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 | 2.13 | ||
Character | \(\chi\) | \(=\) | 5.2 |
Dual form | 5.33.c.a.3.13 |
$q$-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 \(\left(\mathbb{Z}/5\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 65410.6 | + | 65410.6i | 0.998086 | + | 0.998086i | 0.999998 | − | 0.00191196i | \(-0.000608598\pi\) |
−0.00191196 | + | 0.999998i | \(0.500609\pi\) | |||||||
\(3\) | −1.37699e7 | + | 1.37699e7i | −0.319882 | + | 0.319882i | −0.848722 | − | 0.528840i | \(-0.822627\pi\) |
0.528840 | + | 0.848722i | \(0.322627\pi\) | |||||||
\(4\) | 4.26212e9i | 0.992352i | ||||||||
\(5\) | 5.68539e10 | − | 1.41600e11i | 0.372598 | − | 0.927993i | ||||
\(6\) | −1.80139e12 | −0.638540 | ||||||||
\(7\) | −2.41000e12 | − | 2.41000e12i | −0.0725186 | − | 0.0725186i | 0.669917 | − | 0.742436i | \(-0.266330\pi\) |
−0.742436 | + | 0.669917i | \(0.766330\pi\) | |||||||
\(8\) | 2.14856e12 | − | 2.14856e12i | 0.00763321 | − | 0.00763321i | ||||
\(9\) | 1.47380e15i | 0.795351i | ||||||||
\(10\) | 1.29810e16 | − | 5.54333e15i | 1.29810 | − | 0.554333i | ||||
\(11\) | 4.03786e16 | 0.878756 | 0.439378 | − | 0.898302i | \(-0.355199\pi\) | ||||
0.439378 | + | 0.898302i | \(0.355199\pi\) | |||||||
\(12\) | −5.86889e16 | − | 5.86889e16i | −0.317436 | − | 0.317436i | ||||
\(13\) | −2.33631e17 | + | 2.33631e17i | −0.351105 | + | 0.351105i | −0.860520 | − | 0.509416i | \(-0.829862\pi\) |
0.509416 | + | 0.860520i | \(0.329862\pi\) | |||||||
\(14\) | − | 3.15280e17i | − | 0.144760i | ||||||
\(15\) | 1.16695e18 | + | 2.73269e18i | 0.177661 | + | 0.416036i | ||||
\(16\) | 1.85867e19 | 1.00759 | ||||||||
\(17\) | 5.44103e19 | + | 5.44103e19i | 1.11815 | + | 1.11815i | 0.992013 | + | 0.126133i | \(0.0402566\pi\) |
0.126133 | + | 0.992013i | \(0.459743\pi\) | |||||||
\(18\) | −9.64022e19 | + | 9.64022e19i | −0.793829 | + | 0.793829i | ||||
\(19\) | 2.36248e20i | 0.819051i | 0.912299 | + | 0.409526i | \(0.134306\pi\) | ||||
−0.912299 | + | 0.409526i | \(0.865694\pi\) | |||||||
\(20\) | 6.03518e20 | + | 2.42318e20i | 0.920896 | + | 0.369748i | ||||
\(21\) | 6.63710e19 | 0.0463948 | ||||||||
\(22\) | 2.64119e21 | + | 2.64119e21i | 0.877074 | + | 0.877074i | ||||
\(23\) | 9.56472e20 | − | 9.56472e20i | 0.155965 | − | 0.155965i | −0.624811 | − | 0.780776i | \(-0.714824\pi\) |
0.780776 | + | 0.624811i | \(0.214824\pi\) | |||||||
\(24\) | 5.91707e19i | 0.00488345i | ||||||||
\(25\) | −1.68183e22 | − | 1.61011e22i | −0.722342 | − | 0.691536i | ||||
\(26\) | −3.05639e22 | −0.700865 | ||||||||
\(27\) | −4.58099e22 | − | 4.58099e22i | −0.574301 | − | 0.574301i | ||||
\(28\) | 1.02717e22 | − | 1.02717e22i | 0.0719639 | − | 0.0719639i | ||||
\(29\) | 1.73763e22i | 0.0694365i | 0.999397 | + | 0.0347183i | \(0.0110534\pi\) | ||||
−0.999397 | + | 0.0347183i | \(0.988947\pi\) | |||||||
\(30\) | −1.02416e23 | + | 2.55078e23i | −0.237918 | + | 0.592561i | ||||
\(31\) | 2.11052e23 | 0.290136 | 0.145068 | − | 0.989422i | \(-0.453660\pi\) | ||||
0.145068 | + | 0.989422i | \(0.453660\pi\) | |||||||
\(32\) | 1.20654e24 | + | 1.20654e24i | 0.998028 | + | 0.998028i | ||||
\(33\) | −5.56009e23 | + | 5.56009e23i | −0.281099 | + | 0.281099i | ||||
\(34\) | 7.11802e24i | 2.23201i | ||||||||
\(35\) | −4.78276e23 | + | 2.04240e23i | −0.0943170 | + | 0.0402765i | ||||
\(36\) | −6.28152e24 | −0.789268 | ||||||||
\(37\) | 1.04242e25 | + | 1.04242e25i | 0.844921 | + | 0.844921i | 0.989494 | − | 0.144573i | \(-0.0461809\pi\) |
−0.144573 | + | 0.989494i | \(0.546181\pi\) | |||||||
\(38\) | −1.54531e25 | + | 1.54531e25i | −0.817484 | + | 0.817484i | ||||
\(39\) | − | 6.43414e24i | − | 0.224624i | ||||||
\(40\) | −1.82083e23 | − | 4.26390e23i | −0.00423945 | − | 0.00992768i | ||||
\(41\) | −3.86953e25 | −0.606899 | −0.303449 | − | 0.952848i | \(-0.598138\pi\) | ||||
−0.303449 | + | 0.952848i | \(0.598138\pi\) | |||||||
\(42\) | 4.34136e24 | + | 4.34136e24i | 0.0463060 | + | 0.0463060i | ||||
\(43\) | −1.15120e26 | + | 1.15120e26i | −0.842667 | + | 0.842667i | −0.989205 | − | 0.146538i | \(-0.953187\pi\) |
0.146538 | + | 0.989205i | \(0.453187\pi\) | |||||||
\(44\) | 1.72098e26i | 0.872036i | ||||||||
\(45\) | 2.08691e26 | + | 8.37913e25i | 0.738080 | + | 0.296346i | ||||
\(46\) | 1.25127e26 | 0.311333 | ||||||||
\(47\) | 5.56550e26 | + | 5.56550e26i | 0.981609 | + | 0.981609i | 0.999834 | − | 0.0182247i | \(-0.00580141\pi\) |
−0.0182247 | + | 0.999834i | \(0.505801\pi\) | |||||||
\(48\) | −2.55937e26 | + | 2.55937e26i | −0.322310 | + | 0.322310i | ||||
\(49\) | − | 1.09281e27i | − | 0.989482i | ||||||
\(50\) | −4.69167e25 | − | 2.15328e27i | −0.0307473 | − | 1.41117i | ||||
\(51\) | −1.49845e27 | −0.715350 | ||||||||
\(52\) | −9.95763e26 | − | 9.95763e26i | −0.348419 | − | 0.348419i | ||||
\(53\) | 1.97322e27 | − | 1.97322e27i | 0.509052 | − | 0.509052i | −0.405183 | − | 0.914235i | \(-0.632792\pi\) |
0.914235 | + | 0.405183i | \(0.132792\pi\) | |||||||
\(54\) | − | 5.99291e27i | − | 1.14640i | ||||||
\(55\) | 2.29568e27 | − | 5.71763e27i | 0.327422 | − | 0.815480i | ||||
\(56\) | −1.03561e25 | −0.00110710 | ||||||||
\(57\) | −3.25311e27 | − | 3.25311e27i | −0.262000 | − | 0.262000i | ||||
\(58\) | −1.13659e27 | + | 1.13659e27i | −0.0693037 | + | 0.0693037i | ||||
\(59\) | 2.24378e28i | 1.04075i | 0.853937 | + | 0.520377i | \(0.174208\pi\) | ||||
−0.853937 | + | 0.520377i | \(0.825792\pi\) | |||||||
\(60\) | −1.16471e28 | + | 4.97369e27i | −0.412854 | + | 0.176302i | ||||
\(61\) | 4.54027e28 | 1.23539 | 0.617695 | − | 0.786418i | \(-0.288067\pi\) | ||||
0.617695 | + | 0.786418i | \(0.288067\pi\) | |||||||
\(62\) | 1.38050e28 | + | 1.38050e28i | 0.289581 | + | 0.289581i | ||||
\(63\) | 3.55187e27 | − | 3.55187e27i | 0.0576777 | − | 0.0576777i | ||||
\(64\) | 7.80117e28i | 0.984646i | ||||||||
\(65\) | 1.97994e28 | + | 4.63651e28i | 0.195002 | + | 0.456643i | ||||
\(66\) | −7.27377e28 | −0.561121 | ||||||||
\(67\) | −1.71739e29 | − | 1.71739e29i | −1.04153 | − | 1.04153i | −0.999099 | − | 0.0424295i | \(-0.986490\pi\) |
−0.0424295 | − | 0.999099i | \(-0.513510\pi\) | |||||||
\(68\) | −2.31903e29 | + | 2.31903e29i | −1.10959 | + | 1.10959i | ||||
\(69\) | 2.63410e28i | 0.0997808i | ||||||||
\(70\) | −4.46437e28 | − | 1.79249e28i | −0.134336 | − | 0.0539371i | ||||
\(71\) | 4.36893e29 | 1.04771 | 0.523855 | − | 0.851807i | \(-0.324493\pi\) | ||||
0.523855 | + | 0.851807i | \(0.324493\pi\) | |||||||
\(72\) | 3.16654e27 | + | 3.16654e27i | 0.00607108 | + | 0.00607108i | ||||
\(73\) | 6.60223e29 | − | 6.60223e29i | 1.01514 | − | 1.01514i | 0.0152535 | − | 0.999884i | \(-0.495144\pi\) |
0.999884 | − | 0.0152535i | \(-0.00485552\pi\) | |||||||
\(74\) | 1.36371e30i | 1.68661i | ||||||||
\(75\) | 4.53296e29 | − | 9.87664e27i | 0.452274 | − | 0.00985437i | ||||
\(76\) | −1.00692e30 | −0.812787 | ||||||||
\(77\) | −9.73126e28 | − | 9.73126e28i | −0.0637261 | − | 0.0637261i | ||||
\(78\) | 4.20861e29 | − | 4.20861e29i | 0.224194 | − | 0.224194i | ||||
\(79\) | − | 2.22778e30i | − | 0.967918i | −0.875091 | − | 0.483959i | \(-0.839198\pi\) | ||
0.875091 | − | 0.483959i | \(-0.160802\pi\) | |||||||
\(80\) | 1.05673e30 | − | 2.63189e30i | 0.375425 | − | 0.935036i | ||||
\(81\) | −1.46939e30 | −0.427933 | ||||||||
\(82\) | −2.53108e30 | − | 2.53108e30i | −0.605737 | − | 0.605737i | ||||
\(83\) | 1.54776e30 | − | 1.54776e30i | 0.305108 | − | 0.305108i | −0.537901 | − | 0.843008i | \(-0.680782\pi\) |
0.843008 | + | 0.537901i | \(0.180782\pi\) | |||||||
\(84\) | 2.82881e29i | 0.0460400i | ||||||||
\(85\) | 1.07980e31 | − | 4.61109e30i | 1.45425 | − | 0.621013i | ||||
\(86\) | −1.50602e31 | −1.68211 | ||||||||
\(87\) | −2.39269e29 | − | 2.39269e29i | −0.0222115 | − | 0.0222115i | ||||
\(88\) | 8.67557e28 | − | 8.67557e28i | 0.00670773 | − | 0.00670773i | ||||
\(89\) | 2.18479e31i | 1.40984i | 0.709288 | + | 0.704919i | \(0.249017\pi\) | ||||
−0.709288 | + | 0.704919i | \(0.750983\pi\) | |||||||
\(90\) | 8.16976e30 | + | 1.91314e31i | 0.440889 | + | 1.03245i | ||||
\(91\) | 1.12610e30 | 0.0509232 | ||||||||
\(92\) | 4.07660e30 | + | 4.07660e30i | 0.154772 | + | 0.154772i | ||||
\(93\) | −2.90615e30 | + | 2.90615e30i | −0.0928093 | + | 0.0928093i | ||||
\(94\) | 7.28085e31i | 1.95946i | ||||||||
\(95\) | 3.34529e31 | + | 1.34316e31i | 0.760074 | + | 0.305176i | ||||
\(96\) | −3.32279e31 | −0.638503 | ||||||||
\(97\) | −7.63959e31 | − | 7.63959e31i | −1.24372 | − | 1.24372i | −0.958447 | − | 0.285272i | \(-0.907916\pi\) |
−0.285272 | − | 0.958447i | \(-0.592084\pi\) | |||||||
\(98\) | 7.14814e31 | − | 7.14814e31i | 0.987588 | − | 0.987588i | ||||
\(99\) | 5.95100e31i | 0.698919i | ||||||||
\(100\) | 6.86247e31 | − | 7.16818e31i | 0.686247 | − | 0.716818i | ||||
\(101\) | −1.39281e32 | −1.18782 | −0.593908 | − | 0.804533i | \(-0.702416\pi\) | ||||
−0.593908 | + | 0.804533i | \(0.702416\pi\) | |||||||
\(102\) | −9.80143e31 | − | 9.80143e31i | −0.713981 | − | 0.713981i | ||||
\(103\) | 3.23271e31 | − | 3.23271e31i | 0.201452 | − | 0.201452i | −0.599170 | − | 0.800622i | \(-0.704503\pi\) |
0.800622 | + | 0.599170i | \(0.204503\pi\) | |||||||
\(104\) | 1.00394e30i | 0.00536011i | ||||||||
\(105\) | 3.77345e30 | − | 9.39816e30i | 0.0172866 | − | 0.0430541i | ||||
\(106\) | 2.58139e32 | 1.01616 | ||||||||
\(107\) | −6.53958e31 | − | 6.53958e31i | −0.221518 | − | 0.221518i | 0.587619 | − | 0.809138i | \(-0.300065\pi\) |
−0.809138 | + | 0.587619i | \(0.800065\pi\) | |||||||
\(108\) | 1.95247e32 | − | 1.95247e32i | 0.569909 | − | 0.569909i | ||||
\(109\) | 4.51565e32i | 1.13736i | 0.822560 | + | 0.568678i | \(0.192545\pi\) | ||||
−0.822560 | + | 0.568678i | \(0.807455\pi\) | |||||||
\(110\) | 5.24155e32 | − | 2.23832e32i | 1.14071 | − | 0.487123i | ||||
\(111\) | −2.87081e32 | −0.540551 | ||||||||
\(112\) | −4.47941e31 | − | 4.47941e31i | −0.0730689 | − | 0.0730689i | ||||
\(113\) | −2.81489e32 | + | 2.81489e32i | −0.398297 | + | 0.398297i | −0.877632 | − | 0.479335i | \(-0.840878\pi\) |
0.479335 | + | 0.877632i | \(0.340878\pi\) | |||||||
\(114\) | − | 4.25576e32i | − | 0.522997i | ||||||
\(115\) | −8.10578e31 | − | 1.89816e32i | −0.0866222 | − | 0.202847i | ||||
\(116\) | −7.40597e31 | −0.0689055 | ||||||||
\(117\) | −3.44325e32 | − | 3.44325e32i | −0.279251 | − | 0.279251i | ||||
\(118\) | −1.46767e33 | + | 1.46767e33i | −1.03876 | + | 1.03876i | ||||
\(119\) | − | 2.62258e32i | − | 0.162173i | ||||||
\(120\) | 8.37861e30 | + | 3.36409e30i | 0.00453181 | + | 0.00181956i | ||||
\(121\) | −4.80945e32 | −0.227788 | ||||||||
\(122\) | 2.96981e33 | + | 2.96981e33i | 1.23303 | + | 1.23303i | ||||
\(123\) | 5.32829e32 | − | 5.32829e32i | 0.194136 | − | 0.194136i | ||||
\(124\) | 8.99527e32i | 0.287917i | ||||||||
\(125\) | −3.23611e33 | + | 1.46608e33i | −0.910883 | + | 0.412664i | ||||
\(126\) | 4.64659e32 | 0.115135 | ||||||||
\(127\) | 1.16769e33 | + | 1.16769e33i | 0.254957 | + | 0.254957i | 0.822999 | − | 0.568042i | \(-0.192299\pi\) |
−0.568042 | + | 0.822999i | \(0.692299\pi\) | |||||||
\(128\) | 7.92654e31 | − | 7.92654e31i | 0.0152660 | − | 0.0152660i | ||||
\(129\) | − | 3.17038e33i | − | 0.539109i | ||||||
\(130\) | −1.73767e33 | + | 4.32786e33i | −0.261141 | + | 0.650398i | ||||
\(131\) | 1.31659e34 | 1.75029 | 0.875146 | − | 0.483859i | \(-0.160765\pi\) | ||||
0.875146 | + | 0.483859i | \(0.160765\pi\) | |||||||
\(132\) | −2.36978e33 | − | 2.36978e33i | −0.278949 | − | 0.278949i | ||||
\(133\) | 5.69359e32 | − | 5.69359e32i | 0.0593964 | − | 0.0593964i | ||||
\(134\) | − | 2.24671e34i | − | 2.07907i | ||||||
\(135\) | −9.09118e33 | + | 3.88224e33i | −0.746930 | + | 0.318964i | ||||
\(136\) | 2.33807e32 | 0.0170701 | ||||||||
\(137\) | −1.20768e34 | − | 1.20768e34i | −0.784192 | − | 0.784192i | 0.196343 | − | 0.980535i | \(-0.437093\pi\) |
−0.980535 | + | 0.196343i | \(0.937093\pi\) | |||||||
\(138\) | −1.72298e33 | + | 1.72298e33i | −0.0995899 | + | 0.0995899i | ||||
\(139\) | − | 3.31670e34i | − | 1.70792i | −0.520335 | − | 0.853962i | \(-0.674193\pi\) | ||
0.520335 | − | 0.853962i | \(-0.325807\pi\) | |||||||
\(140\) | −8.70494e32 | − | 2.03847e33i | −0.0399685 | − | 0.0935956i | ||||
\(141\) | −1.53273e34 | −0.627999 | ||||||||
\(142\) | 2.85774e34 | + | 2.85774e34i | 1.04571 | + | 1.04571i | ||||
\(143\) | −9.43369e33 | + | 9.43369e33i | −0.308535 | + | 0.308535i | ||||
\(144\) | 2.73932e34i | 0.801387i | ||||||||
\(145\) | 2.46049e33 | + | 9.87907e32i | 0.0644366 | + | 0.0258719i | ||||
\(146\) | 8.63711e34 | 2.02639 | ||||||||
\(147\) | 1.50479e34 | + | 1.50479e34i | 0.316518 | + | 0.316518i | ||||
\(148\) | −4.44293e34 | + | 4.44293e34i | −0.838459 | + | 0.838459i | ||||
\(149\) | 2.73185e34i | 0.462889i | 0.972848 | + | 0.231445i | \(0.0743452\pi\) | ||||
−0.972848 | + | 0.231445i | \(0.925655\pi\) | |||||||
\(150\) | 3.02964e34 | + | 2.90043e34i | 0.461244 | + | 0.441573i | ||||
\(151\) | −1.13348e35 | −1.55161 | −0.775806 | − | 0.630971i | \(-0.782657\pi\) | ||||
−0.775806 | + | 0.630971i | \(0.782657\pi\) | |||||||
\(152\) | 5.07593e32 | + | 5.07593e32i | 0.00625199 | + | 0.00625199i | ||||
\(153\) | −8.01900e34 | + | 8.01900e34i | −0.889318 | + | 0.889318i | ||||
\(154\) | − | 1.27306e34i | − | 0.127208i | ||||||
\(155\) | 1.19991e34 | − | 2.98850e34i | 0.108104 | − | 0.269244i | ||||
\(156\) | 2.74231e34 | 0.222906 | ||||||||
\(157\) | −1.25103e35 | − | 1.25103e35i | −0.918067 | − | 0.918067i | 0.0788216 | − | 0.996889i | \(-0.474884\pi\) |
−0.996889 | + | 0.0788216i | \(0.974884\pi\) | |||||||
\(158\) | 1.45720e35 | − | 1.45720e35i | 0.966066 | − | 0.966066i | ||||
\(159\) | 5.43421e34i | 0.325673i | ||||||||
\(160\) | 2.39443e35 | − | 1.02250e35i | 1.29803 | − | 0.554300i | ||||
\(161\) | −4.61020e33 | −0.0226207 | ||||||||
\(162\) | −9.61135e34 | − | 9.61135e34i | −0.427114 | − | 0.427114i | ||||
\(163\) | −1.85939e35 | + | 1.85939e35i | −0.748806 | + | 0.748806i | −0.974255 | − | 0.225449i | \(-0.927615\pi\) |
0.225449 | + | 0.974255i | \(0.427615\pi\) | |||||||
\(164\) | − | 1.64924e35i | − | 0.602257i | ||||||
\(165\) | 4.71199e34 | + | 1.10342e35i | 0.156121 | + | 0.365594i | ||||
\(166\) | 2.02479e35 | 0.609047 | ||||||||
\(167\) | −3.31985e35 | − | 3.31985e35i | −0.907099 | − | 0.907099i | 0.0889380 | − | 0.996037i | \(-0.471653\pi\) |
−0.996037 | + | 0.0889380i | \(0.971653\pi\) | |||||||
\(168\) | 1.42602e32 | − | 1.42602e32i | 0.000354141 | − | 0.000354141i | ||||
\(169\) | 3.33613e35i | 0.753451i | ||||||||
\(170\) | 1.00792e36 | + | 4.04687e35i | 2.07129 | + | 0.831643i | ||||
\(171\) | −3.48183e35 | −0.651433 | ||||||||
\(172\) | −4.90656e35 | − | 4.90656e35i | −0.836223 | − | 0.836223i | ||||
\(173\) | 5.39012e35 | − | 5.39012e35i | 0.837260 | − | 0.837260i | −0.151237 | − | 0.988497i | \(-0.548326\pi\) |
0.988497 | + | 0.151237i | \(0.0483258\pi\) | |||||||
\(174\) | − | 3.13014e34i | − | 0.0443380i | ||||||
\(175\) | 1.72861e33 | + | 7.93359e34i | 0.00223403 | + | 0.102532i | ||||
\(176\) | 7.50507e35 | 0.885425 | ||||||||
\(177\) | −3.08966e35 | − | 3.08966e35i | −0.332919 | − | 0.332919i | ||||
\(178\) | −1.42908e36 | + | 1.42908e36i | −1.40714 | + | 1.40714i | ||||
\(179\) | − | 1.15335e36i | − | 1.03828i | −0.854691 | − | 0.519138i | \(-0.826253\pi\) | ||
0.854691 | − | 0.519138i | \(-0.173747\pi\) | |||||||
\(180\) | −3.57129e35 | + | 8.89466e35i | −0.294079 | + | 0.732435i | ||||
\(181\) | −1.17921e36 | −0.888657 | −0.444328 | − | 0.895864i | \(-0.646558\pi\) | ||||
−0.444328 | + | 0.895864i | \(0.646558\pi\) | |||||||
\(182\) | 7.36590e34 | + | 7.36590e34i | 0.0508257 | + | 0.0508257i | ||||
\(183\) | −6.25189e35 | + | 6.25189e35i | −0.395179 | + | 0.395179i | ||||
\(184\) | − | 4.11007e33i | − | 0.00238103i | ||||||
\(185\) | 2.06873e36 | − | 8.83418e35i | 1.09890 | − | 0.469265i | ||||
\(186\) | −3.80187e35 | −0.185263 | ||||||||
\(187\) | 2.19701e36 | + | 2.19701e36i | 0.982578 | + | 0.982578i | ||||
\(188\) | −2.37208e36 | + | 2.37208e36i | −0.974102 | + | 0.974102i | ||||
\(189\) | 2.20804e35i | 0.0832949i | ||||||||
\(190\) | 1.30960e36 | + | 3.06674e36i | 0.454027 | + | 1.06321i | ||||
\(191\) | 4.73722e36 | 1.51004 | 0.755022 | − | 0.655700i | \(-0.227626\pi\) | ||||
0.755022 | + | 0.655700i | \(0.227626\pi\) | |||||||
\(192\) | −1.07421e36 | − | 1.07421e36i | −0.314971 | − | 0.314971i | ||||
\(193\) | −2.77871e36 | + | 2.77871e36i | −0.749767 | + | 0.749767i | −0.974435 | − | 0.224669i | \(-0.927870\pi\) |
0.224669 | + | 0.974435i | \(0.427870\pi\) | |||||||
\(194\) | − | 9.99420e36i | − | 2.48268i | ||||||
\(195\) | −9.11077e35 | − | 3.65806e35i | −0.208450 | − | 0.0836945i | ||||
\(196\) | 4.65769e36 | 0.981915 | ||||||||
\(197\) | −1.66306e36 | − | 1.66306e36i | −0.323184 | − | 0.323184i | 0.526803 | − | 0.849987i | \(-0.323390\pi\) |
−0.849987 | + | 0.526803i | \(0.823390\pi\) | |||||||
\(198\) | −3.89259e36 | + | 3.89259e36i | −0.697582 | + | 0.697582i | ||||
\(199\) | − | 1.08501e37i | − | 1.79385i | −0.442185 | − | 0.896924i | \(-0.645796\pi\) | ||
0.442185 | − | 0.896924i | \(-0.354204\pi\) | |||||||
\(200\) | −7.07292e34 | + | 1.54108e33i | −0.0107924 | + | 0.000235151i | ||||
\(201\) | 4.72964e36 | 0.666333 | ||||||||
\(202\) | −9.11044e36 | − | 9.11044e36i | −1.18554 | − | 1.18554i | ||||
\(203\) | 4.18768e34 | − | 4.18768e34i | 0.00503544 | − | 0.00503544i | ||||
\(204\) | − | 6.38656e36i | − | 0.709879i | ||||||
\(205\) | −2.19998e36 | + | 5.47927e36i | −0.226129 | + | 0.563198i | ||||
\(206\) | 4.22907e36 | 0.402133 | ||||||||
\(207\) | 1.40965e36 | + | 1.40965e36i | 0.124047 | + | 0.124047i | ||||
\(208\) | −4.34244e36 | + | 4.34244e36i | −0.353769 | + | 0.353769i | ||||
\(209\) | 9.53938e36i | 0.719746i | ||||||||
\(210\) | 8.61562e35 | − | 3.67916e35i | 0.0602252 | − | 0.0257181i | ||||
\(211\) | 1.30546e37 | 0.845756 | 0.422878 | − | 0.906187i | \(-0.361020\pi\) | ||||
0.422878 | + | 0.906187i | \(0.361020\pi\) | |||||||
\(212\) | 8.41011e36 | + | 8.41011e36i | 0.505159 | + | 0.505159i | ||||
\(213\) | −6.01596e36 | + | 6.01596e36i | −0.335144 | + | 0.335144i | ||||
\(214\) | − | 8.55516e36i | − | 0.442189i | ||||||
\(215\) | 9.75605e36 | + | 2.28461e37i | 0.468014 | + | 1.09597i | ||||
\(216\) | −1.96850e35 | −0.00876751 | ||||||||
\(217\) | −5.08635e35 | − | 5.08635e35i | −0.0210402 | − | 0.0210402i | ||||
\(218\) | −2.95371e37 | + | 2.95371e37i | −1.13518 | + | 1.13518i | ||||
\(219\) | 1.81824e37i | 0.649449i | ||||||||
\(220\) | 2.43692e37 | + | 9.78447e36i | 0.809243 | + | 0.324918i | ||||
\(221\) | −2.54239e37 | −0.785173 | ||||||||
\(222\) | −1.87781e37 | − | 1.87781e37i | −0.539516 | − | 0.539516i | ||||
\(223\) | 1.94206e37 | − | 1.94206e37i | 0.519260 | − | 0.519260i | −0.398087 | − | 0.917348i | \(-0.630326\pi\) |
0.917348 | + | 0.398087i | \(0.130326\pi\) | |||||||
\(224\) | − | 5.81554e36i | − | 0.144751i | ||||||
\(225\) | 2.37298e37 | − | 2.47869e37i | 0.550014 | − | 0.574515i | ||||
\(226\) | −3.68247e37 | −0.795069 | ||||||||
\(227\) | −3.21519e37 | − | 3.21519e37i | −0.646835 | − | 0.646835i | 0.305392 | − | 0.952227i | \(-0.401212\pi\) |
−0.952227 | + | 0.305392i | \(0.901212\pi\) | |||||||
\(228\) | 1.38651e37 | − | 1.38651e37i | 0.259996 | − | 0.259996i | ||||
\(229\) | 1.49373e37i | 0.261158i | 0.991438 | + | 0.130579i | \(0.0416836\pi\) | ||||
−0.991438 | + | 0.130579i | \(0.958316\pi\) | |||||||
\(230\) | 7.11394e36 | − | 1.77180e37i | 0.116002 | − | 0.288915i | ||||
\(231\) | 2.67997e36 | 0.0407697 | ||||||||
\(232\) | 3.73339e34 | + | 3.73339e34i | 0.000530024 | + | 0.000530024i | ||||
\(233\) | 1.20900e37 | − | 1.20900e37i | 0.160225 | − | 0.160225i | −0.622441 | − | 0.782667i | \(-0.713859\pi\) |
0.782667 | + | 0.622441i | \(0.213859\pi\) | |||||||
\(234\) | − | 4.50450e37i | − | 0.557434i | ||||||
\(235\) | 1.10450e38 | − | 4.71658e37i | 1.27667 | − | 0.545181i | ||||
\(236\) | −9.56325e37 | −1.03279 | ||||||||
\(237\) | 3.06763e37 | + | 3.06763e37i | 0.309620 | + | 0.309620i | ||||
\(238\) | 1.71545e37 | − | 1.71545e37i | 0.161862 | − | 0.161862i | ||||
\(239\) | 7.27736e37i | 0.642107i | 0.947061 | + | 0.321054i | \(0.104037\pi\) | ||||
−0.947061 | + | 0.321054i | \(0.895963\pi\) | |||||||
\(240\) | 2.16898e37 | + | 5.07919e37i | 0.179009 | + | 0.419193i | ||||
\(241\) | 9.00368e37 | 0.695260 | 0.347630 | − | 0.937632i | \(-0.386986\pi\) | ||||
0.347630 | + | 0.937632i | \(0.386986\pi\) | |||||||
\(242\) | −3.14589e37 | − | 3.14589e37i | −0.227352 | − | 0.227352i | ||||
\(243\) | 1.05120e38 | − | 1.05120e38i | 0.711189 | − | 0.711189i | ||||
\(244\) | 1.93512e38i | 1.22594i | ||||||||
\(245\) | −1.54743e38 | − | 6.21306e37i | −0.918233 | − | 0.368679i | ||||
\(246\) | 6.97053e37 | 0.387529 | ||||||||
\(247\) | −5.51949e37 | − | 5.51949e37i | −0.287573 | − | 0.287573i | ||||
\(248\) | 4.53456e35 | − | 4.53456e35i | 0.00221467 | − | 0.00221467i | ||||
\(249\) | 4.26248e37i | 0.195197i | ||||||||
\(250\) | −3.07573e38 | − | 1.15779e38i | −1.32101 | − | 0.497266i | ||||
\(251\) | −2.59110e38 | −1.04401 | −0.522004 | − | 0.852943i | \(-0.674816\pi\) | ||||
−0.522004 | + | 0.852943i | \(0.674816\pi\) | |||||||
\(252\) | 1.51385e37 | + | 1.51385e37i | 0.0572366 | + | 0.0572366i | ||||
\(253\) | 3.86210e37 | − | 3.86210e37i | 0.137055 | − | 0.137055i | ||||
\(254\) | 1.52758e38i | 0.508938i | ||||||||
\(255\) | −8.51926e37 | + | 2.12181e38i | −0.266538 | + | 0.663840i | ||||
\(256\) | 3.45427e38 | 1.01512 | ||||||||
\(257\) | 1.25730e38 | + | 1.25730e38i | 0.347143 | + | 0.347143i | 0.859044 | − | 0.511901i | \(-0.171059\pi\) |
−0.511901 | + | 0.859044i | \(0.671059\pi\) | |||||||
\(258\) | 2.07377e38 | − | 2.07377e38i | 0.538077 | − | 0.538077i | ||||
\(259\) | − | 5.02448e37i | − | 0.122545i | ||||||
\(260\) | −1.97613e38 | + | 8.43875e37i | −0.453151 | + | 0.193511i | ||||
\(261\) | −2.56091e37 | −0.0552264 | ||||||||
\(262\) | 8.61190e38 | + | 8.61190e38i | 1.74694 | + | 1.74694i | ||||
\(263\) | −6.36717e38 | + | 6.36717e38i | −1.21522 | + | 1.21522i | −0.245932 | + | 0.969287i | \(0.579094\pi\) |
−0.969287 | + | 0.245932i | \(0.920906\pi\) | |||||||
\(264\) | 2.38923e36i | 0.00429137i | ||||||||
\(265\) | −1.67224e38 | − | 3.91595e38i | −0.282725 | − | 0.662068i | ||||
\(266\) | 7.44842e37 | 0.118565 | ||||||||
\(267\) | −3.00843e38 | − | 3.00843e38i | −0.450982 | − | 0.450982i | ||||
\(268\) | 7.31971e38 | − | 7.31971e38i | 1.03356 | − | 1.03356i | ||||
\(269\) | − | 3.80922e38i | − | 0.506757i | −0.967367 | − | 0.253378i | \(-0.918458\pi\) | ||
0.967367 | − | 0.253378i | \(-0.0815417\pi\) | |||||||
\(270\) | −8.48599e38 | − | 3.40720e38i | −1.06385 | − | 0.427147i | ||||
\(271\) | −4.25519e38 | −0.502818 | −0.251409 | − | 0.967881i | \(-0.580894\pi\) | ||||
−0.251409 | + | 0.967881i | \(0.580894\pi\) | |||||||
\(272\) | 1.01131e39 | + | 1.01131e39i | 1.12663 | + | 1.12663i | ||||
\(273\) | −1.55063e37 | + | 1.55063e37i | −0.0162894 | + | 0.0162894i | ||||
\(274\) | − | 1.57990e39i | − | 1.56538i | ||||||
\(275\) | −6.79101e38 | − | 6.50139e38i | −0.634763 | − | 0.607691i | ||||
\(276\) | −1.12269e38 | −0.0990177 | ||||||||
\(277\) | 1.69345e38 | + | 1.69345e38i | 0.140960 | + | 0.140960i | 0.774065 | − | 0.633106i | \(-0.218220\pi\) |
−0.633106 | + | 0.774065i | \(0.718220\pi\) | |||||||
\(278\) | 2.16947e39 | − | 2.16947e39i | 1.70466 | − | 1.70466i | ||||
\(279\) | 3.11048e38i | 0.230760i | ||||||||
\(280\) | −5.88782e35 | + | 1.46642e36i | −0.000412502 | + | 0.00102738i | ||||
\(281\) | −1.02067e39 | −0.675439 | −0.337719 | − | 0.941247i | \(-0.609655\pi\) | ||||
−0.337719 | + | 0.941247i | \(0.609655\pi\) | |||||||
\(282\) | −1.00257e39 | − | 1.00257e39i | −0.626797 | − | 0.626797i | ||||
\(283\) | 6.11215e37 | − | 6.11215e37i | 0.0361086 | − | 0.0361086i | −0.688822 | − | 0.724931i | \(-0.741872\pi\) |
0.724931 | + | 0.688822i | \(0.241872\pi\) | |||||||
\(284\) | 1.86209e39i | 1.03970i | ||||||||
\(285\) | −6.45594e38 | + | 2.75690e38i | −0.340755 | + | 0.145514i | ||||
\(286\) | −1.23413e39 | −0.615890 | ||||||||
\(287\) | 9.32558e37 | + | 9.32558e37i | 0.0440114 | + | 0.0440114i | ||||
\(288\) | −1.77820e39 | + | 1.77820e39i | −0.793782 | + | 0.793782i | ||||
\(289\) | 3.55306e39i | 1.50050i | ||||||||
\(290\) | 9.63222e37 | + | 2.25561e38i | 0.0384909 | + | 0.0901357i | ||||
\(291\) | 2.10392e39 | 0.795687 | ||||||||
\(292\) | 2.81395e39 | + | 2.81395e39i | 1.00737 | + | 1.00737i | ||||
\(293\) | 1.82353e39 | − | 1.82353e39i | 0.618061 | − | 0.618061i | −0.326972 | − | 0.945034i | \(-0.606028\pi\) |
0.945034 | + | 0.326972i | \(0.106028\pi\) | |||||||
\(294\) | 1.96858e39i | 0.631824i | ||||||||
\(295\) | 3.17720e39 | + | 1.27568e39i | 0.965812 | + | 0.387782i | ||||
\(296\) | 4.47941e37 | 0.0128989 | ||||||||
\(297\) | −1.84974e39 | − | 1.84974e39i | −0.504670 | − | 0.504670i | ||||
\(298\) | −1.78692e39 | + | 1.78692e39i | −0.462003 | + | 0.462003i | ||||
\(299\) | 4.46923e38i | 0.109520i | ||||||||
\(300\) | 4.20954e37 | + | 1.93200e39i | 0.00977901 | + | 0.448816i | ||||
\(301\) | 5.54880e38 | 0.122218 | ||||||||
\(302\) | −7.41417e39 | − | 7.41417e39i | −1.54864 | − | 1.54864i | ||||
\(303\) | 1.91788e39 | − | 1.91788e39i | 0.379961 | − | 0.379961i | ||||
\(304\) | 4.39109e39i | 0.825267i | ||||||||
\(305\) | 2.58132e39 | − | 6.42904e39i | 0.460303 | − | 1.14643i | ||||
\(306\) | −1.04905e40 | −1.77523 | ||||||||
\(307\) | −2.15113e39 | − | 2.15113e39i | −0.345504 | − | 0.345504i | 0.512928 | − | 0.858432i | \(-0.328561\pi\) |
−0.858432 | + | 0.512928i | \(0.828561\pi\) | |||||||
\(308\) | 4.14758e38 | − | 4.14758e38i | 0.0632388 | − | 0.0632388i | ||||
\(309\) | 8.90282e38i | 0.128882i | ||||||||
\(310\) | 2.73966e39 | − | 1.16993e39i | 0.376626 | − | 0.160832i | ||||
\(311\) | 6.46580e39 | 0.844221 | 0.422111 | − | 0.906544i | \(-0.361289\pi\) | ||||
0.422111 | + | 0.906544i | \(0.361289\pi\) | |||||||
\(312\) | −1.38241e37 | − | 1.38241e37i | −0.00171460 | − | 0.00171460i | ||||
\(313\) | 3.70925e38 | − | 3.70925e38i | 0.0437096 | − | 0.0437096i | −0.684914 | − | 0.728624i | \(-0.740160\pi\) |
0.728624 | + | 0.684914i | \(0.240160\pi\) | |||||||
\(314\) | − | 1.63662e40i | − | 1.83262i | ||||||
\(315\) | −3.01009e38 | − | 7.04883e38i | −0.0320339 | − | 0.0750151i | ||||
\(316\) | 9.49506e39 | 0.960516 | ||||||||
\(317\) | 7.00150e39 | + | 7.00150e39i | 0.673353 | + | 0.673353i | 0.958488 | − | 0.285134i | \(-0.0920383\pi\) |
−0.285134 | + | 0.958488i | \(0.592038\pi\) | |||||||
\(318\) | −3.55455e39 | + | 3.55455e39i | −0.325050 | + | 0.325050i | ||||
\(319\) | 7.01629e38i | 0.0610178i | ||||||||
\(320\) | 1.10465e40 | + | 4.43527e39i | 0.913745 | + | 0.366877i | ||||
\(321\) | 1.80099e39 | 0.141720 | ||||||||
\(322\) | −3.01556e38 | − | 3.01556e38i | −0.0225774 | − | 0.0225774i | ||||
\(323\) | −1.28543e40 | + | 1.28543e40i | −0.915819 | + | 0.915819i | ||||
\(324\) | − | 6.26271e39i | − | 0.424661i | ||||||
\(325\) | 7.69099e39 | − | 1.67575e38i | 0.496419 | − | 0.0108162i | ||||
\(326\) | −2.43248e40 | −1.49475 | ||||||||
\(327\) | −6.21800e39 | − | 6.21800e39i | −0.363820 | − | 0.363820i | ||||
\(328\) | −8.31390e37 | + | 8.31390e37i | −0.00463258 | + | 0.00463258i | ||||
\(329\) | − | 2.68258e39i | − | 0.142370i | ||||||
\(330\) | −4.13542e39 | + | 1.02997e40i | −0.209072 | + | 0.520716i | ||||
\(331\) | 3.52235e40 | 1.69662 | 0.848310 | − | 0.529500i | \(-0.177620\pi\) | ||||
0.848310 | + | 0.529500i | \(0.177620\pi\) | |||||||
\(332\) | 6.59672e39 | + | 6.59672e39i | 0.302774 | + | 0.302774i | ||||
\(333\) | −1.53632e40 | + | 1.53632e40i | −0.672009 | + | 0.672009i | ||||
\(334\) | − | 4.34306e40i | − | 1.81073i | ||||||
\(335\) | −3.40823e40 | + | 1.45543e40i | −1.35460 | + | 0.578460i | ||||
\(336\) | 1.23362e39 | 0.0467469 | ||||||||
\(337\) | 3.64439e39 | + | 3.64439e39i | 0.131688 | + | 0.131688i | 0.769878 | − | 0.638191i | \(-0.220317\pi\) |
−0.638191 | + | 0.769878i | \(0.720317\pi\) | |||||||
\(338\) | −2.18218e40 | + | 2.18218e40i | −0.752009 | + | 0.752009i | ||||
\(339\) | − | 7.75215e39i | − | 0.254816i | ||||||
\(340\) | 1.96530e40 | + | 4.60222e40i | 0.616264 | + | 1.44313i | ||||
\(341\) | 8.52197e39 | 0.254959 | ||||||||
\(342\) | −2.27748e40 | − | 2.27748e40i | −0.650186 | − | 0.650186i | ||||
\(343\) | −5.29536e39 | + | 5.29536e39i | −0.144274 | + | 0.144274i | ||||
\(344\) | 4.94685e38i | 0.0128645i | ||||||||
\(345\) | 3.72990e39 | + | 1.49759e39i | 0.0925959 | + | 0.0371781i | ||||
\(346\) | 7.05141e40 | 1.67132 | ||||||||
\(347\) | −1.53522e40 | − | 1.53522e40i | −0.347454 | − | 0.347454i | 0.511706 | − | 0.859161i | \(-0.329014\pi\) |
−0.859161 | + | 0.511706i | \(0.829014\pi\) | |||||||
\(348\) | 1.01979e39 | − | 1.01979e39i | 0.0220416 | − | 0.0220416i | ||||
\(349\) | − | 1.04767e40i | − | 0.216280i | −0.994136 | − | 0.108140i | \(-0.965510\pi\) | ||
0.994136 | − | 0.108140i | \(-0.0344896\pi\) | |||||||
\(350\) | −5.07634e39 | + | 5.30248e39i | −0.100106 | + | 0.104566i | ||||
\(351\) | 2.14052e40 | 0.403279 | ||||||||
\(352\) | 4.87185e40 | + | 4.87185e40i | 0.877023 | + | 0.877023i | ||||
\(353\) | −3.88369e40 | + | 3.88369e40i | −0.668113 | + | 0.668113i | −0.957279 | − | 0.289166i | \(-0.906622\pi\) |
0.289166 | + | 0.957279i | \(0.406622\pi\) | |||||||
\(354\) | − | 4.04192e40i | − | 0.664563i | ||||||
\(355\) | 2.48391e40 | − | 6.18642e40i | 0.390374 | − | 0.972268i | ||||
\(356\) | −9.31183e40 | −1.39906 | ||||||||
\(357\) | 3.61127e39 | + | 3.61127e39i | 0.0518762 | + | 0.0518762i | ||||
\(358\) | 7.54413e40 | − | 7.54413e40i | 1.03629 | − | 1.03629i | ||||
\(359\) | 1.83934e40i | 0.241630i | 0.992675 | + | 0.120815i | \(0.0385508\pi\) | ||||
−0.992675 | + | 0.120815i | \(0.961449\pi\) | |||||||
\(360\) | 6.28415e38 | − | 2.68354e38i | 0.00789598 | − | 0.00337185i | ||||
\(361\) | 2.73852e40 | 0.329155 | ||||||||
\(362\) | −7.71328e40 | − | 7.71328e40i | −0.886956 | − | 0.886956i | ||||
\(363\) | 6.62256e39 | − | 6.62256e39i | 0.0728652 | − | 0.0728652i | ||||
\(364\) | 4.79958e39i | 0.0505337i | ||||||||
\(365\) | −5.59516e40 | − | 1.31024e41i | −0.563803 | − | 1.32028i | ||||
\(366\) | −8.17880e40 | −0.788846 | ||||||||
\(367\) | −2.37750e40 | − | 2.37750e40i | −0.219514 | − | 0.219514i | 0.588780 | − | 0.808294i | \(-0.299609\pi\) |
−0.808294 | + | 0.588780i | \(0.799609\pi\) | |||||||
\(368\) | 1.77777e40 | − | 1.77777e40i | 0.157149 | − | 0.157149i | ||||
\(369\) | − | 5.70291e40i | − | 0.482697i | ||||||
\(370\) | 1.93102e41 | + | 7.75321e40i | 1.56516 | + | 0.628426i | ||||
\(371\) | −9.51095e39 | −0.0738314 | ||||||||
\(372\) | −1.23864e40 | − | 1.23864e40i | −0.0920995 | − | 0.0920995i | ||||
\(373\) | −8.19579e40 | + | 8.19579e40i | −0.583780 | + | 0.583780i | −0.935940 | − | 0.352160i | \(-0.885447\pi\) |
0.352160 | + | 0.935940i | \(0.385447\pi\) | |||||||
\(374\) | 2.87416e41i | 1.96140i | ||||||||
\(375\) | 2.43731e40 | − | 6.47485e40i | 0.159372 | − | 0.423379i | ||||
\(376\) | 2.39156e39 | 0.0149857 | ||||||||
\(377\) | −4.05963e39 | − | 4.05963e39i | −0.0243795 | − | 0.0243795i | ||||
\(378\) | −1.44429e40 | + | 1.44429e40i | −0.0831355 | + | 0.0831355i | ||||
\(379\) | 2.83892e41i | 1.56648i | 0.621718 | + | 0.783241i | \(0.286435\pi\) | ||||
−0.621718 | + | 0.783241i | \(0.713565\pi\) | |||||||
\(380\) | −5.72472e40 | + | 1.42580e41i | −0.302843 | + | 0.754261i | ||||
\(381\) | −3.21578e40 | −0.163112 | ||||||||
\(382\) | 3.09864e41 | + | 3.09864e41i | 1.50715 | + | 1.50715i | ||||
\(383\) | 1.27021e41 | − | 1.27021e41i | 0.592510 | − | 0.592510i | −0.345799 | − | 0.938309i | \(-0.612392\pi\) |
0.938309 | + | 0.345799i | \(0.112392\pi\) | |||||||
\(384\) | 2.18295e39i | 0.00976662i | ||||||||
\(385\) | −1.93121e40 | + | 8.24692e39i | −0.0828816 | + | 0.0353932i | ||||
\(386\) | −3.63514e41 | −1.49666 | ||||||||
\(387\) | −1.69664e41 | − | 1.69664e41i | −0.670216 | − | 0.670216i | ||||
\(388\) | 3.25608e41 | − | 3.25608e41i | 1.23421 | − | 1.23421i | ||||
\(389\) | 3.13956e41i | 1.14202i | 0.820942 | + | 0.571012i | \(0.193449\pi\) | ||||
−0.820942 | + | 0.571012i | \(0.806551\pi\) | |||||||
\(390\) | −3.56665e40 | − | 8.35216e40i | −0.124517 | − | 0.291585i | ||||
\(391\) | 1.04084e41 | 0.348783 | ||||||||
\(392\) | −2.34797e39 | − | 2.34797e39i | −0.00755292 | − | 0.00755292i | ||||
\(393\) | −1.81293e41 | + | 1.81293e41i | −0.559887 | + | 0.559887i | ||||
\(394\) | − | 2.17564e41i | − | 0.645130i | ||||||
\(395\) | −3.15455e41 | − | 1.26658e41i | −0.898221 | − | 0.360644i | ||||
\(396\) | −2.53639e41 | −0.693574 | ||||||||
\(397\) | −3.19598e41 | − | 3.19598e41i | −0.839375 | − | 0.839375i | 0.149401 | − | 0.988777i | \(-0.452265\pi\) |
−0.988777 | + | 0.149401i | \(0.952265\pi\) | |||||||
\(398\) | 7.09713e41 | − | 7.09713e41i | 1.79042 | − | 1.79042i | ||||
\(399\) | 1.56800e40i | 0.0379997i | ||||||||
\(400\) | −3.12598e41 | − | 2.99267e41i | −0.727824 | − | 0.696784i | ||||
\(401\) | 3.83293e41 | 0.857475 | 0.428737 | − | 0.903429i | \(-0.358959\pi\) | ||||
0.428737 | + | 0.903429i | \(0.358959\pi\) | |||||||
\(402\) | 3.09369e41 | + | 3.09369e41i | 0.665058 | + | 0.665058i | ||||
\(403\) | −4.93081e40 | + | 4.93081e40i | −0.101868 | + | 0.101868i | ||||
\(404\) | − | 5.93631e41i | − | 1.17873i | ||||||
\(405\) | −8.35404e40 | + | 2.08066e41i | −0.159447 | + | 0.397119i | ||||
\(406\) | 5.47838e39 | 0.0100516 | ||||||||
\(407\) | 4.20916e41 | + | 4.20916e41i | 0.742480 | + | 0.742480i | ||||
\(408\) | −3.21950e39 | + | 3.21950e39i | −0.00546042 | + | 0.00546042i | ||||
\(409\) | 4.66428e40i | 0.0760696i | 0.999276 | + | 0.0380348i | \(0.0121098\pi\) | ||||
−0.999276 | + | 0.0380348i | \(0.987890\pi\) | |||||||
\(410\) | −5.02304e41 | + | 2.14500e41i | −0.787816 | + | 0.336424i | ||||
\(411\) | 3.32592e41 | 0.501698 | ||||||||
\(412\) | 1.37782e41 | + | 1.37782e41i | 0.199911 | + | 0.199911i | ||||
\(413\) | 5.40752e40 | − | 5.40752e40i | 0.0754739 | − | 0.0754739i | ||||
\(414\) | 1.84412e41i | 0.247619i | ||||||||
\(415\) | −1.31167e41 | − | 3.07159e41i | −0.169455 | − | 0.396820i | ||||
\(416\) | −5.63771e41 | −0.700824 | ||||||||
\(417\) | 4.56705e41 | + | 4.56705e41i | 0.546335 | + | 0.546335i | ||||
\(418\) | −6.23976e41 | + | 6.23976e41i | −0.718369 | + | 0.718369i | ||||
\(419\) | − | 3.48405e41i | − | 0.386065i | −0.981192 | − | 0.193032i | \(-0.938168\pi\) | ||
0.981192 | − | 0.193032i | \(-0.0618322\pi\) | |||||||
\(420\) | 4.00561e40 | + | 1.60829e40i | 0.0427248 | + | 0.0171544i | ||||
\(421\) | 1.07614e42 | 1.10499 | 0.552493 | − | 0.833517i | \(-0.313677\pi\) | ||||
0.552493 | + | 0.833517i | \(0.313677\pi\) | |||||||
\(422\) | 8.53911e41 | + | 8.53911e41i | 0.844138 | + | 0.844138i | ||||
\(423\) | −8.20244e41 | + | 8.20244e41i | −0.780724 | + | 0.780724i | ||||
\(424\) | − | 8.47916e39i | − | 0.00777140i | ||||||
\(425\) | −3.90266e40 | − | 1.79116e42i | −0.0344459 | − | 1.58092i | ||||
\(426\) | −7.87015e41 | −0.669005 | ||||||||
\(427\) | −1.09421e41 | − | 1.09421e41i | −0.0895887 | − | 0.0895887i | ||||
\(428\) | 2.78725e41 | − | 2.78725e41i | 0.219824 | − | 0.219824i | ||||
\(429\) | − | 2.59802e41i | − | 0.197390i | ||||||
\(430\) | −8.56228e41 | + | 2.13253e42i | −0.626750 | + | 1.56099i | ||||
\(431\) | 8.14206e41 | 0.574246 | 0.287123 | − | 0.957894i | \(-0.407301\pi\) | ||||
0.287123 | + | 0.957894i | \(0.407301\pi\) | |||||||
\(432\) | −8.51457e41 | − | 8.51457e41i | −0.578659 | − | 0.578659i | ||||
\(433\) | −4.99540e40 | + | 4.99540e40i | −0.0327163 | + | 0.0327163i | −0.723276 | − | 0.690559i | \(-0.757364\pi\) |
0.690559 | + | 0.723276i | \(0.257364\pi\) | |||||||
\(434\) | − | 6.65402e40i | − | 0.0419999i | ||||||
\(435\) | −4.74840e40 | + | 2.02772e40i | −0.0288881 | + | 0.0123362i | ||||
\(436\) | −1.92462e42 | −1.12866 | ||||||||
\(437\) | 2.25965e41 | + | 2.25965e41i | 0.127743 | + | 0.127743i | ||||
\(438\) | −1.18932e42 | + | 1.18932e42i | −0.648206 | + | 0.648206i | ||||
\(439\) | 1.09081e42i | 0.573215i | 0.958048 | + | 0.286607i | \(0.0925275\pi\) | ||||
−0.958048 | + | 0.286607i | \(0.907472\pi\) | |||||||
\(440\) | −7.35226e39 | − | 1.72171e40i | −0.00372544 | − | 0.00872401i | ||||
\(441\) | 1.61059e42 | 0.786985 | ||||||||
\(442\) | −1.66299e42 | − | 1.66299e42i | −0.783670 | − | 0.783670i | ||||
\(443\) | 2.11887e42 | − | 2.11887e42i | 0.963043 | − | 0.963043i | −0.0362982 | − | 0.999341i | \(-0.511557\pi\) |
0.999341 | + | 0.0362982i | \(0.0115566\pi\) | |||||||
\(444\) | − | 1.22357e42i | − | 0.536416i | ||||||
\(445\) | 3.09367e42 | + | 1.24214e42i | 1.30832 | + | 0.525302i | ||||
\(446\) | 2.54063e42 | 1.03653 | ||||||||
\(447\) | −3.76173e41 | − | 3.76173e41i | −0.148070 | − | 0.148070i | ||||
\(448\) | 1.88009e41 | − | 1.88009e41i | 0.0714051 | − | 0.0714051i | ||||
\(449\) | 5.09144e42i | 1.86595i | 0.359947 | + | 0.932973i | \(0.382795\pi\) | ||||
−0.359947 | + | 0.932973i | \(0.617205\pi\) | |||||||
\(450\) | 3.17350e42 | − | 6.91458e40i | 1.12238 | − | 0.0244549i | ||||
\(451\) | −1.56246e42 | −0.533316 | ||||||||
\(452\) | −1.19974e42 | − | 1.19974e42i | −0.395251 | − | 0.395251i | ||||
\(453\) | 1.56079e42 | − | 1.56079e42i | 0.496333 | − | 0.496333i | ||||
\(454\) | − | 4.20615e42i | − | 1.29119i | ||||||
\(455\) | 6.40233e40 | − | 1.59457e41i | 0.0189739 | − | 0.0472564i | ||||
\(456\) | −1.39790e40 | −0.00399980 | ||||||||
\(457\) | −3.78147e42 | − | 3.78147e42i | −1.04472 | − | 1.04472i | −0.998952 | − | 0.0457712i | \(-0.985425\pi\) |
−0.0457712 | − | 0.998952i | \(-0.514575\pi\) | |||||||
\(458\) | −9.77055e41 | + | 9.77055e41i | −0.260658 | + | 0.260658i | ||||
\(459\) | − | 4.98507e42i | − | 1.28430i | ||||||
\(460\) | 8.09019e41 | − | 3.45478e41i | 0.201295 | − | 0.0859597i | ||||
\(461\) | −6.34710e42 | −1.52532 | −0.762659 | − | 0.646801i | \(-0.776107\pi\) | ||||
−0.762659 | + | 0.646801i | \(0.776107\pi\) | |||||||
\(462\) | 1.75298e41 | + | 1.75298e41i | 0.0406917 | + | 0.0406917i | ||||
\(463\) | −5.21645e42 | + | 5.21645e42i | −1.16971 | + | 1.16971i | −0.187437 | + | 0.982277i | \(0.560018\pi\) |
−0.982277 | + | 0.187437i | \(0.939982\pi\) | |||||||
\(464\) | 3.22968e41i | 0.0699635i | ||||||||
\(465\) | 2.46287e41 | + | 5.76739e41i | 0.0515459 | + | 0.120707i | ||||
\(466\) | 1.58163e42 | 0.319838 | ||||||||
\(467\) | −2.03137e42 | − | 2.03137e42i | −0.396935 | − | 0.396935i | 0.480216 | − | 0.877151i | \(-0.340558\pi\) |
−0.877151 | + | 0.480216i | \(0.840558\pi\) | |||||||
\(468\) | 1.46756e42 | − | 1.46756e42i | 0.277116 | − | 0.277116i | ||||
\(469\) | 8.27782e41i | 0.151060i | ||||||||
\(470\) | 1.03097e43 | + | 4.13945e42i | 1.81837 | + | 0.730090i | ||||
\(471\) | 3.44532e42 | 0.587347 | ||||||||
\(472\) | 4.82089e40 | + | 4.82089e40i | 0.00794429 | + | 0.00794429i | ||||
\(473\) | −4.64839e42 | + | 4.64839e42i | −0.740499 | + | 0.740499i | ||||
\(474\) | 4.01310e42i | 0.618055i | ||||||||
\(475\) | 3.80385e42 | − | 3.97330e42i | 0.566403 | − | 0.591635i | ||||
\(476\) | 1.11778e42 | 0.160932 | ||||||||
\(477\) | 2.90814e42 | + | 2.90814e42i | 0.404875 | + | 0.404875i | ||||
\(478\) | −4.76017e42 | + | 4.76017e42i | −0.640878 | + | 0.640878i | ||||
\(479\) | 3.78435e42i | 0.492746i | 0.969175 | + | 0.246373i | \(0.0792388\pi\) | ||||
−0.969175 | + | 0.246373i | \(0.920761\pi\) | |||||||
\(480\) | −1.88913e42 | + | 4.70508e42i | −0.237905 | + | 0.592526i | ||||
\(481\) | −4.87084e42 | −0.593311 | ||||||||
\(482\) | 5.88936e42 | + | 5.88936e42i | 0.693930 | + | 0.693930i | ||||
\(483\) | 6.34820e40 | − | 6.34820e40i | 0.00723596 | − | 0.00723596i | ||||
\(484\) | − | 2.04985e42i | − | 0.226045i | ||||||
\(485\) | −1.51611e43 | + | 6.47429e42i | −1.61757 | + | 0.690756i | ||||
\(486\) | 1.37519e43 | 1.41966 | ||||||||
\(487\) | 2.37482e41 | + | 2.37482e41i | 0.0237229 | + | 0.0237229i | 0.718869 | − | 0.695146i | \(-0.244660\pi\) |
−0.695146 | + | 0.718869i | \(0.744660\pi\) | |||||||
\(488\) | 9.75502e40 | − | 9.75502e40i | 0.00942999 | − | 0.00942999i | ||||
\(489\) | − | 5.12072e42i | − | 0.479060i | ||||||
\(490\) | −6.05781e42 | − | 1.41858e43i | −0.548502 | − | 1.28445i | ||||
\(491\) | −3.26077e42 | −0.285769 | −0.142885 | − | 0.989739i | \(-0.545638\pi\) | ||||
−0.142885 | + | 0.989739i | \(0.545638\pi\) | |||||||
\(492\) | 2.27098e42 | + | 2.27098e42i | 0.192651 | + | 0.192651i | ||||
\(493\) | −9.45448e41 | + | 9.45448e41i | −0.0776402 | + | 0.0776402i | ||||
\(494\) | − | 7.22066e42i | − | 0.574045i | ||||||
\(495\) | 8.42665e42 | + | 3.38338e42i | 0.648592 | + | 0.260416i | ||||
\(496\) | 3.92276e42 | 0.292338 | ||||||||
\(497\) | −1.05291e42 | − | 1.05291e42i | −0.0759785 | − | 0.0759785i | ||||
\(498\) | −2.78811e42 | + | 2.78811e42i | −0.194823 | + | 0.194823i | ||||
\(499\) | − | 2.79514e43i | − | 1.89145i | −0.324973 | − | 0.945723i | \(-0.605355\pi\) | ||
0.324973 | − | 0.945723i | \(-0.394645\pi\) | |||||||
\(500\) | −6.24859e42 | − | 1.37927e43i | −0.409508 | − | 0.903917i | ||||
\(501\) | 9.14279e42 | 0.580330 | ||||||||
\(502\) | −1.69485e43 | − | 1.69485e43i | −1.04201 | − | 1.04201i | ||||
\(503\) | 1.43967e43 | − | 1.43967e43i | 0.857385 | − | 0.857385i | −0.133644 | − | 0.991029i | \(-0.542668\pi\) |
0.991029 | + | 0.133644i | \(0.0426679\pi\) | |||||||
\(504\) | − | 1.52628e40i | − | 0.000880531i | ||||||
\(505\) | −7.91865e42 | + | 1.97222e43i | −0.442577 | + | 1.10229i | ||||
\(506\) | 5.05245e42 | 0.273586 | ||||||||
\(507\) | −4.59381e42 | − | 4.59381e42i | −0.241016 | − | 0.241016i | ||||
\(508\) | −4.97682e42 | + | 4.97682e42i | −0.253007 | + | 0.253007i | ||||
\(509\) | − | 5.03625e42i | − | 0.248098i | −0.992276 | − | 0.124049i | \(-0.960412\pi\) | ||
0.992276 | − | 0.124049i | \(-0.0395880\pi\) | |||||||
\(510\) | −1.94514e43 | + | 8.30638e42i | −0.928597 | + | 0.396542i | ||||
\(511\) | −3.18228e42 | −0.147233 | ||||||||
\(512\) | 2.22542e43 | + | 2.22542e43i | 0.997911 | + | 0.997911i | ||||
\(513\) | 1.08225e43 | − | 1.08225e43i | 0.470382 | − | 0.470382i | ||||
\(514\) | 1.64481e43i | 0.692957i | ||||||||
\(515\) | −2.73962e42 | − | 6.41546e42i | −0.111886 | − | 0.262007i | ||||
\(516\) | 1.35126e43 | 0.534986 | ||||||||
\(517\) | 2.24727e43 | + | 2.24727e43i | 0.862595 | + | 0.862595i | ||||
\(518\) | 3.28654e42 | − | 3.28654e42i | 0.122310 | − | 0.122310i | ||||
\(519\) | 1.48443e43i | 0.535649i | ||||||||
\(520\) | 1.42158e41 | + | 5.70778e40i | 0.00497414 | + | 0.00199716i | ||||
\(521\) | 5.72502e42 | 0.194256 | 0.0971278 | − | 0.995272i | \(-0.469034\pi\) | ||||
0.0971278 | + | 0.995272i | \(0.469034\pi\) | |||||||
\(522\) | −1.67511e42 | − | 1.67511e42i | −0.0551207 | − | 0.0551207i | ||||
\(523\) | 1.53307e43 | − | 1.53307e43i | 0.489254 | − | 0.489254i | −0.418817 | − | 0.908071i | \(-0.637555\pi\) |
0.908071 | + | 0.418817i | \(0.137555\pi\) | |||||||
\(524\) | 5.61147e43i | 1.73691i | ||||||||
\(525\) | −1.11625e42 | − | 1.06864e42i | −0.0335129 | − | 0.0320837i | ||||
\(526\) | −8.32961e43 | −2.42579 | ||||||||
\(527\) | 1.14834e43 | + | 1.14834e43i | 0.324414 | + | 0.324414i | ||||
\(528\) | −1.03344e43 | + | 1.03344e43i | −0.283232 | + | 0.283232i | ||||
\(529\) | 3.57792e43i | 0.951350i | ||||||||
\(530\) | 1.46762e43 | − | 3.65526e43i | 0.378617 | − | 0.942985i | ||||
\(531\) | −3.30688e43 | −0.827764 | ||||||||
\(532\) | 2.42668e42 | + | 2.42668e42i | 0.0589422 | + | 0.0589422i | ||||
\(533\) | 9.04041e42 | − | 9.04041e42i | 0.213085 | − | 0.213085i | ||||
\(534\) | − | 3.93566e43i | − | 0.900239i | ||||||
\(535\) | −1.29781e43 | + | 5.54207e42i | −0.288105 | + | 0.123030i | ||||
\(536\) | −7.37981e41 | −0.0159004 | ||||||||
\(537\) | 1.58815e43 | + | 1.58815e43i | 0.332126 | + | 0.332126i | ||||
\(538\) | 2.49163e43 | − | 2.49163e43i | 0.505787 | − | 0.505787i | ||||
\(539\) | − | 4.41262e43i | − | 0.869514i | ||||||
\(540\) | −1.65466e43 | − | 3.87477e43i | −0.316525 | − | 0.741218i | ||||
\(541\) | −4.11451e43 | −0.764121 | −0.382061 | − | 0.924137i | \(-0.624785\pi\) | ||||
−0.382061 | + | 0.924137i | \(0.624785\pi\) | |||||||
\(542\) | −2.78335e43 | − | 2.78335e43i | −0.501855 | − | 0.501855i | ||||
\(543\) | 1.62376e43 | − | 1.62376e43i | 0.284266 | − | 0.284266i | ||||
\(544\) | 1.31297e44i | 2.23188i | ||||||||
\(545\) | 6.39418e43 | + | 2.56732e43i | 1.05546 | + | 0.423776i | ||||
\(546\) | −2.02855e42 | −0.0325165 | ||||||||
\(547\) | −6.22056e42 | − | 6.22056e42i | −0.0968350 | − | 0.0968350i | 0.657030 | − | 0.753865i | \(-0.271813\pi\) |
−0.753865 | + | 0.657030i | \(0.771813\pi\) | |||||||
\(548\) | 5.14728e43 | − | 5.14728e43i | 0.778195 | − | 0.778195i | ||||
\(549\) | 6.69145e43i | 0.982568i | ||||||||
\(550\) | −1.89443e42 | − | 8.69464e43i | −0.0270194 | − | 1.24008i | ||||
\(551\) | −4.10511e42 | −0.0568721 | ||||||||
\(552\) | 5.65952e40 | + | 5.65952e40i | 0.000761648 | + | 0.000761648i | ||||
\(553\) | −5.36896e42 | + | 5.36896e42i | −0.0701920 | + | 0.0701920i | ||||
\(554\) | 2.21538e43i | 0.281380i | ||||||||
\(555\) | −1.63216e43 | + | 4.06508e43i | −0.201408 | + | 0.501627i | ||||
\(556\) | 1.41362e44 | 1.69486 | ||||||||
\(557\) | −2.82497e43 | − | 2.82497e43i | −0.329102 | − | 0.329102i | 0.523143 | − | 0.852245i | \(-0.324759\pi\) |
−0.852245 | + | 0.523143i | \(0.824759\pi\) | |||||||
\(558\) | −2.03458e43 | + | 2.03458e43i | −0.230318 | + | 0.230318i | ||||
\(559\) | − | 5.37913e43i | − | 0.591729i | ||||||
\(560\) | −8.88959e42 | + | 3.79615e42i | −0.0950328 | + | 0.0405822i | ||||
\(561\) | −6.05052e43 | −0.628619 | ||||||||
\(562\) | −6.67629e43 | − | 6.67629e43i | −0.674146 | − | 0.674146i | ||||
\(563\) | 7.55262e43 | − | 7.55262e43i | 0.741248 | − | 0.741248i | −0.231570 | − | 0.972818i | \(-0.574386\pi\) |
0.972818 | + | 0.231570i | \(0.0743863\pi\) | |||||||
\(564\) | − | 6.53266e43i | − | 0.623196i | ||||||
\(565\) | 2.38553e43 | + | 5.58628e43i | 0.221212 | + | 0.518021i | ||||
\(566\) | 7.99599e42 | 0.0720791 | ||||||||
\(567\) | 3.54123e42 | + | 3.54123e42i | 0.0310331 | + | 0.0310331i | ||||
\(568\) | 9.38689e41 | − | 9.38689e41i | 0.00799739 | − | 0.00799739i | ||||
\(569\) | − | 4.96293e43i | − | 0.411095i | −0.978647 | − | 0.205547i | \(-0.934103\pi\) | ||
0.978647 | − | 0.205547i | \(-0.0658975\pi\) | |||||||
\(570\) | −6.02617e43 | − | 2.41956e43i | −0.485338 | − | 0.194867i | ||||
\(571\) | 9.85215e43 | 0.771531 | 0.385765 | − | 0.922597i | \(-0.373937\pi\) | ||||
0.385765 | + | 0.922597i | \(0.373937\pi\) | |||||||
\(572\) | −4.02075e43 | − | 4.02075e43i | −0.306176 | − | 0.306176i | ||||
\(573\) | −6.52309e43 | + | 6.52309e43i | −0.483036 | + | 0.483036i | ||||
\(574\) | 1.21998e43i | 0.0878544i | ||||||||
\(575\) | −3.14865e43 | + | 6.86043e41i | −0.220515 | + | 0.00480469i | ||||
\(576\) | −1.14974e44 | −0.783139 | ||||||||
\(577\) | 9.44045e43 | + | 9.44045e43i | 0.625431 | + | 0.625431i | 0.946915 | − | 0.321484i | \(-0.104182\pi\) |
−0.321484 | + | 0.946915i | \(0.604182\pi\) | |||||||
\(578\) | −2.32408e44 | + | 2.32408e44i | −1.49763 | + | 1.49763i | ||||
\(579\) | − | 7.65250e43i | − | 0.479674i | ||||||
\(580\) | −4.21058e42 | + | 1.04869e43i | −0.0256740 | + | 0.0639438i | ||||
\(581\) | −7.46020e42 | −0.0442519 | ||||||||
\(582\) | 1.37619e44 | + | 1.37619e44i | 0.794164 | + | 0.794164i | ||||
\(583\) | 7.96760e43 | − | 7.96760e43i | 0.447333 | − | 0.447333i | ||||
\(584\) | − | 2.83705e42i | − | 0.0154975i | ||||||
\(585\) | −6.83329e43 | + | 2.91804e43i | −0.363192 | + | 0.155095i | ||||
\(586\) | 2.38557e44 | 1.23376 | ||||||||
\(587\) | −1.18485e44 | − | 1.18485e44i | −0.596284 | − | 0.596284i | 0.343037 | − | 0.939322i | \(-0.388544\pi\) |
−0.939322 | + | 0.343037i | \(0.888544\pi\) | |||||||
\(588\) | −6.41359e43 | + | 6.41359e43i | −0.314097 | + | 0.314097i | ||||
\(589\) | 4.98606e43i | 0.237636i | ||||||||
\(590\) | 1.24380e44 | + | 2.91265e44i | 0.576923 | + | 1.35100i | ||||
\(591\) | 4.58004e43 | 0.206761 | ||||||||
\(592\) | 1.93752e44 | + | 1.93752e44i | 0.851333 | + | 0.851333i | ||||
\(593\) | −2.63119e44 | + | 2.63119e44i | −1.12532 | + | 1.12532i | −0.134396 | + | 0.990928i | \(0.542909\pi\) |
−0.990928 | + | 0.134396i | \(0.957091\pi\) | |||||||
\(594\) | − | 2.41985e44i | − | 1.00741i | ||||||
\(595\) | −3.71359e43 | − | 1.49104e43i | −0.150495 | − | 0.0604252i | ||||
\(596\) | −1.16435e44 | −0.459349 | ||||||||
\(597\) | 1.49405e44 | + | 1.49405e44i | 0.573820 | + | 0.573820i | ||||
\(598\) | −2.92335e43 | + | 2.92335e43i | −0.109310 | + | 0.109310i | ||||
\(599\) | − | 3.25999e44i | − | 1.18682i | −0.804899 | − | 0.593412i | \(-0.797780\pi\) | ||
0.804899 | − | 0.593412i | \(-0.202220\pi\) | |||||||
\(600\) | 9.52713e41 | − | 9.95154e41i | 0.00337708 | − | 0.00352753i | ||||
\(601\) | 1.17707e44 | 0.406268 | 0.203134 | − | 0.979151i | \(-0.434887\pi\) | ||||
0.203134 | + | 0.979151i | \(0.434887\pi\) | |||||||
\(602\) | 3.62950e43 | + | 3.62950e43i | 0.121984 | + | 0.121984i | ||||
\(603\) | 2.53109e44 | − | 2.53109e44i | 0.828381 | − | 0.828381i | ||||
\(604\) | − | 4.83103e44i | − | 1.53975i | ||||||
\(605\) | −2.73436e43 | + | 6.81021e43i | −0.0848731 | + | 0.211385i | ||||
\(606\) | 2.50899e44 | 0.758468 | ||||||||
\(607\) | −3.62966e44 | − | 3.62966e44i | −1.06868 | − | 1.06868i | −0.997461 | − | 0.0712188i | \(-0.977311\pi\) |
−0.0712188 | − | 0.997461i | \(-0.522689\pi\) | |||||||
\(608\) | −2.85043e44 | + | 2.85043e44i | −0.817436 | + | 0.817436i | ||||
\(609\) | 1.15328e42i | 0.00322149i | ||||||||
\(610\) | 5.89373e44 | − | 2.51682e44i | 1.60366 | − | 0.684817i | ||||
\(611\) | −2.60055e44 | −0.689295 | ||||||||
\(612\) | −3.41779e44 | − | 3.41779e44i | −0.882517 | − | 0.882517i | ||||
\(613\) | −9.76216e43 | + | 9.76216e43i | −0.245572 | + | 0.245572i | −0.819150 | − | 0.573579i | \(-0.805555\pi\) |
0.573579 | + | 0.819150i | \(0.305555\pi\) | |||||||
\(614\) | − | 2.81414e44i | − | 0.689686i | ||||||
\(615\) | −4.51555e43 | − | 1.05742e44i | −0.107822 | − | 0.252492i | ||||
\(616\) | −4.18163e41 | −0.000972870 | ||||||||
\(617\) | −5.44998e44 | − | 5.44998e44i | −1.23547 | − | 1.23547i | −0.961833 | − | 0.273637i | \(-0.911773\pi\) |
−0.273637 | − | 0.961833i | \(-0.588227\pi\) | |||||||
\(618\) | −5.82338e43 | + | 5.82338e43i | −0.128635 | + | 0.128635i | ||||
\(619\) | 3.11910e44i | 0.671396i | 0.941970 | + | 0.335698i | \(0.108972\pi\) | ||||
−0.941970 | + | 0.335698i | \(0.891028\pi\) | |||||||
\(620\) | 1.27373e44 | + | 5.11416e43i | 0.267185 | + | 0.107277i | ||||
\(621\) | −8.76318e43 | −0.179142 | ||||||||
\(622\) | 4.22932e44 | + | 4.22932e44i | 0.842606 | + | 0.842606i | ||||
\(623\) | 5.26535e43 | − | 5.26535e43i | 0.102239 | − | 0.102239i | ||||
\(624\) | − | 1.19590e44i | − | 0.226329i | ||||||
\(625\) | 2.36119e43 | + | 5.41587e44i | 0.0435563 | + | 0.999051i | ||||
\(626\) | 4.85248e43 | 0.0872518 | ||||||||
\(627\) | −1.31356e44 | − | 1.31356e44i | −0.230234 | − | 0.230234i | ||||
\(628\) | 5.33205e44 | − | 5.33205e44i | 0.911046 | − | 0.911046i | ||||
\(629\) | 1.13437e45i | 1.88949i | ||||||||
\(630\) | 2.64177e43 | − | 6.57960e43i | 0.0428989 | − | 0.106844i | ||||
\(631\) | 7.85800e44 | 1.24406 | 0.622031 | − | 0.782993i | \(-0.286308\pi\) | ||||
0.622031 | + | 0.782993i | \(0.286308\pi\) | |||||||
\(632\) | −4.78651e42 | − | 4.78651e42i | −0.00738832 | − | 0.00738832i | ||||
\(633\) | −1.79761e44 | + | 1.79761e44i | −0.270542 | + | 0.270542i | ||||
\(634\) | 9.15944e44i | 1.34413i | ||||||||
\(635\) | 2.31732e44 | − | 9.89575e43i | 0.331594 | − | 0.141602i | ||||
\(636\) | −2.31612e44 | −0.323183 | ||||||||
\(637\) | 2.55314e44 | + | 2.55314e44i | 0.347412 | + | 0.347412i | ||||
\(638\) | −4.58939e43 | + | 4.58939e43i | −0.0609010 | + | 0.0609010i | ||||
\(639\) | 6.43893e44i | 0.833297i | ||||||||
\(640\) | −6.71748e42 | − | 1.57306e43i | −0.00847865 | − | 0.0198548i | ||||
\(641\) | −9.24961e43 | −0.113866 | −0.0569331 | − | 0.998378i | \(-0.518132\pi\) | ||||
−0.0569331 | + | 0.998378i | \(0.518132\pi\) | |||||||
\(642\) | 1.17803e44 | + | 1.17803e44i | 0.141448 | + | 0.141448i | ||||
\(643\) | −8.15227e43 | + | 8.15227e43i | −0.0954779 | + | 0.0954779i | −0.753232 | − | 0.657754i | \(-0.771506\pi\) |
0.657754 | + | 0.753232i | \(0.271506\pi\) | |||||||
\(644\) | − | 1.96492e43i | − | 0.0224477i | ||||||
\(645\) | −4.48928e44 | − | 1.80249e44i | −0.500289 | − | 0.200871i | ||||
\(646\) | −1.68162e45 | −1.82813 | ||||||||
\(647\) | −9.40725e44 | − | 9.40725e44i | −0.997687 | − | 0.997687i | 0.00231036 | − | 0.999997i | \(-0.499265\pi\) |
−0.999997 | + | 0.00231036i | \(0.999265\pi\) | |||||||
\(648\) | −3.15706e42 | + | 3.15706e42i | −0.00326650 | + | 0.00326650i | ||||
\(649\) | 9.06007e44i | 0.914568i | ||||||||
\(650\) | 5.14033e44 | + | 4.92111e44i | 0.506265 | + | 0.484674i | ||||
\(651\) | 1.40077e43 | 0.0134608 | ||||||||
\(652\) | −7.92495e44 | − | 7.92495e44i | −0.743079 | − | 0.743079i | ||||
\(653\) | 6.72204e43 | − | 6.72204e43i | 0.0615022 | − | 0.0615022i | −0.675687 | − | 0.737189i | \(-0.736153\pi\) |
0.737189 | + | 0.675687i | \(0.236153\pi\) | |||||||
\(654\) | − | 8.13445e44i | − | 0.726247i | ||||||
\(655\) | 7.48533e44 | − | 1.86430e45i | 0.652154 | − | 1.62426i | ||||
\(656\) | −7.19219e44 | −0.611505 | ||||||||
\(657\) | 9.73037e44 | + | 9.73037e44i | 0.807390 | + | 0.807390i | ||||
\(658\) | 1.75469e44 | − | 1.75469e44i | 0.142097 | − | 0.142097i | ||||
\(659\) | − | 2.22598e45i | − | 1.75936i | −0.475563 | − | 0.879682i | \(-0.657756\pi\) | ||
0.475563 | − | 0.879682i | \(-0.342244\pi\) | |||||||
\(660\) | −4.70292e44 | + | 2.00831e44i | −0.362798 | + | 0.154927i | ||||
\(661\) | 1.67203e45 | 1.25899 | 0.629494 | − | 0.777006i | \(-0.283262\pi\) | ||||
0.629494 | + | 0.777006i | \(0.283262\pi\) | |||||||
\(662\) | 2.30399e45 | + | 2.30399e45i | 1.69337 | + | 1.69337i | ||||
\(663\) | 3.50084e44 | − | 3.50084e44i | 0.251163 | − | 0.251163i | ||||
\(664\) | − | 6.65088e42i | − | 0.00465790i | ||||||
\(665\) | −4.82513e43 | − | 1.12992e44i | −0.0329885 | − | 0.0772504i | ||||
\(666\) | −2.00984e45 | −1.34144 | ||||||||
\(667\) | 1.66199e43 | + | 1.66199e43i | 0.0108297 | + | 0.0108297i | ||||
\(668\) | 1.41496e45 | − | 1.41496e45i | 0.900162 | − | 0.900162i | ||||
\(669\) | 5.34839e44i | 0.332204i | ||||||||
\(670\) | −3.18135e45 | − | 1.27734e45i | −1.92936 | − | 0.774657i | ||||
\(671\) | 1.83330e45 | 1.08561 | ||||||||
\(672\) | 8.00793e43 | + | 8.00793e43i | 0.0463033 | + | 0.0463033i | ||||
\(673\) | −1.58210e44 | + | 1.58210e44i | −0.0893292 | + | 0.0893292i | −0.750359 | − | 0.661030i | \(-0.770120\pi\) |
0.661030 | + | 0.750359i | \(0.270120\pi\) | |||||||
\(674\) | 4.76763e44i | 0.262872i | ||||||||
\(675\) | 3.28578e43 | + | 1.50804e45i | 0.0176921 | + | 0.811991i | ||||
\(676\) | −1.42190e45 | −0.747689 | ||||||||
\(677\) | 2.03805e44 | + | 2.03805e44i | 0.104664 | + | 0.104664i | 0.757500 | − | 0.652836i | \(-0.226421\pi\) |
−0.652836 | + | 0.757500i | \(0.726421\pi\) | |||||||
\(678\) | 5.07072e44 | − | 5.07072e44i | 0.254328 | − | 0.254328i | ||||
\(679\) | 3.68229e44i | 0.180385i | ||||||||
\(680\) | 1.32929e43 | − | 3.31072e43i | 0.00636027 | − | 0.0158409i | ||||
\(681\) | 8.85457e44 | 0.413822 | ||||||||
\(682\) | 5.57427e44 | + | 5.57427e44i | 0.254471 | + | 0.254471i | ||||
\(683\) | 2.20201e45 | − | 2.20201e45i | 0.981947 | − | 0.981947i | −0.0178927 | − | 0.999840i | \(-0.505696\pi\) |
0.999840 | + | 0.0178927i | \(0.00569572\pi\) | |||||||
\(684\) | − | 1.48400e45i | − | 0.646451i | ||||||
\(685\) | −2.39669e45 | + | 1.02347e45i | −1.01991 | + | 0.435537i | ||||
\(686\) | −6.92745e44 | −0.287997 | ||||||||
\(687\) | −2.05684e44 | − | 2.05684e44i | −0.0835398 | − | 0.0835398i | ||||
\(688\) | −2.13971e45 | + | 2.13971e45i | −0.849063 | + | 0.849063i | ||||
\(689\) | 9.22011e44i | 0.357461i | ||||||||
\(690\) | 1.46017e44 | + | 3.41933e44i | 0.0553118 | + | 0.129526i | ||||
\(691\) | 3.26068e45 | 1.20687 | 0.603434 | − | 0.797413i | \(-0.293799\pi\) | ||||
0.603434 | + | 0.797413i | \(0.293799\pi\) | |||||||
\(692\) | 2.29733e45 | + | 2.29733e45i | 0.830857 | + | 0.830857i | ||||
\(693\) | 1.43419e44 | − | 1.43419e44i | 0.0506846 | − | 0.0506846i | ||||
\(694\) | − | 2.00839e45i | − | 0.693579i | ||||||
\(695\) | −4.69646e45 | − | 1.88567e45i | −1.58494 | − | 0.636369i | ||||
\(696\) | −1.02817e42 | −0.000339090 | ||||||||
\(697\) | −2.10542e45 | − | 2.10542e45i | −0.678601 | − | 0.678601i | ||||
\(698\) | 6.85286e44 | − | 6.85286e44i | 0.215867 | − | 0.215867i | ||||
\(699\) | 3.32956e44i | 0.102507i | ||||||||
\(700\) | −3.38139e44 | + | 7.36754e42i | −0.101748 | + | 0.00221694i | ||||
\(701\) | −8.04654e44 | −0.236658 | −0.118329 | − | 0.992974i | \(-0.537754\pi\) | ||||
−0.118329 | + | 0.992974i | \(0.537754\pi\) | |||||||
\(702\) | 1.40013e45 | + | 1.40013e45i | 0.402508 | + | 0.402508i | ||||
\(703\) | −2.46270e45 | + | 2.46270e45i | −0.692034 | + | 0.692034i | ||||
\(704\) | 3.15000e45i | 0.865264i | ||||||||
\(705\) | −8.71414e44 | + | 2.17035e45i | −0.233991 | + | 0.582778i | ||||
\(706\) | −5.08069e45 | −1.33367 | ||||||||
\(707\) | 3.35667e44 | + | 3.35667e44i | 0.0861387 | + | 0.0861387i | ||||
\(708\) | 1.31685e45 | − | 1.31685e45i | 0.330372 | − | 0.330372i | ||||
\(709\) | 5.73694e45i | 1.40715i | 0.710621 | + | 0.703575i | \(0.248414\pi\) | ||||
−0.710621 | + | 0.703575i | \(0.751586\pi\) | |||||||
\(710\) | 5.67131e45 | − | 2.42184e45i | 1.36003 | − | 0.580780i | ||||
\(711\) | 3.28330e45 | 0.769834 | ||||||||
\(712\) | 4.69414e43 | + | 4.69414e43i | 0.0107616 | + | 0.0107616i | ||||
\(713\) | 2.01865e44 | − | 2.01865e44i | 0.0452510 | − | 0.0452510i | ||||
\(714\) | 4.72430e44i | 0.103554i | ||||||||
\(715\) | 7.99473e44 | + | 1.87216e45i | 0.171359 | + | 0.401278i | ||||
\(716\) | 4.91572e45 | 1.03034 | ||||||||
\(717\) | −1.00208e45 | − | 1.00208e45i | −0.205399 | − | 0.205399i | ||||
\(718\) | −1.20312e45 | + | 1.20312e45i | −0.241168 | + | 0.241168i | ||||
\(719\) | − | 3.47833e45i | − | 0.681881i | −0.940085 | − | 0.340941i | \(-0.889255\pi\) | ||
0.940085 | − | 0.340941i | \(-0.110745\pi\) | |||||||
\(720\) | 3.87888e45 | + | 1.55741e45i | 0.743681 | + | 0.298595i | ||||
\(721\) | −1.55817e44 | −0.0292180 | ||||||||
\(722\) | 1.79128e45 | + | 1.79128e45i | 0.328525 | + | 0.328525i | ||||
\(723\) | −1.23980e45 | + | 1.23980e45i | −0.222401 | + | 0.222401i | ||||
\(724\) | − | 5.02594e45i | − | 0.881861i | ||||||
\(725\) | 2.79776e44 | − | 2.92240e44i | 0.0480179 | − | 0.0501569i | ||||
\(726\) | 8.66371e44 | 0.145451 | ||||||||
\(727\) | −6.97830e45 | − | 6.97830e45i | −1.14604 | − | 1.14604i | −0.987325 | − | 0.158713i | \(-0.949266\pi\) |
−0.158713 | − | 0.987325i | \(-0.550734\pi\) | |||||||
\(728\) | 2.41950e42 | − | 2.41950e42i | 0.000388707 | − | 0.000388707i | ||||
\(729\) | 1.72175e44i | 0.0270602i | ||||||||
\(730\) | 4.91053e45 | − | 1.22302e46i | 0.755027 | − | 1.88047i | ||||
\(731\) | −1.25275e46 | −1.88445 | ||||||||
\(732\) | −2.66463e45 | − | 2.66463e45i | −0.392157 | − | 0.392157i | ||||
\(733\) | −7.35143e44 | + | 7.35143e44i | −0.105854 | + | 0.105854i | −0.758050 | − | 0.652196i | \(-0.773848\pi\) |
0.652196 | + | 0.758050i | \(0.273848\pi\) | |||||||
\(734\) | − | 3.11027e45i | − | 0.438188i | ||||||
\(735\) | 2.98632e45 | − | 1.27526e45i | 0.411660 | − | 0.175793i | ||||
\(736\) | 2.30805e45 | 0.311315 | ||||||||
\(737\) | −6.93457e45 | − | 6.93457e45i | −0.915250 | − | 0.915250i | ||||
\(738\) | 3.73031e45 | − | 3.73031e45i | 0.481773 | − | 0.481773i | ||||
\(739\) | 3.26989e45i | 0.413259i | 0.978419 | + | 0.206629i | \(0.0662495\pi\) | ||||
−0.978419 | + | 0.206629i | \(0.933751\pi\) | |||||||
\(740\) | 3.76523e45 | + | 8.81719e45i | 0.465676 | + | 1.09049i | ||||
\(741\) | 1.52005e45 | 0.183979 | ||||||||
\(742\) | −6.22117e44 | − | 6.22117e44i | −0.0736901 | − | 0.0736901i | ||||
\(743\) | 4.52346e45 | − | 4.52346e45i | 0.524385 | − | 0.524385i | −0.394508 | − | 0.918893i | \(-0.629085\pi\) |
0.918893 | + | 0.394508i | \(0.129085\pi\) | |||||||
\(744\) | 1.24881e43i | 0.00141687i | ||||||||
\(745\) | 3.86832e45 | + | 1.55316e45i | 0.429558 | + | 0.172471i | ||||
\(746\) | −1.07218e46 | −1.16533 | ||||||||
\(747\) | 2.28108e45 | + | 2.28108e45i | 0.242667 | + | 0.242667i | ||||
\(748\) | −9.36394e45 | + | 9.36394e45i | −0.975063 | + | 0.975063i | ||||
\(749\) | 3.15208e44i | 0.0321284i | ||||||||
\(750\) | 5.82950e45 | − | 2.64098e45i | 0.581636 | − | 0.263502i | ||||
\(751\) | 7.01790e45 | 0.685438 | 0.342719 | − | 0.939438i | \(-0.388652\pi\) | ||||
0.342719 | + | 0.939438i | \(0.388652\pi\) | |||||||
\(752\) | 1.03445e46 | + | 1.03445e46i | 0.989059 | + | 0.989059i | ||||
\(753\) | 3.56791e45 | − | 3.56791e45i | 0.333960 | − | 0.333960i | ||||
\(754\) | − | 5.31085e44i | − | 0.0486657i | ||||||
\(755\) | −6.44428e45 | + | 1.60502e46i | −0.578127 | + | 1.43989i | ||||
\(756\) | −9.41094e44 | −0.0826579 | ||||||||
\(757\) | −3.74911e45 | − | 3.74911e45i | −0.322399 | − | 0.322399i | 0.527287 | − | 0.849687i | \(-0.323209\pi\) |
−0.849687 | + | 0.527287i | \(0.823209\pi\) | |||||||
\(758\) | −1.85695e46 | + | 1.85695e46i | −1.56348 | + | 1.56348i | ||||
\(759\) | 1.06361e45i | 0.0876830i | ||||||||
\(760\) | 1.00734e44 | − | 4.30168e43i | 0.00813128 | − | 0.00347233i | ||||
\(761\) | 1.12062e46 | 0.885738 | 0.442869 | − | 0.896586i | \(-0.353961\pi\) | ||||
0.442869 | + | 0.896586i | \(0.353961\pi\) | |||||||
\(762\) | −2.10346e45 | − | 2.10346e45i | −0.162800 | − | 0.162800i | ||||
\(763\) | 1.08827e45 | − | 1.08827e45i | 0.0824794 | − | 0.0824794i | ||||
\(764\) | 2.01906e46i | 1.49850i | ||||||||
\(765\) | 6.79583e45 | + | 1.59141e46i | 0.493923 | + | 1.15664i | ||||
\(766\) | 1.66170e46 | 1.18275 | ||||||||
\(767\) | −5.24216e45 | − | 5.24216e45i | −0.365413 | − | 0.365413i | ||||
\(768\) | −4.75649e45 | + | 4.75649e45i | −0.324719 | + | 0.324719i | ||||
\(769\) | − | 1.41937e46i | − | 0.949017i | −0.880251 | − | 0.474509i | \(-0.842626\pi\) | ||
0.880251 | − | 0.474509i | \(-0.157374\pi\) | |||||||
\(770\) | −1.80265e45 | − | 7.23781e44i | −0.118048 | − | 0.0473975i | ||||
\(771\) | −3.46257e45 | −0.222090 | ||||||||
\(772\) | −1.18432e46 | − | 1.18432e46i | −0.744033 | − | 0.744033i | ||||
\(773\) | 1.48517e46 | − | 1.48517e46i | 0.913912 | − | 0.913912i | −0.0826654 | − | 0.996577i | \(-0.526343\pi\) |
0.996577 | + | 0.0826654i | \(0.0263433\pi\) | |||||||
\(774\) | − | 2.21957e46i | − | 1.33787i | ||||||
\(775\) | −3.54954e45 | − | 3.39816e45i | −0.209577 | − | 0.200639i | ||||
\(776\) | −3.28282e44 | −0.0189871 | ||||||||
\(777\) | 6.91866e44 | + | 6.91866e44i | 0.0391999 | + | 0.0391999i | ||||
\(778\) | −2.05360e46 | + | 2.05360e46i | −1.13984 | + | 1.13984i | ||||
\(779\) | − | 9.14169e45i | − | 0.497081i | ||||||
\(780\) | 1.55911e45 | − | 3.88312e45i | 0.0830544 | − | 0.206856i | ||||
\(781\) | 1.76411e46 | 0.920682 | ||||||||
\(782\) | 6.80819e45 | + | 6.80819e45i | 0.348116 | + | 0.348116i | ||||
\(783\) | 7.96005e44 | − | 7.96005e44i | 0.0398775 | − | 0.0398775i | ||||
\(784\) | − | 2.03118e46i | − | 0.996992i | ||||||
\(785\) | −2.48273e46 | + | 1.06021e46i | −1.19403 | + | 0.509890i | ||||
\(786\) | −2.37170e46 | −1.11763 | ||||||||
\(787\) | 9.31777e45 | + | 9.31777e45i | 0.430246 | + | 0.430246i | 0.888712 | − | 0.458466i | \(-0.151601\pi\) |
−0.458466 | + | 0.888712i | \(0.651601\pi\) | |||||||
\(788\) | 7.08818e45 | − | 7.08818e45i | 0.320712 | − | 0.320712i | ||||
\(789\) | − | 1.75350e46i | − | 0.777454i | ||||||
\(790\) | −1.23493e46 | − | 2.89188e46i | −0.536549 | − | 1.25646i | ||||
\(791\) | 1.35678e45 | 0.0577678 | ||||||||
\(792\) | 1.27861e44 | + | 1.27861e44i | 0.00533500 | + | 0.00533500i | ||||
\(793\) | −1.06075e46 | + | 1.06075e46i | −0.433751 | + | 0.433751i | ||||
\(794\) | − | 4.18102e46i | − | 1.67554i | ||||||
\(795\) | 7.69487e45 | + | 3.08956e45i | 0.302223 | + | 0.121345i | ||||
\(796\) | 4.62445e46 | 1.78013 | ||||||||
\(797\) | 1.50949e46 | + | 1.50949e46i | 0.569505 | + | 0.569505i | 0.931990 | − | 0.362485i | \(-0.118072\pi\) |
−0.362485 | + | 0.931990i | \(0.618072\pi\) | |||||||
\(798\) | −1.02564e45 | + | 1.02564e45i | −0.0379270 | + | 0.0379270i | ||||
\(799\) | 6.05642e46i | 2.19517i | ||||||||
\(800\) | −8.65409e44 | − | 3.97186e46i | −0.0307455 | − | 1.41109i | ||||
\(801\) | −3.21994e46 | −1.12132 | ||||||||
\(802\) | 2.50714e46 | + | 2.50714e46i | 0.855834 | + | 0.855834i | ||||
\(803\) | 2.66589e46 | − | 2.66589e46i | 0.892058 | − | 0.892058i | ||||
\(804\) | 2.01583e46i | 0.661237i | ||||||||
\(805\) | −2.62108e44 | + | 6.52807e44i | −0.00842842 | + | 0.0209919i | ||||
\(806\) | −6.45055e45 | −0.203346 | ||||||||
\(807\) | 5.24525e45 | + | 5.24525e45i | 0.162102 | + | 0.162102i | ||||
\(808\) | −2.99253e44 | + | 2.99253e44i | −0.00906685 | + | 0.00906685i | ||||
\(809\) | − | 1.95564e46i | − | 0.580914i | −0.956888 | − | 0.290457i | \(-0.906193\pi\) | ||
0.956888 | − | 0.290457i | \(-0.0938074\pi\) | |||||||
\(810\) | −1.90741e46 | + | 8.14530e45i | −0.555501 | + | 0.237217i | ||||
\(811\) | 2.96178e46 | 0.845704 | 0.422852 | − | 0.906199i | \(-0.361029\pi\) | ||||
0.422852 | + | 0.906199i | \(0.361029\pi\) | |||||||
\(812\) | 1.78484e44 | + | 1.78484e44i | 0.00499693 | + | 0.00499693i | ||||
\(813\) | 5.85935e45 | − | 5.85935e45i | 0.160842 | − | 0.160842i | ||||
\(814\) | 5.50647e46i | 1.48212i | ||||||||
\(815\) | 1.57577e46 | + | 3.69005e46i | 0.415883 | + | 0.973890i | ||||
\(816\) | −2.78513e46 | −0.720779 | ||||||||
\(817\) | −2.71969e46 | − | 2.71969e46i | −0.690188 | − | 0.690188i | ||||
\(818\) | −3.05093e45 | + | 3.05093e45i | −0.0759240 | + | 0.0759240i | ||||
\(819\) | 1.65965e45i | 0.0405018i | ||||||||
\(820\) | −2.33533e46 | − | 9.37656e45i | −0.558890 | − | 0.224400i | ||||
\(821\) | −6.76066e46 | −1.58671 | −0.793356 | − | 0.608758i | \(-0.791668\pi\) | ||||
−0.793356 | + | 0.608758i | \(0.791668\pi\) | |||||||
\(822\) | 2.17550e46 | + | 2.17550e46i | 0.500738 | + | 0.500738i | ||||
\(823\) | 4.81030e45 | − | 4.81030e45i | 0.108586 | − | 0.108586i | −0.650726 | − | 0.759313i | \(-0.725535\pi\) |
0.759313 | + | 0.650726i | \(0.225535\pi\) | |||||||
\(824\) | − | 1.38913e44i | − | 0.00307545i | ||||||
\(825\) | 1.83035e46 | − | 3.98805e44i | 0.397439 | − | 0.00865959i | ||||
\(826\) | 7.07417e45 | 0.150659 | ||||||||
\(827\) | −3.39657e46 | − | 3.39657e46i | −0.709500 | − | 0.709500i | 0.256930 | − | 0.966430i | \(-0.417289\pi\) |
−0.966430 | + | 0.256930i | \(0.917289\pi\) | |||||||
\(828\) | −6.00809e45 | + | 6.00809e45i | −0.123098 | + | 0.123098i | ||||
\(829\) | 2.44834e46i | 0.492039i | 0.969265 | + | 0.246019i | \(0.0791227\pi\) | ||||
−0.969265 | + | 0.246019i | \(0.920877\pi\) | |||||||
\(830\) | 1.15117e46 | − | 2.86712e46i | 0.226930 | − | 0.565192i | ||||
\(831\) | −4.66371e45 | −0.0901810 | ||||||||
\(832\) | −1.82259e46 | − | 1.82259e46i | −0.345714 | − | 0.345714i | ||||
\(833\) | 5.94602e46 | − | 5.94602e46i | 1.10639 | − | 1.10639i | ||||
\(834\) | 5.97467e46i | 1.09058i | ||||||||
\(835\) | −6.58839e46 | + | 2.81346e46i | −1.17976 | + | 0.503799i | ||||
\(836\) | −4.06580e46 | −0.714242 | ||||||||
\(837\) | −9.66826e45 | − | 9.66826e45i | −0.166625 | − | 0.166625i | ||||
\(838\) | 2.27894e46 | − | 2.27894e46i | 0.385326 | − | 0.385326i | ||||
\(839\) | 5.76799e46i | 0.956826i | 0.878135 | + | 0.478413i | \(0.158788\pi\) | ||||
−0.878135 | + | 0.478413i | \(0.841212\pi\) | |||||||
\(840\) | −1.20850e43 | − | 2.82999e43i | −0.000196688 | − | 0.000460593i | ||||
\(841\) | 6.23214e46 | 0.995179 | ||||||||
\(842\) | 7.03912e46 | + | 7.03912e46i | 1.10287 | + | 1.10287i | ||||
\(843\) | 1.40546e46 | − | 1.40546e46i | 0.216061 | − | 0.216061i | ||||
\(844\) | 5.56404e46i | 0.839288i | ||||||||
\(845\) | 4.72397e46 | + | 1.89672e46i | 0.699197 | + | 0.280734i | ||||
\(846\) | −1.07305e47 | −1.55846 | ||||||||
\(847\) | 1.15908e45 | + | 1.15908e45i | 0.0165188 | + | 0.0165188i | ||||
\(848\) | 3.66758e46 | − | 3.66758e46i | 0.512915 | − | 0.512915i | ||||
\(849\) | 1.68327e45i | 0.0231010i | ||||||||
\(850\) | 1.14608e47 | − | 1.19713e47i | 1.54352 | − | 1.61228i | ||||
\(851\) | 1.99410e46 | 0.263556 | ||||||||
\(852\) | −2.56408e46 | − | 2.56408e46i | −0.332581 | − | 0.332581i | ||||
\(853\) | 5.36884e46 | − | 5.36884e46i | 0.683433 | − | 0.683433i | −0.277339 | − | 0.960772i | \(-0.589453\pi\) |
0.960772 | + | 0.277339i | \(0.0894525\pi\) | |||||||
\(854\) | − | 1.43145e46i | − | 0.178834i | ||||||
\(855\) | −1.97955e46 | + | 4.93029e46i | −0.242722 | + | 0.604525i | ||||
\(856\) | −2.81013e44 | −0.00338179 | ||||||||
\(857\) | −5.34870e46 | − | 5.34870e46i | −0.631764 | − | 0.631764i | 0.316746 | − | 0.948510i | \(-0.397410\pi\) |
−0.948510 | + | 0.316746i | \(0.897410\pi\) | |||||||
\(858\) | 1.69938e46 | − | 1.69938e46i | 0.197012 | − | 0.197012i | ||||
\(859\) | − | 2.66594e44i | − | 0.00303361i | −0.999999 | − | 0.00151681i | \(-0.999517\pi\) | ||
0.999999 | − | 0.00151681i | \(-0.000482815\pi\) | |||||||
\(860\) | −9.73728e46 | + | 4.15814e46i | −1.08758 | + | 0.464434i | ||||
\(861\) | −2.56824e45 | −0.0281569 | ||||||||
\(862\) | 5.32577e46 | + | 5.32577e46i | 0.573147 | + | 0.573147i | ||||
\(863\) | −1.10646e47 | + | 1.10646e47i | −1.16886 | + | 1.16886i | −0.186381 | + | 0.982478i | \(0.559676\pi\) |
−0.982478 | + | 0.186381i | \(0.940324\pi\) | |||||||
\(864\) | − | 1.10543e47i | − | 1.14634i | ||||||
\(865\) | −4.56794e46 | − | 1.06969e47i | −0.465011 | − | 1.08893i | ||||
\(866\) | −6.53504e45 | −0.0653073 | ||||||||
\(867\) | −4.89252e46 | − | 4.89252e46i | −0.479984 | − | 0.479984i | ||||
\(868\) | 2.16786e45 | − | 2.16786e45i | 0.0208793 | − | 0.0208793i | ||||
\(869\) | − | 8.99546e46i | − | 0.850564i | ||||||
\(870\) | −4.43230e45 | − | 1.77961e45i | −0.0411454 | − | 0.0165202i | ||||
\(871\) | 8.02469e46 | 0.731371 | ||||||||
\(872\) | 9.70213e44 | + | 9.70213e44i | 0.00868167 | + | 0.00868167i | ||||
\(873\) | 1.12592e47 | − | 1.12592e47i | 0.989192 | − | 0.989192i | ||||
\(874\) | 2.95610e46i | 0.254998i | ||||||||
\(875\) | 1.13323e46 | + | 4.26578e45i | 0.0959817 | + | 0.0361302i | ||||
\(876\) | −7.74955e46 | −0.644482 | ||||||||
\(877\) | −3.60474e44 | − | 3.60474e44i | −0.00294361 | − | 0.00294361i | 0.705633 | − | 0.708577i | \(-0.250663\pi\) |
−0.708577 | + | 0.705633i | \(0.750663\pi\) | |||||||
\(878\) | −7.13506e46 | + | 7.13506e46i | −0.572118 | + | 0.572118i | ||||
\(879\) | 5.02197e46i | 0.395414i | ||||||||
\(880\) | 4.26692e46 | − | 1.06272e47i | 0.329907 | − | 0.821669i | ||||
\(881\) | −5.47673e46 | −0.415821 | −0.207911 | − | 0.978148i | \(-0.566666\pi\) | ||||
−0.207911 | + | 0.978148i | \(0.566666\pi\) | |||||||
\(882\) | 1.05349e47 | + | 1.05349e47i | 0.785479 | + | 0.785479i | ||||
\(883\) | −1.47209e47 | + | 1.47209e47i | −1.07786 | + | 1.07786i | −0.0811591 | + | 0.996701i | \(0.525862\pi\) |
−0.996701 | + | 0.0811591i | \(0.974138\pi\) | |||||||
\(884\) | − | 1.08360e47i | − | 0.779168i | ||||||
\(885\) | −6.13156e46 | + | 2.61838e46i | −0.432991 | + | 0.184901i | ||||
\(886\) | 2.77194e47 | 1.92240 | ||||||||
\(887\) | 4.23244e46 | + | 4.23244e46i | 0.288279 | + | 0.288279i | 0.836399 | − | 0.548120i | \(-0.184656\pi\) |
−0.548120 | + | 0.836399i | \(0.684656\pi\) | |||||||
\(888\) | −6.16809e44 | + | 6.16809e44i | −0.00412613 | + | 0.00412613i | ||||
\(889\) | − | 5.62826e45i | − | 0.0369782i | ||||||
\(890\) | 1.21110e47 | + | 2.83608e47i | 0.781519 | + | 1.83011i | ||||
\(891\) | −5.93318e46 | −0.376049 | ||||||||
\(892\) | 8.27730e46 | + | 8.27730e46i | 0.515289 | + | 0.515289i | ||||
\(893\) | −1.31484e47 | + | 1.31484e47i | −0.803988 | + | 0.803988i | ||||
\(894\) | − | 4.92114e46i | − | 0.295573i | ||||||
\(895\) | −1.63315e47 | − | 6.55724e46i | −0.963513 | − | 0.386859i | ||||
\(896\) | −3.82060e44 | −0.00221413 | ||||||||
\(897\) | −6.15407e45 | − | 6.15407e45i | −0.0350335 | − | 0.0350335i | ||||
\(898\) | −3.33034e47 | + | 3.33034e47i | −1.86237 | + | 1.86237i | ||||
\(899\) | 3.66728e45i | 0.0201460i | ||||||||
\(900\) | 1.05645e47 | + | 1.01139e47i | 0.570121 | + | 0.545807i | ||||
\(901\) | 2.14727e47 | 1.13839 | ||||||||
\(902\) | −1.02201e47 | − | 1.02201e47i | −0.532295 | − | 0.532295i | ||||
\(903\) | −7.64064e45 | + | 7.64064e45i | −0.0390954 | + | 0.0390954i | ||||
\(904\) | 1.20959e45i | 0.00608056i | ||||||||
\(905\) | −6.70427e46 | + | 1.66977e47i | −0.331111 | + | 0.824667i | ||||
\(906\) | 2.04184e47 | 0.990767 | ||||||||
\(907\) | −1.38270e46 | − | 1.38270e46i | −0.0659192 | − | 0.0659192i | 0.673379 | − | 0.739298i | \(-0.264842\pi\) |
−0.739298 | + | 0.673379i | \(0.764842\pi\) | |||||||
\(908\) | 1.37035e47 | − | 1.37035e47i | 0.641888 | − | 0.641888i | ||||
\(909\) | − | 2.05272e47i | − | 0.944730i | ||||||
\(910\) | 1.46180e46 | − | 6.24235e45i | 0.0661035 | − | 0.0282284i | ||||
\(911\) | 4.26071e46 | 0.189316 | 0.0946581 | − | 0.995510i | \(-0.469824\pi\) | ||||
0.0946581 | + | 0.995510i | \(0.469824\pi\) | |||||||
\(912\) | −6.04647e46 | − | 6.04647e46i | −0.263988 | − | 0.263988i | ||||
\(913\) | 6.24962e46 | − | 6.24962e46i | 0.268115 | − | 0.268115i | ||||
\(914\) | − | 4.94696e47i | − | 2.08545i | ||||||
\(915\) | 5.29827e46 | + | 1.24072e47i | 0.219481 | + | 0.513966i | ||||
\(916\) | −6.36644e46 | −0.259161 | ||||||||
\(917\) | −3.17299e46 | − | 3.17299e46i | −0.126929 | − | 0.126929i | ||||
\(918\) | 3.26076e47 | − | 3.26076e47i | 1.28185 | − | 1.28185i | ||||
\(919\) | 2.35910e47i | 0.911377i | 0.890139 | + | 0.455689i | \(0.150607\pi\) | ||||
−0.890139 | + | 0.455689i | \(0.849393\pi\) | |||||||
\(920\) | −5.81988e44 | − | 2.33673e44i | −0.00220957 | − | 0.000887164i | ||||
\(921\) | 5.92417e46 | 0.221041 | ||||||||
\(922\) | −4.15167e47 | − | 4.15167e47i | −1.52240 | − | 1.52240i | ||||
\(923\) | −1.02072e47 | + | 1.02072e47i | −0.367856 | + | 0.367856i | ||||
\(924\) | 1.14223e46i | 0.0404579i | ||||||||
\(925\) | −7.47692e45 | − | 3.43159e47i | −0.0260289 | − | 1.19462i | ||||
\(926\) | −6.82422e47 | −2.33495 | ||||||||
\(927\) | 4.76438e46 | + | 4.76438e46i | 0.160225 | + | 0.160225i | ||||
\(928\) | −2.09652e46 | + | 2.09652e46i | −0.0692996 | + | 0.0692996i | ||||
\(929\) | 3.17649e46i | 0.103204i | 0.998668 | + | 0.0516019i | \(0.0164327\pi\) | ||||
−0.998668 | + | 0.0516019i | \(0.983567\pi\) | |||||||
\(930\) | −2.16151e46 | + | 5.38346e46i | −0.0690287 | + | 0.171923i | ||||
\(931\) | 2.58175e47 | 0.810436 | ||||||||
\(932\) | 5.15290e46 | + | 5.15290e46i | 0.159000 | + | 0.159000i | ||||
\(933\) | −8.90334e46 | + | 8.90334e46i | −0.270051 | + | 0.270051i | ||||
\(934\) | − | 2.65746e47i | − | 0.792351i | ||||||
\(935\) | 4.36007e47 | − | 1.86189e47i | 1.27793 | − | 0.545719i | ||||
\(936\) | −1.47961e45 | −0.00426317 | ||||||||
\(937\) | −2.00815e47 | − | 2.00815e47i | −0.568803 | − | 0.568803i | 0.362990 | − | 0.931793i | \(-0.381756\pi\) |
−0.931793 | + | 0.362990i | \(0.881756\pi\) | |||||||
\(938\) | −5.41457e46 | + | 5.41457e46i | −0.150771 | + | 0.150771i | ||||
\(939\) | 1.02152e46i | 0.0279638i | ||||||||
\(940\) | 2.01026e47 | + | 4.70750e47i | 0.541012 | + | 1.26691i | ||||
\(941\) | 6.14677e47 | 1.62635 | 0.813173 | − | 0.582022i | \(-0.197738\pi\) | ||||
0.813173 | + | 0.582022i | \(0.197738\pi\) | |||||||
\(942\) | 2.25360e47 | + | 2.25360e47i | 0.586223 | + | 0.586223i | ||||
\(943\) | −3.70109e46 | + | 3.70109e46i | −0.0946549 | + | 0.0946549i | ||||
\(944\) | 4.17045e47i | 1.04865i | ||||||||
\(945\) | 3.12660e46 | + | 1.25536e46i | 0.0772971 | + | 0.0310355i | ||||
\(946\) | −6.08108e47 | −1.47816 | ||||||||
\(947\) | 2.97164e47 | + | 2.97164e47i | 0.710226 | + | 0.710226i | 0.966582 | − | 0.256356i | \(-0.0825219\pi\) |
−0.256356 | + | 0.966582i | \(0.582522\pi\) | |||||||
\(948\) | −1.30746e47 | + | 1.30746e47i | −0.307252 | + | 0.307252i | ||||
\(949\) | 3.08497e47i | 0.712839i | ||||||||
\(950\) | 5.08708e47 | − | 1.10840e46i | 1.15582 | − | 0.0251836i | ||||
\(951\) | −1.92820e47 | −0.430787 | ||||||||
\(952\) | −5.63477e44 | − | 5.63477e44i | −0.00123790 | − | 0.00123790i | ||||
\(953\) | 1.32281e47 | − | 1.32281e47i | 0.285766 | − | 0.285766i | −0.549637 | − | 0.835404i | \(-0.685234\pi\) |
0.835404 | + | 0.549637i | \(0.185234\pi\) | |||||||
\(954\) | 3.80446e47i | 0.808200i | ||||||||
\(955\) | 2.69329e47 | − | 6.70792e47i | 0.562639 | − | 1.40131i | ||||
\(956\) | −3.10170e47 | −0.637197 | ||||||||
\(957\) | −9.66135e45 | − | 9.66135e45i | −0.0195185 | − | 0.0195185i | ||||
\(958\) | −2.47536e47 | + | 2.47536e47i | −0.491803 | + | 0.491803i | ||||
\(959\) | 5.82103e46i | 0.113737i | ||||||||
\(960\) | −2.13182e47 | + | 9.10359e46i | −0.409648 | + | 0.174933i | ||||
\(961\) | −4.84602e47 | −0.915821 | ||||||||
\(962\) | −3.18604e47 | − | 3.18604e47i | −0.592176 | − | 0.592176i | ||||
\(963\) | 9.63804e46 | − | 9.63804e46i | 0.176185 | − | 0.176185i | ||||
\(964\) | 3.83748e47i | 0.689943i | ||||||||
\(965\) | 2.35486e47 | + | 5.51447e47i | 0.416417 | + | 0.975140i | ||||
\(966\) | 8.30478e45 | 0.0144442 | ||||||||
\(967\) | −5.79946e47 | − | 5.79946e47i | −0.992119 | − | 0.992119i | 0.00785024 | − | 0.999969i | \(-0.497501\pi\) |
−0.999969 | + | 0.00785024i | \(0.997501\pi\) | |||||||
\(968\) | −1.03334e45 | + | 1.03334e45i | −0.00173875 | + | 0.00173875i | ||||
\(969\) | − | 3.54006e47i | − | 0.585909i | ||||||
\(970\) | −1.41518e48 | − | 5.68209e47i | −2.30391 | − | 0.925039i | ||||
\(971\) | 5.43310e47 | 0.870042 | 0.435021 | − | 0.900420i | \(-0.356741\pi\) | ||||
0.435021 | + | 0.900420i | \(0.356741\pi\) | |||||||
\(972\) | 4.48034e47 | + | 4.48034e47i | 0.705750 | + | 0.705750i | ||||
\(973\) | −7.99325e46 | + | 7.99325e46i | −0.123856 | + | 0.123856i | ||||
\(974\) | 3.10677e46i | 0.0473550i | ||||||||
\(975\) | −1.03597e47 | + | 1.08212e47i | −0.155336 | + | 0.162256i | ||||
\(976\) | 8.43888e47 | 1.24477 | ||||||||
\(977\) | 4.22661e47 | + | 4.22661e47i | 0.613309 | + | 0.613309i | 0.943807 | − | 0.330498i | \(-0.107217\pi\) |
−0.330498 | + | 0.943807i | \(0.607217\pi\) | |||||||
\(978\) | 3.34949e47 | − | 3.34949e47i | 0.478143 | − | 0.478143i | ||||
\(979\) | 8.82187e47i | 1.23890i | ||||||||
\(980\) | 2.64808e47 | − | 6.59532e47i | 0.365859 | − | 0.911210i | ||||
\(981\) | −6.65517e47 | −0.904596 | ||||||||
\(982\) | −2.13289e47 | − | 2.13289e47i | −0.285222 | − | 0.285222i | ||||
\(983\) | 8.81873e47 | − | 8.81873e47i | 1.16025 | − | 1.16025i | 0.175823 | − | 0.984422i | \(-0.443741\pi\) |
0.984422 | − | 0.175823i | \(-0.0562587\pi\) | |||||||
\(984\) | − | 2.28963e45i | − | 0.00296376i | ||||||
\(985\) | −3.30042e47 | + | 1.40939e47i | −0.420330 | + | 0.179495i | ||||
\(986\) | −1.23685e47 | −0.154983 | ||||||||
\(987\) | 3.69388e46 | + | 3.69388e46i | 0.0455416 | + | 0.0455416i | ||||
\(988\) | 2.35247e47 | − | 2.35247e47i | 0.285373 | − | 0.285373i | ||||
\(989\) | 2.20218e47i | 0.262853i | ||||||||
\(990\) | 3.29883e47 | + | 7.72501e47i | 0.387434 | + | 0.907268i | ||||
\(991\) | −3.21330e46 | −0.0371341 | −0.0185671 | − | 0.999828i | \(-0.505910\pi\) | ||||
−0.0185671 | + | 0.999828i | \(0.505910\pi\) | |||||||
\(992\) | 2.54642e47 | + | 2.54642e47i | 0.289564 | + | 0.289564i | ||||
\(993\) | −4.85023e47 | + | 4.85023e47i | −0.542719 | + | 0.542719i | ||||
\(994\) | − | 1.37743e47i | − | 0.151666i | ||||||
\(995\) | −1.53638e48 | − | 6.16872e47i | −1.66468 | − | 0.668383i | ||||
\(996\) | −1.81672e47 | −0.193704 | ||||||||
\(997\) | 2.42029e47 | + | 2.42029e47i | 0.253948 | + | 0.253948i | 0.822587 | − | 0.568639i | \(-0.192530\pi\) |
−0.568639 | + | 0.822587i | \(0.692530\pi\) | |||||||
\(998\) | 1.82831e48 | − | 1.82831e48i | 1.88783 | − | 1.88783i | ||||
\(999\) | − | 9.55066e47i | − | 0.970478i |
(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.2.13 | ✓ | 30 | |
5.2 | odd | 4 | 25.33.c.b.18.3 | 30 | |||
5.3 | odd | 4 | inner | 5.33.c.a.3.13 | yes | 30 | |
5.4 | even | 2 | 25.33.c.b.7.3 | 30 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5.33.c.a.2.13 | ✓ | 30 | 1.1 | even | 1 | trivial | |
5.33.c.a.3.13 | yes | 30 | 5.3 | odd | 4 | inner | |
25.33.c.b.7.3 | 30 | 5.4 | even | 2 | |||
25.33.c.b.18.3 | 30 | 5.2 | odd | 4 |