Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8,21,Mod(3,8)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 21, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8.3");
S:= CuspForms(chi, 21);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8 = 2^{3} \) |
Weight: | \( k \) | \(=\) | \( 21 \) |
Character orbit: | \([\chi]\) | \(=\) | 8.d (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(20.2811012082\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} + 66008406614424 x^{16} + \cdots + 53\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | multiple of \( 2^{153}\cdot 3^{15}\cdot 5^{4}\cdot 7^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 3.5 | ||
Root | \(-2443.39 + 2.11221e6i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8.3 |
Dual form | 8.21.d.b.3.6 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/8\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(7\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −749.926 | − | 697.272i | −0.732349 | − | 0.680929i | ||||
\(3\) | −16119.5 | −0.272986 | −0.136493 | − | 0.990641i | \(-0.543583\pi\) | ||||
−0.136493 | + | 0.990641i | \(0.543583\pi\) | |||||||
\(4\) | 76200.7 | + | 1.04580e6i | 0.0726707 | + | 0.997356i | ||||
\(5\) | − | 8.44883e6i | − | 0.865160i | −0.901596 | − | 0.432580i | \(-0.857603\pi\) | ||
0.901596 | − | 0.432580i | \(-0.142397\pi\) | |||||||
\(6\) | 1.20885e7 | + | 1.12397e7i | 0.199921 | + | 0.185884i | ||||
\(7\) | − | 6.17349e7i | − | 0.218550i | −0.994012 | − | 0.109275i | \(-0.965147\pi\) | ||
0.994012 | − | 0.109275i | \(-0.0348529\pi\) | |||||||
\(8\) | 6.72064e8 | − | 8.37407e8i | 0.625909 | − | 0.779896i | ||||
\(9\) | −3.22694e9 | −0.925479 | ||||||||
\(10\) | −5.89113e9 | + | 6.33599e9i | −0.589113 | + | 0.633599i | ||||
\(11\) | −2.72862e10 | −1.05200 | −0.526001 | − | 0.850484i | \(-0.676309\pi\) | ||||
−0.526001 | + | 0.850484i | \(0.676309\pi\) | |||||||
\(12\) | −1.22832e9 | − | 1.68579e10i | −0.0198381 | − | 0.272264i | ||||
\(13\) | − | 6.05890e10i | − | 0.439501i | −0.975556 | − | 0.219751i | \(-0.929476\pi\) | ||
0.975556 | − | 0.219751i | \(-0.0705244\pi\) | |||||||
\(14\) | −4.30460e10 | + | 4.62966e10i | −0.148817 | + | 0.160055i | ||||
\(15\) | 1.36191e11i | 0.236176i | ||||||||
\(16\) | −1.08790e12 | + | 1.59382e11i | −0.989438 | + | 0.144957i | ||||
\(17\) | −3.07828e11 | −0.152693 | −0.0763466 | − | 0.997081i | \(-0.524326\pi\) | ||||
−0.0763466 | + | 0.997081i | \(0.524326\pi\) | |||||||
\(18\) | 2.41997e12 | + | 2.25006e12i | 0.677774 | + | 0.630186i | ||||
\(19\) | 7.50547e12 | 1.22417 | 0.612085 | − | 0.790792i | \(-0.290331\pi\) | ||||
0.612085 | + | 0.790792i | \(0.290331\pi\) | |||||||
\(20\) | 8.83581e12 | − | 6.43807e11i | 0.862873 | − | 0.0628717i | ||||
\(21\) | 9.95139e11i | 0.0596610i | ||||||||
\(22\) | 2.04626e13 | + | 1.90259e13i | 0.770433 | + | 0.716339i | ||||
\(23\) | 5.30705e13i | 1.28107i | 0.767927 | + | 0.640537i | \(0.221288\pi\) | ||||
−0.767927 | + | 0.640537i | \(0.778712\pi\) | |||||||
\(24\) | −1.08334e13 | + | 1.34986e13i | −0.170864 | + | 0.212901i | ||||
\(25\) | 2.39847e13 | 0.251498 | ||||||||
\(26\) | −4.22470e13 | + | 4.54372e13i | −0.299269 | + | 0.321869i | ||||
\(27\) | 1.08222e14 | 0.525629 | ||||||||
\(28\) | 6.45626e13 | − | 4.70425e12i | 0.217972 | − | 0.0158822i | ||||
\(29\) | 5.67356e14i | 1.34858i | 0.738468 | + | 0.674288i | \(0.235549\pi\) | ||||
−0.738468 | + | 0.674288i | \(0.764451\pi\) | |||||||
\(30\) | 9.49623e13 | − | 1.02133e14i | 0.160819 | − | 0.172964i | ||||
\(31\) | − | 1.32605e14i | − | 0.161787i | −0.996723 | − | 0.0808935i | \(-0.974223\pi\) | ||
0.996723 | − | 0.0808935i | \(-0.0257774\pi\) | |||||||
\(32\) | 9.26975e14 | + | 6.39036e14i | 0.823320 | + | 0.567578i | ||||
\(33\) | 4.39842e14 | 0.287182 | ||||||||
\(34\) | 2.30848e14 | + | 2.14640e14i | 0.111825 | + | 0.103973i | ||||
\(35\) | −5.21588e14 | −0.189081 | ||||||||
\(36\) | −2.45895e14 | − | 3.37475e15i | −0.0672551 | − | 0.923032i | ||||
\(37\) | − | 2.44065e14i | − | 0.0507561i | −0.999678 | − | 0.0253781i | \(-0.991921\pi\) | ||
0.999678 | − | 0.0253781i | \(-0.00807896\pi\) | |||||||
\(38\) | −5.62854e15 | − | 5.23335e15i | −0.896520 | − | 0.833574i | ||||
\(39\) | 9.76667e14i | 0.119978i | ||||||||
\(40\) | −7.07511e15 | − | 5.67816e15i | −0.674735 | − | 0.541511i | ||||
\(41\) | −1.67160e16 | −1.24535 | −0.622677 | − | 0.782479i | \(-0.713955\pi\) | ||||
−0.622677 | + | 0.782479i | \(0.713955\pi\) | |||||||
\(42\) | 6.93882e14 | − | 7.46280e14i | 0.0406249 | − | 0.0436927i | ||||
\(43\) | −8.85654e14 | −0.0409807 | −0.0204904 | − | 0.999790i | \(-0.506523\pi\) | ||||
−0.0204904 | + | 0.999790i | \(0.506523\pi\) | |||||||
\(44\) | −2.07923e15 | − | 2.85360e16i | −0.0764497 | − | 1.04922i | ||||
\(45\) | 2.72639e16i | 0.800687i | ||||||||
\(46\) | 3.70045e16 | − | 3.97989e16i | 0.872321 | − | 0.938194i | ||||
\(47\) | 7.52013e16i | 1.42971i | 0.699274 | + | 0.714853i | \(0.253507\pi\) | ||||
−0.699274 | + | 0.714853i | \(0.746493\pi\) | |||||||
\(48\) | 1.75364e16 | − | 2.56916e15i | 0.270103 | − | 0.0395712i | ||||
\(49\) | 7.59811e16 | 0.952236 | ||||||||
\(50\) | −1.79868e16 | − | 1.67239e16i | −0.184184 | − | 0.171252i | ||||
\(51\) | 4.96205e15 | 0.0416831 | ||||||||
\(52\) | 6.33642e16 | − | 4.61693e15i | 0.438339 | − | 0.0319389i | ||||
\(53\) | 2.98647e17i | 1.70765i | 0.520560 | + | 0.853825i | \(0.325723\pi\) | ||||
−0.520560 | + | 0.853825i | \(0.674277\pi\) | |||||||
\(54\) | −8.11586e16 | − | 7.54603e16i | −0.384944 | − | 0.357916i | ||||
\(55\) | 2.30537e17i | 0.910150i | ||||||||
\(56\) | −5.16973e16 | − | 4.14898e16i | −0.170446 | − | 0.136792i | ||||
\(57\) | −1.20985e17 | −0.334181 | ||||||||
\(58\) | 3.95601e17 | − | 4.25475e17i | 0.918285 | − | 0.987629i | ||||
\(59\) | −6.61197e16 | −0.129363 | −0.0646816 | − | 0.997906i | \(-0.520603\pi\) | ||||
−0.0646816 | + | 0.997906i | \(0.520603\pi\) | |||||||
\(60\) | −1.42429e17 | + | 1.03779e16i | −0.235552 | + | 0.0171631i | ||||
\(61\) | 1.14850e17i | 0.161002i | 0.996755 | + | 0.0805011i | \(0.0256520\pi\) | ||||
−0.996755 | + | 0.0805011i | \(0.974348\pi\) | |||||||
\(62\) | −9.24618e16 | + | 9.94440e16i | −0.110165 | + | 0.118485i | ||||
\(63\) | 1.99215e17i | 0.202263i | ||||||||
\(64\) | −2.49581e17 | − | 1.12558e18i | −0.216477 | − | 0.976288i | ||||
\(65\) | −5.11906e17 | −0.380239 | ||||||||
\(66\) | −3.29848e17 | − | 3.06689e17i | −0.210317 | − | 0.195550i | ||||
\(67\) | 1.03362e18 | 0.567041 | 0.283520 | − | 0.958966i | \(-0.408498\pi\) | ||||
0.283520 | + | 0.958966i | \(0.408498\pi\) | |||||||
\(68\) | −2.34567e16 | − | 3.21928e17i | −0.0110963 | − | 0.152289i | ||||
\(69\) | − | 8.55472e17i | − | 0.349715i | ||||||
\(70\) | 3.91152e17 | + | 3.63688e17i | 0.138473 | + | 0.128751i | ||||
\(71\) | − | 4.52275e18i | − | 1.38937i | −0.719313 | − | 0.694687i | \(-0.755543\pi\) | ||
0.719313 | − | 0.694687i | \(-0.244457\pi\) | |||||||
\(72\) | −2.16871e18 | + | 2.70227e18i | −0.579265 | + | 0.721778i | ||||
\(73\) | −3.78599e18 | −0.880949 | −0.440475 | − | 0.897765i | \(-0.645190\pi\) | ||||
−0.440475 | + | 0.897765i | \(0.645190\pi\) | |||||||
\(74\) | −1.70180e17 | + | 1.83031e17i | −0.0345613 | + | 0.0371712i | ||||
\(75\) | −3.86623e17 | −0.0686555 | ||||||||
\(76\) | 5.71922e17 | + | 7.84925e18i | 0.0889613 | + | 1.22093i | ||||
\(77\) | 1.68451e18i | 0.229915i | ||||||||
\(78\) | 6.81002e17 | − | 7.32428e17i | 0.0816963 | − | 0.0878656i | ||||
\(79\) | − | 9.29391e18i | − | 0.981584i | −0.871277 | − | 0.490792i | \(-0.836707\pi\) | ||
0.871277 | − | 0.490792i | \(-0.163293\pi\) | |||||||
\(80\) | 1.34659e18 | + | 9.19147e18i | 0.125411 | + | 0.856022i | ||||
\(81\) | 9.50717e18 | 0.781990 | ||||||||
\(82\) | 1.25357e19 | + | 1.16556e19i | 0.912035 | + | 0.847998i | ||||
\(83\) | 2.33949e19 | 1.50779 | 0.753895 | − | 0.656995i | \(-0.228173\pi\) | ||||
0.753895 | + | 0.656995i | \(0.228173\pi\) | |||||||
\(84\) | −1.04072e18 | + | 7.58303e16i | −0.0595033 | + | 0.00433561i | ||||
\(85\) | 2.60079e18i | 0.132104i | ||||||||
\(86\) | 6.64174e17 | + | 6.17541e17i | 0.0300122 | + | 0.0279050i | ||||
\(87\) | − | 9.14552e18i | − | 0.368142i | ||||||
\(88\) | −1.83381e19 | + | 2.28497e19i | −0.658457 | + | 0.820453i | ||||
\(89\) | −4.76585e19 | −1.52841 | −0.764206 | − | 0.644972i | \(-0.776869\pi\) | ||||
−0.764206 | + | 0.644972i | \(0.776869\pi\) | |||||||
\(90\) | 1.90103e19 | − | 2.04459e19i | 0.545211 | − | 0.586383i | ||||
\(91\) | −3.74046e18 | −0.0960530 | ||||||||
\(92\) | −5.55013e19 | + | 4.04401e18i | −1.27769 | + | 0.0930966i | ||||
\(93\) | 2.13754e18i | 0.0441656i | ||||||||
\(94\) | 5.24358e19 | − | 5.63954e19i | 0.973529 | − | 1.04704i | ||||
\(95\) | − | 6.34124e19i | − | 1.05910i | ||||||
\(96\) | −1.49424e19 | − | 1.03010e19i | −0.224755 | − | 0.154941i | ||||
\(97\) | −7.53216e19 | −1.02142 | −0.510708 | − | 0.859754i | \(-0.670617\pi\) | ||||
−0.510708 | + | 0.859754i | \(0.670617\pi\) | |||||||
\(98\) | −5.69801e19 | − | 5.29794e19i | −0.697369 | − | 0.648405i | ||||
\(99\) | 8.80512e19 | 0.973606 | ||||||||
\(100\) | 1.82765e18 | + | 2.50833e19i | 0.0182765 | + | 0.250833i | ||||
\(101\) | 1.89365e20i | 1.71430i | 0.515067 | + | 0.857150i | \(0.327767\pi\) | ||||
−0.515067 | + | 0.857150i | \(0.672233\pi\) | |||||||
\(102\) | −3.72117e18 | − | 3.45990e18i | −0.0305266 | − | 0.0283832i | ||||
\(103\) | − | 1.17747e19i | − | 0.0876148i | −0.999040 | − | 0.0438074i | \(-0.986051\pi\) | ||
0.999040 | − | 0.0438074i | \(-0.0139488\pi\) | |||||||
\(104\) | −5.07377e19 | − | 4.07197e19i | −0.342766 | − | 0.275088i | ||||
\(105\) | 8.40776e18 | 0.0516163 | ||||||||
\(106\) | 2.08238e20 | − | 2.23963e20i | 1.16279 | − | 1.25060i | ||||
\(107\) | 1.12580e20 | 0.572300 | 0.286150 | − | 0.958185i | \(-0.407624\pi\) | ||||
0.286150 | + | 0.958185i | \(0.407624\pi\) | |||||||
\(108\) | 8.24661e18 | + | 1.13179e20i | 0.0381978 | + | 0.524239i | ||||
\(109\) | 4.23608e20i | 1.78937i | 0.446701 | + | 0.894683i | \(0.352599\pi\) | ||||
−0.446701 | + | 0.894683i | \(0.647401\pi\) | |||||||
\(110\) | 1.60747e20 | − | 1.72885e20i | 0.619748 | − | 0.666548i | ||||
\(111\) | 3.93422e18i | 0.0138557i | ||||||||
\(112\) | 9.83943e18 | + | 6.71613e19i | 0.0316803 | + | 0.216242i | ||||
\(113\) | −5.17406e20 | −1.52422 | −0.762109 | − | 0.647449i | \(-0.775836\pi\) | ||||
−0.762109 | + | 0.647449i | \(0.775836\pi\) | |||||||
\(114\) | 9.07296e19 | + | 8.43592e19i | 0.244737 | + | 0.227554i | ||||
\(115\) | 4.48383e20 | 1.10833 | ||||||||
\(116\) | −5.93343e20 | + | 4.32329e19i | −1.34501 | + | 0.0980019i | ||||
\(117\) | 1.95517e20i | 0.406749i | ||||||||
\(118\) | 4.95849e19 | + | 4.61034e19i | 0.0947390 | + | 0.0880872i | ||||
\(119\) | 1.90038e19i | 0.0333711i | ||||||||
\(120\) | 1.14048e20 | + | 9.15293e19i | 0.184193 | + | 0.147825i | ||||
\(121\) | 7.17883e19 | 0.106709 | ||||||||
\(122\) | 8.00815e19 | − | 8.61288e19i | 0.109631 | − | 0.117910i | ||||
\(123\) | 2.69454e20 | 0.339964 | ||||||||
\(124\) | 1.38679e20 | − | 1.01046e19i | 0.161359 | − | 0.0117572i | ||||
\(125\) | − | 1.00839e21i | − | 1.08275i | ||||||
\(126\) | 1.38907e20 | − | 1.49397e20i | 0.137727 | − | 0.148127i | ||||
\(127\) | − | 1.68672e21i | − | 1.54527i | −0.634848 | − | 0.772637i | \(-0.718937\pi\) | ||
0.634848 | − | 0.772637i | \(-0.281063\pi\) | |||||||
\(128\) | −5.97670e20 | + | 1.01813e21i | −0.506246 | + | 0.862389i | ||||
\(129\) | 1.42763e19 | 0.0111872 | ||||||||
\(130\) | 3.83891e20 | + | 3.56938e20i | 0.278468 | + | 0.258916i | ||||
\(131\) | −1.48144e21 | −0.995340 | −0.497670 | − | 0.867367i | \(-0.665811\pi\) | ||||
−0.497670 | + | 0.867367i | \(0.665811\pi\) | |||||||
\(132\) | 3.35162e19 | + | 4.59988e20i | 0.0208697 | + | 0.286422i | ||||
\(133\) | − | 4.63350e20i | − | 0.267542i | ||||||
\(134\) | −7.75141e20 | − | 7.20716e20i | −0.415272 | − | 0.386115i | ||||
\(135\) | − | 9.14351e20i | − | 0.454753i | ||||||
\(136\) | −2.06880e20 | + | 2.57778e20i | −0.0955719 | + | 0.119085i | ||||
\(137\) | −5.06132e20 | −0.217299 | −0.108650 | − | 0.994080i | \(-0.534653\pi\) | ||||
−0.108650 | + | 0.994080i | \(0.534653\pi\) | |||||||
\(138\) | −5.96496e20 | + | 6.41540e20i | −0.238131 | + | 0.256114i | ||||
\(139\) | 8.38666e20 | 0.311488 | 0.155744 | − | 0.987797i | \(-0.450223\pi\) | ||||
0.155744 | + | 0.987797i | \(0.450223\pi\) | |||||||
\(140\) | −3.97454e19 | − | 5.45478e20i | −0.0137406 | − | 0.188581i | ||||
\(141\) | − | 1.21221e21i | − | 0.390290i | ||||||
\(142\) | −3.15358e21 | + | 3.39172e21i | −0.946065 | + | 1.01751i | ||||
\(143\) | 1.65325e21i | 0.462357i | ||||||||
\(144\) | 3.51059e21 | − | 5.14317e20i | 0.915704 | − | 0.134155i | ||||
\(145\) | 4.79349e21 | 1.16673 | ||||||||
\(146\) | 2.83921e21 | + | 2.63986e21i | 0.645163 | + | 0.599864i | ||||
\(147\) | −1.22478e21 | −0.259947 | ||||||||
\(148\) | 2.55244e20 | − | 1.85979e19i | 0.0506219 | − | 0.00368848i | ||||
\(149\) | − | 2.35561e21i | − | 0.436758i | −0.975864 | − | 0.218379i | \(-0.929923\pi\) | ||
0.975864 | − | 0.218379i | \(-0.0700769\pi\) | |||||||
\(150\) | 2.89938e20 | + | 2.69581e20i | 0.0502798 | + | 0.0467495i | ||||
\(151\) | 1.21038e22i | 1.96405i | 0.188748 | + | 0.982026i | \(0.439557\pi\) | ||||
−0.188748 | + | 0.982026i | \(0.560443\pi\) | |||||||
\(152\) | 5.04416e21 | − | 6.28514e21i | 0.766219 | − | 0.954726i | ||||
\(153\) | 9.93345e20 | 0.141314 | ||||||||
\(154\) | 1.17456e21 | − | 1.26326e21i | 0.156556 | − | 0.168378i | ||||
\(155\) | −1.12036e21 | −0.139972 | ||||||||
\(156\) | −1.02140e21 | + | 7.44227e19i | −0.119660 | + | 0.00871886i | ||||
\(157\) | 3.90370e21i | 0.429022i | 0.976722 | + | 0.214511i | \(0.0688159\pi\) | ||||
−0.976722 | + | 0.214511i | \(0.931184\pi\) | |||||||
\(158\) | −6.48038e21 | + | 6.96974e21i | −0.668389 | + | 0.718862i | ||||
\(159\) | − | 4.81405e21i | − | 0.466165i | ||||||
\(160\) | 5.39911e21 | − | 7.83186e21i | 0.491046 | − | 0.712303i | ||||
\(161\) | 3.27630e21 | 0.279979 | ||||||||
\(162\) | −7.12967e21 | − | 6.62908e21i | −0.572689 | − | 0.532480i | ||||
\(163\) | −1.79709e22 | −1.35735 | −0.678677 | − | 0.734437i | \(-0.737446\pi\) | ||||
−0.678677 | + | 0.734437i | \(0.737446\pi\) | |||||||
\(164\) | −1.27377e21 | − | 1.74816e22i | −0.0905007 | − | 1.24206i | ||||
\(165\) | − | 3.71615e21i | − | 0.248458i | ||||||
\(166\) | −1.75445e22 | − | 1.63126e22i | −1.10423 | − | 1.02670i | ||||
\(167\) | 2.50440e22i | 1.48436i | 0.670202 | + | 0.742179i | \(0.266207\pi\) | ||||
−0.670202 | + | 0.742179i | \(0.733793\pi\) | |||||||
\(168\) | 8.33337e20 | + | 6.68797e20i | 0.0465294 | + | 0.0373424i | ||||
\(169\) | 1.53339e22 | 0.806838 | ||||||||
\(170\) | 1.81346e21 | − | 1.95040e21i | 0.0899535 | − | 0.0967462i | ||||
\(171\) | −2.42197e22 | −1.13294 | ||||||||
\(172\) | −6.74874e19 | − | 9.26220e20i | −0.00297809 | − | 0.0408723i | ||||
\(173\) | − | 1.68015e22i | − | 0.699658i | −0.936814 | − | 0.349829i | \(-0.886240\pi\) | ||
0.936814 | − | 0.349829i | \(-0.113760\pi\) | |||||||
\(174\) | −6.37691e21 | + | 6.85846e21i | −0.250679 | + | 0.269609i | ||||
\(175\) | − | 1.48070e21i | − | 0.0549649i | ||||||
\(176\) | 2.96846e22 | − | 4.34893e21i | 1.04089 | − | 0.152495i | ||||
\(177\) | 1.06582e21 | 0.0353143 | ||||||||
\(178\) | 3.57404e22 | + | 3.32309e22i | 1.11933 | + | 1.04074i | ||||
\(179\) | 4.08453e22 | 1.20952 | 0.604759 | − | 0.796409i | \(-0.293270\pi\) | ||||
0.604759 | + | 0.796409i | \(0.293270\pi\) | |||||||
\(180\) | −2.85127e22 | + | 2.07753e21i | −0.798570 | + | 0.0581865i | ||||
\(181\) | 5.55662e20i | 0.0147240i | 0.999973 | + | 0.00736199i | \(0.00234341\pi\) | ||||
−0.999973 | + | 0.00736199i | \(0.997657\pi\) | |||||||
\(182\) | 2.80507e21 | + | 2.60812e21i | 0.0703443 | + | 0.0654053i | ||||
\(183\) | − | 1.85133e21i | − | 0.0439513i | ||||||
\(184\) | 4.44416e22 | + | 3.56668e22i | 0.999106 | + | 0.801836i | ||||
\(185\) | −2.06206e21 | −0.0439122 | ||||||||
\(186\) | 1.49044e21 | − | 1.60299e21i | 0.0300736 | − | 0.0323446i | ||||
\(187\) | 8.39948e21 | 0.160634 | ||||||||
\(188\) | −7.86458e22 | + | 5.73040e21i | −1.42593 | + | 0.103898i | ||||
\(189\) | − | 6.68109e21i | − | 0.114876i | ||||||
\(190\) | −4.42157e22 | + | 4.75546e22i | −0.721174 | + | 0.775633i | ||||
\(191\) | − | 5.34999e22i | − | 0.827979i | −0.910282 | − | 0.413989i | \(-0.864135\pi\) | ||
0.910282 | − | 0.413989i | \(-0.135865\pi\) | |||||||
\(192\) | 4.02313e21 | + | 1.81439e22i | 0.0590951 | + | 0.266513i | ||||
\(193\) | −2.35465e22 | −0.328362 | −0.164181 | − | 0.986430i | \(-0.552498\pi\) | ||||
−0.164181 | + | 0.986430i | \(0.552498\pi\) | |||||||
\(194\) | 5.64856e22 | + | 5.25196e22i | 0.748033 | + | 0.695511i | ||||
\(195\) | 8.25169e21 | 0.103800 | ||||||||
\(196\) | 5.78981e21 | + | 7.94613e22i | 0.0691996 | + | 0.949718i | ||||
\(197\) | − | 3.39087e22i | − | 0.385167i | −0.981281 | − | 0.192583i | \(-0.938313\pi\) | ||
0.981281 | − | 0.192583i | \(-0.0616866\pi\) | |||||||
\(198\) | −6.60318e22 | − | 6.13956e22i | −0.713019 | − | 0.662957i | ||||
\(199\) | − | 7.22475e22i | − | 0.741809i | −0.928671 | − | 0.370904i | \(-0.879048\pi\) | ||
0.928671 | − | 0.370904i | \(-0.120952\pi\) | |||||||
\(200\) | 1.61193e22 | − | 2.00850e22i | 0.157415 | − | 0.196143i | ||||
\(201\) | −1.66615e22 | −0.154794 | ||||||||
\(202\) | 1.32039e23 | − | 1.42010e23i | 1.16732 | − | 1.25547i | ||||
\(203\) | 3.50257e22 | 0.294731 | ||||||||
\(204\) | 3.78112e20 | + | 5.18933e21i | 0.00302914 | + | 0.0415729i | ||||
\(205\) | 1.41230e23i | 1.07743i | ||||||||
\(206\) | −8.21016e21 | + | 8.83015e21i | −0.0596595 | + | 0.0641646i | ||||
\(207\) | − | 1.71255e23i | − | 1.18561i | ||||||
\(208\) | 9.65679e21 | + | 6.59147e22i | 0.0637088 | + | 0.434859i | ||||
\(209\) | −2.04796e23 | −1.28783 | ||||||||
\(210\) | −6.30519e21 | − | 5.86249e21i | −0.0378012 | − | 0.0351471i | ||||
\(211\) | 1.30256e23 | 0.744688 | 0.372344 | − | 0.928095i | \(-0.378554\pi\) | ||||
0.372344 | + | 0.928095i | \(0.378554\pi\) | |||||||
\(212\) | −3.12326e23 | + | 2.27571e22i | −1.70314 | + | 0.124096i | ||||
\(213\) | 7.29046e22i | 0.379279i | ||||||||
\(214\) | −8.44266e22 | − | 7.84988e22i | −0.419123 | − | 0.389696i | ||||
\(215\) | 7.48274e21i | 0.0354549i | ||||||||
\(216\) | 7.27323e22 | − | 9.06261e22i | 0.328995 | − | 0.409936i | ||||
\(217\) | −8.18637e21 | −0.0353585 | ||||||||
\(218\) | 2.95370e23 | − | 3.17675e23i | 1.21843 | − | 1.31044i | ||||
\(219\) | 6.10285e22 | 0.240487 | ||||||||
\(220\) | −2.41096e23 | + | 1.75671e22i | −0.907744 | + | 0.0661412i | ||||
\(221\) | 1.86510e22i | 0.0671088i | ||||||||
\(222\) | 2.74322e21 | − | 2.95037e21i | 0.00943476 | − | 0.0101472i | ||||
\(223\) | 4.41000e23i | 1.45007i | 0.688710 | + | 0.725037i | \(0.258177\pi\) | ||||
−0.688710 | + | 0.725037i | \(0.741823\pi\) | |||||||
\(224\) | 3.94509e22 | − | 5.72268e22i | 0.124044 | − | 0.179936i | ||||
\(225\) | −7.73974e22 | −0.232756 | ||||||||
\(226\) | 3.88016e23 | + | 3.60772e23i | 1.11626 | + | 1.03788i | ||||
\(227\) | −1.05199e23 | −0.289568 | −0.144784 | − | 0.989463i | \(-0.546249\pi\) | ||||
−0.144784 | + | 0.989463i | \(0.546249\pi\) | |||||||
\(228\) | −9.21912e21 | − | 1.26526e23i | −0.0242852 | − | 0.333298i | ||||
\(229\) | 6.05893e23i | 1.52771i | 0.645387 | + | 0.763855i | \(0.276696\pi\) | ||||
−0.645387 | + | 0.763855i | \(0.723304\pi\) | |||||||
\(230\) | −3.36254e23 | − | 3.12645e23i | −0.811688 | − | 0.754698i | ||||
\(231\) | − | 2.71536e22i | − | 0.0627636i | ||||||
\(232\) | 4.75108e23 | + | 3.81299e23i | 1.05175 | + | 0.844085i | ||||
\(233\) | −1.04700e23 | −0.222018 | −0.111009 | − | 0.993819i | \(-0.535408\pi\) | ||||
−0.111009 | + | 0.993819i | \(0.535408\pi\) | |||||||
\(234\) | 1.36329e23 | − | 1.46623e23i | 0.276967 | − | 0.297882i | ||||
\(235\) | 6.35363e23 | 1.23693 | ||||||||
\(236\) | −5.03837e21 | − | 6.91482e22i | −0.00940091 | − | 0.129021i | ||||
\(237\) | 1.49814e23i | 0.267959i | ||||||||
\(238\) | 1.32508e22 | − | 1.42514e22i | 0.0227233 | − | 0.0244393i | ||||
\(239\) | − | 6.86162e22i | − | 0.112836i | −0.998407 | − | 0.0564180i | \(-0.982032\pi\) | ||
0.998407 | − | 0.0564180i | \(-0.0179680\pi\) | |||||||
\(240\) | −2.17064e22 | − | 1.48162e23i | −0.0342354 | − | 0.233682i | ||||
\(241\) | 7.40316e23 | 1.12007 | 0.560037 | − | 0.828467i | \(-0.310787\pi\) | ||||
0.560037 | + | 0.828467i | \(0.310787\pi\) | |||||||
\(242\) | −5.38359e22 | − | 5.00560e22i | −0.0781481 | − | 0.0726611i | ||||
\(243\) | −5.30599e23 | −0.739101 | ||||||||
\(244\) | −1.20110e23 | + | 8.75163e21i | −0.160576 | + | 0.0117001i | ||||
\(245\) | − | 6.41951e23i | − | 0.823836i | ||||||
\(246\) | −2.02070e23 | − | 1.87883e23i | −0.248973 | − | 0.231492i | ||||
\(247\) | − | 4.54749e23i | − | 0.538025i | ||||||
\(248\) | −1.11045e23 | − | 8.91192e22i | −0.126177 | − | 0.101264i | ||||
\(249\) | −3.77116e23 | −0.411605 | ||||||||
\(250\) | −7.03119e23 | + | 7.56214e23i | −0.737274 | + | 0.792948i | ||||
\(251\) | −1.33787e24 | −1.34796 | −0.673980 | − | 0.738750i | \(-0.735417\pi\) | ||||
−0.673980 | + | 0.738750i | \(0.735417\pi\) | |||||||
\(252\) | −2.08340e23 | + | 1.51803e22i | −0.201728 | + | 0.0146986i | ||||
\(253\) | − | 1.44809e24i | − | 1.34769i | ||||||
\(254\) | −1.17610e24 | + | 1.26491e24i | −1.05222 | + | 1.13168i | ||||
\(255\) | − | 4.19235e22i | − | 0.0360625i | ||||||
\(256\) | 1.15812e24 | − | 3.46783e23i | 0.957975 | − | 0.286852i | ||||
\(257\) | −4.81853e23 | −0.383339 | −0.191670 | − | 0.981459i | \(-0.561390\pi\) | ||||
−0.191670 | + | 0.981459i | \(0.561390\pi\) | |||||||
\(258\) | −1.07062e22 | − | 9.95448e21i | −0.00819290 | − | 0.00761766i | ||||
\(259\) | −1.50673e22 | −0.0110927 | ||||||||
\(260\) | −3.90076e22 | − | 5.35353e23i | −0.0276322 | − | 0.379234i | ||||
\(261\) | − | 1.83083e24i | − | 1.24808i | ||||||
\(262\) | 1.11097e24 | + | 1.03297e24i | 0.728936 | + | 0.677756i | ||||
\(263\) | − | 5.98683e23i | − | 0.378128i | −0.981965 | − | 0.189064i | \(-0.939455\pi\) | ||
0.981965 | − | 0.189064i | \(-0.0605454\pi\) | |||||||
\(264\) | 2.95602e23 | − | 3.68327e23i | 0.179750 | − | 0.223972i | ||||
\(265\) | 2.52321e24 | 1.47739 | ||||||||
\(266\) | −3.23081e23 | + | 3.47478e23i | −0.182177 | + | 0.195934i | ||||
\(267\) | 7.68234e23 | 0.417235 | ||||||||
\(268\) | 7.87629e22 | + | 1.08097e24i | 0.0412072 | + | 0.565542i | ||||
\(269\) | − | 5.30086e22i | − | 0.0267192i | −0.999911 | − | 0.0133596i | \(-0.995747\pi\) | ||
0.999911 | − | 0.0133596i | \(-0.00425262\pi\) | |||||||
\(270\) | −6.37551e23 | + | 6.85695e23i | −0.309654 | + | 0.333038i | ||||
\(271\) | 3.52114e24i | 1.64812i | 0.566500 | + | 0.824062i | \(0.308297\pi\) | ||||
−0.566500 | + | 0.824062i | \(0.691703\pi\) | |||||||
\(272\) | 3.34886e23 | − | 4.90623e22i | 0.151080 | − | 0.0221339i | ||||
\(273\) | 6.02945e22 | 0.0262211 | ||||||||
\(274\) | 3.79561e23 | + | 3.52911e23i | 0.159139 | + | 0.147965i | ||||
\(275\) | −6.54453e23 | −0.264577 | ||||||||
\(276\) | 8.94655e23 | − | 6.51876e22i | 0.348791 | − | 0.0254140i | ||||
\(277\) | 6.25325e23i | 0.235130i | 0.993065 | + | 0.117565i | \(0.0375088\pi\) | ||||
−0.993065 | + | 0.117565i | \(0.962491\pi\) | |||||||
\(278\) | −6.28937e23 | − | 5.84778e23i | −0.228118 | − | 0.212101i | ||||
\(279\) | 4.27910e23i | 0.149730i | ||||||||
\(280\) | −3.50541e23 | + | 4.36782e23i | −0.118347 | + | 0.147463i | ||||
\(281\) | 4.32696e24 | 1.40968 | 0.704838 | − | 0.709368i | \(-0.251020\pi\) | ||||
0.704838 | + | 0.709368i | \(0.251020\pi\) | |||||||
\(282\) | −8.45241e23 | + | 9.09068e23i | −0.265760 | + | 0.285828i | ||||
\(283\) | −4.60817e24 | −1.39851 | −0.699253 | − | 0.714874i | \(-0.746484\pi\) | ||||
−0.699253 | + | 0.714874i | \(0.746484\pi\) | |||||||
\(284\) | 4.72991e24 | − | 3.44637e23i | 1.38570 | − | 0.100967i | ||||
\(285\) | 1.02218e24i | 0.289120i | ||||||||
\(286\) | 1.15276e24 | − | 1.23981e24i | 0.314832 | − | 0.338606i | ||||
\(287\) | 1.03196e24i | 0.272172i | ||||||||
\(288\) | −2.99130e24 | − | 2.06213e24i | −0.761965 | − | 0.525281i | ||||
\(289\) | −3.96947e24 | −0.976685 | ||||||||
\(290\) | −3.59476e24 | − | 3.34236e24i | −0.854457 | − | 0.794463i | ||||
\(291\) | 1.21415e24 | 0.278832 | ||||||||
\(292\) | −2.88495e23 | − | 3.95940e24i | −0.0640192 | − | 0.878620i | ||||
\(293\) | 2.84512e24i | 0.610133i | 0.952331 | + | 0.305066i | \(0.0986786\pi\) | ||||
−0.952331 | + | 0.305066i | \(0.901321\pi\) | |||||||
\(294\) | 9.18494e23 | + | 8.54004e23i | 0.190372 | + | 0.177006i | ||||
\(295\) | 5.58634e23i | 0.111920i | ||||||||
\(296\) | −2.04382e23 | − | 1.64027e23i | −0.0395845 | − | 0.0317687i | ||||
\(297\) | −2.95298e24 | −0.552962 | ||||||||
\(298\) | −1.64250e24 | + | 1.76653e24i | −0.297401 | + | 0.319859i | ||||
\(299\) | 3.21549e24 | 0.563034 | ||||||||
\(300\) | −2.94609e22 | − | 4.04332e23i | −0.00498924 | − | 0.0684739i | ||||
\(301\) | 5.46758e22i | 0.00895633i | ||||||||
\(302\) | 8.43965e24 | − | 9.07696e24i | 1.33738 | − | 1.43837i | ||||
\(303\) | − | 3.05248e24i | − | 0.467980i | ||||||
\(304\) | −8.16519e24 | + | 1.19624e24i | −1.21124 | + | 0.177452i | ||||
\(305\) | 9.70346e23 | 0.139293 | ||||||||
\(306\) | −7.44935e23 | − | 6.92631e23i | −0.103491 | − | 0.0962250i | ||||
\(307\) | 5.66512e24 | 0.761773 | 0.380887 | − | 0.924622i | \(-0.375619\pi\) | ||||
0.380887 | + | 0.924622i | \(0.375619\pi\) | |||||||
\(308\) | −1.76167e24 | + | 1.28361e23i | −0.229307 | + | 0.0167081i | ||||
\(309\) | 1.89803e23i | 0.0239176i | ||||||||
\(310\) | 8.40185e23 | + | 7.81194e23i | 0.102508 | + | 0.0953108i | ||||
\(311\) | 4.13896e24i | 0.488975i | 0.969652 | + | 0.244488i | \(0.0786198\pi\) | ||||
−0.969652 | + | 0.244488i | \(0.921380\pi\) | |||||||
\(312\) | 8.17868e23 | + | 6.56383e23i | 0.0935702 | + | 0.0750951i | ||||
\(313\) | −1.13021e25 | −1.25233 | −0.626163 | − | 0.779692i | \(-0.715375\pi\) | ||||
−0.626163 | + | 0.779692i | \(0.715375\pi\) | |||||||
\(314\) | 2.72194e24 | − | 2.92749e24i | 0.292134 | − | 0.314194i | ||||
\(315\) | 1.68314e24 | 0.174990 | ||||||||
\(316\) | 9.71960e24 | − | 7.08202e23i | 0.978989 | − | 0.0713324i | ||||
\(317\) | 9.80341e24i | 0.956720i | 0.878164 | + | 0.478360i | \(0.158769\pi\) | ||||
−0.878164 | + | 0.478360i | \(0.841231\pi\) | |||||||
\(318\) | −3.35670e24 | + | 3.61018e24i | −0.317425 | + | 0.341395i | ||||
\(319\) | − | 1.54810e25i | − | 1.41871i | ||||||
\(320\) | −9.50986e24 | + | 2.10867e24i | −0.844645 | + | 0.187287i | ||||
\(321\) | −1.81474e24 | −0.156230 | ||||||||
\(322\) | −2.45698e24 | − | 2.28447e24i | −0.205042 | − | 0.190646i | ||||
\(323\) | −2.31040e24 | −0.186922 | ||||||||
\(324\) | 7.24453e23 | + | 9.94263e24i | 0.0568277 | + | 0.779922i | ||||
\(325\) | − | 1.45321e24i | − | 0.110534i | ||||||
\(326\) | 1.34768e25 | + | 1.25306e25i | 0.994057 | + | 0.924262i | ||||
\(327\) | − | 6.82837e24i | − | 0.488472i | ||||||
\(328\) | −1.12342e25 | + | 1.39981e25i | −0.779478 | + | 0.971248i | ||||
\(329\) | 4.64255e24 | 0.312462 | ||||||||
\(330\) | −2.59116e24 | + | 2.78683e24i | −0.169182 | + | 0.181958i | ||||
\(331\) | 1.53387e25 | 0.971648 | 0.485824 | − | 0.874057i | \(-0.338520\pi\) | ||||
0.485824 | + | 0.874057i | \(0.338520\pi\) | |||||||
\(332\) | 1.78271e24 | + | 2.44665e25i | 0.109572 | + | 1.50380i | ||||
\(333\) | 7.87585e23i | 0.0469737i | ||||||||
\(334\) | 1.74624e25 | − | 1.87811e25i | 1.01074 | − | 1.08707i | ||||
\(335\) | − | 8.73291e24i | − | 0.490581i | ||||||
\(336\) | −1.58607e23 | − | 1.08261e24i | −0.00864829 | − | 0.0590309i | ||||
\(337\) | 7.89256e24 | 0.417752 | 0.208876 | − | 0.977942i | \(-0.433019\pi\) | ||||
0.208876 | + | 0.977942i | \(0.433019\pi\) | |||||||
\(338\) | −1.14993e25 | − | 1.06919e25i | −0.590887 | − | 0.549400i | ||||
\(339\) | 8.34035e24 | 0.416090 | ||||||||
\(340\) | −2.71991e24 | + | 1.98182e23i | −0.131755 | + | 0.00960008i | ||||
\(341\) | 3.61830e24i | 0.170200i | ||||||||
\(342\) | 1.81630e25 | + | 1.68877e25i | 0.829710 | + | 0.771455i | ||||
\(343\) | − | 9.61666e24i | − | 0.426661i | ||||||
\(344\) | −5.95216e23 | + | 7.41653e23i | −0.0256502 | + | 0.0319607i | ||||
\(345\) | −7.22773e24 | −0.302560 | ||||||||
\(346\) | −1.17152e25 | + | 1.25998e25i | −0.476418 | + | 0.512394i | ||||
\(347\) | 1.50298e24 | 0.0593825 | 0.0296912 | − | 0.999559i | \(-0.490548\pi\) | ||||
0.0296912 | + | 0.999559i | \(0.490548\pi\) | |||||||
\(348\) | 9.56441e24 | − | 6.96895e23i | 0.367169 | − | 0.0267531i | ||||
\(349\) | − | 3.33846e25i | − | 1.24535i | −0.782480 | − | 0.622676i | \(-0.786046\pi\) | ||
0.782480 | − | 0.622676i | \(-0.213954\pi\) | |||||||
\(350\) | −1.03245e24 | + | 1.11041e24i | −0.0374272 | + | 0.0402535i | ||||
\(351\) | − | 6.55708e24i | − | 0.231015i | ||||||
\(352\) | −2.52937e25 | − | 1.74369e25i | −0.866134 | − | 0.597093i | ||||
\(353\) | −4.35082e25 | −1.44818 | −0.724092 | − | 0.689703i | \(-0.757741\pi\) | ||||
−0.724092 | + | 0.689703i | \(0.757741\pi\) | |||||||
\(354\) | −7.99285e23 | − | 7.43166e23i | −0.0258624 | − | 0.0240466i | ||||
\(355\) | −3.82119e25 | −1.20203 | ||||||||
\(356\) | −3.63161e24 | − | 4.98415e25i | −0.111071 | − | 1.52437i | ||||
\(357\) | − | 3.06332e23i | − | 0.00910983i | ||||||
\(358\) | −3.06310e25 | − | 2.84803e25i | −0.885789 | − | 0.823596i | ||||
\(359\) | 5.13216e25i | 1.44330i | 0.692259 | + | 0.721649i | \(0.256615\pi\) | ||||
−0.692259 | + | 0.721649i | \(0.743385\pi\) | |||||||
\(360\) | 2.28310e25 | + | 1.83231e25i | 0.624453 | + | 0.501157i | ||||
\(361\) | 1.87421e25 | 0.498593 | ||||||||
\(362\) | 3.87447e23 | − | 4.16705e23i | 0.0100260 | − | 0.0107831i | ||||
\(363\) | −1.15720e24 | −0.0291300 | ||||||||
\(364\) | −2.85026e23 | − | 3.91178e24i | −0.00698023 | − | 0.0957990i | ||||
\(365\) | 3.19872e25i | 0.762162i | ||||||||
\(366\) | −1.29088e24 | + | 1.38836e24i | −0.0299277 | + | 0.0321877i | ||||
\(367\) | − | 9.79775e23i | − | 0.0221037i | −0.999939 | − | 0.0110519i | \(-0.996482\pi\) | ||
0.999939 | − | 0.0110519i | \(-0.00351799\pi\) | |||||||
\(368\) | −8.45847e24 | − | 5.77353e25i | −0.185701 | − | 1.26754i | ||||
\(369\) | 5.39415e25 | 1.15255 | ||||||||
\(370\) | 1.54639e24 | + | 1.43782e24i | 0.0321590 | + | 0.0299011i | ||||
\(371\) | 1.84369e25 | 0.373207 | ||||||||
\(372\) | −2.23544e24 | + | 1.62882e23i | −0.0440488 | + | 0.00320954i | ||||
\(373\) | 1.20006e25i | 0.230204i | 0.993354 | + | 0.115102i | \(0.0367196\pi\) | ||||
−0.993354 | + | 0.115102i | \(0.963280\pi\) | |||||||
\(374\) | −6.29898e24 | − | 5.85672e24i | −0.117640 | − | 0.109380i | ||||
\(375\) | 1.62547e25i | 0.295574i | ||||||||
\(376\) | 6.29742e25 | + | 5.05401e25i | 1.11502 | + | 0.894866i | ||||
\(377\) | 3.43755e25 | 0.592701 | ||||||||
\(378\) | −4.65854e24 | + | 5.01032e24i | −0.0782225 | + | 0.0841294i | ||||
\(379\) | −5.23113e25 | −0.855468 | −0.427734 | − | 0.903905i | \(-0.640688\pi\) | ||||
−0.427734 | + | 0.903905i | \(0.640688\pi\) | |||||||
\(380\) | 6.63169e25 | − | 4.83207e24i | 1.05630 | − | 0.0769657i | ||||
\(381\) | 2.71892e25i | 0.421838i | ||||||||
\(382\) | −3.73039e25 | + | 4.01209e25i | −0.563795 | + | 0.606369i | ||||
\(383\) | 1.18449e26i | 1.74399i | 0.489515 | + | 0.871995i | \(0.337174\pi\) | ||||
−0.489515 | + | 0.871995i | \(0.662826\pi\) | |||||||
\(384\) | 9.63417e24 | − | 1.64118e25i | 0.138198 | − | 0.235420i | ||||
\(385\) | 1.42322e25 | 0.198913 | ||||||||
\(386\) | 1.76581e25 | + | 1.64183e25i | 0.240476 | + | 0.223591i | ||||
\(387\) | 2.85796e24 | 0.0379268 | ||||||||
\(388\) | −5.73956e24 | − | 7.87716e25i | −0.0742269 | − | 1.01871i | ||||
\(389\) | − | 2.42607e25i | − | 0.305779i | −0.988243 | − | 0.152889i | \(-0.951142\pi\) | ||
0.988243 | − | 0.152889i | \(-0.0488578\pi\) | |||||||
\(390\) | −6.18816e24 | − | 5.75367e24i | −0.0760178 | − | 0.0706804i | ||||
\(391\) | − | 1.63366e25i | − | 0.195611i | ||||||
\(392\) | 5.10642e25 | − | 6.36271e25i | 0.596013 | − | 0.742645i | ||||
\(393\) | 2.38802e25 | 0.271714 | ||||||||
\(394\) | −2.36436e25 | + | 2.54290e25i | −0.262271 | + | 0.282077i | ||||
\(395\) | −7.85226e25 | −0.849227 | ||||||||
\(396\) | 6.70956e24 | + | 9.20842e25i | 0.0707526 | + | 0.971031i | ||||
\(397\) | − | 1.38755e26i | − | 1.42673i | −0.700791 | − | 0.713366i | \(-0.747170\pi\) | ||
0.700791 | − | 0.713366i | \(-0.252830\pi\) | |||||||
\(398\) | −5.03761e25 | + | 5.41802e25i | −0.505119 | + | 0.543263i | ||||
\(399\) | 7.46899e24i | 0.0730353i | ||||||||
\(400\) | −2.60930e25 | + | 3.82273e24i | −0.248842 | + | 0.0364564i | ||||
\(401\) | 4.99079e25 | 0.464222 | 0.232111 | − | 0.972689i | \(-0.425437\pi\) | ||||
0.232111 | + | 0.972689i | \(0.425437\pi\) | |||||||
\(402\) | 1.24949e25 | + | 1.16176e25i | 0.113363 | + | 0.105404i | ||||
\(403\) | −8.03442e24 | −0.0711056 | ||||||||
\(404\) | −1.98039e26 | + | 1.44298e25i | −1.70977 | + | 0.124579i | ||||
\(405\) | − | 8.03244e25i | − | 0.676546i | ||||||
\(406\) | −2.62666e25 | − | 2.44224e25i | −0.215846 | − | 0.200691i | ||||
\(407\) | 6.65962e24i | 0.0533956i | ||||||||
\(408\) | 3.33482e24 | − | 4.15526e24i | 0.0260898 | − | 0.0325085i | ||||
\(409\) | −9.92475e25 | −0.757682 | −0.378841 | − | 0.925462i | \(-0.623677\pi\) | ||||
−0.378841 | + | 0.925462i | \(0.623677\pi\) | |||||||
\(410\) | 9.84759e25 | − | 1.05912e26i | 0.733654 | − | 0.789056i | ||||
\(411\) | 8.15862e24 | 0.0593196 | ||||||||
\(412\) | 1.23140e25 | − | 8.97240e23i | 0.0873832 | − | 0.00636703i | ||||
\(413\) | 4.08190e24i | 0.0282723i | ||||||||
\(414\) | −1.19412e26 | + | 1.28429e26i | −0.807315 | + | 0.868279i | ||||
\(415\) | − | 1.97660e26i | − | 1.30448i | ||||||
\(416\) | 3.87186e25 | − | 5.61645e25i | 0.249451 | − | 0.361850i | ||||
\(417\) | −1.35189e25 | −0.0850317 | ||||||||
\(418\) | 1.53582e26 | + | 1.42798e26i | 0.943141 | + | 0.876921i | ||||
\(419\) | 8.81396e25 | 0.528483 | 0.264241 | − | 0.964457i | \(-0.414878\pi\) | ||||
0.264241 | + | 0.964457i | \(0.414878\pi\) | |||||||
\(420\) | 6.40677e23 | + | 8.79286e24i | 0.00375099 | + | 0.0514799i | ||||
\(421\) | − | 5.58973e25i | − | 0.319573i | −0.987152 | − | 0.159786i | \(-0.948919\pi\) | ||
0.987152 | − | 0.159786i | \(-0.0510805\pi\) | |||||||
\(422\) | −9.76826e25 | − | 9.08241e25i | −0.545372 | − | 0.507080i | ||||
\(423\) | − | 2.42671e26i | − | 1.32316i | ||||||
\(424\) | 2.50089e26 | + | 2.00710e26i | 1.33179 | + | 1.06883i | ||||
\(425\) | −7.38318e24 | −0.0384020 | ||||||||
\(426\) | 5.08343e25 | − | 5.46731e25i | 0.258262 | − | 0.277765i | ||||
\(427\) | 7.09024e24 | 0.0351870 | ||||||||
\(428\) | 8.57868e24 | + | 1.17737e26i | 0.0415894 | + | 0.570787i | ||||
\(429\) | − | 2.66496e25i | − | 0.126217i | ||||||
\(430\) | 5.21750e24 | − | 5.61150e24i | 0.0241423 | − | 0.0259653i | ||||
\(431\) | 2.02264e26i | 0.914420i | 0.889359 | + | 0.457210i | \(0.151151\pi\) | ||||
−0.889359 | + | 0.457210i | \(0.848849\pi\) | |||||||
\(432\) | −1.17735e26 | + | 1.72487e25i | −0.520077 | + | 0.0761936i | ||||
\(433\) | 9.70735e25 | 0.419008 | 0.209504 | − | 0.977808i | \(-0.432815\pi\) | ||||
0.209504 | + | 0.977808i | \(0.432815\pi\) | |||||||
\(434\) | 6.13917e24 | + | 5.70813e24i | 0.0258948 | + | 0.0240767i | ||||
\(435\) | −7.72689e25 | −0.318502 | ||||||||
\(436\) | −4.43011e26 | + | 3.22792e25i | −1.78464 | + | 0.130034i | ||||
\(437\) | 3.98319e26i | 1.56825i | ||||||||
\(438\) | −4.57668e25 | − | 4.25534e25i | −0.176120 | − | 0.163754i | ||||
\(439\) | − | 1.06665e26i | − | 0.401214i | −0.979672 | − | 0.200607i | \(-0.935708\pi\) | ||
0.979672 | − | 0.200607i | \(-0.0642915\pi\) | |||||||
\(440\) | 1.93053e26 | + | 1.54935e26i | 0.709823 | + | 0.569671i | ||||
\(441\) | −2.45187e26 | −0.881274 | ||||||||
\(442\) | 1.30048e25 | − | 1.39869e25i | 0.0456964 | − | 0.0491471i | ||||
\(443\) | 3.37450e26 | 1.15924 | 0.579618 | − | 0.814888i | \(-0.303202\pi\) | ||||
0.579618 | + | 0.814888i | \(0.303202\pi\) | |||||||
\(444\) | −4.11442e24 | + | 2.99790e23i | −0.0138191 | + | 0.00100690i | ||||
\(445\) | 4.02659e26i | 1.32232i | ||||||||
\(446\) | 3.07497e26 | − | 3.30717e26i | 0.987398 | − | 1.06196i | ||||
\(447\) | 3.79714e25i | 0.119229i | ||||||||
\(448\) | −6.94878e25 | + | 1.54079e25i | −0.213368 | + | 0.0473110i | ||||
\(449\) | −2.12762e26 | −0.638896 | −0.319448 | − | 0.947604i | \(-0.603498\pi\) | ||||
−0.319448 | + | 0.947604i | \(0.603498\pi\) | |||||||
\(450\) | 5.80423e25 | + | 5.39670e25i | 0.170459 | + | 0.158491i | ||||
\(451\) | 4.56116e26 | 1.31012 | ||||||||
\(452\) | −3.94267e25 | − | 5.41105e26i | −0.110766 | − | 1.52019i | ||||
\(453\) | − | 1.95108e26i | − | 0.536158i | ||||||
\(454\) | 7.88910e25 | + | 7.33519e25i | 0.212065 | + | 0.197176i | ||||
\(455\) | 3.16025e25i | 0.0831012i | ||||||||
\(456\) | −8.13095e25 | + | 1.01314e26i | −0.209167 | + | 0.260627i | ||||
\(457\) | −1.99071e26 | −0.501010 | −0.250505 | − | 0.968115i | \(-0.580597\pi\) | ||||
−0.250505 | + | 0.968115i | \(0.580597\pi\) | |||||||
\(458\) | 4.22472e26 | − | 4.54375e26i | 1.04026 | − | 1.11882i | ||||
\(459\) | −3.33139e25 | −0.0802599 | ||||||||
\(460\) | 3.41671e25 | + | 4.68921e26i | 0.0805434 | + | 1.10540i | ||||
\(461\) | 5.96463e26i | 1.37586i | 0.725777 | + | 0.687930i | \(0.241481\pi\) | ||||
−0.725777 | + | 0.687930i | \(0.758519\pi\) | |||||||
\(462\) | −1.89334e25 | + | 2.03632e25i | −0.0427375 | + | 0.0459648i | ||||
\(463\) | 2.47453e26i | 0.546617i | 0.961926 | + | 0.273308i | \(0.0881179\pi\) | ||||
−0.961926 | + | 0.273308i | \(0.911882\pi\) | |||||||
\(464\) | −9.04263e25 | − | 6.17225e26i | −0.195486 | − | 1.33433i | ||||
\(465\) | 1.80597e25 | 0.0382103 | ||||||||
\(466\) | 7.85174e25 | + | 7.30046e25i | 0.162595 | + | 0.151179i | ||||
\(467\) | −5.31638e26 | −1.07757 | −0.538787 | − | 0.842442i | \(-0.681117\pi\) | ||||
−0.538787 | + | 0.842442i | \(0.681117\pi\) | |||||||
\(468\) | −2.04473e26 | + | 1.48986e25i | −0.405674 | + | 0.0295587i | ||||
\(469\) | − | 6.38107e25i | − | 0.123927i | ||||||
\(470\) | −4.76475e26 | − | 4.43021e26i | −0.905861 | − | 0.842259i | ||||
\(471\) | − | 6.29259e25i | − | 0.117117i | ||||||
\(472\) | −4.44367e25 | + | 5.53691e25i | −0.0809695 | + | 0.100890i | ||||
\(473\) | 2.41662e25 | 0.0431118 | ||||||||
\(474\) | 1.04461e26 | − | 1.12349e26i | 0.182461 | − | 0.196239i | ||||
\(475\) | 1.80017e26 | 0.307877 | ||||||||
\(476\) | −1.98742e25 | + | 1.44810e24i | −0.0332828 | + | 0.00242510i | ||||
\(477\) | − | 9.63716e26i | − | 1.58039i | ||||||
\(478\) | −4.78441e25 | + | 5.14571e25i | −0.0768334 | + | 0.0826354i | ||||
\(479\) | − | 3.84647e26i | − | 0.604932i | −0.953160 | − | 0.302466i | \(-0.902190\pi\) | ||
0.953160 | − | 0.302466i | \(-0.0978099\pi\) | |||||||
\(480\) | −8.70311e25 | + | 1.26246e26i | −0.134049 | + | 0.194449i | ||||
\(481\) | −1.47877e25 | −0.0223074 | ||||||||
\(482\) | −5.55182e26 | − | 5.16202e26i | −0.820286 | − | 0.762692i | ||||
\(483\) | −5.28125e25 | −0.0764303 | ||||||||
\(484\) | 5.47032e24 | + | 7.50765e25i | 0.00775460 | + | 0.106427i | ||||
\(485\) | 6.36379e26i | 0.883688i | ||||||||
\(486\) | 3.97910e26 | + | 3.69972e26i | 0.541280 | + | 0.503275i | ||||
\(487\) | − | 3.66749e25i | − | 0.0488741i | −0.999701 | − | 0.0244371i | \(-0.992221\pi\) | ||
0.999701 | − | 0.0244371i | \(-0.00777934\pi\) | |||||||
\(488\) | 9.61760e25 | + | 7.71864e25i | 0.125565 | + | 0.100773i | ||||
\(489\) | 2.89682e26 | 0.370538 | ||||||||
\(490\) | −4.47614e26 | + | 4.81415e26i | −0.560974 | + | 0.603336i | ||||
\(491\) | −7.55878e26 | −0.928190 | −0.464095 | − | 0.885785i | \(-0.653620\pi\) | ||||
−0.464095 | + | 0.885785i | \(0.653620\pi\) | |||||||
\(492\) | 2.05326e25 | + | 2.81796e26i | 0.0247054 | + | 0.339065i | ||||
\(493\) | − | 1.74648e26i | − | 0.205918i | ||||||
\(494\) | −3.17084e26 | + | 3.41028e26i | −0.366357 | + | 0.394022i | ||||
\(495\) | − | 7.43929e26i | − | 0.842325i | ||||||
\(496\) | 2.11349e25 | + | 1.44261e26i | 0.0234522 | + | 0.160078i | ||||
\(497\) | −2.79212e26 | −0.303647 | ||||||||
\(498\) | 2.82809e26 | + | 2.62952e26i | 0.301439 | + | 0.280274i | ||||
\(499\) | 7.77009e26 | 0.811746 | 0.405873 | − | 0.913929i | \(-0.366967\pi\) | ||||
0.405873 | + | 0.913929i | \(0.366967\pi\) | |||||||
\(500\) | 1.05457e27 | − | 7.68397e25i | 1.07988 | − | 0.0786839i | ||||
\(501\) | − | 4.03697e26i | − | 0.405209i | ||||||
\(502\) | 1.00330e27 | + | 9.32859e26i | 0.987178 | + | 0.917866i | ||||
\(503\) | 1.47036e27i | 1.41822i | 0.705097 | + | 0.709110i | \(0.250903\pi\) | ||||
−0.705097 | + | 0.709110i | \(0.749097\pi\) | |||||||
\(504\) | 1.66824e26 | + | 1.33885e26i | 0.157744 | + | 0.126598i | ||||
\(505\) | 1.59992e27 | 1.48314 | ||||||||
\(506\) | −1.00971e27 | + | 1.08596e27i | −0.917684 | + | 0.986982i | ||||
\(507\) | −2.47176e26 | −0.220256 | ||||||||
\(508\) | 1.76398e27 | − | 1.28529e26i | 1.54119 | − | 0.112296i | ||||
\(509\) | − | 8.27692e26i | − | 0.709073i | −0.935042 | − | 0.354536i | \(-0.884639\pi\) | ||
0.935042 | − | 0.354536i | \(-0.115361\pi\) | |||||||
\(510\) | −2.92321e25 | + | 3.14395e25i | −0.0245560 | + | 0.0264104i | ||||
\(511\) | 2.33728e26i | 0.192531i | ||||||||
\(512\) | −1.11031e27 | − | 5.47463e26i | −0.896898 | − | 0.442237i | ||||
\(513\) | 8.12259e26 | 0.643459 | ||||||||
\(514\) | 3.61354e26 | + | 3.35982e26i | 0.280738 | + | 0.261027i | ||||
\(515\) | −9.94824e25 | −0.0758008 | ||||||||
\(516\) | 1.08787e24 | + | 1.49302e25i | 0.000812978 | + | 0.0111576i | ||||
\(517\) | − | 2.05196e27i | − | 1.50405i | ||||||
\(518\) | 1.12994e25 | + | 1.05060e25i | 0.00812376 | + | 0.00755338i | ||||
\(519\) | 2.70832e26i | 0.190997i | ||||||||
\(520\) | −3.44034e26 | + | 4.28674e26i | −0.237995 | + | 0.296547i | ||||
\(521\) | −3.49221e26 | −0.236986 | −0.118493 | − | 0.992955i | \(-0.537806\pi\) | ||||
−0.118493 | + | 0.992955i | \(0.537806\pi\) | |||||||
\(522\) | −1.27658e27 | + | 1.37298e27i | −0.849853 | + | 0.914029i | ||||
\(523\) | −1.26906e27 | −0.828831 | −0.414415 | − | 0.910088i | \(-0.636014\pi\) | ||||
−0.414415 | + | 0.910088i | \(0.636014\pi\) | |||||||
\(524\) | −1.12887e26 | − | 1.54930e27i | −0.0723320 | − | 0.992708i | ||||
\(525\) | 2.38681e25i | 0.0150046i | ||||||||
\(526\) | −4.17444e26 | + | 4.48967e26i | −0.257479 | + | 0.276922i | ||||
\(527\) | 4.08196e25i | 0.0247038i | ||||||||
\(528\) | −4.78503e26 | + | 7.01028e25i | −0.284149 | + | 0.0416290i | ||||
\(529\) | −1.10032e27 | −0.641153 | ||||||||
\(530\) | −1.89222e27 | − | 1.75937e27i | −1.08197 | − | 1.00600i | ||||
\(531\) | 2.13365e26 | 0.119723 | ||||||||
\(532\) | 4.84573e26 | − | 3.53076e25i | 0.266835 | − | 0.0194425i | ||||
\(533\) | 1.01280e27i | 0.547335i | ||||||||
\(534\) | −5.76118e26 | − | 5.35668e26i | −0.305562 | − | 0.284108i | ||||
\(535\) | − | 9.51169e26i | − | 0.495131i | ||||||
\(536\) | 6.94662e26 | − | 8.65564e26i | 0.354916 | − | 0.442233i | ||||
\(537\) | −6.58408e26 | −0.330181 | ||||||||
\(538\) | −3.69614e25 | + | 3.97525e25i | −0.0181939 | + | 0.0195678i | ||||
\(539\) | −2.07324e27 | −1.00175 | ||||||||
\(540\) | 9.56232e26 | − | 6.96742e25i | 0.453550 | − | 0.0330472i | ||||
\(541\) | 2.64356e26i | 0.123088i | 0.998104 | + | 0.0615440i | \(0.0196025\pi\) | ||||
−0.998104 | + | 0.0615440i | \(0.980398\pi\) | |||||||
\(542\) | 2.45519e27 | − | 2.64059e27i | 1.12226 | − | 1.20700i | ||||
\(543\) | − | 8.95702e24i | − | 0.00401944i | ||||||
\(544\) | −2.85349e26 | − | 1.96713e26i | −0.125715 | − | 0.0866653i | ||||
\(545\) | 3.57899e27 | 1.54809 | ||||||||
\(546\) | −4.52164e25 | − | 4.20416e25i | −0.0192030 | − | 0.0178547i | ||||
\(547\) | −7.85407e26 | −0.327507 | −0.163754 | − | 0.986501i | \(-0.552360\pi\) | ||||
−0.163754 | + | 0.986501i | \(0.552360\pi\) | |||||||
\(548\) | −3.85676e25 | − | 5.29315e26i | −0.0157913 | − | 0.216725i | ||||
\(549\) | − | 3.70614e26i | − | 0.149004i | ||||||
\(550\) | 4.90791e26 | + | 4.56331e26i | 0.193762 | + | 0.180158i | ||||
\(551\) | 4.25827e27i | 1.65089i | ||||||||
\(552\) | −7.16378e26 | − | 5.74932e26i | −0.272742 | − | 0.218890i | ||||
\(553\) | −5.73759e26 | −0.214525 | ||||||||
\(554\) | 4.36021e26 | − | 4.68947e26i | 0.160107 | − | 0.172197i | ||||
\(555\) | 3.32395e25 | 0.0119874 | ||||||||
\(556\) | 6.39069e25 | + | 8.77080e26i | 0.0226360 | + | 0.310664i | ||||
\(557\) | 1.79432e27i | 0.624236i | 0.950043 | + | 0.312118i | \(0.101038\pi\) | ||||
−0.950043 | + | 0.312118i | \(0.898962\pi\) | |||||||
\(558\) | 2.98369e26 | − | 3.20900e26i | 0.101956 | − | 0.109655i | ||||
\(559\) | 5.36609e25i | 0.0180111i | ||||||||
\(560\) | 5.67435e26 | − | 8.31317e25i | 0.187084 | − | 0.0274086i | ||||
\(561\) | −1.35396e26 | −0.0438507 | ||||||||
\(562\) | −3.24490e27 | − | 3.01706e27i | −1.03238 | − | 0.959890i | ||||
\(563\) | 4.71503e27 | 1.47367 | 0.736836 | − | 0.676071i | \(-0.236319\pi\) | ||||
0.736836 | + | 0.676071i | \(0.236319\pi\) | |||||||
\(564\) | 1.26774e27 | − | 9.23714e25i | 0.389258 | − | 0.0283626i | ||||
\(565\) | 4.37147e27i | 1.31869i | ||||||||
\(566\) | 3.45579e27 | + | 3.21315e27i | 1.02420 | + | 0.952284i | ||||
\(567\) | − | 5.86924e26i | − | 0.170904i | ||||||
\(568\) | −3.78738e27 | − | 3.03958e27i | −1.08357 | − | 0.869621i | ||||
\(569\) | −1.72052e27 | −0.483656 | −0.241828 | − | 0.970319i | \(-0.577747\pi\) | ||||
−0.241828 | + | 0.970319i | \(0.577747\pi\) | |||||||
\(570\) | 7.12737e26 | − | 7.66559e26i | 0.196870 | − | 0.211737i | ||||
\(571\) | 1.40979e27 | 0.382641 | 0.191321 | − | 0.981528i | \(-0.438723\pi\) | ||||
0.191321 | + | 0.981528i | \(0.438723\pi\) | |||||||
\(572\) | −1.72897e27 | + | 1.25978e26i | −0.461134 | + | 0.0335998i | ||||
\(573\) | 8.62394e26i | 0.226026i | ||||||||
\(574\) | 7.19556e26 | − | 7.73893e26i | 0.185330 | − | 0.199325i | ||||
\(575\) | 1.27288e27i | 0.322188i | ||||||||
\(576\) | 8.05384e26 | + | 3.63219e27i | 0.200345 | + | 0.903534i | ||||
\(577\) | −6.12456e27 | −1.49733 | −0.748663 | − | 0.662950i | \(-0.769304\pi\) | ||||
−0.748663 | + | 0.662950i | \(0.769304\pi\) | |||||||
\(578\) | 2.97681e27 | + | 2.76780e27i | 0.715274 | + | 0.665053i | ||||
\(579\) | 3.79559e26 | 0.0896382 | ||||||||
\(580\) | 3.65267e26 | + | 5.01305e27i | 0.0847873 | + | 1.16365i | ||||
\(581\) | − | 1.44428e27i | − | 0.329527i | ||||||
\(582\) | −9.10522e26 | − | 8.46592e26i | −0.204202 | − | 0.189865i | ||||
\(583\) | − | 8.14894e27i | − | 1.79645i | ||||||
\(584\) | −2.54443e27 | + | 3.17042e27i | −0.551394 | + | 0.687049i | ||||
\(585\) | 1.65189e27 | 0.351903 | ||||||||
\(586\) | 1.98382e27 | − | 2.13363e27i | 0.415457 | − | 0.446830i | ||||
\(587\) | 3.87893e27 | 0.798604 | 0.399302 | − | 0.916820i | \(-0.369253\pi\) | ||||
0.399302 | + | 0.916820i | \(0.369253\pi\) | |||||||
\(588\) | −9.33291e25 | − | 1.28088e27i | −0.0188905 | − | 0.259260i | ||||
\(589\) | − | 9.95264e26i | − | 0.198055i | ||||||
\(590\) | 3.89520e26 | − | 4.18934e26i | 0.0762095 | − | 0.0819644i | ||||
\(591\) | 5.46593e26i | 0.105145i | ||||||||
\(592\) | 3.88996e25 | + | 2.65518e26i | 0.00735746 | + | 0.0502200i | ||||
\(593\) | −5.05296e27 | −0.939722 | −0.469861 | − | 0.882740i | \(-0.655696\pi\) | ||||
−0.469861 | + | 0.882740i | \(0.655696\pi\) | |||||||
\(594\) | 2.21451e27 | + | 2.05903e27i | 0.404962 | + | 0.376528i | ||||
\(595\) | 1.60560e26 | 0.0288713 | ||||||||
\(596\) | 2.46351e27 | − | 1.79499e26i | 0.435603 | − | 0.0317395i | ||||
\(597\) | 1.16460e27i | 0.202503i | ||||||||
\(598\) | −2.41138e27 | − | 2.24207e27i | −0.412338 | − | 0.383387i | ||||
\(599\) | − | 6.42777e27i | − | 1.08092i | −0.841371 | − | 0.540459i | \(-0.818251\pi\) | ||
0.841371 | − | 0.540459i | \(-0.181749\pi\) | |||||||
\(600\) | −2.59835e26 | + | 3.23761e26i | −0.0429720 | + | 0.0535441i | ||||
\(601\) | 6.13048e27 | 0.997126 | 0.498563 | − | 0.866854i | \(-0.333861\pi\) | ||||
0.498563 | + | 0.866854i | \(0.333861\pi\) | |||||||
\(602\) | 3.81239e25 | − | 4.10028e25i | 0.00609863 | − | 0.00655916i | ||||
\(603\) | −3.33545e27 | −0.524784 | ||||||||
\(604\) | −1.26582e28 | + | 9.22319e26i | −1.95886 | + | 0.142729i | ||||
\(605\) | − | 6.06527e26i | − | 0.0923202i | ||||||
\(606\) | −2.12841e27 | + | 2.28914e27i | −0.318661 | + | 0.342725i | ||||
\(607\) | − | 8.59036e27i | − | 1.26510i | −0.774520 | − | 0.632549i | \(-0.782009\pi\) | ||
0.774520 | − | 0.632549i | \(-0.217991\pi\) | |||||||
\(608\) | 6.95739e27 | + | 4.79627e27i | 1.00788 | + | 0.694812i | ||||
\(609\) | −5.64598e26 | −0.0804575 | ||||||||
\(610\) | −7.27687e26 | − | 6.76595e26i | −0.102011 | − | 0.0948484i | ||||
\(611\) | 4.55638e27 | 0.628358 | ||||||||
\(612\) | 7.56936e25 | + | 1.03884e27i | 0.0102694 | + | 0.140941i | ||||
\(613\) | − | 6.53893e27i | − | 0.872774i | −0.899759 | − | 0.436387i | \(-0.856258\pi\) | ||
0.899759 | − | 0.436387i | \(-0.143742\pi\) | |||||||
\(614\) | −4.24842e27 | − | 3.95013e27i | −0.557884 | − | 0.518714i | ||||
\(615\) | − | 2.27657e27i | − | 0.294124i | ||||||
\(616\) | 1.41062e27 | + | 1.13210e27i | 0.179310 | + | 0.143906i | ||||
\(617\) | −4.14779e27 | −0.518759 | −0.259379 | − | 0.965776i | \(-0.583518\pi\) | ||||
−0.259379 | + | 0.965776i | \(0.583518\pi\) | |||||||
\(618\) | 1.32344e26 | − | 1.42338e26i | 0.0162862 | − | 0.0175160i | ||||
\(619\) | −2.89355e27 | −0.350368 | −0.175184 | − | 0.984536i | \(-0.556052\pi\) | ||||
−0.175184 | + | 0.984536i | \(0.556052\pi\) | |||||||
\(620\) | −8.53721e25 | − | 1.17167e27i | −0.0101718 | − | 0.139602i | ||||
\(621\) | 5.74341e27i | 0.673370i | ||||||||
\(622\) | 2.88598e27 | − | 3.10391e27i | 0.332958 | − | 0.358101i | ||||
\(623\) | 2.94220e27i | 0.334034i | ||||||||
\(624\) | −1.55663e26 | − | 1.06251e27i | −0.0173916 | − | 0.118710i | ||||
\(625\) | −6.23232e27 | −0.685250 | ||||||||
\(626\) | 8.47576e27 | + | 7.88066e27i | 0.917140 | + | 0.852745i | ||||
\(627\) | 3.30122e27 | 0.351559 | ||||||||
\(628\) | −4.08250e27 | + | 2.97465e26i | −0.427888 | + | 0.0311773i | ||||
\(629\) | 7.51302e25i | 0.00775011i | ||||||||
\(630\) | −1.26223e27 | − | 1.17360e27i | −0.128154 | − | 0.119156i | ||||
\(631\) | 1.13124e28i | 1.13048i | 0.824928 | + | 0.565238i | \(0.191216\pi\) | ||||
−0.824928 | + | 0.565238i | \(0.808784\pi\) | |||||||
\(632\) | −7.78279e27 | − | 6.24610e27i | −0.765534 | − | 0.614382i | ||||
\(633\) | −2.09967e27 | −0.203289 | ||||||||
\(634\) | 6.83564e27 | − | 7.35183e27i | 0.651458 | − | 0.700653i | ||||
\(635\) | −1.42508e28 | −1.33691 | ||||||||
\(636\) | 5.03455e27 | − | 3.66834e26i | 0.464932 | − | 0.0338765i | ||||
\(637\) | − | 4.60362e27i | − | 0.418509i | ||||||
\(638\) | −1.07945e28 | + | 1.16096e28i | −0.966038 | + | 1.03899i | ||||
\(639\) | 1.45947e28i | 1.28584i | ||||||||
\(640\) | 8.60200e27 | + | 5.04961e27i | 0.746104 | + | 0.437984i | ||||
\(641\) | 2.31014e28 | 1.97268 | 0.986341 | − | 0.164713i | \(-0.0526699\pi\) | ||||
0.986341 | + | 0.164713i | \(0.0526699\pi\) | |||||||
\(642\) | 1.36092e27 | + | 1.26537e27i | 0.114415 | + | 0.106381i | ||||
\(643\) | 1.26662e28 | 1.04843 | 0.524213 | − | 0.851587i | \(-0.324360\pi\) | ||||
0.524213 | + | 0.851587i | \(0.324360\pi\) | |||||||
\(644\) | 2.49657e26 | + | 3.42637e27i | 0.0203462 | + | 0.279239i | ||||
\(645\) | − | 1.20618e26i | − | 0.00967868i | ||||||
\(646\) | 1.73263e27 | + | 1.61097e27i | 0.136892 | + | 0.127281i | ||||
\(647\) | 3.27969e27i | 0.255147i | 0.991829 | + | 0.127573i | \(0.0407188\pi\) | ||||
−0.991829 | + | 0.127573i | \(0.959281\pi\) | |||||||
\(648\) | 6.38943e27 | − | 7.96137e27i | 0.489454 | − | 0.609871i | ||||
\(649\) | 1.80416e27 | 0.136090 | ||||||||
\(650\) | −1.01328e27 | + | 1.08980e27i | −0.0752657 | + | 0.0809494i | ||||
\(651\) | 1.31961e26 | 0.00965238 | ||||||||
\(652\) | −1.36939e27 | − | 1.87940e28i | −0.0986398 | − | 1.35376i | ||||
\(653\) | − | 2.38862e27i | − | 0.169440i | −0.996405 | − | 0.0847200i | \(-0.973000\pi\) | ||
0.996405 | − | 0.0847200i | \(-0.0269996\pi\) | |||||||
\(654\) | −4.76123e27 | + | 5.12077e27i | −0.332615 | + | 0.357732i | ||||
\(655\) | 1.25164e28i | 0.861128i | ||||||||
\(656\) | 1.81853e28 | − | 2.66422e27i | 1.23220 | − | 0.180523i | ||||
\(657\) | 1.22172e28 | 0.815300 | ||||||||
\(658\) | −3.48157e27 | − | 3.23712e27i | −0.228832 | − | 0.212765i | ||||
\(659\) | −3.24782e27 | −0.210251 | −0.105125 | − | 0.994459i | \(-0.533524\pi\) | ||||
−0.105125 | + | 0.994459i | \(0.533524\pi\) | |||||||
\(660\) | 3.88636e27 | − | 2.83173e26i | 0.247801 | − | 0.0180556i | ||||
\(661\) | 2.77284e28i | 1.74145i | 0.491774 | + | 0.870723i | \(0.336349\pi\) | ||||
−0.491774 | + | 0.870723i | \(0.663651\pi\) | |||||||
\(662\) | −1.15029e28 | − | 1.06952e28i | −0.711585 | − | 0.661623i | ||||
\(663\) | − | 3.00646e26i | − | 0.0183198i | ||||||
\(664\) | 1.57229e28 | − | 1.95911e28i | 0.943739 | − | 1.17592i | ||||
\(665\) | −3.91476e27 | −0.231467 | ||||||||
\(666\) | 5.49160e26 | − | 5.90630e26i | 0.0319858 | − | 0.0344012i | ||||
\(667\) | −3.01098e28 | −1.72763 | ||||||||
\(668\) | −2.61911e28 | + | 1.90837e27i | −1.48043 | + | 0.107869i | ||||
\(669\) | − | 7.10872e27i | − | 0.395850i | ||||||
\(670\) | −6.08921e27 | + | 6.54903e27i | −0.334051 | + | 0.359277i | ||||
\(671\) | − | 3.13382e27i | − | 0.169375i | ||||||
\(672\) | −6.35930e26 | + | 9.22469e26i | −0.0338623 | + | 0.0491201i | ||||
\(673\) | −1.45343e28 | −0.762504 | −0.381252 | − | 0.924471i | \(-0.624507\pi\) | ||||
−0.381252 | + | 0.924471i | \(0.624507\pi\) | |||||||
\(674\) | −5.91883e27 | − | 5.50325e27i | −0.305940 | − | 0.284460i | ||||
\(675\) | 2.59568e27 | 0.132195 | ||||||||
\(676\) | 1.16846e27 | + | 1.60363e28i | 0.0586335 | + | 0.804705i | ||||
\(677\) | − | 3.77095e28i | − | 1.86451i | −0.361807 | − | 0.932253i | \(-0.617840\pi\) | ||
0.361807 | − | 0.932253i | \(-0.382160\pi\) | |||||||
\(678\) | −6.25464e27 | − | 5.81549e27i | −0.304723 | − | 0.283328i | ||||
\(679\) | 4.64998e27i | 0.223230i | ||||||||
\(680\) | 2.17792e27 | + | 1.74790e27i | 0.103027 | + | 0.0826850i | ||||
\(681\) | 1.69575e27 | 0.0790481 | ||||||||
\(682\) | 2.52293e27 | − | 2.71345e27i | 0.115894 | − | 0.124646i | ||||
\(683\) | −3.81940e28 | −1.72897 | −0.864487 | − | 0.502655i | \(-0.832357\pi\) | ||||
−0.864487 | + | 0.502655i | \(0.832357\pi\) | |||||||
\(684\) | −1.84556e27 | − | 2.53291e28i | −0.0823318 | − | 1.12995i | ||||
\(685\) | 4.27622e27i | 0.187999i | ||||||||
\(686\) | −6.70542e27 | + | 7.21178e27i | −0.290526 | + | 0.312465i | ||||
\(687\) | − | 9.76672e27i | − | 0.417044i | ||||||
\(688\) | 9.63501e26 | − | 1.41157e26i | 0.0405479 | − | 0.00594044i | ||||
\(689\) | 1.80947e28 | 0.750515 | ||||||||
\(690\) | 5.42026e27 | + | 5.03969e27i | 0.221579 | + | 0.206022i | ||||
\(691\) | 4.53729e28 | 1.82817 | 0.914084 | − | 0.405526i | \(-0.132912\pi\) | ||||
0.914084 | + | 0.405526i | \(0.132912\pi\) | |||||||
\(692\) | 1.75710e28 | − | 1.28028e27i | 0.697808 | − | 0.0508446i | ||||
\(693\) | − | 5.43583e27i | − | 0.212781i | ||||||
\(694\) | −1.12712e27 | − | 1.04798e27i | −0.0434887 | − | 0.0404353i | ||||
\(695\) | − | 7.08574e27i | − | 0.269487i | ||||||
\(696\) | −7.65852e27 | − | 6.14637e27i | −0.287113 | − | 0.230423i | ||||
\(697\) | 5.14565e27 | 0.190157 | ||||||||
\(698\) | −2.32781e28 | + | 2.50360e28i | −0.847996 | + | 0.912032i | ||||
\(699\) | 1.68772e27 | 0.0606079 | ||||||||
\(700\) | 1.54852e27 | − | 1.12830e26i | 0.0548196 | − | 0.00399434i | ||||
\(701\) | − | 2.44859e28i | − | 0.854545i | −0.904123 | − | 0.427273i | \(-0.859474\pi\) | ||
0.904123 | − | 0.427273i | \(-0.140526\pi\) | |||||||
\(702\) | −4.57207e27 | + | 4.91732e27i | −0.157305 | + | 0.169183i | ||||
\(703\) | − | 1.83182e27i | − | 0.0621342i | ||||||
\(704\) | 6.81012e27 | + | 3.07129e28i | 0.227734 | + | 1.02706i | ||||
\(705\) | −1.02418e28 | −0.337663 | ||||||||
\(706\) | 3.26279e28 | + | 3.03370e28i | 1.06058 | + | 0.986111i | ||||
\(707\) | 1.16905e28 | 0.374660 | ||||||||
\(708\) | 8.12162e25 | + | 1.11464e27i | 0.00256632 | + | 0.0352210i | ||||
\(709\) | 2.07454e27i | 0.0646339i | 0.999478 | + | 0.0323169i | \(0.0102886\pi\) | ||||
−0.999478 | + | 0.0323169i | \(0.989711\pi\) | |||||||
\(710\) | 2.86561e28 | + | 2.66441e28i | 0.880306 | + | 0.818497i | ||||
\(711\) | 2.99909e28i | 0.908435i | ||||||||
\(712\) | −3.20296e28 | + | 3.99096e28i | −0.956647 | + | 1.19200i | ||||
\(713\) | 7.03742e27 | 0.207261 | ||||||||
\(714\) | −2.13597e26 | + | 2.29726e26i | −0.00620315 | + | 0.00667158i | ||||
\(715\) | 1.39680e28 | 0.400012 | ||||||||
\(716\) | 3.11244e27 | + | 4.27162e28i | 0.0878964 | + | 1.20632i | ||||
\(717\) | 1.10606e27i | 0.0308026i | ||||||||
\(718\) | 3.57851e28 | − | 3.84874e28i | 0.982783 | − | 1.05700i | ||||
\(719\) | − | 6.81553e28i | − | 1.84591i | −0.384906 | − | 0.922956i | \(-0.625766\pi\) | ||
0.384906 | − | 0.922956i | \(-0.374234\pi\) | |||||||
\(720\) | −4.34537e27 | − | 2.96604e28i | −0.116065 | − | 0.792230i | ||||
\(721\) | −7.26910e26 | −0.0191482 | ||||||||
\(722\) | −1.40552e28 | − | 1.30683e28i | −0.365144 | − | 0.339507i | ||||
\(723\) | −1.19336e28 | −0.305765 | ||||||||
\(724\) | −5.81113e26 | + | 4.23418e25i | −0.0146850 | + | 0.00107000i | ||||
\(725\) | 1.36079e28i | 0.339164i | ||||||||
\(726\) | 8.67810e26 | + | 8.06879e26i | 0.0213333 | + | 0.0198355i | ||||
\(727\) | − | 3.11037e27i | − | 0.0754167i | −0.999289 | − | 0.0377083i | \(-0.987994\pi\) | ||
0.999289 | − | 0.0377083i | \(-0.0120058\pi\) | |||||||
\(728\) | −2.51383e27 | + | 3.13229e27i | −0.0601204 | + | 0.0749114i | ||||
\(729\) | −2.45964e28 | −0.580225 | ||||||||
\(730\) | 2.23038e28 | − | 2.39880e28i | 0.518979 | − | 0.558169i | ||||
\(731\) | 2.72629e26 | 0.00625747 | ||||||||
\(732\) | 1.93612e27 | − | 1.41072e26i | 0.0438351 | − | 0.00319397i | ||||
\(733\) | 5.70653e28i | 1.27448i | 0.770667 | + | 0.637239i | \(0.219923\pi\) | ||||
−0.770667 | + | 0.637239i | \(0.780077\pi\) | |||||||
\(734\) | −6.83170e26 | + | 7.34759e26i | −0.0150511 | + | 0.0161877i | ||||
\(735\) | 1.03480e28i | 0.224896i | ||||||||
\(736\) | −3.39139e28 | + | 4.91950e28i | −0.727110 | + | 1.05473i | ||||
\(737\) | −2.82037e28 | −0.596528 | ||||||||
\(738\) | −4.04521e28 | − | 3.76119e28i | −0.844069 | − | 0.784805i | ||||
\(739\) | 5.29434e28 | 1.08985 | 0.544926 | − | 0.838484i | \(-0.316558\pi\) | ||||
0.544926 | + | 0.838484i | \(0.316558\pi\) | |||||||
\(740\) | −1.57131e26 | − | 2.15651e27i | −0.00319113 | − | 0.0437961i | ||||
\(741\) | 7.33035e27i | 0.146873i | ||||||||
\(742\) | −1.38263e28 | − | 1.28556e28i | −0.273318 | − | 0.254127i | ||||
\(743\) | − | 3.40637e28i | − | 0.664360i | −0.943216 | − | 0.332180i | \(-0.892216\pi\) | ||
0.943216 | − | 0.332180i | \(-0.107784\pi\) | |||||||
\(744\) | 1.78999e27 | + | 1.43656e27i | 0.0344446 | + | 0.0276436i | ||||
\(745\) | −1.99022e28 | −0.377866 | ||||||||
\(746\) | 8.36766e27 | − | 8.99954e27i | 0.156753 | − | 0.168590i | ||||
\(747\) | −7.54942e28 | −1.39543 | ||||||||
\(748\) | 6.40046e26 | + | 8.78420e27i | 0.0116733 | + | 0.160209i | ||||
\(749\) | − | 6.95012e27i | − | 0.125076i | ||||||
\(750\) | 1.13340e28 | − | 1.21898e28i | 0.201265 | − | 0.216464i | ||||
\(751\) | − | 1.46366e28i | − | 0.256473i | −0.991744 | − | 0.128236i | \(-0.959068\pi\) | ||
0.991744 | − | 0.128236i | \(-0.0409316\pi\) | |||||||
\(752\) | −1.19857e28 | − | 8.18114e28i | −0.207246 | − | 1.41461i | ||||
\(753\) | 2.15659e28 | 0.367974 | ||||||||
\(754\) | −2.57791e28 | − | 2.39691e28i | −0.434064 | − | 0.403588i | ||||
\(755\) | 1.02263e29 | 1.69922 | ||||||||
\(756\) | 6.98711e27 | − | 5.09104e26i | 0.114572 | − | 0.00834812i | ||||
\(757\) | 7.96001e28i | 1.28812i | 0.764977 | + | 0.644058i | \(0.222751\pi\) | ||||
−0.764977 | + | 0.644058i | \(0.777249\pi\) | |||||||
\(758\) | 3.92296e28 | + | 3.64752e28i | 0.626501 | + | 0.582513i | ||||
\(759\) | 2.33426e28i | 0.367901i | ||||||||
\(760\) | −5.31020e28 | − | 4.26172e28i | −0.825991 | − | 0.662902i | ||||
\(761\) | −2.73143e28 | −0.419318 | −0.209659 | − | 0.977775i | \(-0.567235\pi\) | ||||
−0.209659 | + | 0.977775i | \(0.567235\pi\) | |||||||
\(762\) | 1.89582e28 | − | 2.03898e28i | 0.287242 | − | 0.308933i | ||||
\(763\) | 2.61514e28 | 0.391066 | ||||||||
\(764\) | 5.59504e28 | − | 4.07673e27i | 0.825789 | − | 0.0601697i | ||||
\(765\) | − | 8.39260e27i | − | 0.122259i | ||||||
\(766\) | 8.25912e28 | − | 8.88280e28i | 1.18753 | − | 1.27721i | ||||
\(767\) | 4.00613e27i | 0.0568553i | ||||||||
\(768\) | −1.86684e28 | + | 5.58998e27i | −0.261514 | + | 0.0783065i | ||||
\(769\) | −9.32051e28 | −1.28877 | −0.644387 | − | 0.764700i | \(-0.722887\pi\) | ||||
−0.644387 | + | 0.764700i | \(0.722887\pi\) | |||||||
\(770\) | −1.06731e28 | − | 9.92369e27i | −0.145674 | − | 0.135446i | ||||
\(771\) | 7.76725e27 | 0.104646 | ||||||||
\(772\) | −1.79426e27 | − | 2.46250e28i | −0.0238623 | − | 0.327494i | ||||
\(773\) | − | 5.86801e28i | − | 0.770364i | −0.922841 | − | 0.385182i | \(-0.874139\pi\) | ||
0.922841 | − | 0.385182i | \(-0.125861\pi\) | |||||||
\(774\) | −2.14325e27 | − | 1.99277e27i | −0.0277756 | − | 0.0258254i | ||||
\(775\) | − | 3.18050e27i | − | 0.0406891i | ||||||
\(776\) | −5.06210e28 | + | 6.30749e28i | −0.639313 | + | 0.796598i | ||||
\(777\) | 2.42879e26 | 0.00302816 | ||||||||
\(778\) | −1.69163e28 | + | 1.81937e28i | −0.208214 | + | 0.223937i | ||||
\(779\) | −1.25461e29 | −1.52453 | ||||||||
\(780\) | 6.28785e26 | + | 8.62965e27i | 0.00754321 | + | 0.103525i | ||||
\(781\) | 1.23409e29i | 1.46162i | ||||||||
\(782\) | −1.13910e28 | + | 1.22512e28i | −0.133197 | + | 0.143256i | ||||
\(783\) | 6.14005e28i | 0.708850i | ||||||||
\(784\) | −8.26597e28 | + | 1.21100e28i | −0.942178 | + | 0.138033i | ||||
\(785\) | 3.29817e28 | 0.371173 | ||||||||
\(786\) | −1.79083e28 | − | 1.66510e28i | −0.198989 | − | 0.185018i | ||||
\(787\) | 1.04151e29 | 1.14266 | 0.571328 | − | 0.820722i | \(-0.306429\pi\) | ||||
0.571328 | + | 0.820722i | \(0.306429\pi\) | |||||||
\(788\) | 3.54618e28 | − | 2.58387e27i | 0.384148 | − | 0.0279903i | ||||
\(789\) | 9.65049e27i | 0.103224i | ||||||||
\(790\) | 5.88861e28 | + | 5.47516e28i | 0.621931 | + | 0.578264i | ||||
\(791\) | 3.19420e28i | 0.333118i | ||||||||
\(792\) | 5.91760e28 | − | 7.37347e28i | 0.609388 | − | 0.759312i | ||||
\(793\) | 6.95863e27 | 0.0707607 | ||||||||
\(794\) | −9.67497e28 | + | 1.04056e29i | −0.971504 | + | 1.04487i | ||||
\(795\) | −4.06731e28 | −0.403307 | ||||||||
\(796\) | 7.55567e28 | − | 5.50531e27i | 0.739847 | − | 0.0539077i | ||||
\(797\) | − | 8.25588e28i | − | 0.798326i | −0.916880 | − | 0.399163i | \(-0.869301\pi\) | ||
0.916880 | − | 0.399163i | \(-0.130699\pi\) | |||||||
\(798\) | 5.20791e27 | − | 5.60118e27i | 0.0497319 | − | 0.0534873i | ||||
\(799\) | − | 2.31491e28i | − | 0.218306i | ||||||
\(800\) | 2.22333e28 | + | 1.53271e28i | 0.207063 | + | 0.142745i | ||||
\(801\) | 1.53791e29 | 1.41451 | ||||||||
\(802\) | −3.74272e28 | − | 3.47994e28i | −0.339973 | − | 0.316103i | ||||
\(803\) | 1.03305e29 | 0.926761 | ||||||||
\(804\) | −1.26962e27 | − | 1.74247e28i | −0.0112490 | − | 0.154385i | ||||
\(805\) | − | 2.76809e28i | − | 0.242226i | ||||||
\(806\) | 6.02521e27 | + | 5.60217e27i | 0.0520741 | + | 0.0484179i | ||||
\(807\) | 8.54474e26i | 0.00729396i | ||||||||
\(808\) | 1.58576e29 | + | 1.27266e29i | 1.33698 | + | 1.07300i | ||||
\(809\) | 1.14500e29 | 0.953495 | 0.476748 | − | 0.879040i | \(-0.341816\pi\) | ||||
0.476748 | + | 0.879040i | \(0.341816\pi\) | |||||||
\(810\) | −5.60079e28 | + | 6.02373e28i | −0.460680 | + | 0.495468i | ||||
\(811\) | −2.20639e29 | −1.79256 | −0.896279 | − | 0.443491i | \(-0.853740\pi\) | ||||
−0.896279 | + | 0.443491i | \(0.853740\pi\) | |||||||
\(812\) | 2.66898e27 | + | 3.66300e28i | 0.0214183 | + | 0.293952i | ||||
\(813\) | − | 5.67591e28i | − | 0.449915i | ||||||
\(814\) | 4.64356e27 | − | 4.99422e27i | 0.0363586 | − | 0.0391042i | ||||
\(815\) | 1.51833e29i | 1.17433i | ||||||||
\(816\) | −5.39821e27 | + | 7.90862e26i | −0.0412428 | + | 0.00604225i | ||||
\(817\) | −6.64725e27 | −0.0501674 | ||||||||
\(818\) | 7.44283e28 | + | 6.92025e28i | 0.554887 | + | 0.515928i | ||||
\(819\) | 1.20703e28 | 0.0888950 | ||||||||
\(820\) | −1.47699e29 | + | 1.07619e28i | −1.07458 | + | 0.0782976i | ||||
\(821\) | − | 1.50901e29i | − | 1.08458i | −0.840192 | − | 0.542288i | \(-0.817558\pi\) | ||
0.840192 | − | 0.542288i | \(-0.182442\pi\) | |||||||
\(822\) | −6.11836e27 | − | 5.68877e27i | −0.0434427 | − | 0.0403925i | ||||
\(823\) | − | 2.60574e29i | − | 1.82781i | −0.405924 | − | 0.913907i | \(-0.633050\pi\) | ||
0.405924 | − | 0.913907i | \(-0.366950\pi\) | |||||||
\(824\) | −9.86022e27 | − | 7.91336e27i | −0.0683305 | − | 0.0548389i | ||||
\(825\) | 1.05495e28 | 0.0722257 | ||||||||
\(826\) | 2.84619e27 | − | 3.06112e27i | 0.0192514 | − | 0.0207052i | ||||
\(827\) | −2.63817e29 | −1.76298 | −0.881491 | − | 0.472201i | \(-0.843460\pi\) | ||||
−0.881491 | + | 0.472201i | \(0.843460\pi\) | |||||||
\(828\) | 1.79100e29 | − | 1.30498e28i | 1.18247 | − | 0.0861589i | ||||
\(829\) | − | 1.66562e29i | − | 1.08650i | −0.839571 | − | 0.543250i | \(-0.817193\pi\) | ||
0.839571 | − | 0.543250i | \(-0.182807\pi\) | |||||||
\(830\) | −1.37823e29 | + | 1.48230e29i | −0.888258 | + | 0.955335i | ||||
\(831\) | − | 1.00799e28i | − | 0.0641871i | ||||||
\(832\) | −6.81980e28 | + | 1.51219e28i | −0.429080 | + | 0.0951419i | ||||
\(833\) | −2.33891e28 | −0.145400 | ||||||||
\(834\) | 1.01382e28 | + | 9.42635e27i | 0.0622729 | + | 0.0579006i | ||||
\(835\) | 2.11592e29 | 1.28421 | ||||||||
\(836\) | −1.56056e28 | − | 2.14176e29i | −0.0935875 | − | 1.28443i | ||||
\(837\) | − | 1.43508e28i | − | 0.0850399i | ||||||
\(838\) | −6.60981e28 | − | 6.14572e28i | −0.387034 | − | 0.359859i | ||||
\(839\) | 2.45841e28i | 0.142244i | 0.997468 | + | 0.0711221i | \(0.0226580\pi\) | ||||
−0.997468 | + | 0.0711221i | \(0.977342\pi\) | |||||||
\(840\) | 5.65055e27 | − | 7.04072e27i | 0.0323071 | − | 0.0402554i | ||||
\(841\) | −1.44898e29 | −0.818657 | ||||||||
\(842\) | −3.89756e28 | + | 4.19188e28i | −0.217606 | + | 0.234039i | ||||
\(843\) | −6.97486e28 | −0.384822 | ||||||||
\(844\) | 9.92563e27 | + | 1.36223e29i | 0.0541170 | + | 0.742720i | ||||
\(845\) | − | 1.29554e29i | − | 0.698044i | ||||||
\(846\) | −1.69207e29 | + | 1.81985e29i | −0.900981 | + | 0.969018i | ||||
\(847\) | − | 4.43185e27i | − | 0.0233212i | ||||||
\(848\) | −4.75989e28 | − | 3.24897e29i | −0.247536 | − | 1.68961i | ||||
\(849\) | 7.42817e28 | 0.381773 | ||||||||
\(850\) | 5.53684e27 | + | 5.14808e27i | 0.0281237 | + | 0.0261491i | ||||
\(851\) | 1.29526e28 | 0.0650224 | ||||||||
\(852\) | −7.62439e28 | + | 5.55538e27i | −0.378276 | + | 0.0275625i | ||||
\(853\) | 4.10833e28i | 0.201453i | 0.994914 | + | 0.100727i | \(0.0321168\pi\) | ||||
−0.994914 | + | 0.100727i | \(0.967883\pi\) | |||||||
\(854\) | −5.31715e27 | − | 4.94382e27i | −0.0257692 | − | 0.0239599i | ||||
\(855\) | 2.04628e29i | 0.980178i | ||||||||
\(856\) | 7.56610e28 | − | 9.42753e28i | 0.358207 | − | 0.446334i | ||||
\(857\) | 1.78159e29 | 0.833682 | 0.416841 | − | 0.908979i | \(-0.363137\pi\) | ||||
0.416841 | + | 0.908979i | \(0.363137\pi\) | |||||||
\(858\) | −1.85820e28 | + | 1.99852e28i | −0.0859447 | + | 0.0924348i | ||||
\(859\) | −1.16232e29 | −0.531366 | −0.265683 | − | 0.964060i | \(-0.585597\pi\) | ||||
−0.265683 | + | 0.964060i | \(0.585597\pi\) | |||||||
\(860\) | −7.82547e27 | + | 5.70190e26i | −0.0353611 | + | 0.00257653i | ||||
\(861\) | − | 1.66347e28i | − | 0.0742992i | ||||||
\(862\) | 1.41033e29 | − | 1.51683e29i | 0.622655 | − | 0.669675i | ||||
\(863\) | 2.20822e29i | 0.963683i | 0.876259 | + | 0.481841i | \(0.160032\pi\) | ||||
−0.876259 | + | 0.481841i | \(0.839968\pi\) | |||||||
\(864\) | 1.00319e29 | + | 6.91579e28i | 0.432760 | + | 0.298335i | ||||
\(865\) | −1.41953e29 | −0.605316 | ||||||||
\(866\) | −7.27979e28 | − | 6.76866e28i | −0.306860 | − | 0.285315i | ||||
\(867\) | 6.39861e28 | 0.266621 | ||||||||
\(868\) | −6.23807e26 | − | 8.56134e27i | −0.00256953 | − | 0.0352650i | ||||
\(869\) | 2.53596e29i | 1.03263i | ||||||||
\(870\) | 5.79459e28 | + | 5.38774e28i | 0.233255 | + | 0.216877i | ||||
\(871\) | − | 6.26262e28i | − | 0.249215i | ||||||
\(872\) | 3.54733e29 | + | 2.84692e29i | 1.39552 | + | 1.11998i | ||||
\(873\) | 2.43059e29 | 0.945298 | ||||||||
\(874\) | 2.77736e29 | − | 2.98709e29i | 1.06787 | − | 1.14851i | ||||
\(875\) | −6.22526e28 | −0.236634 | ||||||||
\(876\) | 4.65041e27 | + | 6.38238e28i | 0.0174763 | + | 0.239851i | ||||
\(877\) | 4.03997e29i | 1.50100i | 0.660868 | + | 0.750502i | \(0.270188\pi\) | ||||
−0.660868 | + | 0.750502i | \(0.729812\pi\) | |||||||
\(878\) | −7.43744e28 | + | 7.99908e28i | −0.273199 | + | 0.293829i | ||||
\(879\) | − | 4.58620e28i | − | 0.166558i | ||||||
\(880\) | −3.67434e28 | − | 2.50800e29i | −0.131933 | − | 0.900537i | ||||
\(881\) | −1.24285e29 | −0.441226 | −0.220613 | − | 0.975361i | \(-0.570806\pi\) | ||||
−0.220613 | + | 0.975361i | \(0.570806\pi\) | |||||||
\(882\) | 1.83872e29 | + | 1.70962e29i | 0.645400 | + | 0.600085i | ||||
\(883\) | 4.93807e29 | 1.71376 | 0.856880 | − | 0.515515i | \(-0.172399\pi\) | ||||
0.856880 | + | 0.515515i | \(0.172399\pi\) | |||||||
\(884\) | −1.95053e28 | + | 1.42122e27i | −0.0669314 | + | 0.00487684i | ||||
\(885\) | − | 9.00493e27i | − | 0.0305525i | ||||||
\(886\) | −2.53062e29 | − | 2.35294e29i | −0.848966 | − | 0.789358i | ||||
\(887\) | 2.63289e29i | 0.873367i | 0.899615 | + | 0.436684i | \(0.143847\pi\) | ||||
−0.899615 | + | 0.436684i | \(0.856153\pi\) | |||||||
\(888\) | 3.29454e27 | + | 2.64405e27i | 0.0108060 | + | 0.00867241i | ||||
\(889\) | −1.04130e29 | −0.337720 | ||||||||
\(890\) | 2.80763e29 | − | 3.01964e29i | 0.900408 | − | 0.968401i | ||||
\(891\) | −2.59415e29 | −0.822655 | ||||||||
\(892\) | −4.61199e29 | + | 3.36045e28i | −1.44624 | + | 0.105378i | ||||
\(893\) | 5.64421e29i | 1.75021i | ||||||||
\(894\) | 2.64764e28 | − | 2.84757e28i | 0.0811864 | − | 0.0873171i | ||||
\(895\) | − | 3.45095e29i | − | 1.04643i | ||||||
\(896\) | 6.28541e28 | + | 3.68971e28i | 0.188475 | + | 0.110640i | ||||
\(897\) | −5.18322e28 | −0.153700 | ||||||||
\(898\) | 1.59556e29 | + | 1.48353e29i | 0.467895 | + | 0.435043i | ||||
\(899\) | 7.52343e28 | 0.218182 | ||||||||
\(900\) | −5.89774e27 | − | 8.09425e28i | −0.0169145 | − | 0.232141i | ||||
\(901\) | − | 9.19319e28i | − | 0.260747i | ||||||
\(902\) | −3.42053e29 | − | 3.18037e29i | −0.959462 | − | 0.892096i | ||||
\(903\) | − | 8.81349e26i | − | 0.00244495i | ||||||
\(904\) | −3.47730e29 | + | 4.33280e29i | −0.954021 | + | 1.18873i | ||||
\(905\) | 4.69469e27 | 0.0127386 | ||||||||
\(906\) | −1.36043e29 | + | 1.46316e29i | −0.365086 | + | 0.392655i | ||||
\(907\) | 1.56123e29 | 0.414376 | 0.207188 | − | 0.978301i | \(-0.433569\pi\) | ||||
0.207188 | + | 0.978301i | \(0.433569\pi\) | |||||||
\(908\) | −8.01620e27 | − | 1.10017e29i | −0.0210431 | − | 0.288803i | ||||
\(909\) | − | 6.11072e29i | − | 1.58655i | ||||||
\(910\) | 2.20355e28 | − | 2.36995e28i | 0.0565860 | − | 0.0608591i | ||||
\(911\) | − | 4.36036e28i | − | 0.110749i | −0.998466 | − | 0.0553743i | \(-0.982365\pi\) | ||
0.998466 | − | 0.0553743i | \(-0.0176352\pi\) | |||||||
\(912\) | 1.31619e29 | − | 1.92828e28i | 0.330652 | − | 0.0484419i | ||||
\(913\) | −6.38359e29 | −1.58620 | ||||||||
\(914\) | 1.49289e29 | + | 1.38807e29i | 0.366915 | + | 0.341153i | ||||
\(915\) | −1.56415e28 | −0.0380249 | ||||||||
\(916\) | −6.33645e29 | + | 4.61695e28i | −1.52367 | + | 0.111020i | ||||
\(917\) | 9.14567e28i | 0.217531i | ||||||||
\(918\) | 2.49829e28 | + | 2.32288e28i | 0.0587782 | + | 0.0546513i | ||||
\(919\) | − | 4.60052e29i | − | 1.07066i | −0.844643 | − | 0.535331i | \(-0.820187\pi\) | ||
0.844643 | − | 0.535331i | \(-0.179813\pi\) | |||||||
\(920\) | 3.01342e29 | − | 3.75479e29i | 0.693716 | − | 0.864386i | ||||
\(921\) | −9.13192e28 | −0.207953 | ||||||||
\(922\) | 4.15897e29 | − | 4.47303e29i | 0.936864 | − | 1.00761i | ||||
\(923\) | −2.74029e29 | −0.610632 | ||||||||
\(924\) | 2.83973e28 | − | 2.06912e27i | 0.0625976 | − | 0.00456107i | ||||
\(925\) | − | 5.85384e27i | − | 0.0127651i | ||||||
\(926\) | 1.72542e29 | − | 1.85571e29i | 0.372207 | − | 0.400314i | ||||
\(927\) | 3.79963e28i | 0.0810857i | ||||||||
\(928\) | −3.62561e29 | + | 5.25925e29i | −0.765422 | + | 1.11031i | ||||
\(929\) | 4.28630e29 | 0.895212 | 0.447606 | − | 0.894231i | \(-0.352277\pi\) | ||||
0.447606 | + | 0.894231i | \(0.352277\pi\) | |||||||
\(930\) | −1.35434e28 | − | 1.25925e28i | −0.0279833 | − | 0.0260185i | ||||
\(931\) | 5.70274e29 | 1.16570 | ||||||||
\(932\) | −7.97824e27 | − | 1.09496e29i | −0.0161342 | − | 0.221431i | ||||
\(933\) | − | 6.67181e28i | − | 0.133483i | ||||||
\(934\) | 3.98689e29 | + | 3.70696e29i | 0.789160 | + | 0.733751i | ||||
\(935\) | − | 7.09657e28i | − | 0.138974i | ||||||
\(936\) | 1.63728e29 | + | 1.31400e29i | 0.317222 | + | 0.254588i | ||||
\(937\) | −7.15749e29 | −1.37203 | −0.686017 | − | 0.727585i | \(-0.740643\pi\) | ||||
−0.686017 | + | 0.727585i | \(0.740643\pi\) | |||||||
\(938\) | −4.44934e28 | + | 4.78533e28i | −0.0843853 | + | 0.0907576i | ||||
\(939\) | 1.82185e29 | 0.341867 | ||||||||
\(940\) | 4.84151e28 | + | 6.64465e29i | 0.0898882 | + | 1.23365i | ||||
\(941\) | − | 1.37461e29i | − | 0.252513i | −0.991998 | − | 0.126257i | \(-0.959704\pi\) | ||
0.991998 | − | 0.126257i | \(-0.0402963\pi\) | |||||||
\(942\) | −4.38764e28 | + | 4.71897e28i | −0.0797485 | + | 0.0857706i | ||||
\(943\) | − | 8.87124e29i | − | 1.59539i | ||||||
\(944\) | 7.19315e28 | − | 1.05383e28i | 0.127997 | − | 0.0187521i | ||||
\(945\) | −5.64474e28 | −0.0993862 | ||||||||
\(946\) | −1.81228e28 | − | 1.68504e28i | −0.0315729 | − | 0.0293561i | ||||
\(947\) | 7.72513e29 | 1.33170 | 0.665849 | − | 0.746086i | \(-0.268069\pi\) | ||||
0.665849 | + | 0.746086i | \(0.268069\pi\) | |||||||
\(948\) | −1.56676e29 | + | 1.14159e28i | −0.267250 | + | 0.0194727i | ||||
\(949\) | 2.29389e29i | 0.387179i | ||||||||
\(950\) | −1.34999e29 | − | 1.25521e29i | −0.225473 | − | 0.209642i | ||||
\(951\) | − | 1.58027e29i | − | 0.261171i | ||||||
\(952\) | 1.59139e28 | + | 1.27718e28i | 0.0260260 | + | 0.0208872i | ||||
\(953\) | 1.64663e29 | 0.266481 | 0.133241 | − | 0.991084i | \(-0.457462\pi\) | ||||
0.133241 | + | 0.991084i | \(0.457462\pi\) | |||||||
\(954\) | −6.71972e29 | + | 7.22716e29i | −1.07614 | + | 1.15740i | ||||
\(955\) | −4.52011e29 | −0.716334 | ||||||||
\(956\) | 7.17591e28 | − | 5.22860e27i | 0.112538 | − | 0.00819987i | ||||
\(957\) | 2.49547e29i | 0.387286i | ||||||||
\(958\) | −2.68203e29 | + | 2.88456e29i | −0.411916 | + | 0.443022i | ||||
\(959\) | 3.12460e28i | 0.0474907i | ||||||||
\(960\) | 1.53295e29 | − | 3.39907e28i | 0.230576 | − | 0.0511267i | ||||
\(961\) | 6.54206e29 | 0.973825 | ||||||||
\(962\) | 1.10896e28 | + | 1.03110e28i | 0.0163368 | + | 0.0151898i | ||||
\(963\) | −3.63289e29 | −0.529651 | ||||||||
\(964\) | 5.64126e28 | + | 7.74226e29i | 0.0813966 | + | 1.11711i | ||||
\(965\) | 1.98940e29i | 0.284086i | ||||||||
\(966\) | 3.96054e28 | + | 3.68247e28i | 0.0559736 | + | 0.0520436i | ||||
\(967\) | 4.55583e29i | 0.637240i | 0.947883 | + | 0.318620i | \(0.103219\pi\) | ||||
−0.947883 | + | 0.318620i | \(0.896781\pi\) | |||||||
\(968\) | 4.82464e28 | − | 6.01161e28i | 0.0667899 | − | 0.0832218i | ||||
\(969\) | 3.72425e28 | 0.0510272 | ||||||||
\(970\) | 4.43729e29 | − | 4.77237e29i | 0.601729 | − | 0.647168i | ||||
\(971\) | −1.41934e30 | −1.90500 | −0.952501 | − | 0.304534i | \(-0.901499\pi\) | ||||
−0.952501 | + | 0.304534i | \(0.901499\pi\) | |||||||
\(972\) | −4.04320e28 | − | 5.54902e29i | −0.0537109 | − | 0.737146i | ||||
\(973\) | − | 5.17750e28i | − | 0.0680756i | ||||||
\(974\) | −2.55724e28 | + | 2.75034e28i | −0.0332798 | + | 0.0357929i | ||||
\(975\) | 2.34251e28i | 0.0301742i | ||||||||
\(976\) | −1.83050e28 | − | 1.24945e29i | −0.0233384 | − | 0.159302i | ||||
\(977\) | 7.03797e29 | 0.888182 | 0.444091 | − | 0.895982i | \(-0.353527\pi\) | ||||
0.444091 | + | 0.895982i | \(0.353527\pi\) | |||||||
\(978\) | −2.17240e29 | − | 2.01987e29i | −0.271363 | − | 0.252310i | ||||
\(979\) | 1.30042e30 | 1.60789 | ||||||||
\(980\) | 6.71355e29 | − | 4.89171e28i | 0.821658 | − | 0.0598687i | ||||
\(981\) | − | 1.36696e30i | − | 1.65602i | ||||||
\(982\) | 5.66852e29 | + | 5.27052e29i | 0.679759 | + | 0.632032i | ||||
\(983\) | 1.22719e30i | 1.45672i | 0.685193 | + | 0.728362i | \(0.259718\pi\) | ||||
−0.685193 | + | 0.728362i | \(0.740282\pi\) | |||||||
\(984\) | 1.81090e29 | − | 2.25643e29i | 0.212787 | − | 0.265137i | ||||
\(985\) | −2.86489e29 | −0.333231 | ||||||||
\(986\) | −1.21777e29 | + | 1.30973e29i | −0.140216 | + | 0.150804i | ||||
\(987\) | −7.48358e28 | −0.0852978 | ||||||||
\(988\) | 4.75578e29 | − | 3.46522e28i | 0.536602 | − | 0.0390986i | ||||
\(989\) | − | 4.70021e28i | − | 0.0524994i | ||||||
\(990\) | −5.18721e29 | + | 5.57891e29i | −0.573564 | + | 0.616876i | ||||
\(991\) | − | 7.91296e28i | − | 0.0866168i | −0.999062 | − | 0.0433084i | \(-0.986210\pi\) | ||
0.999062 | − | 0.0433084i | \(-0.0137898\pi\) | |||||||
\(992\) | 8.47395e28 | − | 1.22922e29i | 0.0918267 | − | 0.133202i | ||||
\(993\) | −2.47253e29 | −0.265246 | ||||||||
\(994\) | 2.09388e29 | + | 1.94686e29i | 0.222376 | + | 0.206762i | ||||
\(995\) | −6.10407e29 | −0.641783 | ||||||||
\(996\) | −2.87365e28 | − | 3.94389e29i | −0.0299116 | − | 0.410517i | ||||
\(997\) | 1.33035e30i | 1.37092i | 0.728109 | + | 0.685462i | \(0.240400\pi\) | ||||
−0.728109 | + | 0.685462i | \(0.759600\pi\) | |||||||
\(998\) | −5.82699e29 | − | 5.41786e29i | −0.594482 | − | 0.552742i | ||||
\(999\) | − | 2.64133e28i | − | 0.0266789i |
(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 | 8.21.d.b.3.5 | ✓ | 18 | |
3.2 | odd | 2 | 72.21.b.b.19.14 | 18 | |||
4.3 | odd | 2 | 32.21.d.b.15.11 | 18 | |||
8.3 | odd | 2 | inner | 8.21.d.b.3.6 | yes | 18 | |
8.5 | even | 2 | 32.21.d.b.15.12 | 18 | |||
24.11 | even | 2 | 72.21.b.b.19.13 | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8.21.d.b.3.5 | ✓ | 18 | 1.1 | even | 1 | trivial | |
8.21.d.b.3.6 | yes | 18 | 8.3 | odd | 2 | inner | |
32.21.d.b.15.11 | 18 | 4.3 | odd | 2 | |||
32.21.d.b.15.12 | 18 | 8.5 | even | 2 | |||
72.21.b.b.19.13 | 18 | 24.11 | even | 2 | |||
72.21.b.b.19.14 | 18 | 3.2 | odd | 2 |