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: | \(0\) |
Dimension: | \(11\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{11} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{11} - 2 x^{10} - 977 x^{9} + 2592 x^{8} + 344686 x^{7} - 1160956 x^{6} - 53409536 x^{5} + \cdots + 238240894976 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{6}\cdot 3^{4}\cdot 7 \) |
Twist minimal: | no (minimal twist has level 43) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-19.3827\) 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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −17.3827 | −1.53643 | −0.768216 | − | 0.640191i | \(-0.778855\pi\) | ||||
−0.768216 | + | 0.640191i | \(0.778855\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 174.160 | 1.36062 | ||||||||
\(5\) | 230.747 | 0.825547 | 0.412773 | − | 0.910834i | \(-0.364560\pi\) | ||||
0.412773 | + | 0.910834i | \(0.364560\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1110.68 | −1.22390 | −0.611949 | − | 0.790897i | \(-0.709614\pi\) | ||||
−0.611949 | + | 0.790897i | \(0.709614\pi\) | |||||||
\(8\) | −802.384 | −0.554074 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −4011.02 | −1.26840 | ||||||||
\(11\) | 607.968 | 0.137723 | 0.0688615 | − | 0.997626i | \(-0.478063\pi\) | ||||
0.0688615 | + | 0.997626i | \(0.478063\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 13041.8 | 1.64640 | 0.823202 | − | 0.567748i | \(-0.192185\pi\) | ||||
0.823202 | + | 0.567748i | \(0.192185\pi\) | |||||||
\(14\) | 19306.6 | 1.88044 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −8344.81 | −0.509327 | ||||||||
\(17\) | 20609.8 | 1.01743 | 0.508713 | − | 0.860936i | \(-0.330122\pi\) | ||||
0.508713 | + | 0.860936i | \(0.330122\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −24170.2 | −0.808430 | −0.404215 | − | 0.914664i | \(-0.632455\pi\) | ||||
−0.404215 | + | 0.914664i | \(0.632455\pi\) | |||||||
\(20\) | 40186.9 | 1.12326 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −10568.2 | −0.211602 | ||||||||
\(23\) | −60316.5 | −1.03369 | −0.516843 | − | 0.856080i | \(-0.672893\pi\) | ||||
−0.516843 | + | 0.856080i | \(0.672893\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −24880.7 | −0.318472 | ||||||||
\(26\) | −226703. | −2.52959 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −193435. | −1.66526 | ||||||||
\(29\) | 77712.2 | 0.591693 | 0.295846 | − | 0.955236i | \(-0.404398\pi\) | ||||
0.295846 | + | 0.955236i | \(0.404398\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 34644.3 | 0.208865 | 0.104433 | − | 0.994532i | \(-0.466697\pi\) | ||||
0.104433 | + | 0.994532i | \(0.466697\pi\) | |||||||
\(32\) | 247761. | 1.33662 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −358255. | −1.56320 | ||||||||
\(35\) | −256286. | −1.01038 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 489896. | 1.59000 | 0.795002 | − | 0.606607i | \(-0.207470\pi\) | ||||
0.795002 | + | 0.606607i | \(0.207470\pi\) | |||||||
\(38\) | 420144. | 1.24210 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −185148. | −0.457414 | ||||||||
\(41\) | 809882. | 1.83518 | 0.917589 | − | 0.397529i | \(-0.130132\pi\) | ||||
0.917589 | + | 0.397529i | \(0.130132\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 79507.0 | 0.152499 | ||||||||
\(44\) | 105884. | 0.187389 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.04847e6 | 1.58819 | ||||||||
\(47\) | −289158. | −0.406249 | −0.203125 | − | 0.979153i | \(-0.565110\pi\) | ||||
−0.203125 | + | 0.979153i | \(0.565110\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 410063. | 0.497925 | ||||||||
\(50\) | 432494. | 0.489311 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.27136e6 | 2.24014 | ||||||||
\(53\) | −892274. | −0.823252 | −0.411626 | − | 0.911353i | \(-0.635039\pi\) | ||||
−0.411626 | + | 0.911353i | \(0.635039\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 140287. | 0.113697 | ||||||||
\(56\) | 891191. | 0.678129 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.35085e6 | −0.909096 | ||||||||
\(59\) | 1.51749e6 | 0.961930 | 0.480965 | − | 0.876740i | \(-0.340286\pi\) | ||||
0.480965 | + | 0.876740i | \(0.340286\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −160538. | −0.0905570 | −0.0452785 | − | 0.998974i | \(-0.514418\pi\) | ||||
−0.0452785 | + | 0.998974i | \(0.514418\pi\) | |||||||
\(62\) | −602213. | −0.320907 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −3.23863e6 | −1.54430 | ||||||||
\(65\) | 3.00937e6 | 1.35918 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.42938e6 | −0.986811 | −0.493406 | − | 0.869799i | \(-0.664248\pi\) | ||||
−0.493406 | + | 0.869799i | \(0.664248\pi\) | |||||||
\(68\) | 3.58940e6 | 1.38433 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 4.45495e6 | 1.55239 | ||||||||
\(71\) | −993231. | −0.329341 | −0.164671 | − | 0.986349i | \(-0.552656\pi\) | ||||
−0.164671 | + | 0.986349i | \(0.552656\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.67982e6 | −0.806262 | −0.403131 | − | 0.915142i | \(-0.632078\pi\) | ||||
−0.403131 | + | 0.915142i | \(0.632078\pi\) | |||||||
\(74\) | −8.51574e6 | −2.44293 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −4.20947e6 | −1.09997 | ||||||||
\(77\) | −675257. | −0.168559 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.46840e6 | −1.01966 | −0.509832 | − | 0.860274i | \(-0.670292\pi\) | ||||
−0.509832 | + | 0.860274i | \(0.670292\pi\) | |||||||
\(80\) | −1.92554e6 | −0.420473 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −1.40780e7 | −2.81963 | ||||||||
\(83\) | 4.10044e6 | 0.787150 | 0.393575 | − | 0.919292i | \(-0.371238\pi\) | ||||
0.393575 | + | 0.919292i | \(0.371238\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.75566e6 | 0.839932 | ||||||||
\(86\) | −1.38205e6 | −0.234304 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −487824. | −0.0763087 | ||||||||
\(89\) | 2.96316e6 | 0.445543 | 0.222772 | − | 0.974871i | \(-0.428490\pi\) | ||||
0.222772 | + | 0.974871i | \(0.428490\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.44853e7 | −2.01503 | ||||||||
\(92\) | −1.05047e7 | −1.40646 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 5.02636e6 | 0.624175 | ||||||||
\(95\) | −5.57721e6 | −0.667397 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9.83610e6 | −1.09426 | −0.547132 | − | 0.837046i | \(-0.684280\pi\) | ||||
−0.547132 | + | 0.837046i | \(0.684280\pi\) | |||||||
\(98\) | −7.12801e6 | −0.765028 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −4.33321e6 | −0.433321 | ||||||||
\(101\) | 1.11991e7 | 1.08158 | 0.540788 | − | 0.841159i | \(-0.318126\pi\) | ||||
0.540788 | + | 0.841159i | \(0.318126\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.09902e6 | 0.189272 | 0.0946359 | − | 0.995512i | \(-0.469831\pi\) | ||||
0.0946359 | + | 0.995512i | \(0.469831\pi\) | |||||||
\(104\) | −1.04646e7 | −0.912229 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.55102e7 | 1.26487 | ||||||||
\(107\) | −1.39300e7 | −1.09928 | −0.549639 | − | 0.835402i | \(-0.685235\pi\) | ||||
−0.549639 | + | 0.835402i | \(0.685235\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.48819e7 | 1.84031 | 0.920154 | − | 0.391557i | \(-0.128063\pi\) | ||||
0.920154 | + | 0.391557i | \(0.128063\pi\) | |||||||
\(110\) | −2.43857e6 | −0.174687 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 9.26840e6 | 0.623364 | ||||||||
\(113\) | 1.72023e7 | 1.12153 | 0.560766 | − | 0.827974i | \(-0.310507\pi\) | ||||
0.560766 | + | 0.827974i | \(0.310507\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.39179e7 | −0.853357 | ||||||||
\(116\) | 1.35343e7 | 0.805071 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −2.63781e7 | −1.47794 | ||||||||
\(119\) | −2.28908e7 | −1.24522 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.91175e7 | −0.981032 | ||||||||
\(122\) | 2.79058e6 | 0.139135 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 6.03365e6 | 0.284187 | ||||||||
\(125\) | −2.37683e7 | −1.08846 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.68734e7 | −1.59735 | −0.798675 | − | 0.601763i | \(-0.794465\pi\) | ||||
−0.798675 | + | 0.601763i | \(0.794465\pi\) | |||||||
\(128\) | 2.45829e7 | 1.03609 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −5.23110e7 | −2.08829 | ||||||||
\(131\) | −2.41863e7 | −0.939981 | −0.469991 | − | 0.882671i | \(-0.655743\pi\) | ||||
−0.469991 | + | 0.882671i | \(0.655743\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.68453e7 | 0.989435 | ||||||||
\(134\) | 4.22293e7 | 1.51617 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.65370e7 | −0.563729 | ||||||||
\(137\) | 4.37084e6 | 0.145226 | 0.0726128 | − | 0.997360i | \(-0.476866\pi\) | ||||
0.0726128 | + | 0.997360i | \(0.476866\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.60325e7 | 0.822174 | 0.411087 | − | 0.911596i | \(-0.365149\pi\) | ||||
0.411087 | + | 0.911596i | \(0.365149\pi\) | |||||||
\(140\) | −4.46347e7 | −1.37475 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1.72651e7 | 0.506010 | ||||||||
\(143\) | 7.92901e6 | 0.226748 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.79319e7 | 0.488470 | ||||||||
\(146\) | 4.65827e7 | 1.23877 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 8.53202e7 | 2.16340 | ||||||||
\(149\) | −2.65502e7 | −0.657530 | −0.328765 | − | 0.944412i | \(-0.606632\pi\) | ||||
−0.328765 | + | 0.944412i | \(0.606632\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.28071e7 | 1.24817 | 0.624084 | − | 0.781357i | \(-0.285472\pi\) | ||||
0.624084 | + | 0.781357i | \(0.285472\pi\) | |||||||
\(152\) | 1.93938e7 | 0.447930 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1.17378e7 | 0.258979 | ||||||||
\(155\) | 7.99408e6 | 0.172428 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.72632e7 | −1.38717 | −0.693584 | − | 0.720376i | \(-0.743969\pi\) | ||||
−0.693584 | + | 0.720376i | \(0.743969\pi\) | |||||||
\(158\) | 7.76730e7 | 1.56664 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 5.71702e7 | 1.10344 | ||||||||
\(161\) | 6.69922e7 | 1.26513 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.59234e7 | 1.01143 | 0.505717 | − | 0.862700i | \(-0.331228\pi\) | ||||
0.505717 | + | 0.862700i | \(0.331228\pi\) | |||||||
\(164\) | 1.41049e8 | 2.49699 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −7.12770e7 | −1.20940 | ||||||||
\(167\) | −1.13304e7 | −0.188252 | −0.0941258 | − | 0.995560i | \(-0.530006\pi\) | ||||
−0.0941258 | + | 0.995560i | \(0.530006\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.07341e8 | 1.71065 | ||||||||
\(170\) | −8.26664e7 | −1.29050 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1.38469e7 | 0.207493 | ||||||||
\(173\) | 3.43489e7 | 0.504373 | 0.252186 | − | 0.967679i | \(-0.418850\pi\) | ||||
0.252186 | + | 0.967679i | \(0.418850\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.76344e7 | 0.389778 | ||||||||
\(176\) | −5.07338e6 | −0.0701460 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −5.15078e7 | −0.684547 | ||||||||
\(179\) | −1.06394e8 | −1.38654 | −0.693268 | − | 0.720680i | \(-0.743830\pi\) | ||||
−0.693268 | + | 0.720680i | \(0.743830\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.03201e8 | −1.29363 | −0.646815 | − | 0.762647i | \(-0.723899\pi\) | ||||
−0.646815 | + | 0.762647i | \(0.723899\pi\) | |||||||
\(182\) | 2.51794e8 | 3.09596 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 4.83970e7 | 0.572739 | ||||||||
\(185\) | 1.13042e8 | 1.31262 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.25301e7 | 0.140123 | ||||||||
\(188\) | −5.03597e7 | −0.552752 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 9.69471e7 | 1.02541 | ||||||||
\(191\) | −6.61411e7 | −0.686839 | −0.343419 | − | 0.939182i | \(-0.611585\pi\) | ||||
−0.343419 | + | 0.939182i | \(0.611585\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.13623e7 | 0.514273 | 0.257136 | − | 0.966375i | \(-0.417221\pi\) | ||||
0.257136 | + | 0.966375i | \(0.417221\pi\) | |||||||
\(194\) | 1.70978e8 | 1.68126 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 7.14164e7 | 0.677488 | ||||||||
\(197\) | 9.19611e7 | 0.856983 | 0.428492 | − | 0.903546i | \(-0.359045\pi\) | ||||
0.428492 | + | 0.903546i | \(0.359045\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.18358e7 | 0.556230 | 0.278115 | − | 0.960548i | \(-0.410290\pi\) | ||||
0.278115 | + | 0.960548i | \(0.410290\pi\) | |||||||
\(200\) | 1.99639e7 | 0.176457 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −1.94670e8 | −1.66177 | ||||||||
\(203\) | −8.63132e7 | −0.724171 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.86878e8 | 1.51503 | ||||||||
\(206\) | −3.64867e7 | −0.290803 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.08832e8 | −0.838558 | ||||||||
\(209\) | −1.46947e7 | −0.111339 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.45231e8 | 1.06431 | 0.532157 | − | 0.846646i | \(-0.321382\pi\) | ||||
0.532157 | + | 0.846646i | \(0.321382\pi\) | |||||||
\(212\) | −1.55398e8 | −1.12014 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 2.42142e8 | 1.68897 | ||||||||
\(215\) | 1.83460e7 | 0.125895 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.84787e7 | −0.255630 | ||||||||
\(218\) | −4.32515e8 | −2.82751 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 2.44324e7 | 0.154699 | ||||||||
\(221\) | 2.68789e8 | 1.67509 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.18865e8 | 0.717775 | 0.358888 | − | 0.933381i | \(-0.383156\pi\) | ||||
0.358888 | + | 0.933381i | \(0.383156\pi\) | |||||||
\(224\) | −2.75183e8 | −1.63589 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −2.99023e8 | −1.72316 | ||||||||
\(227\) | 2.33026e8 | 1.32225 | 0.661125 | − | 0.750276i | \(-0.270079\pi\) | ||||
0.661125 | + | 0.750276i | \(0.270079\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.52042e8 | 1.38691 | 0.693457 | − | 0.720498i | \(-0.256087\pi\) | ||||
0.693457 | + | 0.720498i | \(0.256087\pi\) | |||||||
\(230\) | 2.41931e8 | 1.31112 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −6.23551e7 | −0.327841 | ||||||||
\(233\) | −1.61379e8 | −0.835799 | −0.417899 | − | 0.908493i | \(-0.637234\pi\) | ||||
−0.417899 | + | 0.908493i | \(0.637234\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.67224e7 | −0.335378 | ||||||||
\(236\) | 2.64286e8 | 1.30882 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 3.97906e8 | 1.91320 | ||||||||
\(239\) | 3.28589e8 | 1.55690 | 0.778449 | − | 0.627707i | \(-0.216007\pi\) | ||||
0.778449 | + | 0.627707i | \(0.216007\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.95088e7 | −0.273855 | −0.136928 | − | 0.990581i | \(-0.543723\pi\) | ||||
−0.136928 | + | 0.990581i | \(0.543723\pi\) | |||||||
\(242\) | 3.32315e8 | 1.50729 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −2.79592e7 | −0.123214 | ||||||||
\(245\) | 9.46209e7 | 0.411060 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.15223e8 | −1.33100 | ||||||||
\(248\) | −2.77981e7 | −0.115727 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 4.13158e8 | 1.67235 | ||||||||
\(251\) | 1.34270e8 | 0.535944 | 0.267972 | − | 0.963427i | \(-0.413646\pi\) | ||||
0.267972 | + | 0.963427i | \(0.413646\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.66705e7 | −0.142362 | ||||||||
\(254\) | 6.40960e8 | 2.45422 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1.27732e7 | −0.0475837 | ||||||||
\(257\) | 2.54950e8 | 0.936892 | 0.468446 | − | 0.883492i | \(-0.344814\pi\) | ||||
0.468446 | + | 0.883492i | \(0.344814\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5.44117e8 | −1.94600 | ||||||||
\(260\) | 5.24111e8 | 1.84934 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 4.20424e8 | 1.44422 | ||||||||
\(263\) | −1.82117e8 | −0.617314 | −0.308657 | − | 0.951173i | \(-0.599879\pi\) | ||||
−0.308657 | + | 0.951173i | \(0.599879\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.05890e8 | −0.679633 | ||||||||
\(266\) | −4.66645e8 | −1.52020 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −4.23101e8 | −1.34268 | ||||||||
\(269\) | 4.86909e8 | 1.52516 | 0.762579 | − | 0.646895i | \(-0.223933\pi\) | ||||
0.762579 | + | 0.646895i | \(0.223933\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.57858e7 | −0.170267 | −0.0851336 | − | 0.996370i | \(-0.527132\pi\) | ||||
−0.0851336 | + | 0.996370i | \(0.527132\pi\) | |||||||
\(272\) | −1.71985e8 | −0.518202 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −7.59772e7 | −0.223129 | ||||||||
\(275\) | −1.51266e7 | −0.0438610 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6.88409e8 | 1.94611 | 0.973055 | − | 0.230572i | \(-0.0740596\pi\) | ||||
0.973055 | + | 0.230572i | \(0.0740596\pi\) | |||||||
\(278\) | −4.52516e8 | −1.26322 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 2.05640e8 | 0.559828 | ||||||||
\(281\) | −2.36816e8 | −0.636707 | −0.318353 | − | 0.947972i | \(-0.603130\pi\) | ||||
−0.318353 | + | 0.947972i | \(0.603130\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3.02454e8 | 0.793245 | 0.396623 | − | 0.917982i | \(-0.370182\pi\) | ||||
0.396623 | + | 0.917982i | \(0.370182\pi\) | |||||||
\(284\) | −1.72981e8 | −0.448109 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.37828e8 | −0.348383 | ||||||||
\(287\) | −8.99518e8 | −2.24607 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.44250e7 | 0.0351539 | ||||||||
\(290\) | −3.11705e8 | −0.750501 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −4.66718e8 | −1.09702 | ||||||||
\(293\) | 6.95562e8 | 1.61547 | 0.807735 | − | 0.589546i | \(-0.200693\pi\) | ||||
0.807735 | + | 0.589546i | \(0.200693\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.50157e8 | 0.794118 | ||||||||
\(296\) | −3.93085e8 | −0.880979 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 4.61515e8 | 1.01025 | ||||||||
\(299\) | −7.86637e8 | −1.70187 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.83067e7 | −0.186643 | ||||||||
\(302\) | −9.17932e8 | −1.91773 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 2.01696e8 | 0.411755 | ||||||||
\(305\) | −3.70436e7 | −0.0747591 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6.66587e8 | 1.31484 | 0.657420 | − | 0.753525i | \(-0.271648\pi\) | ||||
0.657420 | + | 0.753525i | \(0.271648\pi\) | |||||||
\(308\) | −1.17603e8 | −0.229345 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1.38959e8 | −0.264924 | ||||||||
\(311\) | 8.68038e8 | 1.63635 | 0.818177 | − | 0.574967i | \(-0.194985\pi\) | ||||
0.818177 | + | 0.574967i | \(0.194985\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.01957e8 | 1.10958 | 0.554792 | − | 0.831989i | \(-0.312798\pi\) | ||||
0.554792 | + | 0.831989i | \(0.312798\pi\) | |||||||
\(314\) | 1.16922e9 | 2.13129 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −7.78215e8 | −1.38738 | ||||||||
\(317\) | 8.81210e8 | 1.55372 | 0.776859 | − | 0.629675i | \(-0.216812\pi\) | ||||
0.776859 | + | 0.629675i | \(0.216812\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.72466e7 | 0.0814897 | ||||||||
\(320\) | −7.47305e8 | −1.27489 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −1.16451e9 | −1.94378 | ||||||||
\(323\) | −4.98143e8 | −0.822517 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.24489e8 | −0.524334 | ||||||||
\(326\) | −9.72103e8 | −1.55400 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −6.49837e8 | −1.01682 | ||||||||
\(329\) | 3.21161e8 | 0.497208 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.76684e8 | −1.32876 | −0.664378 | − | 0.747397i | \(-0.731303\pi\) | ||||
−0.664378 | + | 0.747397i | \(0.731303\pi\) | |||||||
\(332\) | 7.14133e8 | 1.07102 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1.96954e8 | 0.289236 | ||||||||
\(335\) | −5.60574e8 | −0.814659 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.84104e8 | −0.546694 | −0.273347 | − | 0.961916i | \(-0.588131\pi\) | ||||
−0.273347 | + | 0.961916i | \(0.588131\pi\) | |||||||
\(338\) | −1.86587e9 | −2.62829 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 8.28244e8 | 1.14283 | ||||||||
\(341\) | 2.10626e7 | 0.0287655 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 4.59244e8 | 0.614488 | ||||||||
\(344\) | −6.37952e7 | −0.0844954 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −5.97078e8 | −0.774934 | ||||||||
\(347\) | 9.79801e8 | 1.25888 | 0.629441 | − | 0.777049i | \(-0.283284\pi\) | ||||
0.629441 | + | 0.777049i | \(0.283284\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.02828e9 | −1.29485 | −0.647427 | − | 0.762128i | \(-0.724155\pi\) | ||||
−0.647427 | + | 0.762128i | \(0.724155\pi\) | |||||||
\(350\) | −4.80362e8 | −0.598867 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.50631e8 | 0.184083 | ||||||||
\(353\) | 1.21223e9 | 1.46680 | 0.733402 | − | 0.679795i | \(-0.237931\pi\) | ||||
0.733402 | + | 0.679795i | \(0.237931\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.29185e8 | −0.271887 | ||||||||
\(356\) | 5.16063e8 | 0.606217 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.84942e9 | 2.13032 | ||||||||
\(359\) | −1.13679e9 | −1.29673 | −0.648365 | − | 0.761330i | \(-0.724547\pi\) | ||||
−0.648365 | + | 0.761330i | \(0.724547\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.09674e8 | −0.346441 | ||||||||
\(362\) | 1.79392e9 | 1.98757 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −2.52275e9 | −2.74170 | ||||||||
\(365\) | −6.18362e8 | −0.665607 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.53409e9 | 1.62002 | 0.810009 | − | 0.586418i | \(-0.199462\pi\) | ||||
0.810009 | + | 0.586418i | \(0.199462\pi\) | |||||||
\(368\) | 5.03330e8 | 0.526484 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −1.96498e9 | −2.01676 | ||||||||
\(371\) | 9.91029e8 | 1.00758 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8.11683e8 | −0.809852 | −0.404926 | − | 0.914350i | \(-0.632703\pi\) | ||||
−0.404926 | + | 0.914350i | \(0.632703\pi\) | |||||||
\(374\) | −2.17808e8 | −0.215289 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2.32016e8 | 0.225092 | ||||||||
\(377\) | 1.01351e9 | 0.974166 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.21198e8 | 0.208710 | 0.104355 | − | 0.994540i | \(-0.466722\pi\) | ||||
0.104355 | + | 0.994540i | \(0.466722\pi\) | |||||||
\(380\) | −9.71325e8 | −0.908076 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 1.14971e9 | 1.05528 | ||||||||
\(383\) | −1.31039e9 | −1.19180 | −0.595901 | − | 0.803058i | \(-0.703205\pi\) | ||||
−0.595901 | + | 0.803058i | \(0.703205\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.55814e8 | −0.139153 | ||||||||
\(386\) | −8.92817e8 | −0.790145 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −1.71305e9 | −1.48888 | ||||||||
\(389\) | −2.22960e8 | −0.192045 | −0.0960226 | − | 0.995379i | \(-0.530612\pi\) | ||||
−0.0960226 | + | 0.995379i | \(0.530612\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.24311e9 | −1.05170 | ||||||||
\(392\) | −3.29028e8 | −0.275887 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −1.59854e9 | −1.31670 | ||||||||
\(395\) | −1.03107e9 | −0.841780 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −6.55657e8 | −0.525909 | −0.262954 | − | 0.964808i | \(-0.584697\pi\) | ||||
−0.262954 | + | 0.964808i | \(0.584697\pi\) | |||||||
\(398\) | −1.07488e9 | −0.854610 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2.07624e8 | 0.162207 | ||||||||
\(401\) | 7.45083e8 | 0.577031 | 0.288516 | − | 0.957475i | \(-0.406838\pi\) | ||||
0.288516 | + | 0.957475i | \(0.406838\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.51825e8 | 0.343877 | ||||||||
\(404\) | 1.95043e9 | 1.47162 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.50036e9 | 1.11264 | ||||||||
\(407\) | 2.97841e8 | 0.218980 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.87681e8 | −0.352456 | −0.176228 | − | 0.984349i | \(-0.556390\pi\) | ||||
−0.176228 | + | 0.984349i | \(0.556390\pi\) | |||||||
\(410\) | −3.24846e9 | −2.32773 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 3.65565e8 | 0.257528 | ||||||||
\(413\) | −1.68544e9 | −1.17730 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 9.46167e8 | 0.649829 | ||||||||
\(416\) | 3.23125e9 | 2.20062 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 2.55434e8 | 0.171065 | ||||||||
\(419\) | −1.39810e9 | −0.928518 | −0.464259 | − | 0.885700i | \(-0.653679\pi\) | ||||
−0.464259 | + | 0.885700i | \(0.653679\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.54250e9 | −1.66063 | −0.830316 | − | 0.557293i | \(-0.811840\pi\) | ||||
−0.830316 | + | 0.557293i | \(0.811840\pi\) | |||||||
\(422\) | −2.52451e9 | −1.63525 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 7.15947e8 | 0.456142 | ||||||||
\(425\) | −5.12785e8 | −0.324022 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.78306e8 | 0.110833 | ||||||||
\(428\) | −2.42605e9 | −1.49570 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −3.18904e8 | −0.193429 | ||||||||
\(431\) | −6.45199e8 | −0.388171 | −0.194086 | − | 0.980985i | \(-0.562174\pi\) | ||||
−0.194086 | + | 0.980985i | \(0.562174\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.41525e9 | −0.837770 | −0.418885 | − | 0.908039i | \(-0.637579\pi\) | ||||
−0.418885 | + | 0.908039i | \(0.637579\pi\) | |||||||
\(434\) | 6.68865e8 | 0.392757 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 4.33342e9 | 2.50397 | ||||||||
\(437\) | 1.45786e9 | 0.835663 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.20780e9 | 1.80959 | 0.904797 | − | 0.425844i | \(-0.140023\pi\) | ||||
0.904797 | + | 0.425844i | \(0.140023\pi\) | |||||||
\(440\) | −1.12564e8 | −0.0629964 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −4.67230e9 | −2.57367 | ||||||||
\(443\) | 3.24734e9 | 1.77466 | 0.887328 | − | 0.461138i | \(-0.152559\pi\) | ||||
0.887328 | + | 0.461138i | \(0.152559\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6.83741e8 | 0.367817 | ||||||||
\(446\) | −2.06621e9 | −1.10281 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 3.59707e9 | 1.89006 | ||||||||
\(449\) | 9.00041e8 | 0.469246 | 0.234623 | − | 0.972086i | \(-0.424615\pi\) | ||||
0.234623 | + | 0.972086i | \(0.424615\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.92383e8 | 0.252746 | ||||||||
\(452\) | 2.99595e9 | 1.52598 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −4.05063e9 | −2.03155 | ||||||||
\(455\) | −3.34244e9 | −1.66350 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.56466e9 | 1.74708 | 0.873538 | − | 0.486756i | \(-0.161820\pi\) | ||||
0.873538 | + | 0.486756i | \(0.161820\pi\) | |||||||
\(458\) | −4.38119e9 | −2.13090 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −2.42394e9 | −1.16110 | ||||||||
\(461\) | −2.12032e9 | −1.00797 | −0.503986 | − | 0.863712i | \(-0.668134\pi\) | ||||
−0.503986 | + | 0.863712i | \(0.668134\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.32103e9 | −0.618555 | −0.309278 | − | 0.950972i | \(-0.600087\pi\) | ||||
−0.309278 | + | 0.950972i | \(0.600087\pi\) | |||||||
\(464\) | −6.48494e8 | −0.301365 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 2.80521e9 | 1.28415 | ||||||||
\(467\) | −2.75292e7 | −0.0125079 | −0.00625395 | − | 0.999980i | \(-0.501991\pi\) | ||||
−0.00625395 | + | 0.999980i | \(0.501991\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.69826e9 | 1.20776 | ||||||||
\(470\) | 1.15982e9 | 0.515285 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −1.21761e9 | −0.532980 | ||||||||
\(473\) | 4.83377e7 | 0.0210026 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.01370e8 | 0.257463 | ||||||||
\(476\) | −3.98667e9 | −1.69428 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −5.71178e9 | −2.39207 | ||||||||
\(479\) | −3.09426e9 | −1.28642 | −0.643209 | − | 0.765691i | \(-0.722397\pi\) | ||||
−0.643209 | + | 0.765691i | \(0.722397\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.38914e9 | 2.61779 | ||||||||
\(482\) | 1.03443e9 | 0.420760 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −3.32951e9 | −1.33482 | ||||||||
\(485\) | −2.26965e9 | −0.903366 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.45364e9 | 0.962629 | 0.481315 | − | 0.876548i | \(-0.340159\pi\) | ||||
0.481315 | + | 0.876548i | \(0.340159\pi\) | |||||||
\(488\) | 1.28813e8 | 0.0501753 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −1.64477e9 | −0.631566 | ||||||||
\(491\) | 3.55312e9 | 1.35464 | 0.677321 | − | 0.735688i | \(-0.263141\pi\) | ||||
0.677321 | + | 0.735688i | \(0.263141\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.60163e9 | 0.602003 | ||||||||
\(494\) | 5.47945e9 | 2.04500 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.89100e8 | −0.106381 | ||||||||
\(497\) | 1.10316e9 | 0.403080 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.61280e9 | 0.581069 | 0.290534 | − | 0.956865i | \(-0.406167\pi\) | ||||
0.290534 | + | 0.956865i | \(0.406167\pi\) | |||||||
\(500\) | −4.13948e9 | −1.48099 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −2.33397e9 | −0.823442 | ||||||||
\(503\) | 3.82508e9 | 1.34015 | 0.670074 | − | 0.742294i | \(-0.266262\pi\) | ||||
0.670074 | + | 0.742294i | \(0.266262\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.58415e9 | 0.892891 | ||||||||
\(506\) | 6.37435e8 | 0.218730 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −6.42186e9 | −2.17339 | ||||||||
\(509\) | −9.34320e8 | −0.314039 | −0.157019 | − | 0.987596i | \(-0.550189\pi\) | ||||
−0.157019 | + | 0.987596i | \(0.550189\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.97642e9 | 0.986782 | ||||||||
\(512\) | −2.92457e9 | −0.962981 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −4.43174e9 | −1.43947 | ||||||||
\(515\) | 4.84343e8 | 0.156253 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.75799e8 | −0.0559499 | ||||||||
\(518\) | 9.45825e9 | 2.98990 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −2.41467e9 | −0.753088 | ||||||||
\(521\) | −1.99243e9 | −0.617237 | −0.308619 | − | 0.951186i | \(-0.599867\pi\) | ||||
−0.308619 | + | 0.951186i | \(0.599867\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.41120e9 | −0.737017 | −0.368509 | − | 0.929624i | \(-0.620132\pi\) | ||||
−0.368509 | + | 0.929624i | \(0.620132\pi\) | |||||||
\(524\) | −4.21228e9 | −1.27896 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 3.16570e9 | 0.948460 | ||||||||
\(527\) | 7.14012e8 | 0.212505 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2.33258e8 | 0.0685081 | ||||||||
\(530\) | 3.57893e9 | 1.04421 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 4.67537e9 | 1.34625 | ||||||||
\(533\) | 1.05623e10 | 3.02145 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3.21431e9 | −0.907506 | ||||||||
\(536\) | 1.94930e9 | 0.546766 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −8.46382e9 | −2.34330 | ||||||||
\(539\) | 2.49305e8 | 0.0685757 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.57719e9 | 1.24282 | 0.621410 | − | 0.783486i | \(-0.286560\pi\) | ||||
0.621410 | + | 0.783486i | \(0.286560\pi\) | |||||||
\(542\) | 9.69710e8 | 0.261604 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 5.10630e9 | 1.35991 | ||||||||
\(545\) | 5.74143e9 | 1.51926 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.95785e9 | 0.511475 | 0.255737 | − | 0.966746i | \(-0.417682\pi\) | ||||
0.255737 | + | 0.966746i | \(0.417682\pi\) | |||||||
\(548\) | 7.61225e8 | 0.197597 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 2.62943e8 | 0.0673894 | ||||||||
\(551\) | −1.87832e9 | −0.478342 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.96295e9 | 1.24796 | ||||||||
\(554\) | −1.19664e10 | −2.99007 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 4.53381e9 | 1.11867 | ||||||||
\(557\) | 5.46100e9 | 1.33899 | 0.669497 | − | 0.742814i | \(-0.266510\pi\) | ||||
0.669497 | + | 0.742814i | \(0.266510\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.03692e9 | 0.251074 | ||||||||
\(560\) | 2.13866e9 | 0.514616 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 4.11652e9 | 0.978256 | ||||||||
\(563\) | −1.67608e9 | −0.395836 | −0.197918 | − | 0.980219i | \(-0.563418\pi\) | ||||
−0.197918 | + | 0.980219i | \(0.563418\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.96938e9 | 0.925877 | ||||||||
\(566\) | −5.25749e9 | −1.21877 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 7.96953e8 | 0.182479 | ||||||||
\(569\) | 6.70164e8 | 0.152506 | 0.0762532 | − | 0.997088i | \(-0.475704\pi\) | ||||
0.0762532 | + | 0.997088i | \(0.475704\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.11196e9 | −0.924320 | −0.462160 | − | 0.886797i | \(-0.652925\pi\) | ||||
−0.462160 | + | 0.886797i | \(0.652925\pi\) | |||||||
\(572\) | 1.38092e9 | 0.308518 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 1.56361e10 | 3.45094 | ||||||||
\(575\) | 1.50071e9 | 0.329201 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3.72343e9 | 0.806915 | 0.403458 | − | 0.914998i | \(-0.367808\pi\) | ||||
0.403458 | + | 0.914998i | \(0.367808\pi\) | |||||||
\(578\) | −2.50746e8 | −0.0540116 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 3.12301e9 | 0.664624 | ||||||||
\(581\) | −4.55427e9 | −0.963391 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −5.42474e8 | −0.113381 | ||||||||
\(584\) | 2.15025e9 | 0.446729 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.20908e10 | −2.48206 | ||||||||
\(587\) | 5.57358e9 | 1.13737 | 0.568684 | − | 0.822556i | \(-0.307453\pi\) | ||||
0.568684 | + | 0.822556i | \(0.307453\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −8.37359e8 | −0.168853 | ||||||||
\(590\) | −6.08668e9 | −1.22011 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −4.08809e9 | −0.809832 | ||||||||
\(593\) | 7.08618e9 | 1.39547 | 0.697735 | − | 0.716356i | \(-0.254191\pi\) | ||||
0.697735 | + | 0.716356i | \(0.254191\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5.28200e9 | −1.02799 | ||||||||
\(596\) | −4.62397e9 | −0.894650 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 1.36739e10 | 2.61480 | ||||||||
\(599\) | 9.43000e9 | 1.79274 | 0.896371 | − | 0.443304i | \(-0.146194\pi\) | ||||
0.896371 | + | 0.443304i | \(0.146194\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8.09030e9 | −1.52021 | −0.760106 | − | 0.649799i | \(-0.774853\pi\) | ||||
−0.760106 | + | 0.649799i | \(0.774853\pi\) | |||||||
\(602\) | 1.53501e9 | 0.286764 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 9.19688e9 | 1.69829 | ||||||||
\(605\) | −4.41132e9 | −0.809888 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5.71746e9 | −1.03763 | −0.518815 | − | 0.854886i | \(-0.673627\pi\) | ||||
−0.518815 | + | 0.854886i | \(0.673627\pi\) | |||||||
\(608\) | −5.98843e9 | −1.08056 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 6.43920e8 | 0.114862 | ||||||||
\(611\) | −3.77115e9 | −0.668851 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2.69282e9 | −0.472166 | −0.236083 | − | 0.971733i | \(-0.575864\pi\) | ||||
−0.236083 | + | 0.971733i | \(0.575864\pi\) | |||||||
\(614\) | −1.15871e10 | −2.02016 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 5.41816e8 | 0.0933940 | ||||||||
\(617\) | −3.24038e9 | −0.555390 | −0.277695 | − | 0.960669i | \(-0.589571\pi\) | ||||
−0.277695 | + | 0.960669i | \(0.589571\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2.96275e9 | −0.502086 | −0.251043 | − | 0.967976i | \(-0.580773\pi\) | ||||
−0.251043 | + | 0.967976i | \(0.580773\pi\) | |||||||
\(620\) | 1.39225e9 | 0.234610 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −1.50889e10 | −2.51415 | ||||||||
\(623\) | −3.29112e9 | −0.545299 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −3.54067e9 | −0.580103 | ||||||||
\(626\) | −1.04637e10 | −1.70480 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −1.17146e10 | −1.88741 | ||||||||
\(629\) | 1.00967e10 | 1.61771 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.21319e9 | −0.350685 | −0.175342 | − | 0.984508i | \(-0.556103\pi\) | ||||
−0.175342 | + | 0.984508i | \(0.556103\pi\) | |||||||
\(632\) | 3.58537e9 | 0.564969 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −1.53179e10 | −2.38718 | ||||||||
\(635\) | −8.50843e9 | −1.31869 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.34796e9 | 0.819786 | ||||||||
\(638\) | −8.21275e8 | −0.125203 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 5.67243e9 | 0.855341 | ||||||||
\(641\) | 3.46476e9 | 0.519600 | 0.259800 | − | 0.965662i | \(-0.416343\pi\) | ||||
0.259800 | + | 0.965662i | \(0.416343\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6.65219e9 | 0.986794 | 0.493397 | − | 0.869804i | \(-0.335755\pi\) | ||||
0.493397 | + | 0.869804i | \(0.335755\pi\) | |||||||
\(644\) | 1.16674e10 | 1.72136 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 8.65908e9 | 1.26374 | ||||||||
\(647\) | 5.79744e9 | 0.841533 | 0.420766 | − | 0.907169i | \(-0.361761\pi\) | ||||
0.420766 | + | 0.907169i | \(0.361761\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 9.22585e8 | 0.132480 | ||||||||
\(650\) | 5.64051e9 | 0.805604 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 9.73962e9 | 1.37618 | ||||||||
\(653\) | −5.81937e9 | −0.817861 | −0.408931 | − | 0.912566i | \(-0.634098\pi\) | ||||
−0.408931 | + | 0.912566i | \(0.634098\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5.58092e9 | −0.775999 | ||||||||
\(656\) | −6.75832e9 | −0.934706 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −5.58267e9 | −0.763926 | ||||||||
\(659\) | 6.30400e9 | 0.858059 | 0.429029 | − | 0.903290i | \(-0.358856\pi\) | ||||
0.429029 | + | 0.903290i | \(0.358856\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5.51668e9 | −0.742973 | −0.371486 | − | 0.928438i | \(-0.621152\pi\) | ||||
−0.371486 | + | 0.928438i | \(0.621152\pi\) | |||||||
\(662\) | 1.52392e10 | 2.04154 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −3.29013e9 | −0.436139 | ||||||||
\(665\) | 6.19448e9 | 0.816825 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4.68733e9 | −0.611625 | ||||||||
\(668\) | −1.97331e9 | −0.256140 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 9.74431e9 | 1.25167 | ||||||||
\(671\) | −9.76017e7 | −0.0124718 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5.21617e9 | 0.659628 | 0.329814 | − | 0.944046i | \(-0.393014\pi\) | ||||
0.329814 | + | 0.944046i | \(0.393014\pi\) | |||||||
\(674\) | 6.67678e9 | 0.839958 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.86944e10 | 2.32755 | ||||||||
\(677\) | −3.56727e9 | −0.441851 | −0.220925 | − | 0.975291i | \(-0.570908\pi\) | ||||
−0.220925 | + | 0.975291i | \(0.570908\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.09247e10 | 1.33927 | ||||||||
\(680\) | −3.81586e9 | −0.465384 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −3.66127e8 | −0.0441963 | ||||||||
\(683\) | 6.40635e9 | 0.769375 | 0.384688 | − | 0.923047i | \(-0.374309\pi\) | ||||
0.384688 | + | 0.923047i | \(0.374309\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.00856e9 | 0.119890 | ||||||||
\(686\) | −7.98291e9 | −0.944120 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −6.63471e8 | −0.0776716 | ||||||||
\(689\) | −1.16369e10 | −1.35541 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.21339e10 | −1.39903 | −0.699513 | − | 0.714620i | \(-0.746600\pi\) | ||||
−0.699513 | + | 0.714620i | \(0.746600\pi\) | |||||||
\(692\) | 5.98220e9 | 0.686261 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1.70316e10 | −1.93419 | ||||||||
\(695\) | 6.00693e9 | 0.678744 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.66915e10 | 1.86716 | ||||||||
\(698\) | 1.78743e10 | 1.98946 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 4.81280e9 | 0.530341 | ||||||||
\(701\) | −1.62846e10 | −1.78552 | −0.892759 | − | 0.450535i | \(-0.851233\pi\) | ||||
−0.892759 | + | 0.450535i | \(0.851233\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.18409e10 | −1.28541 | ||||||||
\(704\) | −1.96898e9 | −0.212686 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −2.10718e10 | −2.25364 | ||||||||
\(707\) | −1.24386e10 | −1.32374 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3.23891e9 | −0.341301 | −0.170650 | − | 0.985332i | \(-0.554587\pi\) | ||||
−0.170650 | + | 0.985332i | \(0.554587\pi\) | |||||||
\(710\) | 3.98387e9 | 0.417735 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −2.37759e9 | −0.246864 | ||||||||
\(713\) | −2.08962e9 | −0.215901 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.82960e9 | 0.187191 | ||||||||
\(716\) | −1.85295e10 | −1.88655 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 1.97605e10 | 1.99234 | ||||||||
\(719\) | −8.54046e9 | −0.856900 | −0.428450 | − | 0.903565i | \(-0.640940\pi\) | ||||
−0.428450 | + | 0.903565i | \(0.640940\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.33133e9 | −0.231649 | ||||||||
\(722\) | 5.38298e9 | 0.532283 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −1.79735e10 | −1.76014 | ||||||||
\(725\) | −1.93353e9 | −0.188438 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −9.39101e9 | −0.906445 | −0.453223 | − | 0.891397i | \(-0.649726\pi\) | ||||
−0.453223 | + | 0.891397i | \(0.649726\pi\) | |||||||
\(728\) | 1.16228e10 | 1.11648 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 1.07488e10 | 1.02266 | ||||||||
\(731\) | 1.63862e9 | 0.155156 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 6.63206e9 | 0.621991 | 0.310996 | − | 0.950411i | \(-0.399338\pi\) | ||||
0.310996 | + | 0.950411i | \(0.399338\pi\) | |||||||
\(734\) | −2.66667e10 | −2.48905 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.49441e10 | −1.38165 | ||||||||
\(737\) | −1.47699e9 | −0.135907 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 9.73593e9 | 0.887405 | 0.443703 | − | 0.896174i | \(-0.353665\pi\) | ||||
0.443703 | + | 0.896174i | \(0.353665\pi\) | |||||||
\(740\) | 1.96874e10 | 1.78598 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −1.72268e10 | −1.54807 | ||||||||
\(743\) | 1.04679e9 | 0.0936265 | 0.0468132 | − | 0.998904i | \(-0.485093\pi\) | ||||
0.0468132 | + | 0.998904i | \(0.485093\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6.12638e9 | −0.542822 | ||||||||
\(746\) | 1.41093e10 | 1.24428 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 2.18224e9 | 0.190654 | ||||||||
\(749\) | 1.54717e10 | 1.34540 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.53753e10 | 1.32460 | 0.662300 | − | 0.749239i | \(-0.269580\pi\) | ||||
0.662300 | + | 0.749239i | \(0.269580\pi\) | |||||||
\(752\) | 2.41297e9 | 0.206914 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −1.76176e10 | −1.49674 | ||||||||
\(755\) | 1.21851e10 | 1.03042 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.40954e9 | −0.118098 | −0.0590489 | − | 0.998255i | \(-0.518807\pi\) | ||||
−0.0590489 | + | 0.998255i | \(0.518807\pi\) | |||||||
\(758\) | −3.84502e9 | −0.320669 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 4.47506e9 | 0.369787 | ||||||||
\(761\) | 1.37074e10 | 1.12748 | 0.563740 | − | 0.825952i | \(-0.309362\pi\) | ||||
0.563740 | + | 0.825952i | \(0.309362\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.76358e10 | −2.25235 | ||||||||
\(764\) | −1.15191e10 | −0.934529 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 2.27781e10 | 1.83112 | ||||||||
\(767\) | 1.97908e10 | 1.58373 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −3.22094e9 | −0.255412 | −0.127706 | − | 0.991812i | \(-0.540761\pi\) | ||||
−0.127706 | + | 0.991812i | \(0.540761\pi\) | |||||||
\(770\) | 2.70847e9 | 0.213799 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 8.94524e9 | 0.699732 | ||||||||
\(773\) | −1.47558e10 | −1.14904 | −0.574518 | − | 0.818492i | \(-0.694810\pi\) | ||||
−0.574518 | + | 0.818492i | \(0.694810\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −8.61973e8 | −0.0665178 | ||||||||
\(776\) | 7.89234e9 | 0.606303 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 3.87566e9 | 0.295064 | ||||||||
\(779\) | −1.95750e10 | −1.48361 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.03853e8 | −0.0453579 | ||||||||
\(782\) | 2.16087e10 | 1.61586 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −3.42190e9 | −0.253607 | ||||||||
\(785\) | −1.55208e10 | −1.14517 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −5.55719e9 | −0.406390 | −0.203195 | − | 0.979138i | \(-0.565133\pi\) | ||||
−0.203195 | + | 0.979138i | \(0.565133\pi\) | |||||||
\(788\) | 1.60159e10 | 1.16603 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 1.79228e10 | 1.29334 | ||||||||
\(791\) | −1.91062e10 | −1.37264 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.09370e9 | −0.149094 | ||||||||
\(794\) | 1.13971e10 | 0.808023 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.07693e10 | 0.756820 | ||||||||
\(797\) | 1.17611e10 | 0.822891 | 0.411446 | − | 0.911434i | \(-0.365024\pi\) | ||||
0.411446 | + | 0.911434i | \(0.365024\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.95949e9 | −0.413328 | ||||||||
\(800\) | −6.16446e9 | −0.425677 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −1.29516e10 | −0.886569 | ||||||||
\(803\) | −1.62925e9 | −0.111041 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.54583e10 | 1.04442 | ||||||||
\(806\) | −7.85396e9 | −0.528343 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −8.98595e9 | −0.599273 | ||||||||
\(809\) | −1.25815e10 | −0.835433 | −0.417717 | − | 0.908577i | \(-0.637170\pi\) | ||||
−0.417717 | + | 0.908577i | \(0.637170\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.43090e10 | 1.60027 | 0.800136 | − | 0.599818i | \(-0.204760\pi\) | ||||
0.800136 | + | 0.599818i | \(0.204760\pi\) | |||||||
\(812\) | −1.50323e10 | −0.985325 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −5.17730e9 | −0.336448 | ||||||||
\(815\) | 1.29042e10 | 0.834986 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.92170e9 | −0.123284 | ||||||||
\(818\) | 8.47724e9 | 0.541524 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 3.25467e10 | 2.06138 | ||||||||
\(821\) | 9.75294e9 | 0.615084 | 0.307542 | − | 0.951534i | \(-0.400494\pi\) | ||||
0.307542 | + | 0.951534i | \(0.400494\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.00621e10 | −0.629202 | −0.314601 | − | 0.949224i | \(-0.601871\pi\) | ||||
−0.314601 | + | 0.949224i | \(0.601871\pi\) | |||||||
\(824\) | −1.68422e9 | −0.104871 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2.92976e10 | 1.80885 | ||||||||
\(827\) | 1.80699e10 | 1.11093 | 0.555464 | − | 0.831541i | \(-0.312541\pi\) | ||||
0.555464 | + | 0.831541i | \(0.312541\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −5.71510e9 | −0.348404 | −0.174202 | − | 0.984710i | \(-0.555735\pi\) | ||||
−0.174202 | + | 0.984710i | \(0.555735\pi\) | |||||||
\(830\) | −1.64470e10 | −0.998419 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −4.22376e10 | −2.54254 | ||||||||
\(833\) | 8.45131e9 | 0.506601 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.61447e9 | −0.155410 | ||||||||
\(836\) | −2.55923e9 | −0.151491 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 2.43029e10 | 1.42660 | ||||||||
\(839\) | 1.09882e10 | 0.642332 | 0.321166 | − | 0.947023i | \(-0.395925\pi\) | ||||
0.321166 | + | 0.947023i | \(0.395925\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.12107e10 | −0.649900 | ||||||||
\(842\) | 4.41956e10 | 2.55145 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 2.52933e10 | 1.44813 | ||||||||
\(845\) | 2.47686e10 | 1.41222 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.12334e10 | 1.20068 | ||||||||
\(848\) | 7.44586e9 | 0.419305 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 8.91362e9 | 0.497838 | ||||||||
\(851\) | −2.95488e10 | −1.64357 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.69850e10 | 1.48868 | 0.744338 | − | 0.667803i | \(-0.232765\pi\) | ||||
0.744338 | + | 0.667803i | \(0.232765\pi\) | |||||||
\(854\) | −3.09944e9 | −0.170287 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.11772e10 | 0.609082 | ||||||||
\(857\) | −4.73891e9 | −0.257185 | −0.128593 | − | 0.991698i | \(-0.541046\pi\) | ||||
−0.128593 | + | 0.991698i | \(0.541046\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.73970e10 | −0.936479 | −0.468239 | − | 0.883602i | \(-0.655111\pi\) | ||||
−0.468239 | + | 0.883602i | \(0.655111\pi\) | |||||||
\(860\) | 3.19514e9 | 0.171295 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1.12153e10 | 0.596399 | ||||||||
\(863\) | −9.17138e9 | −0.485732 | −0.242866 | − | 0.970060i | \(-0.578088\pi\) | ||||
−0.242866 | + | 0.970060i | \(0.578088\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 7.92592e9 | 0.416383 | ||||||||
\(866\) | 2.46009e10 | 1.28718 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −6.70144e9 | −0.347816 | ||||||||
\(869\) | −2.71664e9 | −0.140431 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.16836e10 | −1.62469 | ||||||||
\(872\) | −1.99648e10 | −1.01967 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −2.53416e10 | −1.28394 | ||||||||
\(875\) | 2.63989e10 | 1.33216 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −4.84972e9 | −0.242783 | −0.121392 | − | 0.992605i | \(-0.538736\pi\) | ||||
−0.121392 | + | 0.992605i | \(0.538736\pi\) | |||||||
\(878\) | −5.57603e10 | −2.78032 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1.17067e9 | −0.0579088 | ||||||||
\(881\) | 5.10633e9 | 0.251590 | 0.125795 | − | 0.992056i | \(-0.459852\pi\) | ||||
0.125795 | + | 0.992056i | \(0.459852\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.88460e10 | 1.41001 | 0.705006 | − | 0.709201i | \(-0.250944\pi\) | ||||
0.705006 | + | 0.709201i | \(0.250944\pi\) | |||||||
\(884\) | 4.68123e10 | 2.27917 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −5.64476e10 | −2.72664 | ||||||||
\(887\) | 7.47479e9 | 0.359638 | 0.179819 | − | 0.983700i | \(-0.442449\pi\) | ||||
0.179819 | + | 0.983700i | \(0.442449\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.09544e10 | 1.95499 | ||||||||
\(890\) | −1.18853e10 | −0.565126 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 2.07016e10 | 0.976622 | ||||||||
\(893\) | 6.98900e9 | 0.328424 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.45501e10 | −1.14465 | ||||||||
\(896\) | −2.73037e10 | −1.26807 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −1.56452e10 | −0.720964 | ||||||||
\(899\) | 2.69229e9 | 0.123584 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.83896e10 | −0.837597 | ||||||||
\(902\) | −8.55896e9 | −0.388328 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1.38029e10 | −0.621412 | ||||||||
\(905\) | −2.38134e10 | −1.06795 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.37329e9 | 0.150116 | 0.0750581 | − | 0.997179i | \(-0.476086\pi\) | ||||
0.0750581 | + | 0.997179i | \(0.476086\pi\) | |||||||
\(908\) | 4.05837e10 | 1.79908 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 5.81007e10 | 2.55586 | ||||||||
\(911\) | 1.87342e10 | 0.820958 | 0.410479 | − | 0.911870i | \(-0.365362\pi\) | ||||
0.410479 | + | 0.911870i | \(0.365362\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.49294e9 | 0.108409 | ||||||||
\(914\) | −6.19636e10 | −2.68426 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 4.38956e10 | 1.88707 | ||||||||
\(917\) | 2.68632e10 | 1.15044 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.69873e10 | 1.14698 | 0.573489 | − | 0.819214i | \(-0.305590\pi\) | ||||
0.573489 | + | 0.819214i | \(0.305590\pi\) | |||||||
\(920\) | 1.11675e10 | 0.472823 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 3.68570e10 | 1.54868 | ||||||||
\(923\) | −1.29535e10 | −0.542229 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.21889e10 | −0.506372 | ||||||||
\(926\) | 2.29631e10 | 0.950368 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 1.92541e10 | 0.790868 | ||||||||
\(929\) | −1.85412e10 | −0.758721 | −0.379360 | − | 0.925249i | \(-0.623856\pi\) | ||||
−0.379360 | + | 0.925249i | \(0.623856\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −9.91129e9 | −0.402537 | ||||||||
\(932\) | −2.81058e10 | −1.13721 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 4.78533e8 | 0.0192176 | ||||||||
\(935\) | 2.89129e9 | 0.115678 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 4.42644e10 | 1.75779 | 0.878893 | − | 0.477020i | \(-0.158283\pi\) | ||||
0.878893 | + | 0.477020i | \(0.158283\pi\) | |||||||
\(938\) | −4.69032e10 | −1.85563 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −1.16204e10 | −0.456323 | ||||||||
\(941\) | −3.74450e10 | −1.46498 | −0.732488 | − | 0.680780i | \(-0.761641\pi\) | ||||
−0.732488 | + | 0.680780i | \(0.761641\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −4.88493e10 | −1.89700 | ||||||||
\(944\) | −1.26632e10 | −0.489937 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −8.40242e8 | −0.0322690 | ||||||||
\(947\) | 3.20475e10 | 1.22622 | 0.613111 | − | 0.789996i | \(-0.289918\pi\) | ||||
0.613111 | + | 0.789996i | \(0.289918\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.49498e10 | −1.32743 | ||||||||
\(950\) | −1.04535e10 | −0.395574 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 1.83673e10 | 0.689946 | ||||||||
\(953\) | −3.72778e10 | −1.39517 | −0.697583 | − | 0.716504i | \(-0.745741\pi\) | ||||
−0.697583 | + | 0.716504i | \(0.745741\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.52619e10 | −0.567018 | ||||||||
\(956\) | 5.72270e10 | 2.11835 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 5.37867e10 | 1.97649 | ||||||||
\(959\) | −4.85460e9 | −0.177741 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.63124e10 | −0.956375 | ||||||||
\(962\) | −1.11061e11 | −4.02205 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −1.03640e10 | −0.372614 | ||||||||
\(965\) | 1.18517e10 | 0.424556 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 9.26852e8 | 0.0329623 | 0.0164812 | − | 0.999864i | \(-0.494754\pi\) | ||||
0.0164812 | + | 0.999864i | \(0.494754\pi\) | |||||||
\(968\) | 1.53396e10 | 0.543564 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 3.94528e10 | 1.38796 | ||||||||
\(971\) | 1.22212e10 | 0.428398 | 0.214199 | − | 0.976790i | \(-0.431286\pi\) | ||||
0.214199 | + | 0.976790i | \(0.431286\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.89137e10 | −1.00626 | ||||||||
\(974\) | −4.26510e10 | −1.47901 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.33966e9 | 0.0461231 | ||||||||
\(977\) | 1.62117e10 | 0.556157 | 0.278078 | − | 0.960558i | \(-0.410303\pi\) | ||||
0.278078 | + | 0.960558i | \(0.410303\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.80151e9 | 0.0613616 | ||||||||
\(980\) | 1.64792e10 | 0.559298 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −6.17630e10 | −2.08132 | ||||||||
\(983\) | 7.23772e9 | 0.243033 | 0.121516 | − | 0.992589i | \(-0.461224\pi\) | ||||
0.121516 | + | 0.992589i | \(0.461224\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.12198e10 | 0.707480 | ||||||||
\(986\) | −2.78408e10 | −0.924937 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −5.48992e10 | −1.81099 | ||||||||
\(989\) | −4.79559e9 | −0.157636 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.83836e10 | 1.57921 | 0.789606 | − | 0.613614i | \(-0.210285\pi\) | ||||
0.789606 | + | 0.613614i | \(0.210285\pi\) | |||||||
\(992\) | 8.58351e9 | 0.279173 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −1.91759e10 | −0.619305 | ||||||||
\(995\) | 1.42685e10 | 0.459194 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4.51500e10 | −1.44286 | −0.721431 | − | 0.692486i | \(-0.756515\pi\) | ||||
−0.721431 | + | 0.692486i | \(0.756515\pi\) | |||||||
\(998\) | −2.80348e10 | −0.892772 | ||||||||
\(999\) | 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.b.1.1 | 11 | ||
3.2 | odd | 2 | 43.8.a.a.1.11 | ✓ | 11 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.8.a.a.1.11 | ✓ | 11 | 3.2 | odd | 2 | ||
387.8.a.b.1.1 | 11 | 1.1 | even | 1 | trivial |