Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [15,10,Mod(1,15)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(15, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("15.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 15 = 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 15.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: | \(7.72553754246\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{241}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 60 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(8.26209\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 15.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −7.78626 | −0.344107 | −0.172054 | − | 0.985088i | \(-0.555040\pi\) | ||||
−0.172054 | + | 0.985088i | \(0.555040\pi\) | |||||||
\(3\) | −81.0000 | −0.577350 | ||||||||
\(4\) | −451.374 | −0.881590 | ||||||||
\(5\) | 625.000 | 0.447214 | ||||||||
\(6\) | 630.687 | 0.198671 | ||||||||
\(7\) | 1839.88 | 0.289633 | 0.144816 | − | 0.989459i | \(-0.453741\pi\) | ||||
0.144816 | + | 0.989459i | \(0.453741\pi\) | |||||||
\(8\) | 7501.08 | 0.647469 | ||||||||
\(9\) | 6561.00 | 0.333333 | ||||||||
\(10\) | −4866.41 | −0.153890 | ||||||||
\(11\) | 44385.9 | 0.914066 | 0.457033 | − | 0.889450i | \(-0.348912\pi\) | ||||
0.457033 | + | 0.889450i | \(0.348912\pi\) | |||||||
\(12\) | 36561.3 | 0.508986 | ||||||||
\(13\) | 136584. | 1.32634 | 0.663169 | − | 0.748470i | \(-0.269211\pi\) | ||||
0.663169 | + | 0.748470i | \(0.269211\pi\) | |||||||
\(14\) | −14325.8 | −0.0996648 | ||||||||
\(15\) | −50625.0 | −0.258199 | ||||||||
\(16\) | 172698. | 0.658791 | ||||||||
\(17\) | −253591. | −0.736399 | −0.368199 | − | 0.929747i | \(-0.620026\pi\) | ||||
−0.368199 | + | 0.929747i | \(0.620026\pi\) | |||||||
\(18\) | −51085.7 | −0.114702 | ||||||||
\(19\) | 85435.7 | 0.150400 | 0.0752001 | − | 0.997168i | \(-0.476040\pi\) | ||||
0.0752001 | + | 0.997168i | \(0.476040\pi\) | |||||||
\(20\) | −282109. | −0.394259 | ||||||||
\(21\) | −149030. | −0.167220 | ||||||||
\(22\) | −345600. | −0.314537 | ||||||||
\(23\) | −979409. | −0.729775 | −0.364887 | − | 0.931052i | \(-0.618892\pi\) | ||||
−0.364887 | + | 0.931052i | \(0.618892\pi\) | |||||||
\(24\) | −607588. | −0.373816 | ||||||||
\(25\) | 390625. | 0.200000 | ||||||||
\(26\) | −1.06348e6 | −0.456403 | ||||||||
\(27\) | −531441. | −0.192450 | ||||||||
\(28\) | −830473. | −0.255337 | ||||||||
\(29\) | 2.58640e6 | 0.679054 | 0.339527 | − | 0.940596i | \(-0.389733\pi\) | ||||
0.339527 | + | 0.940596i | \(0.389733\pi\) | |||||||
\(30\) | 394180. | 0.0888482 | ||||||||
\(31\) | 8.94787e6 | 1.74017 | 0.870085 | − | 0.492901i | \(-0.164064\pi\) | ||||
0.870085 | + | 0.492901i | \(0.164064\pi\) | |||||||
\(32\) | −5.18523e6 | −0.874164 | ||||||||
\(33\) | −3.59526e6 | −0.527736 | ||||||||
\(34\) | 1.97452e6 | 0.253400 | ||||||||
\(35\) | 1.14992e6 | 0.129528 | ||||||||
\(36\) | −2.96147e6 | −0.293863 | ||||||||
\(37\) | 1.56064e7 | 1.36897 | 0.684486 | − | 0.729026i | \(-0.260026\pi\) | ||||
0.684486 | + | 0.729026i | \(0.260026\pi\) | |||||||
\(38\) | −665225. | −0.0517538 | ||||||||
\(39\) | −1.10633e7 | −0.765761 | ||||||||
\(40\) | 4.68818e6 | 0.289557 | ||||||||
\(41\) | 2.44893e7 | 1.35347 | 0.676735 | − | 0.736227i | \(-0.263394\pi\) | ||||
0.676735 | + | 0.736227i | \(0.263394\pi\) | |||||||
\(42\) | 1.16039e6 | 0.0575415 | ||||||||
\(43\) | 1.27592e7 | 0.569135 | 0.284568 | − | 0.958656i | \(-0.408150\pi\) | ||||
0.284568 | + | 0.958656i | \(0.408150\pi\) | |||||||
\(44\) | −2.00346e7 | −0.805832 | ||||||||
\(45\) | 4.10062e6 | 0.149071 | ||||||||
\(46\) | 7.62593e6 | 0.251121 | ||||||||
\(47\) | −6.16764e7 | −1.84365 | −0.921825 | − | 0.387607i | \(-0.873302\pi\) | ||||
−0.921825 | + | 0.387607i | \(0.873302\pi\) | |||||||
\(48\) | −1.39886e7 | −0.380353 | ||||||||
\(49\) | −3.69685e7 | −0.916113 | ||||||||
\(50\) | −3.04151e6 | −0.0688215 | ||||||||
\(51\) | 2.05408e7 | 0.425160 | ||||||||
\(52\) | −6.16504e7 | −1.16929 | ||||||||
\(53\) | 5.70418e6 | 0.0993006 | 0.0496503 | − | 0.998767i | \(-0.484189\pi\) | ||||
0.0496503 | + | 0.998767i | \(0.484189\pi\) | |||||||
\(54\) | 4.13794e6 | 0.0662235 | ||||||||
\(55\) | 2.77412e7 | 0.408783 | ||||||||
\(56\) | 1.38011e7 | 0.187528 | ||||||||
\(57\) | −6.92029e6 | −0.0868336 | ||||||||
\(58\) | −2.01384e7 | −0.233668 | ||||||||
\(59\) | 8.35095e7 | 0.897226 | 0.448613 | − | 0.893726i | \(-0.351918\pi\) | ||||
0.448613 | + | 0.893726i | \(0.351918\pi\) | |||||||
\(60\) | 2.28508e7 | 0.227626 | ||||||||
\(61\) | 1.48622e8 | 1.37435 | 0.687177 | − | 0.726490i | \(-0.258850\pi\) | ||||
0.687177 | + | 0.726490i | \(0.258850\pi\) | |||||||
\(62\) | −6.96704e7 | −0.598806 | ||||||||
\(63\) | 1.20714e7 | 0.0965443 | ||||||||
\(64\) | −4.80479e7 | −0.357985 | ||||||||
\(65\) | 8.53649e7 | 0.593156 | ||||||||
\(66\) | 2.79936e7 | 0.181598 | ||||||||
\(67\) | −1.68003e8 | −1.01854 | −0.509272 | − | 0.860606i | \(-0.670085\pi\) | ||||
−0.509272 | + | 0.860606i | \(0.670085\pi\) | |||||||
\(68\) | 1.14464e8 | 0.649202 | ||||||||
\(69\) | 7.93321e7 | 0.421336 | ||||||||
\(70\) | −8.95360e6 | −0.0445714 | ||||||||
\(71\) | 2.10986e8 | 0.985349 | 0.492675 | − | 0.870214i | \(-0.336019\pi\) | ||||
0.492675 | + | 0.870214i | \(0.336019\pi\) | |||||||
\(72\) | 4.92146e7 | 0.215823 | ||||||||
\(73\) | −1.43534e8 | −0.591566 | −0.295783 | − | 0.955255i | \(-0.595580\pi\) | ||||
−0.295783 | + | 0.955255i | \(0.595580\pi\) | |||||||
\(74\) | −1.21515e8 | −0.471074 | ||||||||
\(75\) | −3.16406e7 | −0.115470 | ||||||||
\(76\) | −3.85635e7 | −0.132591 | ||||||||
\(77\) | 8.16646e7 | 0.264744 | ||||||||
\(78\) | 8.61416e7 | 0.263504 | ||||||||
\(79\) | −4.55960e8 | −1.31706 | −0.658529 | − | 0.752555i | \(-0.728821\pi\) | ||||
−0.658529 | + | 0.752555i | \(0.728821\pi\) | |||||||
\(80\) | 1.07936e8 | 0.294620 | ||||||||
\(81\) | 4.30467e7 | 0.111111 | ||||||||
\(82\) | −1.90680e8 | −0.465739 | ||||||||
\(83\) | −3.55106e8 | −0.821309 | −0.410655 | − | 0.911791i | \(-0.634700\pi\) | ||||
−0.410655 | + | 0.911791i | \(0.634700\pi\) | |||||||
\(84\) | 6.72683e7 | 0.147419 | ||||||||
\(85\) | −1.58494e8 | −0.329328 | ||||||||
\(86\) | −9.93465e7 | −0.195844 | ||||||||
\(87\) | −2.09498e8 | −0.392052 | ||||||||
\(88\) | 3.32942e8 | 0.591830 | ||||||||
\(89\) | −4.24540e8 | −0.717239 | −0.358620 | − | 0.933484i | \(-0.616752\pi\) | ||||
−0.358620 | + | 0.933484i | \(0.616752\pi\) | |||||||
\(90\) | −3.19285e7 | −0.0512965 | ||||||||
\(91\) | 2.51297e8 | 0.384151 | ||||||||
\(92\) | 4.42080e8 | 0.643362 | ||||||||
\(93\) | −7.24777e8 | −1.00469 | ||||||||
\(94\) | 4.80228e8 | 0.634413 | ||||||||
\(95\) | 5.33973e7 | 0.0672610 | ||||||||
\(96\) | 4.20003e8 | 0.504699 | ||||||||
\(97\) | 1.19905e9 | 1.37520 | 0.687598 | − | 0.726092i | \(-0.258665\pi\) | ||||
0.687598 | + | 0.726092i | \(0.258665\pi\) | |||||||
\(98\) | 2.87846e8 | 0.315241 | ||||||||
\(99\) | 2.91216e8 | 0.304689 | ||||||||
\(100\) | −1.76318e8 | −0.176318 | ||||||||
\(101\) | −1.77085e9 | −1.69331 | −0.846654 | − | 0.532144i | \(-0.821387\pi\) | ||||
−0.846654 | + | 0.532144i | \(0.821387\pi\) | |||||||
\(102\) | −1.59936e8 | −0.146301 | ||||||||
\(103\) | 3.03322e8 | 0.265544 | 0.132772 | − | 0.991147i | \(-0.457612\pi\) | ||||
0.132772 | + | 0.991147i | \(0.457612\pi\) | |||||||
\(104\) | 1.02453e9 | 0.858763 | ||||||||
\(105\) | −9.31438e7 | −0.0747829 | ||||||||
\(106\) | −4.44142e7 | −0.0341701 | ||||||||
\(107\) | −1.95414e8 | −0.144121 | −0.0720607 | − | 0.997400i | \(-0.522958\pi\) | ||||
−0.0720607 | + | 0.997400i | \(0.522958\pi\) | |||||||
\(108\) | 2.39879e8 | 0.169662 | ||||||||
\(109\) | 2.31494e9 | 1.57080 | 0.785401 | − | 0.618988i | \(-0.212457\pi\) | ||||
0.785401 | + | 0.618988i | \(0.212457\pi\) | |||||||
\(110\) | −2.16000e8 | −0.140665 | ||||||||
\(111\) | −1.26412e9 | −0.790377 | ||||||||
\(112\) | 3.17743e8 | 0.190808 | ||||||||
\(113\) | 1.31945e9 | 0.761270 | 0.380635 | − | 0.924725i | \(-0.375706\pi\) | ||||
0.380635 | + | 0.924725i | \(0.375706\pi\) | |||||||
\(114\) | 5.38832e7 | 0.0298801 | ||||||||
\(115\) | −6.12130e8 | −0.326365 | ||||||||
\(116\) | −1.16743e9 | −0.598648 | ||||||||
\(117\) | 8.96126e8 | 0.442113 | ||||||||
\(118\) | −6.50227e8 | −0.308742 | ||||||||
\(119\) | −4.66576e8 | −0.213285 | ||||||||
\(120\) | −3.79742e8 | −0.167176 | ||||||||
\(121\) | −3.87842e8 | −0.164483 | ||||||||
\(122\) | −1.15721e9 | −0.472925 | ||||||||
\(123\) | −1.98363e9 | −0.781426 | ||||||||
\(124\) | −4.03884e9 | −1.53412 | ||||||||
\(125\) | 2.44141e8 | 0.0894427 | ||||||||
\(126\) | −9.39914e7 | −0.0332216 | ||||||||
\(127\) | 3.18960e9 | 1.08798 | 0.543988 | − | 0.839093i | \(-0.316914\pi\) | ||||
0.543988 | + | 0.839093i | \(0.316914\pi\) | |||||||
\(128\) | 3.02895e9 | 0.997349 | ||||||||
\(129\) | −1.03350e9 | −0.328590 | ||||||||
\(130\) | −6.64673e8 | −0.204109 | ||||||||
\(131\) | −5.40115e9 | −1.60238 | −0.801190 | − | 0.598410i | \(-0.795799\pi\) | ||||
−0.801190 | + | 0.598410i | \(0.795799\pi\) | |||||||
\(132\) | 1.62281e9 | 0.465247 | ||||||||
\(133\) | 1.57191e8 | 0.0435608 | ||||||||
\(134\) | 1.30811e9 | 0.350488 | ||||||||
\(135\) | −3.32151e8 | −0.0860663 | ||||||||
\(136\) | −1.90220e9 | −0.476796 | ||||||||
\(137\) | 1.19903e7 | 0.00290795 | 0.00145398 | − | 0.999999i | \(-0.499537\pi\) | ||||
0.00145398 | + | 0.999999i | \(0.499537\pi\) | |||||||
\(138\) | −6.17701e8 | −0.144985 | ||||||||
\(139\) | 9.15482e8 | 0.208010 | 0.104005 | − | 0.994577i | \(-0.466834\pi\) | ||||
0.104005 | + | 0.994577i | \(0.466834\pi\) | |||||||
\(140\) | −5.19046e8 | −0.114190 | ||||||||
\(141\) | 4.99578e9 | 1.06443 | ||||||||
\(142\) | −1.64279e9 | −0.339066 | ||||||||
\(143\) | 6.06239e9 | 1.21236 | ||||||||
\(144\) | 1.13307e9 | 0.219597 | ||||||||
\(145\) | 1.61650e9 | 0.303682 | ||||||||
\(146\) | 1.11760e9 | 0.203562 | ||||||||
\(147\) | 2.99445e9 | 0.528918 | ||||||||
\(148\) | −7.04432e9 | −1.20687 | ||||||||
\(149\) | 5.00462e9 | 0.831827 | 0.415913 | − | 0.909404i | \(-0.363462\pi\) | ||||
0.415913 | + | 0.909404i | \(0.363462\pi\) | |||||||
\(150\) | 2.46362e8 | 0.0397341 | ||||||||
\(151\) | 3.20554e9 | 0.501770 | 0.250885 | − | 0.968017i | \(-0.419278\pi\) | ||||
0.250885 | + | 0.968017i | \(0.419278\pi\) | |||||||
\(152\) | 6.40860e8 | 0.0973794 | ||||||||
\(153\) | −1.66381e9 | −0.245466 | ||||||||
\(154\) | −6.35862e8 | −0.0911002 | ||||||||
\(155\) | 5.59242e9 | 0.778228 | ||||||||
\(156\) | 4.99368e9 | 0.675088 | ||||||||
\(157\) | −4.63430e8 | −0.0608745 | −0.0304373 | − | 0.999537i | \(-0.509690\pi\) | ||||
−0.0304373 | + | 0.999537i | \(0.509690\pi\) | |||||||
\(158\) | 3.55023e9 | 0.453210 | ||||||||
\(159\) | −4.62038e8 | −0.0573312 | ||||||||
\(160\) | −3.24077e9 | −0.390938 | ||||||||
\(161\) | −1.80199e9 | −0.211367 | ||||||||
\(162\) | −3.35173e8 | −0.0382342 | ||||||||
\(163\) | −1.27948e10 | −1.41968 | −0.709840 | − | 0.704363i | \(-0.751233\pi\) | ||||
−0.709840 | + | 0.704363i | \(0.751233\pi\) | |||||||
\(164\) | −1.10538e10 | −1.19320 | ||||||||
\(165\) | −2.24703e9 | −0.236011 | ||||||||
\(166\) | 2.76495e9 | 0.282619 | ||||||||
\(167\) | −1.85699e10 | −1.84750 | −0.923752 | − | 0.382992i | \(-0.874894\pi\) | ||||
−0.923752 | + | 0.382992i | \(0.874894\pi\) | |||||||
\(168\) | −1.11789e9 | −0.108269 | ||||||||
\(169\) | 8.05063e9 | 0.759171 | ||||||||
\(170\) | 1.23408e9 | 0.113324 | ||||||||
\(171\) | 5.60544e8 | 0.0501334 | ||||||||
\(172\) | −5.75917e9 | −0.501744 | ||||||||
\(173\) | 4.90746e9 | 0.416533 | 0.208266 | − | 0.978072i | \(-0.433218\pi\) | ||||
0.208266 | + | 0.978072i | \(0.433218\pi\) | |||||||
\(174\) | 1.63121e9 | 0.134908 | ||||||||
\(175\) | 7.18702e8 | 0.0579266 | ||||||||
\(176\) | 7.66536e9 | 0.602179 | ||||||||
\(177\) | −6.76427e9 | −0.518014 | ||||||||
\(178\) | 3.30558e9 | 0.246807 | ||||||||
\(179\) | −1.28930e10 | −0.938678 | −0.469339 | − | 0.883018i | \(-0.655508\pi\) | ||||
−0.469339 | + | 0.883018i | \(0.655508\pi\) | |||||||
\(180\) | −1.85092e9 | −0.131420 | ||||||||
\(181\) | 2.66233e10 | 1.84378 | 0.921889 | − | 0.387453i | \(-0.126645\pi\) | ||||
0.921889 | + | 0.387453i | \(0.126645\pi\) | |||||||
\(182\) | −1.95667e9 | −0.132189 | ||||||||
\(183\) | −1.20384e10 | −0.793483 | ||||||||
\(184\) | −7.34663e9 | −0.472506 | ||||||||
\(185\) | 9.75400e9 | 0.612223 | ||||||||
\(186\) | 5.64331e9 | 0.345721 | ||||||||
\(187\) | −1.12558e10 | −0.673117 | ||||||||
\(188\) | 2.78391e10 | 1.62534 | ||||||||
\(189\) | −9.77786e8 | −0.0557399 | ||||||||
\(190\) | −4.15766e8 | −0.0231450 | ||||||||
\(191\) | −2.72802e10 | −1.48319 | −0.741595 | − | 0.670848i | \(-0.765930\pi\) | ||||
−0.741595 | + | 0.670848i | \(0.765930\pi\) | |||||||
\(192\) | 3.89188e9 | 0.206683 | ||||||||
\(193\) | −9.65442e9 | −0.500862 | −0.250431 | − | 0.968134i | \(-0.580572\pi\) | ||||
−0.250431 | + | 0.968134i | \(0.580572\pi\) | |||||||
\(194\) | −9.33612e9 | −0.473215 | ||||||||
\(195\) | −6.91455e9 | −0.342459 | ||||||||
\(196\) | 1.66866e10 | 0.807636 | ||||||||
\(197\) | 1.21091e10 | 0.572812 | 0.286406 | − | 0.958108i | \(-0.407539\pi\) | ||||
0.286406 | + | 0.958108i | \(0.407539\pi\) | |||||||
\(198\) | −2.26748e9 | −0.104846 | ||||||||
\(199\) | 1.89741e10 | 0.857673 | 0.428837 | − | 0.903382i | \(-0.358924\pi\) | ||||
0.428837 | + | 0.903382i | \(0.358924\pi\) | |||||||
\(200\) | 2.93011e9 | 0.129494 | ||||||||
\(201\) | 1.36082e10 | 0.588056 | ||||||||
\(202\) | 1.37883e10 | 0.582680 | ||||||||
\(203\) | 4.75866e9 | 0.196676 | ||||||||
\(204\) | −9.27161e9 | −0.374817 | ||||||||
\(205\) | 1.53058e10 | 0.605290 | ||||||||
\(206\) | −2.36174e9 | −0.0913757 | ||||||||
\(207\) | −6.42590e9 | −0.243258 | ||||||||
\(208\) | 2.35878e10 | 0.873779 | ||||||||
\(209\) | 3.79214e9 | 0.137476 | ||||||||
\(210\) | 7.25242e8 | 0.0257333 | ||||||||
\(211\) | −8.91928e9 | −0.309784 | −0.154892 | − | 0.987931i | \(-0.549503\pi\) | ||||
−0.154892 | + | 0.987931i | \(0.549503\pi\) | |||||||
\(212\) | −2.57472e9 | −0.0875424 | ||||||||
\(213\) | −1.70898e10 | −0.568892 | ||||||||
\(214\) | 1.52154e9 | 0.0495933 | ||||||||
\(215\) | 7.97450e9 | 0.254525 | ||||||||
\(216\) | −3.98638e9 | −0.124605 | ||||||||
\(217\) | 1.64630e10 | 0.504010 | ||||||||
\(218\) | −1.80248e10 | −0.540524 | ||||||||
\(219\) | 1.16263e10 | 0.341541 | ||||||||
\(220\) | −1.25216e10 | −0.360379 | ||||||||
\(221\) | −3.46364e10 | −0.976714 | ||||||||
\(222\) | 9.84275e9 | 0.271975 | ||||||||
\(223\) | −4.42755e10 | −1.19892 | −0.599462 | − | 0.800403i | \(-0.704619\pi\) | ||||
−0.599462 | + | 0.800403i | \(0.704619\pi\) | |||||||
\(224\) | −9.54018e9 | −0.253187 | ||||||||
\(225\) | 2.56289e9 | 0.0666667 | ||||||||
\(226\) | −1.02735e10 | −0.261959 | ||||||||
\(227\) | −5.40045e10 | −1.34994 | −0.674968 | − | 0.737847i | \(-0.735843\pi\) | ||||
−0.674968 | + | 0.737847i | \(0.735843\pi\) | |||||||
\(228\) | 3.12364e9 | 0.0765516 | ||||||||
\(229\) | 5.80250e9 | 0.139430 | 0.0697149 | − | 0.997567i | \(-0.477791\pi\) | ||||
0.0697149 | + | 0.997567i | \(0.477791\pi\) | |||||||
\(230\) | 4.76621e9 | 0.112305 | ||||||||
\(231\) | −6.61483e9 | −0.152850 | ||||||||
\(232\) | 1.94008e10 | 0.439667 | ||||||||
\(233\) | 5.41865e10 | 1.20445 | 0.602226 | − | 0.798326i | \(-0.294281\pi\) | ||||
0.602226 | + | 0.798326i | \(0.294281\pi\) | |||||||
\(234\) | −6.97747e9 | −0.152134 | ||||||||
\(235\) | −3.85477e10 | −0.824505 | ||||||||
\(236\) | −3.76940e10 | −0.790986 | ||||||||
\(237\) | 3.69328e10 | 0.760404 | ||||||||
\(238\) | 3.63288e9 | 0.0733930 | ||||||||
\(239\) | 7.91761e10 | 1.56965 | 0.784826 | − | 0.619716i | \(-0.212752\pi\) | ||||
0.784826 | + | 0.619716i | \(0.212752\pi\) | |||||||
\(240\) | −8.74284e9 | −0.170099 | ||||||||
\(241\) | −6.14920e10 | −1.17420 | −0.587100 | − | 0.809514i | \(-0.699730\pi\) | ||||
−0.587100 | + | 0.809514i | \(0.699730\pi\) | |||||||
\(242\) | 3.01984e9 | 0.0565998 | ||||||||
\(243\) | −3.48678e9 | −0.0641500 | ||||||||
\(244\) | −6.70841e10 | −1.21162 | ||||||||
\(245\) | −2.31053e10 | −0.409698 | ||||||||
\(246\) | 1.54451e10 | 0.268894 | ||||||||
\(247\) | 1.16691e10 | 0.199481 | ||||||||
\(248\) | 6.71187e10 | 1.12671 | ||||||||
\(249\) | 2.87636e10 | 0.474183 | ||||||||
\(250\) | −1.90094e9 | −0.0307779 | ||||||||
\(251\) | 2.89319e10 | 0.460093 | 0.230046 | − | 0.973180i | \(-0.426112\pi\) | ||||
0.230046 | + | 0.973180i | \(0.426112\pi\) | |||||||
\(252\) | −5.44873e9 | −0.0851125 | ||||||||
\(253\) | −4.34719e10 | −0.667062 | ||||||||
\(254\) | −2.48350e10 | −0.374381 | ||||||||
\(255\) | 1.28380e10 | 0.190137 | ||||||||
\(256\) | 1.01633e9 | 0.0147896 | ||||||||
\(257\) | 1.22388e11 | 1.75001 | 0.875005 | − | 0.484114i | \(-0.160858\pi\) | ||||
0.875005 | + | 0.484114i | \(0.160858\pi\) | |||||||
\(258\) | 8.04706e9 | 0.113070 | ||||||||
\(259\) | 2.87139e10 | 0.396499 | ||||||||
\(260\) | −3.85315e10 | −0.522921 | ||||||||
\(261\) | 1.69694e10 | 0.226351 | ||||||||
\(262\) | 4.20548e10 | 0.551391 | ||||||||
\(263\) | −6.24892e10 | −0.805386 | −0.402693 | − | 0.915335i | \(-0.631926\pi\) | ||||
−0.402693 | + | 0.915335i | \(0.631926\pi\) | |||||||
\(264\) | −2.69683e10 | −0.341693 | ||||||||
\(265\) | 3.56511e9 | 0.0444086 | ||||||||
\(266\) | −1.22393e9 | −0.0149896 | ||||||||
\(267\) | 3.43878e10 | 0.414098 | ||||||||
\(268\) | 7.58321e10 | 0.897938 | ||||||||
\(269\) | 1.27214e11 | 1.48132 | 0.740659 | − | 0.671881i | \(-0.234513\pi\) | ||||
0.740659 | + | 0.671881i | \(0.234513\pi\) | |||||||
\(270\) | 2.58621e9 | 0.0296161 | ||||||||
\(271\) | 1.54116e10 | 0.173574 | 0.0867871 | − | 0.996227i | \(-0.472340\pi\) | ||||
0.0867871 | + | 0.996227i | \(0.472340\pi\) | |||||||
\(272\) | −4.37946e10 | −0.485133 | ||||||||
\(273\) | −2.03551e10 | −0.221790 | ||||||||
\(274\) | −9.33596e7 | −0.00100065 | ||||||||
\(275\) | 1.73382e10 | 0.182813 | ||||||||
\(276\) | −3.58085e10 | −0.371445 | ||||||||
\(277\) | −9.20867e10 | −0.939806 | −0.469903 | − | 0.882718i | \(-0.655711\pi\) | ||||
−0.469903 | + | 0.882718i | \(0.655711\pi\) | |||||||
\(278\) | −7.12818e9 | −0.0715776 | ||||||||
\(279\) | 5.87070e10 | 0.580057 | ||||||||
\(280\) | 8.62567e9 | 0.0838652 | ||||||||
\(281\) | −7.78782e10 | −0.745139 | −0.372570 | − | 0.928004i | \(-0.621523\pi\) | ||||
−0.372570 | + | 0.928004i | \(0.621523\pi\) | |||||||
\(282\) | −3.88985e10 | −0.366279 | ||||||||
\(283\) | 2.92463e10 | 0.271039 | 0.135520 | − | 0.990775i | \(-0.456730\pi\) | ||||
0.135520 | + | 0.990775i | \(0.456730\pi\) | |||||||
\(284\) | −9.52334e10 | −0.868674 | ||||||||
\(285\) | −4.32518e9 | −0.0388331 | ||||||||
\(286\) | −4.72034e10 | −0.417182 | ||||||||
\(287\) | 4.50572e10 | 0.392009 | ||||||||
\(288\) | −3.40203e10 | −0.291388 | ||||||||
\(289\) | −5.42796e10 | −0.457717 | ||||||||
\(290\) | −1.25865e10 | −0.104499 | ||||||||
\(291\) | −9.71231e10 | −0.793970 | ||||||||
\(292\) | 6.47877e10 | 0.521519 | ||||||||
\(293\) | −2.27403e11 | −1.80257 | −0.901285 | − | 0.433227i | \(-0.857375\pi\) | ||||
−0.901285 | + | 0.433227i | \(0.857375\pi\) | |||||||
\(294\) | −2.33155e10 | −0.182005 | ||||||||
\(295\) | 5.21935e10 | 0.401252 | ||||||||
\(296\) | 1.17065e11 | 0.886368 | ||||||||
\(297\) | −2.35885e10 | −0.175912 | ||||||||
\(298\) | −3.89673e10 | −0.286238 | ||||||||
\(299\) | −1.33771e11 | −0.967927 | ||||||||
\(300\) | 1.42818e10 | 0.101797 | ||||||||
\(301\) | 2.34754e10 | 0.164840 | ||||||||
\(302\) | −2.49592e10 | −0.172663 | ||||||||
\(303\) | 1.43439e11 | 0.977632 | ||||||||
\(304\) | 1.47546e10 | 0.0990823 | ||||||||
\(305\) | 9.28887e10 | 0.614630 | ||||||||
\(306\) | 1.29548e10 | 0.0844668 | ||||||||
\(307\) | −6.02579e10 | −0.387160 | −0.193580 | − | 0.981084i | \(-0.562010\pi\) | ||||
−0.193580 | + | 0.981084i | \(0.562010\pi\) | |||||||
\(308\) | −3.68613e10 | −0.233395 | ||||||||
\(309\) | −2.45691e10 | −0.153312 | ||||||||
\(310\) | −4.35440e10 | −0.267794 | ||||||||
\(311\) | 1.36816e11 | 0.829308 | 0.414654 | − | 0.909979i | \(-0.363903\pi\) | ||||
0.414654 | + | 0.909979i | \(0.363903\pi\) | |||||||
\(312\) | −8.29866e10 | −0.495807 | ||||||||
\(313\) | 2.25535e11 | 1.32820 | 0.664101 | − | 0.747643i | \(-0.268815\pi\) | ||||
0.664101 | + | 0.747643i | \(0.268815\pi\) | |||||||
\(314\) | 3.60839e9 | 0.0209474 | ||||||||
\(315\) | 7.54465e9 | 0.0431759 | ||||||||
\(316\) | 2.05809e11 | 1.16111 | ||||||||
\(317\) | −1.28386e11 | −0.714089 | −0.357045 | − | 0.934087i | \(-0.616216\pi\) | ||||
−0.357045 | + | 0.934087i | \(0.616216\pi\) | |||||||
\(318\) | 3.59755e9 | 0.0197281 | ||||||||
\(319\) | 1.14800e11 | 0.620701 | ||||||||
\(320\) | −3.00299e10 | −0.160096 | ||||||||
\(321\) | 1.58285e10 | 0.0832086 | ||||||||
\(322\) | 1.40308e10 | 0.0727328 | ||||||||
\(323\) | −2.16657e10 | −0.110755 | ||||||||
\(324\) | −1.94302e10 | −0.0979545 | ||||||||
\(325\) | 5.33530e10 | 0.265268 | ||||||||
\(326\) | 9.96239e10 | 0.488522 | ||||||||
\(327\) | −1.87510e11 | −0.906902 | ||||||||
\(328\) | 1.83696e11 | 0.876329 | ||||||||
\(329\) | −1.13477e11 | −0.533981 | ||||||||
\(330\) | 1.74960e10 | 0.0812131 | ||||||||
\(331\) | 1.15018e10 | 0.0526673 | 0.0263337 | − | 0.999653i | \(-0.491617\pi\) | ||||
0.0263337 | + | 0.999653i | \(0.491617\pi\) | |||||||
\(332\) | 1.60286e11 | 0.724058 | ||||||||
\(333\) | 1.02394e11 | 0.456324 | ||||||||
\(334\) | 1.44590e11 | 0.635740 | ||||||||
\(335\) | −1.05002e11 | −0.455506 | ||||||||
\(336\) | −2.57372e10 | −0.110163 | ||||||||
\(337\) | −2.79631e11 | −1.18100 | −0.590502 | − | 0.807036i | \(-0.701070\pi\) | ||||
−0.590502 | + | 0.807036i | \(0.701070\pi\) | |||||||
\(338\) | −6.26843e10 | −0.261236 | ||||||||
\(339\) | −1.06875e11 | −0.439519 | ||||||||
\(340\) | 7.15402e10 | 0.290332 | ||||||||
\(341\) | 3.97159e11 | 1.59063 | ||||||||
\(342\) | −4.36454e9 | −0.0172513 | ||||||||
\(343\) | −1.42263e11 | −0.554969 | ||||||||
\(344\) | 9.57078e10 | 0.368497 | ||||||||
\(345\) | 4.95826e10 | 0.188427 | ||||||||
\(346\) | −3.82107e10 | −0.143332 | ||||||||
\(347\) | 9.07088e10 | 0.335867 | 0.167933 | − | 0.985798i | \(-0.446291\pi\) | ||||
0.167933 | + | 0.985798i | \(0.446291\pi\) | |||||||
\(348\) | 9.45621e10 | 0.345629 | ||||||||
\(349\) | −3.98825e11 | −1.43902 | −0.719511 | − | 0.694481i | \(-0.755634\pi\) | ||||
−0.719511 | + | 0.694481i | \(0.755634\pi\) | |||||||
\(350\) | −5.59600e9 | −0.0199330 | ||||||||
\(351\) | −7.25862e10 | −0.255254 | ||||||||
\(352\) | −2.30151e11 | −0.799044 | ||||||||
\(353\) | −4.56192e11 | −1.56373 | −0.781865 | − | 0.623448i | \(-0.785731\pi\) | ||||
−0.781865 | + | 0.623448i | \(0.785731\pi\) | |||||||
\(354\) | 5.26684e10 | 0.178252 | ||||||||
\(355\) | 1.31866e11 | 0.440662 | ||||||||
\(356\) | 1.91627e11 | 0.632311 | ||||||||
\(357\) | 3.77926e10 | 0.123140 | ||||||||
\(358\) | 1.00389e11 | 0.323006 | ||||||||
\(359\) | 1.89176e11 | 0.601094 | 0.300547 | − | 0.953767i | \(-0.402831\pi\) | ||||
0.300547 | + | 0.953767i | \(0.402831\pi\) | |||||||
\(360\) | 3.07591e10 | 0.0965190 | ||||||||
\(361\) | −3.15388e11 | −0.977380 | ||||||||
\(362\) | −2.07296e11 | −0.634458 | ||||||||
\(363\) | 3.14152e10 | 0.0949643 | ||||||||
\(364\) | −1.13429e11 | −0.338664 | ||||||||
\(365\) | −8.97090e10 | −0.264556 | ||||||||
\(366\) | 9.37339e10 | 0.273044 | ||||||||
\(367\) | −3.17920e10 | −0.0914787 | −0.0457394 | − | 0.998953i | \(-0.514564\pi\) | ||||
−0.0457394 | + | 0.998953i | \(0.514564\pi\) | |||||||
\(368\) | −1.69142e11 | −0.480769 | ||||||||
\(369\) | 1.60674e11 | 0.451156 | ||||||||
\(370\) | −7.59472e10 | −0.210671 | ||||||||
\(371\) | 1.04950e10 | 0.0287607 | ||||||||
\(372\) | 3.27146e11 | 0.885723 | ||||||||
\(373\) | −4.46388e11 | −1.19405 | −0.597025 | − | 0.802222i | \(-0.703651\pi\) | ||||
−0.597025 | + | 0.802222i | \(0.703651\pi\) | |||||||
\(374\) | 8.76409e10 | 0.231625 | ||||||||
\(375\) | −1.97754e10 | −0.0516398 | ||||||||
\(376\) | −4.62639e11 | −1.19371 | ||||||||
\(377\) | 3.53260e11 | 0.900655 | ||||||||
\(378\) | 7.61330e9 | 0.0191805 | ||||||||
\(379\) | 3.53467e11 | 0.879978 | 0.439989 | − | 0.898003i | \(-0.354982\pi\) | ||||
0.439989 | + | 0.898003i | \(0.354982\pi\) | |||||||
\(380\) | −2.41022e10 | −0.0592966 | ||||||||
\(381\) | −2.58357e11 | −0.628143 | ||||||||
\(382\) | 2.12411e11 | 0.510377 | ||||||||
\(383\) | 3.14974e11 | 0.747963 | 0.373981 | − | 0.927436i | \(-0.377992\pi\) | ||||
0.373981 | + | 0.927436i | \(0.377992\pi\) | |||||||
\(384\) | −2.45345e11 | −0.575820 | ||||||||
\(385\) | 5.10403e10 | 0.118397 | ||||||||
\(386\) | 7.51718e10 | 0.172350 | ||||||||
\(387\) | 8.37131e10 | 0.189712 | ||||||||
\(388\) | −5.41220e11 | −1.21236 | ||||||||
\(389\) | −4.20729e11 | −0.931600 | −0.465800 | − | 0.884890i | \(-0.654233\pi\) | ||||
−0.465800 | + | 0.884890i | \(0.654233\pi\) | |||||||
\(390\) | 5.38385e10 | 0.117843 | ||||||||
\(391\) | 2.48369e11 | 0.537405 | ||||||||
\(392\) | −2.77303e11 | −0.593155 | ||||||||
\(393\) | 4.37493e11 | 0.925134 | ||||||||
\(394\) | −9.42843e10 | −0.197109 | ||||||||
\(395\) | −2.84975e11 | −0.589007 | ||||||||
\(396\) | −1.31447e11 | −0.268611 | ||||||||
\(397\) | 5.63093e11 | 1.13769 | 0.568844 | − | 0.822446i | \(-0.307391\pi\) | ||||
0.568844 | + | 0.822446i | \(0.307391\pi\) | |||||||
\(398\) | −1.47737e11 | −0.295132 | ||||||||
\(399\) | −1.27325e10 | −0.0251498 | ||||||||
\(400\) | 6.74602e10 | 0.131758 | ||||||||
\(401\) | 2.75897e11 | 0.532841 | 0.266420 | − | 0.963857i | \(-0.414159\pi\) | ||||
0.266420 | + | 0.963857i | \(0.414159\pi\) | |||||||
\(402\) | −1.05957e11 | −0.202355 | ||||||||
\(403\) | 1.22213e12 | 2.30805 | ||||||||
\(404\) | 7.99317e11 | 1.49280 | ||||||||
\(405\) | 2.69042e10 | 0.0496904 | ||||||||
\(406\) | −3.70521e10 | −0.0676778 | ||||||||
\(407\) | 6.92703e11 | 1.25133 | ||||||||
\(408\) | 1.54079e11 | 0.275278 | ||||||||
\(409\) | −6.54552e10 | −0.115662 | −0.0578308 | − | 0.998326i | \(-0.518418\pi\) | ||||
−0.0578308 | + | 0.998326i | \(0.518418\pi\) | |||||||
\(410\) | −1.19175e11 | −0.208285 | ||||||||
\(411\) | −9.71214e8 | −0.00167891 | ||||||||
\(412\) | −1.36912e11 | −0.234101 | ||||||||
\(413\) | 1.53647e11 | 0.259866 | ||||||||
\(414\) | 5.00337e10 | 0.0837069 | ||||||||
\(415\) | −2.21941e11 | −0.367301 | ||||||||
\(416\) | −7.08218e11 | −1.15944 | ||||||||
\(417\) | −7.41541e10 | −0.120094 | ||||||||
\(418\) | −2.95266e10 | −0.0473064 | ||||||||
\(419\) | 2.70250e10 | 0.0428354 | 0.0214177 | − | 0.999771i | \(-0.493182\pi\) | ||||
0.0214177 | + | 0.999771i | \(0.493182\pi\) | |||||||
\(420\) | 4.20427e10 | 0.0659278 | ||||||||
\(421\) | −4.29698e11 | −0.666644 | −0.333322 | − | 0.942813i | \(-0.608170\pi\) | ||||
−0.333322 | + | 0.942813i | \(0.608170\pi\) | |||||||
\(422\) | 6.94478e10 | 0.106599 | ||||||||
\(423\) | −4.04659e11 | −0.614550 | ||||||||
\(424\) | 4.27875e10 | 0.0642940 | ||||||||
\(425\) | −9.90589e10 | −0.147280 | ||||||||
\(426\) | 1.33066e11 | 0.195760 | ||||||||
\(427\) | 2.73446e11 | 0.398058 | ||||||||
\(428\) | 8.82048e10 | 0.127056 | ||||||||
\(429\) | −4.91054e11 | −0.699957 | ||||||||
\(430\) | −6.20915e10 | −0.0875839 | ||||||||
\(431\) | −9.44700e11 | −1.31870 | −0.659350 | − | 0.751836i | \(-0.729169\pi\) | ||||
−0.659350 | + | 0.751836i | \(0.729169\pi\) | |||||||
\(432\) | −9.17789e10 | −0.126784 | ||||||||
\(433\) | 2.10762e11 | 0.288136 | 0.144068 | − | 0.989568i | \(-0.453982\pi\) | ||||
0.144068 | + | 0.989568i | \(0.453982\pi\) | |||||||
\(434\) | −1.28185e11 | −0.173434 | ||||||||
\(435\) | −1.30936e11 | −0.175331 | ||||||||
\(436\) | −1.04491e12 | −1.38480 | ||||||||
\(437\) | −8.36765e10 | −0.109758 | ||||||||
\(438\) | −9.05253e10 | −0.117527 | ||||||||
\(439\) | 7.69079e11 | 0.988282 | 0.494141 | − | 0.869382i | \(-0.335483\pi\) | ||||
0.494141 | + | 0.869382i | \(0.335483\pi\) | |||||||
\(440\) | 2.08089e11 | 0.264674 | ||||||||
\(441\) | −2.42550e11 | −0.305371 | ||||||||
\(442\) | 2.69688e11 | 0.336094 | ||||||||
\(443\) | −6.49894e11 | −0.801726 | −0.400863 | − | 0.916138i | \(-0.631290\pi\) | ||||
−0.400863 | + | 0.916138i | \(0.631290\pi\) | |||||||
\(444\) | 5.70590e11 | 0.696788 | ||||||||
\(445\) | −2.65338e11 | −0.320759 | ||||||||
\(446\) | 3.44741e11 | 0.412559 | ||||||||
\(447\) | −4.05374e11 | −0.480255 | ||||||||
\(448\) | −8.84023e10 | −0.103684 | ||||||||
\(449\) | −4.51858e11 | −0.524679 | −0.262339 | − | 0.964976i | \(-0.584494\pi\) | ||||
−0.262339 | + | 0.964976i | \(0.584494\pi\) | |||||||
\(450\) | −1.99553e10 | −0.0229405 | ||||||||
\(451\) | 1.08698e12 | 1.23716 | ||||||||
\(452\) | −5.95564e11 | −0.671128 | ||||||||
\(453\) | −2.59649e11 | −0.289697 | ||||||||
\(454\) | 4.20493e11 | 0.464523 | ||||||||
\(455\) | 1.57061e11 | 0.171797 | ||||||||
\(456\) | −5.19097e10 | −0.0562220 | ||||||||
\(457\) | −6.18434e11 | −0.663240 | −0.331620 | − | 0.943413i | \(-0.607595\pi\) | ||||
−0.331620 | + | 0.943413i | \(0.607595\pi\) | |||||||
\(458\) | −4.51798e10 | −0.0479788 | ||||||||
\(459\) | 1.34768e11 | 0.141720 | ||||||||
\(460\) | 2.76300e11 | 0.287720 | ||||||||
\(461\) | −2.76450e11 | −0.285078 | −0.142539 | − | 0.989789i | \(-0.545527\pi\) | ||||
−0.142539 | + | 0.989789i | \(0.545527\pi\) | |||||||
\(462\) | 5.15048e10 | 0.0525967 | ||||||||
\(463\) | 6.09969e11 | 0.616870 | 0.308435 | − | 0.951245i | \(-0.400195\pi\) | ||||
0.308435 | + | 0.951245i | \(0.400195\pi\) | |||||||
\(464\) | 4.46666e11 | 0.447355 | ||||||||
\(465\) | −4.52986e11 | −0.449310 | ||||||||
\(466\) | −4.21910e11 | −0.414461 | ||||||||
\(467\) | 2.83260e11 | 0.275587 | 0.137794 | − | 0.990461i | \(-0.455999\pi\) | ||||
0.137794 | + | 0.990461i | \(0.455999\pi\) | |||||||
\(468\) | −4.04488e11 | −0.389762 | ||||||||
\(469\) | −3.09104e11 | −0.295004 | ||||||||
\(470\) | 3.00143e11 | 0.283718 | ||||||||
\(471\) | 3.75378e10 | 0.0351459 | ||||||||
\(472\) | 6.26412e11 | 0.580926 | ||||||||
\(473\) | 5.66328e11 | 0.520227 | ||||||||
\(474\) | −2.87568e11 | −0.261661 | ||||||||
\(475\) | 3.33733e10 | 0.0300800 | ||||||||
\(476\) | 2.10600e11 | 0.188030 | ||||||||
\(477\) | 3.74251e10 | 0.0331002 | ||||||||
\(478\) | −6.16485e11 | −0.540129 | ||||||||
\(479\) | −1.39149e12 | −1.20773 | −0.603865 | − | 0.797087i | \(-0.706373\pi\) | ||||
−0.603865 | + | 0.797087i | \(0.706373\pi\) | |||||||
\(480\) | 2.62502e11 | 0.225708 | ||||||||
\(481\) | 2.13158e12 | 1.81572 | ||||||||
\(482\) | 4.78793e11 | 0.404051 | ||||||||
\(483\) | 1.45961e11 | 0.122033 | ||||||||
\(484\) | 1.75062e11 | 0.145007 | ||||||||
\(485\) | 7.49406e11 | 0.615006 | ||||||||
\(486\) | 2.71490e10 | 0.0220745 | ||||||||
\(487\) | −1.41532e11 | −0.114018 | −0.0570092 | − | 0.998374i | \(-0.518156\pi\) | ||||
−0.0570092 | + | 0.998374i | \(0.518156\pi\) | |||||||
\(488\) | 1.11483e12 | 0.889851 | ||||||||
\(489\) | 1.03638e12 | 0.819652 | ||||||||
\(490\) | 1.79904e11 | 0.140980 | ||||||||
\(491\) | −4.66246e11 | −0.362034 | −0.181017 | − | 0.983480i | \(-0.557939\pi\) | ||||
−0.181017 | + | 0.983480i | \(0.557939\pi\) | |||||||
\(492\) | 8.95359e11 | 0.688897 | ||||||||
\(493\) | −6.55887e11 | −0.500055 | ||||||||
\(494\) | −9.08589e10 | −0.0686430 | ||||||||
\(495\) | 1.82010e11 | 0.136261 | ||||||||
\(496\) | 1.54528e12 | 1.14641 | ||||||||
\(497\) | 3.88188e11 | 0.285389 | ||||||||
\(498\) | −2.23961e11 | −0.163170 | ||||||||
\(499\) | −2.21254e12 | −1.59749 | −0.798746 | − | 0.601668i | \(-0.794503\pi\) | ||||
−0.798746 | + | 0.601668i | \(0.794503\pi\) | |||||||
\(500\) | −1.10199e11 | −0.0788518 | ||||||||
\(501\) | 1.50416e12 | 1.06666 | ||||||||
\(502\) | −2.25271e11 | −0.158321 | ||||||||
\(503\) | 3.39574e11 | 0.236526 | 0.118263 | − | 0.992982i | \(-0.462267\pi\) | ||||
0.118263 | + | 0.992982i | \(0.462267\pi\) | |||||||
\(504\) | 9.05488e10 | 0.0625094 | ||||||||
\(505\) | −1.10678e12 | −0.757270 | ||||||||
\(506\) | 3.38484e11 | 0.229541 | ||||||||
\(507\) | −6.52101e11 | −0.438308 | ||||||||
\(508\) | −1.43970e12 | −0.959149 | ||||||||
\(509\) | −5.66691e11 | −0.374211 | −0.187106 | − | 0.982340i | \(-0.559911\pi\) | ||||
−0.187106 | + | 0.982340i | \(0.559911\pi\) | |||||||
\(510\) | −9.99603e10 | −0.0654277 | ||||||||
\(511\) | −2.64086e11 | −0.171337 | ||||||||
\(512\) | −1.55874e12 | −1.00244 | ||||||||
\(513\) | −4.54040e10 | −0.0289445 | ||||||||
\(514\) | −9.52947e11 | −0.602191 | ||||||||
\(515\) | 1.89576e11 | 0.118755 | ||||||||
\(516\) | 4.66493e11 | 0.289682 | ||||||||
\(517\) | −2.73756e12 | −1.68522 | ||||||||
\(518\) | −2.23574e11 | −0.136438 | ||||||||
\(519\) | −3.97504e11 | −0.240485 | ||||||||
\(520\) | 6.40329e11 | 0.384050 | ||||||||
\(521\) | 4.42970e11 | 0.263393 | 0.131697 | − | 0.991290i | \(-0.457958\pi\) | ||||
0.131697 | + | 0.991290i | \(0.457958\pi\) | |||||||
\(522\) | −1.32128e11 | −0.0778892 | ||||||||
\(523\) | −1.44683e11 | −0.0845591 | −0.0422796 | − | 0.999106i | \(-0.513462\pi\) | ||||
−0.0422796 | + | 0.999106i | \(0.513462\pi\) | |||||||
\(524\) | 2.43794e12 | 1.41264 | ||||||||
\(525\) | −5.82149e10 | −0.0334439 | ||||||||
\(526\) | 4.86557e11 | 0.277139 | ||||||||
\(527\) | −2.26910e12 | −1.28146 | ||||||||
\(528\) | −6.20894e11 | −0.347668 | ||||||||
\(529\) | −8.41911e11 | −0.467429 | ||||||||
\(530\) | −2.77589e10 | −0.0152813 | ||||||||
\(531\) | 5.47906e11 | 0.299075 | ||||||||
\(532\) | −7.09520e10 | −0.0384028 | ||||||||
\(533\) | 3.34484e12 | 1.79516 | ||||||||
\(534\) | −2.67752e11 | −0.142494 | ||||||||
\(535\) | −1.22134e11 | −0.0644531 | ||||||||
\(536\) | −1.26020e12 | −0.659475 | ||||||||
\(537\) | 1.04434e12 | 0.541946 | ||||||||
\(538\) | −9.90519e11 | −0.509733 | ||||||||
\(539\) | −1.64088e12 | −0.837388 | ||||||||
\(540\) | 1.49924e11 | 0.0758752 | ||||||||
\(541\) | −3.10308e11 | −0.155742 | −0.0778710 | − | 0.996963i | \(-0.524812\pi\) | ||||
−0.0778710 | + | 0.996963i | \(0.524812\pi\) | |||||||
\(542\) | −1.19999e11 | −0.0597281 | ||||||||
\(543\) | −2.15649e12 | −1.06451 | ||||||||
\(544\) | 1.31493e12 | 0.643733 | ||||||||
\(545\) | 1.44684e12 | 0.702484 | ||||||||
\(546\) | 1.58490e11 | 0.0763194 | ||||||||
\(547\) | 1.68502e12 | 0.804750 | 0.402375 | − | 0.915475i | \(-0.368185\pi\) | ||||
0.402375 | + | 0.915475i | \(0.368185\pi\) | |||||||
\(548\) | −5.41211e9 | −0.00256362 | ||||||||
\(549\) | 9.75108e11 | 0.458118 | ||||||||
\(550\) | −1.35000e11 | −0.0629074 | ||||||||
\(551\) | 2.20971e11 | 0.102130 | ||||||||
\(552\) | 5.95077e11 | 0.272802 | ||||||||
\(553\) | −8.38911e11 | −0.381463 | ||||||||
\(554\) | 7.17011e11 | 0.323394 | ||||||||
\(555\) | −7.90074e11 | −0.353467 | ||||||||
\(556\) | −4.13225e11 | −0.183379 | ||||||||
\(557\) | −2.31328e12 | −1.01831 | −0.509156 | − | 0.860674i | \(-0.670042\pi\) | ||||
−0.509156 | + | 0.860674i | \(0.670042\pi\) | |||||||
\(558\) | −4.57108e11 | −0.199602 | ||||||||
\(559\) | 1.74270e12 | 0.754865 | ||||||||
\(560\) | 1.98590e11 | 0.0853317 | ||||||||
\(561\) | 9.11723e11 | 0.388624 | ||||||||
\(562\) | 6.06380e11 | 0.256408 | ||||||||
\(563\) | 7.03648e11 | 0.295167 | 0.147583 | − | 0.989050i | \(-0.452850\pi\) | ||||
0.147583 | + | 0.989050i | \(0.452850\pi\) | |||||||
\(564\) | −2.25497e12 | −0.938392 | ||||||||
\(565\) | 8.24653e11 | 0.340450 | ||||||||
\(566\) | −2.27720e11 | −0.0932666 | ||||||||
\(567\) | 7.92007e10 | 0.0321814 | ||||||||
\(568\) | 1.58262e12 | 0.637983 | ||||||||
\(569\) | 3.21997e12 | 1.28779 | 0.643896 | − | 0.765113i | \(-0.277317\pi\) | ||||
0.643896 | + | 0.765113i | \(0.277317\pi\) | |||||||
\(570\) | 3.36770e10 | 0.0133628 | ||||||||
\(571\) | −1.21116e12 | −0.476801 | −0.238401 | − | 0.971167i | \(-0.576623\pi\) | ||||
−0.238401 | + | 0.971167i | \(0.576623\pi\) | |||||||
\(572\) | −2.73641e12 | −1.06880 | ||||||||
\(573\) | 2.20969e12 | 0.856320 | ||||||||
\(574\) | −3.50827e11 | −0.134893 | ||||||||
\(575\) | −3.82582e11 | −0.145955 | ||||||||
\(576\) | −3.15242e11 | −0.119328 | ||||||||
\(577\) | 7.30673e11 | 0.274430 | 0.137215 | − | 0.990541i | \(-0.456185\pi\) | ||||
0.137215 | + | 0.990541i | \(0.456185\pi\) | |||||||
\(578\) | 4.22635e11 | 0.157504 | ||||||||
\(579\) | 7.82008e11 | 0.289173 | ||||||||
\(580\) | −7.29646e11 | −0.267723 | ||||||||
\(581\) | −6.53352e11 | −0.237878 | ||||||||
\(582\) | 7.56226e11 | 0.273211 | ||||||||
\(583\) | 2.53185e11 | 0.0907673 | ||||||||
\(584\) | −1.07666e12 | −0.383021 | ||||||||
\(585\) | 5.60079e11 | 0.197719 | ||||||||
\(586\) | 1.77062e12 | 0.620278 | ||||||||
\(587\) | 4.55331e12 | 1.58291 | 0.791453 | − | 0.611230i | \(-0.209325\pi\) | ||||
0.791453 | + | 0.611230i | \(0.209325\pi\) | |||||||
\(588\) | −1.35162e12 | −0.466289 | ||||||||
\(589\) | 7.64467e11 | 0.261722 | ||||||||
\(590\) | −4.06392e11 | −0.138074 | ||||||||
\(591\) | −9.80833e11 | −0.330713 | ||||||||
\(592\) | 2.69520e12 | 0.901867 | ||||||||
\(593\) | 3.00074e12 | 0.996510 | 0.498255 | − | 0.867030i | \(-0.333974\pi\) | ||||
0.498255 | + | 0.867030i | \(0.333974\pi\) | |||||||
\(594\) | 1.83666e11 | 0.0605327 | ||||||||
\(595\) | −2.91610e11 | −0.0953841 | ||||||||
\(596\) | −2.25896e12 | −0.733330 | ||||||||
\(597\) | −1.53690e12 | −0.495178 | ||||||||
\(598\) | 1.04158e12 | 0.333071 | ||||||||
\(599\) | −4.03514e12 | −1.28067 | −0.640336 | − | 0.768095i | \(-0.721205\pi\) | ||||
−0.640336 | + | 0.768095i | \(0.721205\pi\) | |||||||
\(600\) | −2.37339e11 | −0.0747633 | ||||||||
\(601\) | 2.04760e12 | 0.640192 | 0.320096 | − | 0.947385i | \(-0.396285\pi\) | ||||
0.320096 | + | 0.947385i | \(0.396285\pi\) | |||||||
\(602\) | −1.82785e11 | −0.0567227 | ||||||||
\(603\) | −1.10227e12 | −0.339514 | ||||||||
\(604\) | −1.44690e12 | −0.442355 | ||||||||
\(605\) | −2.42401e11 | −0.0735590 | ||||||||
\(606\) | −1.11685e12 | −0.336410 | ||||||||
\(607\) | 3.15792e12 | 0.944175 | 0.472088 | − | 0.881552i | \(-0.343501\pi\) | ||||
0.472088 | + | 0.881552i | \(0.343501\pi\) | |||||||
\(608\) | −4.43004e11 | −0.131474 | ||||||||
\(609\) | −3.85451e11 | −0.113551 | ||||||||
\(610\) | −7.23256e11 | −0.211499 | ||||||||
\(611\) | −8.42399e12 | −2.44530 | ||||||||
\(612\) | 7.51000e11 | 0.216401 | ||||||||
\(613\) | −2.89302e12 | −0.827520 | −0.413760 | − | 0.910386i | \(-0.635785\pi\) | ||||
−0.413760 | + | 0.910386i | \(0.635785\pi\) | |||||||
\(614\) | 4.69183e11 | 0.133225 | ||||||||
\(615\) | −1.23977e12 | −0.349464 | ||||||||
\(616\) | 6.12573e11 | 0.171413 | ||||||||
\(617\) | 6.03603e12 | 1.67675 | 0.838375 | − | 0.545094i | \(-0.183506\pi\) | ||||
0.838375 | + | 0.545094i | \(0.183506\pi\) | |||||||
\(618\) | 1.91301e11 | 0.0527558 | ||||||||
\(619\) | 4.05606e12 | 1.11044 | 0.555222 | − | 0.831702i | \(-0.312633\pi\) | ||||
0.555222 | + | 0.831702i | \(0.312633\pi\) | |||||||
\(620\) | −2.52427e12 | −0.686078 | ||||||||
\(621\) | 5.20498e11 | 0.140445 | ||||||||
\(622\) | −1.06529e12 | −0.285371 | ||||||||
\(623\) | −7.81102e11 | −0.207736 | ||||||||
\(624\) | −1.91061e12 | −0.504477 | ||||||||
\(625\) | 1.52588e11 | 0.0400000 | ||||||||
\(626\) | −1.75607e12 | −0.457044 | ||||||||
\(627\) | −3.07163e11 | −0.0793716 | ||||||||
\(628\) | 2.09180e11 | 0.0536664 | ||||||||
\(629\) | −3.95764e12 | −1.00811 | ||||||||
\(630\) | −5.87446e10 | −0.0148571 | ||||||||
\(631\) | −5.34498e12 | −1.34219 | −0.671095 | − | 0.741372i | \(-0.734176\pi\) | ||||
−0.671095 | + | 0.741372i | \(0.734176\pi\) | |||||||
\(632\) | −3.42020e12 | −0.852755 | ||||||||
\(633\) | 7.22461e11 | 0.178854 | ||||||||
\(634\) | 9.99651e11 | 0.245723 | ||||||||
\(635\) | 1.99350e12 | 0.486558 | ||||||||
\(636\) | 2.08552e11 | 0.0505426 | ||||||||
\(637\) | −5.04929e12 | −1.21507 | ||||||||
\(638\) | −8.93859e11 | −0.213588 | ||||||||
\(639\) | 1.38428e12 | 0.328450 | ||||||||
\(640\) | 1.89309e12 | 0.446028 | ||||||||
\(641\) | 4.81739e12 | 1.12707 | 0.563534 | − | 0.826093i | \(-0.309441\pi\) | ||||
0.563534 | + | 0.826093i | \(0.309441\pi\) | |||||||
\(642\) | −1.23245e11 | −0.0286327 | ||||||||
\(643\) | −5.85505e11 | −0.135077 | −0.0675385 | − | 0.997717i | \(-0.521515\pi\) | ||||
−0.0675385 | + | 0.997717i | \(0.521515\pi\) | |||||||
\(644\) | 8.13372e11 | 0.186339 | ||||||||
\(645\) | −6.45935e11 | −0.146950 | ||||||||
\(646\) | 1.68695e11 | 0.0381114 | ||||||||
\(647\) | 4.54903e12 | 1.02059 | 0.510293 | − | 0.860001i | \(-0.329537\pi\) | ||||
0.510293 | + | 0.860001i | \(0.329537\pi\) | |||||||
\(648\) | 3.22897e11 | 0.0719410 | ||||||||
\(649\) | 3.70664e12 | 0.820124 | ||||||||
\(650\) | −4.15421e11 | −0.0912805 | ||||||||
\(651\) | −1.33350e12 | −0.290991 | ||||||||
\(652\) | 5.77526e12 | 1.25158 | ||||||||
\(653\) | −7.04350e12 | −1.51593 | −0.757965 | − | 0.652295i | \(-0.773806\pi\) | ||||
−0.757965 | + | 0.652295i | \(0.773806\pi\) | |||||||
\(654\) | 1.46001e12 | 0.312072 | ||||||||
\(655\) | −3.37572e12 | −0.716606 | ||||||||
\(656\) | 4.22925e12 | 0.891653 | ||||||||
\(657\) | −9.41729e11 | −0.197189 | ||||||||
\(658\) | 8.83561e11 | 0.183747 | ||||||||
\(659\) | 5.23559e12 | 1.08139 | 0.540694 | − | 0.841219i | \(-0.318162\pi\) | ||||
0.540694 | + | 0.841219i | \(0.318162\pi\) | |||||||
\(660\) | 1.01425e12 | 0.208065 | ||||||||
\(661\) | −5.79017e12 | −1.17974 | −0.589868 | − | 0.807500i | \(-0.700820\pi\) | ||||
−0.589868 | + | 0.807500i | \(0.700820\pi\) | |||||||
\(662\) | −8.95563e10 | −0.0181232 | ||||||||
\(663\) | 2.80555e12 | 0.563906 | ||||||||
\(664\) | −2.66368e12 | −0.531772 | ||||||||
\(665\) | 9.82445e10 | 0.0194810 | ||||||||
\(666\) | −7.97263e11 | −0.157025 | ||||||||
\(667\) | −2.53314e12 | −0.495557 | ||||||||
\(668\) | 8.38197e12 | 1.62874 | ||||||||
\(669\) | 3.58632e12 | 0.692199 | ||||||||
\(670\) | 8.17570e11 | 0.156743 | ||||||||
\(671\) | 6.59671e12 | 1.25625 | ||||||||
\(672\) | 7.72755e11 | 0.146177 | ||||||||
\(673\) | −5.92328e10 | −0.0111300 | −0.00556499 | − | 0.999985i | \(-0.501771\pi\) | ||||
−0.00556499 | + | 0.999985i | \(0.501771\pi\) | |||||||
\(674\) | 2.17728e12 | 0.406392 | ||||||||
\(675\) | −2.07594e11 | −0.0384900 | ||||||||
\(676\) | −3.63385e12 | −0.669278 | ||||||||
\(677\) | 4.57177e12 | 0.836440 | 0.418220 | − | 0.908346i | \(-0.362654\pi\) | ||||
0.418220 | + | 0.908346i | \(0.362654\pi\) | |||||||
\(678\) | 8.32157e11 | 0.151242 | ||||||||
\(679\) | 2.20611e12 | 0.398302 | ||||||||
\(680\) | −1.18888e12 | −0.213229 | ||||||||
\(681\) | 4.37436e12 | 0.779386 | ||||||||
\(682\) | −3.09238e12 | −0.547348 | ||||||||
\(683\) | −9.71286e12 | −1.70787 | −0.853934 | − | 0.520382i | \(-0.825790\pi\) | ||||
−0.853934 | + | 0.520382i | \(0.825790\pi\) | |||||||
\(684\) | −2.53015e11 | −0.0441971 | ||||||||
\(685\) | 7.49393e9 | 0.00130048 | ||||||||
\(686\) | 1.10770e12 | 0.190969 | ||||||||
\(687\) | −4.70003e11 | −0.0804998 | ||||||||
\(688\) | 2.20349e12 | 0.374941 | ||||||||
\(689\) | 7.79098e11 | 0.131706 | ||||||||
\(690\) | −3.86063e11 | −0.0648391 | ||||||||
\(691\) | 2.23726e12 | 0.373306 | 0.186653 | − | 0.982426i | \(-0.440236\pi\) | ||||
0.186653 | + | 0.982426i | \(0.440236\pi\) | |||||||
\(692\) | −2.21510e12 | −0.367211 | ||||||||
\(693\) | 5.35801e11 | 0.0882478 | ||||||||
\(694\) | −7.06282e11 | −0.115574 | ||||||||
\(695\) | 5.72176e11 | 0.0930247 | ||||||||
\(696\) | −1.57146e12 | −0.253842 | ||||||||
\(697\) | −6.21025e12 | −0.996693 | ||||||||
\(698\) | 3.10535e12 | 0.495178 | ||||||||
\(699\) | −4.38911e12 | −0.695391 | ||||||||
\(700\) | −3.24404e11 | −0.0510675 | ||||||||
\(701\) | −2.29477e10 | −0.00358929 | −0.00179464 | − | 0.999998i | \(-0.500571\pi\) | ||||
−0.00179464 | + | 0.999998i | \(0.500571\pi\) | |||||||
\(702\) | 5.65175e11 | 0.0878347 | ||||||||
\(703\) | 1.33334e12 | 0.205894 | ||||||||
\(704\) | −2.13265e12 | −0.327222 | ||||||||
\(705\) | 3.12237e12 | 0.476028 | ||||||||
\(706\) | 3.55203e12 | 0.538091 | ||||||||
\(707\) | −3.25815e12 | −0.490438 | ||||||||
\(708\) | 3.05322e12 | 0.456676 | ||||||||
\(709\) | −9.57637e12 | −1.42329 | −0.711644 | − | 0.702540i | \(-0.752049\pi\) | ||||
−0.711644 | + | 0.702540i | \(0.752049\pi\) | |||||||
\(710\) | −1.02674e12 | −0.151635 | ||||||||
\(711\) | −2.99156e12 | −0.439020 | ||||||||
\(712\) | −3.18451e12 | −0.464390 | ||||||||
\(713\) | −8.76362e12 | −1.26993 | ||||||||
\(714\) | −2.94263e11 | −0.0423735 | ||||||||
\(715\) | 3.78899e12 | 0.542184 | ||||||||
\(716\) | 5.81959e12 | 0.827529 | ||||||||
\(717\) | −6.41326e12 | −0.906239 | ||||||||
\(718\) | −1.47298e12 | −0.206841 | ||||||||
\(719\) | −5.46390e12 | −0.762469 | −0.381235 | − | 0.924478i | \(-0.624501\pi\) | ||||
−0.381235 | + | 0.924478i | \(0.624501\pi\) | |||||||
\(720\) | 7.08170e11 | 0.0982068 | ||||||||
\(721\) | 5.58075e11 | 0.0769102 | ||||||||
\(722\) | 2.45570e12 | 0.336324 | ||||||||
\(723\) | 4.98085e12 | 0.677925 | ||||||||
\(724\) | −1.20171e13 | −1.62546 | ||||||||
\(725\) | 1.01031e12 | 0.135811 | ||||||||
\(726\) | −2.44607e11 | −0.0326779 | ||||||||
\(727\) | 6.59842e12 | 0.876062 | 0.438031 | − | 0.898960i | \(-0.355676\pi\) | ||||
0.438031 | + | 0.898960i | \(0.355676\pi\) | |||||||
\(728\) | 1.88500e12 | 0.248726 | ||||||||
\(729\) | 2.82430e11 | 0.0370370 | ||||||||
\(730\) | 6.98498e11 | 0.0910358 | ||||||||
\(731\) | −3.23561e12 | −0.419111 | ||||||||
\(732\) | 5.43381e12 | 0.699527 | ||||||||
\(733\) | 6.91041e11 | 0.0884170 | 0.0442085 | − | 0.999022i | \(-0.485923\pi\) | ||||
0.0442085 | + | 0.999022i | \(0.485923\pi\) | |||||||
\(734\) | 2.47541e11 | 0.0314785 | ||||||||
\(735\) | 1.87153e12 | 0.236539 | ||||||||
\(736\) | 5.07846e12 | 0.637943 | ||||||||
\(737\) | −7.45694e12 | −0.931016 | ||||||||
\(738\) | −1.25105e12 | −0.155246 | ||||||||
\(739\) | 7.60189e12 | 0.937608 | 0.468804 | − | 0.883302i | \(-0.344685\pi\) | ||||
0.468804 | + | 0.883302i | \(0.344685\pi\) | |||||||
\(740\) | −4.40270e12 | −0.539730 | ||||||||
\(741\) | −9.45200e11 | −0.115171 | ||||||||
\(742\) | −8.17167e10 | −0.00989677 | ||||||||
\(743\) | −2.23002e12 | −0.268448 | −0.134224 | − | 0.990951i | \(-0.542854\pi\) | ||||
−0.134224 | + | 0.990951i | \(0.542854\pi\) | |||||||
\(744\) | −5.43661e12 | −0.650504 | ||||||||
\(745\) | 3.12789e12 | 0.372004 | ||||||||
\(746\) | 3.47569e12 | 0.410882 | ||||||||
\(747\) | −2.32985e12 | −0.273770 | ||||||||
\(748\) | 5.08060e12 | 0.593414 | ||||||||
\(749\) | −3.59538e11 | −0.0417423 | ||||||||
\(750\) | 1.53976e11 | 0.0177696 | ||||||||
\(751\) | 1.65708e12 | 0.190092 | 0.0950459 | − | 0.995473i | \(-0.469700\pi\) | ||||
0.0950459 | + | 0.995473i | \(0.469700\pi\) | |||||||
\(752\) | −1.06514e13 | −1.21458 | ||||||||
\(753\) | −2.34348e12 | −0.265635 | ||||||||
\(754\) | −2.75058e12 | −0.309922 | ||||||||
\(755\) | 2.00346e12 | 0.224398 | ||||||||
\(756\) | 4.41347e11 | 0.0491397 | ||||||||
\(757\) | −1.28420e13 | −1.42135 | −0.710675 | − | 0.703521i | \(-0.751610\pi\) | ||||
−0.710675 | + | 0.703521i | \(0.751610\pi\) | |||||||
\(758\) | −2.75218e12 | −0.302807 | ||||||||
\(759\) | 3.52122e12 | 0.385129 | ||||||||
\(760\) | 4.00538e11 | 0.0435494 | ||||||||
\(761\) | 1.61852e13 | 1.74939 | 0.874694 | − | 0.484676i | \(-0.161063\pi\) | ||||
0.874694 | + | 0.484676i | \(0.161063\pi\) | |||||||
\(762\) | 2.01164e12 | 0.216149 | ||||||||
\(763\) | 4.25921e12 | 0.454955 | ||||||||
\(764\) | 1.23136e13 | 1.30757 | ||||||||
\(765\) | −1.03988e12 | −0.109776 | ||||||||
\(766\) | −2.45247e12 | −0.257380 | ||||||||
\(767\) | 1.14060e13 | 1.19002 | ||||||||
\(768\) | −8.23228e10 | −0.00853875 | ||||||||
\(769\) | 5.30462e12 | 0.546998 | 0.273499 | − | 0.961872i | \(-0.411819\pi\) | ||||
0.273499 | + | 0.961872i | \(0.411819\pi\) | |||||||
\(770\) | −3.97414e11 | −0.0407413 | ||||||||
\(771\) | −9.91345e12 | −1.01037 | ||||||||
\(772\) | 4.35775e12 | 0.441555 | ||||||||
\(773\) | −1.26188e13 | −1.27119 | −0.635596 | − | 0.772022i | \(-0.719245\pi\) | ||||
−0.635596 | + | 0.772022i | \(0.719245\pi\) | |||||||
\(774\) | −6.51812e11 | −0.0652812 | ||||||||
\(775\) | 3.49526e12 | 0.348034 | ||||||||
\(776\) | 8.99418e12 | 0.890397 | ||||||||
\(777\) | −2.32582e12 | −0.228919 | ||||||||
\(778\) | 3.27591e12 | 0.320571 | ||||||||
\(779\) | 2.09226e12 | 0.203562 | ||||||||
\(780\) | 3.12105e12 | 0.301908 | ||||||||
\(781\) | 9.36478e12 | 0.900675 | ||||||||
\(782\) | −1.93387e12 | −0.184925 | ||||||||
\(783\) | −1.37452e12 | −0.130684 | ||||||||
\(784\) | −6.38438e12 | −0.603527 | ||||||||
\(785\) | −2.89644e11 | −0.0272239 | ||||||||
\(786\) | −3.40644e12 | −0.318346 | ||||||||
\(787\) | 1.22887e13 | 1.14188 | 0.570941 | − | 0.820991i | \(-0.306579\pi\) | ||||
0.570941 | + | 0.820991i | \(0.306579\pi\) | |||||||
\(788\) | −5.46571e12 | −0.504985 | ||||||||
\(789\) | 5.06162e12 | 0.464990 | ||||||||
\(790\) | 2.21889e12 | 0.202682 | ||||||||
\(791\) | 2.42762e12 | 0.220489 | ||||||||
\(792\) | 2.18443e12 | 0.197277 | ||||||||
\(793\) | 2.02993e13 | 1.82286 | ||||||||
\(794\) | −4.38439e12 | −0.391487 | ||||||||
\(795\) | −2.88774e11 | −0.0256393 | ||||||||
\(796\) | −8.56441e12 | −0.756116 | ||||||||
\(797\) | −3.56495e12 | −0.312962 | −0.156481 | − | 0.987681i | \(-0.550015\pi\) | ||||
−0.156481 | + | 0.987681i | \(0.550015\pi\) | |||||||
\(798\) | 9.91385e10 | 0.00865425 | ||||||||
\(799\) | 1.56405e13 | 1.35766 | ||||||||
\(800\) | −2.02548e12 | −0.174833 | ||||||||
\(801\) | −2.78541e12 | −0.239080 | ||||||||
\(802\) | −2.14821e12 | −0.183354 | ||||||||
\(803\) | −6.37090e12 | −0.540730 | ||||||||
\(804\) | −6.14240e12 | −0.518425 | ||||||||
\(805\) | −1.12624e12 | −0.0945260 | ||||||||
\(806\) | −9.51585e12 | −0.794218 | ||||||||
\(807\) | −1.03043e13 | −0.855239 | ||||||||
\(808\) | −1.32833e13 | −1.09636 | ||||||||
\(809\) | −3.11624e12 | −0.255778 | −0.127889 | − | 0.991789i | \(-0.540820\pi\) | ||||
−0.127889 | + | 0.991789i | \(0.540820\pi\) | |||||||
\(810\) | −2.09483e11 | −0.0170988 | ||||||||
\(811\) | −2.30256e12 | −0.186904 | −0.0934518 | − | 0.995624i | \(-0.529790\pi\) | ||||
−0.0934518 | + | 0.995624i | \(0.529790\pi\) | |||||||
\(812\) | −2.14793e12 | −0.173388 | ||||||||
\(813\) | −1.24834e12 | −0.100213 | ||||||||
\(814\) | −5.39357e12 | −0.430593 | ||||||||
\(815\) | −7.99677e12 | −0.634900 | ||||||||
\(816\) | 3.54737e12 | 0.280092 | ||||||||
\(817\) | 1.09009e12 | 0.0855980 | ||||||||
\(818\) | 5.09651e11 | 0.0398000 | ||||||||
\(819\) | 1.64876e12 | 0.128050 | ||||||||
\(820\) | −6.90864e12 | −0.533617 | ||||||||
\(821\) | −6.28720e12 | −0.482962 | −0.241481 | − | 0.970406i | \(-0.577633\pi\) | ||||
−0.241481 | + | 0.970406i | \(0.577633\pi\) | |||||||
\(822\) | 7.56212e9 | 0.000577724 0 | ||||||||
\(823\) | 3.76056e12 | 0.285728 | 0.142864 | − | 0.989742i | \(-0.454369\pi\) | ||||
0.142864 | + | 0.989742i | \(0.454369\pi\) | |||||||
\(824\) | 2.27524e12 | 0.171932 | ||||||||
\(825\) | −1.40440e12 | −0.105547 | ||||||||
\(826\) | −1.19634e12 | −0.0894219 | ||||||||
\(827\) | 1.75054e13 | 1.30136 | 0.650679 | − | 0.759353i | \(-0.274484\pi\) | ||||
0.650679 | + | 0.759353i | \(0.274484\pi\) | |||||||
\(828\) | 2.90049e12 | 0.214454 | ||||||||
\(829\) | −2.42570e12 | −0.178378 | −0.0891891 | − | 0.996015i | \(-0.528428\pi\) | ||||
−0.0891891 | + | 0.996015i | \(0.528428\pi\) | |||||||
\(830\) | 1.72809e12 | 0.126391 | ||||||||
\(831\) | 7.45902e12 | 0.542597 | ||||||||
\(832\) | −6.56257e12 | −0.474809 | ||||||||
\(833\) | 9.37486e12 | 0.674625 | ||||||||
\(834\) | 5.77383e11 | 0.0413254 | ||||||||
\(835\) | −1.16062e13 | −0.826229 | ||||||||
\(836\) | −1.71167e12 | −0.121197 | ||||||||
\(837\) | −4.75526e12 | −0.334896 | ||||||||
\(838\) | −2.10424e11 | −0.0147400 | ||||||||
\(839\) | 9.69596e11 | 0.0675557 | 0.0337778 | − | 0.999429i | \(-0.489246\pi\) | ||||
0.0337778 | + | 0.999429i | \(0.489246\pi\) | |||||||
\(840\) | −6.98679e11 | −0.0484196 | ||||||||
\(841\) | −7.81769e12 | −0.538885 | ||||||||
\(842\) | 3.34574e12 | 0.229397 | ||||||||
\(843\) | 6.30813e12 | 0.430206 | ||||||||
\(844\) | 4.02593e12 | 0.273102 | ||||||||
\(845\) | 5.03164e12 | 0.339512 | ||||||||
\(846\) | 3.15078e12 | 0.211471 | ||||||||
\(847\) | −7.13582e11 | −0.0476397 | ||||||||
\(848\) | 9.85101e11 | 0.0654183 | ||||||||
\(849\) | −2.36895e12 | −0.156485 | ||||||||
\(850\) | 7.71298e11 | 0.0506801 | ||||||||
\(851\) | −1.52850e13 | −0.999042 | ||||||||
\(852\) | 7.71391e12 | 0.501529 | ||||||||
\(853\) | −2.11898e13 | −1.37043 | −0.685215 | − | 0.728340i | \(-0.740292\pi\) | ||||
−0.685215 | + | 0.728340i | \(0.740292\pi\) | |||||||
\(854\) | −2.12912e12 | −0.136975 | ||||||||
\(855\) | 3.50340e11 | 0.0224203 | ||||||||
\(856\) | −1.46582e12 | −0.0933142 | ||||||||
\(857\) | 8.34904e12 | 0.528717 | 0.264358 | − | 0.964425i | \(-0.414840\pi\) | ||||
0.264358 | + | 0.964425i | \(0.414840\pi\) | |||||||
\(858\) | 3.82347e12 | 0.240860 | ||||||||
\(859\) | −8.24621e12 | −0.516755 | −0.258378 | − | 0.966044i | \(-0.583188\pi\) | ||||
−0.258378 | + | 0.966044i | \(0.583188\pi\) | |||||||
\(860\) | −3.59948e12 | −0.224387 | ||||||||
\(861\) | −3.64964e12 | −0.226326 | ||||||||
\(862\) | 7.35568e12 | 0.453775 | ||||||||
\(863\) | 4.35663e12 | 0.267364 | 0.133682 | − | 0.991024i | \(-0.457320\pi\) | ||||
0.133682 | + | 0.991024i | \(0.457320\pi\) | |||||||
\(864\) | 2.75564e12 | 0.168233 | ||||||||
\(865\) | 3.06716e12 | 0.186279 | ||||||||
\(866\) | −1.64105e12 | −0.0991497 | ||||||||
\(867\) | 4.39665e12 | 0.264263 | ||||||||
\(868\) | −7.43096e12 | −0.444331 | ||||||||
\(869\) | −2.02382e13 | −1.20388 | ||||||||
\(870\) | 1.01951e12 | 0.0603327 | ||||||||
\(871\) | −2.29464e13 | −1.35093 | ||||||||
\(872\) | 1.73646e13 | 1.01705 | ||||||||
\(873\) | 7.86697e12 | 0.458399 | ||||||||
\(874\) | 6.51527e11 | 0.0377686 | ||||||||
\(875\) | 4.49189e11 | 0.0259055 | ||||||||
\(876\) | −5.24780e12 | −0.301099 | ||||||||
\(877\) | −1.21873e12 | −0.0695680 | −0.0347840 | − | 0.999395i | \(-0.511074\pi\) | ||||
−0.0347840 | + | 0.999395i | \(0.511074\pi\) | |||||||
\(878\) | −5.98825e12 | −0.340075 | ||||||||
\(879\) | 1.84197e13 | 1.04071 | ||||||||
\(880\) | 4.79085e12 | 0.269303 | ||||||||
\(881\) | 3.98577e12 | 0.222905 | 0.111453 | − | 0.993770i | \(-0.464450\pi\) | ||||
0.111453 | + | 0.993770i | \(0.464450\pi\) | |||||||
\(882\) | 1.88856e12 | 0.105080 | ||||||||
\(883\) | 2.19963e13 | 1.21766 | 0.608831 | − | 0.793300i | \(-0.291639\pi\) | ||||
0.608831 | + | 0.793300i | \(0.291639\pi\) | |||||||
\(884\) | 1.56340e13 | 0.861061 | ||||||||
\(885\) | −4.22767e12 | −0.231663 | ||||||||
\(886\) | 5.06025e12 | 0.275880 | ||||||||
\(887\) | 1.39860e13 | 0.758640 | 0.379320 | − | 0.925266i | \(-0.376158\pi\) | ||||
0.379320 | + | 0.925266i | \(0.376158\pi\) | |||||||
\(888\) | −9.48226e12 | −0.511745 | ||||||||
\(889\) | 5.86847e12 | 0.315113 | ||||||||
\(890\) | 2.06599e12 | 0.110376 | ||||||||
\(891\) | 1.91067e12 | 0.101563 | ||||||||
\(892\) | 1.99848e13 | 1.05696 | ||||||||
\(893\) | −5.26936e12 | −0.277285 | ||||||||
\(894\) | 3.15635e12 | 0.165259 | ||||||||
\(895\) | −8.05815e12 | −0.419790 | ||||||||
\(896\) | 5.57290e12 | 0.288865 | ||||||||
\(897\) | 1.08355e13 | 0.558833 | ||||||||
\(898\) | 3.51829e12 | 0.180546 | ||||||||
\(899\) | 2.31428e13 | 1.18167 | ||||||||
\(900\) | −1.15682e12 | −0.0587727 | ||||||||
\(901\) | −1.44653e12 | −0.0731248 | ||||||||
\(902\) | −8.46349e12 | −0.425716 | ||||||||
\(903\) | −1.90150e12 | −0.0951705 | ||||||||
\(904\) | 9.89727e12 | 0.492899 | ||||||||
\(905\) | 1.66396e13 | 0.824563 | ||||||||
\(906\) | 2.02169e12 | 0.0996869 | ||||||||
\(907\) | −8.00749e12 | −0.392884 | −0.196442 | − | 0.980515i | \(-0.562939\pi\) | ||||
−0.196442 | + | 0.980515i | \(0.562939\pi\) | |||||||
\(908\) | 2.43762e13 | 1.19009 | ||||||||
\(909\) | −1.16186e13 | −0.564436 | ||||||||
\(910\) | −1.22292e12 | −0.0591168 | ||||||||
\(911\) | −4.09248e13 | −1.96858 | −0.984291 | − | 0.176555i | \(-0.943505\pi\) | ||||
−0.984291 | + | 0.176555i | \(0.943505\pi\) | |||||||
\(912\) | −1.19512e12 | −0.0572052 | ||||||||
\(913\) | −1.57617e13 | −0.750731 | ||||||||
\(914\) | 4.81529e12 | 0.228226 | ||||||||
\(915\) | −7.52398e12 | −0.354857 | ||||||||
\(916\) | −2.61910e12 | −0.122920 | ||||||||
\(917\) | −9.93745e12 | −0.464102 | ||||||||
\(918\) | −1.04934e12 | −0.0487669 | ||||||||
\(919\) | 8.12730e12 | 0.375860 | 0.187930 | − | 0.982182i | \(-0.439822\pi\) | ||||
0.187930 | + | 0.982182i | \(0.439822\pi\) | |||||||
\(920\) | −4.59164e12 | −0.211311 | ||||||||
\(921\) | 4.88089e12 | 0.223527 | ||||||||
\(922\) | 2.15252e12 | 0.0980973 | ||||||||
\(923\) | 2.88172e13 | 1.30691 | ||||||||
\(924\) | 2.98576e12 | 0.134751 | ||||||||
\(925\) | 6.09625e12 | 0.273795 | ||||||||
\(926\) | −4.74938e12 | −0.212269 | ||||||||
\(927\) | 1.99010e12 | 0.0885147 | ||||||||
\(928\) | −1.34111e13 | −0.593605 | ||||||||
\(929\) | −4.43436e13 | −1.95326 | −0.976631 | − | 0.214923i | \(-0.931050\pi\) | ||||
−0.976631 | + | 0.214923i | \(0.931050\pi\) | |||||||
\(930\) | 3.52707e12 | 0.154611 | ||||||||
\(931\) | −3.15843e12 | −0.137783 | ||||||||
\(932\) | −2.44584e13 | −1.06183 | ||||||||
\(933\) | −1.10821e13 | −0.478801 | ||||||||
\(934\) | −2.20554e12 | −0.0948317 | ||||||||
\(935\) | −7.03490e12 | −0.301027 | ||||||||
\(936\) | 6.72192e12 | 0.286254 | ||||||||
\(937\) | −3.56882e13 | −1.51250 | −0.756251 | − | 0.654281i | \(-0.772971\pi\) | ||||
−0.756251 | + | 0.654281i | \(0.772971\pi\) | |||||||
\(938\) | 2.40677e12 | 0.101513 | ||||||||
\(939\) | −1.82683e13 | −0.766838 | ||||||||
\(940\) | 1.73994e13 | 0.726875 | ||||||||
\(941\) | 3.76351e13 | 1.56473 | 0.782366 | − | 0.622818i | \(-0.214012\pi\) | ||||
0.782366 | + | 0.622818i | \(0.214012\pi\) | |||||||
\(942\) | −2.92279e11 | −0.0120940 | ||||||||
\(943\) | −2.39850e13 | −0.987727 | ||||||||
\(944\) | 1.44219e13 | 0.591085 | ||||||||
\(945\) | −6.11116e11 | −0.0249276 | ||||||||
\(946\) | −4.40958e12 | −0.179014 | ||||||||
\(947\) | −1.01014e13 | −0.408139 | −0.204070 | − | 0.978956i | \(-0.565417\pi\) | ||||
−0.204070 | + | 0.978956i | \(0.565417\pi\) | |||||||
\(948\) | −1.66705e13 | −0.670365 | ||||||||
\(949\) | −1.96045e13 | −0.784616 | ||||||||
\(950\) | −2.59853e11 | −0.0103508 | ||||||||
\(951\) | 1.03993e13 | 0.412280 | ||||||||
\(952\) | −3.49982e12 | −0.138096 | ||||||||
\(953\) | 1.49469e13 | 0.586993 | 0.293497 | − | 0.955960i | \(-0.405181\pi\) | ||||
0.293497 | + | 0.955960i | \(0.405181\pi\) | |||||||
\(954\) | −2.91402e11 | −0.0113900 | ||||||||
\(955\) | −1.70501e13 | −0.663303 | ||||||||
\(956\) | −3.57380e13 | −1.38379 | ||||||||
\(957\) | −9.29876e12 | −0.358362 | ||||||||
\(958\) | 1.08345e13 | 0.415589 | ||||||||
\(959\) | 2.20607e10 | 0.000842238 0 | ||||||||
\(960\) | 2.43243e12 | 0.0924313 | ||||||||
\(961\) | 5.36247e13 | 2.02819 | ||||||||
\(962\) | −1.65970e13 | −0.624803 | ||||||||
\(963\) | −1.28211e12 | −0.0480405 | ||||||||
\(964\) | 2.77559e13 | 1.03516 | ||||||||
\(965\) | −6.03401e12 | −0.223992 | ||||||||
\(966\) | −1.13649e12 | −0.0419923 | ||||||||
\(967\) | 2.42942e13 | 0.893475 | 0.446738 | − | 0.894665i | \(-0.352586\pi\) | ||||
0.446738 | + | 0.894665i | \(0.352586\pi\) | |||||||
\(968\) | −2.90924e12 | −0.106498 | ||||||||
\(969\) | 1.75492e12 | 0.0639441 | ||||||||
\(970\) | −5.83507e12 | −0.211628 | ||||||||
\(971\) | −1.07032e13 | −0.386392 | −0.193196 | − | 0.981160i | \(-0.561885\pi\) | ||||
−0.193196 | + | 0.981160i | \(0.561885\pi\) | |||||||
\(972\) | 1.57384e12 | 0.0565540 | ||||||||
\(973\) | 1.68437e12 | 0.0602464 | ||||||||
\(974\) | 1.10201e12 | 0.0392346 | ||||||||
\(975\) | −4.32160e12 | −0.153152 | ||||||||
\(976\) | 2.56667e13 | 0.905412 | ||||||||
\(977\) | −1.53038e13 | −0.537372 | −0.268686 | − | 0.963228i | \(-0.586589\pi\) | ||||
−0.268686 | + | 0.963228i | \(0.586589\pi\) | |||||||
\(978\) | −8.06954e12 | −0.282048 | ||||||||
\(979\) | −1.88436e13 | −0.655604 | ||||||||
\(980\) | 1.04291e13 | 0.361186 | ||||||||
\(981\) | 1.51883e13 | 0.523600 | ||||||||
\(982\) | 3.63032e12 | 0.124578 | ||||||||
\(983\) | 3.27251e13 | 1.11787 | 0.558934 | − | 0.829212i | \(-0.311210\pi\) | ||||
0.558934 | + | 0.829212i | \(0.311210\pi\) | |||||||
\(984\) | −1.48794e13 | −0.505949 | ||||||||
\(985\) | 7.56816e12 | 0.256169 | ||||||||
\(986\) | 5.10691e12 | 0.172073 | ||||||||
\(987\) | 9.19163e12 | 0.308294 | ||||||||
\(988\) | −5.26714e12 | −0.175861 | ||||||||
\(989\) | −1.24965e13 | −0.415340 | ||||||||
\(990\) | −1.41718e12 | −0.0468884 | ||||||||
\(991\) | 3.05488e13 | 1.00615 | 0.503075 | − | 0.864243i | \(-0.332202\pi\) | ||||
0.503075 | + | 0.864243i | \(0.332202\pi\) | |||||||
\(992\) | −4.63967e13 | −1.52119 | ||||||||
\(993\) | −9.31649e11 | −0.0304075 | ||||||||
\(994\) | −3.02253e12 | −0.0982046 | ||||||||
\(995\) | 1.18588e13 | 0.383563 | ||||||||
\(996\) | −1.29831e13 | −0.418035 | ||||||||
\(997\) | 4.87857e13 | 1.56374 | 0.781870 | − | 0.623441i | \(-0.214266\pi\) | ||||
0.781870 | + | 0.623441i | \(0.214266\pi\) | |||||||
\(998\) | 1.72274e13 | 0.549709 | ||||||||
\(999\) | −8.29388e12 | −0.263459 |
(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 | 15.10.a.d.1.1 | ✓ | 2 | |
3.2 | odd | 2 | 45.10.a.d.1.2 | 2 | |||
4.3 | odd | 2 | 240.10.a.r.1.2 | 2 | |||
5.2 | odd | 4 | 75.10.b.f.49.2 | 4 | |||
5.3 | odd | 4 | 75.10.b.f.49.3 | 4 | |||
5.4 | even | 2 | 75.10.a.f.1.2 | 2 | |||
15.2 | even | 4 | 225.10.b.i.199.3 | 4 | |||
15.8 | even | 4 | 225.10.b.i.199.2 | 4 | |||
15.14 | odd | 2 | 225.10.a.k.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
15.10.a.d.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
45.10.a.d.1.2 | 2 | 3.2 | odd | 2 | |||
75.10.a.f.1.2 | 2 | 5.4 | even | 2 | |||
75.10.b.f.49.2 | 4 | 5.2 | odd | 4 | |||
75.10.b.f.49.3 | 4 | 5.3 | odd | 4 | |||
225.10.a.k.1.1 | 2 | 15.14 | odd | 2 | |||
225.10.b.i.199.2 | 4 | 15.8 | even | 4 | |||
225.10.b.i.199.3 | 4 | 15.2 | even | 4 | |||
240.10.a.r.1.2 | 2 | 4.3 | odd | 2 |