1
New Number: 5.133 | AESZ: | Superseeker: 192 1016256 | Hash: 0f3cb34d2bc462fbc58cdf15040595d1
Degree: 5
\(\theta^4+2^{4} x\left(24\theta^4-96\theta^3-70\theta^2-22\theta-3\right)-2^{10} x^{2}\left(124\theta^4+496\theta^3-271\theta^2-202\theta-45\right)-2^{17} 3^{2} x^{3}\left(32\theta^4-56\theta^3-66\theta^2-31\theta-5\right)+2^{24} 3^{3} x^{4}(\theta+1)(2\theta+1)(6\theta^2+11\theta+6)+2^{32} 3^{3} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 48, 5136, 710400, 112104720, ... --> OEIS Normalized instanton numbers (n0=1): 192, -9940, 1016256, -134713756, 20854352960, ... ; Common denominator:...
\((256z-1)(64z+1)(192z-1)(1+384z)^2\)
| \(-\frac{ 1}{ 64}\) | \(-\frac{ 1}{ 384}\) | \(0\) | \(\frac{ 1}{ 256}\) | \(\frac{ 1}{ 192}\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) |
| \(1\) | \(3\) | \(0\) | \(1\) | \(1\) | \(1\) |
| \(2\) | \(4\) | \(0\) | \(2\) | \(2\) | \(\frac{ 3}{ 2}\) |
2
New Number: 8.46 | AESZ: | Superseeker: 192 616896 | Hash: e38642e59fc2f9e3117437fcdbfe450e
Degree: 8
\(\theta^4-2^{5} x\left(11\theta^4+46\theta^3+32\theta^2+9\theta+1\right)-2^{8} x^{2}\left(613\theta^4+892\theta^3-29\theta^2-66\theta-7\right)-2^{13} x^{3}\left(1315\theta^4+978\theta^3+2243\theta^2+1068\theta+179\right)+2^{18} x^{4}\left(949\theta^4-2986\theta^3-3302\theta^2-1569\theta-313\right)+2^{23} x^{5}\left(420\theta^4+1566\theta^3-1116\theta^2-1290\theta-353\right)-2^{26} x^{6}\left(709\theta^4-1416\theta^3-1163\theta^2-72\theta+131\right)-2^{31} 5 x^{7}\left(19\theta^4-10\theta^3-71\theta^2-66\theta-19\right)-2^{36} 5^{2} x^{8}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 32, 6224, 1859072, 679223056, ... --> OEIS Normalized instanton numbers (n0=1): 192, 3108, 616896, 73692781, 15330708544, ... ; Common denominator:...
\(-(16z+1)(16384z^3+2560z^2+624z-1)(-1-128z+2560z^2)^2\)
| ≈\(-0.078921-0.179189I\) | ≈\(-0.078921+0.179189I\) | \(-\frac{ 1}{ 16}\) | \(\frac{ 1}{ 40}-\frac{ 1}{ 160}\sqrt{ 26}\) | \(0\) | ≈\(0.001592\) | \(\frac{ 1}{ 40}+\frac{ 1}{ 160}\sqrt{ 26}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(3\) | \(0\) | \(1\) | \(3\) | \(1\) |
| \(2\) | \(2\) | \(2\) | \(4\) | \(0\) | \(2\) | \(4\) | \(1\) |