1
New Number: 12.16 | AESZ: | Superseeker: 288 -8252768 | Hash: e5412f8624ff9afc10459abda2d297d0
Degree: 12
\(\theta^4-2^{4} x\left(160\theta^4+224\theta^3+200\theta^2+88\theta+17\right)+2^{12} x^{2}\left(992\theta^4+1184\theta^3+1664\theta^2+1368\theta+399\right)-2^{22} x^{3}\left(1172\theta^4+1104\theta^3+542\theta^2+912\theta+331\right)+2^{28} x^{4}\left(16624\theta^4+15104\theta^3+5408\theta^2-752\theta-1829\right)-2^{37} x^{5}\left(23072\theta^4+16784\theta^3+23748\theta^2+1100\theta-4281\right)+2^{47} x^{6}\left(12696\theta^4+8556\theta^3+18218\theta^2+6591\theta+144\right)-2^{52} x^{7}\left(167440\theta^4+175808\theta^3+289048\theta^2+160176\theta+37033\right)+2^{61} x^{8}\left(96496\theta^4+172672\theta^3+241896\theta^2+158752\theta+44823\right)-2^{70} x^{9}\left(36784\theta^4+100224\theta^3+148008\theta^2+108576\theta+32891\right)+2^{79} x^{10}\left(8720\theta^4+32704\theta^3+54968\theta^2+44784\theta+14529\right)-2^{91} x^{11}\left(144\theta^4+696\theta^3+1352\theta^2+1222\theta+427\right)+2^{99} x^{12}\left((2\theta+3)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 272, 85264, 30040320, 11678489872, ... --> OEIS Normalized instanton numbers (n0=1): 288, 59200, -8252768, -1223488576, 585571467872, ... ; Common denominator:...
\((512z-1)(65536z^2-768z+1)(134217728z^3-655360z^2+256z-1)^2(256z-1)^3\)
| \(0\) | ≈\(3.7e-05-0.001244I\) | ≈\(3.7e-05+0.001244I\) | \(\frac{ 3}{ 512}-\frac{ 1}{ 512}\sqrt{ 5}\) | \(\frac{ 1}{ 512}\) | \(\frac{ 1}{ 256}\) | ≈\(0.004808\) | \(\frac{ 3}{ 512}+\frac{ 1}{ 512}\sqrt{ 5}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 3}{ 2}\) |
| \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(\frac{ 3}{ 2}\) |
| \(0\) | \(3\) | \(3\) | \(1\) | \(1\) | \(0\) | \(3\) | \(1\) | \(\frac{ 3}{ 2}\) |
| \(0\) | \(4\) | \(4\) | \(2\) | \(2\) | \(0\) | \(4\) | \(2\) | \(\frac{ 3}{ 2}\) |
2
New Number: 8.64 | AESZ: | Superseeker: 0 -32768 | Hash: 00b5810e4a2d21fec464e4e87169df86
Degree: 8
\(\theta^4-2^{4} x\left(32\theta^4+16\theta^3+14\theta^2+6\theta+1\right)+2^{10} x^{2}\left(86\theta^4+176\theta^3+184\theta^2+76\theta+13\right)-2^{16} x^{3}\left(61\theta^4+510\theta^3+620\theta^2+327\theta+68\right)-2^{22} x^{4}\left(110\theta^4-260\theta^3-942\theta^2-608\theta-141\right)+2^{26} x^{5}\left(708\theta^4+2160\theta^3-666\theta^2-1230\theta-397\right)+2^{32} x^{6}\left(134\theta^4-1536\theta^3-1488\theta^2-492\theta-29\right)-2^{38} 5 x^{7}\left(73\theta^4+170\theta^3+168\theta^2+83\theta+17\right)-2^{44} 5^{2} x^{8}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 16, 272, -15104, -2814704, ... --> OEIS Normalized instanton numbers (n0=1): 0, -1116, -32768, -2011784, -92274688, ... ; Common denominator:...
\(-(64z-1)(65536z^3+14336z^2-192z+1)(-1+128z+10240z^2)^2\)
| ≈\(-0.23168\) | \(-\frac{ 1}{ 160}-\frac{ 1}{ 320}\sqrt{ 14}\) | \(0\) | \(-\frac{ 1}{ 160}+\frac{ 1}{ 320}\sqrt{ 14}\) | ≈\(0.006465-0.004906I\) | ≈\(0.006465+0.004906I\) | \(\frac{ 1}{ 64}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(1\) | \(3\) | \(0\) | \(3\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(2\) | \(4\) | \(0\) | \(4\) | \(2\) | \(2\) | \(2\) | \(1\) |