Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [98,10,Mod(1,98)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(98, 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("98.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 98 = 2 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 98.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: | \(50.4735119441\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{106}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 106 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-10.2956\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 98.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 16.0000 | 0.707107 | ||||||||
\(3\) | −123.548 | −0.880620 | −0.440310 | − | 0.897846i | \(-0.645131\pi\) | ||||
−0.440310 | + | 0.897846i | \(0.645131\pi\) | |||||||
\(4\) | 256.000 | 0.500000 | ||||||||
\(5\) | 1276.66 | 0.913502 | 0.456751 | − | 0.889595i | \(-0.349013\pi\) | ||||
0.456751 | + | 0.889595i | \(0.349013\pi\) | |||||||
\(6\) | −1976.76 | −0.622692 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 4096.00 | 0.353553 | ||||||||
\(9\) | −4419.00 | −0.224508 | ||||||||
\(10\) | 20426.5 | 0.645944 | ||||||||
\(11\) | −27644.0 | −0.569290 | −0.284645 | − | 0.958633i | \(-0.591876\pi\) | ||||
−0.284645 | + | 0.958633i | \(0.591876\pi\) | |||||||
\(12\) | −31628.2 | −0.440310 | ||||||||
\(13\) | −83312.2 | −0.809028 | −0.404514 | − | 0.914532i | \(-0.632559\pi\) | ||||
−0.404514 | + | 0.914532i | \(0.632559\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −157728. | −0.804448 | ||||||||
\(16\) | 65536.0 | 0.250000 | ||||||||
\(17\) | 554234. | 1.60943 | 0.804717 | − | 0.593658i | \(-0.202317\pi\) | ||||
0.804717 | + | 0.593658i | \(0.202317\pi\) | |||||||
\(18\) | −70704.0 | −0.158751 | ||||||||
\(19\) | −343503. | −0.604700 | −0.302350 | − | 0.953197i | \(-0.597771\pi\) | ||||
−0.302350 | + | 0.953197i | \(0.597771\pi\) | |||||||
\(20\) | 326824. | 0.456751 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −442304. | −0.402549 | ||||||||
\(23\) | −535704. | −0.399162 | −0.199581 | − | 0.979881i | \(-0.563958\pi\) | ||||
−0.199581 | + | 0.979881i | \(0.563958\pi\) | |||||||
\(24\) | −506051. | −0.311346 | ||||||||
\(25\) | −323269. | −0.165514 | ||||||||
\(26\) | −1.33300e6 | −0.572069 | ||||||||
\(27\) | 2.97774e6 | 1.07833 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.59101e6 | −0.680264 | −0.340132 | − | 0.940378i | \(-0.610472\pi\) | ||||
−0.340132 | + | 0.940378i | \(0.610472\pi\) | |||||||
\(30\) | −2.52365e6 | −0.568831 | ||||||||
\(31\) | 6.09724e6 | 1.18578 | 0.592892 | − | 0.805282i | \(-0.297986\pi\) | ||||
0.592892 | + | 0.805282i | \(0.297986\pi\) | |||||||
\(32\) | 1.04858e6 | 0.176777 | ||||||||
\(33\) | 3.41535e6 | 0.501328 | ||||||||
\(34\) | 8.86775e6 | 1.13804 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.13126e6 | −0.112254 | ||||||||
\(37\) | −1.78079e7 | −1.56209 | −0.781043 | − | 0.624477i | \(-0.785312\pi\) | ||||
−0.781043 | + | 0.624477i | \(0.785312\pi\) | |||||||
\(38\) | −5.49605e6 | −0.427587 | ||||||||
\(39\) | 1.02930e7 | 0.712446 | ||||||||
\(40\) | 5.22919e6 | 0.322972 | ||||||||
\(41\) | −3.05338e7 | −1.68754 | −0.843769 | − | 0.536707i | \(-0.819668\pi\) | ||||
−0.843769 | + | 0.536707i | \(0.819668\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.75976e6 | −0.390736 | −0.195368 | − | 0.980730i | \(-0.562590\pi\) | ||||
−0.195368 | + | 0.980730i | \(0.562590\pi\) | |||||||
\(44\) | −7.07686e6 | −0.284645 | ||||||||
\(45\) | −5.64155e6 | −0.205089 | ||||||||
\(46\) | −8.57126e6 | −0.282250 | ||||||||
\(47\) | −2.72730e7 | −0.815252 | −0.407626 | − | 0.913149i | \(-0.633643\pi\) | ||||
−0.407626 | + | 0.913149i | \(0.633643\pi\) | |||||||
\(48\) | −8.09681e6 | −0.220155 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −5.17230e6 | −0.117036 | ||||||||
\(51\) | −6.84743e7 | −1.41730 | ||||||||
\(52\) | −2.13279e7 | −0.404514 | ||||||||
\(53\) | −8.34885e7 | −1.45340 | −0.726700 | − | 0.686955i | \(-0.758947\pi\) | ||||
−0.726700 | + | 0.686955i | \(0.758947\pi\) | |||||||
\(54\) | 4.76439e7 | 0.762492 | ||||||||
\(55\) | −3.52919e7 | −0.520048 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.24390e7 | 0.532511 | ||||||||
\(58\) | −4.14561e7 | −0.481019 | ||||||||
\(59\) | −8.15475e7 | −0.876147 | −0.438073 | − | 0.898939i | \(-0.644339\pi\) | ||||
−0.438073 | + | 0.898939i | \(0.644339\pi\) | |||||||
\(60\) | −4.03784e7 | −0.402224 | ||||||||
\(61\) | −4.98442e7 | −0.460925 | −0.230463 | − | 0.973081i | \(-0.574024\pi\) | ||||
−0.230463 | + | 0.973081i | \(0.574024\pi\) | |||||||
\(62\) | 9.75558e7 | 0.838476 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.67772e7 | 0.125000 | ||||||||
\(65\) | −1.06361e8 | −0.739049 | ||||||||
\(66\) | 5.46456e7 | 0.354493 | ||||||||
\(67\) | −1.85493e8 | −1.12458 | −0.562290 | − | 0.826940i | \(-0.690080\pi\) | ||||
−0.562290 | + | 0.826940i | \(0.690080\pi\) | |||||||
\(68\) | 1.41884e8 | 0.804717 | ||||||||
\(69\) | 6.61849e7 | 0.351510 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.70271e8 | 1.72925 | 0.864623 | − | 0.502421i | \(-0.167557\pi\) | ||||
0.864623 | + | 0.502421i | \(0.167557\pi\) | |||||||
\(72\) | −1.81002e7 | −0.0793757 | ||||||||
\(73\) | 2.46011e8 | 1.01391 | 0.506957 | − | 0.861972i | \(-0.330770\pi\) | ||||
0.506957 | + | 0.861972i | \(0.330770\pi\) | |||||||
\(74\) | −2.84927e8 | −1.10456 | ||||||||
\(75\) | 3.99391e7 | 0.145755 | ||||||||
\(76\) | −8.79369e7 | −0.302350 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 1.64688e8 | 0.503776 | ||||||||
\(79\) | −5.19907e8 | −1.50177 | −0.750886 | − | 0.660432i | \(-0.770373\pi\) | ||||
−0.750886 | + | 0.660432i | \(0.770373\pi\) | |||||||
\(80\) | 8.36671e7 | 0.228376 | ||||||||
\(81\) | −2.80914e8 | −0.725087 | ||||||||
\(82\) | −4.88541e8 | −1.19327 | ||||||||
\(83\) | 2.98889e8 | 0.691287 | 0.345643 | − | 0.938366i | \(-0.387661\pi\) | ||||
0.345643 | + | 0.938366i | \(0.387661\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 7.07568e8 | 1.47022 | ||||||||
\(86\) | −1.40156e8 | −0.276292 | ||||||||
\(87\) | 3.20112e8 | 0.599054 | ||||||||
\(88\) | −1.13230e8 | −0.201275 | ||||||||
\(89\) | −2.97527e8 | −0.502656 | −0.251328 | − | 0.967902i | \(-0.580867\pi\) | ||||
−0.251328 | + | 0.967902i | \(0.580867\pi\) | |||||||
\(90\) | −9.02648e7 | −0.145020 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −1.37140e8 | −0.199581 | ||||||||
\(93\) | −7.53299e8 | −1.04422 | ||||||||
\(94\) | −4.36367e8 | −0.576470 | ||||||||
\(95\) | −4.38536e8 | −0.552395 | ||||||||
\(96\) | −1.29549e8 | −0.155673 | ||||||||
\(97\) | −7.80734e8 | −0.895427 | −0.447713 | − | 0.894177i | \(-0.647762\pi\) | ||||
−0.447713 | + | 0.894177i | \(0.647762\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.22159e8 | 0.127810 | ||||||||
\(100\) | −8.27569e7 | −0.0827569 | ||||||||
\(101\) | −1.30232e9 | −1.24529 | −0.622646 | − | 0.782504i | \(-0.713942\pi\) | ||||
−0.622646 | + | 0.782504i | \(0.713942\pi\) | |||||||
\(102\) | −1.09559e9 | −1.00218 | ||||||||
\(103\) | 2.14949e9 | 1.88177 | 0.940887 | − | 0.338720i | \(-0.109994\pi\) | ||||
0.940887 | + | 0.338720i | \(0.109994\pi\) | |||||||
\(104\) | −3.41247e8 | −0.286035 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.33582e9 | −1.02771 | ||||||||
\(107\) | −8.34888e8 | −0.615745 | −0.307873 | − | 0.951428i | \(-0.599617\pi\) | ||||
−0.307873 | + | 0.951428i | \(0.599617\pi\) | |||||||
\(108\) | 7.62302e8 | 0.539163 | ||||||||
\(109\) | 1.02563e9 | 0.695937 | 0.347969 | − | 0.937506i | \(-0.386872\pi\) | ||||
0.347969 | + | 0.937506i | \(0.386872\pi\) | |||||||
\(110\) | −5.64671e8 | −0.367729 | ||||||||
\(111\) | 2.20012e9 | 1.37560 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.65902e8 | −0.268808 | −0.134404 | − | 0.990927i | \(-0.542912\pi\) | ||||
−0.134404 | + | 0.990927i | \(0.542912\pi\) | |||||||
\(114\) | 6.79024e8 | 0.376542 | ||||||||
\(115\) | −6.83911e8 | −0.364636 | ||||||||
\(116\) | −6.63298e8 | −0.340132 | ||||||||
\(117\) | 3.68157e8 | 0.181634 | ||||||||
\(118\) | −1.30476e9 | −0.619529 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −6.46054e8 | −0.284415 | ||||||||
\(121\) | −1.59376e9 | −0.675909 | ||||||||
\(122\) | −7.97508e8 | −0.325923 | ||||||||
\(123\) | 3.77238e9 | 1.48608 | ||||||||
\(124\) | 1.56089e9 | 0.592892 | ||||||||
\(125\) | −2.90618e9 | −1.06470 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.84044e8 | −0.267438 | −0.133719 | − | 0.991019i | \(-0.542692\pi\) | ||||
−0.133719 | + | 0.991019i | \(0.542692\pi\) | |||||||
\(128\) | 2.68435e8 | 0.0883883 | ||||||||
\(129\) | 1.08225e9 | 0.344090 | ||||||||
\(130\) | −1.70178e9 | −0.522587 | ||||||||
\(131\) | −5.77364e9 | −1.71289 | −0.856444 | − | 0.516240i | \(-0.827331\pi\) | ||||
−0.856444 | + | 0.516240i | \(0.827331\pi\) | |||||||
\(132\) | 8.74329e8 | 0.250664 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −2.96789e9 | −0.795199 | ||||||||
\(135\) | 3.80156e9 | 0.985054 | ||||||||
\(136\) | 2.27014e9 | 0.569021 | ||||||||
\(137\) | 7.17672e9 | 1.74054 | 0.870269 | − | 0.492576i | \(-0.163945\pi\) | ||||
0.870269 | + | 0.492576i | \(0.163945\pi\) | |||||||
\(138\) | 1.05896e9 | 0.248555 | ||||||||
\(139\) | 3.11320e9 | 0.707359 | 0.353679 | − | 0.935367i | \(-0.384930\pi\) | ||||
0.353679 | + | 0.935367i | \(0.384930\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.36951e9 | 0.717927 | ||||||||
\(142\) | 5.92433e9 | 1.22276 | ||||||||
\(143\) | 2.30308e9 | 0.460572 | ||||||||
\(144\) | −2.89604e8 | −0.0561271 | ||||||||
\(145\) | −3.30783e9 | −0.621423 | ||||||||
\(146\) | 3.93617e9 | 0.716945 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −4.55882e9 | −0.781043 | ||||||||
\(149\) | 6.87070e9 | 1.14199 | 0.570996 | − | 0.820953i | \(-0.306557\pi\) | ||||
0.570996 | + | 0.820953i | \(0.306557\pi\) | |||||||
\(150\) | 6.39026e8 | 0.103064 | ||||||||
\(151\) | 9.06756e9 | 1.41936 | 0.709682 | − | 0.704522i | \(-0.248838\pi\) | ||||
0.709682 | + | 0.704522i | \(0.248838\pi\) | |||||||
\(152\) | −1.40699e9 | −0.213794 | ||||||||
\(153\) | −2.44916e9 | −0.361332 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 7.78409e9 | 1.08322 | ||||||||
\(156\) | 2.63501e9 | 0.356223 | ||||||||
\(157\) | 3.35488e9 | 0.440686 | 0.220343 | − | 0.975422i | \(-0.429282\pi\) | ||||
0.220343 | + | 0.975422i | \(0.429282\pi\) | |||||||
\(158\) | −8.31852e9 | −1.06191 | ||||||||
\(159\) | 1.03148e10 | 1.27989 | ||||||||
\(160\) | 1.33867e9 | 0.161486 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −4.49462e9 | −0.512714 | ||||||||
\(163\) | 6.57962e9 | 0.730056 | 0.365028 | − | 0.930996i | \(-0.381059\pi\) | ||||
0.365028 | + | 0.930996i | \(0.381059\pi\) | |||||||
\(164\) | −7.81665e9 | −0.843769 | ||||||||
\(165\) | 4.36023e9 | 0.457965 | ||||||||
\(166\) | 4.78222e9 | 0.488814 | ||||||||
\(167\) | −3.22471e8 | −0.0320824 | −0.0160412 | − | 0.999871i | \(-0.505106\pi\) | ||||
−0.0160412 | + | 0.999871i | \(0.505106\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.66357e9 | −0.345473 | ||||||||
\(170\) | 1.13211e10 | 1.03960 | ||||||||
\(171\) | 1.51794e9 | 0.135760 | ||||||||
\(172\) | −2.24250e9 | −0.195368 | ||||||||
\(173\) | 1.67229e9 | 0.141940 | 0.0709699 | − | 0.997478i | \(-0.477391\pi\) | ||||
0.0709699 | + | 0.997478i | \(0.477391\pi\) | |||||||
\(174\) | 5.12180e9 | 0.423595 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.81168e9 | −0.142323 | ||||||||
\(177\) | 1.00750e10 | 0.771552 | ||||||||
\(178\) | −4.76043e9 | −0.355432 | ||||||||
\(179\) | 8.42902e9 | 0.613675 | 0.306838 | − | 0.951762i | \(-0.400729\pi\) | ||||
0.306838 | + | 0.951762i | \(0.400729\pi\) | |||||||
\(180\) | −1.44424e9 | −0.102544 | ||||||||
\(181\) | −2.02316e10 | −1.40113 | −0.700563 | − | 0.713591i | \(-0.747068\pi\) | ||||
−0.700563 | + | 0.713591i | \(0.747068\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 6.15813e9 | 0.405900 | ||||||||
\(184\) | −2.19424e9 | −0.141125 | ||||||||
\(185\) | −2.27346e10 | −1.42697 | ||||||||
\(186\) | −1.20528e10 | −0.738378 | ||||||||
\(187\) | −1.53213e10 | −0.916235 | ||||||||
\(188\) | −6.98188e9 | −0.407626 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −7.01658e9 | −0.390602 | ||||||||
\(191\) | −1.78228e10 | −0.969004 | −0.484502 | − | 0.874790i | \(-0.660999\pi\) | ||||
−0.484502 | + | 0.874790i | \(0.660999\pi\) | |||||||
\(192\) | −2.07278e9 | −0.110077 | ||||||||
\(193\) | 1.54567e10 | 0.801881 | 0.400940 | − | 0.916104i | \(-0.368683\pi\) | ||||
0.400940 | + | 0.916104i | \(0.368683\pi\) | |||||||
\(194\) | −1.24917e10 | −0.633162 | ||||||||
\(195\) | 1.31407e10 | 0.650821 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.03655e10 | 0.963376 | 0.481688 | − | 0.876343i | \(-0.340024\pi\) | ||||
0.481688 | + | 0.876343i | \(0.340024\pi\) | |||||||
\(198\) | 1.95454e9 | 0.0903757 | ||||||||
\(199\) | 2.77025e10 | 1.25222 | 0.626109 | − | 0.779735i | \(-0.284646\pi\) | ||||
0.626109 | + | 0.779735i | \(0.284646\pi\) | |||||||
\(200\) | −1.32411e9 | −0.0585179 | ||||||||
\(201\) | 2.29172e10 | 0.990328 | ||||||||
\(202\) | −2.08371e10 | −0.880554 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −1.75294e10 | −0.708650 | ||||||||
\(205\) | −3.89812e10 | −1.54157 | ||||||||
\(206\) | 3.43918e10 | 1.33062 | ||||||||
\(207\) | 2.36728e9 | 0.0896153 | ||||||||
\(208\) | −5.45995e9 | −0.202257 | ||||||||
\(209\) | 9.49581e9 | 0.344250 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.30691e10 | −0.453914 | −0.226957 | − | 0.973905i | \(-0.572878\pi\) | ||||
−0.226957 | + | 0.973905i | \(0.572878\pi\) | |||||||
\(212\) | −2.13731e10 | −0.726700 | ||||||||
\(213\) | −4.57460e10 | −1.52281 | ||||||||
\(214\) | −1.33582e10 | −0.435398 | ||||||||
\(215\) | −1.11832e10 | −0.356939 | ||||||||
\(216\) | 1.21968e10 | 0.381246 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 1.64100e10 | 0.492102 | ||||||||
\(219\) | −3.03940e10 | −0.892872 | ||||||||
\(220\) | −9.03474e9 | −0.260024 | ||||||||
\(221\) | −4.61745e10 | −1.30208 | ||||||||
\(222\) | 3.52020e10 | 0.972700 | ||||||||
\(223\) | 4.18178e10 | 1.13237 | 0.566187 | − | 0.824277i | \(-0.308418\pi\) | ||||
0.566187 | + | 0.824277i | \(0.308418\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.42853e9 | 0.0371592 | ||||||||
\(226\) | −7.45444e9 | −0.190076 | ||||||||
\(227\) | 5.61223e10 | 1.40288 | 0.701438 | − | 0.712731i | \(-0.252542\pi\) | ||||
0.701438 | + | 0.712731i | \(0.252542\pi\) | |||||||
\(228\) | 1.08644e10 | 0.266255 | ||||||||
\(229\) | 4.49082e9 | 0.107911 | 0.0539556 | − | 0.998543i | \(-0.482817\pi\) | ||||
0.0539556 | + | 0.998543i | \(0.482817\pi\) | |||||||
\(230\) | −1.09426e10 | −0.257836 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.06128e10 | −0.240510 | ||||||||
\(233\) | −6.44663e10 | −1.43295 | −0.716475 | − | 0.697613i | \(-0.754245\pi\) | ||||
−0.716475 | + | 0.697613i | \(0.754245\pi\) | |||||||
\(234\) | 5.89051e9 | 0.128434 | ||||||||
\(235\) | −3.48182e10 | −0.744735 | ||||||||
\(236\) | −2.08762e10 | −0.438073 | ||||||||
\(237\) | 6.42333e10 | 1.32249 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.23198e9 | −0.0244238 | −0.0122119 | − | 0.999925i | \(-0.503887\pi\) | ||||
−0.0122119 | + | 0.999925i | \(0.503887\pi\) | |||||||
\(240\) | −1.03369e10 | −0.201112 | ||||||||
\(241\) | 8.88350e9 | 0.169632 | 0.0848160 | − | 0.996397i | \(-0.472970\pi\) | ||||
0.0848160 | + | 0.996397i | \(0.472970\pi\) | |||||||
\(242\) | −2.55001e10 | −0.477940 | ||||||||
\(243\) | −2.39047e10 | −0.439800 | ||||||||
\(244\) | −1.27601e10 | −0.230463 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 6.03580e10 | 1.05082 | ||||||||
\(247\) | 2.86180e10 | 0.489219 | ||||||||
\(248\) | 2.49743e10 | 0.419238 | ||||||||
\(249\) | −3.69270e10 | −0.608761 | ||||||||
\(250\) | −4.64988e10 | −0.752856 | ||||||||
\(251\) | −9.92817e10 | −1.57884 | −0.789419 | − | 0.613855i | \(-0.789618\pi\) | ||||
−0.789419 | + | 0.613855i | \(0.789618\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.48090e10 | 0.227239 | ||||||||
\(254\) | −1.25447e10 | −0.189108 | ||||||||
\(255\) | −8.74183e10 | −1.29471 | ||||||||
\(256\) | 4.29497e9 | 0.0625000 | ||||||||
\(257\) | 5.56657e10 | 0.795955 | 0.397977 | − | 0.917395i | \(-0.369712\pi\) | ||||
0.397977 | + | 0.917395i | \(0.369712\pi\) | |||||||
\(258\) | 1.73159e10 | 0.243309 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −2.72285e10 | −0.369525 | ||||||||
\(261\) | 1.14497e10 | 0.152725 | ||||||||
\(262\) | −9.23783e10 | −1.21119 | ||||||||
\(263\) | −9.97727e10 | −1.28591 | −0.642955 | − | 0.765904i | \(-0.722292\pi\) | ||||
−0.642955 | + | 0.765904i | \(0.722292\pi\) | |||||||
\(264\) | 1.39893e10 | 0.177246 | ||||||||
\(265\) | −1.06586e11 | −1.32768 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3.67587e10 | 0.442649 | ||||||||
\(268\) | −4.74862e10 | −0.562290 | ||||||||
\(269\) | 1.97349e10 | 0.229800 | 0.114900 | − | 0.993377i | \(-0.463345\pi\) | ||||
0.114900 | + | 0.993377i | \(0.463345\pi\) | |||||||
\(270\) | 6.08250e10 | 0.696538 | ||||||||
\(271\) | −5.88440e10 | −0.662735 | −0.331368 | − | 0.943502i | \(-0.607510\pi\) | ||||
−0.331368 | + | 0.943502i | \(0.607510\pi\) | |||||||
\(272\) | 3.63223e10 | 0.402359 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.14828e11 | 1.23075 | ||||||||
\(275\) | 8.93645e9 | 0.0942254 | ||||||||
\(276\) | 1.69433e10 | 0.175755 | ||||||||
\(277\) | −4.19495e10 | −0.428122 | −0.214061 | − | 0.976820i | \(-0.568669\pi\) | ||||
−0.214061 | + | 0.976820i | \(0.568669\pi\) | |||||||
\(278\) | 4.98111e10 | 0.500178 | ||||||||
\(279\) | −2.69437e10 | −0.266218 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.62716e10 | 0.251367 | 0.125684 | − | 0.992070i | \(-0.459888\pi\) | ||||
0.125684 | + | 0.992070i | \(0.459888\pi\) | |||||||
\(282\) | 5.39121e10 | 0.507651 | ||||||||
\(283\) | 1.23717e11 | 1.14654 | 0.573271 | − | 0.819366i | \(-0.305674\pi\) | ||||
0.573271 | + | 0.819366i | \(0.305674\pi\) | |||||||
\(284\) | 9.47893e10 | 0.864623 | ||||||||
\(285\) | 5.41801e10 | 0.486450 | ||||||||
\(286\) | 3.68493e10 | 0.325674 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −4.63366e9 | −0.0396879 | ||||||||
\(289\) | 1.88588e11 | 1.59028 | ||||||||
\(290\) | −5.29253e10 | −0.439412 | ||||||||
\(291\) | 9.64577e10 | 0.788531 | ||||||||
\(292\) | 6.29787e10 | 0.506957 | ||||||||
\(293\) | −3.33848e10 | −0.264633 | −0.132316 | − | 0.991208i | \(-0.542242\pi\) | ||||
−0.132316 | + | 0.991208i | \(0.542242\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.04108e11 | −0.800362 | ||||||||
\(296\) | −7.29412e10 | −0.552281 | ||||||||
\(297\) | −8.23167e10 | −0.613881 | ||||||||
\(298\) | 1.09931e11 | 0.807510 | ||||||||
\(299\) | 4.46307e10 | 0.322934 | ||||||||
\(300\) | 1.02244e10 | 0.0728773 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 1.45081e11 | 1.00364 | ||||||||
\(303\) | 1.60898e11 | 1.09663 | ||||||||
\(304\) | −2.25118e10 | −0.151175 | ||||||||
\(305\) | −6.36340e10 | −0.421056 | ||||||||
\(306\) | −3.91866e10 | −0.255500 | ||||||||
\(307\) | 2.32773e11 | 1.49558 | 0.747791 | − | 0.663935i | \(-0.231115\pi\) | ||||
0.747791 | + | 0.663935i | \(0.231115\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.65564e11 | −1.65713 | ||||||||
\(310\) | 1.24545e11 | 0.765949 | ||||||||
\(311\) | −7.62815e9 | −0.0462378 | −0.0231189 | − | 0.999733i | \(-0.507360\pi\) | ||||
−0.0231189 | + | 0.999733i | \(0.507360\pi\) | |||||||
\(312\) | 4.21602e10 | 0.251888 | ||||||||
\(313\) | −1.69667e11 | −0.999188 | −0.499594 | − | 0.866260i | \(-0.666517\pi\) | ||||
−0.499594 | + | 0.866260i | \(0.666517\pi\) | |||||||
\(314\) | 5.36781e10 | 0.311612 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.33096e11 | −0.750886 | ||||||||
\(317\) | −8.60051e10 | −0.478363 | −0.239182 | − | 0.970975i | \(-0.576879\pi\) | ||||
−0.239182 | + | 0.970975i | \(0.576879\pi\) | |||||||
\(318\) | 1.65037e11 | 0.905021 | ||||||||
\(319\) | 7.16258e10 | 0.387268 | ||||||||
\(320\) | 2.14188e10 | 0.114188 | ||||||||
\(321\) | 1.03148e11 | 0.542237 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.90381e11 | −0.973225 | ||||||||
\(324\) | −7.19139e10 | −0.362544 | ||||||||
\(325\) | 2.69323e10 | 0.133905 | ||||||||
\(326\) | 1.05274e11 | 0.516228 | ||||||||
\(327\) | −1.26714e11 | −0.612856 | ||||||||
\(328\) | −1.25066e11 | −0.596635 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 6.97637e10 | 0.323830 | ||||||||
\(331\) | 3.59276e11 | 1.64514 | 0.822568 | − | 0.568667i | \(-0.192541\pi\) | ||||
0.822568 | + | 0.568667i | \(0.192541\pi\) | |||||||
\(332\) | 7.65155e10 | 0.345643 | ||||||||
\(333\) | 7.86932e10 | 0.350702 | ||||||||
\(334\) | −5.15954e9 | −0.0226857 | ||||||||
\(335\) | −2.36811e11 | −1.02731 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.23831e11 | −0.945335 | −0.472668 | − | 0.881241i | \(-0.656709\pi\) | ||||
−0.472668 | + | 0.881241i | \(0.656709\pi\) | |||||||
\(338\) | −5.86171e10 | −0.244286 | ||||||||
\(339\) | 5.75611e10 | 0.236718 | ||||||||
\(340\) | 1.81137e11 | 0.735111 | ||||||||
\(341\) | −1.68552e11 | −0.675055 | ||||||||
\(342\) | 2.42871e10 | 0.0959970 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −3.58800e10 | −0.138146 | ||||||||
\(345\) | 8.44955e10 | 0.321106 | ||||||||
\(346\) | 2.67566e10 | 0.100367 | ||||||||
\(347\) | 1.24895e11 | 0.462449 | 0.231224 | − | 0.972900i | \(-0.425727\pi\) | ||||
0.231224 | + | 0.972900i | \(0.425727\pi\) | |||||||
\(348\) | 8.19488e10 | 0.299527 | ||||||||
\(349\) | 4.14076e9 | 0.0149405 | 0.00747025 | − | 0.999972i | \(-0.497622\pi\) | ||||
0.00747025 | + | 0.999972i | \(0.497622\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.48082e11 | −0.872397 | ||||||||
\(352\) | −2.89868e10 | −0.100637 | ||||||||
\(353\) | 1.72793e11 | 0.592297 | 0.296149 | − | 0.955142i | \(-0.404298\pi\) | ||||
0.296149 | + | 0.955142i | \(0.404298\pi\) | |||||||
\(354\) | 1.61200e11 | 0.545570 | ||||||||
\(355\) | 4.72709e11 | 1.57967 | ||||||||
\(356\) | −7.61669e10 | −0.251328 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.34864e11 | 0.433934 | ||||||||
\(359\) | −2.15079e10 | −0.0683397 | −0.0341699 | − | 0.999416i | \(-0.510879\pi\) | ||||
−0.0341699 | + | 0.999416i | \(0.510879\pi\) | |||||||
\(360\) | −2.31078e10 | −0.0725099 | ||||||||
\(361\) | −2.04693e11 | −0.634338 | ||||||||
\(362\) | −3.23706e11 | −0.990745 | ||||||||
\(363\) | 1.96905e11 | 0.595219 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.14071e11 | 0.926212 | ||||||||
\(366\) | 9.85301e10 | 0.287015 | ||||||||
\(367\) | −5.48596e11 | −1.57854 | −0.789270 | − | 0.614047i | \(-0.789541\pi\) | ||||
−0.789270 | + | 0.614047i | \(0.789541\pi\) | |||||||
\(368\) | −3.51079e10 | −0.0997906 | ||||||||
\(369\) | 1.34929e11 | 0.378866 | ||||||||
\(370\) | −3.63754e11 | −1.00902 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −1.92844e11 | −0.522112 | ||||||||
\(373\) | −1.26024e11 | −0.337104 | −0.168552 | − | 0.985693i | \(-0.553909\pi\) | ||||
−0.168552 | + | 0.985693i | \(0.553909\pi\) | |||||||
\(374\) | −2.45140e11 | −0.647876 | ||||||||
\(375\) | 3.59051e11 | 0.937596 | ||||||||
\(376\) | −1.11710e11 | −0.288235 | ||||||||
\(377\) | 2.15863e11 | 0.550353 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5.31002e10 | −0.132197 | −0.0660983 | − | 0.997813i | \(-0.521055\pi\) | ||||
−0.0660983 | + | 0.997813i | \(0.521055\pi\) | |||||||
\(380\) | −1.12265e11 | −0.276197 | ||||||||
\(381\) | 9.68667e10 | 0.235512 | ||||||||
\(382\) | −2.85165e11 | −0.685189 | ||||||||
\(383\) | 6.22690e11 | 1.47869 | 0.739346 | − | 0.673326i | \(-0.235135\pi\) | ||||
0.739346 | + | 0.673326i | \(0.235135\pi\) | |||||||
\(384\) | −3.31645e10 | −0.0778365 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 2.47308e11 | 0.567015 | ||||||||
\(387\) | 3.87094e10 | 0.0877236 | ||||||||
\(388\) | −1.99868e11 | −0.447713 | ||||||||
\(389\) | −2.37879e11 | −0.526724 | −0.263362 | − | 0.964697i | \(-0.584831\pi\) | ||||
−0.263362 | + | 0.964697i | \(0.584831\pi\) | |||||||
\(390\) | 2.10251e11 | 0.460200 | ||||||||
\(391\) | −2.96906e11 | −0.642426 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7.13319e11 | 1.50840 | ||||||||
\(394\) | 3.25847e11 | 0.681210 | ||||||||
\(395\) | −6.63744e11 | −1.37187 | ||||||||
\(396\) | 3.12727e10 | 0.0639052 | ||||||||
\(397\) | −1.69545e11 | −0.342554 | −0.171277 | − | 0.985223i | \(-0.554789\pi\) | ||||
−0.171277 | + | 0.985223i | \(0.554789\pi\) | |||||||
\(398\) | 4.43240e11 | 0.885453 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.11858e10 | −0.0413784 | ||||||||
\(401\) | −9.03546e11 | −1.74502 | −0.872510 | − | 0.488596i | \(-0.837509\pi\) | ||||
−0.872510 | + | 0.488596i | \(0.837509\pi\) | |||||||
\(402\) | 3.66675e11 | 0.700268 | ||||||||
\(403\) | −5.07974e11 | −0.959333 | ||||||||
\(404\) | −3.33393e11 | −0.622646 | ||||||||
\(405\) | −3.58631e11 | −0.662369 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.92282e11 | 0.889281 | ||||||||
\(408\) | −2.80471e11 | −0.501091 | ||||||||
\(409\) | 1.04510e12 | 1.84673 | 0.923363 | − | 0.383927i | \(-0.125429\pi\) | ||||
0.923363 | + | 0.383927i | \(0.125429\pi\) | |||||||
\(410\) | −6.23699e11 | −1.09005 | ||||||||
\(411\) | −8.86667e11 | −1.53275 | ||||||||
\(412\) | 5.50269e11 | 0.940887 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 3.78764e10 | 0.0633676 | ||||||||
\(415\) | 3.81579e11 | 0.631492 | ||||||||
\(416\) | −8.73592e10 | −0.143017 | ||||||||
\(417\) | −3.84628e11 | −0.622914 | ||||||||
\(418\) | 1.51933e11 | 0.243421 | ||||||||
\(419\) | 4.17508e11 | 0.661761 | 0.330881 | − | 0.943673i | \(-0.392654\pi\) | ||||
0.330881 | + | 0.943673i | \(0.392654\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.67897e11 | 0.260480 | 0.130240 | − | 0.991482i | \(-0.458425\pi\) | ||||
0.130240 | + | 0.991482i | \(0.458425\pi\) | |||||||
\(422\) | −2.09105e11 | −0.320966 | ||||||||
\(423\) | 1.20519e11 | 0.183031 | ||||||||
\(424\) | −3.41969e11 | −0.513855 | ||||||||
\(425\) | −1.79167e11 | −0.266384 | ||||||||
\(426\) | −7.31937e11 | −1.07679 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −2.13731e11 | −0.307873 | ||||||||
\(429\) | −2.84540e11 | −0.405589 | ||||||||
\(430\) | −1.78931e11 | −0.252394 | ||||||||
\(431\) | −1.60399e11 | −0.223900 | −0.111950 | − | 0.993714i | \(-0.535710\pi\) | ||||
−0.111950 | + | 0.993714i | \(0.535710\pi\) | |||||||
\(432\) | 1.95149e11 | 0.269582 | ||||||||
\(433\) | −4.44852e10 | −0.0608163 | −0.0304081 | − | 0.999538i | \(-0.509681\pi\) | ||||
−0.0304081 | + | 0.999538i | \(0.509681\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.08674e11 | 0.547237 | ||||||||
\(436\) | 2.62560e11 | 0.347969 | ||||||||
\(437\) | 1.84016e11 | 0.241373 | ||||||||
\(438\) | −4.86304e11 | −0.631356 | ||||||||
\(439\) | 5.75085e11 | 0.738995 | 0.369498 | − | 0.929232i | \(-0.379530\pi\) | ||||
0.369498 | + | 0.929232i | \(0.379530\pi\) | |||||||
\(440\) | −1.44556e11 | −0.183865 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −7.38792e11 | −0.920708 | ||||||||
\(443\) | −8.29838e11 | −1.02371 | −0.511855 | − | 0.859072i | \(-0.671041\pi\) | ||||
−0.511855 | + | 0.859072i | \(0.671041\pi\) | |||||||
\(444\) | 5.63232e11 | 0.687802 | ||||||||
\(445\) | −3.79840e11 | −0.459178 | ||||||||
\(446\) | 6.69085e11 | 0.800709 | ||||||||
\(447\) | −8.48858e11 | −1.00566 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 8.23705e11 | 0.956452 | 0.478226 | − | 0.878237i | \(-0.341280\pi\) | ||||
0.478226 | + | 0.878237i | \(0.341280\pi\) | |||||||
\(450\) | 2.28564e10 | 0.0262755 | ||||||||
\(451\) | 8.44076e11 | 0.960699 | ||||||||
\(452\) | −1.19271e11 | −0.134404 | ||||||||
\(453\) | −1.12027e12 | −1.24992 | ||||||||
\(454\) | 8.97957e11 | 0.991983 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.73830e11 | 0.188271 | ||||||||
\(457\) | −1.59828e12 | −1.71408 | −0.857039 | − | 0.515252i | \(-0.827698\pi\) | ||||
−0.857039 | + | 0.515252i | \(0.827698\pi\) | |||||||
\(458\) | 7.18532e10 | 0.0763047 | ||||||||
\(459\) | 1.65037e12 | 1.73550 | ||||||||
\(460\) | −1.75081e11 | −0.182318 | ||||||||
\(461\) | 1.27501e12 | 1.31480 | 0.657402 | − | 0.753540i | \(-0.271655\pi\) | ||||
0.657402 | + | 0.753540i | \(0.271655\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3.13766e11 | −0.317316 | −0.158658 | − | 0.987334i | \(-0.550717\pi\) | ||||
−0.158658 | + | 0.987334i | \(0.550717\pi\) | |||||||
\(464\) | −1.69804e11 | −0.170066 | ||||||||
\(465\) | −9.61705e11 | −0.953902 | ||||||||
\(466\) | −1.03146e12 | −1.01325 | ||||||||
\(467\) | −9.41486e11 | −0.915984 | −0.457992 | − | 0.888956i | \(-0.651431\pi\) | ||||
−0.457992 | + | 0.888956i | \(0.651431\pi\) | |||||||
\(468\) | 9.42481e10 | 0.0908169 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −5.57092e11 | −0.526607 | ||||||||
\(471\) | −4.14488e11 | −0.388077 | ||||||||
\(472\) | −3.34019e11 | −0.309765 | ||||||||
\(473\) | 2.42155e11 | 0.222442 | ||||||||
\(474\) | 1.02773e12 | 0.935142 | ||||||||
\(475\) | 1.11044e11 | 0.100086 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.68936e11 | 0.326301 | ||||||||
\(478\) | −1.97117e10 | −0.0172702 | ||||||||
\(479\) | −7.10040e11 | −0.616273 | −0.308137 | − | 0.951342i | \(-0.599705\pi\) | ||||
−0.308137 | + | 0.951342i | \(0.599705\pi\) | |||||||
\(480\) | −1.65390e11 | −0.142208 | ||||||||
\(481\) | 1.48362e12 | 1.26377 | ||||||||
\(482\) | 1.42136e11 | 0.119948 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −4.08002e11 | −0.337954 | ||||||||
\(485\) | −9.96730e11 | −0.817974 | ||||||||
\(486\) | −3.82475e11 | −0.310986 | ||||||||
\(487\) | 1.21863e12 | 0.981729 | 0.490864 | − | 0.871236i | \(-0.336681\pi\) | ||||
0.490864 | + | 0.871236i | \(0.336681\pi\) | |||||||
\(488\) | −2.04162e11 | −0.162962 | ||||||||
\(489\) | −8.12896e11 | −0.642902 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5.76219e10 | −0.0447426 | −0.0223713 | − | 0.999750i | \(-0.507122\pi\) | ||||
−0.0223713 | + | 0.999750i | \(0.507122\pi\) | |||||||
\(492\) | 9.65728e11 | 0.743040 | ||||||||
\(493\) | −1.43602e12 | −1.09484 | ||||||||
\(494\) | 4.57889e11 | 0.345930 | ||||||||
\(495\) | 1.55955e11 | 0.116755 | ||||||||
\(496\) | 3.99589e11 | 0.296446 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −5.90832e11 | −0.430459 | ||||||||
\(499\) | 2.38874e12 | 1.72471 | 0.862357 | − | 0.506300i | \(-0.168987\pi\) | ||||
0.862357 | + | 0.506300i | \(0.168987\pi\) | |||||||
\(500\) | −7.43981e11 | −0.532350 | ||||||||
\(501\) | 3.98406e10 | 0.0282524 | ||||||||
\(502\) | −1.58851e12 | −1.11641 | ||||||||
\(503\) | −1.80042e12 | −1.25406 | −0.627030 | − | 0.778995i | \(-0.715730\pi\) | ||||
−0.627030 | + | 0.778995i | \(0.715730\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.66261e12 | −1.13758 | ||||||||
\(506\) | 2.36944e11 | 0.160682 | ||||||||
\(507\) | 4.52625e11 | 0.304231 | ||||||||
\(508\) | −2.00715e11 | −0.133719 | ||||||||
\(509\) | 1.32860e12 | 0.877335 | 0.438668 | − | 0.898649i | \(-0.355451\pi\) | ||||
0.438668 | + | 0.898649i | \(0.355451\pi\) | |||||||
\(510\) | −1.39869e12 | −0.915496 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 6.87195e10 | 0.0441942 | ||||||||
\(513\) | −1.02286e12 | −0.652064 | ||||||||
\(514\) | 8.90651e11 | 0.562825 | ||||||||
\(515\) | 2.74416e12 | 1.71901 | ||||||||
\(516\) | 2.77055e11 | 0.172045 | ||||||||
\(517\) | 7.53934e11 | 0.464115 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2.06607e11 | −0.124995 | ||||||||
\(520\) | −4.35656e11 | −0.261293 | ||||||||
\(521\) | 2.19083e12 | 1.30268 | 0.651341 | − | 0.758785i | \(-0.274207\pi\) | ||||
0.651341 | + | 0.758785i | \(0.274207\pi\) | |||||||
\(522\) | 1.83194e11 | 0.107993 | ||||||||
\(523\) | 5.08236e11 | 0.297035 | 0.148518 | − | 0.988910i | \(-0.452550\pi\) | ||||
0.148518 | + | 0.988910i | \(0.452550\pi\) | |||||||
\(524\) | −1.47805e12 | −0.856444 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.59636e12 | −0.909276 | ||||||||
\(527\) | 3.37930e12 | 1.90844 | ||||||||
\(528\) | 2.23828e11 | 0.125332 | ||||||||
\(529\) | −1.51417e12 | −0.840669 | ||||||||
\(530\) | −1.70538e12 | −0.938815 | ||||||||
\(531\) | 3.60359e11 | 0.196702 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.54384e12 | 1.36527 | ||||||||
\(534\) | 5.88140e11 | 0.313000 | ||||||||
\(535\) | −1.06587e12 | −0.562485 | ||||||||
\(536\) | −7.59779e11 | −0.397599 | ||||||||
\(537\) | −1.04139e12 | −0.540415 | ||||||||
\(538\) | 3.15758e11 | 0.162493 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 9.73199e11 | 0.492527 | ||||||||
\(541\) | 1.00015e12 | 0.501968 | 0.250984 | − | 0.967991i | \(-0.419246\pi\) | ||||
0.250984 | + | 0.967991i | \(0.419246\pi\) | |||||||
\(542\) | −9.41504e11 | −0.468625 | ||||||||
\(543\) | 2.49957e12 | 1.23386 | ||||||||
\(544\) | 5.81157e11 | 0.284511 | ||||||||
\(545\) | 1.30937e12 | 0.635740 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.35970e12 | −1.60457 | −0.802283 | − | 0.596944i | \(-0.796381\pi\) | ||||
−0.802283 | + | 0.596944i | \(0.796381\pi\) | |||||||
\(548\) | 1.83724e12 | 0.870269 | ||||||||
\(549\) | 2.20262e11 | 0.103482 | ||||||||
\(550\) | 1.42983e11 | 0.0666274 | ||||||||
\(551\) | 8.90019e11 | 0.411355 | ||||||||
\(552\) | 2.71093e11 | 0.124278 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −6.71191e11 | −0.302728 | ||||||||
\(555\) | 2.80881e12 | 1.25662 | ||||||||
\(556\) | 7.96978e11 | 0.353679 | ||||||||
\(557\) | 1.39008e11 | 0.0611913 | 0.0305957 | − | 0.999532i | \(-0.490260\pi\) | ||||
0.0305957 | + | 0.999532i | \(0.490260\pi\) | |||||||
\(558\) | −4.31099e11 | −0.188245 | ||||||||
\(559\) | 7.29795e11 | 0.316117 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.89290e12 | 0.806855 | ||||||||
\(562\) | 4.20346e11 | 0.177743 | ||||||||
\(563\) | 3.88167e12 | 1.62829 | 0.814143 | − | 0.580664i | \(-0.197207\pi\) | ||||
0.814143 | + | 0.580664i | \(0.197207\pi\) | |||||||
\(564\) | 8.62594e11 | 0.358964 | ||||||||
\(565\) | −5.94798e11 | −0.245557 | ||||||||
\(566\) | 1.97947e12 | 0.810728 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1.51663e12 | 0.611381 | ||||||||
\(569\) | 1.24560e12 | 0.498164 | 0.249082 | − | 0.968482i | \(-0.419871\pi\) | ||||
0.249082 | + | 0.968482i | \(0.419871\pi\) | |||||||
\(570\) | 8.66882e11 | 0.343972 | ||||||||
\(571\) | −2.56587e12 | −1.01012 | −0.505059 | − | 0.863085i | \(-0.668529\pi\) | ||||
−0.505059 | + | 0.863085i | \(0.668529\pi\) | |||||||
\(572\) | 5.89589e11 | 0.230286 | ||||||||
\(573\) | 2.20196e12 | 0.853324 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.73176e11 | 0.0660669 | ||||||||
\(576\) | −7.41385e10 | −0.0280636 | ||||||||
\(577\) | −3.78810e12 | −1.42276 | −0.711378 | − | 0.702810i | \(-0.751928\pi\) | ||||
−0.711378 | + | 0.702810i | \(0.751928\pi\) | |||||||
\(578\) | 3.01741e12 | 1.12450 | ||||||||
\(579\) | −1.90964e12 | −0.706152 | ||||||||
\(580\) | −8.46804e11 | −0.310711 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 1.54332e12 | 0.557575 | ||||||||
\(583\) | 2.30796e12 | 0.827407 | ||||||||
\(584\) | 1.00766e12 | 0.358473 | ||||||||
\(585\) | 4.70010e11 | 0.165923 | ||||||||
\(586\) | −5.34156e11 | −0.187124 | ||||||||
\(587\) | 2.25752e12 | 0.784802 | 0.392401 | − | 0.919794i | \(-0.371645\pi\) | ||||
0.392401 | + | 0.919794i | \(0.371645\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.09442e12 | −0.717043 | ||||||||
\(590\) | −1.66573e12 | −0.565941 | ||||||||
\(591\) | −2.51610e12 | −0.848369 | ||||||||
\(592\) | −1.16706e12 | −0.390522 | ||||||||
\(593\) | 4.52765e12 | 1.50358 | 0.751790 | − | 0.659402i | \(-0.229191\pi\) | ||||
0.751790 | + | 0.659402i | \(0.229191\pi\) | |||||||
\(594\) | −1.31707e12 | −0.434079 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1.75890e12 | 0.570996 | ||||||||
\(597\) | −3.42258e12 | −1.10273 | ||||||||
\(598\) | 7.14091e11 | 0.228349 | ||||||||
\(599\) | 3.89624e12 | 1.23659 | 0.618293 | − | 0.785947i | \(-0.287824\pi\) | ||||
0.618293 | + | 0.785947i | \(0.287824\pi\) | |||||||
\(600\) | 1.63591e11 | 0.0515321 | ||||||||
\(601\) | −4.27283e12 | −1.33592 | −0.667960 | − | 0.744197i | \(-0.732832\pi\) | ||||
−0.667960 | + | 0.744197i | \(0.732832\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 8.19693e11 | 0.252478 | ||||||||
\(604\) | 2.32129e12 | 0.709682 | ||||||||
\(605\) | −2.03468e12 | −0.617444 | ||||||||
\(606\) | 2.57437e12 | 0.775433 | ||||||||
\(607\) | −4.84102e12 | −1.44740 | −0.723699 | − | 0.690116i | \(-0.757559\pi\) | ||||
−0.723699 | + | 0.690116i | \(0.757559\pi\) | |||||||
\(608\) | −3.60189e11 | −0.106897 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1.01814e12 | −0.297732 | ||||||||
\(611\) | 2.27217e12 | 0.659562 | ||||||||
\(612\) | −6.26985e11 | −0.180666 | ||||||||
\(613\) | −6.72388e12 | −1.92330 | −0.961652 | − | 0.274274i | \(-0.911563\pi\) | ||||
−0.961652 | + | 0.274274i | \(0.911563\pi\) | |||||||
\(614\) | 3.72437e12 | 1.05754 | ||||||||
\(615\) | 4.81603e12 | 1.35754 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 8.50617e11 | 0.236293 | 0.118146 | − | 0.992996i | \(-0.462305\pi\) | ||||
0.118146 | + | 0.992996i | \(0.462305\pi\) | |||||||
\(618\) | −4.24902e12 | −1.17177 | ||||||||
\(619\) | 5.97444e12 | 1.63565 | 0.817823 | − | 0.575469i | \(-0.195181\pi\) | ||||
0.817823 | + | 0.575469i | \(0.195181\pi\) | |||||||
\(620\) | 1.99273e12 | 0.541608 | ||||||||
\(621\) | −1.59519e12 | −0.430427 | ||||||||
\(622\) | −1.22050e11 | −0.0326951 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 6.74564e11 | 0.178112 | ||||||||
\(625\) | −3.07881e12 | −0.807091 | ||||||||
\(626\) | −2.71467e12 | −0.706533 | ||||||||
\(627\) | −1.17318e12 | −0.303153 | ||||||||
\(628\) | 8.58850e11 | 0.220343 | ||||||||
\(629\) | −9.86976e12 | −2.51408 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5.96909e12 | −1.49891 | −0.749455 | − | 0.662055i | \(-0.769685\pi\) | ||||
−0.749455 | + | 0.662055i | \(0.769685\pi\) | |||||||
\(632\) | −2.12954e12 | −0.530957 | ||||||||
\(633\) | 1.61465e12 | 0.399726 | ||||||||
\(634\) | −1.37608e12 | −0.338254 | ||||||||
\(635\) | −1.00096e12 | −0.244306 | ||||||||
\(636\) | 2.64059e12 | 0.639947 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 1.14601e12 | 0.273840 | ||||||||
\(639\) | −1.63623e12 | −0.388230 | ||||||||
\(640\) | 3.42700e11 | 0.0807430 | ||||||||
\(641\) | −4.21558e12 | −0.986272 | −0.493136 | − | 0.869952i | \(-0.664149\pi\) | ||||
−0.493136 | + | 0.869952i | \(0.664149\pi\) | |||||||
\(642\) | 1.65037e12 | 0.383420 | ||||||||
\(643\) | −5.53403e12 | −1.27671 | −0.638354 | − | 0.769743i | \(-0.720385\pi\) | ||||
−0.638354 | + | 0.769743i | \(0.720385\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.38166e12 | 0.314327 | ||||||||
\(646\) | −3.04610e12 | −0.688174 | ||||||||
\(647\) | −2.51909e12 | −0.565165 | −0.282582 | − | 0.959243i | \(-0.591191\pi\) | ||||
−0.282582 | + | 0.959243i | \(0.591191\pi\) | |||||||
\(648\) | −1.15062e12 | −0.256357 | ||||||||
\(649\) | 2.25430e12 | 0.498782 | ||||||||
\(650\) | 4.30916e11 | 0.0946853 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1.68438e12 | 0.365028 | ||||||||
\(653\) | −7.60345e12 | −1.63645 | −0.818223 | − | 0.574901i | \(-0.805040\pi\) | ||||
−0.818223 | + | 0.574901i | \(0.805040\pi\) | |||||||
\(654\) | −2.02742e12 | −0.433355 | ||||||||
\(655\) | −7.37097e12 | −1.56473 | ||||||||
\(656\) | −2.00106e12 | −0.421884 | ||||||||
\(657\) | −1.08712e12 | −0.227632 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −4.45281e12 | −0.919708 | −0.459854 | − | 0.887994i | \(-0.652098\pi\) | ||||
−0.459854 | + | 0.887994i | \(0.652098\pi\) | |||||||
\(660\) | 1.11622e12 | 0.228982 | ||||||||
\(661\) | −5.31348e12 | −1.08261 | −0.541305 | − | 0.840826i | \(-0.682070\pi\) | ||||
−0.541305 | + | 0.840826i | \(0.682070\pi\) | |||||||
\(662\) | 5.74841e12 | 1.16329 | ||||||||
\(663\) | 5.70475e12 | 1.14664 | ||||||||
\(664\) | 1.22425e12 | 0.244407 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1.25909e12 | 0.247984 | ||||||||
\(667\) | 1.38801e12 | 0.271536 | ||||||||
\(668\) | −8.25527e10 | −0.0160412 | ||||||||
\(669\) | −5.16649e12 | −0.997191 | ||||||||
\(670\) | −3.78898e12 | −0.726416 | ||||||||
\(671\) | 1.37789e12 | 0.262400 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2.03778e12 | −0.382904 | −0.191452 | − | 0.981502i | \(-0.561320\pi\) | ||||
−0.191452 | + | 0.981502i | \(0.561320\pi\) | |||||||
\(674\) | −3.58130e12 | −0.668453 | ||||||||
\(675\) | −9.62612e11 | −0.178478 | ||||||||
\(676\) | −9.37874e11 | −0.172737 | ||||||||
\(677\) | −1.00898e13 | −1.84601 | −0.923004 | − | 0.384790i | \(-0.874274\pi\) | ||||
−0.923004 | + | 0.384790i | \(0.874274\pi\) | |||||||
\(678\) | 9.20977e11 | 0.167385 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 2.89820e12 | 0.519802 | ||||||||
\(681\) | −6.93377e12 | −1.23540 | ||||||||
\(682\) | −2.69683e12 | −0.477336 | ||||||||
\(683\) | 9.29076e12 | 1.63365 | 0.816823 | − | 0.576888i | \(-0.195733\pi\) | ||||
0.816823 | + | 0.576888i | \(0.195733\pi\) | |||||||
\(684\) | 3.88593e11 | 0.0678801 | ||||||||
\(685\) | 9.16222e12 | 1.58999 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −5.54830e11 | −0.0950287 | ||||||||
\(688\) | −5.74079e11 | −0.0976841 | ||||||||
\(689\) | 6.95561e12 | 1.17584 | ||||||||
\(690\) | 1.35193e12 | 0.227056 | ||||||||
\(691\) | 6.85546e12 | 1.14389 | 0.571947 | − | 0.820291i | \(-0.306188\pi\) | ||||
0.571947 | + | 0.820291i | \(0.306188\pi\) | |||||||
\(692\) | 4.28106e11 | 0.0709699 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 1.99833e12 | 0.327001 | ||||||||
\(695\) | 3.97449e12 | 0.646174 | ||||||||
\(696\) | 1.31118e12 | 0.211798 | ||||||||
\(697\) | −1.69229e13 | −2.71598 | ||||||||
\(698\) | 6.62521e10 | 0.0105645 | ||||||||
\(699\) | 7.96465e12 | 1.26188 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.51709e12 | 0.393702 | 0.196851 | − | 0.980433i | \(-0.436928\pi\) | ||||
0.196851 | + | 0.980433i | \(0.436928\pi\) | |||||||
\(702\) | −3.96932e12 | −0.616878 | ||||||||
\(703\) | 6.11708e12 | 0.944594 | ||||||||
\(704\) | −4.63789e11 | −0.0711613 | ||||||||
\(705\) | 4.30171e12 | 0.655828 | ||||||||
\(706\) | 2.76469e12 | 0.418817 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 2.57920e12 | 0.385776 | ||||||||
\(709\) | −6.59233e12 | −0.979785 | −0.489892 | − | 0.871783i | \(-0.662964\pi\) | ||||
−0.489892 | + | 0.871783i | \(0.662964\pi\) | |||||||
\(710\) | 7.56335e12 | 1.11700 | ||||||||
\(711\) | 2.29747e12 | 0.337160 | ||||||||
\(712\) | −1.21867e12 | −0.177716 | ||||||||
\(713\) | −3.26631e12 | −0.473320 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.94025e12 | 0.420734 | ||||||||
\(716\) | 2.15783e12 | 0.306838 | ||||||||
\(717\) | 1.52208e11 | 0.0215081 | ||||||||
\(718\) | −3.44127e11 | −0.0483235 | ||||||||
\(719\) | −7.89215e11 | −0.110132 | −0.0550662 | − | 0.998483i | \(-0.517537\pi\) | ||||
−0.0550662 | + | 0.998483i | \(0.517537\pi\) | |||||||
\(720\) | −3.69725e11 | −0.0512722 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −3.27509e12 | −0.448545 | ||||||||
\(723\) | −1.09754e12 | −0.149381 | ||||||||
\(724\) | −5.17929e12 | −0.700563 | ||||||||
\(725\) | 8.37592e11 | 0.112593 | ||||||||
\(726\) | 3.15048e12 | 0.420883 | ||||||||
\(727\) | −4.67869e12 | −0.621183 | −0.310592 | − | 0.950543i | \(-0.600527\pi\) | ||||
−0.310592 | + | 0.950543i | \(0.600527\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 8.48259e12 | 1.11238 | ||||||||
\(730\) | 5.02514e12 | 0.654931 | ||||||||
\(731\) | −4.85496e12 | −0.628865 | ||||||||
\(732\) | 1.57648e12 | 0.202950 | ||||||||
\(733\) | −7.38248e12 | −0.944571 | −0.472285 | − | 0.881446i | \(-0.656571\pi\) | ||||
−0.472285 | + | 0.881446i | \(0.656571\pi\) | |||||||
\(734\) | −8.77754e12 | −1.11620 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −5.61726e11 | −0.0705626 | ||||||||
\(737\) | 5.12777e12 | 0.640213 | ||||||||
\(738\) | 2.15886e12 | 0.267899 | ||||||||
\(739\) | −3.72777e12 | −0.459780 | −0.229890 | − | 0.973217i | \(-0.573837\pi\) | ||||
−0.229890 | + | 0.973217i | \(0.573837\pi\) | |||||||
\(740\) | −5.82006e12 | −0.713485 | ||||||||
\(741\) | −3.53569e12 | −0.430816 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 8.63062e12 | 1.03894 | 0.519472 | − | 0.854487i | \(-0.326129\pi\) | ||||
0.519472 | + | 0.854487i | \(0.326129\pi\) | |||||||
\(744\) | −3.08551e12 | −0.369189 | ||||||||
\(745\) | 8.77154e12 | 1.04321 | ||||||||
\(746\) | −2.01639e12 | −0.238368 | ||||||||
\(747\) | −1.32079e12 | −0.155200 | ||||||||
\(748\) | −3.92224e12 | −0.458118 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 5.74482e12 | 0.662980 | ||||||||
\(751\) | 1.71581e13 | 1.96829 | 0.984146 | − | 0.177359i | \(-0.0567555\pi\) | ||||
0.984146 | + | 0.177359i | \(0.0567555\pi\) | |||||||
\(752\) | −1.78736e12 | −0.203813 | ||||||||
\(753\) | 1.22660e13 | 1.39036 | ||||||||
\(754\) | 3.45380e12 | 0.389158 | ||||||||
\(755\) | 1.15762e13 | 1.29659 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −6.69732e12 | −0.741258 | −0.370629 | − | 0.928781i | \(-0.620858\pi\) | ||||
−0.370629 | + | 0.928781i | \(0.620858\pi\) | |||||||
\(758\) | −8.49604e11 | −0.0934770 | ||||||||
\(759\) | −1.82962e12 | −0.200111 | ||||||||
\(760\) | −1.79625e12 | −0.195301 | ||||||||
\(761\) | 3.08096e12 | 0.333008 | 0.166504 | − | 0.986041i | \(-0.446752\pi\) | ||||
0.166504 | + | 0.986041i | \(0.446752\pi\) | |||||||
\(762\) | 1.54987e12 | 0.166532 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −4.56263e12 | −0.484502 | ||||||||
\(765\) | −3.12674e12 | −0.330077 | ||||||||
\(766\) | 9.96305e12 | 1.04559 | ||||||||
\(767\) | 6.79391e12 | 0.708827 | ||||||||
\(768\) | −5.30633e11 | −0.0550387 | ||||||||
\(769\) | −3.26639e11 | −0.0336821 | −0.0168410 | − | 0.999858i | \(-0.505361\pi\) | ||||
−0.0168410 | + | 0.999858i | \(0.505361\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −6.87736e12 | −0.700934 | ||||||||
\(772\) | 3.95692e12 | 0.400940 | ||||||||
\(773\) | −1.96236e13 | −1.97684 | −0.988421 | − | 0.151736i | \(-0.951513\pi\) | ||||
−0.988421 | + | 0.151736i | \(0.951513\pi\) | |||||||
\(774\) | 6.19350e11 | 0.0620300 | ||||||||
\(775\) | −1.97105e12 | −0.196263 | ||||||||
\(776\) | −3.19789e12 | −0.316581 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −3.80607e12 | −0.372450 | ||||||||
\(779\) | 1.04885e13 | 1.02045 | ||||||||
\(780\) | 3.36401e12 | 0.325411 | ||||||||
\(781\) | −1.02358e13 | −0.984443 | ||||||||
\(782\) | −4.75049e12 | −0.454264 | ||||||||
\(783\) | −7.71535e12 | −0.733547 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4.28304e12 | 0.402567 | ||||||||
\(786\) | 1.14131e13 | 1.06660 | ||||||||
\(787\) | −1.46792e13 | −1.36400 | −0.682001 | − | 0.731351i | \(-0.738890\pi\) | ||||
−0.682001 | + | 0.731351i | \(0.738890\pi\) | |||||||
\(788\) | 5.21356e12 | 0.481688 | ||||||||
\(789\) | 1.23267e13 | 1.13240 | ||||||||
\(790\) | −1.06199e13 | −0.970060 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 5.00363e11 | 0.0451878 | ||||||||
\(793\) | 4.15263e12 | 0.372902 | ||||||||
\(794\) | −2.71273e12 | −0.242222 | ||||||||
\(795\) | 1.31685e13 | 1.16919 | ||||||||
\(796\) | 7.09184e12 | 0.626109 | ||||||||
\(797\) | 9.49591e12 | 0.833632 | 0.416816 | − | 0.908991i | \(-0.363146\pi\) | ||||
0.416816 | + | 0.908991i | \(0.363146\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.51156e13 | −1.31209 | ||||||||
\(800\) | −3.38972e11 | −0.0292590 | ||||||||
\(801\) | 1.31477e12 | 0.112851 | ||||||||
\(802\) | −1.44567e13 | −1.23392 | ||||||||
\(803\) | −6.80072e12 | −0.577211 | ||||||||
\(804\) | 5.86680e12 | 0.495164 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −8.12759e12 | −0.678351 | ||||||||
\(807\) | −2.43820e12 | −0.202366 | ||||||||
\(808\) | −5.33429e12 | −0.440277 | ||||||||
\(809\) | 1.44737e13 | 1.18799 | 0.593993 | − | 0.804470i | \(-0.297551\pi\) | ||||
0.593993 | + | 0.804470i | \(0.297551\pi\) | |||||||
\(810\) | −5.73809e12 | −0.468366 | ||||||||
\(811\) | −7.11471e12 | −0.577516 | −0.288758 | − | 0.957402i | \(-0.593242\pi\) | ||||
−0.288758 | + | 0.957402i | \(0.593242\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 7.27003e12 | 0.583618 | ||||||||
\(814\) | 7.87651e12 | 0.628817 | ||||||||
\(815\) | 8.39992e12 | 0.666908 | ||||||||
\(816\) | −4.48753e12 | −0.354325 | ||||||||
\(817\) | 3.00901e12 | 0.236278 | ||||||||
\(818\) | 1.67216e13 | 1.30583 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −9.97919e12 | −0.770785 | ||||||||
\(821\) | 7.47018e12 | 0.573835 | 0.286918 | − | 0.957955i | \(-0.407369\pi\) | ||||
0.286918 | + | 0.957955i | \(0.407369\pi\) | |||||||
\(822\) | −1.41867e13 | −1.08382 | ||||||||
\(823\) | 1.58484e13 | 1.20417 | 0.602085 | − | 0.798432i | \(-0.294337\pi\) | ||||
0.602085 | + | 0.798432i | \(0.294337\pi\) | |||||||
\(824\) | 8.80430e12 | 0.665308 | ||||||||
\(825\) | −1.10408e12 | −0.0829767 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.27588e12 | 0.169190 | 0.0845948 | − | 0.996415i | \(-0.473040\pi\) | ||||
0.0845948 | + | 0.996415i | \(0.473040\pi\) | |||||||
\(828\) | 6.06023e11 | 0.0448077 | ||||||||
\(829\) | 1.27889e13 | 0.940453 | 0.470226 | − | 0.882546i | \(-0.344172\pi\) | ||||
0.470226 | + | 0.882546i | \(0.344172\pi\) | |||||||
\(830\) | 6.10526e12 | 0.446532 | ||||||||
\(831\) | 5.18275e12 | 0.377013 | ||||||||
\(832\) | −1.39775e12 | −0.101129 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −6.15404e12 | −0.440467 | ||||||||
\(835\) | −4.11686e11 | −0.0293074 | ||||||||
\(836\) | 2.43093e12 | 0.172125 | ||||||||
\(837\) | 1.81560e13 | 1.27866 | ||||||||
\(838\) | 6.68012e12 | 0.467936 | ||||||||
\(839\) | −1.07948e13 | −0.752119 | −0.376060 | − | 0.926595i | \(-0.622721\pi\) | ||||
−0.376060 | + | 0.926595i | \(0.622721\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7.79383e12 | −0.537241 | ||||||||
\(842\) | 2.68636e12 | 0.184187 | ||||||||
\(843\) | −3.24580e12 | −0.221359 | ||||||||
\(844\) | −3.34568e12 | −0.226957 | ||||||||
\(845\) | −4.67713e12 | −0.315591 | ||||||||
\(846\) | 1.92831e12 | 0.129422 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −5.47150e12 | −0.363350 | ||||||||
\(849\) | −1.52849e13 | −1.00967 | ||||||||
\(850\) | −2.86667e12 | −0.188362 | ||||||||
\(851\) | 9.53977e12 | 0.623526 | ||||||||
\(852\) | −1.17110e13 | −0.761404 | ||||||||
\(853\) | 1.76557e13 | 1.14187 | 0.570933 | − | 0.820997i | \(-0.306582\pi\) | ||||
0.570933 | + | 0.820997i | \(0.306582\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.93789e12 | 0.124017 | ||||||||
\(856\) | −3.41970e12 | −0.217699 | ||||||||
\(857\) | 1.64326e13 | 1.04062 | 0.520309 | − | 0.853978i | \(-0.325817\pi\) | ||||
0.520309 | + | 0.853978i | \(0.325817\pi\) | |||||||
\(858\) | −4.55265e12 | −0.286795 | ||||||||
\(859\) | −8.44024e11 | −0.0528914 | −0.0264457 | − | 0.999650i | \(-0.508419\pi\) | ||||
−0.0264457 | + | 0.999650i | \(0.508419\pi\) | |||||||
\(860\) | −2.86290e12 | −0.178469 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −2.56639e12 | −0.158321 | ||||||||
\(863\) | −2.46263e12 | −0.151130 | −0.0755649 | − | 0.997141i | \(-0.524076\pi\) | ||||
−0.0755649 | + | 0.997141i | \(0.524076\pi\) | |||||||
\(864\) | 3.12239e12 | 0.190623 | ||||||||
\(865\) | 2.13494e12 | 0.129662 | ||||||||
\(866\) | −7.11763e11 | −0.0430036 | ||||||||
\(867\) | −2.32996e13 | −1.40043 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.43723e13 | 0.854944 | ||||||||
\(870\) | 6.53879e12 | 0.386955 | ||||||||
\(871\) | 1.54538e13 | 0.909818 | ||||||||
\(872\) | 4.20097e12 | 0.246051 | ||||||||
\(873\) | 3.45006e12 | 0.201031 | ||||||||
\(874\) | 2.94426e12 | 0.170677 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −7.78086e12 | −0.446436 | ||||||||
\(877\) | 3.00332e12 | 0.171437 | 0.0857184 | − | 0.996319i | \(-0.472681\pi\) | ||||
0.0857184 | + | 0.996319i | \(0.472681\pi\) | |||||||
\(878\) | 9.20136e12 | 0.522549 | ||||||||
\(879\) | 4.12461e12 | 0.233041 | ||||||||
\(880\) | −2.31289e12 | −0.130012 | ||||||||
\(881\) | 4.67820e11 | 0.0261630 | 0.0130815 | − | 0.999914i | \(-0.495836\pi\) | ||||
0.0130815 | + | 0.999914i | \(0.495836\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −9.28272e12 | −0.513869 | −0.256934 | − | 0.966429i | \(-0.582712\pi\) | ||||
−0.256934 | + | 0.966429i | \(0.582712\pi\) | |||||||
\(884\) | −1.18207e13 | −0.651039 | ||||||||
\(885\) | 1.28623e13 | 0.704815 | ||||||||
\(886\) | −1.32774e13 | −0.723872 | ||||||||
\(887\) | −9.97831e12 | −0.541253 | −0.270627 | − | 0.962684i | \(-0.587231\pi\) | ||||
−0.270627 | + | 0.962684i | \(0.587231\pi\) | |||||||
\(888\) | 9.01171e12 | 0.486350 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −6.07744e12 | −0.324688 | ||||||||
\(891\) | 7.76558e12 | 0.412785 | ||||||||
\(892\) | 1.07054e13 | 0.566187 | ||||||||
\(893\) | 9.36835e12 | 0.492983 | ||||||||
\(894\) | −1.35817e13 | −0.711109 | ||||||||
\(895\) | 1.07610e13 | 0.560594 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −5.51401e12 | −0.284382 | ||||||||
\(898\) | 1.31793e13 | 0.676313 | ||||||||
\(899\) | −1.57980e13 | −0.806646 | ||||||||
\(900\) | 3.65703e11 | 0.0185796 | ||||||||
\(901\) | −4.62722e13 | −2.33915 | ||||||||
\(902\) | 1.35052e13 | 0.679317 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1.90834e12 | −0.0950379 | ||||||||
\(905\) | −2.58289e13 | −1.27993 | ||||||||
\(906\) | −1.79244e13 | −0.883827 | ||||||||
\(907\) | −1.03996e12 | −0.0510249 | −0.0255124 | − | 0.999675i | \(-0.508122\pi\) | ||||
−0.0255124 | + | 0.999675i | \(0.508122\pi\) | |||||||
\(908\) | 1.43673e13 | 0.701438 | ||||||||
\(909\) | 5.75494e12 | 0.279578 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.92798e13 | 1.40843 | 0.704215 | − | 0.709986i | \(-0.251299\pi\) | ||||
0.704215 | + | 0.709986i | \(0.251299\pi\) | |||||||
\(912\) | 2.78128e12 | 0.133128 | ||||||||
\(913\) | −8.26248e12 | −0.393543 | ||||||||
\(914\) | −2.55725e13 | −1.21204 | ||||||||
\(915\) | 7.86183e12 | 0.370791 | ||||||||
\(916\) | 1.14965e12 | 0.0539556 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 2.64059e13 | 1.22718 | ||||||||
\(919\) | −1.31519e13 | −0.608231 | −0.304115 | − | 0.952635i | \(-0.598361\pi\) | ||||
−0.304115 | + | 0.952635i | \(0.598361\pi\) | |||||||
\(920\) | −2.80130e12 | −0.128918 | ||||||||
\(921\) | −2.87585e13 | −1.31704 | ||||||||
\(922\) | 2.04002e13 | 0.929706 | ||||||||
\(923\) | −3.08481e13 | −1.39901 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.75675e12 | 0.258547 | ||||||||
\(926\) | −5.02026e12 | −0.224376 | ||||||||
\(927\) | −9.49859e12 | −0.422474 | ||||||||
\(928\) | −2.71687e12 | −0.120255 | ||||||||
\(929\) | 3.36952e13 | 1.48422 | 0.742108 | − | 0.670280i | \(-0.233826\pi\) | ||||
0.742108 | + | 0.670280i | \(0.233826\pi\) | |||||||
\(930\) | −1.53873e13 | −0.674510 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −1.65034e13 | −0.716475 | ||||||||
\(933\) | 9.42439e11 | 0.0407180 | ||||||||
\(934\) | −1.50638e13 | −0.647699 | ||||||||
\(935\) | −1.95600e13 | −0.836983 | ||||||||
\(936\) | 1.50797e12 | 0.0642172 | ||||||||
\(937\) | 1.90556e13 | 0.807598 | 0.403799 | − | 0.914848i | \(-0.367689\pi\) | ||||
0.403799 | + | 0.914848i | \(0.367689\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.09619e13 | 0.879905 | ||||||||
\(940\) | −8.91347e12 | −0.372367 | ||||||||
\(941\) | −1.67435e13 | −0.696134 | −0.348067 | − | 0.937470i | \(-0.613162\pi\) | ||||
−0.348067 | + | 0.937470i | \(0.613162\pi\) | |||||||
\(942\) | −6.63180e12 | −0.274412 | ||||||||
\(943\) | 1.63571e13 | 0.673601 | ||||||||
\(944\) | −5.34430e12 | −0.219037 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 3.87448e12 | 0.157291 | ||||||||
\(947\) | −2.34965e13 | −0.949355 | −0.474677 | − | 0.880160i | \(-0.657435\pi\) | ||||
−0.474677 | + | 0.880160i | \(0.657435\pi\) | |||||||
\(948\) | 1.64437e13 | 0.661245 | ||||||||
\(949\) | −2.04957e13 | −0.820285 | ||||||||
\(950\) | 1.77670e12 | 0.0707716 | ||||||||
\(951\) | 1.06257e13 | 0.421256 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.77607e13 | 1.09022 | 0.545108 | − | 0.838366i | \(-0.316489\pi\) | ||||
0.545108 | + | 0.838366i | \(0.316489\pi\) | |||||||
\(954\) | 5.90297e12 | 0.230729 | ||||||||
\(955\) | −2.27536e13 | −0.885187 | ||||||||
\(956\) | −3.15387e11 | −0.0122119 | ||||||||
\(957\) | −8.84919e12 | −0.341036 | ||||||||
\(958\) | −1.13606e13 | −0.435771 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −2.64624e12 | −0.100556 | ||||||||
\(961\) | 1.07367e13 | 0.406083 | ||||||||
\(962\) | 2.37379e13 | 0.893622 | ||||||||
\(963\) | 3.68937e12 | 0.138240 | ||||||||
\(964\) | 2.27418e12 | 0.0848160 | ||||||||
\(965\) | 1.97330e13 | 0.732520 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.72985e13 | −0.636193 | −0.318097 | − | 0.948058i | \(-0.603044\pi\) | ||||
−0.318097 | + | 0.948058i | \(0.603044\pi\) | |||||||
\(968\) | −6.52803e12 | −0.238970 | ||||||||
\(969\) | 2.35212e13 | 0.857041 | ||||||||
\(970\) | −1.59477e13 | −0.578395 | ||||||||
\(971\) | 1.21004e13 | 0.436832 | 0.218416 | − | 0.975856i | \(-0.429911\pi\) | ||||
0.218416 | + | 0.975856i | \(0.429911\pi\) | |||||||
\(972\) | −6.11961e12 | −0.219900 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 1.94981e13 | 0.694187 | ||||||||
\(975\) | −3.32742e12 | −0.117920 | ||||||||
\(976\) | −3.26659e12 | −0.115231 | ||||||||
\(977\) | −2.99686e13 | −1.05230 | −0.526151 | − | 0.850391i | \(-0.676365\pi\) | ||||
−0.526151 | + | 0.850391i | \(0.676365\pi\) | |||||||
\(978\) | −1.30063e13 | −0.454601 | ||||||||
\(979\) | 8.22483e12 | 0.286157 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.53225e12 | −0.156244 | ||||||||
\(982\) | −9.21950e11 | −0.0316378 | ||||||||
\(983\) | −7.63647e11 | −0.0260857 | −0.0130428 | − | 0.999915i | \(-0.504152\pi\) | ||||
−0.0130428 | + | 0.999915i | \(0.504152\pi\) | |||||||
\(984\) | 1.54516e13 | 0.525408 | ||||||||
\(985\) | 2.59997e13 | 0.880046 | ||||||||
\(986\) | −2.29764e13 | −0.774169 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 7.32622e12 | 0.244610 | ||||||||
\(989\) | 4.69264e12 | 0.155967 | ||||||||
\(990\) | 2.49528e12 | 0.0825584 | ||||||||
\(991\) | −4.14811e13 | −1.36621 | −0.683107 | − | 0.730318i | \(-0.739372\pi\) | ||||
−0.683107 | + | 0.730318i | \(0.739372\pi\) | |||||||
\(992\) | 6.39342e12 | 0.209619 | ||||||||
\(993\) | −4.43876e13 | −1.44874 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.53666e13 | 1.14390 | ||||||||
\(996\) | −9.45331e12 | −0.304381 | ||||||||
\(997\) | −5.09261e13 | −1.63235 | −0.816173 | − | 0.577808i | \(-0.803908\pi\) | ||||
−0.816173 | + | 0.577808i | \(0.803908\pi\) | |||||||
\(998\) | 3.82199e13 | 1.21956 | ||||||||
\(999\) | −5.30274e13 | −1.68444 |
(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 | 98.10.a.f.1.1 | ✓ | 2 | |
7.2 | even | 3 | 98.10.c.g.67.2 | 4 | |||
7.3 | odd | 6 | 98.10.c.g.79.1 | 4 | |||
7.4 | even | 3 | 98.10.c.g.79.2 | 4 | |||
7.5 | odd | 6 | 98.10.c.g.67.1 | 4 | |||
7.6 | odd | 2 | inner | 98.10.a.f.1.2 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
98.10.a.f.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
98.10.a.f.1.2 | yes | 2 | 7.6 | odd | 2 | inner | |
98.10.c.g.67.1 | 4 | 7.5 | odd | 6 | |||
98.10.c.g.67.2 | 4 | 7.2 | even | 3 | |||
98.10.c.g.79.1 | 4 | 7.3 | odd | 6 | |||
98.10.c.g.79.2 | 4 | 7.4 | even | 3 |