Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5,33,Mod(2,5)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 33, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5.2");
S:= CuspForms(chi, 33);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5 \) |
Weight: | \( k \) | \(=\) | \( 33 \) |
Character orbit: | \([\chi]\) | \(=\) | 5.c (of order \(4\), degree \(2\), 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: | \(32.4333275711\) |
Analytic rank: | \(0\) |
Dimension: | \(30\) |
Relative dimension: | \(15\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 3.12 | ||
Character | \(\chi\) | \(=\) | 5.3 |
Dual form | 5.33.c.a.2.12 |
$q$-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 \(\left(\mathbb{Z}/5\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 61735.6 | − | 61735.6i | 0.942010 | − | 0.942010i | −0.0563981 | − | 0.998408i | \(-0.517962\pi\) |
0.998408 | + | 0.0563981i | \(0.0179616\pi\) | |||||||
\(3\) | −5.69775e7 | − | 5.69775e7i | −1.32362 | − | 1.32362i | −0.910823 | − | 0.412796i | \(-0.864552\pi\) |
−0.412796 | − | 0.910823i | \(-0.635448\pi\) | |||||||
\(4\) | − | 3.32760e9i | − | 0.774767i | ||||||
\(5\) | 7.47335e10 | − | 1.33034e11i | 0.489774 | − | 0.871850i | ||||
\(6\) | −7.03508e12 | −2.49373 | ||||||||
\(7\) | −1.03601e13 | + | 1.03601e13i | −0.311742 | + | 0.311742i | −0.845584 | − | 0.533842i | \(-0.820748\pi\) |
0.533842 | + | 0.845584i | \(0.320748\pi\) | |||||||
\(8\) | 5.97211e13 | + | 5.97211e13i | 0.212172 | + | 0.212172i | ||||
\(9\) | 4.63985e15i | 2.50394i | ||||||||
\(10\) | −3.59920e15 | − | 1.28266e16i | −0.359920 | − | 1.28266i | ||||
\(11\) | −8.55661e16 | −1.86217 | −0.931084 | − | 0.364806i | \(-0.881135\pi\) | ||||
−0.931084 | + | 0.364806i | \(0.881135\pi\) | |||||||
\(12\) | −1.89598e17 | + | 1.89598e17i | −1.02550 | + | 1.02550i | ||||
\(13\) | −2.19299e16 | − | 2.19299e16i | −0.0329567 | − | 0.0329567i | 0.690436 | − | 0.723393i | \(-0.257419\pi\) |
−0.723393 | + | 0.690436i | \(0.757419\pi\) | |||||||
\(14\) | 1.27917e18i | 0.587328i | ||||||||
\(15\) | −1.18381e19 | + | 3.32180e18i | −1.80227 | + | 0.505723i | ||||
\(16\) | 2.16658e19 | 1.17450 | ||||||||
\(17\) | 9.87369e18 | − | 9.87369e18i | 0.202907 | − | 0.202907i | −0.598337 | − | 0.801244i | \(-0.704172\pi\) |
0.801244 | + | 0.598337i | \(0.204172\pi\) | |||||||
\(18\) | 2.86444e20 | + | 2.86444e20i | 2.35874 | + | 2.35874i | ||||
\(19\) | 1.02268e20i | 0.354554i | 0.984161 | + | 0.177277i | \(0.0567288\pi\) | ||||
−0.984161 | + | 0.177277i | \(0.943271\pi\) | |||||||
\(20\) | −4.42683e20 | − | 2.48683e20i | −0.675480 | − | 0.379460i | ||||
\(21\) | 1.18058e21 | 0.825256 | ||||||||
\(22\) | −5.28247e21 | + | 5.28247e21i | −1.75418 | + | 1.75418i | ||||
\(23\) | 3.76150e21 | + | 3.76150e21i | 0.613360 | + | 0.613360i | 0.943820 | − | 0.330460i | \(-0.107204\pi\) |
−0.330460 | + | 0.943820i | \(0.607204\pi\) | |||||||
\(24\) | − | 6.80552e21i | − | 0.561670i | ||||||
\(25\) | −1.21129e22 | − | 1.98842e22i | −0.520244 | − | 0.854018i | ||||
\(26\) | −2.70771e21 | −0.0620910 | ||||||||
\(27\) | 1.58786e23 | − | 1.58786e23i | 1.99064 | − | 1.99064i | ||||
\(28\) | 3.44743e22 | + | 3.44743e22i | 0.241527 | + | 0.241527i | ||||
\(29\) | − | 1.14249e23i | − | 0.456545i | −0.973597 | − | 0.228273i | \(-0.926692\pi\) | ||
0.973597 | − | 0.228273i | \(-0.0733078\pi\) | |||||||
\(30\) | −5.25756e23 | + | 9.35902e23i | −1.22136 | + | 2.17415i | ||||
\(31\) | −8.94834e23 | −1.23014 | −0.615071 | − | 0.788472i | \(-0.710873\pi\) | ||||
−0.615071 | + | 0.788472i | \(0.710873\pi\) | |||||||
\(32\) | 1.08105e24 | − | 1.08105e24i | 0.894222 | − | 0.894222i | ||||
\(33\) | 4.87534e24 | + | 4.87534e24i | 2.46480 | + | 2.46480i | ||||
\(34\) | − | 1.21912e24i | − | 0.382281i | ||||||
\(35\) | 6.03996e23 | + | 2.15249e24i | 0.119109 | + | 0.424475i | ||||
\(36\) | 1.54395e25 | 1.93997 | ||||||||
\(37\) | −2.29758e24 | + | 2.29758e24i | −0.186227 | + | 0.186227i | −0.794063 | − | 0.607836i | \(-0.792038\pi\) |
0.607836 | + | 0.794063i | \(0.292038\pi\) | |||||||
\(38\) | 6.31357e24 | + | 6.31357e24i | 0.333993 | + | 0.333993i | ||||
\(39\) | 2.49902e24i | 0.0872441i | ||||||||
\(40\) | 1.24081e25 | − | 3.48175e24i | 0.288898 | − | 0.0810658i | ||||
\(41\) | −1.78531e25 | −0.280009 | −0.140004 | − | 0.990151i | \(-0.544712\pi\) | ||||
−0.140004 | + | 0.990151i | \(0.544712\pi\) | |||||||
\(42\) | 7.28841e25 | − | 7.28841e25i | 0.777399 | − | 0.777399i | ||||
\(43\) | −4.64984e25 | − | 4.64984e25i | −0.340363 | − | 0.340363i | 0.516140 | − | 0.856504i | \(-0.327368\pi\) |
−0.856504 | + | 0.516140i | \(0.827368\pi\) | |||||||
\(44\) | 2.84730e26i | 1.44275i | ||||||||
\(45\) | 6.17256e26 | + | 3.46752e26i | 2.18306 | + | 1.22636i | ||||
\(46\) | 4.64437e26 | 1.15558 | ||||||||
\(47\) | −2.49694e26 | + | 2.49694e26i | −0.440394 | + | 0.440394i | −0.892144 | − | 0.451750i | \(-0.850800\pi\) |
0.451750 | + | 0.892144i | \(0.350800\pi\) | |||||||
\(48\) | −1.23446e27 | − | 1.23446e27i | −1.55460 | − | 1.55460i | ||||
\(49\) | 8.89764e26i | 0.805634i | ||||||||
\(50\) | −1.97535e27 | − | 4.79765e26i | −1.29457 | − | 0.314419i | ||||
\(51\) | −1.12516e27 | −0.537143 | ||||||||
\(52\) | −7.29739e25 | + | 7.29739e25i | −0.0255337 | + | 0.0255337i | ||||
\(53\) | −7.86695e25 | − | 7.86695e25i | −0.0202952 | − | 0.0202952i | 0.696886 | − | 0.717182i | \(-0.254568\pi\) |
−0.717182 | + | 0.696886i | \(0.754568\pi\) | |||||||
\(54\) | − | 1.96055e28i | − | 3.75041i | ||||||
\(55\) | −6.39466e27 | + | 1.13832e28i | −0.912040 | + | 1.62353i | ||||
\(56\) | −1.23743e27 | −0.132286 | ||||||||
\(57\) | 5.82697e27 | − | 5.82697e27i | 0.469294 | − | 0.469294i | ||||
\(58\) | −7.05322e27 | − | 7.05322e27i | −0.430070 | − | 0.430070i | ||||
\(59\) | 1.58816e28i | 0.736653i | 0.929697 | + | 0.368326i | \(0.120069\pi\) | ||||
−0.929697 | + | 0.368326i | \(0.879931\pi\) | |||||||
\(60\) | 1.10536e28 | + | 3.93923e28i | 0.391818 | + | 1.39634i | ||||
\(61\) | 2.93362e28 | 0.798226 | 0.399113 | − | 0.916902i | \(-0.369318\pi\) | ||||
0.399113 | + | 0.916902i | \(0.369318\pi\) | |||||||
\(62\) | −5.52431e28 | + | 5.52431e28i | −1.15881 | + | 1.15881i | ||||
\(63\) | −4.80693e28 | − | 4.80693e28i | −0.780583 | − | 0.780583i | ||||
\(64\) | − | 4.04246e28i | − | 0.510230i | ||||||
\(65\) | −4.55632e27 | + | 1.27852e27i | −0.0448745 | + | 0.0125919i | ||||
\(66\) | 6.01964e29 | 4.64374 | ||||||||
\(67\) | −1.50191e29 | + | 1.50191e29i | −0.910849 | + | 0.910849i | −0.996339 | − | 0.0854901i | \(-0.972754\pi\) |
0.0854901 | + | 0.996339i | \(0.472754\pi\) | |||||||
\(68\) | −3.28557e28 | − | 3.28557e28i | −0.157206 | − | 0.157206i | ||||
\(69\) | − | 4.28642e29i | − | 1.62371i | ||||||
\(70\) | 1.70173e29 | + | 9.55972e28i | 0.512062 | + | 0.287658i | ||||
\(71\) | −4.66076e29 | −1.11769 | −0.558847 | − | 0.829271i | \(-0.688756\pi\) | ||||
−0.558847 | + | 0.829271i | \(0.688756\pi\) | |||||||
\(72\) | −2.77097e29 | + | 2.77097e29i | −0.531265 | + | 0.531265i | ||||
\(73\) | −7.79180e27 | − | 7.79180e27i | −0.0119804 | − | 0.0119804i | 0.701091 | − | 0.713072i | \(-0.252697\pi\) |
−0.713072 | + | 0.701091i | \(0.752697\pi\) | |||||||
\(74\) | 2.83685e29i | 0.350855i | ||||||||
\(75\) | −4.42788e29 | + | 1.82311e30i | −0.441790 | + | 1.81900i | ||||
\(76\) | 3.40307e29 | 0.274696 | ||||||||
\(77\) | 8.86473e29 | − | 8.86473e29i | 0.580516 | − | 0.580516i | ||||
\(78\) | 1.54279e29 | + | 1.54279e29i | 0.0821849 | + | 0.0821849i | ||||
\(79\) | − | 4.15998e30i | − | 1.80741i | −0.428151 | − | 0.903707i | \(-0.640835\pi\) | ||
0.428151 | − | 0.903707i | \(-0.359165\pi\) | |||||||
\(80\) | 1.61916e30 | − | 2.88228e30i | 0.575241 | − | 1.02399i | ||||
\(81\) | −9.49677e30 | −2.76577 | ||||||||
\(82\) | −1.10217e30 | + | 1.10217e30i | −0.263771 | + | 0.263771i | ||||
\(83\) | 3.04621e30 | + | 3.04621e30i | 0.600495 | + | 0.600495i | 0.940444 | − | 0.339949i | \(-0.110410\pi\) |
−0.339949 | + | 0.940444i | \(0.610410\pi\) | |||||||
\(84\) | − | 3.92851e30i | − | 0.639381i | ||||||
\(85\) | −5.75638e29 | − | 2.05143e30i | −0.0775259 | − | 0.276283i | ||||
\(86\) | −5.74121e30 | −0.641252 | ||||||||
\(87\) | −6.50961e30 | + | 6.50961e30i | −0.604292 | + | 0.604292i | ||||
\(88\) | −5.11010e30 | − | 5.11010e30i | −0.395100 | − | 0.395100i | ||||
\(89\) | 2.29726e31i | 1.48241i | 0.671277 | + | 0.741207i | \(0.265746\pi\) | ||||
−0.671277 | + | 0.741207i | \(0.734254\pi\) | |||||||
\(90\) | 5.95136e31 | − | 1.66997e31i | 3.21171 | − | 0.901216i | ||||
\(91\) | 4.54392e29 | 0.0205479 | ||||||||
\(92\) | 1.25168e31 | − | 1.25168e31i | 0.475211 | − | 0.475211i | ||||
\(93\) | 5.09854e31 | + | 5.09854e31i | 1.62824 | + | 1.62824i | ||||
\(94\) | 3.08300e31i | 0.829712i | ||||||||
\(95\) | 1.36051e31 | + | 7.64284e30i | 0.309117 | + | 0.173651i | ||||
\(96\) | −1.23191e32 | −2.36722 | ||||||||
\(97\) | −5.10741e31 | + | 5.10741e31i | −0.831482 | + | 0.831482i | −0.987720 | − | 0.156237i | \(-0.950064\pi\) |
0.156237 | + | 0.987720i | \(0.450064\pi\) | |||||||
\(98\) | 5.49301e31 | + | 5.49301e31i | 0.758915 | + | 0.758915i | ||||
\(99\) | − | 3.97014e32i | − | 4.66275i | ||||||
\(100\) | −6.61665e31 | + | 4.03068e31i | −0.661665 | + | 0.403068i | ||||
\(101\) | 6.91754e31 | 0.589943 | 0.294971 | − | 0.955506i | \(-0.404690\pi\) | ||||
0.294971 | + | 0.955506i | \(0.404690\pi\) | |||||||
\(102\) | −6.94622e31 | + | 6.94622e31i | −0.505994 | + | 0.505994i | ||||
\(103\) | 8.39908e31 | + | 8.39908e31i | 0.523403 | + | 0.523403i | 0.918597 | − | 0.395195i | \(-0.129323\pi\) |
−0.395195 | + | 0.918597i | \(0.629323\pi\) | |||||||
\(104\) | − | 2.61936e30i | − | 0.0139850i | ||||||
\(105\) | 8.82293e31 | − | 1.57058e32i | 0.404188 | − | 0.719499i | ||||
\(106\) | −9.71341e30 | −0.0382365 | ||||||||
\(107\) | −2.15784e32 | + | 2.15784e32i | −0.730934 | + | 0.730934i | −0.970805 | − | 0.239871i | \(-0.922895\pi\) |
0.239871 | + | 0.970805i | \(0.422895\pi\) | |||||||
\(108\) | −5.28377e32 | − | 5.28377e32i | −1.54228 | − | 1.54228i | ||||
\(109\) | 6.55094e31i | 0.164998i | 0.996591 | + | 0.0824991i | \(0.0262902\pi\) | ||||
−0.996591 | + | 0.0824991i | \(0.973710\pi\) | |||||||
\(110\) | 3.07969e32 | + | 1.09752e33i | 0.670231 | + | 2.38853i | ||||
\(111\) | 2.61820e32 | 0.492987 | ||||||||
\(112\) | −2.24459e32 | + | 2.24459e32i | −0.366142 | + | 0.366142i | ||||
\(113\) | −7.35282e32 | − | 7.35282e32i | −1.04040 | − | 1.04040i | −0.999149 | − | 0.0412468i | \(-0.986867\pi\) |
−0.0412468 | − | 0.999149i | \(-0.513133\pi\) | |||||||
\(114\) | − | 7.19463e32i | − | 0.884160i | ||||||
\(115\) | 7.81516e32 | − | 2.19296e32i | 0.835166 | − | 0.234350i | ||||
\(116\) | −3.80174e32 | −0.353716 | ||||||||
\(117\) | 1.01751e32 | − | 1.01751e32i | 0.0825214 | − | 0.0825214i | ||||
\(118\) | 9.80462e32 | + | 9.80462e32i | 0.693935 | + | 0.693935i | ||||
\(119\) | 2.04585e32i | 0.126509i | ||||||||
\(120\) | −9.05363e32 | − | 5.08600e32i | −0.489692 | − | 0.275091i | ||||
\(121\) | 5.21018e33 | 2.46767 | ||||||||
\(122\) | 1.81109e33 | − | 1.81109e33i | 0.751937 | − | 0.751937i | ||||
\(123\) | 1.01722e33 | + | 1.01722e33i | 0.370625 | + | 0.370625i | ||||
\(124\) | 2.97765e33i | 0.953073i | ||||||||
\(125\) | −3.55050e33 | + | 1.25407e32i | −0.999377 | + | 0.0352988i | ||||
\(126\) | −5.93517e33 | −1.47063 | ||||||||
\(127\) | −2.07759e33 | + | 2.07759e33i | −0.453629 | + | 0.453629i | −0.896557 | − | 0.442928i | \(-0.853940\pi\) |
0.442928 | + | 0.896557i | \(0.353940\pi\) | |||||||
\(128\) | 2.14743e33 | + | 2.14743e33i | 0.413581 | + | 0.413581i | ||||
\(129\) | 5.29873e33i | 0.901023i | ||||||||
\(130\) | −2.02357e32 | + | 3.60217e32i | −0.0304105 | + | 0.0541340i | ||||
\(131\) | −6.33043e33 | −0.841575 | −0.420787 | − | 0.907159i | \(-0.638246\pi\) | ||||
−0.420787 | + | 0.907159i | \(0.638246\pi\) | |||||||
\(132\) | 1.62232e34 | − | 1.62232e34i | 1.90965 | − | 1.90965i | ||||
\(133\) | −1.05951e33 | − | 1.05951e33i | −0.110529 | − | 0.110529i | ||||
\(134\) | 1.85442e34i | 1.71606i | ||||||||
\(135\) | −9.25727e33 | − | 3.29906e34i | −0.760576 | − | 2.71050i | ||||
\(136\) | 1.17934e33 | 0.0861023 | ||||||||
\(137\) | −1.10531e34 | + | 1.10531e34i | −0.717723 | + | 0.717723i | −0.968138 | − | 0.250416i | \(-0.919433\pi\) |
0.250416 | + | 0.968138i | \(0.419433\pi\) | |||||||
\(138\) | −2.64624e34 | − | 2.64624e34i | −1.52955 | − | 1.52955i | ||||
\(139\) | − | 1.64912e34i | − | 0.849212i | −0.905378 | − | 0.424606i | \(-0.860413\pi\) | ||
0.905378 | − | 0.424606i | \(-0.139587\pi\) | |||||||
\(140\) | 7.16262e33 | − | 2.00986e33i | 0.328869 | − | 0.0922818i | ||||
\(141\) | 2.84538e34 | 1.16583 | ||||||||
\(142\) | −2.87735e34 | + | 2.87735e34i | −1.05288 | + | 1.05288i | ||||
\(143\) | 1.87646e33 | + | 1.87646e33i | 0.0613708 | + | 0.0613708i | ||||
\(144\) | 1.00526e35i | 2.94088i | ||||||||
\(145\) | −1.51989e34 | − | 8.53822e33i | −0.398039 | − | 0.223604i | ||||
\(146\) | −9.62063e32 | −0.0225714 | ||||||||
\(147\) | 5.06965e34 | − | 5.06965e34i | 1.06635 | − | 1.06635i | ||||
\(148\) | 7.64541e33 | + | 7.64541e33i | 0.144282 | + | 0.144282i | ||||
\(149\) | − | 8.38777e34i | − | 1.42124i | −0.703578 | − | 0.710618i | \(-0.748416\pi\) | ||
0.703578 | − | 0.710618i | \(-0.251584\pi\) | |||||||
\(150\) | 8.52149e34 | + | 1.39887e35i | 1.29735 | + | 2.12969i | ||||
\(151\) | 8.61859e34 | 1.17979 | 0.589895 | − | 0.807480i | \(-0.299169\pi\) | ||||
0.589895 | + | 0.807480i | \(0.299169\pi\) | |||||||
\(152\) | −6.10755e33 | + | 6.10755e33i | −0.0752263 | + | 0.0752263i | ||||
\(153\) | 4.58124e34 | + | 4.58124e34i | 0.508066 | + | 0.508066i | ||||
\(154\) | − | 1.09454e35i | − | 1.09370i | ||||||
\(155\) | −6.68741e34 | + | 1.19043e35i | −0.602491 | + | 1.07250i | ||||
\(156\) | 8.31574e33 | 0.0675939 | ||||||||
\(157\) | 7.99304e34 | − | 7.99304e34i | 0.586567 | − | 0.586567i | −0.350133 | − | 0.936700i | \(-0.613864\pi\) |
0.936700 | + | 0.350133i | \(0.113864\pi\) | |||||||
\(158\) | −2.56819e35 | − | 2.56819e35i | −1.70260 | − | 1.70260i | ||||
\(159\) | 8.96478e33i | 0.0537261i | ||||||||
\(160\) | −6.30253e34 | − | 2.24606e35i | −0.341661 | − | 1.21759i | ||||
\(161\) | −7.79390e34 | −0.382420 | ||||||||
\(162\) | −5.86288e35 | + | 5.86288e35i | −2.60538 | + | 2.60538i | ||||
\(163\) | −7.63676e34 | − | 7.63676e34i | −0.307544 | − | 0.307544i | 0.536412 | − | 0.843956i | \(-0.319779\pi\) |
−0.843956 | + | 0.536412i | \(0.819779\pi\) | |||||||
\(164\) | 5.94079e34i | 0.216942i | ||||||||
\(165\) | 1.01294e36 | − | 2.84233e35i | 3.35613 | − | 0.941742i | ||||
\(166\) | 3.76119e35 | 1.13135 | ||||||||
\(167\) | −2.94497e35 | + | 2.94497e35i | −0.804670 | + | 0.804670i | −0.983821 | − | 0.179152i | \(-0.942665\pi\) |
0.179152 | + | 0.983821i | \(0.442665\pi\) | |||||||
\(168\) | 7.05058e34 | + | 7.05058e34i | 0.175096 | + | 0.175096i | ||||
\(169\) | − | 4.41817e35i | − | 0.997828i | ||||||
\(170\) | −1.62184e35 | − | 9.11089e34i | −0.333291 | − | 0.187231i | ||||
\(171\) | −4.74508e35 | −0.887780 | ||||||||
\(172\) | −1.54728e35 | + | 1.54728e35i | −0.263702 | + | 0.263702i | ||||
\(173\) | −5.38786e35 | − | 5.38786e35i | −0.836909 | − | 0.836909i | 0.151542 | − | 0.988451i | \(-0.451576\pi\) |
−0.988451 | + | 0.151542i | \(0.951576\pi\) | |||||||
\(174\) | 8.03749e35i | 1.13850i | ||||||||
\(175\) | 3.31492e35 | + | 8.05113e34i | 0.428415 | + | 0.104051i | ||||
\(176\) | −1.85385e36 | −2.18712 | ||||||||
\(177\) | 9.04895e35 | − | 9.04895e35i | 0.975048 | − | 0.975048i | ||||
\(178\) | 1.41822e36 | + | 1.41822e36i | 1.39645 | + | 1.39645i | ||||
\(179\) | 9.32800e35i | 0.839730i | 0.907586 | + | 0.419865i | \(0.137923\pi\) | ||||
−0.907586 | + | 0.419865i | \(0.862077\pi\) | |||||||
\(180\) | 1.15385e36 | − | 2.05398e36i | 0.950145 | − | 1.69136i | ||||
\(181\) | 3.47006e35 | 0.261505 | 0.130753 | − | 0.991415i | \(-0.458261\pi\) | ||||
0.130753 | + | 0.991415i | \(0.458261\pi\) | |||||||
\(182\) | 2.80522e34 | − | 2.80522e34i | 0.0193564 | − | 0.0193564i | ||||
\(183\) | −1.67150e36 | − | 1.67150e36i | −1.05655 | − | 1.05655i | ||||
\(184\) | 4.49282e35i | 0.260276i | ||||||||
\(185\) | 1.33949e35 | + | 4.77361e35i | 0.0711528 | + | 0.253571i | ||||
\(186\) | 6.29522e36 | 3.06764 | ||||||||
\(187\) | −8.44853e35 | + | 8.44853e35i | −0.377847 | + | 0.377847i | ||||
\(188\) | 8.30880e35 | + | 8.30880e35i | 0.341203 | + | 0.341203i | ||||
\(189\) | 3.29009e36i | 1.24113i | ||||||||
\(190\) | 1.31175e36 | − | 3.68082e35i | 0.454773 | − | 0.127611i | ||||
\(191\) | −4.24705e36 | −1.35380 | −0.676899 | − | 0.736076i | \(-0.736676\pi\) | ||||
−0.676899 | + | 0.736076i | \(0.736676\pi\) | |||||||
\(192\) | −2.30329e36 | + | 2.30329e36i | −0.675350 | + | 0.675350i | ||||
\(193\) | −1.42983e36 | − | 1.42983e36i | −0.385805 | − | 0.385805i | 0.487383 | − | 0.873188i | \(-0.337951\pi\) |
−0.873188 | + | 0.487383i | \(0.837951\pi\) | |||||||
\(194\) | 6.30618e36i | 1.56653i | ||||||||
\(195\) | 3.32454e35 | + | 1.86761e35i | 0.0760638 | + | 0.0427299i | ||||
\(196\) | 2.96078e36 | 0.624178 | ||||||||
\(197\) | −2.95153e35 | + | 2.95153e35i | −0.0573571 | + | 0.0573571i | −0.735204 | − | 0.677846i | \(-0.762913\pi\) |
0.677846 | + | 0.735204i | \(0.262913\pi\) | |||||||
\(198\) | −2.45099e37 | − | 2.45099e37i | −4.39236 | − | 4.39236i | ||||
\(199\) | 5.87230e35i | 0.0970865i | 0.998821 | + | 0.0485432i | \(0.0154579\pi\) | ||||
−0.998821 | + | 0.0485432i | \(0.984542\pi\) | |||||||
\(200\) | 4.64110e35 | − | 1.91090e36i | 0.0708175 | − | 0.291580i | ||||
\(201\) | 1.71150e37 | 2.41123 | ||||||||
\(202\) | 4.27059e36 | − | 4.27059e36i | 0.555732 | − | 0.555732i | ||||
\(203\) | 1.18363e36 | + | 1.18363e36i | 0.142324 | + | 0.142324i | ||||
\(204\) | 3.74407e36i | 0.416161i | ||||||||
\(205\) | −1.33422e36 | + | 2.37506e36i | −0.137141 | + | 0.244126i | ||||
\(206\) | 1.03704e37 | 0.986102 | ||||||||
\(207\) | −1.74528e37 | + | 1.74528e37i | −1.53582 | + | 1.53582i | ||||
\(208\) | −4.75128e35 | − | 4.75128e35i | −0.0387077 | − | 0.0387077i | ||||
\(209\) | − | 8.75067e36i | − | 0.660238i | ||||||
\(210\) | −4.24916e36 | − | 1.51429e37i | −0.297026 | − | 1.05853i | ||||
\(211\) | −1.33337e37 | −0.863837 | −0.431919 | − | 0.901913i | \(-0.642163\pi\) | ||||
−0.431919 | + | 0.901913i | \(0.642163\pi\) | |||||||
\(212\) | −2.61780e35 | + | 2.61780e35i | −0.0157240 | + | 0.0157240i | ||||
\(213\) | 2.65558e37 | + | 2.65558e37i | 1.47940 | + | 1.47940i | ||||
\(214\) | 2.66431e37i | 1.37709i | ||||||||
\(215\) | −9.66085e36 | + | 2.71087e36i | −0.463447 | + | 0.130045i | ||||
\(216\) | 1.89658e37 | 0.844717 | ||||||||
\(217\) | 9.27057e36 | − | 9.27057e36i | 0.383487 | − | 0.383487i | ||||
\(218\) | 4.04426e36 | + | 4.04426e36i | 0.155430 | + | 0.155430i | ||||
\(219\) | 8.87914e35i | 0.0317150i | ||||||||
\(220\) | 3.78786e37 | + | 2.12788e37i | 1.25786 | + | 0.706619i | ||||
\(221\) | −4.33058e35 | −0.0133743 | ||||||||
\(222\) | 1.61636e37 | − | 1.61636e37i | 0.464399 | − | 0.464399i | ||||
\(223\) | −3.45110e37 | − | 3.45110e37i | −0.922742 | − | 0.922742i | 0.0744808 | − | 0.997222i | \(-0.476270\pi\) |
−0.997222 | + | 0.0744808i | \(0.976270\pi\) | |||||||
\(224\) | 2.23995e37i | 0.557533i | ||||||||
\(225\) | 9.22594e37 | − | 5.62018e37i | 2.13841 | − | 1.30266i | ||||
\(226\) | −9.07861e37 | −1.96013 | ||||||||
\(227\) | −2.61000e37 | + | 2.61000e37i | −0.525082 | + | 0.525082i | −0.919102 | − | 0.394020i | \(-0.871084\pi\) |
0.394020 | + | 0.919102i | \(0.371084\pi\) | |||||||
\(228\) | −1.93898e37 | − | 1.93898e37i | −0.363593 | − | 0.363593i | ||||
\(229\) | − | 9.71954e36i | − | 0.169933i | −0.996384 | − | 0.0849666i | \(-0.972922\pi\) | ||
0.996384 | − | 0.0849666i | \(-0.0270784\pi\) | |||||||
\(230\) | 3.47090e37 | − | 6.17858e37i | 0.565974 | − | 1.00750i | ||||
\(231\) | −1.01018e38 | −1.53676 | ||||||||
\(232\) | 6.82307e36 | − | 6.82307e36i | 0.0968661 | − | 0.0968661i | ||||
\(233\) | 9.69228e36 | + | 9.69228e36i | 0.128449 | + | 0.128449i | 0.768409 | − | 0.639959i | \(-0.221049\pi\) |
−0.639959 | + | 0.768409i | \(0.721049\pi\) | |||||||
\(234\) | − | 1.25634e37i | − | 0.155472i | ||||||
\(235\) | 1.45572e37 | + | 5.18781e37i | 0.168264 | + | 0.599651i | ||||
\(236\) | 5.28477e37 | 0.570734 | ||||||||
\(237\) | −2.37025e38 | + | 2.37025e38i | −2.39233 | + | 2.39233i | ||||
\(238\) | 1.26302e37 | + | 1.26302e37i | 0.119173 | + | 0.119173i | ||||
\(239\) | − | 1.50334e38i | − | 1.32645i | −0.748421 | − | 0.663224i | \(-0.769188\pi\) | ||
0.748421 | − | 0.663224i | \(-0.230812\pi\) | |||||||
\(240\) | −2.56480e38 | + | 7.19693e37i | −2.11677 | + | 0.593974i | ||||
\(241\) | −1.52390e37 | −0.117675 | −0.0588374 | − | 0.998268i | \(-0.518739\pi\) | ||||
−0.0588374 | + | 0.998268i | \(0.518739\pi\) | |||||||
\(242\) | 3.21653e38 | − | 3.21653e38i | 2.32457 | − | 2.32457i | ||||
\(243\) | 2.46867e38 | + | 2.46867e38i | 1.67018 | + | 1.67018i | ||||
\(244\) | − | 9.76190e37i | − | 0.618439i | ||||||
\(245\) | 1.18369e38 | + | 6.64952e37i | 0.702392 | + | 0.394578i | ||||
\(246\) | 1.25598e38 | 0.698266 | ||||||||
\(247\) | 2.24273e36 | − | 2.24273e36i | 0.0116849 | − | 0.0116849i | ||||
\(248\) | −5.34405e37 | − | 5.34405e37i | −0.261002 | − | 0.261002i | ||||
\(249\) | − | 3.47130e38i | − | 1.58966i | ||||||
\(250\) | −2.11450e38 | + | 2.26934e38i | −0.908171 | + | 0.974675i | ||||
\(251\) | −5.17146e37 | −0.208369 | −0.104185 | − | 0.994558i | \(-0.533223\pi\) | ||||
−0.104185 | + | 0.994558i | \(0.533223\pi\) | |||||||
\(252\) | −1.59955e38 | + | 1.59955e38i | −0.604769 | + | 0.604769i | ||||
\(253\) | −3.21857e38 | − | 3.21857e38i | −1.14218 | − | 1.14218i | ||||
\(254\) | 2.56523e38i | 0.854647i | ||||||||
\(255\) | −8.40869e37 | + | 1.49684e38i | −0.263079 | + | 0.468308i | ||||
\(256\) | 4.38768e38 | 1.28942 | ||||||||
\(257\) | 2.18819e38 | − | 2.18819e38i | 0.604165 | − | 0.604165i | −0.337250 | − | 0.941415i | \(-0.609497\pi\) |
0.941415 | + | 0.337250i | \(0.109497\pi\) | |||||||
\(258\) | 3.27120e38 | + | 3.27120e38i | 0.848773 | + | 0.848773i | ||||
\(259\) | − | 4.76063e37i | − | 0.116110i | ||||||
\(260\) | 4.25439e36 | + | 1.51616e37i | 0.00975582 | + | 0.0347673i | ||||
\(261\) | 5.30097e38 | 1.14316 | ||||||||
\(262\) | −3.90813e38 | + | 3.90813e38i | −0.792772 | + | 0.792772i | ||||
\(263\) | 1.06849e38 | + | 1.06849e38i | 0.203928 | + | 0.203928i | 0.801681 | − | 0.597753i | \(-0.203939\pi\) |
−0.597753 | + | 0.801681i | \(0.703939\pi\) | |||||||
\(264\) | 5.82321e38i | 1.04592i | ||||||||
\(265\) | −1.63449e37 | + | 4.58645e36i | −0.0276344 | + | 0.00775429i | ||||
\(266\) | −1.30818e38 | −0.208239 | ||||||||
\(267\) | 1.30892e39 | − | 1.30892e39i | 1.96215 | − | 1.96215i | ||||
\(268\) | 4.99774e38 | + | 4.99774e38i | 0.705695 | + | 0.705695i | ||||
\(269\) | 4.10399e37i | 0.0545972i | 0.999627 | + | 0.0272986i | \(0.00869049\pi\) | ||||
−0.999627 | + | 0.0272986i | \(0.991310\pi\) | |||||||
\(270\) | −2.60820e39 | − | 1.46519e39i | −3.26979 | − | 1.83685i | ||||
\(271\) | −1.55602e39 | −1.83868 | −0.919339 | − | 0.393466i | \(-0.871276\pi\) | ||||
−0.919339 | + | 0.393466i | \(0.871276\pi\) | |||||||
\(272\) | 2.13921e38 | − | 2.13921e38i | 0.238315 | − | 0.238315i | ||||
\(273\) | −2.58901e37 | − | 2.58901e37i | −0.0271977 | − | 0.0271977i | ||||
\(274\) | 1.36474e39i | 1.35220i | ||||||||
\(275\) | 1.03645e39 | + | 1.70141e39i | 0.968781 | + | 1.59032i | ||||
\(276\) | −1.42635e39 | −1.25800 | ||||||||
\(277\) | 3.64318e38 | − | 3.64318e38i | 0.303253 | − | 0.303253i | −0.539032 | − | 0.842285i | \(-0.681210\pi\) |
0.842285 | + | 0.539032i | \(0.181210\pi\) | |||||||
\(278\) | −1.01810e39 | − | 1.01810e39i | −0.799967 | − | 0.799967i | ||||
\(279\) | − | 4.15189e39i | − | 3.08020i | ||||||
\(280\) | −9.24778e37 | + | 1.64620e38i | −0.0647901 | + | 0.115333i | ||||
\(281\) | −2.51689e39 | −1.66557 | −0.832785 | − | 0.553597i | \(-0.813255\pi\) | ||||
−0.832785 | + | 0.553597i | \(0.813255\pi\) | |||||||
\(282\) | 1.75661e39 | − | 1.75661e39i | 1.09822 | − | 1.09822i | ||||
\(283\) | 1.72092e39 | + | 1.72092e39i | 1.01666 | + | 1.01666i | 0.999859 | + | 0.0168046i | \(0.00534931\pi\) |
0.0168046 | + | 0.999859i | \(0.494651\pi\) | |||||||
\(284\) | 1.55091e39i | 0.865953i | ||||||||
\(285\) | −3.39713e38 | − | 1.21065e39i | −0.179306 | − | 0.639002i | ||||
\(286\) | 2.31688e38 | 0.115624 | ||||||||
\(287\) | 1.84960e38 | − | 1.84960e38i | 0.0872906 | − | 0.0872906i | ||||
\(288\) | 5.01590e39 | + | 5.01590e39i | 2.23908 | + | 2.23908i | ||||
\(289\) | 2.17293e39i | 0.917658i | ||||||||
\(290\) | −1.46543e39 | + | 4.11204e38i | −0.585594 | + | 0.164320i | ||||
\(291\) | 5.82015e39 | 2.20113 | ||||||||
\(292\) | −2.59280e37 | + | 2.59280e37i | −0.00928203 | + | 0.00928203i | ||||
\(293\) | 5.49378e38 | + | 5.49378e38i | 0.186204 | + | 0.186204i | 0.794053 | − | 0.607849i | \(-0.207967\pi\) |
−0.607849 | + | 0.794053i | \(0.707967\pi\) | |||||||
\(294\) | − | 6.25956e39i | − | 2.00903i | ||||||
\(295\) | 2.11279e39 | + | 1.18689e39i | 0.642251 | + | 0.360793i | ||||
\(296\) | −2.74428e38 | −0.0790243 | ||||||||
\(297\) | −1.35867e40 | + | 1.35867e40i | −3.70691 | + | 3.70691i | ||||
\(298\) | −5.17824e39 | − | 5.17824e39i | −1.33882 | − | 1.33882i | ||||
\(299\) | − | 1.64979e38i | − | 0.0404286i | ||||||
\(300\) | 6.06658e39 | + | 1.47342e39i | 1.40930 | + | 0.342284i | ||||
\(301\) | 9.63457e38 | 0.212211 | ||||||||
\(302\) | 5.32074e39 | − | 5.32074e39i | 1.11138 | − | 1.11138i | ||||
\(303\) | −3.94144e39 | − | 3.94144e39i | −0.780860 | − | 0.780860i | ||||
\(304\) | 2.21571e39i | 0.416424i | ||||||||
\(305\) | 2.19239e39 | − | 3.90270e39i | 0.390950 | − | 0.695933i | ||||
\(306\) | 5.65651e39 | 0.957207 | ||||||||
\(307\) | 4.68457e39 | − | 4.68457e39i | 0.752412 | − | 0.752412i | −0.222517 | − | 0.974929i | \(-0.571427\pi\) |
0.974929 | + | 0.222517i | \(0.0714273\pi\) | |||||||
\(308\) | −2.94983e39 | − | 2.94983e39i | −0.449764 | − | 0.449764i | ||||
\(309\) | − | 9.57117e39i | − | 1.38557i | ||||||
\(310\) | 3.22068e39 | + | 1.14777e40i | 0.442752 | + | 1.57786i | ||||
\(311\) | −1.00131e40 | −1.30738 | −0.653690 | − | 0.756762i | \(-0.726780\pi\) | ||||
−0.653690 | + | 0.756762i | \(0.726780\pi\) | |||||||
\(312\) | −1.49244e38 | + | 1.49244e38i | −0.0185108 | + | 0.0185108i | ||||
\(313\) | 5.88189e37 | + | 5.88189e37i | 0.00693119 | + | 0.00693119i | 0.710564 | − | 0.703633i | \(-0.248440\pi\) |
−0.703633 | + | 0.710564i | \(0.748440\pi\) | |||||||
\(314\) | − | 9.86910e39i | − | 1.10510i | ||||||
\(315\) | −9.98722e39 | + | 2.80245e39i | −1.06286 | + | 0.298242i | ||||
\(316\) | −1.38427e40 | −1.40032 | ||||||||
\(317\) | −6.78896e39 | + | 6.78896e39i | −0.652912 | + | 0.652912i | −0.953693 | − | 0.300781i | \(-0.902753\pi\) |
0.300781 | + | 0.953693i | \(0.402753\pi\) | |||||||
\(318\) | 5.53446e38 | + | 5.53446e38i | 0.0506106 | + | 0.0506106i | ||||
\(319\) | 9.77583e39i | 0.850164i | ||||||||
\(320\) | −5.37783e39 | − | 3.02107e39i | −0.444844 | − | 0.249897i | ||||
\(321\) | 2.45896e40 | 1.93496 | ||||||||
\(322\) | −4.81161e39 | + | 4.81161e39i | −0.360244 | + | 0.360244i | ||||
\(323\) | 1.00976e39 | + | 1.00976e39i | 0.0719414 | + | 0.0719414i | ||||
\(324\) | 3.16014e40i | 2.14282i | ||||||||
\(325\) | −1.70424e38 | + | 7.01692e38i | −0.0110001 | + | 0.0452911i | ||||
\(326\) | −9.42920e39 | −0.579420 | ||||||||
\(327\) | 3.73256e39 | − | 3.73256e39i | 0.218395 | − | 0.218395i | ||||
\(328\) | −1.06621e39 | − | 1.06621e39i | −0.0594101 | − | 0.0594101i | ||||
\(329\) | − | 5.17370e39i | − | 0.274579i | ||||||
\(330\) | 4.49869e40 | − | 8.00815e40i | 2.27438 | − | 4.04864i | ||||
\(331\) | −1.12351e40 | −0.541164 | −0.270582 | − | 0.962697i | \(-0.587216\pi\) | ||||
−0.270582 | + | 0.962697i | \(0.587216\pi\) | |||||||
\(332\) | 1.01365e40 | − | 1.01365e40i | 0.465244 | − | 0.465244i | ||||
\(333\) | −1.06604e40 | − | 1.06604e40i | −0.466301 | − | 0.466301i | ||||
\(334\) | 3.63619e40i | 1.51601i | ||||||||
\(335\) | 8.75615e39 | + | 3.12047e40i | 0.348014 | + | 1.24023i | ||||
\(336\) | 2.55783e40 | 0.969265 | ||||||||
\(337\) | 9.32868e39 | − | 9.32868e39i | 0.337087 | − | 0.337087i | −0.518183 | − | 0.855270i | \(-0.673391\pi\) |
0.855270 | + | 0.518183i | \(0.173391\pi\) | |||||||
\(338\) | −2.72759e40 | − | 2.72759e40i | −0.939964 | − | 0.939964i | ||||
\(339\) | 8.37890e40i | 2.75418i | ||||||||
\(340\) | −6.82633e39 | + | 1.91549e39i | −0.214055 | + | 0.0600645i | ||||
\(341\) | 7.65674e40 | 2.29073 | ||||||||
\(342\) | −2.92940e40 | + | 2.92940e40i | −0.836298 | + | 0.836298i | ||||
\(343\) | −2.06600e40 | − | 2.06600e40i | −0.562892 | − | 0.562892i | ||||
\(344\) | − | 5.55387e39i | − | 0.144431i | ||||||
\(345\) | −5.70238e40 | − | 3.20339e40i | −1.41563 | − | 0.795251i | ||||
\(346\) | −6.65245e40 | −1.57675 | ||||||||
\(347\) | 5.51128e40 | − | 5.51128e40i | 1.24733 | − | 1.24733i | 0.290432 | − | 0.956896i | \(-0.406201\pi\) |
0.956896 | − | 0.290432i | \(-0.0937989\pi\) | |||||||
\(348\) | 2.16614e40 | + | 2.16614e40i | 0.468186 | + | 0.468186i | ||||
\(349\) | 2.65606e40i | 0.548316i | 0.961685 | + | 0.274158i | \(0.0883991\pi\) | ||||
−0.961685 | + | 0.274158i | \(0.911601\pi\) | |||||||
\(350\) | 2.54353e40 | − | 1.54945e40i | 0.501589 | − | 0.305554i | ||||
\(351\) | −6.96434e39 | −0.131210 | ||||||||
\(352\) | −9.25011e40 | + | 9.25011e40i | −1.66519 | + | 1.66519i | ||||
\(353\) | 2.73054e40 | + | 2.73054e40i | 0.469736 | + | 0.469736i | 0.901829 | − | 0.432093i | \(-0.142225\pi\) |
−0.432093 | + | 0.901829i | \(0.642225\pi\) | |||||||
\(354\) | − | 1.11728e41i | − | 1.83701i | ||||||
\(355\) | −3.48315e40 | + | 6.20038e40i | −0.547417 | + | 0.974462i | ||||
\(356\) | 7.64434e40 | 1.14852 | ||||||||
\(357\) | 1.16567e40 | − | 1.16567e40i | 0.167450 | − | 0.167450i | ||||
\(358\) | 5.75869e40 | + | 5.75869e40i | 0.791035 | + | 0.791035i | ||||
\(359\) | − | 1.19173e41i | − | 1.56556i | −0.622301 | − | 0.782778i | \(-0.713802\pi\) | ||
0.622301 | − | 0.782778i | \(-0.286198\pi\) | |||||||
\(360\) | 1.61548e40 | + | 5.75716e40i | 0.202984 | + | 0.723383i | ||||
\(361\) | 7.27397e40 | 0.874292 | ||||||||
\(362\) | 2.14226e40 | − | 2.14226e40i | 0.246341 | − | 0.246341i | ||||
\(363\) | −2.96863e41 | − | 2.96863e41i | −3.26625 | − | 3.26625i | ||||
\(364\) | − | 1.51203e39i | − | 0.0159199i | ||||||
\(365\) | −1.61888e39 | + | 4.54263e38i | −0.0163128 | + | 0.00457743i | ||||
\(366\) | −2.06382e41 | −1.99056 | ||||||||
\(367\) | −1.10452e41 | + | 1.10452e41i | −1.01981 | + | 1.01981i | −0.0200069 | + | 0.999800i | \(0.506369\pi\) |
−0.999800 | + | 0.0200069i | \(0.993631\pi\) | |||||||
\(368\) | 8.14958e40 | + | 8.14958e40i | 0.720394 | + | 0.720394i | ||||
\(369\) | − | 8.28357e40i | − | 0.701125i | ||||||
\(370\) | 3.77396e40 | + | 2.12007e40i | 0.305893 | + | 0.171840i | ||||
\(371\) | 1.63005e39 | 0.0126537 | ||||||||
\(372\) | 1.69659e41 | − | 1.69659e41i | 1.26151 | − | 1.26151i | ||||
\(373\) | 2.96728e40 | + | 2.96728e40i | 0.211358 | + | 0.211358i | 0.804844 | − | 0.593486i | \(-0.202249\pi\) |
−0.593486 | + | 0.804844i | \(0.702249\pi\) | |||||||
\(374\) | 1.04315e41i | 0.711871i | ||||||||
\(375\) | 2.09444e41 | + | 1.95153e41i | 1.36952 | + | 1.27607i | ||||
\(376\) | −2.98240e40 | −0.186879 | ||||||||
\(377\) | −2.50547e39 | + | 2.50547e39i | −0.0150462 | + | 0.0150462i | ||||
\(378\) | 2.03115e41 | + | 2.03115e41i | 1.16916 | + | 1.16916i | ||||
\(379\) | 1.74744e41i | 0.964217i | 0.876112 | + | 0.482108i | \(0.160129\pi\) | ||||
−0.876112 | + | 0.482108i | \(0.839871\pi\) | |||||||
\(380\) | 2.54323e40 | − | 4.52722e40i | 0.134539 | − | 0.239494i | ||||
\(381\) | 2.36752e41 | 1.20087 | ||||||||
\(382\) | −2.62194e41 | + | 2.62194e41i | −1.27529 | + | 1.27529i | ||||
\(383\) | 1.41747e41 | + | 1.41747e41i | 0.661201 | + | 0.661201i | 0.955663 | − | 0.294462i | \(-0.0951404\pi\) |
−0.294462 | + | 0.955663i | \(0.595140\pi\) | |||||||
\(384\) | − | 2.44711e41i | − | 1.09485i | ||||||
\(385\) | −5.16816e40 | − | 1.84180e41i | −0.221801 | − | 0.790444i | ||||
\(386\) | −1.76543e41 | −0.726864 | ||||||||
\(387\) | 2.15746e41 | − | 2.15746e41i | 0.852249 | − | 0.852249i | ||||
\(388\) | 1.69954e41 | + | 1.69954e41i | 0.644205 | + | 0.644205i | ||||
\(389\) | − | 4.45856e41i | − | 1.62182i | −0.585174 | − | 0.810908i | \(-0.698974\pi\) | ||
0.585174 | − | 0.810908i | \(-0.301026\pi\) | |||||||
\(390\) | 3.20540e40 | − | 8.99447e39i | 0.111905 | − | 0.0314009i | ||||
\(391\) | 7.42798e40 | 0.248910 | ||||||||
\(392\) | −5.31377e40 | + | 5.31377e40i | −0.170933 | + | 0.170933i | ||||
\(393\) | 3.60692e41 | + | 3.60692e41i | 1.11392 | + | 1.11392i | ||||
\(394\) | 3.64429e40i | 0.108062i | ||||||||
\(395\) | −5.53417e41 | − | 3.10890e41i | −1.57579 | − | 0.885224i | ||||
\(396\) | −1.32110e42 | −3.61254 | ||||||||
\(397\) | −1.42475e41 | + | 1.42475e41i | −0.374187 | + | 0.374187i | −0.869000 | − | 0.494812i | \(-0.835237\pi\) |
0.494812 | + | 0.869000i | \(0.335237\pi\) | |||||||
\(398\) | 3.62530e40 | + | 3.62530e40i | 0.0914564 | + | 0.0914564i | ||||
\(399\) | 1.20736e41i | 0.292597i | ||||||||
\(400\) | −2.62434e41 | − | 4.30805e41i | −0.611028 | − | 1.00305i | ||||
\(401\) | −1.78411e41 | −0.399128 | −0.199564 | − | 0.979885i | \(-0.563953\pi\) | ||||
−0.199564 | + | 0.979885i | \(0.563953\pi\) | |||||||
\(402\) | 1.05660e42 | − | 1.05660e42i | 2.27141 | − | 2.27141i | ||||
\(403\) | 1.96236e40 | + | 1.96236e40i | 0.0405414 | + | 0.0405414i | ||||
\(404\) | − | 2.30188e41i | − | 0.457068i | ||||||
\(405\) | −7.09727e41 | + | 1.26339e42i | −1.35460 | + | 2.41133i | ||||
\(406\) | 1.46144e41 | 0.268142 | ||||||||
\(407\) | 1.96595e41 | − | 1.96595e41i | 0.346786 | − | 0.346786i | ||||
\(408\) | −6.71956e40 | − | 6.71956e40i | −0.113967 | − | 0.113967i | ||||
\(409\) | − | 6.33761e41i | − | 1.03360i | −0.856106 | − | 0.516800i | \(-0.827123\pi\) | ||
0.856106 | − | 0.516800i | \(-0.172877\pi\) | |||||||
\(410\) | 6.42568e40 | + | 2.28995e41i | 0.100781 | + | 0.359157i | ||||
\(411\) | 1.25956e42 | 1.89998 | ||||||||
\(412\) | 2.79488e41 | − | 2.79488e41i | 0.405515 | − | 0.405515i | ||||
\(413\) | −1.64535e41 | − | 1.64535e41i | −0.229646 | − | 0.229646i | ||||
\(414\) | 2.15492e42i | 2.89351i | ||||||||
\(415\) | 6.32902e41 | − | 1.77594e41i | 0.817649 | − | 0.229435i | ||||
\(416\) | −4.74146e40 | −0.0589411 | ||||||||
\(417\) | −9.39629e41 | + | 9.39629e41i | −1.12403 | + | 1.12403i | ||||
\(418\) | −5.40228e41 | − | 5.40228e41i | −0.621951 | − | 0.621951i | ||||
\(419\) | − | 1.73807e41i | − | 0.192594i | −0.995353 | − | 0.0962970i | \(-0.969300\pi\) | ||
0.995353 | − | 0.0962970i | \(-0.0306999\pi\) | |||||||
\(420\) | −5.22624e41 | − | 2.93592e41i | −0.557444 | − | 0.313152i | ||||
\(421\) | 1.56462e41 | 0.160655 | 0.0803276 | − | 0.996769i | \(-0.474403\pi\) | ||||
0.0803276 | + | 0.996769i | \(0.474403\pi\) | |||||||
\(422\) | −8.23165e41 | + | 8.23165e41i | −0.813743 | + | 0.813743i | ||||
\(423\) | −1.15854e42 | − | 1.15854e42i | −1.10272 | − | 1.10272i | ||||
\(424\) | − | 9.39646e39i | − | 0.00861213i | ||||||
\(425\) | −3.15929e41 | − | 7.67313e40i | −0.278847 | − | 0.0677251i | ||||
\(426\) | 3.27888e42 | 2.78723 | ||||||||
\(427\) | −3.03926e41 | + | 3.03926e41i | −0.248841 | + | 0.248841i | ||||
\(428\) | 7.18041e41 | + | 7.18041e41i | 0.566303 | + | 0.566303i | ||||
\(429\) | − | 2.13832e41i | − | 0.162463i | ||||||
\(430\) | −4.29061e41 | + | 7.63775e41i | −0.314068 | + | 0.559075i | ||||
\(431\) | 5.07423e40 | 0.0357877 | 0.0178939 | − | 0.999840i | \(-0.494304\pi\) | ||||
0.0178939 | + | 0.999840i | \(0.494304\pi\) | |||||||
\(432\) | 3.44023e42 | − | 3.44023e42i | 2.33801 | − | 2.33801i | ||||
\(433\) | 2.15420e41 | + | 2.15420e41i | 0.141085 | + | 0.141085i | 0.774122 | − | 0.633037i | \(-0.218192\pi\) |
−0.633037 | + | 0.774122i | \(0.718192\pi\) | |||||||
\(434\) | − | 1.14465e42i | − | 0.722497i | ||||||
\(435\) | 3.79512e41 | + | 1.35248e42i | 0.230886 | + | 0.822818i | ||||
\(436\) | 2.17989e41 | 0.127835 | ||||||||
\(437\) | −3.84681e41 | + | 3.84681e41i | −0.217469 | + | 0.217469i | ||||
\(438\) | 5.48159e40 | + | 5.48159e40i | 0.0298759 | + | 0.0298759i | ||||
\(439\) | − | 1.06578e42i | − | 0.560059i | −0.959991 | − | 0.280029i | \(-0.909656\pi\) | ||
0.959991 | − | 0.280029i | \(-0.0903442\pi\) | |||||||
\(440\) | −1.06171e42 | + | 2.97920e41i | −0.537977 | + | 0.150958i | ||||
\(441\) | −4.12837e42 | −2.01726 | ||||||||
\(442\) | −2.67351e40 | + | 2.67351e40i | −0.0125987 | + | 0.0125987i | ||||
\(443\) | 2.42798e42 | + | 2.42798e42i | 1.10353 | + | 1.10353i | 0.993981 | + | 0.109553i | \(0.0349419\pi\) |
0.109553 | + | 0.993981i | \(0.465058\pi\) | |||||||
\(444\) | − | 8.71233e41i | − | 0.381950i | ||||||
\(445\) | 3.05612e42 | + | 1.71682e42i | 1.29244 | + | 0.726047i | ||||
\(446\) | −4.26112e42 | −1.73846 | ||||||||
\(447\) | −4.77914e42 | + | 4.77914e42i | −1.88118 | + | 1.88118i | ||||
\(448\) | 4.18803e41 | + | 4.18803e41i | 0.159060 | + | 0.159060i | ||||
\(449\) | 2.99100e42i | 1.09616i | 0.836425 | + | 0.548082i | \(0.184642\pi\) | ||||
−0.836425 | + | 0.548082i | \(0.815358\pi\) | |||||||
\(450\) | 2.22604e42 | − | 9.16534e42i | 0.787285 | − | 3.24152i | ||||
\(451\) | 1.52762e42 | 0.521424 | ||||||||
\(452\) | −2.44672e42 | + | 2.44672e42i | −0.806064 | + | 0.806064i | ||||
\(453\) | −4.91065e42 | − | 4.91065e42i | −1.56159 | − | 1.56159i | ||||
\(454\) | 3.22260e42i | 0.989265i | ||||||||
\(455\) | 3.39583e40 | − | 6.04495e40i | 0.0100638 | − | 0.0179147i | ||||
\(456\) | 6.95986e41 | 0.199142 | ||||||||
\(457\) | 2.89287e42 | − | 2.89287e42i | 0.799226 | − | 0.799226i | −0.183747 | − | 0.982974i | \(-0.558823\pi\) |
0.982974 | + | 0.183747i | \(0.0588228\pi\) | |||||||
\(458\) | −6.00042e41 | − | 6.00042e41i | −0.160079 | − | 0.160079i | ||||
\(459\) | − | 3.13562e42i | − | 0.807830i | ||||||
\(460\) | −7.29729e41 | − | 2.60057e42i | −0.181567 | − | 0.647059i | ||||
\(461\) | 2.34084e42 | 0.562544 | 0.281272 | − | 0.959628i | \(-0.409244\pi\) | ||||
0.281272 | + | 0.959628i | \(0.409244\pi\) | |||||||
\(462\) | −6.23641e42 | + | 6.23641e42i | −1.44765 | + | 1.44765i | ||||
\(463\) | −8.44318e41 | − | 8.44318e41i | −0.189326 | − | 0.189326i | 0.606079 | − | 0.795405i | \(-0.292742\pi\) |
−0.795405 | + | 0.606079i | \(0.792742\pi\) | |||||||
\(464\) | − | 2.47529e42i | − | 0.536214i | ||||||
\(465\) | 1.05931e43 | − | 2.97246e42i | 2.21705 | − | 0.622112i | ||||
\(466\) | 1.19672e42 | 0.242001 | ||||||||
\(467\) | 5.12952e42 | − | 5.12952e42i | 1.00232 | − | 1.00232i | 0.00232253 | − | 0.999997i | \(-0.499261\pi\) |
0.999997 | − | 0.00232253i | \(-0.000739285\pi\) | |||||||
\(468\) | −3.38588e41 | − | 3.38588e41i | −0.0639348 | − | 0.0639348i | ||||
\(469\) | − | 3.11198e42i | − | 0.567900i | ||||||
\(470\) | 4.10142e42 | + | 2.30403e42i | 0.723384 | + | 0.406371i | ||||
\(471\) | −9.10847e42 | −1.55278 | ||||||||
\(472\) | −9.48468e41 | + | 9.48468e41i | −0.156297 | + | 0.156297i | ||||
\(473\) | 3.97869e42 | + | 3.97869e42i | 0.633814 | + | 0.633814i | ||||
\(474\) | 2.92658e43i | 4.50720i | ||||||||
\(475\) | 2.03351e42 | − | 1.23876e42i | 0.302795 | − | 0.184454i | ||||
\(476\) | 6.80776e41 | 0.0980151 | ||||||||
\(477\) | 3.65014e41 | − | 3.65014e41i | 0.0508178 | − | 0.0508178i | ||||
\(478\) | −9.28094e42 | − | 9.28094e42i | −1.24953 | − | 1.24953i | ||||
\(479\) | − | 1.13201e43i | − | 1.47395i | −0.675920 | − | 0.736975i | \(-0.736253\pi\) | ||
0.675920 | − | 0.736975i | \(-0.263747\pi\) | |||||||
\(480\) | −9.20648e42 | + | 1.63885e43i | −1.15940 | + | 2.06386i | ||||
\(481\) | 1.00771e41 | 0.0122748 | ||||||||
\(482\) | −9.40788e41 | + | 9.40788e41i | −0.110851 | + | 0.110851i | ||||
\(483\) | 4.44077e42 | + | 4.44077e42i | 0.506179 | + | 0.506179i | ||||
\(484\) | − | 1.73374e43i | − | 1.91187i | ||||||
\(485\) | 2.97763e42 | + | 1.06115e43i | 0.317689 | + | 1.13217i | ||||
\(486\) | 3.04810e43 | 3.14665 | ||||||||
\(487\) | −3.32700e41 | + | 3.32700e41i | −0.0332345 | + | 0.0332345i | −0.723529 | − | 0.690294i | \(-0.757481\pi\) |
0.690294 | + | 0.723529i | \(0.257481\pi\) | |||||||
\(488\) | 1.75199e42 | + | 1.75199e42i | 0.169361 | + | 0.169361i | ||||
\(489\) | 8.70247e42i | 0.814143i | ||||||||
\(490\) | 1.14127e43 | − | 3.20244e42i | 1.03336 | − | 0.289963i | ||||
\(491\) | 9.59647e42 | 0.841023 | 0.420511 | − | 0.907287i | \(-0.361851\pi\) | ||||
0.420511 | + | 0.907287i | \(0.361851\pi\) | |||||||
\(492\) | 3.38491e42 | − | 3.38491e42i | 0.287148 | − | 0.287148i | ||||
\(493\) | −1.12806e42 | − | 1.12806e42i | −0.0926362 | − | 0.0926362i | ||||
\(494\) | − | 2.76912e41i | − | 0.0220146i | ||||||
\(495\) | −5.28162e43 | − | 2.96702e43i | −4.06522 | − | 2.28369i | ||||
\(496\) | −1.93873e43 | −1.44481 | ||||||||
\(497\) | 4.82859e42 | − | 4.82859e42i | 0.348432 | − | 0.348432i | ||||
\(498\) | −2.14303e43 | − | 2.14303e43i | −1.49747 | − | 1.49747i | ||||
\(499\) | 2.82234e42i | 0.190986i | 0.995430 | + | 0.0954928i | \(0.0304427\pi\) | ||||
−0.995430 | + | 0.0954928i | \(0.969557\pi\) | |||||||
\(500\) | 4.17303e41 | + | 1.18146e43i | 0.0273484 | + | 0.774284i | ||||
\(501\) | 3.35594e43 | 2.13015 | ||||||||
\(502\) | −3.19263e42 | + | 3.19263e42i | −0.196286 | + | 0.196286i | ||||
\(503\) | −7.85742e42 | − | 7.85742e42i | −0.467942 | − | 0.467942i | 0.433305 | − | 0.901247i | \(-0.357347\pi\) |
−0.901247 | + | 0.433305i | \(0.857347\pi\) | |||||||
\(504\) | − | 5.74150e42i | − | 0.331236i | ||||||
\(505\) | 5.16972e42 | − | 9.20266e42i | 0.288938 | − | 0.514341i | ||||
\(506\) | −3.97400e43 | −2.15189 | ||||||||
\(507\) | −2.51736e43 | + | 2.51736e43i | −1.32074 | + | 1.32074i | ||||
\(508\) | 6.91340e42 | + | 6.91340e42i | 0.351457 | + | 0.351457i | ||||
\(509\) | 1.76434e43i | 0.869156i | 0.900634 | + | 0.434578i | \(0.143103\pi\) | ||||
−0.900634 | + | 0.434578i | \(0.856897\pi\) | |||||||
\(510\) | 4.04966e42 | + | 1.44320e43i | 0.193328 | + | 0.688974i | ||||
\(511\) | 1.61448e41 | 0.00746960 | ||||||||
\(512\) | 1.78645e43 | − | 1.78645e43i | 0.801070 | − | 0.801070i | ||||
\(513\) | 1.62388e43 | + | 1.62388e43i | 0.705789 | + | 0.705789i | ||||
\(514\) | − | 2.70179e43i | − | 1.13826i | ||||||
\(515\) | 1.74505e43 | − | 4.89668e42i | 0.712678 | − | 0.199980i | ||||
\(516\) | 1.76320e43 | 0.698083 | ||||||||
\(517\) | 2.13653e43 | − | 2.13653e43i | 0.820088 | − | 0.820088i | ||||
\(518\) | −2.93900e42 | − | 2.93900e42i | −0.109376 | − | 0.109376i | ||||
\(519\) | 6.13973e43i | 2.21550i | ||||||||
\(520\) | −3.48463e41 | − | 1.95754e41i | −0.0121928 | − | 0.00684946i | ||||
\(521\) | −4.63252e43 | −1.57186 | −0.785930 | − | 0.618316i | \(-0.787815\pi\) | ||||
−0.785930 | + | 0.618316i | \(0.787815\pi\) | |||||||
\(522\) | 3.27259e43 | − | 3.27259e43i | 1.07687 | − | 1.07687i | ||||
\(523\) | 1.37405e43 | + | 1.37405e43i | 0.438507 | + | 0.438507i | 0.891509 | − | 0.453003i | \(-0.149647\pi\) |
−0.453003 | + | 0.891509i | \(0.649647\pi\) | |||||||
\(524\) | 2.10651e43i | 0.652024i | ||||||||
\(525\) | −1.43003e43 | − | 2.34749e43i | −0.429334 | − | 0.704783i | ||||
\(526\) | 1.31927e43 | 0.384205 | ||||||||
\(527\) | −8.83531e42 | + | 8.83531e42i | −0.249604 | + | 0.249604i | ||||
\(528\) | 1.05628e44 | + | 1.05628e44i | 2.89492 | + | 2.89492i | ||||
\(529\) | − | 9.31114e42i | − | 0.247578i | ||||||
\(530\) | −7.25918e41 | + | 1.29221e42i | −0.0187272 | + | 0.0333365i | ||||
\(531\) | −7.36883e43 | −1.84453 | ||||||||
\(532\) | −3.52561e42 | + | 3.52561e42i | −0.0856344 | + | 0.0856344i | ||||
\(533\) | 3.91517e41 | + | 3.91517e41i | 0.00922816 | + | 0.00922816i | ||||
\(534\) | − | 1.61614e44i | − | 3.69673i | ||||||
\(535\) | 1.25802e43 | + | 4.48328e43i | 0.279272 | + | 0.995257i | ||||
\(536\) | −1.79391e43 | −0.386513 | ||||||||
\(537\) | 5.31486e43 | − | 5.31486e43i | 1.11148 | − | 1.11148i | ||||
\(538\) | 2.53362e42 | + | 2.53362e42i | 0.0514311 | + | 0.0514311i | ||||
\(539\) | − | 7.61337e43i | − | 1.50023i | ||||||
\(540\) | −1.09779e44 | + | 3.08045e43i | −2.10001 | + | 0.589269i | ||||
\(541\) | 4.48481e41 | 0.00832890 | 0.00416445 | − | 0.999991i | \(-0.498674\pi\) | ||||
0.00416445 | + | 0.999991i | \(0.498674\pi\) | |||||||
\(542\) | −9.60616e43 | + | 9.60616e43i | −1.73205 | + | 1.73205i | ||||
\(543\) | −1.97715e43 | − | 1.97715e43i | −0.346133 | − | 0.346133i | ||||
\(544\) | − | 2.13479e43i | − | 0.362888i | ||||||
\(545\) | 8.71495e42 | + | 4.89575e42i | 0.143854 | + | 0.0808118i | ||||
\(546\) | −3.19668e42 | −0.0512410 | ||||||||
\(547\) | 5.86849e43 | − | 5.86849e43i | 0.913543 | − | 0.913543i | −0.0830059 | − | 0.996549i | \(-0.526452\pi\) |
0.996549 | + | 0.0830059i | \(0.0264520\pi\) | |||||||
\(548\) | 3.67804e43 | + | 3.67804e43i | 0.556068 | + | 0.556068i | ||||
\(549\) | 1.36115e44i | 1.99871i | ||||||||
\(550\) | 1.69023e44 | + | 4.10516e43i | 2.41070 | + | 0.585500i | ||||
\(551\) | 1.16840e43 | 0.161870 | ||||||||
\(552\) | 2.55990e43 | − | 2.55990e43i | 0.344506 | − | 0.344506i | ||||
\(553\) | 4.30978e43 | + | 4.30978e43i | 0.563447 | + | 0.563447i | ||||
\(554\) | − | 4.49828e43i | − | 0.571334i | ||||||
\(555\) | 1.95668e43 | − | 3.48309e43i | 0.241452 | − | 0.429811i | ||||
\(556\) | −5.48762e43 | −0.657942 | ||||||||
\(557\) | −1.00298e44 | + | 1.00298e44i | −1.16844 | + | 1.16844i | −0.185869 | + | 0.982575i | \(0.559510\pi\) |
−0.982575 | + | 0.185869i | \(0.940490\pi\) | |||||||
\(558\) | −2.56319e44 | − | 2.56319e44i | −2.90158 | − | 2.90158i | ||||
\(559\) | 2.03941e42i | 0.0224345i | ||||||||
\(560\) | 1.30860e43 | + | 4.66353e43i | 0.139894 | + | 0.498547i | ||||
\(561\) | 9.62752e43 | 1.00025 | ||||||||
\(562\) | −1.55382e44 | + | 1.55382e44i | −1.56898 | + | 1.56898i | ||||
\(563\) | −5.43991e43 | − | 5.43991e43i | −0.533897 | − | 0.533897i | 0.387833 | − | 0.921730i | \(-0.373224\pi\) |
−0.921730 | + | 0.387833i | \(0.873224\pi\) | |||||||
\(564\) | − | 9.46829e43i | − | 0.903245i | ||||||
\(565\) | −1.52767e44 | + | 4.28670e43i | −1.41663 | + | 0.397510i | ||||
\(566\) | 2.12484e44 | 1.91541 | ||||||||
\(567\) | 9.83874e43 | − | 9.83874e43i | 0.862205 | − | 0.862205i | ||||
\(568\) | −2.78346e43 | − | 2.78346e43i | −0.237144 | − | 0.237144i | ||||
\(569\) | − | 6.89044e43i | − | 0.570756i | −0.958415 | − | 0.285378i | \(-0.907881\pi\) | ||
0.958415 | − | 0.285378i | \(-0.0921192\pi\) | |||||||
\(570\) | −9.57128e43 | − | 5.37680e43i | −0.770854 | − | 0.433038i | ||||
\(571\) | −1.52121e44 | −1.19127 | −0.595636 | − | 0.803255i | \(-0.703100\pi\) | ||||
−0.595636 | + | 0.803255i | \(0.703100\pi\) | |||||||
\(572\) | 6.24409e42 | − | 6.24409e42i | 0.0475481 | − | 0.0475481i | ||||
\(573\) | 2.41986e44 | + | 2.41986e44i | 1.79191 | + | 1.79191i | ||||
\(574\) | − | 2.28372e43i | − | 0.164457i | ||||||
\(575\) | 2.92317e43 | − | 1.20357e44i | 0.204724 | − | 0.842918i | ||||
\(576\) | 1.87564e44 | 1.27758 | ||||||||
\(577\) | −1.32520e44 | + | 1.32520e44i | −0.877946 | + | 0.877946i | −0.993322 | − | 0.115376i | \(-0.963193\pi\) |
0.115376 | + | 0.993322i | \(0.463193\pi\) | |||||||
\(578\) | 1.34147e44 | + | 1.34147e44i | 0.864443 | + | 0.864443i | ||||
\(579\) | 1.62936e44i | 1.02132i | ||||||||
\(580\) | −2.84118e43 | + | 5.05760e43i | −0.173241 | + | 0.308387i | ||||
\(581\) | −6.31180e43 | −0.374399 | ||||||||
\(582\) | 3.59310e44 | − | 3.59310e44i | 2.07349 | − | 2.07349i | ||||
\(583\) | 6.73144e42 | + | 6.73144e42i | 0.0377930 | + | 0.0377930i | ||||
\(584\) | − | 9.30670e41i | − | 0.00508382i | ||||||
\(585\) | −5.93212e42 | − | 2.11406e43i | −0.0315295 | − | 0.112363i | ||||
\(586\) | 6.78323e43 | 0.350812 | ||||||||
\(587\) | 1.05854e44 | − | 1.05854e44i | 0.532719 | − | 0.532719i | −0.388661 | − | 0.921381i | \(-0.627062\pi\) |
0.921381 | + | 0.388661i | \(0.127062\pi\) | |||||||
\(588\) | −1.68698e44 | − | 1.68698e44i | −0.826175 | − | 0.826175i | ||||
\(589\) | − | 9.15128e43i | − | 0.436151i | ||||||
\(590\) | 2.03708e44 | − | 5.71611e43i | 0.944877 | − | 0.265136i | ||||
\(591\) | 3.36341e43 | 0.151838 | ||||||||
\(592\) | −4.97787e43 | + | 4.97787e43i | −0.218724 | + | 0.218724i | ||||
\(593\) | −9.62572e43 | − | 9.62572e43i | −0.411678 | − | 0.411678i | 0.470645 | − | 0.882323i | \(-0.344021\pi\) |
−0.882323 | + | 0.470645i | \(0.844021\pi\) | |||||||
\(594\) | 1.67757e45i | 6.98389i | ||||||||
\(595\) | 2.72167e43 | + | 1.52893e43i | 0.110297 | + | 0.0619609i | ||||
\(596\) | −2.79111e44 | −1.10113 | ||||||||
\(597\) | 3.34589e43 | − | 3.34589e43i | 0.128506 | − | 0.128506i | ||||
\(598\) | −1.01851e43 | − | 1.01851e43i | −0.0380842 | − | 0.0380842i | ||||
\(599\) | − | 1.37289e44i | − | 0.499813i | −0.968270 | − | 0.249907i | \(-0.919600\pi\) | ||
0.968270 | − | 0.249907i | \(-0.0803999\pi\) | |||||||
\(600\) | −1.35322e44 | + | 8.24343e43i | −0.479676 | + | 0.292205i | ||||
\(601\) | 1.77294e44 | 0.611931 | 0.305966 | − | 0.952043i | \(-0.401021\pi\) | ||||
0.305966 | + | 0.952043i | \(0.401021\pi\) | |||||||
\(602\) | 5.94796e43 | − | 5.94796e43i | 0.199905 | − | 0.199905i | ||||
\(603\) | −6.96862e44 | − | 6.96862e44i | −2.28071 | − | 2.28071i | ||||
\(604\) | − | 2.86792e44i | − | 0.914063i | ||||||
\(605\) | 3.89375e44 | − | 6.93129e44i | 1.20860 | − | 2.15144i | ||||
\(606\) | −4.86654e44 | −1.47116 | ||||||||
\(607\) | −4.34261e44 | + | 4.34261e44i | −1.27859 | + | 1.27859i | −0.337134 | + | 0.941457i | \(0.609457\pi\) |
−0.941457 | + | 0.337134i | \(0.890543\pi\) | |||||||
\(608\) | 1.10557e44 | + | 1.10557e44i | 0.317050 | + | 0.317050i | ||||
\(609\) | − | 1.34880e44i | − | 0.376767i | ||||||
\(610\) | −1.05587e44 | − | 3.76284e44i | −0.287297 | − | 1.02386i | ||||
\(611\) | 1.09515e43 | 0.0290278 | ||||||||
\(612\) | 1.52445e44 | − | 1.52445e44i | 0.393633 | − | 0.393633i | ||||
\(613\) | 5.56557e44 | + | 5.56557e44i | 1.40005 | + | 1.40005i | 0.799862 | + | 0.600184i | \(0.204906\pi\) |
0.600184 | + | 0.799862i | \(0.295094\pi\) | |||||||
\(614\) | − | 5.78409e44i | − | 1.41756i | ||||||
\(615\) | 2.11346e44 | − | 5.93044e43i | 0.504652 | − | 0.141607i | ||||
\(616\) | 1.05882e44 | 0.246338 | ||||||||
\(617\) | −1.35367e44 | + | 1.35367e44i | −0.306866 | + | 0.306866i | −0.843693 | − | 0.536826i | \(-0.819623\pi\) |
0.536826 | + | 0.843693i | \(0.319623\pi\) | |||||||
\(618\) | −5.90882e44 | − | 5.90882e44i | −1.30522 | − | 1.30522i | ||||
\(619\) | − | 2.87188e44i | − | 0.618180i | −0.951033 | − | 0.309090i | \(-0.899976\pi\) | ||
0.951033 | − | 0.309090i | \(-0.100024\pi\) | |||||||
\(620\) | 3.96127e44 | + | 2.22530e44i | 0.830937 | + | 0.466790i | ||||
\(621\) | 1.19455e45 | 2.44196 | ||||||||
\(622\) | −6.18164e44 | + | 6.18164e44i | −1.23157 | + | 1.23157i | ||||
\(623\) | −2.37998e44 | − | 2.37998e44i | −0.462130 | − | 0.462130i | ||||
\(624\) | 5.41432e43i | 0.102469i | ||||||||
\(625\) | −2.48658e44 | + | 4.81708e44i | −0.458693 | + | 0.888595i | ||||
\(626\) | 7.26244e42 | 0.0130585 | ||||||||
\(627\) | −4.98591e44 | + | 4.98591e44i | −0.873904 | + | 0.873904i | ||||
\(628\) | −2.65976e44 | − | 2.65976e44i | −0.454453 | − | 0.454453i | ||||
\(629\) | 4.53711e43i | 0.0755735i | ||||||||
\(630\) | −4.43556e44 | + | 7.89578e44i | −0.720278 | + | 1.28217i | ||||
\(631\) | −8.09467e44 | −1.28153 | −0.640766 | − | 0.767736i | \(-0.721383\pi\) | ||||
−0.640766 | + | 0.767736i | \(0.721383\pi\) | |||||||
\(632\) | 2.48439e44 | − | 2.48439e44i | 0.383483 | − | 0.383483i | ||||
\(633\) | 7.59721e44 | + | 7.59721e44i | 1.14339 | + | 1.14339i | ||||
\(634\) | 8.38240e44i | 1.23010i | ||||||||
\(635\) | 1.21124e44 | + | 4.31656e44i | 0.173321 | + | 0.617672i | ||||
\(636\) | 2.98312e43 | 0.0416252 | ||||||||
\(637\) | 1.95124e43 | − | 1.95124e43i | 0.0265510 | − | 0.0265510i | ||||
\(638\) | 6.03516e44 | + | 6.03516e44i | 0.800863 | + | 0.800863i | ||||
\(639\) | − | 2.16252e45i | − | 2.79864i | ||||||
\(640\) | 4.46166e44 | − | 1.25196e44i | 0.563141 | − | 0.158019i | ||||
\(641\) | 1.01290e45 | 1.24692 | 0.623462 | − | 0.781854i | \(-0.285726\pi\) | ||||
0.623462 | + | 0.781854i | \(0.285726\pi\) | |||||||
\(642\) | 1.51805e45 | − | 1.51805e45i | 1.82275 | − | 1.82275i | ||||
\(643\) | 8.81933e44 | + | 8.81933e44i | 1.03290 | + | 1.03290i | 0.999440 | + | 0.0334640i | \(0.0106539\pi\) |
0.0334640 | + | 0.999440i | \(0.489346\pi\) | |||||||
\(644\) | 2.59350e44i | 0.296287i | ||||||||
\(645\) | 7.04909e44 | + | 3.95992e44i | 0.785557 | + | 0.441297i | ||||
\(646\) | 1.24677e44 | 0.135539 | ||||||||
\(647\) | −9.70562e44 | + | 9.70562e44i | −1.02933 | + | 1.02933i | −0.0297739 | + | 0.999557i | \(0.509479\pi\) |
−0.999557 | + | 0.0297739i | \(0.990521\pi\) | |||||||
\(648\) | −5.67157e44 | − | 5.67157e44i | −0.586818 | − | 0.586818i | ||||
\(649\) | − | 1.35893e45i | − | 1.37177i | ||||||
\(650\) | 3.27981e43 | + | 5.38405e43i | 0.0323025 | + | 0.0530268i | ||||
\(651\) | −1.05643e45 | −1.01518 | ||||||||
\(652\) | −2.54121e44 | + | 2.54121e44i | −0.238275 | + | 0.238275i | ||||
\(653\) | −5.93429e44 | − | 5.93429e44i | −0.542947 | − | 0.542947i | 0.381445 | − | 0.924392i | \(-0.375427\pi\) |
−0.924392 | + | 0.381445i | \(0.875427\pi\) | |||||||
\(654\) | − | 4.60863e44i | − | 0.411461i | ||||||
\(655\) | −4.73096e44 | + | 8.42161e44i | −0.412181 | + | 0.733727i | ||||
\(656\) | −3.86801e44 | −0.328871 | ||||||||
\(657\) | 3.61528e43 | − | 3.61528e43i | 0.0299982 | − | 0.0299982i | ||||
\(658\) | −3.19401e44 | − | 3.19401e44i | −0.258656 | − | 0.258656i | ||||
\(659\) | 1.07603e45i | 0.850471i | 0.905083 | + | 0.425236i | \(0.139809\pi\) | ||||
−0.905083 | + | 0.425236i | \(0.860191\pi\) | |||||||
\(660\) | −9.45814e44 | − | 3.37064e45i | −0.729630 | − | 2.60022i | ||||
\(661\) | 1.82482e44 | 0.137403 | 0.0687017 | − | 0.997637i | \(-0.478114\pi\) | ||||
0.0687017 | + | 0.997637i | \(0.478114\pi\) | |||||||
\(662\) | −6.93605e44 | + | 6.93605e44i | −0.509782 | + | 0.509782i | ||||
\(663\) | 2.46746e43 | + | 2.46746e43i | 0.0177024 | + | 0.0177024i | ||||
\(664\) | 3.63846e44i | 0.254817i | ||||||||
\(665\) | −2.20131e44 | + | 6.17694e43i | −0.150499 | + | 0.0422306i | ||||
\(666\) | −1.31625e45 | −0.878520 | ||||||||
\(667\) | 4.29747e44 | − | 4.29747e44i | 0.280027 | − | 0.280027i | ||||
\(668\) | 9.79969e44 | + | 9.79969e44i | 0.623431 | + | 0.623431i | ||||
\(669\) | 3.93270e45i | 2.44272i | ||||||||
\(670\) | 2.46701e45 | + | 1.38588e45i | 1.49614 | + | 0.840480i | ||||
\(671\) | −2.51018e45 | −1.48643 | ||||||||
\(672\) | 1.27627e45 | − | 1.27627e45i | 0.737962 | − | 0.737962i | ||||
\(673\) | −1.78761e45 | − | 1.78761e45i | −1.00933 | − | 1.00933i | −0.999956 | − | 0.00937027i | \(-0.997017\pi\) |
−0.00937027 | − | 0.999956i | \(-0.502983\pi\) | |||||||
\(674\) | − | 1.15182e45i | − | 0.635079i | ||||||
\(675\) | −5.08069e45 | − | 1.23397e45i | −2.73566 | − | 0.664425i | ||||
\(676\) | −1.47019e45 | −0.773084 | ||||||||
\(677\) | 1.41232e45 | − | 1.41232e45i | 0.725296 | − | 0.725296i | −0.244383 | − | 0.969679i | \(-0.578585\pi\) |
0.969679 | + | 0.244383i | \(0.0785854\pi\) | |||||||
\(678\) | 5.17276e45 | + | 5.17276e45i | 2.59446 | + | 2.59446i | ||||
\(679\) | − | 1.05827e45i | − | 0.518416i | ||||||
\(680\) | 8.81359e43 | − | 1.56891e44i | 0.0421706 | − | 0.0750683i | ||||
\(681\) | 2.97423e45 | 1.39002 | ||||||||
\(682\) | 4.72693e45 | − | 4.72693e45i | 2.15789 | − | 2.15789i | ||||
\(683\) | −1.44954e45 | − | 1.44954e45i | −0.646396 | − | 0.646396i | 0.305724 | − | 0.952120i | \(-0.401102\pi\) |
−0.952120 | + | 0.305724i | \(0.901102\pi\) | |||||||
\(684\) | 1.57897e45i | 0.687822i | ||||||||
\(685\) | 6.44400e44 | + | 2.29648e45i | 0.274225 | + | 0.977268i | ||||
\(686\) | −2.55092e45 | −1.06050 | ||||||||
\(687\) | −5.53795e44 | + | 5.53795e44i | −0.224927 | + | 0.224927i | ||||
\(688\) | −1.00742e45 | − | 1.00742e45i | −0.399758 | − | 0.399758i | ||||
\(689\) | 3.45043e42i | 0.00133772i | ||||||||
\(690\) | −5.49803e45 | + | 1.54277e45i | −2.08267 | + | 0.584406i | ||||
\(691\) | 4.24106e45 | 1.56973 | 0.784866 | − | 0.619665i | \(-0.212732\pi\) | ||||
0.784866 | + | 0.619665i | \(0.212732\pi\) | |||||||
\(692\) | −1.79286e45 | + | 1.79286e45i | −0.648410 | + | 0.648410i | ||||
\(693\) | 4.11310e45 | + | 4.11310e45i | 1.45358 | + | 1.45358i | ||||
\(694\) | − | 6.80484e45i | − | 2.34999i | ||||||
\(695\) | −2.19389e45 | − | 1.23245e45i | −0.740386 | − | 0.415922i | ||||
\(696\) | −7.77522e44 | −0.256428 | ||||||||
\(697\) | −1.76276e44 | + | 1.76276e44i | −0.0568158 | + | 0.0568158i | ||||
\(698\) | 1.63973e45 | + | 1.63973e45i | 0.516519 | + | 0.516519i | ||||
\(699\) | − | 1.10448e45i | − | 0.340036i | ||||||
\(700\) | 2.67909e44 | − | 1.10307e45i | 0.0806156 | − | 0.331922i | ||||
\(701\) | −3.28897e45 | −0.967323 | −0.483661 | − | 0.875255i | \(-0.660693\pi\) | ||||
−0.483661 | + | 0.875255i | \(0.660693\pi\) | |||||||
\(702\) | −4.29948e44 | + | 4.29948e44i | −0.123601 | + | 0.123601i | ||||
\(703\) | −2.34968e44 | − | 2.34968e44i | −0.0660274 | − | 0.0660274i | ||||
\(704\) | 3.45897e45i | 0.950133i | ||||||||
\(705\) | 2.12645e45 | − | 3.78532e45i | 0.570992 | − | 1.01643i | ||||
\(706\) | 3.37143e45 | 0.884992 | ||||||||
\(707\) | −7.16664e44 | + | 7.16664e44i | −0.183910 | + | 0.183910i | ||||
\(708\) | −3.01113e45 | − | 3.01113e45i | −0.755435 | − | 0.755435i | ||||
\(709\) | 7.44075e45i | 1.82506i | 0.409011 | + | 0.912529i | \(0.365874\pi\) | ||||
−0.409011 | + | 0.912529i | \(0.634126\pi\) | |||||||
\(710\) | 1.67750e45 | + | 5.97819e45i | 0.402280 | + | 1.43363i | ||||
\(711\) | 1.93017e46 | 4.52565 | ||||||||
\(712\) | −1.37195e45 | + | 1.37195e45i | −0.314527 | + | 0.314527i | ||||
\(713\) | −3.36592e45 | − | 3.36592e45i | −0.754520 | − | 0.754520i | ||||
\(714\) | − | 1.43927e45i | − | 0.315479i | ||||||
\(715\) | 3.89866e44 | − | 1.09398e44i | 0.0835639 | − | 0.0234483i | ||||
\(716\) | 3.10398e45 | 0.650595 | ||||||||
\(717\) | −8.56564e45 | + | 8.56564e45i | −1.75571 | + | 1.75571i | ||||
\(718\) | −7.35724e45 | − | 7.35724e45i | −1.47477 | − | 1.47477i | ||||
\(719\) | − | 6.10592e45i | − | 1.19698i | −0.801128 | − | 0.598492i | \(-0.795767\pi\) | ||
0.801128 | − | 0.598492i | \(-0.204233\pi\) | |||||||
\(720\) | 1.33733e46 | + | 7.51265e45i | 2.56401 | + | 1.44037i | ||||
\(721\) | −1.74031e45 | −0.326333 | ||||||||
\(722\) | 4.49063e45 | − | 4.49063e45i | 0.823592 | − | 0.823592i | ||||
\(723\) | 8.68279e44 | + | 8.68279e44i | 0.155757 | + | 0.155757i | ||||
\(724\) | − | 1.15470e45i | − | 0.202606i | ||||||
\(725\) | −2.27174e45 | + | 1.38388e45i | −0.389898 | + | 0.237515i | ||||
\(726\) | −3.66540e46 | −6.15369 | ||||||||
\(727\) | 6.94891e44 | − | 6.94891e44i | 0.114121 | − | 0.114121i | −0.647740 | − | 0.761861i | \(-0.724286\pi\) |
0.761861 | + | 0.647740i | \(0.224286\pi\) | |||||||
\(728\) | 2.71368e43 | + | 2.71368e43i | 0.00435970 | + | 0.00435970i | ||||
\(729\) | − | 1.05341e46i | − | 1.65560i | ||||||
\(730\) | −7.18983e43 | + | 1.27987e44i | −0.0110549 | + | 0.0196788i | ||||
\(731\) | −9.18222e44 | −0.138124 | ||||||||
\(732\) | −5.56208e45 | + | 5.56208e45i | −0.818578 | + | 0.818578i | ||||
\(733\) | 1.20300e45 | + | 1.20300e45i | 0.173222 | + | 0.173222i | 0.788393 | − | 0.615172i | \(-0.210913\pi\) |
−0.615172 | + | 0.788393i | \(0.710913\pi\) | |||||||
\(734\) | 1.36377e46i | 1.92134i | ||||||||
\(735\) | −2.95562e45 | − | 1.05331e46i | −0.407428 | − | 1.45197i | ||||
\(736\) | 8.13273e45 | 1.09696 | ||||||||
\(737\) | 1.28512e46 | − | 1.28512e46i | 1.69615 | − | 1.69615i | ||||
\(738\) | −5.11391e45 | − | 5.11391e45i | −0.660467 | − | 0.660467i | ||||
\(739\) | − | 1.35977e46i | − | 1.71853i | −0.511534 | − | 0.859263i | \(-0.670923\pi\) | ||
0.511534 | − | 0.859263i | \(-0.329077\pi\) | |||||||
\(740\) | 1.58847e45 | − | 4.45729e44i | 0.196458 | − | 0.0551269i | ||||
\(741\) | −2.55570e44 | −0.0309327 | ||||||||
\(742\) | 1.00632e44 | − | 1.00632e44i | 0.0119199 | − | 0.0119199i | ||||
\(743\) | 8.14315e45 | + | 8.14315e45i | 0.943999 | + | 0.943999i | 0.998513 | − | 0.0545140i | \(-0.0173609\pi\) |
−0.0545140 | + | 0.998513i | \(0.517361\pi\) | |||||||
\(744\) | 6.08981e45i | 0.690934i | ||||||||
\(745\) | −1.11586e46 | − | 6.26847e45i | −1.23910 | − | 0.696084i | ||||
\(746\) | 3.66374e45 | 0.398202 | ||||||||
\(747\) | −1.41339e46 | + | 1.41339e46i | −1.50360 | + | 1.50360i | ||||
\(748\) | 2.81133e45 | + | 2.81133e45i | 0.292743 | + | 0.292743i | ||||
\(749\) | − | 4.47108e45i | − | 0.455726i | ||||||
\(750\) | 2.49780e46 | − | 8.82245e44i | 2.49217 | − | 0.0880256i | ||||
\(751\) | −5.49332e44 | −0.0536532 | −0.0268266 | − | 0.999640i | \(-0.508540\pi\) | ||||
−0.0268266 | + | 0.999640i | \(0.508540\pi\) | |||||||
\(752\) | −5.40980e45 | + | 5.40980e45i | −0.517244 | + | 0.517244i | ||||
\(753\) | 2.94657e45 | + | 2.94657e45i | 0.275802 | + | 0.275802i | ||||
\(754\) | 3.09353e44i | 0.0283474i | ||||||||
\(755\) | 6.44097e45 | − | 1.14656e46i | 0.577830 | − | 1.02860i | ||||
\(756\) | 1.09481e46 | 0.961589 | ||||||||
\(757\) | −6.12527e45 | + | 6.12527e45i | −0.526734 | + | 0.526734i | −0.919597 | − | 0.392863i | \(-0.871485\pi\) |
0.392863 | + | 0.919597i | \(0.371485\pi\) | |||||||
\(758\) | 1.07879e46 | + | 1.07879e46i | 0.908302 | + | 0.908302i | ||||
\(759\) | 3.66772e46i | 3.02362i | ||||||||
\(760\) | 3.56072e44 | + | 1.26895e45i | 0.0287422 | + | 0.102430i | ||||
\(761\) | −9.60416e45 | −0.759110 | −0.379555 | − | 0.925169i | \(-0.623923\pi\) | ||||
−0.379555 | + | 0.925169i | \(0.623923\pi\) | |||||||
\(762\) | 1.46160e46 | − | 1.46160e46i | 1.13123 | − | 1.13123i | ||||
\(763\) | −6.78684e44 | − | 6.78684e44i | −0.0514369 | − | 0.0514369i | ||||
\(764\) | 1.41325e46i | 1.04888i | ||||||||
\(765\) | 9.51832e45 | − | 2.67087e45i | 0.691795 | − | 0.194120i | ||||
\(766\) | 1.75017e46 | 1.24572 | ||||||||
\(767\) | 3.48283e44 | − | 3.48283e44i | 0.0242776 | − | 0.0242776i | ||||
\(768\) | −2.49999e46 | − | 2.49999e46i | −1.70671 | − | 1.70671i | ||||
\(769\) | 8.25810e45i | 0.552152i | 0.961136 | + | 0.276076i | \(0.0890341\pi\) | ||||
−0.961136 | + | 0.276076i | \(0.910966\pi\) | |||||||
\(770\) | −1.45611e46 | − | 8.17988e45i | −0.953545 | − | 0.535667i | ||||
\(771\) | −2.49355e46 | −1.59937 | ||||||||
\(772\) | −4.75790e45 | + | 4.75790e45i | −0.298909 | + | 0.298909i | ||||
\(773\) | 8.99753e45 | + | 8.99753e45i | 0.553670 | + | 0.553670i | 0.927498 | − | 0.373828i | \(-0.121955\pi\) |
−0.373828 | + | 0.927498i | \(0.621955\pi\) | |||||||
\(774\) | − | 2.66384e46i | − | 1.60565i | ||||||
\(775\) | 1.08390e46 | + | 1.77930e46i | 0.639974 | + | 1.05056i | ||||
\(776\) | −6.10040e45 | −0.352835 | ||||||||
\(777\) | −2.71248e45 | + | 2.71248e45i | −0.153685 | + | 0.153685i | ||||
\(778\) | −2.75252e46 | − | 2.75252e46i | −1.52777 | − | 1.52777i | ||||
\(779\) | − | 1.82580e45i | − | 0.0992782i | ||||||
\(780\) | 6.21464e44 | − | 1.10627e45i | 0.0331057 | − | 0.0589317i | ||||
\(781\) | 3.98803e46 | 2.08133 | ||||||||
\(782\) | 4.58571e45 | − | 4.58571e45i | 0.234476 | − | 0.234476i | ||||
\(783\) | −1.81412e46 | − | 1.81412e46i | −0.908818 | − | 0.908818i | ||||
\(784\) | 1.92774e46i | 0.946220i | ||||||||
\(785\) | −4.65996e45 | − | 1.66069e46i | −0.224113 | − | 0.798683i | ||||
\(786\) | 4.45351e46 | 2.09866 | ||||||||
\(787\) | −5.97003e45 | + | 5.97003e45i | −0.275665 | + | 0.275665i | −0.831376 | − | 0.555711i | \(-0.812446\pi\) |
0.555711 | + | 0.831376i | \(0.312446\pi\) | |||||||
\(788\) | 9.82150e44 | + | 9.82150e44i | 0.0444384 | + | 0.0444384i | ||||
\(789\) | − | 1.21759e46i | − | 0.539846i | ||||||
\(790\) | −5.33585e46 | + | 1.49726e46i | −2.31830 | + | 0.650524i | ||||
\(791\) | 1.52352e46 | 0.648670 | ||||||||
\(792\) | 2.37101e46 | − | 2.37101e46i | 0.989305 | − | 0.989305i | ||||
\(793\) | −6.43339e44 | − | 6.43339e44i | −0.0263069 | − | 0.0263069i | ||||
\(794\) | 1.75915e46i | 0.704977i | ||||||||
\(795\) | 1.19262e45 | + | 6.69969e44i | 0.0468411 | + | 0.0263136i | ||||
\(796\) | 1.95406e45 | 0.0752194 | ||||||||
\(797\) | −2.81050e45 | + | 2.81050e45i | −0.106035 | + | 0.106035i | −0.758134 | − | 0.652099i | \(-0.773889\pi\) |
0.652099 | + | 0.758134i | \(0.273889\pi\) | |||||||
\(798\) | 7.45371e45 | + | 7.45371e45i | 0.275630 | + | 0.275630i | ||||
\(799\) | 4.93079e45i | 0.178718i | ||||||||
\(800\) | −3.45903e46 | − | 8.40114e45i | −1.22890 | − | 0.298468i | ||||
\(801\) | −1.06589e47 | −3.71187 | ||||||||
\(802\) | −1.10143e46 | + | 1.10143e46i | −0.375982 | + | 0.375982i | ||||
\(803\) | 6.66714e44 | + | 6.66714e44i | 0.0223095 | + | 0.0223095i | ||||
\(804\) | − | 5.69518e46i | − | 1.86814i | ||||||
\(805\) | −5.82466e45 | + | 1.03685e46i | −0.187299 | + | 0.333413i | ||||
\(806\) | 2.42295e45 | 0.0763808 | ||||||||
\(807\) | 2.33835e45 | − | 2.33835e45i | 0.0722659 | − | 0.0722659i | ||||
\(808\) | 4.13123e45 | + | 4.13123e45i | 0.125169 | + | 0.125169i | ||||
\(809\) | − | 3.72812e45i | − | 0.110742i | −0.998466 | − | 0.0553712i | \(-0.982366\pi\) | ||
0.998466 | − | 0.0553712i | \(-0.0176342\pi\) | |||||||
\(810\) | 3.41807e46 | + | 1.21812e47i | 0.995453 | + | 3.54755i | ||||
\(811\) | 6.62284e46 | 1.89108 | 0.945542 | − | 0.325501i | \(-0.105533\pi\) | ||||
0.945542 | + | 0.325501i | \(0.105533\pi\) | |||||||
\(812\) | 3.93864e45 | − | 3.93864e45i | 0.110268 | − | 0.110268i | ||||
\(813\) | 8.86579e46 | + | 8.86579e46i | 2.43371 | + | 2.43371i | ||||
\(814\) | − | 2.42738e46i | − | 0.653351i | ||||||
\(815\) | −1.58667e46 | + | 4.45225e45i | −0.418759 | + | 0.117505i | ||||
\(816\) | −2.43774e46 | −0.630876 | ||||||||
\(817\) | 4.75530e45 | − | 4.75530e45i | 0.120677 | − | 0.120677i | ||||
\(818\) | −3.91256e46 | − | 3.91256e46i | −0.973662 | − | 0.973662i | ||||
\(819\) | 2.10831e45i | 0.0514508i | ||||||||
\(820\) | 7.90326e45 | + | 4.43976e45i | 0.189140 | + | 0.106252i | ||||
\(821\) | 2.29806e45 | 0.0539350 | 0.0269675 | − | 0.999636i | \(-0.491415\pi\) | ||||
0.0269675 | + | 0.999636i | \(0.491415\pi\) | |||||||
\(822\) | 7.77597e46 | − | 7.77597e46i | 1.78980 | − | 1.78980i | ||||
\(823\) | −2.97171e46 | − | 2.97171e46i | −0.670824 | − | 0.670824i | 0.287082 | − | 0.957906i | \(-0.407315\pi\) |
−0.957906 | + | 0.287082i | \(0.907315\pi\) | |||||||
\(824\) | 1.00320e46i | 0.222103i | ||||||||
\(825\) | 3.78877e46 | − | 1.55996e47i | 0.822687 | − | 3.38728i | ||||
\(826\) | −2.03154e46 | −0.432657 | ||||||||
\(827\) | −3.13882e45 | + | 3.13882e45i | −0.0655659 | + | 0.0655659i | −0.739129 | − | 0.673563i | \(-0.764763\pi\) |
0.673563 | + | 0.739129i | \(0.264763\pi\) | |||||||
\(828\) | 5.80759e46 | + | 5.80759e46i | 1.18990 | + | 1.18990i | ||||
\(829\) | − | 3.33751e46i | − | 0.670733i | −0.942088 | − | 0.335367i | \(-0.891140\pi\) | ||
0.942088 | − | 0.335367i | \(-0.108860\pi\) | |||||||
\(830\) | 2.81087e46 | − | 5.00364e46i | 0.554103 | − | 0.986363i | ||||
\(831\) | −4.15159e46 | −0.802782 | ||||||||
\(832\) | −8.86507e44 | + | 8.86507e44i | −0.0168155 | + | 0.0168155i | ||||
\(833\) | 8.78526e45 | + | 8.78526e45i | 0.163469 | + | 0.163469i | ||||
\(834\) | 1.16017e47i | 2.11770i | ||||||||
\(835\) | 1.71692e46 | + | 6.11869e46i | 0.307445 | + | 1.09566i | ||||
\(836\) | −2.91187e46 | −0.511531 | ||||||||
\(837\) | −1.42087e47 | + | 1.42087e47i | −2.44877 | + | 2.44877i | ||||
\(838\) | −1.07301e46 | − | 1.07301e46i | −0.181426 | − | 0.181426i | ||||
\(839\) | − | 9.14852e46i | − | 1.51761i | −0.651320 | − | 0.758803i | \(-0.725784\pi\) | ||
0.651320 | − | 0.758803i | \(-0.274216\pi\) | |||||||
\(840\) | 1.46488e46 | − | 4.11050e45i | 0.238415 | − | 0.0669000i | ||||
\(841\) | 4.95705e46 | 0.791566 | ||||||||
\(842\) | 9.65926e45 | − | 9.65926e45i | 0.151339 | − | 0.151339i | ||||
\(843\) | 1.43406e47 | + | 1.43406e47i | 2.20458 | + | 2.20458i | ||||
\(844\) | 4.43692e46i | 0.669272i | ||||||||
\(845\) | −5.87766e46 | − | 3.30186e46i | −0.869956 | − | 0.488710i | ||||
\(846\) | −1.43046e47 | −2.07755 | ||||||||
\(847\) | −5.39780e46 | + | 5.39780e46i | −0.769276 | + | 0.769276i | ||||
\(848\) | −1.70443e45 | − | 1.70443e45i | −0.0238367 | − | 0.0238367i | ||||
\(849\) | − | 1.96107e47i | − | 2.69135i | ||||||
\(850\) | −2.42411e46 | + | 1.47670e46i | −0.326475 | + | 0.198879i | ||||
\(851\) | −1.72847e46 | −0.228448 | ||||||||
\(852\) | 8.83672e46 | − | 8.83672e46i | 1.14619 | − | 1.14619i | ||||
\(853\) | 2.77072e45 | + | 2.77072e45i | 0.0352702 | + | 0.0352702i | 0.724522 | − | 0.689252i | \(-0.242061\pi\) |
−0.689252 | + | 0.724522i | \(0.742061\pi\) | |||||||
\(854\) | 3.75261e46i | 0.468821i | ||||||||
\(855\) | −3.54616e46 | + | 6.31255e46i | −0.434811 | + | 0.774011i | ||||
\(856\) | −2.57737e46 | −0.310167 | ||||||||
\(857\) | 6.39131e46 | − | 6.39131e46i | 0.754913 | − | 0.754913i | −0.220479 | − | 0.975392i | \(-0.570762\pi\) |
0.975392 | + | 0.220479i | \(0.0707621\pi\) | |||||||
\(858\) | −1.32010e46 | − | 1.32010e46i | −0.153042 | − | 0.153042i | ||||
\(859\) | − | 4.12309e45i | − | 0.0469172i | −0.999725 | − | 0.0234586i | \(-0.992532\pi\) | ||
0.999725 | − | 0.0234586i | \(-0.00746779\pi\) | |||||||
\(860\) | 9.02067e45 | + | 3.21474e46i | 0.100754 | + | 0.359063i | ||||
\(861\) | −2.10771e46 | −0.231079 | ||||||||
\(862\) | 3.13261e45 | − | 3.13261e45i | 0.0337124 | − | 0.0337124i | ||||
\(863\) | 5.82335e46 | + | 5.82335e46i | 0.615177 | + | 0.615177i | 0.944290 | − | 0.329113i | \(-0.106750\pi\) |
−0.329113 | + | 0.944290i | \(0.606750\pi\) | |||||||
\(864\) | − | 3.43311e47i | − | 3.56015i | ||||||
\(865\) | −1.11942e47 | + | 3.14113e46i | −1.13956 | + | 0.319763i | ||||
\(866\) | 2.65982e46 | 0.265806 | ||||||||
\(867\) | 1.23808e47 | − | 1.23808e47i | 1.21463 | − | 1.21463i | ||||
\(868\) | −3.08487e46 | − | 3.08487e46i | −0.297113 | − | 0.297113i | ||||
\(869\) | 3.55953e47i | 3.36571i | ||||||||
\(870\) | 1.06926e47 | + | 6.00670e46i | 0.992600 | + | 0.557607i | ||||
\(871\) | 6.58734e45 | 0.0600371 | ||||||||
\(872\) | −3.91229e45 | + | 3.91229e45i | −0.0350080 | + | 0.0350080i | ||||
\(873\) | −2.36976e47 | − | 2.36976e47i | −2.08198 | − | 2.08198i | ||||
\(874\) | 4.74970e46i | 0.409716i | ||||||||
\(875\) | 3.54843e46 | − | 3.80828e46i | 0.300544 | − | 0.322552i | ||||
\(876\) | 2.95462e45 | 0.0245718 | ||||||||
\(877\) | −9.98969e45 | + | 9.98969e45i | −0.0815753 | + | 0.0815753i | −0.746717 | − | 0.665142i | \(-0.768371\pi\) |
0.665142 | + | 0.746717i | \(0.268371\pi\) | |||||||
\(878\) | −6.57963e46 | − | 6.57963e46i | −0.527581 | − | 0.527581i | ||||
\(879\) | − | 6.26044e46i | − | 0.492927i | ||||||
\(880\) | −1.38545e47 | + | 2.46625e47i | −1.07119 | + | 1.90684i | ||||
\(881\) | −8.52837e46 | −0.647517 | −0.323759 | − | 0.946140i | \(-0.604947\pi\) | ||||
−0.323759 | + | 0.946140i | \(0.604947\pi\) | |||||||
\(882\) | −2.54867e47 | + | 2.54867e47i | −1.90028 | + | 1.90028i | ||||
\(883\) | −9.99368e46 | − | 9.99368e46i | −0.731736 | − | 0.731736i | 0.239228 | − | 0.970964i | \(-0.423106\pi\) |
−0.970964 | + | 0.239228i | \(0.923106\pi\) | |||||||
\(884\) | 1.44104e45i | 0.0103619i | ||||||||
\(885\) | −5.27556e46 | − | 1.88008e47i | −0.372543 | − | 1.32765i | ||||
\(886\) | 2.99786e47 | 2.07908 | ||||||||
\(887\) | 7.88123e46 | − | 7.88123e46i | 0.536805 | − | 0.536805i | −0.385784 | − | 0.922589i | \(-0.626069\pi\) |
0.922589 | + | 0.385784i | \(0.126069\pi\) | |||||||
\(888\) | 1.56362e46 | + | 1.56362e46i | 0.104598 | + | 0.104598i | ||||
\(889\) | − | 4.30482e46i | − | 0.282831i | ||||||
\(890\) | 2.94661e47 | − | 8.26827e46i | 1.90144 | − | 0.533549i | ||||
\(891\) | 8.12601e47 | 5.15032 | ||||||||
\(892\) | −1.14839e47 | + | 1.14839e47i | −0.714910 | + | 0.714910i | ||||
\(893\) | −2.55356e46 | − | 2.55356e46i | −0.156143 | − | 0.156143i | ||||
\(894\) | 5.90086e47i | 3.54417i | ||||||||
\(895\) | 1.24094e47 | + | 6.97114e46i | 0.732119 | + | 0.411278i | ||||
\(896\) | −4.44952e46 | −0.257861 | ||||||||
\(897\) | −9.40007e45 | + | 9.40007e45i | −0.0535121 | + | 0.0535121i | ||||
\(898\) | 1.84651e47 | + | 1.84651e47i | 1.03260 | + | 1.03260i | ||||
\(899\) | 1.02234e47i | 0.561616i | ||||||||
\(900\) | −1.87017e47 | − | 3.07002e47i | −1.00926 | − | 1.65677i | ||||
\(901\) | −1.55352e45 | −0.00823606 | ||||||||
\(902\) | 9.43085e46 | − | 9.43085e46i | 0.491186 | − | 0.491186i | ||||
\(903\) | −5.48953e46 | − | 5.48953e46i | −0.280887 | − | 0.280887i | ||||
\(904\) | − | 8.78237e46i | − | 0.441486i | ||||||
\(905\) | 2.59330e46 | − | 4.61635e46i | 0.128078 | − | 0.227993i | ||||
\(906\) | −6.06324e47 | −2.94208 | ||||||||
\(907\) | −3.38706e46 | + | 3.38706e46i | −0.161475 | + | 0.161475i | −0.783220 | − | 0.621745i | \(-0.786424\pi\) |
0.621745 | + | 0.783220i | \(0.286424\pi\) | |||||||
\(908\) | 8.68503e46 | + | 8.68503e46i | 0.406816 | + | 0.406816i | ||||
\(909\) | 3.20963e47i | 1.47718i | ||||||||
\(910\) | −1.63545e45 | − | 5.82832e45i | −0.00739561 | − | 0.0263561i | ||||
\(911\) | 2.31019e47 | 1.02649 | 0.513244 | − | 0.858243i | \(-0.328444\pi\) | ||||
0.513244 | + | 0.858243i | \(0.328444\pi\) | |||||||
\(912\) | 1.26246e47 | − | 1.26246e47i | 0.551187 | − | 0.551187i | ||||
\(913\) | −2.60652e47 | − | 2.60652e47i | −1.11822 | − | 1.11822i | ||||
\(914\) | − | 3.57186e47i | − | 1.50576i | ||||||
\(915\) | −3.47283e47 | + | 9.74488e46i | −1.43862 | + | 0.403682i | ||||
\(916\) | −3.23427e46 | −0.131659 | ||||||||
\(917\) | 6.55839e46 | − | 6.55839e46i | 0.262354 | − | 0.262354i | ||||
\(918\) | −1.93579e47 | − | 1.93579e47i | −0.760984 | − | 0.760984i | ||||
\(919\) | − | 1.98583e47i | − | 0.767173i | −0.923505 | − | 0.383587i | \(-0.874689\pi\) | ||
0.923505 | − | 0.383587i | \(-0.125311\pi\) | |||||||
\(920\) | 5.97696e46 | + | 3.35764e46i | 0.226921 | + | 0.127476i | ||||
\(921\) | −5.33830e47 | −1.99181 | ||||||||
\(922\) | 1.44513e47 | − | 1.44513e47i | 0.529922 | − | 0.529922i | ||||
\(923\) | 1.02210e46 | + | 1.02210e46i | 0.0368355 | + | 0.0368355i | ||||
\(924\) | 3.36147e47i | 1.19063i | ||||||||
\(925\) | 7.35156e46 | + | 1.78551e46i | 0.255924 | + | 0.0621578i | ||||
\(926\) | −1.04249e47 | −0.356694 | ||||||||
\(927\) | −3.89704e47 | + | 3.89704e47i | −1.31057 | + | 1.31057i | ||||
\(928\) | −1.23509e47 | − | 1.23509e47i | −0.408253 | − | 0.408253i | ||||
\(929\) | 1.82549e47i | 0.593099i | 0.955018 | + | 0.296549i | \(0.0958360\pi\) | ||||
−0.955018 | + | 0.296549i | \(0.904164\pi\) | |||||||
\(930\) | 4.70464e47 | − | 8.37477e47i | 1.50245 | − | 2.67452i | ||||
\(931\) | −9.09944e46 | −0.285640 | ||||||||
\(932\) | 3.22520e46 | − | 3.22520e46i | 0.0995182 | − | 0.0995182i | ||||
\(933\) | 5.70521e47 | + | 5.70521e47i | 1.73048 | + | 1.73048i | ||||
\(934\) | − | 6.33347e47i | − | 1.88839i | ||||||
\(935\) | 4.92551e46 | + | 1.75533e47i | 0.144366 | + | 0.514485i | ||||
\(936\) | 1.21534e46 | 0.0350175 | ||||||||
\(937\) | 3.05648e47 | − | 3.05648e47i | 0.865741 | − | 0.865741i | −0.126257 | − | 0.991998i | \(-0.540296\pi\) |
0.991998 | + | 0.126257i | \(0.0402963\pi\) | |||||||
\(938\) | −1.92120e47 | − | 1.92120e47i | −0.534967 | − | 0.534967i | ||||
\(939\) | − | 6.70271e45i | − | 0.0183485i | ||||||
\(940\) | 1.72630e47 | − | 4.84404e46i | 0.464590 | − | 0.130365i | ||||
\(941\) | −5.84361e47 | −1.54613 | −0.773067 | − | 0.634325i | \(-0.781278\pi\) | ||||
−0.773067 | + | 0.634325i | \(0.781278\pi\) | |||||||
\(942\) | −5.62317e47 | + | 5.62317e47i | −1.46274 | + | 1.46274i | ||||
\(943\) | −6.71544e46 | − | 6.71544e46i | −0.171746 | − | 0.171746i | ||||
\(944\) | 3.44088e47i | 0.865201i | ||||||||
\(945\) | 4.37692e47 | + | 2.45880e47i | 1.08208 | + | 0.607874i | ||||
\(946\) | 4.91253e47 | 1.19412 | ||||||||
\(947\) | −4.71287e47 | + | 4.71287e47i | −1.12638 | + | 1.12638i | −0.135621 | + | 0.990761i | \(0.543303\pi\) |
−0.990761 | + | 0.135621i | \(0.956697\pi\) | |||||||
\(948\) | 7.88724e47 | + | 7.88724e47i | 1.85350 | + | 1.85350i | ||||
\(949\) | 3.41747e44i | 0.000789669i | ||||||||
\(950\) | 4.90646e46 | − | 2.02015e47i | 0.111478 | − | 0.458994i | ||||
\(951\) | 7.73635e47 | 1.72841 | ||||||||
\(952\) | −1.22180e46 | + | 1.22180e46i | −0.0268417 | + | 0.0268417i | ||||
\(953\) | −6.90714e46 | − | 6.90714e46i | −0.149215 | − | 0.149215i | 0.628552 | − | 0.777767i | \(-0.283648\pi\) |
−0.777767 | + | 0.628552i | \(0.783648\pi\) | |||||||
\(954\) | − | 4.50688e46i | − | 0.0957418i | ||||||
\(955\) | −3.17397e47 | + | 5.65001e47i | −0.663054 | + | 1.18031i | ||||
\(956\) | −5.00250e47 | −1.02769 | ||||||||
\(957\) | 5.57002e47 | − | 5.57002e47i | 1.12529 | − | 1.12529i | ||||
\(958\) | −6.98854e47 | − | 6.98854e47i | −1.38848 | − | 1.38848i | ||||
\(959\) | − | 2.29023e47i | − | 0.447489i | ||||||
\(960\) | 1.34282e47 | + | 4.78548e47i | 0.258035 | + | 0.919572i | ||||
\(961\) | 2.71583e47 | 0.513249 | ||||||||
\(962\) | 6.22117e45 | − | 6.22117e45i | 0.0115630 | − | 0.0115630i | ||||
\(963\) | −1.00120e48 | − | 1.00120e48i | −1.83021 | − | 1.83021i | ||||
\(964\) | 5.07092e46i | 0.0911705i | ||||||||
\(965\) | −2.97072e47 | + | 8.33594e46i | −0.525321 | + | 0.147407i | ||||
\(966\) | 5.48307e47 | 0.953652 | ||||||||
\(967\) | −4.56680e47 | + | 4.56680e47i | −0.781246 | + | 0.781246i | −0.980041 | − | 0.198795i | \(-0.936297\pi\) |
0.198795 | + | 0.980041i | \(0.436297\pi\) | |||||||
\(968\) | 3.11158e47 | + | 3.11158e47i | 0.523570 | + | 0.523570i | ||||
\(969\) | − | 1.15067e47i | − | 0.190446i | ||||||
\(970\) | 8.38934e47 | + | 4.71283e47i | 1.36578 | + | 0.767245i | ||||
\(971\) | −6.57885e47 | −1.05352 | −0.526759 | − | 0.850015i | \(-0.676593\pi\) | ||||
−0.526759 | + | 0.850015i | \(0.676593\pi\) | |||||||
\(972\) | 8.21476e47 | − | 8.21476e47i | 1.29400 | − | 1.29400i | ||||
\(973\) | 1.70851e47 | + | 1.70851e47i | 0.264735 | + | 0.264735i | ||||
\(974\) | 4.10788e46i | 0.0626145i | ||||||||
\(975\) | 4.96909e46 | − | 3.02703e46i | 0.0745081 | − | 0.0453882i | ||||
\(976\) | 6.35590e47 | 0.937519 | ||||||||
\(977\) | −2.76328e47 | + | 2.76328e47i | −0.400970 | + | 0.400970i | −0.878575 | − | 0.477605i | \(-0.841505\pi\) |
0.477605 | + | 0.878575i | \(0.341505\pi\) | |||||||
\(978\) | 5.37252e47 | + | 5.37252e47i | 0.766931 | + | 0.766931i | ||||
\(979\) | − | 1.96567e48i | − | 2.76050i | ||||||
\(980\) | 2.21269e47 | − | 3.93883e47i | 0.305706 | − | 0.544190i | ||||
\(981\) | −3.03953e47 | −0.413145 | ||||||||
\(982\) | 5.92444e47 | − | 5.92444e47i | 0.792252 | − | 0.792252i | ||||
\(983\) | 8.18609e47 | + | 8.18609e47i | 1.07701 | + | 1.07701i | 0.996776 | + | 0.0802353i | \(0.0255672\pi\) |
0.0802353 | + | 0.996776i | \(0.474433\pi\) | |||||||
\(984\) | 1.21500e47i | 0.157273i | ||||||||
\(985\) | 1.72075e46 | + | 6.13231e46i | 0.0219148 | + | 0.0780988i | ||||
\(986\) | −1.39283e47 | −0.174529 | ||||||||
\(987\) | −2.94784e47 | + | 2.94784e47i | −0.363438 | + | 0.363438i | ||||
\(988\) | −7.46289e45 | − | 7.46289e45i | −0.00905307 | − | 0.00905307i | ||||
\(989\) | − | 3.49808e47i | − | 0.417531i | ||||||
\(990\) | −5.09235e48 | + | 1.42893e48i | −5.98074 | + | 1.67822i | ||||
\(991\) | 1.04066e48 | 1.20263 | 0.601314 | − | 0.799013i | \(-0.294644\pi\) | ||||
0.601314 | + | 0.799013i | \(0.294644\pi\) | |||||||
\(992\) | −9.67358e47 | + | 9.67358e47i | −1.10002 | + | 1.10002i | ||||
\(993\) | 6.40147e47 | + | 6.40147e47i | 0.716295 | + | 0.716295i | ||||
\(994\) | − | 5.96192e47i | − | 0.656454i | ||||||
\(995\) | 7.81213e46 | + | 4.38857e46i | 0.0846448 | + | 0.0475504i | ||||
\(996\) | −1.15511e48 | −1.23161 | ||||||||
\(997\) | −2.58439e47 | + | 2.58439e47i | −0.271167 | + | 0.271167i | −0.829570 | − | 0.558403i | \(-0.811414\pi\) |
0.558403 | + | 0.829570i | \(0.311414\pi\) | |||||||
\(998\) | 1.74239e47 | + | 1.74239e47i | 0.179910 | + | 0.179910i | ||||
\(999\) | 7.29648e47i | 0.741422i |
(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 | 5.33.c.a.3.12 | yes | 30 | |
5.2 | odd | 4 | inner | 5.33.c.a.2.12 | ✓ | 30 | |
5.3 | odd | 4 | 25.33.c.b.7.4 | 30 | |||
5.4 | even | 2 | 25.33.c.b.18.4 | 30 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5.33.c.a.2.12 | ✓ | 30 | 5.2 | odd | 4 | inner | |
5.33.c.a.3.12 | yes | 30 | 1.1 | even | 1 | trivial | |
25.33.c.b.7.4 | 30 | 5.3 | odd | 4 | |||
25.33.c.b.18.4 | 30 | 5.4 | even | 2 |