\) | −1.07394e15 | −0.719498 | ||||||||
\(217\) | 1.34223e15 | 0.872644 | ||||||||
\(218\) | 2.33493e15 | 1.47335 | ||||||||
\(219\) | −7.53884e14 | −0.461761 | ||||||||
\(220\) | 6.18148e14 | 0.367574 | ||||||||
\(221\) | −8.94061e13 | −0.0516199 | ||||||||
\(222\) | −2.24860e15 | −1.26072 | ||||||||
\(223\) | −9.48481e14 | −0.516472 | −0.258236 | − | 0.966082i | \(-0.583141\pi\) | ||||
−0.258236 | + | 0.966082i | \(0.583141\pi\) | |||||||
\(224\) | −2.84426e15 | −1.50438 | ||||||||
\(225\) | −2.00470e15 | −1.03006 | ||||||||
\(226\) | −7.43333e14 | −0.371090 | ||||||||
\(227\) | 3.08998e15 | 1.49895 | 0.749475 | − | 0.662032i | \(-0.230306\pi\) | ||||
0.749475 | + | 0.662032i | \(0.230306\pi\) | |||||||
\(228\) | −6.30023e15 | −2.97016 | ||||||||
\(229\) | 1.36747e15 | 0.626595 | 0.313298 | − | 0.949655i | \(-0.398566\pi\) | ||||
0.313298 | + | 0.949655i | \(0.398566\pi\) | |||||||
\(230\) | −1.11207e15 | −0.495337 | ||||||||
\(231\) | −1.79050e15 | −0.775348 | ||||||||
\(232\) | 5.08904e14 | 0.214271 | ||||||||
\(233\) | −1.47789e14 | −0.0605103 | −0.0302551 | − | 0.999542i | \(-0.509632\pi\) | ||||
−0.0302551 | + | 0.999542i | \(0.509632\pi\) | |||||||
\(234\) | −7.81008e15 | −3.10994 | ||||||||
\(235\) | −2.28144e15 | −0.883626 | ||||||||
\(236\) | −3.75989e14 | −0.141660 | ||||||||
\(237\) | 9.57180e14 | 0.350856 | ||||||||
\(238\) | −2.32458e14 | −0.0829075 | ||||||||
\(239\) | 3.28245e15 | 1.13923 | 0.569616 | − | 0.821911i | \(-0.307092\pi\) | ||||
0.569616 | + | 0.821911i | \(0.307092\pi\) | |||||||
\(240\) | −2.48168e15 | −0.838247 | ||||||||
\(241\) | 4.67657e15 | 1.53751 | 0.768753 | − | 0.639546i | \(-0.220878\pi\) | ||||
0.768753 | + | 0.639546i | \(0.220878\pi\) | |||||||
\(242\) | 3.89326e15 | 1.24599 | ||||||||
\(243\) | 7.39659e14 | 0.230458 | ||||||||
\(244\) | 3.58589e15 | 1.08784 | ||||||||
\(245\) | 3.58675e14 | 0.105955 | ||||||||
\(246\) | 7.81643e15 | 2.24869 | ||||||||
\(247\) | −4.83148e15 | −1.35379 | ||||||||
\(248\) | 1.15218e15 | 0.314474 | ||||||||
\(249\) | −8.69965e15 | −2.31316 | ||||||||
\(250\) | 6.15317e15 | 1.59400 | ||||||||
\(251\) | −6.81787e15 | −1.72096 | −0.860478 | − | 0.509487i | \(-0.829835\pi\) | ||||
−0.860478 | + | 0.509487i | \(0.829835\pi\) | |||||||
\(252\) | −1.13101e16 | −2.78203 | ||||||||
\(253\) | 8.02789e14 | 0.192450 | ||||||||
\(254\) | −4.81322e15 | −1.12465 | ||||||||
\(255\) | −2.79916e14 | −0.0637554 | ||||||||
\(256\) | 1.38964e15 | 0.308562 | ||||||||
\(257\) | −2.01489e15 | −0.436200 | −0.218100 | − | 0.975926i | \(-0.569986\pi\) | ||||
−0.218100 | + | 0.975926i | \(0.569986\pi\) | |||||||
\(258\) | −9.53030e15 | −2.01177 | ||||||||
\(259\) | −2.49716e15 | −0.514041 | ||||||||
\(260\) | 4.44530e15 | 0.892430 | ||||||||
\(261\) | −5.84457e15 | −1.14443 | ||||||||
\(262\) | 1.93411e14 | 0.0369422 | ||||||||
\(263\) | 3.63935e15 | 0.678128 | 0.339064 | − | 0.940763i | \(-0.389890\pi\) | ||||
0.339064 | + | 0.940763i | \(0.389890\pi\) | |||||||
\(264\) | −1.53698e15 | −0.279411 | ||||||||
\(265\) | −4.22588e15 | −0.749582 | ||||||||
\(266\) | −1.25620e16 | −2.17434 | ||||||||
\(267\) | −1.24201e16 | −2.09799 | ||||||||
\(268\) | −5.15351e15 | −0.849624 | ||||||||
\(269\) | 1.43352e15 | 0.230682 | 0.115341 | − | 0.993326i | \(-0.463204\pi\) | ||||
0.115341 | + | 0.993326i | \(0.463204\pi\) | |||||||
\(270\) | −1.26040e16 | −1.97990 | ||||||||
\(271\) | −6.45126e15 | −0.989337 | −0.494669 | − | 0.869082i | \(-0.664711\pi\) | ||||
−0.494669 | + | 0.869082i | \(0.664711\pi\) | |||||||
\(272\) | 2.32587e14 | 0.0348246 | ||||||||
\(273\) | −1.28761e16 | −1.88246 | ||||||||
\(274\) | −7.40478e15 | −1.05714 | ||||||||
\(275\) | −1.47887e15 | −0.206191 | ||||||||
\(276\) | 7.52811e15 | 1.02512 | ||||||||
\(277\) | −1.08394e15 | −0.144174 | −0.0720870 | − | 0.997398i | \(-0.522966\pi\) | ||||
−0.0720870 | + | 0.997398i | \(0.522966\pi\) | |||||||
\(278\) | −7.80975e15 | −1.01472 | ||||||||
\(279\) | −1.32324e16 | −1.67962 | ||||||||
\(280\) | 2.36447e15 | 0.293229 | ||||||||
\(281\) | −4.73489e14 | −0.0573745 | −0.0286873 | − | 0.999588i | \(-0.509133\pi\) | ||||
−0.0286873 | + | 0.999588i | \(0.509133\pi\) | |||||||
\(282\) | 2.77288e16 | 3.28331 | ||||||||
\(283\) | 1.25676e16 | 1.45426 | 0.727128 | − | 0.686501i | \(-0.240854\pi\) | ||||
0.727128 | + | 0.686501i | \(0.240854\pi\) | |||||||
\(284\) | −2.66446e15 | −0.301328 | ||||||||
\(285\) | −1.51266e16 | −1.67205 | ||||||||
\(286\) | −5.76153e15 | −0.622527 | ||||||||
\(287\) | 8.68046e15 | 0.916875 | ||||||||
\(288\) | 2.80402e16 | 2.89554 | ||||||||
\(289\) | −9.87834e15 | −0.997351 | ||||||||
\(290\) | 5.97262e15 | 0.589628 | ||||||||
\(291\) | 2.16652e15 | 0.209150 | ||||||||
\(292\) | −3.51300e15 | −0.331657 | ||||||||
\(293\) | −9.54568e15 | −0.881389 | −0.440694 | − | 0.897657i | \(-0.645268\pi\) | ||||
−0.440694 | + | 0.897657i | \(0.645268\pi\) | |||||||
\(294\) | −4.35935e15 | −0.393699 | ||||||||
\(295\) | −9.02734e14 | −0.0797475 | ||||||||
\(296\) | −2.14359e15 | −0.185244 | ||||||||
\(297\) | 9.09867e15 | 0.769238 | ||||||||
\(298\) | 1.30846e16 | 1.08232 | ||||||||
\(299\) | 5.77311e15 | 0.467247 | ||||||||
\(300\) | −1.38681e16 | −1.09832 | ||||||||
\(301\) | −1.05838e16 | −0.820273 | ||||||||
\(302\) | 1.42416e16 | 1.08023 | ||||||||
\(303\) | −3.98981e16 | −2.96193 | ||||||||
\(304\) | 1.25689e16 | 0.913313 | ||||||||
\(305\) | 8.60959e15 | 0.612397 | ||||||||
\(306\) | 2.29169e15 | 0.159576 | ||||||||
\(307\) | 9.39605e15 | 0.640539 | 0.320270 | − | 0.947326i | \(-0.396226\pi\) | ||||
0.320270 | + | 0.947326i | \(0.396226\pi\) | |||||||
\(308\) | −8.34349e15 | −0.556889 | ||||||||
\(309\) | 2.32781e16 | 1.52131 | ||||||||
\(310\) | 1.35223e16 | 0.865364 | ||||||||
\(311\) | −1.95819e16 | −1.22719 | −0.613595 | − | 0.789621i | \(-0.710277\pi\) | ||||
−0.613595 | + | 0.789621i | \(0.710277\pi\) | |||||||
\(312\) | −1.10529e16 | −0.678379 | ||||||||
\(313\) | −1.21714e16 | −0.731648 | −0.365824 | − | 0.930684i | \(-0.619213\pi\) | ||||
−0.365824 | + | 0.930684i | \(0.619213\pi\) | |||||||
\(314\) | −2.43790e16 | −1.43540 | ||||||||
\(315\) | −2.71551e16 | −1.56615 | ||||||||
\(316\) | 4.46033e15 | 0.252000 | ||||||||
\(317\) | 2.59948e16 | 1.43880 | 0.719401 | − | 0.694595i | \(-0.244416\pi\) | ||||
0.719401 | + | 0.694595i | \(0.244416\pi\) | |||||||
\(318\) | 5.13616e16 | 2.78524 | ||||||||
\(319\) | −4.31156e15 | −0.229084 | ||||||||
\(320\) | −1.94560e16 | −1.01293 | ||||||||
\(321\) | 5.81073e16 | 2.96448 | ||||||||
\(322\) | 1.50102e16 | 0.750453 | ||||||||
\(323\) | 1.41769e15 | 0.0694647 | ||||||||
\(324\) | 3.12953e16 | 1.50292 | ||||||||
\(325\) | −1.06351e16 | −0.500608 | ||||||||
\(326\) | −5.40446e15 | −0.249366 | ||||||||
\(327\) | −3.79501e16 | −1.71653 | ||||||||
\(328\) | 7.45139e15 | 0.330413 | ||||||||
\(329\) | 3.07939e16 | 1.33873 | ||||||||
\(330\) | −1.80384e16 | −0.768879 | ||||||||
\(331\) | 1.78693e16 | 0.746835 | 0.373418 | − | 0.927663i | \(-0.378186\pi\) | ||||
0.373418 | + | 0.927663i | \(0.378186\pi\) | |||||||
\(332\) | −4.05392e16 | −1.66141 | ||||||||
\(333\) | 2.46183e16 | 0.989396 | ||||||||
\(334\) | −1.32107e16 | −0.520683 | ||||||||
\(335\) | −1.23734e16 | −0.478296 | ||||||||
\(336\) | 3.34966e16 | 1.26997 | ||||||||
\(337\) | −1.08602e16 | −0.403873 | −0.201937 | − | 0.979399i | \(-0.564724\pi\) | ||||
−0.201937 | + | 0.979399i | \(0.564724\pi\) | |||||||
\(338\) | −2.47587e14 | −0.00903170 | ||||||||
\(339\) | 1.20815e16 | 0.432339 | ||||||||
\(340\) | −1.30437e15 | −0.0457919 | ||||||||
\(341\) | −9.76156e15 | −0.336214 | ||||||||
\(342\) | 1.23842e17 | 4.18504 | ||||||||
\(343\) | 2.74962e16 | 0.911720 | ||||||||
\(344\) | −9.08521e15 | −0.295601 | ||||||||
\(345\) | 1.80747e16 | 0.577094 | ||||||||
\(346\) | −9.22997e15 | −0.289205 | ||||||||
\(347\) | −2.33541e15 | −0.0718161 | −0.0359081 | − | 0.999355i | \(-0.511432\pi\) | ||||
−0.0359081 | + | 0.999355i | \(0.511432\pi\) | |||||||
\(348\) | −4.04314e16 | −1.22027 | ||||||||
\(349\) | −1.42009e16 | −0.420679 | −0.210340 | − | 0.977628i | \(-0.567457\pi\) | ||||
−0.210340 | + | 0.977628i | \(0.567457\pi\) | |||||||
\(350\) | −2.76514e16 | −0.804034 | ||||||||
\(351\) | 6.54314e16 | 1.86763 | ||||||||
\(352\) | 2.06853e16 | 0.579609 | ||||||||
\(353\) | −6.06526e16 | −1.66845 | −0.834227 | − | 0.551422i | \(-0.814086\pi\) | ||||
−0.834227 | + | 0.551422i | \(0.814086\pi\) | |||||||
\(354\) | 1.09719e16 | 0.296319 | ||||||||
\(355\) | −6.39725e15 | −0.169633 | ||||||||
\(356\) | −5.78762e16 | −1.50687 | ||||||||
\(357\) | 3.77818e15 | 0.0965917 | ||||||||
\(358\) | −8.40385e16 | −2.10979 | ||||||||
\(359\) | −3.99343e16 | −0.984537 | −0.492268 | − | 0.870443i | \(-0.663832\pi\) | ||||
−0.492268 | + | 0.870443i | \(0.663832\pi\) | |||||||
\(360\) | −2.33102e16 | −0.564390 | ||||||||
\(361\) | 3.45585e16 | 0.821785 | ||||||||
\(362\) | 5.44739e16 | 1.27228 | ||||||||
\(363\) | −6.32780e16 | −1.45164 | ||||||||
\(364\) | −6.00007e16 | −1.35206 | ||||||||
\(365\) | −8.43456e15 | −0.186706 | ||||||||
\(366\) | −1.04641e17 | −2.27550 | ||||||||
\(367\) | 4.00665e16 | 0.855958 | 0.427979 | − | 0.903789i | \(-0.359226\pi\) | ||||
0.427979 | + | 0.903789i | \(0.359226\pi\) | |||||||
\(368\) | −1.50185e16 | −0.315222 | ||||||||
\(369\) | −8.55764e16 | −1.76475 | ||||||||
\(370\) | −2.51577e16 | −0.509752 | ||||||||
\(371\) | 5.70391e16 | 1.13564 | ||||||||
\(372\) | −9.15385e16 | −1.79091 | ||||||||
\(373\) | 9.24820e16 | 1.77807 | 0.889037 | − | 0.457835i | \(-0.151375\pi\) | ||||
0.889037 | + | 0.457835i | \(0.151375\pi\) | |||||||
\(374\) | 1.69059e15 | 0.0319428 | ||||||||
\(375\) | −1.00009e17 | −1.85710 | ||||||||
\(376\) | 2.64338e16 | 0.482435 | ||||||||
\(377\) | −3.10058e16 | −0.556191 | ||||||||
\(378\) | 1.70123e17 | 2.99962 | ||||||||
\(379\) | −2.64927e16 | −0.459168 | −0.229584 | − | 0.973289i | \(-0.573737\pi\) | ||||
−0.229584 | + | 0.973289i | \(0.573737\pi\) | |||||||
\(380\) | −7.04879e16 | −1.20094 | ||||||||
\(381\) | 7.82302e16 | 1.31027 | ||||||||
\(382\) | −1.15816e15 | −0.0190703 | ||||||||
\(383\) | −9.07080e16 | −1.46843 | −0.734215 | − | 0.678917i | \(-0.762450\pi\) | ||||
−0.734215 | + | 0.678917i | \(0.762450\pi\) | |||||||
\(384\) | 8.21764e16 | 1.30796 | ||||||||
\(385\) | −2.00324e16 | −0.313500 | ||||||||
\(386\) | 8.00145e16 | 1.23126 | ||||||||
\(387\) | 1.04340e17 | 1.57881 | ||||||||
\(388\) | 1.00957e16 | 0.150221 | ||||||||
\(389\) | 1.12227e16 | 0.164220 | 0.0821100 | − | 0.996623i | \(-0.473834\pi\) | ||||
0.0821100 | + | 0.996623i | \(0.473834\pi\) | |||||||
\(390\) | −1.29720e17 | −1.86675 | ||||||||
\(391\) | −1.69399e15 | −0.0239751 | ||||||||
\(392\) | −4.15576e15 | −0.0578484 | ||||||||
\(393\) | −3.14355e15 | −0.0430397 | ||||||||
\(394\) | 7.94834e15 | 0.107041 | ||||||||
\(395\) | 1.07091e16 | 0.141863 | ||||||||
\(396\) | 8.22545e16 | 1.07187 | ||||||||
\(397\) | −9.03879e16 | −1.15870 | −0.579351 | − | 0.815078i | \(-0.696694\pi\) | ||||
−0.579351 | + | 0.815078i | \(0.696694\pi\) | |||||||
\(398\) | 1.86870e17 | 2.35668 | ||||||||
\(399\) | 2.04172e17 | 2.53322 | ||||||||
\(400\) | 2.76667e16 | 0.337728 | ||||||||
\(401\) | 3.02416e16 | 0.363218 | 0.181609 | − | 0.983371i | \(-0.441870\pi\) | ||||
0.181609 | + | 0.983371i | \(0.441870\pi\) | |||||||
\(402\) | 1.50387e17 | 1.77721 | ||||||||
\(403\) | −7.01984e16 | −0.816290 | ||||||||
\(404\) | −1.85920e17 | −2.12739 | ||||||||
\(405\) | 7.51386e16 | 0.846069 | ||||||||
\(406\) | −8.06158e16 | −0.893308 | ||||||||
\(407\) | 1.81610e16 | 0.198051 | ||||||||
\(408\) | 3.24323e15 | 0.0348086 | ||||||||
\(409\) | 1.03290e17 | 1.09108 | 0.545539 | − | 0.838086i | \(-0.316325\pi\) | ||||
0.545539 | + | 0.838086i | \(0.316325\pi\) | |||||||
\(410\) | 8.74513e16 | 0.909225 | ||||||||
\(411\) | 1.20351e17 | 1.23163 | ||||||||
\(412\) | 1.08473e17 | 1.09267 | ||||||||
\(413\) | 1.21847e16 | 0.120820 | ||||||||
\(414\) | −1.47978e17 | −1.44443 | ||||||||
\(415\) | −9.73329e16 | −0.935292 | ||||||||
\(416\) | 1.48755e17 | 1.40723 | ||||||||
\(417\) | 1.26933e17 | 1.18220 | ||||||||
\(418\) | 9.13590e16 | 0.837733 | ||||||||
\(419\) | 3.96205e15 | 0.0357708 | 0.0178854 | − | 0.999840i | \(-0.494307\pi\) | ||||
0.0178854 | + | 0.999840i | \(0.494307\pi\) | |||||||
\(420\) | −1.87853e17 | −1.66992 | ||||||||
\(421\) | 1.33999e17 | 1.17292 | 0.586461 | − | 0.809977i | \(-0.300521\pi\) | ||||
0.586461 | + | 0.809977i | \(0.300521\pi\) | |||||||
\(422\) | −8.19225e16 | −0.706110 | ||||||||
\(423\) | −3.03582e17 | −2.57670 | ||||||||
\(424\) | 4.89629e16 | 0.409250 | ||||||||
\(425\) | 3.12061e15 | 0.0256869 | ||||||||
\(426\) | 7.77525e16 | 0.630307 | ||||||||
\(427\) | −1.16208e17 | −0.927804 | ||||||||
\(428\) | 2.70772e17 | 2.12922 | ||||||||
\(429\) | 9.36432e16 | 0.725277 | ||||||||
\(430\) | −1.06626e17 | −0.813429 | ||||||||
\(431\) | −9.09820e15 | −0.0683681 | −0.0341840 | − | 0.999416i | \(-0.510883\pi\) | ||||
−0.0341840 | + | 0.999416i | \(0.510883\pi\) | |||||||
\(432\) | −1.70217e17 | −1.25997 | ||||||||
\(433\) | 8.48260e16 | 0.618526 | 0.309263 | − | 0.950977i | \(-0.399918\pi\) | ||||
0.309263 | + | 0.950977i | \(0.399918\pi\) | |||||||
\(434\) | −1.82518e17 | −1.31106 | ||||||||
\(435\) | −9.70743e16 | −0.686948 | ||||||||
\(436\) | −1.76842e17 | −1.23289 | ||||||||
\(437\) | −9.15426e16 | −0.628773 | ||||||||
\(438\) | 1.02514e17 | 0.693748 | ||||||||
\(439\) | −2.47830e17 | −1.65247 | −0.826235 | − | 0.563325i | \(-0.809522\pi\) | ||||
−0.826235 | + | 0.563325i | \(0.809522\pi\) | |||||||
\(440\) | −1.71960e16 | −0.112976 | ||||||||
\(441\) | 4.77274e16 | 0.308971 | ||||||||
\(442\) | 1.21576e16 | 0.0775535 | ||||||||
\(443\) | −2.43051e17 | −1.52782 | −0.763910 | − | 0.645322i | \(-0.776723\pi\) | ||||
−0.763910 | + | 0.645322i | \(0.776723\pi\) | |||||||
\(444\) | 1.70304e17 | 1.05496 | ||||||||
\(445\) | −1.38958e17 | −0.848290 | ||||||||
\(446\) | 1.28976e17 | 0.775945 | ||||||||
\(447\) | −2.12667e17 | −1.26096 | ||||||||
\(448\) | 2.62608e17 | 1.53462 | ||||||||
\(449\) | −3.19926e17 | −1.84267 | −0.921337 | − | 0.388764i | \(-0.872902\pi\) | ||||
−0.921337 | + | 0.388764i | \(0.872902\pi\) | |||||||
\(450\) | 2.72602e17 | 1.54756 | ||||||||
\(451\) | −6.31301e16 | −0.353255 | ||||||||
\(452\) | 5.62984e16 | 0.310525 | ||||||||
\(453\) | −2.31472e17 | −1.25852 | ||||||||
\(454\) | −4.20179e17 | −2.25202 | ||||||||
\(455\) | −1.44059e17 | −0.761144 | ||||||||
\(456\) | 1.75263e17 | 0.912892 | ||||||||
\(457\) | −1.27474e17 | −0.654584 | −0.327292 | − | 0.944923i | \(-0.606136\pi\) | ||||
−0.327292 | + | 0.944923i | \(0.606136\pi\) | |||||||
\(458\) | −1.85950e17 | −0.941394 | ||||||||
\(459\) | −1.91993e16 | −0.0958306 | ||||||||
\(460\) | 8.42255e16 | 0.414494 | ||||||||
\(461\) | −1.02466e17 | −0.497190 | −0.248595 | − | 0.968607i | \(-0.579969\pi\) | ||||
−0.248595 | + | 0.968607i | \(0.579969\pi\) | |||||||
\(462\) | 2.43475e17 | 1.16488 | ||||||||
\(463\) | −2.44233e17 | −1.15220 | −0.576100 | − | 0.817379i | \(-0.695426\pi\) | ||||
−0.576100 | + | 0.817379i | \(0.695426\pi\) | |||||||
\(464\) | 8.06605e16 | 0.375227 | ||||||||
\(465\) | −2.19780e17 | −1.00819 | ||||||||
\(466\) | 2.00966e16 | 0.0909104 | ||||||||
\(467\) | 1.94347e17 | 0.866996 | 0.433498 | − | 0.901155i | \(-0.357279\pi\) | ||||
0.433498 | + | 0.901155i | \(0.357279\pi\) | |||||||
\(468\) | 5.91518e17 | 2.60237 | ||||||||
\(469\) | 1.67010e17 | 0.724636 | ||||||||
\(470\) | 3.10234e17 | 1.32756 | ||||||||
\(471\) | 3.96237e17 | 1.67232 | ||||||||
\(472\) | 1.04595e16 | 0.0435398 | ||||||||
\(473\) | 7.69723e16 | 0.316036 | ||||||||
\(474\) | −1.30159e17 | −0.527125 | ||||||||
\(475\) | 1.68637e17 | 0.673666 | ||||||||
\(476\) | 1.76058e16 | 0.0693763 | ||||||||
\(477\) | −5.62321e17 | −2.18582 | ||||||||
\(478\) | −4.46352e17 | −1.71158 | ||||||||
\(479\) | 1.15328e17 | 0.436268 | 0.218134 | − | 0.975919i | \(-0.430003\pi\) | ||||
0.218134 | + | 0.975919i | \(0.430003\pi\) | |||||||
\(480\) | 4.65727e17 | 1.73806 | ||||||||
\(481\) | 1.30601e17 | 0.480845 | ||||||||
\(482\) | −6.35926e17 | −2.30994 | ||||||||
\(483\) | −2.43964e17 | −0.874318 | ||||||||
\(484\) | −2.94867e17 | −1.04263 | ||||||||
\(485\) | 2.42393e16 | 0.0845667 | ||||||||
\(486\) | −1.00580e17 | −0.346238 | ||||||||
\(487\) | −1.31850e17 | −0.447859 | −0.223929 | − | 0.974605i | \(-0.571888\pi\) | ||||
−0.223929 | + | 0.974605i | \(0.571888\pi\) | |||||||
\(488\) | −9.97544e16 | −0.334351 | ||||||||
\(489\) | 8.78397e16 | 0.290525 | ||||||||
\(490\) | −4.87731e16 | −0.159186 | ||||||||
\(491\) | −4.19330e17 | −1.35060 | −0.675299 | − | 0.737544i | \(-0.735985\pi\) | ||||
−0.675299 | + | 0.737544i | \(0.735985\pi\) | |||||||
\(492\) | −5.91999e17 | −1.88169 | ||||||||
\(493\) | 9.09795e15 | 0.0285390 | ||||||||
\(494\) | 6.56991e17 | 2.03392 | ||||||||
\(495\) | 1.97490e17 | 0.603407 | ||||||||
\(496\) | 1.82619e17 | 0.550699 | ||||||||
\(497\) | 8.63473e16 | 0.256999 | ||||||||
\(498\) | 1.18299e18 | 3.47528 | ||||||||
\(499\) | −1.29858e17 | −0.376544 | −0.188272 | − | 0.982117i | \(-0.560289\pi\) | ||||
−0.188272 | + | 0.982117i | \(0.560289\pi\) | |||||||
\(500\) | −4.66027e17 | −1.33385 | ||||||||
\(501\) | 2.14716e17 | 0.606624 | ||||||||
\(502\) | 9.27103e17 | 2.58556 | ||||||||
\(503\) | −4.03567e17 | −1.11102 | −0.555512 | − | 0.831508i | \(-0.687478\pi\) | ||||
−0.555512 | + | 0.831508i | \(0.687478\pi\) | |||||||
\(504\) | 3.14630e17 | 0.855071 | ||||||||
\(505\) | −4.46386e17 | −1.19761 | ||||||||
\(506\) | −1.09164e17 | −0.289136 | ||||||||
\(507\) | 4.02408e15 | 0.0105224 | ||||||||
\(508\) | 3.64542e17 | 0.941096 | ||||||||
\(509\) | 7.02064e16 | 0.178942 | 0.0894708 | − | 0.995989i | \(-0.471482\pi\) | ||||
0.0894708 | + | 0.995989i | \(0.471482\pi\) | |||||||
\(510\) | 3.80634e16 | 0.0957858 | ||||||||
\(511\) | 1.13846e17 | 0.282867 | ||||||||
\(512\) | −4.93558e17 | −1.21083 | ||||||||
\(513\) | −1.03753e18 | −2.51326 | ||||||||
\(514\) | 2.73987e17 | 0.655345 | ||||||||
\(515\) | 2.60439e17 | 0.615119 | ||||||||
\(516\) | 7.21803e17 | 1.68343 | ||||||||
\(517\) | −2.23954e17 | −0.515786 | ||||||||
\(518\) | 3.39567e17 | 0.772293 | ||||||||
\(519\) | 1.50017e17 | 0.336939 | ||||||||
\(520\) | −1.23662e17 | −0.274292 | ||||||||
\(521\) | −1.64710e17 | −0.360807 | −0.180403 | − | 0.983593i | \(-0.557740\pi\) | ||||
−0.180403 | + | 0.983593i | \(0.557740\pi\) | |||||||
\(522\) | 7.94753e17 | 1.71939 | ||||||||
\(523\) | −8.24266e17 | −1.76119 | −0.880595 | − | 0.473869i | \(-0.842857\pi\) | ||||
−0.880595 | + | 0.473869i | \(0.842857\pi\) | |||||||
\(524\) | −1.46485e16 | −0.0309130 | ||||||||
\(525\) | 4.49424e17 | 0.936743 | ||||||||
\(526\) | −4.94884e17 | −1.01882 | ||||||||
\(527\) | 2.05981e16 | 0.0418850 | ||||||||
\(528\) | −2.43609e17 | −0.489298 | ||||||||
\(529\) | −3.94653e17 | −0.782985 | ||||||||
\(530\) | 5.74641e17 | 1.12617 | ||||||||
\(531\) | −1.20123e17 | −0.232548 | ||||||||
\(532\) | 9.51415e17 | 1.81947 | ||||||||
\(533\) | −4.53988e17 | −0.857665 | ||||||||
\(534\) | 1.68891e18 | 3.15201 | ||||||||
\(535\) | 6.50113e17 | 1.19864 | ||||||||
\(536\) | 1.43363e17 | 0.261136 | ||||||||
\(537\) | 1.36589e18 | 2.45801 | ||||||||
\(538\) | −1.94932e17 | −0.346576 | ||||||||
\(539\) | 3.52087e16 | 0.0618476 | ||||||||
\(540\) | 9.54598e17 | 1.65677 | ||||||||
\(541\) | −7.19658e17 | −1.23408 | −0.617041 | − | 0.786931i | \(-0.711669\pi\) | ||||
−0.617041 | + | 0.786931i | \(0.711669\pi\) | |||||||
\(542\) | 8.77251e17 | 1.48638 | ||||||||
\(543\) | −8.85375e17 | −1.48227 | ||||||||
\(544\) | −4.36487e16 | −0.0722068 | ||||||||
\(545\) | −4.24591e17 | −0.694055 | ||||||||
\(546\) | 1.75090e18 | 2.82820 | ||||||||
\(547\) | −2.44733e17 | −0.390638 | −0.195319 | − | 0.980740i | \(-0.562574\pi\) | ||||
−0.195319 | + | 0.980740i | \(0.562574\pi\) | |||||||
\(548\) | 5.60821e17 | 0.884608 | ||||||||
\(549\) | 1.14564e18 | 1.78578 | ||||||||
\(550\) | 2.01099e17 | 0.309780 | ||||||||
\(551\) | 4.91651e17 | 0.748465 | ||||||||
\(552\) | −2.09421e17 | −0.315077 | ||||||||
\(553\) | −1.44546e17 | −0.214928 | ||||||||
\(554\) | 1.47396e17 | 0.216606 | ||||||||
\(555\) | 4.08892e17 | 0.593888 | ||||||||
\(556\) | 5.91493e17 | 0.849108 | ||||||||
\(557\) | 3.20958e16 | 0.0455397 | 0.0227698 | − | 0.999741i | \(-0.492752\pi\) | ||||
0.0227698 | + | 0.999741i | \(0.492752\pi\) | |||||||
\(558\) | 1.79935e18 | 2.52345 | ||||||||
\(559\) | 5.53532e17 | 0.767301 | ||||||||
\(560\) | 3.74765e17 | 0.513495 | ||||||||
\(561\) | −2.74775e16 | −0.0372150 | ||||||||
\(562\) | 6.43857e16 | 0.0861992 | ||||||||
\(563\) | −1.14519e18 | −1.51556 | −0.757778 | − | 0.652512i | \(-0.773715\pi\) | ||||
−0.757778 | + | 0.652512i | \(0.773715\pi\) | |||||||
\(564\) | −2.10011e18 | −2.74744 | ||||||||
\(565\) | 1.35170e17 | 0.174810 | ||||||||
\(566\) | −1.70896e18 | −2.18487 | ||||||||
\(567\) | −1.01419e18 | −1.28182 | ||||||||
\(568\) | 7.41213e16 | 0.0926145 | ||||||||
\(569\) | 2.98861e17 | 0.369181 | 0.184590 | − | 0.982816i | \(-0.440904\pi\) | ||||
0.184590 | + | 0.982816i | \(0.440904\pi\) | |||||||
\(570\) | 2.05693e18 | 2.51208 | ||||||||
\(571\) | −7.57570e17 | −0.914720 | −0.457360 | − | 0.889282i | \(-0.651205\pi\) | ||||
−0.457360 | + | 0.889282i | \(0.651205\pi\) | |||||||
\(572\) | 4.36365e17 | 0.520925 | ||||||||
\(573\) | 1.88238e16 | 0.0222179 | ||||||||
\(574\) | −1.18038e18 | −1.37751 | ||||||||
\(575\) | −2.01503e17 | −0.232510 | ||||||||
\(576\) | −2.58893e18 | −2.95375 | ||||||||
\(577\) | 2.40451e17 | 0.271259 | 0.135629 | − | 0.990760i | \(-0.456694\pi\) | ||||
0.135629 | + | 0.990760i | \(0.456694\pi\) | |||||||
\(578\) | 1.34327e18 | 1.49842 | ||||||||
\(579\) | −1.30049e18 | −1.43449 | ||||||||
\(580\) | −4.52353e17 | −0.493396 | ||||||||
\(581\) | 1.31376e18 | 1.41700 | ||||||||
\(582\) | −2.94606e17 | −0.314226 | ||||||||
\(583\) | −4.14826e17 | −0.437543 | ||||||||
\(584\) | 9.77265e16 | 0.101936 | ||||||||
\(585\) | 1.42021e18 | 1.46501 | ||||||||
\(586\) | 1.29803e18 | 1.32419 | ||||||||
\(587\) | −9.10215e17 | −0.918325 | −0.459163 | − | 0.888352i | \(-0.651850\pi\) | ||||
−0.459163 | + | 0.888352i | \(0.651850\pi\) | |||||||
\(588\) | 3.30168e17 | 0.329444 | ||||||||
\(589\) | 1.11312e18 | 1.09848 | ||||||||
\(590\) | 1.22755e17 | 0.119812 | ||||||||
\(591\) | −1.29186e17 | −0.124709 | ||||||||
\(592\) | −3.39755e17 | −0.324395 | ||||||||
\(593\) | 1.49529e18 | 1.41211 | 0.706055 | − | 0.708157i | \(-0.250473\pi\) | ||||
0.706055 | + | 0.708157i | \(0.250473\pi\) | |||||||
\(594\) | −1.23725e18 | −1.15570 | ||||||||
\(595\) | 4.22709e16 | 0.0390554 | ||||||||
\(596\) | −9.91000e17 | −0.905676 | ||||||||
\(597\) | −3.03724e18 | −2.74565 | ||||||||
\(598\) | −7.85034e17 | −0.701990 | ||||||||
\(599\) | −1.77688e18 | −1.57175 | −0.785876 | − | 0.618385i | \(-0.787787\pi\) | ||||
−0.785876 | + | 0.618385i | \(0.787787\pi\) | |||||||
\(600\) | 3.85790e17 | 0.337573 | ||||||||
\(601\) | 8.12672e17 | 0.703447 | 0.351724 | − | 0.936104i | \(-0.385596\pi\) | ||||
0.351724 | + | 0.936104i | \(0.385596\pi\) | |||||||
\(602\) | 1.43920e18 | 1.23237 | ||||||||
\(603\) | −1.64647e18 | −1.39474 | ||||||||
\(604\) | −1.07863e18 | −0.903924 | ||||||||
\(605\) | −7.07964e17 | −0.586950 | ||||||||
\(606\) | 5.42540e18 | 4.44999 | ||||||||
\(607\) | −1.43007e17 | −0.116046 | −0.0580231 | − | 0.998315i | \(-0.518480\pi\) | ||||
−0.0580231 | + | 0.998315i | \(0.518480\pi\) | |||||||
\(608\) | −2.35876e18 | −1.89370 | ||||||||
\(609\) | 1.31027e18 | 1.04075 | ||||||||
\(610\) | −1.17074e18 | −0.920063 | ||||||||
\(611\) | −1.61052e18 | −1.25227 | ||||||||
\(612\) | −1.73567e17 | −0.133532 | ||||||||
\(613\) | 1.48247e18 | 1.12848 | 0.564240 | − | 0.825611i | \(-0.309169\pi\) | ||||
0.564240 | + | 0.825611i | \(0.309169\pi\) | |||||||
\(614\) | −1.27769e18 | −0.962343 | ||||||||
\(615\) | −1.42136e18 | −1.05930 | ||||||||
\(616\) | 2.32104e17 | 0.171162 | ||||||||
\(617\) | 2.65142e18 | 1.93475 | 0.967375 | − | 0.253348i | \(-0.0815316\pi\) | ||||
0.967375 | + | 0.253348i | \(0.0815316\pi\) | |||||||
\(618\) | −3.16539e18 | −2.28561 | ||||||||
\(619\) | 2.95294e16 | 0.0210992 | 0.0105496 | − | 0.999944i | \(-0.496642\pi\) | ||||
0.0105496 | + | 0.999944i | \(0.496642\pi\) | |||||||
\(620\) | −1.02415e18 | −0.724129 | ||||||||
\(621\) | 1.23974e18 | 0.867428 | ||||||||
\(622\) | 2.66277e18 | 1.84373 | ||||||||
\(623\) | 1.87560e18 | 1.28519 | ||||||||
\(624\) | −1.75187e18 | −1.18796 | ||||||||
\(625\) | −3.75180e17 | −0.251779 | ||||||||
\(626\) | 1.65508e18 | 1.09922 | ||||||||
\(627\) | −1.48488e18 | −0.976003 | ||||||||
\(628\) | 1.84641e18 | 1.20113 | ||||||||
\(629\) | −3.83220e16 | −0.0246728 | ||||||||
\(630\) | 3.69258e18 | 2.35297 | ||||||||
\(631\) | −2.30017e18 | −1.45067 | −0.725336 | − | 0.688395i | \(-0.758316\pi\) | ||||
−0.725336 | + | 0.688395i | \(0.758316\pi\) | |||||||
\(632\) | −1.24080e17 | −0.0774534 | ||||||||
\(633\) | 1.33150e18 | 0.822656 | ||||||||
\(634\) | −3.53481e18 | −2.16165 | ||||||||
\(635\) | 8.75251e17 | 0.529790 | ||||||||
\(636\) | −3.89001e18 | −2.33066 | ||||||||
\(637\) | 2.53197e17 | 0.150159 | ||||||||
\(638\) | 5.86292e17 | 0.344175 | ||||||||
\(639\) | −8.51256e17 | −0.494658 | ||||||||
\(640\) | 9.19402e17 | 0.528854 | ||||||||
\(641\) | 2.55633e18 | 1.45559 | 0.727795 | − | 0.685795i | \(-0.240545\pi\) | ||||
0.727795 | + | 0.685795i | \(0.240545\pi\) | |||||||
\(642\) | −7.90151e18 | −4.45382 | ||||||||
\(643\) | −2.36777e18 | −1.32120 | −0.660600 | − | 0.750738i | \(-0.729698\pi\) | ||||
−0.660600 | + | 0.750738i | \(0.729698\pi\) | |||||||
\(644\) | −1.13684e18 | −0.627973 | ||||||||
\(645\) | 1.73302e18 | 0.947688 | ||||||||
\(646\) | −1.92779e17 | −0.104363 | ||||||||
\(647\) | 3.11143e18 | 1.66756 | 0.833782 | − | 0.552094i | \(-0.186171\pi\) | ||||
0.833782 | + | 0.552094i | \(0.186171\pi\) | |||||||
\(648\) | −8.70589e17 | −0.461929 | ||||||||
\(649\) | −8.86153e16 | −0.0465499 | ||||||||
\(650\) | 1.44617e18 | 0.752111 | ||||||||
\(651\) | 2.96650e18 | 1.52745 | ||||||||
\(652\) | 4.09321e17 | 0.208668 | ||||||||
\(653\) | 1.66792e17 | 0.0841861 | 0.0420931 | − | 0.999114i | \(-0.486597\pi\) | ||||
0.0420931 | + | 0.999114i | \(0.486597\pi\) | |||||||
\(654\) | 5.16050e18 | 2.57891 | ||||||||
\(655\) | −3.51705e16 | −0.0174024 | ||||||||
\(656\) | 1.18103e18 | 0.578612 | ||||||||
\(657\) | −1.12235e18 | −0.544445 | ||||||||
\(658\) | −4.18740e18 | −2.01129 | ||||||||
\(659\) | −1.38461e18 | −0.658527 | −0.329263 | − | 0.944238i | \(-0.606800\pi\) | ||||
−0.329263 | + | 0.944238i | \(0.606800\pi\) | |||||||
\(660\) | 1.36619e18 | 0.643391 | ||||||||
\(661\) | −1.62332e18 | −0.756996 | −0.378498 | − | 0.925602i | \(-0.623559\pi\) | ||||
−0.378498 | + | 0.925602i | \(0.623559\pi\) | |||||||
\(662\) | −2.42989e18 | −1.12204 | ||||||||
\(663\) | −1.97599e17 | −0.0903539 | ||||||||
\(664\) | 1.12774e18 | 0.510643 | ||||||||
\(665\) | 2.28431e18 | 1.02427 | ||||||||
\(666\) | −3.34763e18 | −1.48646 | ||||||||
\(667\) | −5.87470e17 | −0.258326 | ||||||||
\(668\) | 1.00055e18 | 0.435703 | ||||||||
\(669\) | −2.09627e18 | −0.904017 | ||||||||
\(670\) | 1.68255e18 | 0.718590 | ||||||||
\(671\) | 8.45145e17 | 0.357466 | ||||||||
\(672\) | −6.28618e18 | −2.63322 | ||||||||
\(673\) | −1.22676e18 | −0.508933 | −0.254467 | − | 0.967082i | \(-0.581900\pi\) | ||||
−0.254467 | + | 0.967082i | \(0.581900\pi\) | |||||||
\(674\) | 1.47679e18 | 0.606777 | ||||||||
\(675\) | −2.28381e18 | −0.929361 | ||||||||
\(676\) | 1.87517e16 | 0.00755765 | ||||||||
\(677\) | 4.12504e18 | 1.64665 | 0.823325 | − | 0.567570i | \(-0.192116\pi\) | ||||
0.823325 | + | 0.567570i | \(0.192116\pi\) | |||||||
\(678\) | −1.64286e18 | −0.649544 | ||||||||
\(679\) | −3.27172e17 | −0.128122 | ||||||||
\(680\) | 3.62857e16 | 0.0140743 | ||||||||
\(681\) | 6.82926e18 | 2.62372 | ||||||||
\(682\) | 1.32739e18 | 0.505126 | ||||||||
\(683\) | 4.35534e18 | 1.64168 | 0.820839 | − | 0.571160i | \(-0.193506\pi\) | ||||
0.820839 | + | 0.571160i | \(0.193506\pi\) | |||||||
\(684\) | −9.37954e18 | −3.50201 | ||||||||
\(685\) | 1.34651e18 | 0.497990 | ||||||||
\(686\) | −3.73897e18 | −1.36976 | ||||||||
\(687\) | 3.02229e18 | 1.09677 | ||||||||
\(688\) | −1.43999e18 | −0.517649 | ||||||||
\(689\) | −2.98315e18 | −1.06231 | ||||||||
\(690\) | −2.45782e18 | −0.867023 | ||||||||
\(691\) | 9.48719e17 | 0.331536 | 0.165768 | − | 0.986165i | \(-0.446990\pi\) | ||||
0.165768 | + | 0.986165i | \(0.446990\pi\) | |||||||
\(692\) | 6.99057e17 | 0.242004 | ||||||||
\(693\) | −2.66563e18 | −0.914184 | ||||||||
\(694\) | 3.17572e17 | 0.107896 | ||||||||
\(695\) | 1.42015e18 | 0.478005 | ||||||||
\(696\) | 1.12474e18 | 0.375054 | ||||||||
\(697\) | 1.33212e17 | 0.0440080 | ||||||||
\(698\) | 1.93106e18 | 0.632027 | ||||||||
\(699\) | −3.26634e17 | −0.105915 | ||||||||
\(700\) | 2.09425e18 | 0.672809 | ||||||||
\(701\) | 1.83506e18 | 0.584094 | 0.292047 | − | 0.956404i | \(-0.405664\pi\) | ||||
0.292047 | + | 0.956404i | \(0.405664\pi\) | |||||||
\(702\) | −8.89744e18 | −2.80591 | ||||||||
\(703\) | −2.07091e18 | −0.647071 | ||||||||
\(704\) | −1.90986e18 | −0.591262 | ||||||||
\(705\) | −5.04229e18 | −1.54667 | ||||||||
\(706\) | 8.24762e18 | 2.50668 | ||||||||
\(707\) | 6.02512e18 | 1.81443 | ||||||||
\(708\) | −8.30985e17 | −0.247957 | ||||||||
\(709\) | −1.63548e18 | −0.483552 | −0.241776 | − | 0.970332i | \(-0.577730\pi\) | ||||
−0.241776 | + | 0.970332i | \(0.577730\pi\) | |||||||
\(710\) | 8.69907e17 | 0.254855 | ||||||||
\(711\) | 1.42501e18 | 0.413682 | ||||||||
\(712\) | 1.61003e18 | 0.463142 | ||||||||
\(713\) | −1.33006e18 | −0.379130 | ||||||||
\(714\) | −5.13762e17 | −0.145119 | ||||||||
\(715\) | 1.04769e18 | 0.293255 | ||||||||
\(716\) | 6.36488e18 | 1.76545 | ||||||||
\(717\) | 7.25465e18 | 1.99408 | ||||||||
\(718\) | 5.43032e18 | 1.47916 | ||||||||
\(719\) | −5.55267e17 | −0.149887 | −0.0749435 | − | 0.997188i | \(-0.523878\pi\) | ||||
−0.0749435 | + | 0.997188i | \(0.523878\pi\) | |||||||
\(720\) | −3.69462e18 | −0.988346 | ||||||||
\(721\) | −3.51529e18 | −0.931928 | ||||||||
\(722\) | −4.69931e18 | −1.23465 | ||||||||
\(723\) | 1.03358e19 | 2.69120 | ||||||||
\(724\) | −4.12573e18 | −1.06463 | ||||||||
\(725\) | 1.08222e18 | 0.276770 | ||||||||
\(726\) | 8.60463e18 | 2.18094 | ||||||||
\(727\) | 4.63573e18 | 1.16451 | 0.582257 | − | 0.813005i | \(-0.302170\pi\) | ||||
0.582257 | + | 0.813005i | \(0.302170\pi\) | |||||||
\(728\) | 1.66913e18 | 0.415563 | ||||||||
\(729\) | −3.20992e18 | −0.792072 | ||||||||
\(730\) | 1.14694e18 | 0.280507 | ||||||||
\(731\) | −1.62421e17 | −0.0393713 | ||||||||
\(732\) | 7.92530e18 | 1.90412 | ||||||||
\(733\) | 6.29653e18 | 1.49943 | 0.749713 | − | 0.661763i | \(-0.230191\pi\) | ||||
0.749713 | + | 0.661763i | \(0.230191\pi\) | |||||||
\(734\) | −5.44830e18 | −1.28599 | ||||||||
\(735\) | 7.92719e17 | 0.185461 | ||||||||
\(736\) | 2.81847e18 | 0.653594 | ||||||||
\(737\) | −1.21461e18 | −0.279189 | ||||||||
\(738\) | 1.16368e19 | 2.65135 | ||||||||
\(739\) | −5.80929e18 | −1.31200 | −0.656001 | − | 0.754760i | \(-0.727753\pi\) | ||||
−0.656001 | + | 0.754760i | \(0.727753\pi\) | |||||||
\(740\) | 1.90538e18 | 0.426556 | ||||||||
\(741\) | −1.06782e19 | −2.36963 | ||||||||
\(742\) | −7.75625e18 | −1.70619 | ||||||||
\(743\) | 3.72059e18 | 0.811305 | 0.405652 | − | 0.914027i | \(-0.367044\pi\) | ||||
0.405652 | + | 0.914027i | \(0.367044\pi\) | |||||||
\(744\) | 2.54647e18 | 0.550445 | ||||||||
\(745\) | −2.37935e18 | −0.509850 | ||||||||
\(746\) | −1.25758e19 | −2.67137 | ||||||||
\(747\) | −1.29517e19 | −2.72736 | ||||||||
\(748\) | −1.28041e17 | −0.0267294 | ||||||||
\(749\) | −8.77494e18 | −1.81598 | ||||||||
\(750\) | 1.35993e19 | 2.79009 | ||||||||
\(751\) | −8.73904e18 | −1.77748 | −0.888739 | − | 0.458413i | \(-0.848418\pi\) | ||||
−0.888739 | + | 0.458413i | \(0.848418\pi\) | |||||||
\(752\) | 4.18971e18 | 0.844828 | ||||||||
\(753\) | −1.50684e19 | −3.01231 | ||||||||
\(754\) | 4.21621e18 | 0.835619 | ||||||||
\(755\) | −2.58974e18 | −0.508864 | ||||||||
\(756\) | −1.28847e19 | −2.51006 | ||||||||
\(757\) | −1.18963e18 | −0.229768 | −0.114884 | − | 0.993379i | \(-0.536650\pi\) | ||||
−0.114884 | + | 0.993379i | \(0.536650\pi\) | |||||||
\(758\) | 3.60252e18 | 0.689852 | ||||||||
\(759\) | 1.77427e18 | 0.336859 | ||||||||
\(760\) | 1.96087e18 | 0.369114 | ||||||||
\(761\) | 5.01198e18 | 0.935425 | 0.467713 | − | 0.883881i | \(-0.345078\pi\) | ||||
0.467713 | + | 0.883881i | \(0.345078\pi\) | |||||||
\(762\) | −1.06378e19 | −1.96855 | ||||||||
\(763\) | 5.73095e18 | 1.05152 | ||||||||
\(764\) | 8.77165e16 | 0.0159579 | ||||||||
\(765\) | −4.16728e17 | −0.0751716 | ||||||||
\(766\) | 1.23346e19 | 2.20616 | ||||||||
\(767\) | −6.37261e17 | −0.113018 | ||||||||
\(768\) | 3.07129e18 | 0.540098 | ||||||||
\(769\) | −5.93365e18 | −1.03467 | −0.517334 | − | 0.855784i | \(-0.673075\pi\) | ||||
−0.517334 | + | 0.855784i | \(0.673075\pi\) | |||||||
\(770\) | 2.72403e18 | 0.471001 | ||||||||
\(771\) | −4.45317e18 | −0.763512 | ||||||||
\(772\) | −6.06012e18 | −1.03031 | ||||||||
\(773\) | −1.82934e18 | −0.308409 | −0.154204 | − | 0.988039i | \(-0.549281\pi\) | ||||
−0.154204 | + | 0.988039i | \(0.549281\pi\) | |||||||
\(774\) | −1.41883e19 | −2.37200 | ||||||||
\(775\) | 2.45019e18 | 0.406200 | ||||||||
\(776\) | −2.80847e17 | −0.0461710 | ||||||||
\(777\) | −5.51905e18 | −0.899762 | ||||||||
\(778\) | −1.52608e18 | −0.246723 | ||||||||
\(779\) | 7.19877e18 | 1.15416 | ||||||||
\(780\) | 9.82469e18 | 1.56208 | ||||||||
\(781\) | −6.27975e17 | −0.0990172 | ||||||||
\(782\) | 2.30350e17 | 0.0360201 | ||||||||
\(783\) | −6.65829e18 | −1.03255 | ||||||||
\(784\) | −6.58682e17 | −0.101303 | ||||||||
\(785\) | 4.43316e18 | 0.676178 | ||||||||
\(786\) | 4.27464e17 | 0.0646626 | ||||||||
\(787\) | 5.99750e17 | 0.0899776 | 0.0449888 | − | 0.998987i | \(-0.485675\pi\) | ||||
0.0449888 | + | 0.998987i | \(0.485675\pi\) | |||||||
\(788\) | −6.01989e17 | −0.0895712 | ||||||||
\(789\) | 8.04345e18 | 1.18698 | ||||||||
\(790\) | −1.45623e18 | −0.213135 | ||||||||
\(791\) | −1.82447e18 | −0.264843 | ||||||||
\(792\) | −2.28820e18 | −0.329443 | ||||||||
\(793\) | 6.07770e18 | 0.867888 | ||||||||
\(794\) | 1.22911e19 | 1.74083 | ||||||||
\(795\) | −9.33975e18 | −1.31205 | ||||||||
\(796\) | −1.41531e19 | −1.97205 | ||||||||
\(797\) | 9.62112e18 | 1.32968 | 0.664839 | − | 0.746986i | \(-0.268500\pi\) | ||||
0.664839 | + | 0.746986i | \(0.268500\pi\) | |||||||
\(798\) | −2.77636e19 | −3.80590 | ||||||||
\(799\) | 4.72571e17 | 0.0642559 | ||||||||
\(800\) | −5.19211e18 | −0.700259 | ||||||||
\(801\) | −1.84906e19 | −2.47366 | ||||||||
\(802\) | −4.11230e18 | −0.545696 | ||||||||
\(803\) | −8.27964e17 | −0.108983 | ||||||||
\(804\) | −1.13899e19 | −1.48716 | ||||||||
\(805\) | −2.72950e18 | −0.353517 | ||||||||
\(806\) | 9.54568e18 | 1.22639 | ||||||||
\(807\) | 3.16827e18 | 0.403780 | ||||||||
\(808\) | 5.17202e18 | 0.653862 | ||||||||
\(809\) | 7.79142e18 | 0.977127 | 0.488563 | − | 0.872528i | \(-0.337521\pi\) | ||||
0.488563 | + | 0.872528i | \(0.337521\pi\) | |||||||
\(810\) | −1.02174e19 | −1.27113 | ||||||||
\(811\) | −8.70719e18 | −1.07459 | −0.537295 | − | 0.843395i | \(-0.680554\pi\) | ||||
−0.537295 | + | 0.843395i | \(0.680554\pi\) | |||||||
\(812\) | 6.10566e18 | 0.747512 | ||||||||
\(813\) | −1.42581e19 | −1.73171 | ||||||||
\(814\) | −2.46956e18 | −0.297550 | ||||||||
\(815\) | 9.82763e17 | 0.117469 | ||||||||
\(816\) | 5.14047e17 | 0.0609560 | ||||||||
\(817\) | −8.77720e18 | −1.03255 | ||||||||
\(818\) | −1.40455e19 | −1.63923 | ||||||||
\(819\) | −1.91694e19 | −2.21954 | ||||||||
\(820\) | −6.62337e18 | −0.760832 | ||||||||
\(821\) | 2.21889e18 | 0.252874 | 0.126437 | − | 0.991975i | \(-0.459646\pi\) | ||||
0.126437 | + | 0.991975i | \(0.459646\pi\) | |||||||
\(822\) | −1.63655e19 | −1.85039 | ||||||||
\(823\) | −1.24348e18 | −0.139488 | −0.0697442 | − | 0.997565i | \(-0.522218\pi\) | ||||
−0.0697442 | + | 0.997565i | \(0.522218\pi\) | |||||||
\(824\) | −3.01756e18 | −0.335838 | ||||||||
\(825\) | −3.26851e18 | −0.360910 | ||||||||
\(826\) | −1.65689e18 | −0.181520 | ||||||||
\(827\) | −1.78746e19 | −1.94290 | −0.971449 | − | 0.237248i | \(-0.923755\pi\) | ||||
−0.971449 | + | 0.237248i | \(0.923755\pi\) | |||||||
\(828\) | 1.12076e19 | 1.20869 | ||||||||
\(829\) | 1.22207e19 | 1.30765 | 0.653823 | − | 0.756647i | \(-0.273164\pi\) | ||||
0.653823 | + | 0.756647i | \(0.273164\pi\) | |||||||
\(830\) | 1.32355e19 | 1.40518 | ||||||||
\(831\) | −2.39565e18 | −0.252358 | ||||||||
\(832\) | −1.37344e19 | −1.43552 | ||||||||
\(833\) | −7.42948e16 | −0.00770488 | ||||||||
\(834\) | −1.72606e19 | −1.77613 | ||||||||
\(835\) | 2.40228e18 | 0.245279 | ||||||||
\(836\) | −6.91932e18 | −0.701008 | ||||||||
\(837\) | −1.50746e19 | −1.51541 | ||||||||
\(838\) | −5.38765e17 | −0.0537419 | ||||||||
\(839\) | 1.06014e19 | 1.04933 | 0.524665 | − | 0.851309i | \(-0.324191\pi\) | ||||
0.524665 | + | 0.851309i | \(0.324191\pi\) | |||||||
\(840\) | 5.22579e18 | 0.513259 | ||||||||
\(841\) | −7.10548e18 | −0.692500 | ||||||||
\(842\) | −1.82214e19 | −1.76219 | ||||||||
\(843\) | −1.04647e18 | −0.100427 | ||||||||
\(844\) | 6.20462e18 | 0.590867 | ||||||||
\(845\) | 4.50220e16 | 0.00425458 | ||||||||
\(846\) | 4.12815e19 | 3.87122 | ||||||||
\(847\) | 9.55578e18 | 0.889250 | ||||||||
\(848\) | 7.76054e18 | 0.716670 | ||||||||
\(849\) | 2.77761e19 | 2.54549 | ||||||||
\(850\) | −4.24345e17 | −0.0385919 | ||||||||
\(851\) | 2.47452e18 | 0.223331 | ||||||||
\(852\) | −5.88880e18 | −0.527436 | ||||||||
\(853\) | 4.77561e18 | 0.424483 | 0.212242 | − | 0.977217i | \(-0.431924\pi\) | ||||
0.212242 | + | 0.977217i | \(0.431924\pi\) | |||||||
\(854\) | 1.58022e19 | 1.39393 | ||||||||
\(855\) | −2.25199e19 | −1.97145 | ||||||||
\(856\) | −7.53249e18 | −0.654424 | ||||||||
\(857\) | 4.15881e18 | 0.358587 | 0.179293 | − | 0.983796i | \(-0.442619\pi\) | ||||
0.179293 | + | 0.983796i | \(0.442619\pi\) | |||||||
\(858\) | −1.27337e19 | −1.08965 | ||||||||
\(859\) | −1.40675e19 | −1.19471 | −0.597354 | − | 0.801978i | \(-0.703781\pi\) | ||||
−0.597354 | + | 0.801978i | \(0.703781\pi\) | |||||||
\(860\) | 8.07564e18 | 0.680670 | ||||||||
\(861\) | 1.91849e19 | 1.60487 | ||||||||
\(862\) | 1.23719e18 | 0.102716 | ||||||||
\(863\) | 1.94577e19 | 1.60332 | 0.801662 | − | 0.597777i | \(-0.203949\pi\) | ||||
0.801662 | + | 0.597777i | \(0.203949\pi\) | |||||||
\(864\) | 3.19441e19 | 2.61247 | ||||||||
\(865\) | 1.67841e18 | 0.136236 | ||||||||
\(866\) | −1.15347e19 | −0.929270 | ||||||||
\(867\) | −2.18324e19 | −1.74573 | ||||||||
\(868\) | 1.38235e19 | 1.09708 | ||||||||
\(869\) | 1.05124e18 | 0.0828080 | ||||||||
\(870\) | 1.32003e19 | 1.03207 | ||||||||
\(871\) | −8.73464e18 | −0.677840 | ||||||||
\(872\) | 4.91950e18 | 0.378934 | ||||||||
\(873\) | 3.22543e18 | 0.246601 | ||||||||
\(874\) | 1.24481e19 | 0.944666 | ||||||||
\(875\) | 1.51026e19 | 1.13762 | ||||||||
\(876\) | −7.76418e18 | −0.580522 | ||||||||
\(877\) | −3.63031e18 | −0.269430 | −0.134715 | − | 0.990884i | \(-0.543012\pi\) | ||||
−0.134715 | + | 0.990884i | \(0.543012\pi\) | |||||||
\(878\) | 3.37002e19 | 2.48266 | ||||||||
\(879\) | −2.10972e19 | −1.54276 | ||||||||
\(880\) | −2.72554e18 | −0.197840 | ||||||||
\(881\) | 5.69812e18 | 0.410571 | 0.205286 | − | 0.978702i | \(-0.434188\pi\) | ||||
0.205286 | + | 0.978702i | \(0.434188\pi\) | |||||||
\(882\) | −6.49004e18 | −0.464196 | ||||||||
\(883\) | 1.10293e17 | 0.00783075 | 0.00391538 | − | 0.999992i | \(-0.498754\pi\) | ||||
0.00391538 | + | 0.999992i | \(0.498754\pi\) | |||||||
\(884\) | −9.20785e17 | −0.0648961 | ||||||||
\(885\) | −1.99516e18 | −0.139588 | ||||||||
\(886\) | 3.30503e19 | 2.29539 | ||||||||
\(887\) | 5.78303e18 | 0.398705 | 0.199353 | − | 0.979928i | \(-0.436116\pi\) | ||||
0.199353 | + | 0.979928i | \(0.436116\pi\) | |||||||
\(888\) | −4.73760e18 | −0.324246 | ||||||||
\(889\) | −1.18138e19 | −0.802651 | ||||||||
\(890\) | 1.88957e19 | 1.27447 | ||||||||
\(891\) | 7.37585e18 | 0.493864 | ||||||||
\(892\) | −9.76832e18 | −0.649304 | ||||||||
\(893\) | 2.55376e19 | 1.68518 | ||||||||
\(894\) | 2.89187e19 | 1.89446 | ||||||||
\(895\) | 1.52818e19 | 0.993860 | ||||||||
\(896\) | −1.24097e19 | −0.801233 | ||||||||
\(897\) | 1.27593e19 | 0.817856 | ||||||||
\(898\) | 4.35040e19 | 2.76843 | ||||||||
\(899\) | 7.14338e18 | 0.451301 | ||||||||
\(900\) | −2.06462e19 | −1.29498 | ||||||||
\(901\) | 8.75336e17 | 0.0545084 | ||||||||
\(902\) | 8.58451e18 | 0.530729 | ||||||||
\(903\) | −2.33915e19 | −1.43578 | ||||||||
\(904\) | −1.56614e18 | −0.0954411 | ||||||||
\(905\) | −9.90570e18 | −0.599335 | ||||||||
\(906\) | 3.14759e19 | 1.89080 | ||||||||
\(907\) | 1.57749e19 | 0.940848 | 0.470424 | − | 0.882441i | \(-0.344101\pi\) | ||||
0.470424 | + | 0.882441i | \(0.344101\pi\) | |||||||
\(908\) | 3.18234e19 | 1.88447 | ||||||||
\(909\) | −5.93987e19 | −3.49230 | ||||||||
\(910\) | 1.95894e19 | 1.14354 | ||||||||
\(911\) | 2.45870e19 | 1.42507 | 0.712536 | − | 0.701636i | \(-0.247547\pi\) | ||||
0.712536 | + | 0.701636i | \(0.247547\pi\) | |||||||
\(912\) | 2.77790e19 | 1.59864 | ||||||||
\(913\) | −9.55451e18 | −0.545945 | ||||||||
\(914\) | 1.73340e19 | 0.983444 | ||||||||
\(915\) | 1.90283e19 | 1.07192 | ||||||||
\(916\) | 1.40835e19 | 0.787750 | ||||||||
\(917\) | 4.74716e17 | 0.0263653 | ||||||||
\(918\) | 2.61075e18 | 0.143975 | ||||||||
\(919\) | 1.02050e19 | 0.558810 | 0.279405 | − | 0.960173i | \(-0.409863\pi\) | ||||
0.279405 | + | 0.960173i | \(0.409863\pi\) | |||||||
\(920\) | −2.34303e18 | −0.127397 | ||||||||
\(921\) | 2.07665e19 | 1.12118 | ||||||||
\(922\) | 1.39334e19 | 0.746977 | ||||||||
\(923\) | −4.51596e18 | −0.240403 | ||||||||
\(924\) | −1.84402e19 | −0.974761 | ||||||||
\(925\) | −4.55849e18 | −0.239276 | ||||||||
\(926\) | 3.32111e19 | 1.73106 | ||||||||
\(927\) | 3.46556e19 | 1.79372 | ||||||||
\(928\) | −1.51373e19 | −0.778010 | ||||||||
\(929\) | 1.68307e19 | 0.859013 | 0.429507 | − | 0.903064i | \(-0.358687\pi\) | ||||
0.429507 | + | 0.903064i | \(0.358687\pi\) | |||||||
\(930\) | 2.98860e19 | 1.51471 | ||||||||
\(931\) | −4.01487e18 | −0.202069 | ||||||||
\(932\) | −1.52207e18 | −0.0760730 | ||||||||
\(933\) | −4.32785e19 | −2.14804 | ||||||||
\(934\) | −2.64275e19 | −1.30257 | ||||||||
\(935\) | −3.07422e17 | −0.0150473 | ||||||||
\(936\) | −1.64552e19 | −0.799852 | ||||||||
\(937\) | 2.03322e19 | 0.981469 | 0.490734 | − | 0.871309i | \(-0.336729\pi\) | ||||
0.490734 | + | 0.871309i | \(0.336729\pi\) | |||||||
\(938\) | −2.27103e19 | −1.08869 | ||||||||
\(939\) | −2.69004e19 | −1.28066 | ||||||||
\(940\) | −2.34964e19 | −1.11089 | ||||||||
\(941\) | 2.69186e19 | 1.26392 | 0.631960 | − | 0.775001i | \(-0.282251\pi\) | ||||
0.631960 | + | 0.775001i | \(0.282251\pi\) | |||||||
\(942\) | −5.38809e19 | −2.51249 | ||||||||
\(943\) | −8.60176e18 | −0.398347 | ||||||||
\(944\) | 1.65781e18 | 0.0762459 | ||||||||
\(945\) | −3.09357e19 | −1.41304 | ||||||||
\(946\) | −1.04668e19 | −0.474811 | ||||||||
\(947\) | −2.03943e19 | −0.918827 | −0.459414 | − | 0.888222i | \(-0.651940\pi\) | ||||
−0.459414 | + | 0.888222i | \(0.651940\pi\) | |||||||
\(948\) | 9.85792e18 | 0.441094 | ||||||||
\(949\) | −5.95415e18 | −0.264600 | ||||||||
\(950\) | −2.29315e19 | −1.01211 | ||||||||
\(951\) | 5.74519e19 | 2.51844 | ||||||||
\(952\) | −4.89769e17 | −0.0213231 | ||||||||
\(953\) | 3.03907e19 | 1.31412 | 0.657062 | − | 0.753837i | \(-0.271799\pi\) | ||||
0.657062 | + | 0.753837i | \(0.271799\pi\) | |||||||
\(954\) | 7.64651e19 | 3.28397 | ||||||||
\(955\) | 2.10604e17 | 0.00898347 | ||||||||
\(956\) | 3.38057e19 | 1.43223 | ||||||||
\(957\) | −9.52912e18 | −0.400982 | ||||||||
\(958\) | −1.56824e19 | −0.655447 | ||||||||
\(959\) | −1.81746e19 | −0.754473 | ||||||||
\(960\) | −4.30003e19 | −1.77300 | ||||||||
\(961\) | −8.24463e18 | −0.337652 | ||||||||
\(962\) | −1.77594e19 | −0.722419 | ||||||||
\(963\) | 8.65079e19 | 3.49530 | ||||||||
\(964\) | 4.81636e19 | 1.93294 | ||||||||
\(965\) | −1.45501e19 | −0.580014 | ||||||||
\(966\) | 3.31745e19 | 1.31357 | ||||||||
\(967\) | −5.80632e17 | −0.0228365 | −0.0114182 | − | 0.999935i | \(-0.503635\pi\) | ||||
−0.0114182 | + | 0.999935i | \(0.503635\pi\) | |||||||
\(968\) | 8.20277e18 | 0.320458 | ||||||||
\(969\) | 3.13328e18 | 0.121589 | ||||||||
\(970\) | −3.29609e18 | −0.127053 | ||||||||
\(971\) | 1.45589e19 | 0.557448 | 0.278724 | − | 0.960371i | \(-0.410089\pi\) | ||||
0.278724 | + | 0.960371i | \(0.410089\pi\) | |||||||
\(972\) | 7.61769e18 | 0.289729 | ||||||||
\(973\) | −1.91685e19 | −0.724195 | ||||||||
\(974\) | 1.79291e19 | 0.672861 | ||||||||
\(975\) | −2.35049e19 | −0.876249 | ||||||||
\(976\) | −1.58109e19 | −0.585508 | ||||||||
\(977\) | −2.61387e19 | −0.961546 | −0.480773 | − | 0.876845i | \(-0.659644\pi\) | ||||
−0.480773 | + | 0.876845i | \(0.659644\pi\) | |||||||
\(978\) | −1.19446e19 | −0.436483 | ||||||||
\(979\) | −1.36406e19 | −0.495161 | ||||||||
\(980\) | 3.69396e18 | 0.133206 | ||||||||
\(981\) | −5.64986e19 | −2.02390 | ||||||||
\(982\) | 5.70210e19 | 2.02913 | ||||||||
\(983\) | −2.23630e19 | −0.790557 | −0.395278 | − | 0.918561i | \(-0.629352\pi\) | ||||
−0.395278 | + | 0.918561i | \(0.629352\pi\) | |||||||
\(984\) | 1.64685e19 | 0.578345 | ||||||||
\(985\) | −1.44535e18 | −0.0504241 | ||||||||
\(986\) | −1.23715e18 | −0.0428768 | ||||||||
\(987\) | 6.80586e19 | 2.34326 | ||||||||
\(988\) | −4.97590e19 | −1.70197 | ||||||||
\(989\) | 1.04878e19 | 0.356377 | ||||||||
\(990\) | −2.68549e19 | −0.906556 | ||||||||
\(991\) | −5.93305e18 | −0.198975 | −0.0994877 | − | 0.995039i | \(-0.531720\pi\) | ||||
−0.0994877 | + | 0.995039i | \(0.531720\pi\) | |||||||
\(992\) | −3.42714e19 | −1.14184 | ||||||||
\(993\) | 3.94934e19 | 1.30724 | ||||||||
\(994\) | −1.17416e19 | −0.386115 | ||||||||
\(995\) | −3.39811e19 | −1.11016 | ||||||||
\(996\) | −8.95969e19 | −2.90809 | ||||||||
\(997\) | −4.98509e17 | −0.0160751 | −0.00803756 | − | 0.999968i | \(-0.502558\pi\) | ||||
−0.00803756 | + | 0.999968i | \(0.502558\pi\) | |||||||
\(998\) | 1.76583e19 | 0.565718 | ||||||||
\(999\) | 2.80458e19 | 0.892672 |
(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 | 197.14.a.a.1.18 | ✓ | 104 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
197.14.a.a.1.18 | ✓ | 104 | 1.1 | even | 1 | trivial |