Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [387,8,Mod(1,387)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(387, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("387.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 387 = 3^{2} \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 387.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: | \(120.893004862\) |
Analytic rank: | \(1\) |
Dimension: | \(13\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{13} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{13} - 3 x^{12} - 1279 x^{11} + 3765 x^{10} + 598742 x^{9} - 1518614 x^{8} - 124677082 x^{7} + \cdots + 1551032970660 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{6}\cdot 3^{3} \) |
Twist minimal: | no (minimal twist has level 43) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Root | \(-8.80627\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 387.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 7.80627 | 0.689983 | 0.344992 | − | 0.938606i | \(-0.387882\pi\) | ||||
0.344992 | + | 0.938606i | \(0.387882\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −67.0621 | −0.523923 | ||||||||
\(5\) | 402.005 | 1.43826 | 0.719128 | − | 0.694878i | \(-0.244542\pi\) | ||||
0.719128 | + | 0.694878i | \(0.244542\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −356.766 | −0.393133 | −0.196567 | − | 0.980490i | \(-0.562979\pi\) | ||||
−0.196567 | + | 0.980490i | \(0.562979\pi\) | |||||||
\(8\) | −1522.71 | −1.05148 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 3138.16 | 0.992372 | ||||||||
\(11\) | −338.626 | −0.0767090 | −0.0383545 | − | 0.999264i | \(-0.512212\pi\) | ||||
−0.0383545 | + | 0.999264i | \(0.512212\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1901.99 | −0.240108 | −0.120054 | − | 0.992767i | \(-0.538307\pi\) | ||||
−0.120054 | + | 0.992767i | \(0.538307\pi\) | |||||||
\(14\) | −2785.01 | −0.271255 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3302.71 | −0.201582 | ||||||||
\(17\) | 13710.6 | 0.676841 | 0.338421 | − | 0.940995i | \(-0.390107\pi\) | ||||
0.338421 | + | 0.940995i | \(0.390107\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 32375.1 | 1.08286 | 0.541431 | − | 0.840745i | \(-0.317883\pi\) | ||||
0.541431 | + | 0.840745i | \(0.317883\pi\) | |||||||
\(20\) | −26959.3 | −0.753535 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2643.41 | −0.0529279 | ||||||||
\(23\) | −103235. | −1.76922 | −0.884609 | − | 0.466334i | \(-0.845574\pi\) | ||||
−0.884609 | + | 0.466334i | \(0.845574\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 83482.7 | 1.06858 | ||||||||
\(26\) | −14847.4 | −0.165670 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 23925.5 | 0.205972 | ||||||||
\(29\) | −97.3595 | −0.000741285 0 | −0.000370643 | − | 1.00000i | \(-0.500118\pi\) | ||||
−0.000370643 | 1.00000i | \(0.500118\pi\) | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2919.43 | −0.0176008 | −0.00880039 | − | 0.999961i | \(-0.502801\pi\) | ||||
−0.00880039 | + | 0.999961i | \(0.502801\pi\) | |||||||
\(32\) | 169125. | 0.912394 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 107029. | 0.467009 | ||||||||
\(35\) | −143421. | −0.565426 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −280235. | −0.909529 | −0.454764 | − | 0.890612i | \(-0.650277\pi\) | ||||
−0.454764 | + | 0.890612i | \(0.650277\pi\) | |||||||
\(38\) | 252729. | 0.747157 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −612136. | −1.51230 | ||||||||
\(41\) | 68080.9 | 0.154270 | 0.0771350 | − | 0.997021i | \(-0.475423\pi\) | ||||
0.0771350 | + | 0.997021i | \(0.475423\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −79507.0 | −0.152499 | ||||||||
\(44\) | 22709.0 | 0.0401896 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −805883. | −1.22073 | ||||||||
\(47\) | −145265. | −0.204089 | −0.102044 | − | 0.994780i | \(-0.532538\pi\) | ||||
−0.102044 | + | 0.994780i | \(0.532538\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −696261. | −0.845446 | ||||||||
\(50\) | 651689. | 0.737301 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 127551. | 0.125798 | ||||||||
\(53\) | 450286. | 0.415454 | 0.207727 | − | 0.978187i | \(-0.433393\pi\) | ||||
0.207727 | + | 0.978187i | \(0.433393\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −136129. | −0.110327 | ||||||||
\(56\) | 543250. | 0.413372 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −760.015 | −0.000511474 0 | ||||||||
\(59\) | −2.16940e6 | −1.37518 | −0.687588 | − | 0.726101i | \(-0.741330\pi\) | ||||
−0.687588 | + | 0.726101i | \(0.741330\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −240945. | −0.135914 | −0.0679570 | − | 0.997688i | \(-0.521648\pi\) | ||||
−0.0679570 | + | 0.997688i | \(0.521648\pi\) | |||||||
\(62\) | −22789.9 | −0.0121442 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.74298e6 | 0.831118 | ||||||||
\(65\) | −764608. | −0.345336 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 763129. | 0.309982 | 0.154991 | − | 0.987916i | \(-0.450465\pi\) | ||||
0.154991 | + | 0.987916i | \(0.450465\pi\) | |||||||
\(68\) | −919465. | −0.354613 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −1.11959e6 | −0.390135 | ||||||||
\(71\) | −256406. | −0.0850206 | −0.0425103 | − | 0.999096i | \(-0.513536\pi\) | ||||
−0.0425103 | + | 0.999096i | \(0.513536\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.25607e6 | −1.28050 | −0.640249 | − | 0.768168i | \(-0.721169\pi\) | ||||
−0.640249 | + | 0.768168i | \(0.721169\pi\) | |||||||
\(74\) | −2.18759e6 | −0.627560 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −2.17114e6 | −0.567337 | ||||||||
\(77\) | 120810. | 0.0301568 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.60338e6 | 1.50686 | 0.753428 | − | 0.657531i | \(-0.228399\pi\) | ||||
0.753428 | + | 0.657531i | \(0.228399\pi\) | |||||||
\(80\) | −1.32771e6 | −0.289926 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 531458. | 0.106444 | ||||||||
\(83\) | −1.57834e6 | −0.302989 | −0.151495 | − | 0.988458i | \(-0.548409\pi\) | ||||
−0.151495 | + | 0.988458i | \(0.548409\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.51174e6 | 0.973470 | ||||||||
\(86\) | −620653. | −0.105221 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 515629. | 0.0806580 | ||||||||
\(89\) | −1.01079e7 | −1.51983 | −0.759914 | − | 0.650024i | \(-0.774759\pi\) | ||||
−0.759914 | + | 0.650024i | \(0.774759\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 678564. | 0.0943944 | ||||||||
\(92\) | 6.92319e6 | 0.926934 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1.13398e6 | −0.140818 | ||||||||
\(95\) | 1.30149e7 | 1.55743 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.90764e6 | −0.212224 | −0.106112 | − | 0.994354i | \(-0.533840\pi\) | ||||
−0.106112 | + | 0.994354i | \(0.533840\pi\) | |||||||
\(98\) | −5.43520e6 | −0.583344 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −5.59853e6 | −0.559853 | ||||||||
\(101\) | 8.79838e6 | 0.849724 | 0.424862 | − | 0.905258i | \(-0.360323\pi\) | ||||
0.424862 | + | 0.905258i | \(0.360323\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.98046e7 | 1.78581 | 0.892907 | − | 0.450242i | \(-0.148662\pi\) | ||||
0.892907 | + | 0.450242i | \(0.148662\pi\) | |||||||
\(104\) | 2.89617e6 | 0.252469 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.51506e6 | 0.286657 | ||||||||
\(107\) | −1.19023e7 | −0.939264 | −0.469632 | − | 0.882862i | \(-0.655613\pi\) | ||||
−0.469632 | + | 0.882862i | \(0.655613\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.61101e7 | −1.19153 | −0.595766 | − | 0.803158i | \(-0.703151\pi\) | ||||
−0.595766 | + | 0.803158i | \(0.703151\pi\) | |||||||
\(110\) | −1.06266e6 | −0.0761238 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.17829e6 | 0.0792484 | ||||||||
\(113\) | −7.15228e6 | −0.466305 | −0.233153 | − | 0.972440i | \(-0.574904\pi\) | ||||
−0.233153 | + | 0.972440i | \(0.574904\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.15011e7 | −2.54459 | ||||||||
\(116\) | 6529.14 | 0.000388376 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1.69349e7 | −0.948849 | ||||||||
\(119\) | −4.89149e6 | −0.266089 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.93725e7 | −0.994116 | ||||||||
\(122\) | −1.88088e6 | −0.0937784 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 195783. | 0.00922146 | ||||||||
\(125\) | 2.15382e6 | 0.0986336 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.95885e7 | −0.848569 | −0.424284 | − | 0.905529i | \(-0.639474\pi\) | ||||
−0.424284 | + | 0.905529i | \(0.639474\pi\) | |||||||
\(128\) | −8.04179e6 | −0.338936 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −5.96874e6 | −0.238276 | ||||||||
\(131\) | −3.84474e7 | −1.49423 | −0.747115 | − | 0.664695i | \(-0.768562\pi\) | ||||
−0.747115 | + | 0.664695i | \(0.768562\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.15503e7 | −0.425709 | ||||||||
\(134\) | 5.95719e6 | 0.213882 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.08773e7 | −0.711686 | ||||||||
\(137\) | −5.35857e7 | −1.78044 | −0.890219 | − | 0.455533i | \(-0.849449\pi\) | ||||
−0.890219 | + | 0.455533i | \(0.849449\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.44467e7 | −0.772091 | −0.386046 | − | 0.922480i | \(-0.626159\pi\) | ||||
−0.386046 | + | 0.922480i | \(0.626159\pi\) | |||||||
\(140\) | 9.61815e6 | 0.296240 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −2.00158e6 | −0.0586628 | ||||||||
\(143\) | 644063. | 0.0184184 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −39139.0 | −0.00106616 | ||||||||
\(146\) | −3.32240e7 | −0.883522 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.87932e7 | 0.476523 | ||||||||
\(149\) | −6.83645e7 | −1.69308 | −0.846542 | − | 0.532321i | \(-0.821320\pi\) | ||||
−0.846542 | + | 0.532321i | \(0.821320\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.48140e7 | 1.05924 | 0.529620 | − | 0.848235i | \(-0.322335\pi\) | ||||
0.529620 | + | 0.848235i | \(0.322335\pi\) | |||||||
\(152\) | −4.92978e7 | −1.13861 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 943077. | 0.0208077 | ||||||||
\(155\) | −1.17362e6 | −0.0253144 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.45418e7 | 0.918585 | 0.459293 | − | 0.888285i | \(-0.348103\pi\) | ||||
0.459293 | + | 0.888285i | \(0.348103\pi\) | |||||||
\(158\) | 5.15478e7 | 1.03970 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 6.79889e7 | 1.31225 | ||||||||
\(161\) | 3.68308e7 | 0.695538 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.04717e7 | −0.370251 | −0.185126 | − | 0.982715i | \(-0.559269\pi\) | ||||
−0.185126 | + | 0.982715i | \(0.559269\pi\) | |||||||
\(164\) | −4.56565e6 | −0.0808256 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.23209e7 | −0.209057 | ||||||||
\(167\) | −9.99656e6 | −0.166090 | −0.0830449 | − | 0.996546i | \(-0.526464\pi\) | ||||
−0.0830449 | + | 0.996546i | \(0.526464\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.91310e7 | −0.942348 | ||||||||
\(170\) | 4.30262e7 | 0.671678 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 5.33191e6 | 0.0798975 | ||||||||
\(173\) | −9.15039e7 | −1.34363 | −0.671813 | − | 0.740721i | \(-0.734484\pi\) | ||||
−0.671813 | + | 0.740721i | \(0.734484\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.97838e7 | −0.420094 | ||||||||
\(176\) | 1.11838e6 | 0.0154631 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −7.89047e7 | −1.04866 | ||||||||
\(179\) | 7.48516e7 | 0.975474 | 0.487737 | − | 0.872991i | \(-0.337823\pi\) | ||||
0.487737 | + | 0.872991i | \(0.337823\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.08411e7 | −0.135894 | −0.0679470 | − | 0.997689i | \(-0.521645\pi\) | ||||
−0.0679470 | + | 0.997689i | \(0.521645\pi\) | |||||||
\(182\) | 5.29706e6 | 0.0651305 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.57197e8 | 1.86030 | ||||||||
\(185\) | −1.12656e8 | −1.30813 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.64278e6 | −0.0519198 | ||||||||
\(188\) | 9.74179e6 | 0.106927 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1.01598e8 | 1.07460 | ||||||||
\(191\) | 1.37400e8 | 1.42682 | 0.713410 | − | 0.700747i | \(-0.247150\pi\) | ||||
0.713410 | + | 0.700747i | \(0.247150\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.16548e8 | −1.16695 | −0.583477 | − | 0.812129i | \(-0.698308\pi\) | ||||
−0.583477 | + | 0.812129i | \(0.698308\pi\) | |||||||
\(194\) | −1.48915e7 | −0.146431 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 4.66928e7 | 0.442949 | ||||||||
\(197\) | 1.79080e8 | 1.66884 | 0.834422 | − | 0.551126i | \(-0.185802\pi\) | ||||
0.834422 | + | 0.551126i | \(0.185802\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.30708e8 | −1.17575 | −0.587875 | − | 0.808952i | \(-0.700035\pi\) | ||||
−0.587875 | + | 0.808952i | \(0.700035\pi\) | |||||||
\(200\) | −1.27120e8 | −1.12359 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 6.86825e7 | 0.586295 | ||||||||
\(203\) | 34734.5 | 0.000291424 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.73688e7 | 0.221880 | ||||||||
\(206\) | 1.54600e8 | 1.23218 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 6.28172e6 | 0.0484013 | ||||||||
\(209\) | −1.09631e7 | −0.0830653 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.03753e7 | 0.222604 | 0.111302 | − | 0.993787i | \(-0.464498\pi\) | ||||
0.111302 | + | 0.993787i | \(0.464498\pi\) | |||||||
\(212\) | −3.01972e7 | −0.217666 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −9.29126e7 | −0.648076 | ||||||||
\(215\) | −3.19622e7 | −0.219332 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.04155e6 | 0.00691945 | ||||||||
\(218\) | −1.25760e8 | −0.822137 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 9.12912e6 | 0.0578029 | ||||||||
\(221\) | −2.60775e7 | −0.162515 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8.68403e7 | 0.524390 | 0.262195 | − | 0.965015i | \(-0.415554\pi\) | ||||
0.262195 | + | 0.965015i | \(0.415554\pi\) | |||||||
\(224\) | −6.03379e7 | −0.358692 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −5.58326e7 | −0.321743 | ||||||||
\(227\) | −1.67604e8 | −0.951028 | −0.475514 | − | 0.879708i | \(-0.657738\pi\) | ||||
−0.475514 | + | 0.879708i | \(0.657738\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.15619e8 | 0.636218 | 0.318109 | − | 0.948054i | \(-0.396952\pi\) | ||||
0.318109 | + | 0.948054i | \(0.396952\pi\) | |||||||
\(230\) | −3.23969e8 | −1.75572 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 148250. | 0.000779448 0 | ||||||||
\(233\) | −1.02835e8 | −0.532592 | −0.266296 | − | 0.963891i | \(-0.585800\pi\) | ||||
−0.266296 | + | 0.963891i | \(0.585800\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.83973e7 | −0.293532 | ||||||||
\(236\) | 1.45485e8 | 0.720486 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −3.81843e7 | −0.183597 | ||||||||
\(239\) | −2.55890e8 | −1.21244 | −0.606221 | − | 0.795296i | \(-0.707315\pi\) | ||||
−0.606221 | + | 0.795296i | \(0.707315\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.95565e6 | −0.00899976 | −0.00449988 | − | 0.999990i | \(-0.501432\pi\) | ||||
−0.00449988 | + | 0.999990i | \(0.501432\pi\) | |||||||
\(242\) | −1.51227e8 | −0.685923 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1.61583e7 | 0.0712085 | ||||||||
\(245\) | −2.79900e8 | −1.21597 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6.15771e7 | −0.260004 | ||||||||
\(248\) | 4.44544e6 | 0.0185069 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1.68133e7 | 0.0680556 | ||||||||
\(251\) | 2.99606e8 | 1.19589 | 0.597946 | − | 0.801536i | \(-0.295984\pi\) | ||||
0.597946 | + | 0.801536i | \(0.295984\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.49582e7 | 0.135715 | ||||||||
\(254\) | −1.52913e8 | −0.585498 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −2.85878e8 | −1.06498 | ||||||||
\(257\) | 3.65657e8 | 1.34372 | 0.671859 | − | 0.740679i | \(-0.265496\pi\) | ||||
0.671859 | + | 0.740679i | \(0.265496\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 9.99782e7 | 0.357566 | ||||||||
\(260\) | 5.12763e7 | 0.180930 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −3.00131e8 | −1.03099 | ||||||||
\(263\) | −4.38062e8 | −1.48488 | −0.742438 | − | 0.669914i | \(-0.766331\pi\) | ||||
−0.742438 | + | 0.669914i | \(0.766331\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.81017e8 | 0.597529 | ||||||||
\(266\) | −9.01649e7 | −0.293732 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −5.11771e7 | −0.162407 | ||||||||
\(269\) | 6.37770e7 | 0.199771 | 0.0998853 | − | 0.994999i | \(-0.468152\pi\) | ||||
0.0998853 | + | 0.994999i | \(0.468152\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.49200e8 | 1.06582 | 0.532908 | − | 0.846173i | \(-0.321099\pi\) | ||||
0.532908 | + | 0.846173i | \(0.321099\pi\) | |||||||
\(272\) | −4.52823e7 | −0.136439 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −4.18304e8 | −1.22847 | ||||||||
\(275\) | −2.82694e7 | −0.0819695 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.62910e8 | 0.743238 | 0.371619 | − | 0.928385i | \(-0.378803\pi\) | ||||
0.371619 | + | 0.928385i | \(0.378803\pi\) | |||||||
\(278\) | −1.90838e8 | −0.532730 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 2.18389e8 | 0.594535 | ||||||||
\(281\) | 3.13673e8 | 0.843345 | 0.421673 | − | 0.906748i | \(-0.361443\pi\) | ||||
0.421673 | + | 0.906748i | \(0.361443\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3.05065e7 | 0.0800093 | 0.0400046 | − | 0.999199i | \(-0.487263\pi\) | ||||
0.0400046 | + | 0.999199i | \(0.487263\pi\) | |||||||
\(284\) | 1.71951e7 | 0.0445442 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 5.02773e6 | 0.0127084 | ||||||||
\(287\) | −2.42889e7 | −0.0606487 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.22357e8 | −0.541886 | ||||||||
\(290\) | −305529. | −0.000735631 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 2.85421e8 | 0.670882 | ||||||||
\(293\) | −6.50794e8 | −1.51149 | −0.755747 | − | 0.654863i | \(-0.772726\pi\) | ||||
−0.755747 | + | 0.654863i | \(0.772726\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −8.72110e8 | −1.97785 | ||||||||
\(296\) | 4.26716e8 | 0.956353 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −5.33672e8 | −1.16820 | ||||||||
\(299\) | 1.96353e8 | 0.424803 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.83654e7 | 0.0599523 | ||||||||
\(302\) | 3.49830e8 | 0.730858 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1.06926e8 | −0.218285 | ||||||||
\(305\) | −9.68611e7 | −0.195479 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.64397e8 | −0.324273 | −0.162136 | − | 0.986768i | \(-0.551838\pi\) | ||||
−0.162136 | + | 0.986768i | \(0.551838\pi\) | |||||||
\(308\) | −8.10179e6 | −0.0157999 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −9.16163e6 | −0.0174665 | ||||||||
\(311\) | −6.67878e7 | −0.125903 | −0.0629515 | − | 0.998017i | \(-0.520051\pi\) | ||||
−0.0629515 | + | 0.998017i | \(0.520051\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.66247e8 | 0.675101 | 0.337550 | − | 0.941307i | \(-0.390402\pi\) | ||||
0.337550 | + | 0.941307i | \(0.390402\pi\) | |||||||
\(314\) | 3.47706e8 | 0.633808 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4.42837e8 | −0.789476 | ||||||||
\(317\) | −8.45942e8 | −1.49153 | −0.745767 | − | 0.666206i | \(-0.767917\pi\) | ||||
−0.745767 | + | 0.666206i | \(0.767917\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 32968.5 | 5.68632e−5 0 | ||||||||
\(320\) | 7.00686e8 | 1.19536 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 2.87511e8 | 0.479910 | ||||||||
\(323\) | 4.43883e8 | 0.732926 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.58783e8 | −0.256574 | ||||||||
\(326\) | −1.59807e8 | −0.255467 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −1.03667e8 | −0.162212 | ||||||||
\(329\) | 5.18256e7 | 0.0802341 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.56474e8 | −0.237162 | −0.118581 | − | 0.992944i | \(-0.537835\pi\) | ||||
−0.118581 | + | 0.992944i | \(0.537835\pi\) | |||||||
\(332\) | 1.05847e8 | 0.158743 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −7.80358e7 | −0.114599 | ||||||||
\(335\) | 3.06781e8 | 0.445833 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.10367e9 | 1.57085 | 0.785424 | − | 0.618958i | \(-0.212445\pi\) | ||||
0.785424 | + | 0.618958i | \(0.212445\pi\) | |||||||
\(338\) | −4.61592e8 | −0.650205 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −3.69629e8 | −0.510024 | ||||||||
\(341\) | 988595. | 0.00135014 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5.42214e8 | 0.725506 | ||||||||
\(344\) | 1.21066e8 | 0.160349 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −7.14304e8 | −0.927079 | ||||||||
\(347\) | 7.51448e7 | 0.0965485 | 0.0482743 | − | 0.998834i | \(-0.484628\pi\) | ||||
0.0482743 | + | 0.998834i | \(0.484628\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.40370e8 | 0.554534 | 0.277267 | − | 0.960793i | \(-0.410571\pi\) | ||||
0.277267 | + | 0.960793i | \(0.410571\pi\) | |||||||
\(350\) | −2.32500e8 | −0.289858 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −5.72701e7 | −0.0699888 | ||||||||
\(353\) | 8.89528e7 | 0.107634 | 0.0538168 | − | 0.998551i | \(-0.482861\pi\) | ||||
0.0538168 | + | 0.998551i | \(0.482861\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.03076e8 | −0.122281 | ||||||||
\(356\) | 6.77855e8 | 0.796273 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 5.84312e8 | 0.673061 | ||||||||
\(359\) | 1.09248e9 | 1.24619 | 0.623095 | − | 0.782146i | \(-0.285875\pi\) | ||||
0.623095 | + | 0.782146i | \(0.285875\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.54275e8 | 0.172591 | ||||||||
\(362\) | −8.46289e7 | −0.0937645 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −4.55060e7 | −0.0494554 | ||||||||
\(365\) | −1.71096e9 | −1.84168 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5.91559e8 | −0.624693 | −0.312346 | − | 0.949968i | \(-0.601115\pi\) | ||||
−0.312346 | + | 0.949968i | \(0.601115\pi\) | |||||||
\(368\) | 3.40957e8 | 0.356642 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −8.79422e8 | −0.902591 | ||||||||
\(371\) | −1.60647e8 | −0.163329 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.17638e9 | 1.17373 | 0.586863 | − | 0.809686i | \(-0.300363\pi\) | ||||
0.586863 | + | 0.809686i | \(0.300363\pi\) | |||||||
\(374\) | −3.62428e7 | −0.0358238 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2.21196e8 | 0.214595 | ||||||||
\(377\) | 185177. | 0.000177988 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.58878e9 | 1.49908 | 0.749541 | − | 0.661958i | \(-0.230274\pi\) | ||||
0.749541 | + | 0.661958i | \(0.230274\pi\) | |||||||
\(380\) | −8.72810e8 | −0.815975 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 1.07258e9 | 0.984482 | ||||||||
\(383\) | 1.52083e9 | 1.38320 | 0.691599 | − | 0.722281i | \(-0.256906\pi\) | ||||
0.691599 | + | 0.722281i | \(0.256906\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.85662e7 | 0.0433732 | ||||||||
\(386\) | −9.09805e8 | −0.805179 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1.27930e8 | 0.111189 | ||||||||
\(389\) | −1.81957e9 | −1.56728 | −0.783639 | − | 0.621217i | \(-0.786639\pi\) | ||||
−0.783639 | + | 0.621217i | \(0.786639\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.41542e9 | −1.19748 | ||||||||
\(392\) | 1.06020e9 | 0.888971 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 1.39795e9 | 1.15147 | ||||||||
\(395\) | 2.65459e9 | 2.16724 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.11509e9 | 1.69653 | 0.848265 | − | 0.529571i | \(-0.177647\pi\) | ||||
0.848265 | + | 0.529571i | \(0.177647\pi\) | |||||||
\(398\) | −1.02034e9 | −0.811248 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.75719e8 | −0.215406 | ||||||||
\(401\) | 2.18744e9 | 1.69407 | 0.847034 | − | 0.531539i | \(-0.178386\pi\) | ||||
0.847034 | + | 0.531539i | \(0.178386\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.55272e6 | 0.00422609 | ||||||||
\(404\) | −5.90038e8 | −0.445190 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 271147. | 0.000201078 0 | ||||||||
\(407\) | 9.48949e7 | 0.0697690 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.16511e9 | −0.842045 | −0.421022 | − | 0.907050i | \(-0.638329\pi\) | ||||
−0.421022 | + | 0.907050i | \(0.638329\pi\) | |||||||
\(410\) | 2.13648e8 | 0.153093 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −1.32814e9 | −0.935629 | ||||||||
\(413\) | 7.73968e8 | 0.540627 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6.34499e8 | −0.435776 | ||||||||
\(416\) | −3.21673e8 | −0.219073 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −8.55805e7 | −0.0573136 | ||||||||
\(419\) | 9.59686e8 | 0.637353 | 0.318677 | − | 0.947864i | \(-0.396762\pi\) | ||||
0.318677 | + | 0.947864i | \(0.396762\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.02361e7 | −0.00668572 | −0.00334286 | − | 0.999994i | \(-0.501064\pi\) | ||||
−0.00334286 | + | 0.999994i | \(0.501064\pi\) | |||||||
\(422\) | 2.37118e8 | 0.153593 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −6.85655e8 | −0.436843 | ||||||||
\(425\) | 1.14460e9 | 0.723258 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 8.59610e7 | 0.0534323 | ||||||||
\(428\) | 7.98194e8 | 0.492102 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −2.49505e8 | −0.151335 | ||||||||
\(431\) | 3.14206e9 | 1.89036 | 0.945179 | − | 0.326552i | \(-0.105887\pi\) | ||||
0.945179 | + | 0.326552i | \(0.105887\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.31364e9 | −1.36958 | −0.684792 | − | 0.728739i | \(-0.740107\pi\) | ||||
−0.684792 | + | 0.728739i | \(0.740107\pi\) | |||||||
\(434\) | 8.13063e6 | 0.00477431 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.08038e9 | 0.624271 | ||||||||
\(437\) | −3.34225e9 | −1.91582 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.64208e9 | 0.926337 | 0.463168 | − | 0.886270i | \(-0.346713\pi\) | ||||
0.463168 | + | 0.886270i | \(0.346713\pi\) | |||||||
\(440\) | 2.07285e8 | 0.116007 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −2.03568e8 | −0.112133 | ||||||||
\(443\) | −7.12250e8 | −0.389242 | −0.194621 | − | 0.980879i | \(-0.562348\pi\) | ||||
−0.194621 | + | 0.980879i | \(0.562348\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4.06341e9 | −2.18590 | ||||||||
\(446\) | 6.77899e8 | 0.361820 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −6.21835e8 | −0.326740 | ||||||||
\(449\) | −2.15899e9 | −1.12561 | −0.562805 | − | 0.826590i | \(-0.690278\pi\) | ||||
−0.562805 | + | 0.826590i | \(0.690278\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.30540e7 | −0.0118339 | ||||||||
\(452\) | 4.79647e8 | 0.244308 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −1.30836e9 | −0.656193 | ||||||||
\(455\) | 2.72786e8 | 0.135763 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.05753e9 | −0.518308 | −0.259154 | − | 0.965836i | \(-0.583444\pi\) | ||||
−0.259154 | + | 0.965836i | \(0.583444\pi\) | |||||||
\(458\) | 9.02555e8 | 0.438980 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 2.78315e9 | 1.33317 | ||||||||
\(461\) | 2.93548e9 | 1.39549 | 0.697743 | − | 0.716348i | \(-0.254188\pi\) | ||||
0.697743 | + | 0.716348i | \(0.254188\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.80303e9 | 1.31248 | 0.656242 | − | 0.754550i | \(-0.272145\pi\) | ||||
0.656242 | + | 0.754550i | \(0.272145\pi\) | |||||||
\(464\) | 321551. | 0.000149429 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −8.02756e8 | −0.367479 | ||||||||
\(467\) | −1.35420e9 | −0.615281 | −0.307640 | − | 0.951503i | \(-0.599539\pi\) | ||||
−0.307640 | + | 0.951503i | \(0.599539\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.72258e8 | −0.121864 | ||||||||
\(470\) | −4.55865e8 | −0.202532 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 3.30337e9 | 1.44597 | ||||||||
\(473\) | 2.69231e7 | 0.0116980 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.70276e9 | 1.15712 | ||||||||
\(476\) | 3.28034e8 | 0.139410 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −1.99755e9 | −0.836565 | ||||||||
\(479\) | −1.17660e9 | −0.489165 | −0.244583 | − | 0.969628i | \(-0.578651\pi\) | ||||
−0.244583 | + | 0.969628i | \(0.578651\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.33004e8 | 0.218385 | ||||||||
\(482\) | −1.52663e7 | −0.00620969 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.29916e9 | 0.520840 | ||||||||
\(485\) | −7.66879e8 | −0.305233 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.73453e9 | −0.680504 | −0.340252 | − | 0.940334i | \(-0.610512\pi\) | ||||
−0.340252 | + | 0.940334i | \(0.610512\pi\) | |||||||
\(488\) | 3.66889e8 | 0.142911 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −2.18498e9 | −0.838997 | ||||||||
\(491\) | −7.94788e8 | −0.303016 | −0.151508 | − | 0.988456i | \(-0.548413\pi\) | ||||
−0.151508 | + | 0.988456i | \(0.548413\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.33486e6 | −0.000501732 0 | ||||||||
\(494\) | −4.80687e8 | −0.179398 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 9.64204e6 | 0.00354799 | ||||||||
\(497\) | 9.14769e7 | 0.0334244 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.73492e8 | −0.0985354 | −0.0492677 | − | 0.998786i | \(-0.515689\pi\) | ||||
−0.0492677 | + | 0.998786i | \(0.515689\pi\) | |||||||
\(500\) | −1.44440e8 | −0.0516764 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 2.33880e9 | 0.825146 | ||||||||
\(503\) | −3.20927e9 | −1.12439 | −0.562197 | − | 0.827004i | \(-0.690044\pi\) | ||||
−0.562197 | + | 0.827004i | \(0.690044\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.53699e9 | 1.22212 | ||||||||
\(506\) | 2.72893e8 | 0.0936409 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1.31364e9 | 0.444585 | ||||||||
\(509\) | 2.06801e9 | 0.695090 | 0.347545 | − | 0.937663i | \(-0.387015\pi\) | ||||
0.347545 | + | 0.937663i | \(0.387015\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.51842e9 | 0.503406 | ||||||||
\(512\) | −1.20229e9 | −0.395881 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 2.85442e9 | 0.927143 | ||||||||
\(515\) | 7.96155e9 | 2.56846 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.91906e7 | 0.0156554 | ||||||||
\(518\) | 7.80457e8 | 0.246715 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1.16428e9 | 0.363115 | ||||||||
\(521\) | 3.73056e8 | 0.115569 | 0.0577846 | − | 0.998329i | \(-0.481596\pi\) | ||||
0.0577846 | + | 0.998329i | \(0.481596\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3.23366e9 | 0.988414 | 0.494207 | − | 0.869344i | \(-0.335459\pi\) | ||||
0.494207 | + | 0.869344i | \(0.335459\pi\) | |||||||
\(524\) | 2.57837e9 | 0.782862 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −3.41963e9 | −1.02454 | ||||||||
\(527\) | −4.00273e7 | −0.0119129 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.25272e9 | 2.13013 | ||||||||
\(530\) | 1.41307e9 | 0.412285 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 7.74589e8 | 0.223039 | ||||||||
\(533\) | −1.29489e8 | −0.0370414 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4.78478e9 | −1.35090 | ||||||||
\(536\) | −1.16202e9 | −0.325940 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 4.97861e8 | 0.137838 | ||||||||
\(539\) | 2.35772e8 | 0.0648533 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6.33940e9 | −1.72131 | −0.860653 | − | 0.509192i | \(-0.829944\pi\) | ||||
−0.860653 | + | 0.509192i | \(0.829944\pi\) | |||||||
\(542\) | 2.72595e9 | 0.735395 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 2.31881e9 | 0.617545 | ||||||||
\(545\) | −6.47633e9 | −1.71373 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.18850e9 | 0.571731 | 0.285865 | − | 0.958270i | \(-0.407719\pi\) | ||||
0.285865 | + | 0.958270i | \(0.407719\pi\) | |||||||
\(548\) | 3.59357e9 | 0.932812 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −2.20679e8 | −0.0565576 | ||||||||
\(551\) | −3.15202e6 | −0.000802710 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.35586e9 | −0.592395 | ||||||||
\(554\) | 2.05235e9 | 0.512822 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.63945e9 | 0.404516 | ||||||||
\(557\) | 2.65106e9 | 0.650019 | 0.325009 | − | 0.945711i | \(-0.394633\pi\) | ||||
0.325009 | + | 0.945711i | \(0.394633\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.51221e8 | 0.0366161 | ||||||||
\(560\) | 4.73680e8 | 0.113979 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 2.44862e9 | 0.581894 | ||||||||
\(563\) | 4.33945e9 | 1.02484 | 0.512419 | − | 0.858736i | \(-0.328749\pi\) | ||||
0.512419 | + | 0.858736i | \(0.328749\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.87525e9 | −0.670666 | ||||||||
\(566\) | 2.38142e8 | 0.0552051 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 3.90432e8 | 0.0893976 | ||||||||
\(569\) | −6.16980e8 | −0.140404 | −0.0702018 | − | 0.997533i | \(-0.522364\pi\) | ||||
−0.0702018 | + | 0.997533i | \(0.522364\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.73913e9 | 1.29009 | 0.645045 | − | 0.764145i | \(-0.276839\pi\) | ||||
0.645045 | + | 0.764145i | \(0.276839\pi\) | |||||||
\(572\) | −4.31923e7 | −0.00964983 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −1.89606e8 | −0.0418466 | ||||||||
\(575\) | −8.61837e9 | −1.89055 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5.29584e9 | 1.14768 | 0.573838 | − | 0.818969i | \(-0.305454\pi\) | ||||
0.573838 | + | 0.818969i | \(0.305454\pi\) | |||||||
\(578\) | −1.73578e9 | −0.373892 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 2.62474e6 | 0.000558585 0 | ||||||||
\(581\) | 5.63097e8 | 0.119115 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.52479e8 | −0.0318691 | ||||||||
\(584\) | 6.48075e9 | 1.34642 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −5.08027e9 | −1.04291 | ||||||||
\(587\) | −4.99464e8 | −0.101923 | −0.0509613 | − | 0.998701i | \(-0.516229\pi\) | ||||
−0.0509613 | + | 0.998701i | \(0.516229\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −9.45168e7 | −0.0190592 | ||||||||
\(590\) | −6.80793e9 | −1.36469 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 9.25536e8 | 0.183344 | ||||||||
\(593\) | 1.20268e9 | 0.236842 | 0.118421 | − | 0.992963i | \(-0.462217\pi\) | ||||
0.118421 | + | 0.992963i | \(0.462217\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.96640e9 | −0.382704 | ||||||||
\(596\) | 4.58467e9 | 0.887046 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 1.53278e9 | 0.293107 | ||||||||
\(599\) | 5.47286e9 | 1.04045 | 0.520224 | − | 0.854030i | \(-0.325849\pi\) | ||||
0.520224 | + | 0.854030i | \(0.325849\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4.60823e9 | −0.865912 | −0.432956 | − | 0.901415i | \(-0.642529\pi\) | ||||
−0.432956 | + | 0.901415i | \(0.642529\pi\) | |||||||
\(602\) | 2.21428e8 | 0.0413661 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −3.00532e9 | −0.554960 | ||||||||
\(605\) | −7.78784e9 | −1.42979 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 7.85259e9 | 1.42512 | 0.712562 | − | 0.701610i | \(-0.247535\pi\) | ||||
0.712562 | + | 0.701610i | \(0.247535\pi\) | |||||||
\(608\) | 5.47543e9 | 0.987997 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −7.56124e8 | −0.134877 | ||||||||
\(611\) | 2.76293e8 | 0.0490033 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.04035e10 | −1.82419 | −0.912095 | − | 0.409980i | \(-0.865536\pi\) | ||||
−0.912095 | + | 0.409980i | \(0.865536\pi\) | |||||||
\(614\) | −1.28333e9 | −0.223743 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.83959e8 | −0.0317094 | ||||||||
\(617\) | −2.89619e9 | −0.496397 | −0.248198 | − | 0.968709i | \(-0.579838\pi\) | ||||
−0.248198 | + | 0.968709i | \(0.579838\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.69036e9 | −0.286458 | −0.143229 | − | 0.989690i | \(-0.545749\pi\) | ||||
−0.143229 | + | 0.989690i | \(0.545749\pi\) | |||||||
\(620\) | 7.87057e7 | 0.0132628 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −5.21364e8 | −0.0868710 | ||||||||
\(623\) | 3.60614e9 | 0.597495 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −5.65624e9 | −0.926718 | ||||||||
\(626\) | 2.85902e9 | 0.465808 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −2.98707e9 | −0.481268 | ||||||||
\(629\) | −3.84220e9 | −0.615606 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3.25816e9 | −0.516261 | −0.258131 | − | 0.966110i | \(-0.583106\pi\) | ||||
−0.258131 | + | 0.966110i | \(0.583106\pi\) | |||||||
\(632\) | −1.00550e10 | −1.58443 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −6.60366e9 | −1.02913 | ||||||||
\(635\) | −7.87465e9 | −1.22046 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.32428e9 | 0.202998 | ||||||||
\(638\) | 257361. | 3.92347e−5 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −3.23284e9 | −0.487477 | ||||||||
\(641\) | −1.62115e9 | −0.243119 | −0.121560 | − | 0.992584i | \(-0.538790\pi\) | ||||
−0.121560 | + | 0.992584i | \(0.538790\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −4.87271e8 | −0.0722823 | −0.0361412 | − | 0.999347i | \(-0.511507\pi\) | ||||
−0.0361412 | + | 0.999347i | \(0.511507\pi\) | |||||||
\(644\) | −2.46995e9 | −0.364408 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 3.46507e9 | 0.505707 | ||||||||
\(647\) | −1.32422e10 | −1.92219 | −0.961095 | − | 0.276219i | \(-0.910918\pi\) | ||||
−0.961095 | + | 0.276219i | \(0.910918\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7.34617e8 | 0.105488 | ||||||||
\(650\) | −1.23950e9 | −0.177032 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1.37287e9 | 0.193983 | ||||||||
\(653\) | −1.05133e10 | −1.47755 | −0.738774 | − | 0.673953i | \(-0.764595\pi\) | ||||
−0.738774 | + | 0.673953i | \(0.764595\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.54560e10 | −2.14908 | ||||||||
\(656\) | −2.24852e8 | −0.0310980 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 4.04565e8 | 0.0553602 | ||||||||
\(659\) | −5.82980e9 | −0.793514 | −0.396757 | − | 0.917924i | \(-0.629864\pi\) | ||||
−0.396757 | + | 0.917924i | \(0.629864\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.98936e9 | 0.671954 | 0.335977 | − | 0.941870i | \(-0.390934\pi\) | ||||
0.335977 | + | 0.941870i | \(0.390934\pi\) | |||||||
\(662\) | −1.22148e9 | −0.163638 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 2.40335e9 | 0.318587 | ||||||||
\(665\) | −4.64328e9 | −0.612279 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.00509e7 | 0.00131149 | ||||||||
\(668\) | 6.70391e8 | 0.0870183 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 2.39482e9 | 0.307617 | ||||||||
\(671\) | 8.15904e7 | 0.0104258 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −9.45755e9 | −1.19599 | −0.597993 | − | 0.801502i | \(-0.704035\pi\) | ||||
−0.597993 | + | 0.801502i | \(0.704035\pi\) | |||||||
\(674\) | 8.61554e9 | 1.08386 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 3.96545e9 | 0.493718 | ||||||||
\(677\) | 1.17413e10 | 1.45431 | 0.727155 | − | 0.686474i | \(-0.240842\pi\) | ||||
0.727155 | + | 0.686474i | \(0.240842\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6.80579e8 | 0.0834324 | ||||||||
\(680\) | −8.39277e9 | −1.02359 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 7.71724e6 | 0.000931572 0 | ||||||||
\(683\) | −8.01180e9 | −0.962183 | −0.481091 | − | 0.876670i | \(-0.659759\pi\) | ||||
−0.481091 | + | 0.876670i | \(0.659759\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.15417e10 | −2.56072 | ||||||||
\(686\) | 4.23267e9 | 0.500587 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 2.62589e8 | 0.0307409 | ||||||||
\(689\) | −8.56440e8 | −0.0997538 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9.40691e9 | 1.08461 | 0.542305 | − | 0.840181i | \(-0.317552\pi\) | ||||
0.542305 | + | 0.840181i | \(0.317552\pi\) | |||||||
\(692\) | 6.13645e9 | 0.703956 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 5.86600e8 | 0.0666169 | ||||||||
\(695\) | −9.82769e9 | −1.11046 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 9.33433e8 | 0.104416 | ||||||||
\(698\) | 3.43765e9 | 0.382619 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 1.99736e9 | 0.220097 | ||||||||
\(701\) | −5.77903e9 | −0.633639 | −0.316819 | − | 0.948486i | \(-0.602615\pi\) | ||||
−0.316819 | + | 0.948486i | \(0.602615\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −9.07264e9 | −0.984895 | ||||||||
\(704\) | −5.90219e8 | −0.0637542 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 6.94389e8 | 0.0742654 | ||||||||
\(707\) | −3.13896e9 | −0.334055 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.04068e10 | 1.09662 | 0.548311 | − | 0.836274i | \(-0.315271\pi\) | ||||
0.548311 | + | 0.836274i | \(0.315271\pi\) | |||||||
\(710\) | −8.04642e8 | −0.0843721 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 1.53913e10 | 1.59807 | ||||||||
\(713\) | 3.01388e8 | 0.0311396 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.58916e8 | 0.0264904 | ||||||||
\(716\) | −5.01971e9 | −0.511073 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 8.52822e9 | 0.859851 | ||||||||
\(719\) | −1.83550e10 | −1.84164 | −0.920819 | − | 0.389991i | \(-0.872478\pi\) | ||||
−0.920819 | + | 0.389991i | \(0.872478\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7.06560e9 | −0.702063 | ||||||||
\(722\) | 1.20431e9 | 0.119085 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 7.27030e8 | 0.0711980 | ||||||||
\(725\) | −8.12784e6 | −0.000792122 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.38023e9 | 0.133223 | 0.0666116 | − | 0.997779i | \(-0.478781\pi\) | ||||
0.0666116 | + | 0.997779i | \(0.478781\pi\) | |||||||
\(728\) | −1.03325e9 | −0.0992539 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −1.33562e10 | −1.27073 | ||||||||
\(731\) | −1.09009e9 | −0.103217 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.24467e9 | 0.210518 | 0.105259 | − | 0.994445i | \(-0.466433\pi\) | ||||
0.105259 | + | 0.994445i | \(0.466433\pi\) | |||||||
\(734\) | −4.61787e9 | −0.431028 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.74597e10 | −1.61422 | ||||||||
\(737\) | −2.58415e8 | −0.0237784 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4.41123e9 | 0.402072 | 0.201036 | − | 0.979584i | \(-0.435569\pi\) | ||||
0.201036 | + | 0.979584i | \(0.435569\pi\) | |||||||
\(740\) | 7.55494e9 | 0.685362 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −1.25405e9 | −0.112694 | ||||||||
\(743\) | −1.31411e10 | −1.17536 | −0.587679 | − | 0.809094i | \(-0.699958\pi\) | ||||
−0.587679 | + | 0.809094i | \(0.699958\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.74828e10 | −2.43509 | ||||||||
\(746\) | 9.18315e9 | 0.809852 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 3.11355e8 | 0.0272020 | ||||||||
\(749\) | 4.24633e9 | 0.369256 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.90398e9 | 0.767087 | 0.383543 | − | 0.923523i | \(-0.374704\pi\) | ||||
0.383543 | + | 0.923523i | \(0.374704\pi\) | |||||||
\(752\) | 4.79769e8 | 0.0411405 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1.44554e6 | 0.000122809 0 | ||||||||
\(755\) | 1.80154e10 | 1.52346 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.98575e10 | −1.66375 | −0.831877 | − | 0.554960i | \(-0.812734\pi\) | ||||
−0.831877 | + | 0.554960i | \(0.812734\pi\) | |||||||
\(758\) | 1.24024e10 | 1.03434 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −1.98179e10 | −1.63761 | ||||||||
\(761\) | −4.10456e9 | −0.337614 | −0.168807 | − | 0.985649i | \(-0.553991\pi\) | ||||
−0.168807 | + | 0.985649i | \(0.553991\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.74753e9 | 0.468431 | ||||||||
\(764\) | −9.21432e9 | −0.747544 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.18720e10 | 0.954384 | ||||||||
\(767\) | 4.12618e9 | 0.330190 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.69512e10 | 1.34418 | 0.672091 | − | 0.740468i | \(-0.265396\pi\) | ||||
0.672091 | + | 0.740468i | \(0.265396\pi\) | |||||||
\(770\) | 3.79121e8 | 0.0299268 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 7.81595e9 | 0.611394 | ||||||||
\(773\) | −7.71790e8 | −0.0600995 | −0.0300498 | − | 0.999548i | \(-0.509567\pi\) | ||||
−0.0300498 | + | 0.999548i | \(0.509567\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.43722e8 | −0.0188078 | ||||||||
\(776\) | 2.90478e9 | 0.223150 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −1.42041e10 | −1.08140 | ||||||||
\(779\) | 2.20412e9 | 0.167053 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.68258e7 | 0.00652184 | ||||||||
\(782\) | −1.10492e10 | −0.826240 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 2.29955e9 | 0.170426 | ||||||||
\(785\) | 1.79060e10 | 1.32116 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.55107e10 | −1.13428 | −0.567139 | − | 0.823622i | \(-0.691950\pi\) | ||||
−0.567139 | + | 0.823622i | \(0.691950\pi\) | |||||||
\(788\) | −1.20095e10 | −0.874346 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 2.07224e10 | 1.49536 | ||||||||
\(791\) | 2.55169e9 | 0.183320 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.58275e8 | 0.0326340 | ||||||||
\(794\) | 1.65110e10 | 1.17058 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 8.76553e9 | 0.616003 | ||||||||
\(797\) | −1.44069e10 | −1.00801 | −0.504006 | − | 0.863700i | \(-0.668141\pi\) | ||||
−0.504006 | + | 0.863700i | \(0.668141\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.99168e9 | −0.138136 | ||||||||
\(800\) | 1.41190e10 | 0.974964 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 1.70757e10 | 1.16888 | ||||||||
\(803\) | 1.44122e9 | 0.0982256 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.48062e10 | 1.00036 | ||||||||
\(806\) | 4.33460e7 | 0.00291593 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −1.33974e10 | −0.893469 | ||||||||
\(809\) | 1.32032e10 | 0.876714 | 0.438357 | − | 0.898801i | \(-0.355560\pi\) | ||||
0.438357 | + | 0.898801i | \(0.355560\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.59038e10 | 1.70526 | 0.852629 | − | 0.522517i | \(-0.175007\pi\) | ||||
0.852629 | + | 0.522517i | \(0.175007\pi\) | |||||||
\(812\) | −2.32937e6 | −0.000152684 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 7.40775e8 | 0.0481394 | ||||||||
\(815\) | −8.22971e9 | −0.532516 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.57405e9 | −0.165135 | ||||||||
\(818\) | −9.09516e9 | −0.580997 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.83541e9 | −0.116248 | ||||||||
\(821\) | 1.80408e9 | 0.113777 | 0.0568885 | − | 0.998381i | \(-0.481882\pi\) | ||||
0.0568885 | + | 0.998381i | \(0.481882\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.15004e10 | 1.34445 | 0.672227 | − | 0.740345i | \(-0.265338\pi\) | ||||
0.672227 | + | 0.740345i | \(0.265338\pi\) | |||||||
\(824\) | −3.01566e10 | −1.87775 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 6.04181e9 | 0.373024 | ||||||||
\(827\) | −1.95017e10 | −1.19895 | −0.599477 | − | 0.800392i | \(-0.704625\pi\) | ||||
−0.599477 | + | 0.800392i | \(0.704625\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.50758e10 | 0.919049 | 0.459524 | − | 0.888165i | \(-0.348020\pi\) | ||||
0.459524 | + | 0.888165i | \(0.348020\pi\) | |||||||
\(830\) | −4.95307e9 | −0.300678 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −3.31513e9 | −0.199558 | ||||||||
\(833\) | −9.54619e9 | −0.572233 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4.01866e9 | −0.238880 | ||||||||
\(836\) | 7.35206e8 | 0.0435198 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 7.49157e9 | 0.439763 | ||||||||
\(839\) | 3.01700e10 | 1.76363 | 0.881816 | − | 0.471594i | \(-0.156321\pi\) | ||||
0.881816 | + | 0.471594i | \(0.156321\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.72499e10 | −0.999999 | ||||||||
\(842\) | −7.99060e7 | −0.00461304 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −2.03703e9 | −0.116627 | ||||||||
\(845\) | −2.37709e10 | −1.35534 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 6.91144e9 | 0.390820 | ||||||||
\(848\) | −1.48717e9 | −0.0837480 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 8.93507e9 | 0.499036 | ||||||||
\(851\) | 2.89302e10 | 1.60915 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.64145e9 | −0.0905534 | −0.0452767 | − | 0.998974i | \(-0.514417\pi\) | ||||
−0.0452767 | + | 0.998974i | \(0.514417\pi\) | |||||||
\(854\) | 6.71035e8 | 0.0368674 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.81237e10 | 0.987619 | ||||||||
\(857\) | 2.57589e10 | 1.39796 | 0.698981 | − | 0.715141i | \(-0.253637\pi\) | ||||
0.698981 | + | 0.715141i | \(0.253637\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.14742e10 | −1.15595 | −0.577977 | − | 0.816053i | \(-0.696158\pi\) | ||||
−0.577977 | + | 0.816053i | \(0.696158\pi\) | |||||||
\(860\) | 2.14345e9 | 0.114913 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 2.45278e10 | 1.30432 | ||||||||
\(863\) | 3.38483e9 | 0.179266 | 0.0896332 | − | 0.995975i | \(-0.471431\pi\) | ||||
0.0896332 | + | 0.995975i | \(0.471431\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3.67850e10 | −1.93248 | ||||||||
\(866\) | −1.80609e10 | −0.944990 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −6.98487e7 | −0.00362526 | ||||||||
\(869\) | −2.23608e9 | −0.115589 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.45146e9 | −0.0744290 | ||||||||
\(872\) | 2.45310e10 | 1.25287 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −2.60905e10 | −1.32188 | ||||||||
\(875\) | −7.68410e8 | −0.0387762 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2.37382e10 | −1.18836 | −0.594182 | − | 0.804331i | \(-0.702524\pi\) | ||||
−0.594182 | + | 0.804331i | \(0.702524\pi\) | |||||||
\(878\) | 1.28185e10 | 0.639157 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 4.49596e8 | 0.0222399 | ||||||||
\(881\) | 1.49518e10 | 0.736678 | 0.368339 | − | 0.929692i | \(-0.379927\pi\) | ||||
0.368339 | + | 0.929692i | \(0.379927\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.73527e10 | 1.33702 | 0.668510 | − | 0.743703i | \(-0.266932\pi\) | ||||
0.668510 | + | 0.743703i | \(0.266932\pi\) | |||||||
\(884\) | 1.74881e9 | 0.0851453 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −5.56002e9 | −0.268570 | ||||||||
\(887\) | −3.74606e10 | −1.80236 | −0.901181 | − | 0.433443i | \(-0.857299\pi\) | ||||
−0.901181 | + | 0.433443i | \(0.857299\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 6.98849e9 | 0.333601 | ||||||||
\(890\) | −3.17201e10 | −1.50823 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −5.82370e9 | −0.274740 | ||||||||
\(893\) | −4.70297e9 | −0.221000 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3.00907e10 | 1.40298 | ||||||||
\(896\) | 2.86903e9 | 0.133247 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −1.68536e10 | −0.776652 | ||||||||
\(899\) | 284234. | 1.30472e−5 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6.17372e9 | 0.281197 | ||||||||
\(902\) | −1.79965e8 | −0.00816519 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1.08908e10 | 0.490311 | ||||||||
\(905\) | −4.35819e9 | −0.195450 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −4.76936e9 | −0.212243 | −0.106122 | − | 0.994353i | \(-0.533843\pi\) | ||||
−0.106122 | + | 0.994353i | \(0.533843\pi\) | |||||||
\(908\) | 1.12399e10 | 0.498265 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 2.12944e9 | 0.0936743 | ||||||||
\(911\) | 4.59972e9 | 0.201566 | 0.100783 | − | 0.994908i | \(-0.467865\pi\) | ||||
0.100783 | + | 0.994908i | \(0.467865\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5.34467e8 | 0.0232420 | ||||||||
\(914\) | −8.25540e9 | −0.357624 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −7.75368e9 | −0.333329 | ||||||||
\(917\) | 1.37167e10 | 0.587432 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.59138e10 | 0.676348 | 0.338174 | − | 0.941084i | \(-0.390191\pi\) | ||||
0.338174 | + | 0.941084i | \(0.390191\pi\) | |||||||
\(920\) | 6.31941e10 | 2.67559 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 2.29151e10 | 0.962862 | ||||||||
\(923\) | 4.87682e8 | 0.0204141 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.33948e10 | −0.971903 | ||||||||
\(926\) | 2.18812e10 | 0.905592 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1.64659e7 | −0.000676344 0 | ||||||||
\(929\) | 2.22650e10 | 0.911102 | 0.455551 | − | 0.890210i | \(-0.349442\pi\) | ||||
0.455551 | + | 0.890210i | \(0.349442\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.25415e10 | −0.915502 | ||||||||
\(932\) | 6.89632e9 | 0.279037 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −1.05712e10 | −0.424533 | ||||||||
\(935\) | −1.86642e9 | −0.0746739 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.34525e10 | −0.931322 | −0.465661 | − | 0.884963i | \(-0.654183\pi\) | ||||
−0.465661 | + | 0.884963i | \(0.654183\pi\) | |||||||
\(938\) | −2.12532e9 | −0.0840842 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 3.91625e9 | 0.153788 | ||||||||
\(941\) | −2.99250e10 | −1.17077 | −0.585383 | − | 0.810757i | \(-0.699056\pi\) | ||||
−0.585383 | + | 0.810757i | \(0.699056\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −7.02836e9 | −0.272937 | ||||||||
\(944\) | 7.16492e9 | 0.277210 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.10169e8 | 0.00807143 | ||||||||
\(947\) | 2.94339e10 | 1.12622 | 0.563109 | − | 0.826383i | \(-0.309605\pi\) | ||||
0.563109 | + | 0.826383i | \(0.309605\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 8.09500e9 | 0.307457 | ||||||||
\(950\) | 2.10985e10 | 0.798396 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 7.44830e9 | 0.279787 | ||||||||
\(953\) | −3.72084e10 | −1.39257 | −0.696283 | − | 0.717767i | \(-0.745164\pi\) | ||||
−0.696283 | + | 0.717767i | \(0.745164\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5.52353e10 | 2.05213 | ||||||||
\(956\) | 1.71605e10 | 0.635226 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −9.18488e9 | −0.337516 | ||||||||
\(959\) | 1.91175e10 | 0.699949 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.75041e10 | −0.999690 | ||||||||
\(962\) | 4.16077e9 | 0.150682 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 1.31150e8 | 0.00471518 | ||||||||
\(965\) | −4.68528e10 | −1.67838 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.49635e10 | −0.532159 | −0.266080 | − | 0.963951i | \(-0.585728\pi\) | ||||
−0.266080 | + | 0.963951i | \(0.585728\pi\) | |||||||
\(968\) | 2.94987e10 | 1.04529 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −5.98647e9 | −0.210605 | ||||||||
\(971\) | −3.15367e10 | −1.10548 | −0.552738 | − | 0.833355i | \(-0.686417\pi\) | ||||
−0.552738 | + | 0.833355i | \(0.686417\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 8.72174e9 | 0.303535 | ||||||||
\(974\) | −1.35402e10 | −0.469536 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 7.95773e8 | 0.0273978 | ||||||||
\(977\) | −1.36797e10 | −0.469295 | −0.234648 | − | 0.972080i | \(-0.575394\pi\) | ||||
−0.234648 | + | 0.972080i | \(0.575394\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.42279e9 | 0.116584 | ||||||||
\(980\) | 1.87707e10 | 0.637073 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −6.20433e9 | −0.209076 | ||||||||
\(983\) | −1.28389e10 | −0.431112 | −0.215556 | − | 0.976491i | \(-0.569156\pi\) | ||||
−0.215556 | + | 0.976491i | \(0.569156\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 7.19910e10 | 2.40022 | ||||||||
\(986\) | −1.04203e7 | −0.000346187 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 4.12949e9 | 0.136222 | ||||||||
\(989\) | 8.20794e9 | 0.269803 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −5.51139e10 | −1.79889 | −0.899443 | − | 0.437038i | \(-0.856028\pi\) | ||||
−0.899443 | + | 0.437038i | \(0.856028\pi\) | |||||||
\(992\) | −4.93748e8 | −0.0160588 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 7.14093e8 | 0.0230623 | ||||||||
\(995\) | −5.25451e10 | −1.69103 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 5.87820e10 | 1.87850 | 0.939250 | − | 0.343234i | \(-0.111522\pi\) | ||||
0.939250 | + | 0.343234i | \(0.111522\pi\) | |||||||
\(998\) | −2.13495e9 | −0.0679878 | ||||||||
\(999\) | 0 | 0 |
(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 | 387.8.a.d.1.10 | 13 | ||
3.2 | odd | 2 | 43.8.a.b.1.4 | ✓ | 13 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.8.a.b.1.4 | ✓ | 13 | 3.2 | odd | 2 | ||
387.8.a.d.1.10 | 13 | 1.1 | even | 1 | trivial |