31
New Number: 8.38 | AESZ: 346 | Superseeker: 713/8 571555/2 | Hash: 65579ed94e039ed095e1b5b7db3674ff
Degree: 8
\(2^{6} \theta^4-2^{3} x\left(5006\theta^4+6610\theta^3+4729\theta^2+1424\theta+168\right)+3^{3} x^{2}\left(183763\theta^4+261274\theta^3+109091\theta^2+22352\theta+2040\right)-3^{7} x^{3}\left(12866\theta^4+150366\theta^3+321775\theta^2+141888\theta+21336\right)-3^{10} x^{4}\left(233330\theta^4-119294\theta^3-333065\theta^2-149446\theta-23109\right)-3^{14} x^{5}\left(3165\theta^4-168162\theta^3+37135\theta^2+52394\theta+11440\right)+2 3^{17} x^{6}\left(28397\theta^4+18450\theta^3+13388\theta^2+7299\theta+1586\right)+3^{22} 11 x^{7}\left(113\theta^4+268\theta^3+284\theta^2+150\theta+32\right)+3^{25} 11^{2} x^{8}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 21, 2889, 636357, 171536121, ... --> OEIS Normalized instanton numbers (n0=1): 713/8, 3274, 571555/2, 66913005/2, 20047292157/4, ... ; Common denominator:...
\((27z-1)(6561z^3+2430z^2+457z-1)(-8+567z+24057z^2)^2\)
| ≈\(-0.186267-0.189115I\) | ≈\(-0.186267+0.189115I\) | \(-\frac{ 7}{ 594}-\frac{ 1}{ 1782}\sqrt{ 1497}\) | \(0\) | ≈\(0.002163\) | \(-\frac{ 7}{ 594}+\frac{ 1}{ 1782}\sqrt{ 1497}\) | \(\frac{ 1}{ 27}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(1\) | \(1\) | \(3\) | \(0\) | \(1\) | \(3\) | \(1\) | \(1\) |
| \(2\) | \(2\) | \(4\) | \(0\) | \(2\) | \(4\) | \(2\) | \(1\) |
32
New Number: 8.39 | AESZ: | Superseeker: -12/5 136/3 | Hash: c1330764e09752f7bb8e86b15541c588
Degree: 8
\(5^{2} \theta^4+2 3 5 x\left(51\theta^4+84\theta^3+72\theta^2+30\theta+5\right)+2^{2} 3 x^{2}\left(3297\theta^4+10236\theta^3+13562\theta^2+8110\theta+1830\right)+2^{2} 3^{3} x^{3}\left(3866\theta^4+14088\theta^3+21137\theta^2+14355\theta+3600\right)+2^{3} 3^{3} x^{4}\left(11680\theta^4+38792\theta^3+45641\theta^2+24205\theta+4854\right)+2^{4} 3^{5} x^{5}\left(2624\theta^4+8240\theta^3+8275\theta^2+2971\theta+216\right)+2^{5} 3^{5} x^{6}\left(3248\theta^4+8832\theta^3+9739\theta^2+4803\theta+882\right)+2^{7} 3^{7} x^{7}\left(144\theta^4+384\theta^3+428\theta^2+233\theta+51\right)+2^{9} 3^{7} x^{8}(4\theta+3)(\theta+1)^2(4\theta+5)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -6, 54, -348, -3690, ... --> OEIS Normalized instanton numbers (n0=1): -12/5, -21/5, 136/3, -1743/10, -1056/5, ... ; Common denominator:...
\((1+54z+1152z^2+6048z^3+3456z^4)(5+18z+72z^2)^2\)
| ≈\(-1.540068\) | ≈\(-0.152177\) | \(-\frac{ 1}{ 8}-\frac{ 1}{ 24}\sqrt{ 31}I\) | \(-\frac{ 1}{ 8}+\frac{ 1}{ 24}\sqrt{ 31}I\) | ≈\(-0.028878\) | ≈\(-0.028878\) | \(0\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 3}{ 4}\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(3\) | \(3\) | \(1\) | \(1\) | \(0\) | \(1\) |
| \(2\) | \(2\) | \(4\) | \(4\) | \(2\) | \(2\) | \(0\) | \(\frac{ 5}{ 4}\) |
33
New Number: 8.3 | AESZ: 105 | Superseeker: 8 -104 | Hash: 7b27135451cf2016217211c633b7ab83
Degree: 8
\(\theta^4-2^{2} x(3\theta^2+3\theta+1)(7\theta^2+7\theta+2)+2^{5} 3 x^{2}\left(15\theta^4+28\theta^3+39\theta^2+22\theta+4\right)-2^{10} x^{3}\left(21\theta^4-126\theta^3-386\theta^2-291\theta-76\right)+2^{14} x^{4}\left(37\theta^4+74\theta^3+50\theta^2+13\theta+6\right)+2^{18} x^{5}\left(21\theta^4+210\theta^3+118\theta^2-19\theta-24\right)+2^{21} 3 x^{6}\left(15\theta^4+32\theta^3+45\theta^2+32\theta+8\right)+2^{26} x^{7}(3\theta^2+3\theta+1)(7\theta^2+7\theta+2)+2^{32} x^{8}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 8, 200, 6272, 233896, ... --> OEIS Normalized instanton numbers (n0=1): 8, 71/2, -104, 4202, 50112, ... ; Common denominator:...
\((8z+1)(64z-1)(4z+1)(32z-1)(1+256z^2)^2\)
| \(-\frac{ 1}{ 4}\) | \(-\frac{ 1}{ 8}\) | \(0-\frac{ 1}{ 16}I\) | \(0\) | \(0+\frac{ 1}{ 16}I\) | \(\frac{ 1}{ 64}\) | \(\frac{ 1}{ 32}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(1\) | \(1\) | \(3\) | \(0\) | \(3\) | \(1\) | \(1\) | \(1\) |
| \(2\) | \(2\) | \(4\) | \(0\) | \(4\) | \(2\) | \(2\) | \(1\) |
34
New Number: 8.40 | AESZ: | Superseeker: 5/4 35/2 | Hash: d3cb0fbbc65d6c5dace733d3d1ca181b
Degree: 8
\(2^{4} \theta^4-2^{2} x\theta(2\theta^3+82\theta^2+53\theta+12)-x^{2}\left(4895\theta^4+18410\theta^3+26199\theta^2+18308\theta+5120\right)-x^{3}\left(60679\theta^4+272424\theta^3+497452\theta^2+430092\theta+143808\right)-x^{4}\left(344527\theta^4+1870838\theta^3+4034628\theta^2+3987101\theta+1478544\right)-x^{5}(\theta+1)(1076509\theta^3+5847783\theta^2+11226106\theta+7492832)-2 x^{6}(\theta+1)(\theta+2)(944887\theta^2+4249317\theta+5045304)-2^{8} 13 x^{7}(\theta+3)(\theta+2)(\theta+1)(518\theta+1381)-2^{5} 5 13^{2} 23 x^{8}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, 20, 168, 2652, ... --> OEIS Normalized instanton numbers (n0=1): 5/4, 57/16, 35/2, 459/4, 3615/4, ... ; Common denominator:...
\(-(23z-1)(5z+1)(2z+1)(z+1)(13z+4)^2(4z+1)^2\)
| \(-1\) | \(-\frac{ 1}{ 2}\) | \(-\frac{ 4}{ 13}\) | \(-\frac{ 1}{ 4}\) | \(-\frac{ 1}{ 5}\) | \(0\) | \(\frac{ 1}{ 23}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(\frac{ 1}{ 3}\) | \(1\) | \(0\) | \(1\) | \(2\) |
| \(1\) | \(1\) | \(3\) | \(\frac{ 2}{ 3}\) | \(1\) | \(0\) | \(1\) | \(3\) |
| \(2\) | \(2\) | \(4\) | \(1\) | \(2\) | \(0\) | \(2\) | \(4\) |
35
New Number: 8.41 | AESZ: | Superseeker: 16 7568/3 | Hash: 051d7068f49d14c45c3c3369d63d56b5
Degree: 8
\(3^{2} \theta^4-2^{2} 3^{2} x\left(23\theta^4+58\theta^3+44\theta^2+15\theta+2\right)-2^{5} 3 x^{2}\left(254\theta^4+662\theta^3+623\theta^2+309\theta+66\right)-2^{8} 3 x^{3}\left(569\theta^4+1092\theta^3+602\theta^2+285\theta+78\right)-2^{11} x^{4}\left(2266\theta^4+4076\theta^3+2167\theta^2+537\theta+18\right)-2^{16} x^{5}\left(519\theta^4+798\theta^3+821\theta^2+391\theta+62\right)-2^{19} x^{6}\left(305\theta^4+558\theta^3+625\theta^2+360\theta+82\right)-2^{24} x^{7}\left(26\theta^4+70\theta^3+83\theta^2+48\theta+11\right)-2^{29} x^{8}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 8, 328, 18944, 1324456, ... --> OEIS Normalized instanton numbers (n0=1): 16, 751/6, 7568/3, 229516/3, 8099456/3, ... ; Common denominator:...
\(-(4z+1)(2048z^3+768z^2+112z-1)(3+24z+256z^2)^2\)
| \(-\frac{ 1}{ 4}\) | ≈\(-0.191715-0.145483I\) | ≈\(-0.191715+0.145483I\) | \(-\frac{ 3}{ 64}-\frac{ 1}{ 64}\sqrt{ 39}I\) | \(-\frac{ 3}{ 64}+\frac{ 1}{ 64}\sqrt{ 39}I\) | \(0\) | ≈\(0.00843\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(3\) | \(3\) | \(0\) | \(1\) | \(1\) |
| \(2\) | \(2\) | \(2\) | \(4\) | \(4\) | \(0\) | \(2\) | \(1\) |
36
New Number: 8.42 | AESZ: | Superseeker: -4 140 | Hash: 7bc3855c04953ca11620400320722844
Degree: 8
\(\theta^4+2^{2} x\left(26\theta^4+34\theta^3+29\theta^2+12\theta+2\right)+2^{4} x^{2}\left(305\theta^4+662\theta^3+781\theta^2+436\theta+94\right)+2^{8} x^{3}\left(519\theta^4+1278\theta^3+1541\theta^2+933\theta+213\right)+2^{10} x^{4}\left(2266\theta^4+4988\theta^3+3535\theta^2+633\theta-162\right)+2^{14} 3 x^{5}\left(569\theta^4+1184\theta^3+740\theta^2-81\theta-128\right)+2^{18} 3 x^{6}\left(254\theta^4+354\theta^3+161\theta^2-33\theta-28\right)+2^{22} 3^{2} x^{7}\left(23\theta^4+34\theta^3+8\theta^2-9\theta-4\right)-2^{27} 3^{2} x^{8}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -8, 112, -1664, 23056, ... --> OEIS Normalized instanton numbers (n0=1): -4, 1/2, 140, 1025/2, -9196, ... ; Common denominator:...
\(-(32z+1)(1024z^3-896z^2-48z-1)(1+12z+192z^2)^2\)
| \(-\frac{ 1}{ 32}-\frac{ 1}{ 96}\sqrt{ 39}I\) | \(-\frac{ 1}{ 32}\) | \(-\frac{ 1}{ 32}+\frac{ 1}{ 96}\sqrt{ 39}I\) | ≈\(-0.025859-0.019623I\) | ≈\(-0.025859+0.019623I\) | \(0\) | ≈\(0.926719\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) |
| \(3\) | \(1\) | \(3\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) |
| \(4\) | \(2\) | \(4\) | \(2\) | \(2\) | \(0\) | \(2\) | \(1\) |
37
New Number: 8.43 | AESZ: | Superseeker: 66/7 8716/7 | Hash: 923554dba37f79c41bf0f67b875c36f7
Degree: 8
\(7^{2} \theta^4-2 7 x\left(452\theta^4+640\theta^3+509\theta^2+189\theta+28\right)+2^{2} x^{2}\left(47156\theta^4+78224\theta^3+63963\theta^2+31010\theta+7000\right)-2^{5} x^{3}\left(77224\theta^4+150936\theta^3+155876\theta^2+86751\theta+19838\right)+2^{8} x^{4}\left(65988\theta^4+160584\theta^3+193653\theta^2+117501\theta+28198\right)-2^{12} x^{5}\left(15712\theta^4+46888\theta^3+63382\theta^2+41163\theta+10338\right)+2^{16} x^{6}\left(2088\theta^4+7272\theta^3+10589\theta^2+7140\theta+1828\right)-2^{22} x^{7}\left(36\theta^4+138\theta^3+206\theta^2+137\theta+34\right)+2^{26} x^{8}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 8, 224, 10016, 547936, ... --> OEIS Normalized instanton numbers (n0=1): 66/7, 573/7, 8716/7, 197852/7, 5617614/7, ... ; Common denominator:...
\((1-96z+256z^2)(4z-1)^2(128z^2-88z+7)^2\)
| \(0\) | \(\frac{ 3}{ 16}-\frac{ 1}{ 8}\sqrt{ 2}\) | \(\frac{ 11}{ 32}-\frac{ 1}{ 32}\sqrt{ 65}\) | \(\frac{ 1}{ 4}\) | \(\frac{ 3}{ 16}+\frac{ 1}{ 8}\sqrt{ 2}\) | \(\frac{ 11}{ 32}+\frac{ 1}{ 32}\sqrt{ 65}\) | \(\infty\) |
|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(0\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(1\) |
| \(0\) | \(1\) | \(3\) | \(\frac{ 1}{ 2}\) | \(1\) | \(3\) | \(1\) |
| \(0\) | \(2\) | \(4\) | \(1\) | \(2\) | \(4\) | \(1\) |
38
New Number: 8.44 | AESZ: | Superseeker: -64 -131904 | Hash: 2d570a3dc1cbc5b6596272f33b48fc98
Degree: 8
\(\theta^4-2^{5} x\left(36\theta^4+6\theta^3+8\theta^2+5\theta+1\right)+2^{8} x^{2}\left(2088\theta^4+1080\theta^3+1301\theta^2+574\theta+93\right)-2^{13} x^{3}\left(15712\theta^4+15960\theta^3+16990\theta^2+7785\theta+1381\right)+2^{18} x^{4}\left(65988\theta^4+103368\theta^3+107829\theta^2+52005\theta+9754\right)-2^{24} x^{5}\left(77224\theta^4+157960\theta^3+166412\theta^2+81089\theta+15251\right)+2^{30} x^{6}\left(47156\theta^4+110400\theta^3+112227\theta^2+50868\theta+8885\right)-2^{38} 7 x^{7}\left(452\theta^4+1168\theta^3+1301\theta^2+717\theta+160\right)+2^{46} 7^{2} x^{8}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 32, 2096, 172544, 15870736, ... --> OEIS Normalized instanton numbers (n0=1): -64, -2084, -131904, -10745878, -1015115456, ... ; Common denominator:...
\((1-192z+1024z^2)(128z-1)^2(14336z^2-352z+1)^2\)
| \(0\) | \(\frac{ 11}{ 896}-\frac{ 1}{ 896}\sqrt{ 65}\) | \(\frac{ 3}{ 32}-\frac{ 1}{ 16}\sqrt{ 2}\) | \(\frac{ 1}{ 128}\) | \(\frac{ 11}{ 896}+\frac{ 1}{ 896}\sqrt{ 65}\) | \(\frac{ 3}{ 32}+\frac{ 1}{ 16}\sqrt{ 2}\) | \(\infty\) |
|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(0\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(1\) |
| \(0\) | \(3\) | \(1\) | \(\frac{ 1}{ 2}\) | \(3\) | \(1\) | \(1\) |
| \(0\) | \(4\) | \(2\) | \(1\) | \(4\) | \(2\) | \(1\) |
39
New Number: 8.45 | AESZ: | Superseeker: -12/5 -20 | Hash: 52e4f6959f297529016ddef66a399c12
Degree: 8
\(5^{2} \theta^4+2^{2} 5 x\left(19\theta^4+86\theta^3+73\theta^2+30\theta+5\right)+2^{4} x^{2}\left(709\theta^4+4252\theta^3+7339\theta^2+4830\theta+1165\right)-2^{8} x^{3}\left(420\theta^4+114\theta^3-3294\theta^2-3960\theta-1325\right)-2^{10} x^{4}\left(949\theta^4+6782\theta^3+11350\theta^2+7719\theta+1889\right)+2^{12} x^{5}\left(1315\theta^4+4282\theta^3+7199\theta^2+5744\theta+1691\right)+2^{14} x^{6}\left(613\theta^4+1560\theta^3+973\theta^2-216\theta-249\right)+2^{18} x^{7}\left(11\theta^4-2\theta^3-40\theta^2-39\theta-11\right)-2^{20} x^{8}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -4, -4, 464, -4244, ... --> OEIS Normalized instanton numbers (n0=1): -12/5, -83/5, -20, 3941/20, -13872/5, ... ; Common denominator:...
\(-(8z+1)(128z^3-624z^2-20z-1)(-5+32z+32z^2)^2\)
| \(-\frac{ 1}{ 2}-\frac{ 1}{ 8}\sqrt{ 26}\) | \(-\frac{ 1}{ 8}\) | ≈\(-0.016083-0.036516I\) | ≈\(-0.016083+0.036516I\) | \(0\) | \(-\frac{ 1}{ 2}+\frac{ 1}{ 8}\sqrt{ 26}\) | ≈\(4.907166\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) |
| \(3\) | \(1\) | \(1\) | \(1\) | \(0\) | \(3\) | \(1\) | \(1\) |
| \(4\) | \(2\) | \(2\) | \(2\) | \(0\) | \(4\) | \(2\) | \(1\) |
40
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:...
\(-(16z+1)(16384z^3+2560z^2+624z-1)(-1-128z+2560z^2)^2\)
| ≈\(-0.078921-0.179189I\) | ≈\(-0.078921+0.179189I\) | \(-\frac{ 1}{ 16}\) | \(\frac{ 1}{ 40}-\frac{ 1}{ 160}\sqrt{ 26}\) | \(0\) | ≈\(0.001592\) | \(\frac{ 1}{ 40}+\frac{ 1}{ 160}\sqrt{ 26}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(3\) | \(0\) | \(1\) | \(3\) | \(1\) |
| \(2\) | \(2\) | \(2\) | \(4\) | \(0\) | \(2\) | \(4\) | \(1\) |
41
New Number: 8.47 | AESZ: | Superseeker: 31/3 43174/9 | Hash: b79bf25fcecf028aa40c1a6a8233efe7
Degree: 8
\(3^{4} \theta^4-3^{3} x\left(367\theta^4+398\theta^3+295\theta^2+96\theta+12\right)-2^{4} 3^{3} x^{2}\left(200\theta^4+2081\theta^3+3614\theta^2+2009\theta+392\right)+2^{6} 3 x^{3}\left(72449\theta^4+102684\theta^3-48579\theta^2-77922\theta-22536\right)+2^{10} x^{4}\left(109873\theta^4+619970\theta^3+56260\theta^2-219027\theta-78216\right)-2^{14} 7 x^{5}\left(40669\theta^4-18266\theta^3-36570\theta^2-16190\theta-1955\right)-2^{17} 7 x^{6}\left(80805\theta^4+76590\theta^3+51265\theta^2+23076\theta+4780\right)-2^{24} 7^{2} x^{7}\left(437\theta^4+1117\theta^3+1236\theta^2+664\theta+140\right)-2^{29} 3 7^{2} x^{8}(\theta+1)^2(3\theta+2)(3\theta+4)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 4, 228, 12640, 901540, ... --> OEIS Normalized instanton numbers (n0=1): 31/3, 1964/9, 43174/9, 1469755/9, 19813517/3, ... ; Common denominator:...
\(-(27z+1)(2048z^3+768z^2+112z-1)(-9+168z+3584z^2)^2\)
| ≈\(-0.191715-0.145483I\) | ≈\(-0.191715+0.145483I\) | \(-\frac{ 3}{ 128}-\frac{ 3}{ 896}\sqrt{ 273}\) | \(-\frac{ 1}{ 27}\) | \(0\) | ≈\(0.00843\) | \(-\frac{ 3}{ 128}+\frac{ 3}{ 896}\sqrt{ 273}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 2}{ 3}\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) |
| \(1\) | \(1\) | \(3\) | \(1\) | \(0\) | \(1\) | \(3\) | \(1\) |
| \(2\) | \(2\) | \(4\) | \(2\) | \(0\) | \(2\) | \(4\) | \(\frac{ 4}{ 3}\) |
42
New Number: 8.48 | AESZ: | Superseeker: 359/13 393749/13 | Hash: de7301c14448dbf584c01cc3722d0e58
Degree: 8
\(13^{2} \theta^4-13 x\left(5249\theta^4+4930\theta^3+3687\theta^2+1222\theta+156\right)+2^{4} 3 x^{2}\left(175601\theta^4+188064\theta^3+90243\theta^2+19422\theta+1547\right)-2^{7} x^{3}\left(3336915\theta^4+3777024\theta^3+2377229\theta^2+746148\theta+94185\right)+2^{10} x^{4}\left(8591694\theta^4+11872968\theta^3+7381951\theta^2+2132674\theta+236280\right)-2^{12} x^{5}\left(15421829\theta^4+18326342\theta^3+7032841\theta^2+833608\theta-2718\right)+2^{16} 3^{2} x^{6}\left(334895\theta^4+615600\theta^3+867965\theta^2+590850\theta+138536\right)-2^{19} 3^{4} 7 x^{7}(\theta+1)(2\theta+1)(646\theta^2+1715\theta+1044)+2^{22} 3^{6} 7^{2} x^{8}(2\theta+1)(\theta+1)^2(2\theta+3)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 12, 852, 94800, 12860820, ... --> OEIS Normalized instanton numbers (n0=1): 359/13, 9162/13, 393749/13, 23364200/13, 1734245216/13, ... ; Common denominator:...
\((1-261z+6896z^2-6656z^3+36864z^4)(13-928z+4032z^2)^2\)
| \(0\) | \(\frac{ 29}{ 252}-\frac{ 1}{ 504}\sqrt{ 2545}\) | \(\frac{ 29}{ 252}+\frac{ 1}{ 504}\sqrt{ 2545}\) | \(#ND+#NDI\) | \(\infty\) |
|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(0\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(0\) | \(3\) | \(3\) | \(1\) | \(1\) |
| \(0\) | \(4\) | \(4\) | \(2\) | \(\frac{ 3}{ 2}\) |
43
New Number: 8.49 | AESZ: | Superseeker: 56/3 17704/3 | Hash: 4fa01cbee2fc74e3a62e00386e6fa1c0
Degree: 8
\(3^{2} \theta^4-2^{2} 3 x\left(29\theta^4+178\theta^3+134\theta^2+45\theta+6\right)-2^{5} x^{2}\left(2233\theta^4+2536\theta^3+607\theta^2+132\theta+12\right)-2^{10} x^{3}\left(1274\theta^4+7425\theta^3+20002\theta^2+12717\theta+2670\right)+2^{13} x^{4}\left(2539\theta^4-36538\theta^3-52775\theta^2-31122\theta-6192\right)+2^{20} x^{5}\left(1617\theta^4+9771\theta^3+4484\theta^2-674\theta-556\right)+2^{25} x^{6}\left(1135\theta^4+4272\theta^3+3439\theta^2+858\theta+16\right)-2^{31} 3 x^{7}(2\theta+1)(110\theta^3+225\theta^2+184\theta+57)+2^{37} 3^{2} x^{8}(2\theta+1)(\theta+1)^2(2\theta+3)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 8, 264, 16640, 1130920, ... --> OEIS Normalized instanton numbers (n0=1): 56/3, -83/6, 17704/3, -25024/3, 13408832/3, ... ; Common denominator:...
\((4z-1)(131072z^3+2048z^2+88z-1)(48z+1)^2(64z-3)^2\)
| \(-\frac{ 1}{ 48}\) | ≈\(-0.01214-0.027095I\) | ≈\(-0.01214+0.027095I\) | \(0\) | ≈\(0.008655\) | \(\frac{ 3}{ 64}\) | \(\frac{ 1}{ 4}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(3\) | \(1\) | \(1\) | \(0\) | \(1\) | \(3\) | \(1\) | \(1\) |
| \(4\) | \(2\) | \(2\) | \(0\) | \(2\) | \(4\) | \(2\) | \(\frac{ 3}{ 2}\) |
44
New Number: 8.4 | AESZ: 160 | Superseeker: 6 -325 | Hash: 8ce8667fe6e49ce6625fafe044b1641b
Degree: 8
\(\theta^4-3 x(3\theta^2+3\theta+1)(7\theta^2+7\theta+2)+3^{2} x^{2}\left(171\theta^4+396\theta^3+555\theta^2+318\theta+64\right)-2^{3} 3^{4} x^{3}\left(21\theta^4-126\theta^3-386\theta^2-291\theta-76\right)+2^{4} 3^{5} x^{4}\left(147\theta^4+294\theta^3+102\theta^2-45\theta-14\right)+2^{6} 3^{7} x^{5}\left(21\theta^4+210\theta^3+118\theta^2-19\theta-24\right)+2^{6} 3^{8} x^{6}\left(171\theta^4+288\theta^3+393\theta^2+288\theta+76\right)+2^{9} 3^{10} x^{7}(3\theta^2+3\theta+1)(7\theta^2+7\theta+2)+2^{12} 3^{12} x^{8}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 6, 90, 1176, 3114, ... --> OEIS Normalized instanton numbers (n0=1): 6, 6, -325, -1977/2, -5421, ... ; Common denominator:...
\((27z^2+9z+1)(1728z^2-72z+1)(1+216z^2)^2\)
| \(-\frac{ 1}{ 6}-\frac{ 1}{ 18}\sqrt{ 3}I\) | \(-\frac{ 1}{ 6}+\frac{ 1}{ 18}\sqrt{ 3}I\) | \(0-\frac{ 1}{ 36}\sqrt{ 6}I\) | \(0\) | \(0+\frac{ 1}{ 36}\sqrt{ 6}I\) | \(\frac{ 1}{ 48}-\frac{ 1}{ 144}\sqrt{ 3}I\) | \(\frac{ 1}{ 48}+\frac{ 1}{ 144}\sqrt{ 3}I\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(1\) | \(1\) | \(3\) | \(0\) | \(3\) | \(1\) | \(1\) | \(1\) |
| \(2\) | \(2\) | \(4\) | \(0\) | \(4\) | \(2\) | \(2\) | \(1\) |
45
New Number: 8.50 | AESZ: | Superseeker: 2/23 27/23 | Hash: 68499833fa99ef8841a3d64e042d4a6e
Degree: 8
\(23^{2} \theta^4-2 23 x\theta^2(136\theta^2+2\theta+1)-2^{2} x^{2}\left(7589\theta^4+54926\theta^3+89975\theta^2+69828\theta+21160\right)+x^{3}\left(573259\theta^4+2342274\theta^3+3791849\theta^2+3070914\theta+1010160\right)-2 5 x^{4}\left(122351\theta^4+62266\theta^3-795547\theta^2-1404486\theta-669744\right)-2^{3} 3 5^{2} x^{5}(\theta+1)(16105\theta^3+133047\theta^2+320040\theta+245740)+2^{4} 3^{2} 5^{3} x^{6}(\theta+1)(\theta+2)(3107\theta^2+16911\theta+22834)-2^{4} 3^{4} 5^{4} x^{7}(\theta+3)(\theta+2)(\theta+1)(133\theta+404)+2^{5} 3^{6} 5^{5} x^{8}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, 10, 0, 270, ... --> OEIS Normalized instanton numbers (n0=1): 2/23, 18/23, 27/23, 136/23, 395/23, ... ; Common denominator:...
\((3z-1)(2z-1)(10z-1)(6z+1)(25z^2-5z-1)(-23+90z)^2\)
| \(-\frac{ 1}{ 6}\) | \(\frac{ 1}{ 10}-\frac{ 1}{ 10}\sqrt{ 5}\) | \(0\) | \(\frac{ 1}{ 10}\) | \(\frac{ 23}{ 90}\) | \(\frac{ 1}{ 10}+\frac{ 1}{ 10}\sqrt{ 5}\) | \(\frac{ 1}{ 3}\) | \(\frac{ 1}{ 2}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(2\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(3\) | \(1\) | \(1\) | \(1\) | \(3\) |
| \(2\) | \(2\) | \(0\) | \(2\) | \(4\) | \(2\) | \(2\) | \(2\) | \(4\) |
46
New Number: 8.51 | AESZ: | Superseeker: 58/43 1024/43 | Hash: 85b9064701880ae8e0518e47cff1b030
Degree: 8
\(43^{2} \theta^4-43 x\theta(142\theta^3+890\theta^2+574\theta+129)-x^{2}\left(647269\theta^4+2441818\theta^3+3538503\theta^2+2423953\theta+650848\right)-x^{3}\left(7200000\theta^4+34423908\theta^3+65337898\theta^2+57379329\theta+19251960\right)-x^{4}\left(37610765\theta^4+220029964\theta^3+499781264\theta^2+511393545\theta+194039928\right)-2 x^{5}(\theta+1)(54978121\theta^3+324737370\theta^2+665066226\theta+466789876)-x^{6}(\theta+1)(\theta+2)(185181547\theta^2+915931425\theta+1176131796)-2^{2} 3 101 x^{7}(\theta+3)(\theta+2)(\theta+1)(138979\theta+413408)-2^{2} 3^{2} 5^{2} 7 101^{2} x^{8}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, 22, 204, 3474, ... --> OEIS Normalized instanton numbers (n0=1): 58/43, 211/43, 1024/43, 7544/43, 64880/43, ... ; Common denominator:...
\(-(7z+1)(25z-1)(2z+1)^2(101z+43)^2(3z+1)^2\)
| \(-\frac{ 1}{ 2}\) | \(-\frac{ 43}{ 101}\) | \(-\frac{ 1}{ 3}\) | \(-\frac{ 1}{ 7}\) | \(0\) | \(\frac{ 1}{ 25}\) | \(\infty\) |
|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(\frac{ 1}{ 3}\) | \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(0\) | \(1\) | \(2\) |
| \(\frac{ 2}{ 3}\) | \(3\) | \(\frac{ 1}{ 2}\) | \(1\) | \(0\) | \(1\) | \(3\) |
| \(1\) | \(4\) | \(1\) | \(2\) | \(0\) | \(2\) | \(4\) |
47
New Number: 8.52 | AESZ: | Superseeker: 416 9734432 | Hash: 87729f275f24cb2daf88133571476576
Degree: 8
\(\theta^4+2^{4} x\left(176\theta^4-32\theta^3+4\theta^2+20\theta+5\right)+2^{12} x^{2}\left(640\theta^4+256\theta^3+680\theta^2+224\theta+27\right)+2^{22} x^{3}\left(220\theta^4+648\theta^3+596\theta^2+348\theta+85\right)+2^{30} x^{4}\left(116\theta^4+1024\theta^3+1608\theta^2+1072\theta+281\right)-2^{38} x^{5}\left(32\theta^4-448\theta^3-1588\theta^2-1404\theta-437\right)-2^{46} x^{6}\left(80\theta^4+288\theta^3-88\theta^2-384\theta-179\right)-2^{57} x^{7}\left(2\theta^4+28\theta^3+56\theta^2+42\theta+11\right)+2^{66} x^{8}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -80, 6928, -597248, 95243536, ... --> OEIS Normalized instanton numbers (n0=1): 416, -52752, 9734432, -2404009688, 687625871328, ... ; Common denominator:...
\((1+256z+65536z^2)(256z+1)^2(131072z^2-1024z-1)^2\)
| \(-\frac{ 1}{ 256}\) | \(-\frac{ 1}{ 512}-\frac{ 1}{ 512}\sqrt{ 3}I\) | \(-\frac{ 1}{ 512}+\frac{ 1}{ 512}\sqrt{ 3}I\) | \(\frac{ 1}{ 256}-\frac{ 1}{ 512}\sqrt{ 6}\) | \(0\) | \(\frac{ 1}{ 256}+\frac{ 1}{ 512}\sqrt{ 6}\) | \(\infty\) |
|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) |
| \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(3\) | \(0\) | \(3\) | \(1\) |
| \(1\) | \(2\) | \(2\) | \(4\) | \(0\) | \(4\) | \(1\) |
48
New Number: 8.53 | AESZ: | Superseeker: -64 -64320 | Hash: 0714a480e1c587ebada71771f7e3b555
Degree: 8
\(\theta^4-2^{5} x\left(2\theta^4-20\theta^3-16\theta^2-6\theta-1\right)-2^{8} x^{2}\left(80\theta^4+32\theta^3-472\theta^2-336\theta-91\right)-2^{14} x^{3}\left(32\theta^4+576\theta^3-52\theta^2-300\theta-141\right)+2^{20} x^{4}\left(116\theta^4-560\theta^3-768\theta^2-464\theta-91\right)+2^{26} x^{5}\left(220\theta^4+232\theta^3-28\theta^2-220\theta-95\right)+2^{30} x^{6}\left(640\theta^4+2304\theta^3+3752\theta^2+2928\theta+867\right)+2^{36} x^{7}\left(176\theta^4+736\theta^3+1156\theta^2+788\theta+197\right)+2^{46} x^{8}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -32, 1168, -43520, 1777936, ... --> OEIS Normalized instanton numbers (n0=1): -64, -1604, -64320, -3255802, -191614656, ... ; Common denominator:...
\((1+64z+4096z^2)(64z+1)^2(2048z^2+128z-1)^2\)
| \(-\frac{ 1}{ 32}-\frac{ 1}{ 64}\sqrt{ 6}\) | \(-\frac{ 1}{ 64}\) | \(-\frac{ 1}{ 128}-\frac{ 1}{ 128}\sqrt{ 3}I\) | \(-\frac{ 1}{ 128}+\frac{ 1}{ 128}\sqrt{ 3}I\) | \(0\) | \(-\frac{ 1}{ 32}+\frac{ 1}{ 64}\sqrt{ 6}\) | \(\infty\) |
|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) |
| \(3\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(0\) | \(3\) | \(1\) |
| \(4\) | \(1\) | \(2\) | \(2\) | \(0\) | \(4\) | \(1\) |
49
New Number: 8.54 | AESZ: | Superseeker: 0 1/3 | Hash: bb80872017d0578a4ae56172666b807c
Degree: 8
\(\theta^4+x\theta(3\theta^3-6\theta^2-4\theta-1)-x^{2}\left(211\theta^4+856\theta^3+1433\theta^2+1184\theta+384\right)-2 x^{3}\left(761\theta^4+3288\theta^3+6477\theta^2+6654\theta+2700\right)+2^{2} x^{4}(\theta+1)(2013\theta^3+17379\theta^2+40726\theta+28548)+2^{3} x^{5}(\theta+1)(15719\theta^3+126105\theta^2+325408\theta+269508)+2^{5} 3^{2} x^{6}(\theta+1)(\theta+2)(1817\theta^2+11967\theta+19631)+2^{7} 3^{4} x^{7}(\theta+3)(\theta+2)(\theta+1)(89\theta+350)+2^{9} 3^{3} 43 x^{8}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, 24, 72, 1296, ... --> OEIS Normalized instanton numbers (n0=1): 0, 1/2, 1/3, -1, 2, ... ; Common denominator:...
\((4z+1)(6z+1)(43z^2+13z+1)(2z+1)^2(12z-1)^2\)
| \(-\frac{ 1}{ 2}\) | \(-\frac{ 1}{ 4}\) | \(-\frac{ 1}{ 6}\) | \(-\frac{ 13}{ 86}-\frac{ 1}{ 86}\sqrt{ 3}I\) | \(-\frac{ 13}{ 86}+\frac{ 1}{ 86}\sqrt{ 3}I\) | \(0\) | \(\frac{ 1}{ 12}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(\frac{ 1}{ 2}\) | \(2\) |
| \(3\) | \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(\frac{ 1}{ 2}\) | \(3\) |
| \(4\) | \(2\) | \(2\) | \(2\) | \(2\) | \(0\) | \(1\) | \(4\) |
50
New Number: 8.55 | AESZ: | Superseeker: 1 68/9 | Hash: 39ed8ce7572bc79a333f77c892033bcf
Degree: 8
\(\theta^4-x\left(33\theta^4+98\theta^3+105\theta^2+56\theta+12\right)+2^{3} x^{2}\left(34\theta^4+276\theta^3+609\theta^2+582\theta+216\right)+2^{4} 3 x^{3}\left(11\theta^4-170\theta^3-941\theta^2-1520\theta-846\right)-2^{7} 3^{2} x^{4}(2\theta^2+6\theta+5)(4\theta^2+12\theta-31)+2^{8} 3 x^{5}\left(11\theta^4+302\theta^3+1183\theta^2+1652\theta+726\right)+2^{11} x^{6}\left(34\theta^4+132\theta^3-39\theta^2-708\theta-747\right)-2^{12} x^{7}\left(33\theta^4+298\theta^3+1005\theta^2+1492\theta+816\right)+2^{16} x^{8}\left((\theta+3)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 12, 120, 1216, 13080, ... --> OEIS Normalized instanton numbers (n0=1): 1, -2, 68/9, -30, 150, ... ; Common denominator:...
\((z-1)(16z-1)(16z^2-16z+1)(4z-1)^2(4z+1)^2\)
| \(-\frac{ 1}{ 4}\) | \(0\) | \(\frac{ 1}{ 16}\) | \(\frac{ 1}{ 2}-\frac{ 1}{ 4}\sqrt{ 3}\) | \(\frac{ 1}{ 4}\) | \(\frac{ 1}{ 2}+\frac{ 1}{ 4}\sqrt{ 3}\) | \(1\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(3\) |
| \(1\) | \(0\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(3\) |
| \(3\) | \(0\) | \(1\) | \(1\) | \(-1\) | \(1\) | \(1\) | \(3\) |
| \(4\) | \(0\) | \(2\) | \(2\) | \(1\) | \(2\) | \(2\) | \(3\) |
51
New Number: 8.56 | AESZ: | Superseeker: 80 266256 | Hash: b561c9f1501dce5c055c95391a2176d3
Degree: 8
\(\theta^4-2^{4} x\left(34\theta^4+44\theta^3+31\theta^2+9\theta+1\right)+2^{9} x^{2}\left(94\theta^4-14\theta^3-168\theta^2-98\theta-19\right)-2^{12} x^{3}\left(368\theta^4-1104\theta^3-1505\theta^2-549\theta-60\right)+2^{16} x^{4}\left(28\theta^4-2740\theta^3-154\theta^2+928\theta+331\right)+2^{20} x^{5}\left(678\theta^4+1116\theta^3-2997\theta^2-2295\theta-505\right)-2^{26} x^{6}\left(94\theta^4-561\theta^3-508\theta^2-132\theta+6\right)-2^{28} 5 x^{7}\left(92\theta^4+160\theta^3+97\theta^2+17\theta-2\right)-2^{32} 5^{2} x^{8}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 16, 2512, 533248, 138259216, ... --> OEIS Normalized instanton numbers (n0=1): 80, 3554, 266256, 31532007, 4663446128, ... ; Common denominator:...
\(-(16z+1)(4096z^3+4864z^2+432z-1)(1-64z+1280z^2)^2\)
| ≈\(-1.090586\) | ≈\(-0.099171\) | \(-\frac{ 1}{ 16}\) | \(0\) | ≈\(0.002257\) | \(\frac{ 1}{ 40}-\frac{ 1}{ 80}I\) | \(\frac{ 1}{ 40}+\frac{ 1}{ 80}I\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(3\) | \(3\) | \(1\) |
| \(2\) | \(2\) | \(2\) | \(0\) | \(2\) | \(4\) | \(4\) | \(1\) |
52
New Number: 8.57 | AESZ: | Superseeker: -36/5 -380 | Hash: c2a931d298755811a60b7f8e5dd3afbe
Degree: 8
\(5^{2} \theta^4+2^{2} 5 x\left(92\theta^4+208\theta^3+169\theta^2+65\theta+10\right)+2^{6} x^{2}\left(94\theta^4+937\theta^3+1739\theta^2+1175\theta+285\right)-2^{6} x^{3}\left(678\theta^4+1596\theta^3-2277\theta^2-4335\theta-1645\right)-2^{8} x^{4}\left(28\theta^4+2852\theta^3+8234\theta^2+7096\theta+2017\right)+2^{10} x^{5}\left(368\theta^4+2576\theta^3+4015\theta^2+2323\theta+456\right)-2^{13} x^{6}\left(94\theta^4+390\theta^3+438\theta^2+180\theta+19\right)+2^{14} x^{7}\left(34\theta^4+92\theta^3+103\theta^2+57\theta+13\right)-2^{16} x^{8}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -8, 172, -5696, 231916, ... --> OEIS Normalized instanton numbers (n0=1): -36/5, 132/5, -380, 112043/20, -560656/5, ... ; Common denominator:...
\(-(4z+1)(64z^3-432z^2-76z-1)(5-16z+16z^2)^2\)
| \(-\frac{ 1}{ 4}\) | ≈\(-0.157556\) | ≈\(-0.014327\) | \(0\) | \(\frac{ 1}{ 2}-\frac{ 1}{ 4}I\) | \(\frac{ 1}{ 2}+\frac{ 1}{ 4}I\) | ≈\(6.921883\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(0\) | \(3\) | \(3\) | \(1\) | \(1\) |
| \(2\) | \(2\) | \(2\) | \(0\) | \(4\) | \(4\) | \(2\) | \(1\) |
53
New Number: 8.58 | AESZ: | Superseeker: 286 12179050/3 | Hash: 870f2e78b48eb5ee8f5de2f6a438f2b8
Degree: 8
\(\theta^4-x\left(1114\theta^4+2444\theta^3+1704\theta^2+482\theta+51\right)-x^{2}\left(85922\theta^4+94748\theta^3-21782\theta^2-21164\theta-3273\right)-3^{2} x^{3}\left(173242\theta^4+41004\theta^3+55912\theta^2+32322\theta+5679\right)+3^{2} x^{4}\left(189512\theta^4-918380\theta^3-841954\theta^2-306732\theta-47331\right)+3^{4} x^{5}\left(30338\theta^4+90716\theta^3-87560\theta^2-90566\theta-23193\right)-3^{4} x^{6}\left(19406\theta^4-68364\theta^3-62162\theta^2-14148\theta+1989\right)-3^{6} 5 x^{7}\left(278\theta^4+340\theta^3+8\theta^2-162\theta-63\right)-3^{8} 5^{2} x^{8}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 51, 18267, 10280301, 7092708939, ... --> OEIS Normalized instanton numbers (n0=1): 286, 38919/2, 12179050/3, 2393489451/2, 439227114444, ... ; Common denominator:...
\(-(z+1)(81z^3+549z^2+1187z-1)(-1-36z+45z^2)^2\)
| ≈\(-3.38931-1.781181I\) | ≈\(-3.38931+1.781181I\) | \(-1\) | \(\frac{ 2}{ 5}-\frac{ 1}{ 15}\sqrt{ 41}\) | \(0\) | ≈\(0.000842\) | \(\frac{ 2}{ 5}+\frac{ 1}{ 15}\sqrt{ 41}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(3\) | \(0\) | \(1\) | \(3\) | \(1\) |
| \(2\) | \(2\) | \(2\) | \(4\) | \(0\) | \(2\) | \(4\) | \(1\) |
54
New Number: 8.59 | AESZ: | Superseeker: -26/5 -234/5 | Hash: 53885e46a1519d98ee4697de1c109214
Degree: 8
\(5^{2} \theta^4+5 x\left(278\theta^4+772\theta^3+656\theta^2+270\theta+45\right)+x^{2}\left(19406\theta^4+145988\theta^3+259366\theta^2+172540\theta+41745\right)-3^{2} x^{3}\left(30338\theta^4+30636\theta^3-177680\theta^2-235350\theta-80565\right)-3^{2} x^{4}\left(189512\theta^4+1676428\theta^3+3050258\theta^2+2136012\theta+525339\right)+3^{4} x^{5}\left(173242\theta^4+651964\theta^3+972352\theta^2+649458\theta+161507\right)+3^{4} x^{6}\left(85922\theta^4+248940\theta^3+209506\theta^2+37044\theta-12717\right)+3^{6} x^{7}\left(1114\theta^4+2012\theta^3+1056\theta^2+50\theta-57\right)-3^{8} x^{8}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -9, 123, -1719, 17739, ... --> OEIS Normalized instanton numbers (n0=1): -26/5, -177/10, -234/5, -1837/2, -27716/5, ... ; Common denominator:...
\(-(9z+1)(9z^3-1187z^2-61z-1)(-5+36z+9z^2)^2\)
| \(-2-\frac{ 1}{ 3}\sqrt{ 41}\) | \(-\frac{ 1}{ 9}\) | ≈\(-0.025688-0.0135I\) | ≈\(-0.025688+0.0135I\) | \(0\) | \(-2+\frac{ 1}{ 3}\sqrt{ 41}\) | ≈\(131.940265\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) |
| \(3\) | \(1\) | \(1\) | \(1\) | \(0\) | \(3\) | \(1\) | \(1\) |
| \(4\) | \(2\) | \(2\) | \(2\) | \(0\) | \(4\) | \(2\) | \(1\) |
55
New Number: 8.5 | AESZ: 173 | Superseeker: 11 -2434/3 | Hash: afa82ed9ee239bb5fcac960f8884db01
Degree: 8
\(\theta^4-x(7\theta^2+7\theta+2)(17\theta^2+17\theta+6)+2^{6} x^{2}\left(55\theta^4+112\theta^3+155\theta^2+86\theta+15\right)-2^{6} 3^{2} x^{3}\left(119\theta^4-714\theta^3-2185\theta^2-1656\theta-444\right)+2^{12} 3^{2} x^{4}\left(92\theta^4+184\theta^3+98\theta^2+6\theta+9\right)+2^{12} 3^{4} x^{5}\left(119\theta^4+1190\theta^3+671\theta^2-96\theta-140\right)+2^{18} 3^{4} x^{6}\left(55\theta^4+108\theta^3+149\theta^2+108\theta+27\right)+2^{18} 3^{6} x^{7}(7\theta^2+7\theta+2)(17\theta^2+17\theta+6)+2^{24} 3^{8} x^{8}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 12, 420, 17472, 828324, ... --> OEIS Normalized instanton numbers (n0=1): 11, 229/4, -2434/3, 7512, 54801, ... ; Common denominator:...
\((72z-1)(8z+1)(64z-1)(9z+1)(1+576z^2)^2\)
| \(-\frac{ 1}{ 8}\) | \(-\frac{ 1}{ 9}\) | \(0-\frac{ 1}{ 24}I\) | \(0\) | \(0+\frac{ 1}{ 24}I\) | \(\frac{ 1}{ 72}\) | \(\frac{ 1}{ 64}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(1\) | \(1\) | \(3\) | \(0\) | \(3\) | \(1\) | \(1\) | \(1\) |
| \(2\) | \(2\) | \(4\) | \(0\) | \(4\) | \(2\) | \(2\) | \(1\) |
56
New Number: 8.60 | AESZ: | Superseeker: 247 3584909 | Hash: 540ab51629d98ae18b7d061824bd258b
Degree: 8
\(\theta^4-x\left(1182\theta^4+2172\theta^3+1519\theta^2+433\theta+46\right)+x^{2}\left(70937\theta^4+62468\theta^3-34151\theta^2-26294\theta-4528\right)-2^{3} x^{3}\left(140935\theta^4-41718\theta^3-83276\theta^2-29367\theta-3376\right)+2^{4} 3 x^{4}\left(21007\theta^4-134418\theta^3-100578\theta^2-26137\theta-1974\right)+2^{6} x^{5}\left(29420\theta^4+79292\theta^3-91933\theta^2-88917\theta-22012\right)-2^{6} x^{6}\left(17519\theta^4-73056\theta^3-66923\theta^2-16512\theta+1436\right)-2^{9} 5 x^{7}\left(351\theta^4+510\theta^3+176\theta^2-79\theta-46\right)-2^{12} 5^{2} x^{8}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 46, 15670, 8332840, 5425831846, ... --> OEIS Normalized instanton numbers (n0=1): 247, 38017/2, 3584909, 2039721503/2, 359173241174, ... ; Common denominator:...
\(-(z+1)(64z^3+600z^2+1119z-1)(1-32z+40z^2)^2\)
| ≈\(-6.805514\) | ≈\(-2.570379\) | \(-1\) | \(0\) | ≈\(0.000893\) | \(\frac{ 2}{ 5}-\frac{ 3}{ 20}\sqrt{ 6}\) | \(\frac{ 2}{ 5}+\frac{ 3}{ 20}\sqrt{ 6}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(3\) | \(3\) | \(1\) |
| \(2\) | \(2\) | \(2\) | \(0\) | \(2\) | \(4\) | \(4\) | \(1\) |
57
New Number: 8.61 | AESZ: | Superseeker: -32/5 -863/5 | Hash: 9699709447380eb1373469a1cf5a9586
Degree: 8
\(5^{2} \theta^4+5 x\left(351\theta^4+894\theta^3+752\theta^2+305\theta+50\right)+x^{2}\left(17519\theta^4+143132\theta^3+257359\theta^2+171910\theta+41600\right)-2^{3} x^{3}\left(29420\theta^4+38388\theta^3-153289\theta^2-215145\theta-74900\right)-2^{4} 3 x^{4}\left(21007\theta^4+218446\theta^3+428718\theta^2+312263\theta+79010\right)+2^{6} x^{5}\left(140935\theta^4+605458\theta^3+887488\theta^2+551709\theta+125368\right)-2^{6} x^{6}\left(70937\theta^4+221280\theta^3+204067\theta^2+54336\theta-3916\right)+2^{9} x^{7}\left(1182\theta^4+2556\theta^3+2095\theta^2+817\theta+142\right)-2^{12} x^{8}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -10, 190, -4888, 151246, ... --> OEIS Normalized instanton numbers (n0=1): -32/5, -33/10, -863/5, 715/2, -83882/5, ... ; Common denominator:...
\(-(8z+1)(8z^3-1119z^2-75z-1)(5-32z+8z^2)^2\)
| \(-\frac{ 1}{ 8}\) | ≈\(-0.048631\) | ≈\(-0.018367\) | \(0\) | \(2-\frac{ 3}{ 4}\sqrt{ 6}\) | \(2+\frac{ 3}{ 4}\sqrt{ 6}\) | ≈\(139.941998\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(0\) | \(3\) | \(3\) | \(1\) | \(1\) |
| \(2\) | \(2\) | \(2\) | \(0\) | \(4\) | \(4\) | \(2\) | \(1\) |
58
New Number: 8.62 | AESZ: | Superseeker: 127 1566863/3 | Hash: 4165325308c2b65daacebc1d19717e13
Degree: 8
\(\theta^4+x\left(578\theta^4-572\theta^3-359\theta^2-73\theta-6\right)+3^{2} x^{2}\left(4673\theta^4+1892\theta^3+31601\theta^2+11514\theta+1728\right)-2^{3} 3^{4} x^{3}\left(9185\theta^4-134298\theta^3-35420\theta^2-22329\theta-5544\right)+2^{4} 3^{8} x^{4}\left(19051\theta^4+11846\theta^3+114678\theta^2+65939\theta+14290\right)-2^{6} 3^{12} x^{5}\left(7540\theta^4+8068\theta^3-6459\theta^2-7907\theta-2300\right)-2^{6} 3^{16} x^{6}\left(3919\theta^4+27744\theta^3+29957\theta^2+14208\theta+2556\right)+2^{9} 3^{20} 5 x^{7}\left(199\theta^4+590\theta^3+744\theta^2+449\theta+106\right)-2^{12} 3^{24} 5^{2} x^{8}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 6, -810, -47784, 3354534, ... --> OEIS Normalized instanton numbers (n0=1): 127, -14353/2, 1566863/3, -106847355/2, 6507370854, ... ; Common denominator:...
\(-(81z+1)(419904z^3-22680z^2+79z-1)(-1-288z+29160z^2)^2\)
| \(-\frac{ 1}{ 81}\) | \(\frac{ 2}{ 405}-\frac{ 1}{ 1620}\sqrt{ 154}\) | \(0\) | ≈\(0.001382-0.006675I\) | ≈\(0.001382+0.006675I\) | \(\frac{ 2}{ 405}+\frac{ 1}{ 1620}\sqrt{ 154}\) | ≈\(0.051248\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(1\) | \(3\) | \(0\) | \(1\) | \(1\) | \(3\) | \(1\) | \(1\) |
| \(2\) | \(4\) | \(0\) | \(2\) | \(2\) | \(4\) | \(2\) | \(1\) |
59
New Number: 8.63 | AESZ: | Superseeker: 8/5 67 | Hash: 2c5f91dca73abc39f5d6eb00b9c4ea16
Degree: 8
\(5^{2} \theta^4-5 x\left(199\theta^4+206\theta^3+168\theta^2+65\theta+10\right)+x^{2}\left(3919\theta^4-12068\theta^3-29761\theta^2-21850\theta-5520\right)+2^{3} x^{3}\left(7540\theta^4+22092\theta^3+14577\theta^2+945\theta-1380\right)-2^{4} x^{4}\left(19051\theta^4+64358\theta^3+193446\theta^2+204083\theta+70234\right)+2^{6} x^{5}\left(9185\theta^4+171038\theta^3+422584\theta^2+391123\theta+124848\right)-2^{6} 3^{2} x^{6}\left(4673\theta^4+16800\theta^3+53963\theta^2+64704\theta+24596\right)-2^{9} 3^{4} x^{7}\left(578\theta^4+2884\theta^3+4825\theta^2+3383\theta+858\right)-2^{12} 3^{8} x^{8}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 2, 30, 488, 9934, ... --> OEIS Normalized instanton numbers (n0=1): 8/5, 101/10, 67, 6197/10, 32978/5, ... ; Common denominator:...
\(-(8z+1)(648z^3-79z^2+35z-1)(-5+32z+72z^2)^2\)
| \(-\frac{ 2}{ 9}-\frac{ 1}{ 36}\sqrt{ 154}\) | \(-\frac{ 1}{ 8}\) | \(0\) | ≈\(0.030113\) | ≈\(0.0459-0.221678I\) | ≈\(0.0459+0.221678I\) | \(-\frac{ 2}{ 9}+\frac{ 1}{ 36}\sqrt{ 154}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(3\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(3\) | \(1\) |
| \(4\) | \(2\) | \(0\) | \(2\) | \(2\) | \(2\) | \(4\) | \(1\) |
60
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:...
\(-(64z-1)(65536z^3+14336z^2-192z+1)(-1+128z+10240z^2)^2\)
| ≈\(-0.23168\) | \(-\frac{ 1}{ 160}-\frac{ 1}{ 320}\sqrt{ 14}\) | \(0\) | \(-\frac{ 1}{ 160}+\frac{ 1}{ 320}\sqrt{ 14}\) | ≈\(0.006465-0.004906I\) | ≈\(0.006465+0.004906I\) | \(\frac{ 1}{ 64}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(1\) | \(3\) | \(0\) | \(3\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(2\) | \(4\) | \(0\) | \(4\) | \(2\) | \(2\) | \(2\) | \(1\) |