1
New Number: 5.128 | AESZ: | Superseeker: -50 -20600 | Hash: 5a0123bd26e43e2fd9c7e6c3d21a2a33
Degree: 5
\(\theta^4+2 5 x\left(60\theta^3+45\theta^2+15\theta+2\right)-2^{2} 5^{4} x^{2}\left(8\theta^4+8\theta^3-29\theta^2-20\theta-4\right)-2^{4} 5^{5} x^{3}\left(16\theta^4+216\theta^3+288\theta^2+147\theta+26\right)+2^{6} 5^{7} x^{4}(13\theta^2+37\theta+27)(2\theta+1)^2-2^{8} 5^{9} x^{5}(2\theta+1)^2(2\theta+3)^2\)
Maple LaTexCoefficients of the holomorphic solution: 1, -20, 900, -38000, 122500, ... --> OEIS Normalized instanton numbers (n0=1): -50, -1675/2, -20600, -1433000, -408984396/5, ... ; Common denominator:...
\(-(800000z^3-10000z^2-200z-1)(-1+100z)^2\)
| ≈\(-0.006091-0.003681I\) | ≈\(-0.006091+0.003681I\) | \(0\) | \(\frac{ 1}{ 100}\) | ≈\(0.024681\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) |
| \(1\) | \(1\) | \(0\) | \(3\) | \(1\) | \(\frac{ 3}{ 2}\) |
| \(2\) | \(2\) | \(0\) | \(4\) | \(2\) | \(\frac{ 3}{ 2}\) |
2
New Number: 5.129 | AESZ: | Superseeker: -26 -8344 | Hash: 6c96cbe2aa88f7096e6b9f02e290d167
Degree: 5
\(\theta^4+2 x\left(24\theta^4+228\theta^3+181\theta^2+67\theta+10\right)-2^{2} 5 x^{2}\left(584\theta^4+392\theta^3-1717\theta^2-1320\theta-300\right)-2^{4} 3 5^{2} x^{3}\left(128\theta^4+2328\theta^3+3008\theta^2+1563\theta+290\right)+2^{6} 3^{2} 5^{3} x^{4}(2\theta+1)(266\theta^3+831\theta^2+883\theta+315)-2^{8} 3^{3} 5^{4} x^{5}(2\theta+1)(6\theta+5)(6\theta+7)(2\theta+3)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -20, 900, -52400, 3482500, ... --> OEIS Normalized instanton numbers (n0=1): -26, -561/2, -8344, -278334, -11536332, ... ; Common denominator:...
\(-(20z-1)(108z+1)(80z+1)(-1+60z)^2\)
| \(-\frac{ 1}{ 80}\) | \(-\frac{ 1}{ 108}\) | \(0\) | \(\frac{ 1}{ 60}\) | \(\frac{ 1}{ 20}\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(\frac{ 5}{ 6}\) |
| \(1\) | \(1\) | \(0\) | \(3\) | \(1\) | \(\frac{ 7}{ 6}\) |
| \(2\) | \(2\) | \(0\) | \(4\) | \(2\) | \(\frac{ 3}{ 2}\) |
3
New Number: 5.50 | AESZ: 249 | Superseeker: -44/5 -596 | Hash: 85592af20bbb190e37428e945664c2f3
Degree: 5
\(5^{2} \theta^4+2^{2} 5 x\left(148\theta^4+392\theta^3+341\theta^2+145\theta+25\right)+2^{4} x^{2}\left(4096\theta^4+32128\theta^3+57016\theta^2+37920\theta+9175\right)-2^{8} x^{3}\left(6656\theta^4+7680\theta^3-36960\theta^2-49920\theta-16985\right)-2^{15} x^{4}\left(512\theta^4+4864\theta^3+9136\theta^2+6464\theta+1587\right)+2^{20} x^{5}(4\theta+5)^2(4\theta+3)^2\)
Maple LaTexCoefficients of the holomorphic solution: 1, -20, 684, -28496, 1317100, ... --> OEIS Normalized instanton numbers (n0=1): -44/5, -277/5, -596, -7236, -502128/5, ... ; Common denominator:...
\((1+16z)(64z+1)^2(64z-5)^2\)
| \(-\frac{ 1}{ 16}\) | \(-\frac{ 1}{ 64}\) | \(0\) | \(\frac{ 5}{ 64}\) | \(\infty\) |
|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 3}{ 4}\) |
| \(1\) | \(\frac{ 1}{ 2}\) | \(0\) | \(1\) | \(\frac{ 3}{ 4}\) |
| \(1\) | \(\frac{ 1}{ 2}\) | \(0\) | \(3\) | \(\frac{ 5}{ 4}\) |
| \(2\) | \(1\) | \(0\) | \(4\) | \(\frac{ 5}{ 4}\) |
4
New Number: 5.52 | AESZ: 252 | Superseeker: -232/5 -122168/5 | Hash: cae57e93a6afb98313f62899d1f75e2e
Degree: 5
\(5^{2} \theta^4-2^{2} 5 x\left(36\theta^4-636\theta^3-488\theta^2-170\theta-25\right)-2^{4} x^{2}\left(21301\theta^4+27148\theta^3-86889\theta^2-63110\theta-14975\right)+2^{8} 5 x^{3}\left(3907\theta^4-58863\theta^3-25285\theta^2+10878\theta+7151\right)+2^{10} 59 x^{4}\left(10981\theta^4-29878\theta^3-89811\theta^2-70372\theta-17759\right)+2^{15} 3 59^{2} x^{5}(4\theta+5)(3\theta+2)(3\theta+4)(4\theta+3)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -20, 684, -32240, 1969900, ... --> OEIS Normalized instanton numbers (n0=1): -232/5, -7499/10, -122168/5, -4503443/5, -200467616/5, ... ; Common denominator:...
\((108z+1)(2048z^2+52z+1)(-5+472z)^2\)
| \(-\frac{ 13}{ 1024}-\frac{ 7}{ 1024}\sqrt{ 7}I\) | \(-\frac{ 13}{ 1024}+\frac{ 7}{ 1024}\sqrt{ 7}I\) | \(-\frac{ 1}{ 108}\) | \(0\) | \(\frac{ 5}{ 472}\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 2}{ 3}\) |
| \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(\frac{ 3}{ 4}\) |
| \(1\) | \(1\) | \(1\) | \(0\) | \(3\) | \(\frac{ 5}{ 4}\) |
| \(2\) | \(2\) | \(2\) | \(0\) | \(4\) | \(\frac{ 4}{ 3}\) |
5
New Number: 10.2 | AESZ: | Superseeker: 4 2252/9 | Hash: 4a65f8c6ad1f8eaf4aa56879ebb94205
Degree: 10
\(\theta^4+2^{2} x\left(69\theta^4+42\theta^3+45\theta^2+24\theta+5\right)+2^{4} x^{2}\left(2097\theta^4+2748\theta^3+3311\theta^2+1990\theta+489\right)+2^{8} x^{3}\left(9240\theta^4+19254\theta^3+26269\theta^2+17979\theta+5020\right)+2^{10} 3 x^{4}\left(34845\theta^4+101230\theta^3+156798\theta^2+120187\theta+36857\right)+2^{12} x^{5}\left(792225\theta^4+2972406\theta^3+5205467\theta^2+4394830\theta+1449907\right)+2^{14} x^{6}\left(4064601\theta^4+18714936\theta^3+36737137\theta^2+33711480\theta+11807867\right)+2^{18} x^{7}\left(3474333\theta^4+18927498\theta^3+41213301\theta^2+40674636\theta+14985820\right)+2^{20} x^{8}\left(7544547\theta^4+47365644\theta^3+113299226\theta^2+119329996\theta+45950951\right)+2^{24} 23 x^{9}(2\theta+3)(50786\theta^3+284985\theta^2+515497\theta+282264)+2^{28} 3 7^{2} 23^{2} x^{10}(\theta+1)(2\theta+5)(2\theta+3)(\theta+3)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -20, 436, -9872, 228292, ... --> OEIS Normalized instanton numbers (n0=1): 4, -31, 2252/9, -11109/4, 33312, ... ; Common denominator:...
\((24z+1)(8z+1)(784z^2+52z+1)(32z+1)^2(736z^2+64z+1)^2\)
| \(-\frac{ 1}{ 8}\) | \(-\frac{ 1}{ 23}-\frac{ 3}{ 184}\sqrt{ 2}\) | \(-\frac{ 1}{ 24}\) | \(-\frac{ 13}{ 392}-\frac{ 3}{ 392}\sqrt{ 3}I\) | \(-\frac{ 13}{ 392}+\frac{ 3}{ 392}\sqrt{ 3}I\) | \(-\frac{ 1}{ 32}\) | \(-\frac{ 1}{ 23}+\frac{ 3}{ 184}\sqrt{ 2}\) | \(0\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(0\) | \(\frac{ 3}{ 2}\) |
| \(1\) | \(3\) | \(1\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(3\) | \(0\) | \(\frac{ 5}{ 2}\) |
| \(2\) | \(4\) | \(2\) | \(2\) | \(2\) | \(1\) | \(4\) | \(0\) | \(3\) |
6
New Number: 6.30 | AESZ: | Superseeker: 4 436 | Hash: bc45bbf252bff0ad05b31f8e076f64cb
Degree: 6
\(\theta^4+2^{2} x(\theta^2+\theta+1)(18\theta^2+18\theta+5)+2^{4} x^{2}\left(39\theta^4+156\theta^3+337\theta^2+362\theta+135\right)-2^{6} x^{3}\left(1124\theta^4+6744\theta^3+14434\theta^2+12954\theta+4329\right)-2^{8} 3 7 x^{4}\left(445\theta^4+3560\theta^3+10034\theta^2+11656\theta+4779\right)-2^{10} 3^{2} 7^{2} x^{5}(\theta+4)(\theta+1)(62\theta^2+310\theta+345)-2^{12} 3^{4} 7^{3} x^{6}(\theta+5)(\theta+4)(\theta+2)(\theta+1)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -20, 480, -11264, 285712, ... --> OEIS Normalized instanton numbers (n0=1): 4, 71/2, 436, 6728, 127212, ... ; Common denominator:...
\(-(-1+36z)(12z+1)^2(28z+1)^3\)
| \(-\frac{ 1}{ 12}\) | \(-\frac{ 1}{ 28}\) | \(0\) | \(\frac{ 1}{ 36}\) | \(\infty\) |
|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(\frac{ 1}{ 2}\) | \(0\) | \(0\) | \(1\) | \(2\) |
| \(\frac{ 1}{ 2}\) | \(-\frac{ 1}{ 4}\) | \(0\) | \(1\) | \(4\) |
| \(1\) | \(\frac{ 1}{ 4}\) | \(0\) | \(2\) | \(5\) |
7
New Number: 7.15 | AESZ: | Superseeker: -2 -952 | Hash: d9a911258d890c112974a4ba19e93e6d
Degree: 7
\(\theta^4+2 x\left(138\theta^4+156\theta^3+137\theta^2+59\theta+10\right)+2^{2} x^{2}\left(4796\theta^4+15824\theta^3+16719\theta^2+7610\theta+1400\right)-2^{4} 5 x^{3}\left(5876\theta^4-28824\theta^3-58439\theta^2-39075\theta-9350\right)-2^{6} 5 x^{4}\left(184592\theta^4+414976\theta^3-60816\theta^2-180968\theta-60145\right)+2^{10} 3 x^{5}\left(240624\theta^4-905760\theta^3-1250920\theta^2-576920\theta-83925\right)+2^{18} 3^{2} x^{6}\left(13608\theta^4+48276\theta^3+66402\theta^2+41679\theta+9935\right)-2^{20} 3^{5} x^{7}(6\theta+5)^2(6\theta+7)^2\)
Maple LaTexCoefficients of the holomorphic solution: 1, -20, 900, -55280, 3962500, ... --> OEIS Normalized instanton numbers (n0=1): -2, -343/2, -952, -45148, -17303644/25, ... ; Common denominator:...
\(-(-1-16z+256z^2)(32z-1)^2(108z+1)^3\)
| \(\frac{ 1}{ 32}-\frac{ 1}{ 32}\sqrt{ 5}\) | \(-\frac{ 1}{ 108}\) | \(0\) | \(\frac{ 1}{ 32}\) | \(\frac{ 1}{ 32}+\frac{ 1}{ 32}\sqrt{ 5}\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 5}{ 6}\) |
| \(1\) | \(\frac{ 1}{ 2}\) | \(0\) | \(1\) | \(1\) | \(\frac{ 5}{ 6}\) |
| \(1\) | \(\frac{ 3}{ 2}\) | \(0\) | \(3\) | \(1\) | \(\frac{ 7}{ 6}\) |
| \(2\) | \(2\) | \(0\) | \(4\) | \(2\) | \(\frac{ 7}{ 6}\) |
8
New Number: 9.8 | AESZ: | Superseeker: 6/17 688/17 | Hash: 0574d9effd306eb6c9288752b7670904
Degree: 9
\(17^{2} \theta^4-2 17 x\left(164\theta^4-164\theta^3-167\theta^2-85\theta-17\right)-2^{2} x^{2}\left(35300\theta^4+95864\theta^3+121575\theta^2+70856\theta+16235\right)+2^{2} x^{3}\left(427984\theta^4-277824\theta^3-1460293\theta^2-1490475\theta-492694\right)+2^{4} x^{4}\left(2088512\theta^4+6692704\theta^3+7319011\theta^2+3820745\theta+794302\right)-2^{6} x^{5}\left(1379872\theta^4-6413120\theta^3-11843583\theta^2-9110135\theta-2589134\right)-2^{8} x^{6}\left(13237904\theta^4+37140384\theta^3+64254239\theta^2+57084594\theta+19379105\right)-2^{10} 3^{2} 5 x^{7}\left(255072\theta^4+803200\theta^3+1114259\theta^2+709496\theta+167515\right)+2^{12} 3^{3} 5^{2} 7 x^{8}(2224\theta^2+11008\theta+12225)(\theta+1)^2+2^{18} 3^{3} 5^{4} 7^{2} x^{9}(\theta+1)^2(\theta+2)^2\)
Maple LaTexCoefficients of the holomorphic solution: 1, -2, 18, -20, 1330, ... --> OEIS Normalized instanton numbers (n0=1): 6/17, 83/17, 688/17, 7350/17, 5150, ... ; Common denominator:...
\((4z-1)(12z+1)(1600z^3+272z^2+8z-1)(-17+164z+1680z^2)^2\)
| \(-\frac{ 41}{ 840}-\frac{ 1}{ 840}\sqrt{ 8821}\) | ≈\(-0.106819-0.053966I\) | ≈\(-0.106819+0.053966I\) | \(-\frac{ 1}{ 12}\) | \(0\) | ≈\(0.043637\) | \(-\frac{ 41}{ 840}+\frac{ 1}{ 840}\sqrt{ 8821}\) | \(\frac{ 1}{ 4}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(3\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(3\) | \(1\) | \(2\) |
| \(4\) | \(2\) | \(2\) | \(2\) | \(0\) | \(2\) | \(4\) | \(2\) | \(2\) |