1
New Number: 10.8 | AESZ: | Superseeker: 7 -2044/9 | Hash: 772d055ae4c1a5d6a65a2b1f3ffa351b
Degree: 10
\(\theta^4-x\left(147\theta^2+10+60\theta+174\theta^3+111\theta^4\right)+2^{2} x^{2}\left(1269\theta^4+3576\theta^3+4595\theta^2+2722\theta+639\right)-2^{2} x^{3}\left(28236\theta^4+92256\theta^3+135641\theta^2+100407\theta+29996\right)+2^{4} 3 x^{4}\left(34932\theta^4+117280\theta^3+166025\theta^2+128238\theta+41467\right)-2^{6} x^{5}\left(266139\theta^4+937698\theta^3+1398643\theta^2+1056533\theta+325061\right)+2^{8} x^{6}\left(478785\theta^4+1758504\theta^3+2952901\theta^2+2388960\theta+754208\right)-2^{8} x^{7}\left(2371176\theta^4+9770640\theta^3+17775969\theta^2+15468753\theta+5209610\right)+2^{10} x^{8}\left(1853604\theta^4+9368112\theta^3+18957629\theta^2+17669710\theta+6248237\right)-2^{12} 11 x^{9}(2\theta+3)(36502\theta^3+178659\theta^2+286703\theta+145866)+2^{16} 3 5^{2} 11^{2} x^{10}(\theta+1)(2\theta+5)(2\theta+3)(\theta+3)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 10, 154, 2548, 27370, ... --> OEIS Normalized instanton numbers (n0=1): 7, -31/4, -2044/9, -1380, -8520, ... ; Common denominator:...
\((3z-1)(6400z^3-2352z^2+84z-1)(4z-1)^2(88z^2-8z+1)^2\)
| \(0\) | ≈\(0.019222-0.010265I\) | ≈\(0.019222+0.010265I\) | \(\frac{ 1}{ 22}-\frac{ 3}{ 44}\sqrt{ 2}I\) | \(\frac{ 1}{ 22}+\frac{ 3}{ 44}\sqrt{ 2}I\) | \(\frac{ 1}{ 4}\) | ≈\(0.329056\) | \(\frac{ 1}{ 3}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(\frac{ 3}{ 2}\) |
| \(0\) | \(1\) | \(1\) | \(3\) | \(3\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(\frac{ 5}{ 2}\) |
| \(0\) | \(2\) | \(2\) | \(4\) | \(4\) | \(1\) | \(2\) | \(2\) | \(3\) |
2
New Number: 13.11 | AESZ: | Superseeker: 7 -2044/9 | Hash: d6e183df7853fe5068c8b8cdeb3f63cb
Degree: 13
\(\theta^4-x\left(98\theta^4+164\theta^3+137\theta^2+55\theta+9\right)+x^{2}\left(3822\theta^4+11400\theta^3+14901\theta^2+8746\theta+2007\right)-x^{3}\left(64148\theta^4+196344\theta^3+271665\theta^2+199855\theta+60354\right)+x^{4}\left(802771\theta^4+2242504\theta^3+2203855\theta^2+1316868\theta+390636\right)-2 3 x^{5}\left(1040145\theta^4+2982426\theta^3+3578912\theta^2+1897395\theta+345411\right)+2 3^{2} x^{6}\left(1927994\theta^4+4917832\theta^3+7329041\theta^2+5154630\theta+1338003\right)-2 3^{5} x^{7}\left(219316\theta^4+761432\theta^3+1064075\theta^2+703129\theta+181966\right)+3^{4} x^{8}\left(754759\theta^4+7471824\theta^3+13904030\theta^2+8830464\theta+1544112\right)+3^{7} x^{9}\left(174966\theta^4+736236\theta^3+1307237\theta^2+1340471\theta+568265\right)-3^{10} x^{10}(\theta+1)(8018\theta^3+62342\theta^2+139257\theta+108861)-3^{9} x^{11}(\theta+1)(\theta+2)(28988\theta^2+81396\theta+36331)+3^{12} x^{12}(\theta+3)(\theta+2)(\theta+1)(1061\theta+5386)+2 3^{15} 17 x^{13}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 9, 135, 2115, 18063, ... --> OEIS Normalized instanton numbers (n0=1): 7, -31/4, -2044/9, -1380, -8520, ... ; Common denominator:...
\((2z-1)(4131z^3-2187z^2+81z-1)(3z-1)^2(81z^2-6z+1)^2(z+1)^3\)
| \(-1\) | \(0\) | ≈\(0.019487-0.01067I\) | ≈\(0.019487+0.01067I\) | \(\frac{ 1}{ 27}-\frac{ 2}{ 27}\sqrt{ 2}I\) | \(\frac{ 1}{ 27}+\frac{ 2}{ 27}\sqrt{ 2}I\) | \(\frac{ 1}{ 3}\) | ≈\(0.490438\) | \(\frac{ 1}{ 2}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(\frac{ 1}{ 2}\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(2\) |
| \(\frac{ 3}{ 2}\) | \(0\) | \(1\) | \(1\) | \(3\) | \(3\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(3\) |
| \(2\) | \(0\) | \(2\) | \(2\) | \(4\) | \(4\) | \(1\) | \(2\) | \(2\) | \(4\) |