31
New Number: 8.21 | AESZ: 251 | Superseeker: -9 -3145/3 | Hash: dd2b60d18804c72129ba319fc8b50023
Degree: 8
\(\theta^4-3 x\theta(-2-11\theta-18\theta^2+27\theta^3)-2 3^{2} x^{2}\left(39\theta^4+480\theta^3+474\theta^2+276\theta+64\right)+2^{3} 3^{4} x^{3}\left(348\theta^4+1152\theta^3+1759\theta^2+1110\theta+260\right)-2^{3} 3^{5} x^{4}\left(3420\theta^4+15912\theta^3+28437\theta^2+20544\theta+5296\right)+2^{4} 3^{7} x^{5}\left(1125\theta^4+12546\theta^3+31089\theta^2+26448\theta+7480\right)+2^{5} 3^{9} x^{6}\left(1395\theta^4+3240\theta^3-3378\theta^2-7146\theta-2696\right)-2^{7} 3^{11} x^{7}\left(351\theta^4+2646\theta^3+4767\theta^2+3309\theta+800\right)-2^{7} 3^{13} x^{8}(3\theta+2)(3\theta+4)(6\theta+5)(6\theta+7)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, 72, -1440, 48600, ... --> OEIS Normalized instanton numbers (n0=1): -9, -27/4, -3145/3, -20907/4, -327348, ... ; Common denominator:...
\(-(54z+1)(27z-1)(432z^2-36z+1)(-1+36z+324z^2)^2\)
| \(-\frac{ 1}{ 18}-\frac{ 1}{ 18}\sqrt{ 2}\) | \(-\frac{ 1}{ 54}\) | \(0\) | \(-\frac{ 1}{ 18}+\frac{ 1}{ 18}\sqrt{ 2}\) | \(\frac{ 1}{ 27}\) | \(\frac{ 1}{ 24}-\frac{ 1}{ 72}\sqrt{ 3}I\) | \(\frac{ 1}{ 24}+\frac{ 1}{ 72}\sqrt{ 3}I\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 2}{ 3}\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(\frac{ 5}{ 6}\) |
| \(3\) | \(1\) | \(0\) | \(3\) | \(1\) | \(1\) | \(1\) | \(\frac{ 7}{ 6}\) |
| \(4\) | \(2\) | \(0\) | \(4\) | \(2\) | \(2\) | \(2\) | \(\frac{ 4}{ 3}\) |
32
New Number: 8.35 | AESZ: 326 | Superseeker: 11/13 385/39 | Hash: 946b91838924db64fe0ebdf0d473e621
Degree: 8
\(13^{2} \theta^4-13 x\theta(56\theta^3+178\theta^2+115\theta+26)-x^{2}\left(28466\theta^4+109442\theta^3+165603\theta^2+117338\theta+32448\right)-x^{3}\left(233114\theta^4+1257906\theta^3+2622815\theta^2+2467842\theta+872352\right)-x^{4}\left(989585\theta^4+6852298\theta^3+17737939\theta^2+19969754\theta+8108448\right)-x^{5}(\theta+1)(2458967\theta^3+18007287\theta^2+44047582\theta+35386584)-3^{2} x^{6}(\theta+1)(\theta+2)(393163\theta^2+2539029\theta+4164444)-3^{3} 11 x^{7}(\theta+3)(\theta+2)(\theta+1)(8683\theta+34604)-3^{3} 11^{2} 13 17 x^{8}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, 12, 96, 1116, ... --> OEIS Normalized instanton numbers (n0=1): 11/13, 30/13, 385/39, 672/13, 4437/13, ... ; Common denominator:...
\(-(3z+1)(13z^2+5z+1)(153z^3+75z^2+14z-1)(13+11z)^2\)
| \(-\frac{ 13}{ 11}\) | \(-\frac{ 1}{ 3}\) | ≈\(-0.272124-0.216493I\) | ≈\(-0.272124+0.216493I\) | \(-\frac{ 5}{ 26}-\frac{ 3}{ 26}\sqrt{ 3}I\) | \(-\frac{ 5}{ 26}+\frac{ 3}{ 26}\sqrt{ 3}I\) | \(0\) | ≈\(0.054052\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(2\) |
| \(3\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(3\) |
| \(4\) | \(2\) | \(2\) | \(2\) | \(2\) | \(2\) | \(0\) | \(2\) | \(4\) |
33
New Number: 8.36 | AESZ: 327 | Superseeker: 24/29 284/29 | Hash: 586c1906112cbba9b2d54c57ce2add99
Degree: 8
\(29^{2} \theta^4+2 29 x\theta(24\theta^3-198\theta^2-128\theta-29)-2^{2} x^{2}\left(44284\theta^4+172954\theta^3+248589\theta^2+172057\theta+47096\right)-2^{2} x^{3}\left(525708\theta^4+2414772\theta^3+4447643\theta^2+3839049\theta+1275594\right)-2^{3} x^{4}\left(1415624\theta^4+7911004\theta^3+17395449\theta^2+17396359\theta+6496262\right)-2^{4} x^{5}(\theta+1)(2152040\theta^3+12186636\theta^2+24179373\theta+16560506)-2^{5} x^{6}(\theta+1)(\theta+2)(1912256\theta^2+9108540\theta+11349571)-2^{8} 41 x^{7}(\theta+3)(\theta+2)(\theta+1)(5671\theta+16301)-2^{8} 3 19 41^{2} x^{8}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, 14, 96, 1266, ... --> OEIS Normalized instanton numbers (n0=1): 24/29, 72/29, 284/29, 1616/29, 10632/29, ... ; Common denominator:...
\(-(6z+1)(152z^3+84z^2+14z-1)(2z+1)^2(82z+29)^2\)
| \(-\frac{ 1}{ 2}\) | \(-\frac{ 29}{ 82}\) | ≈\(-0.302804-0.180271I\) | ≈\(-0.302804+0.180271I\) | \(-\frac{ 1}{ 6}\) | \(0\) | ≈\(0.052976\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(2\) |
| \(\frac{ 1}{ 2}\) | \(3\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(3\) |
| \(1\) | \(4\) | \(2\) | \(2\) | \(2\) | \(0\) | \(2\) | \(4\) |
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: 8.50 | 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:...
\((3z-1)(2z-1)(10z-1)(6z+1)(25z^2-5z-1)(-23+90z)^2\)
| \(-\frac{ 1}{ 6}\) | \(\frac{ 1}{ 10}-\frac{ 1}{ 10}\sqrt{ 5}\) | \(0\) | \(\frac{ 1}{ 10}\) | \(\frac{ 23}{ 90}\) | \(\frac{ 1}{ 10}+\frac{ 1}{ 10}\sqrt{ 5}\) | \(\frac{ 1}{ 3}\) | \(\frac{ 1}{ 2}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(2\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(3\) | \(1\) | \(1\) | \(1\) | \(3\) |
| \(2\) | \(2\) | \(0\) | \(2\) | \(4\) | \(2\) | \(2\) | \(2\) | \(4\) |
36
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:...
\(-(7z+1)(25z-1)(2z+1)^2(101z+43)^2(3z+1)^2\)
| \(-\frac{ 1}{ 2}\) | \(-\frac{ 43}{ 101}\) | \(-\frac{ 1}{ 3}\) | \(-\frac{ 1}{ 7}\) | \(0\) | \(\frac{ 1}{ 25}\) | \(\infty\) |
|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(\frac{ 1}{ 3}\) | \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(0\) | \(1\) | \(2\) |
| \(\frac{ 2}{ 3}\) | \(3\) | \(\frac{ 1}{ 2}\) | \(1\) | \(0\) | \(1\) | \(3\) |
| \(1\) | \(4\) | \(1\) | \(2\) | \(0\) | \(2\) | \(4\) |
37
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:...
\((4z+1)(6z+1)(43z^2+13z+1)(2z+1)^2(12z-1)^2\)
| \(-\frac{ 1}{ 2}\) | \(-\frac{ 1}{ 4}\) | \(-\frac{ 1}{ 6}\) | \(-\frac{ 13}{ 86}-\frac{ 1}{ 86}\sqrt{ 3}I\) | \(-\frac{ 13}{ 86}+\frac{ 1}{ 86}\sqrt{ 3}I\) | \(0\) | \(\frac{ 1}{ 12}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(\frac{ 1}{ 2}\) | \(2\) |
| \(3\) | \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(\frac{ 1}{ 2}\) | \(3\) |
| \(4\) | \(2\) | \(2\) | \(2\) | \(2\) | \(0\) | \(1\) | \(4\) |
38
New Number: 8.68 | AESZ: | Superseeker: 6/17 33/17 | Hash: 0c0662f5b46ac6cb0bd298a63cf364c7
Degree: 8
\(17^{2} \theta^4+17 x\theta(165\theta^3-114\theta^2-74\theta-17)-x^{2}\left(20619\theta^4+122880\theta^3+175353\theta^2+126480\theta+36992\right)-2 x^{3}\left(201857\theta^4+853944\theta^3+1437673\theta^2+1174122\theta+375972\right)-2^{2} x^{4}\left(571275\theta^4+2711616\theta^3+5301571\theta^2+4856674\theta+1694372\right)-2^{3} 3 x^{5}(\theta+1)(295815\theta^3+1523993\theta^2+2924668\theta+1983212)-2^{5} x^{6}(\theta+1)(\theta+2)(558823\theta^2+2951265\theta+4136951)-2^{7} 3 37 x^{7}(\theta+3)(\theta+2)(\theta+1)(2797\theta+9878)-2^{9} 3^{2} 7 37^{2} x^{8}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, 8, 24, 288, ... --> OEIS Normalized instanton numbers (n0=1): 6/17, 25/34, 33/17, 157/17, 577/17, ... ; Common denominator:...
\(-(12z-1)(6z+1)(7z^2-z+1)(4z+1)^2(74z+17)^2\)
| \(-\frac{ 1}{ 4}\) | \(-\frac{ 17}{ 74}\) | \(-\frac{ 1}{ 6}\) | \(0\) | \(\frac{ 1}{ 14}-\frac{ 3}{ 14}\sqrt{ 3}I\) | \(\frac{ 1}{ 14}+\frac{ 3}{ 14}\sqrt{ 3}I\) | \(\frac{ 1}{ 12}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(2\) |
| \(\frac{ 1}{ 2}\) | \(3\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(3\) |
| \(1\) | \(4\) | \(2\) | \(0\) | \(2\) | \(2\) | \(2\) | \(4\) |
39
New Number: 8.72 | AESZ: | Superseeker: 32/3 14279/9 | Hash: d1b06e21c273cae807016268cd540d98
Degree: 8
\(3^{2} \theta^4-2 3 x\theta(85\theta^3+176\theta^2+112\theta+24)-2^{2} x^{2}\left(6581\theta^4+25808\theta^3+38672\theta^2+26184\theta+6912\right)-x^{3}\left(433513\theta^4+2497158\theta^3+5333997\theta^2+4967532\theta+1724868\right)-2 x^{4}\left(1751393\theta^4+13178758\theta^3+35803021\theta^2+40983788\theta+16698948\right)-2^{2} x^{5}(\theta+1)(3719315\theta^3+30248511\theta^2+79801768\theta+66666732)-2^{3} 3^{3} x^{6}(\theta+1)(\theta+2)(144041\theta^2+1060683\theta+1963346)-2^{7} 3^{4} x^{7}(\theta+3)(\theta+2)(\theta+1)(2449\theta+10862)-2^{9} 3^{3} 7 71 x^{8}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, 192, 7524, 438912, ... --> OEIS Normalized instanton numbers (n0=1): 32/3, 284/3, 14279/9, 118940/3, 1226784, ... ; Common denominator:...
\(-(7z+1)(6z+1)(639z^2+87z-1)(2z+3)^2(8z+1)^2\)
| \(-\frac{ 3}{ 2}\) | \(-\frac{ 1}{ 6}\) | \(-\frac{ 29}{ 426}-\frac{ 5}{ 142}\sqrt{ 5}\) | \(-\frac{ 1}{ 7}\) | \(-\frac{ 1}{ 8}\) | \(0\) | \(-\frac{ 29}{ 426}+\frac{ 5}{ 142}\sqrt{ 5}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(0\) | \(1\) | \(2\) |
| \(3\) | \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(3\) |
| \(4\) | \(2\) | \(2\) | \(2\) | \(1\) | \(0\) | \(2\) | \(4\) |
40
New Number: 8.73 | AESZ: | Superseeker: 161/13 26946/13 | Hash: 13db5d8c98a3d4f31589970217896191
Degree: 8
\(13^{2} \theta^4-13 x\theta(614\theta^3+1804\theta^2+1149\theta+247)-x^{2}\left(775399\theta^4+2692636\theta^3+3693483\theta^2+2450110\theta+648960\right)-2^{2} x^{3}\left(5408420\theta^4+24616488\theta^3+45163287\theta^2+38795913\theta+12838410\right)-2^{5} x^{4}\left(9763642\theta^4+55386224\theta^3+123097843\theta^2+124066416\theta+46600563\right)-2^{9} 3 x^{5}(\theta+1)(1717504\theta^3+9940776\theta^2+20063523\theta+13933966)-2^{13} 3^{2} x^{6}(\theta+1)(\theta+2)(178975\theta^2+874119\theta+1112486)-2^{19} 3^{4} x^{7}(\theta+3)(\theta+2)(\theta+1)(857\theta+2533)-2^{23} 3^{6} 7 x^{8}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, 240, 10440, 679104, ... --> OEIS Normalized instanton numbers (n0=1): 161/13, 1406/13, 26946/13, 742982/13, 25168759/13, ... ; Common denominator:...
\(-(-1+96z+896z^2)(9z+1)^2(96z+13)^2(8z+1)^2\)
| \(-\frac{ 13}{ 96}\) | \(-\frac{ 1}{ 8}\) | \(-\frac{ 3}{ 56}-\frac{ 5}{ 112}\sqrt{ 2}\) | \(-\frac{ 1}{ 9}\) | \(0\) | \(-\frac{ 3}{ 56}+\frac{ 5}{ 112}\sqrt{ 2}\) | \(\infty\) |
|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(0\) | \(1\) | \(0\) | \(0\) | \(1\) | \(2\) |
| \(3\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(3\) |
| \(4\) | \(1\) | \(2\) | \(1\) | \(0\) | \(2\) | \(4\) |
41
New Number: 8.74 | AESZ: | Superseeker: 4 436 | Hash: a0fbd8561e58a032d489a1dabee1e026
Degree: 8
\(\theta^4-2^{2} x\theta(22\theta^3+14\theta^2+9\theta+2)+2^{4} x^{2}\left(109\theta^4-74\theta^3-293\theta^2-258\theta-80\right)+2^{8} x^{3}\left(39\theta^4+414\theta^3+674\theta^2+504\theta+144\right)-2^{10} x^{4}\left(405\theta^4+1170\theta^3+1321\theta^2+424\theta-104\right)-2^{14} x^{5}(\theta+1)(12\theta^3+558\theta^2+1495\theta+1255)+2^{16} x^{6}(\theta+1)(\theta+2)(467\theta^2+1593\theta+1540)-2^{20} 5 x^{7}(\theta+3)(\theta+2)(\theta+1)(\theta-40)-2^{22} 5^{2} 7 x^{8}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, 80, 1536, 56592, ... --> OEIS Normalized instanton numbers (n0=1): 4, 71/2, 436, 6728, 127212, ... ; Common denominator:...
\(-(-1+56z)(20z-1)^2(8z-1)^2(8z+1)^3\)
| \(-\frac{ 1}{ 8}\) | \(0\) | \(\frac{ 1}{ 56}\) | \(\frac{ 1}{ 20}\) | \(\frac{ 1}{ 8}\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(0\) | \(0\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(2\) |
| \(-\frac{ 1}{ 4}\) | \(0\) | \(1\) | \(3\) | \(\frac{ 1}{ 2}\) | \(3\) |
| \(\frac{ 1}{ 4}\) | \(0\) | \(2\) | \(4\) | \(1\) | \(4\) |
42
New Number: 8.82 | AESZ: | Superseeker: 0 -1/3 | Hash: 8bab1ddc8b31cb2c21f01402f27895ce
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:...
\((6z-1)(4z-1)(43z^2-13z+1)(12z+1)^2(-1+2z)^2\)
| \(-\frac{ 1}{ 12}\) | \(0\) | \(\frac{ 13}{ 86}-\frac{ 1}{ 86}\sqrt{ 3}I\) | \(\frac{ 13}{ 86}+\frac{ 1}{ 86}\sqrt{ 3}I\) | \(\frac{ 1}{ 6}\) | \(\frac{ 1}{ 4}\) | \(\frac{ 1}{ 2}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(\frac{ 1}{ 2}\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(2\) |
| \(\frac{ 1}{ 2}\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(3\) | \(3\) |
| \(1\) | \(0\) | \(2\) | \(2\) | \(2\) | \(2\) | \(4\) | \(4\) |
43
New Number: 8.84 | AESZ: | Superseeker: 1/5 224/5 | Hash: 258fab6f0a4f132fe597fc6f30e54eea
Degree: 8
\(5^{2} \theta^4+5 x\theta^2(-1-2\theta+107\theta^2)+2^{2} x^{2}\left(2174\theta^4+5942\theta^3+8569\theta^2+5200\theta+1200\right)+2^{2} 3^{2} x^{3}\left(308\theta^4-4248\theta^3-17051\theta^2-16785\theta-5280\right)-2^{4} 3^{2} x^{4}\left(7060\theta^4+39500\theta^3+69820\theta^2+52851\theta+14688\right)-2^{6} 3^{4} x^{5}\left(881\theta^4+3974\theta^3+8648\theta^2+7983\theta+2581\right)+2^{7} 3^{4} x^{6}\left(1192\theta^4+2376\theta^3-1132\theta^2-4185\theta-1926\right)+2^{8} 3^{6} x^{7}\left(68\theta^4+568\theta^3+1095\theta^2+811\theta+210\right)-2^{12} 3^{8} x^{8}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, -12, 144, 324, ... --> OEIS Normalized instanton numbers (n0=1): 1/5, -6, 224/5, -448/5, -4334/5, ... ; Common denominator:...
\(-(9z-1)(576z^3+368z^2+16z+1)(-5-36z+72z^2)^2\)
| ≈\(-0.597246\) | \(\frac{ 1}{ 4}-\frac{ 1}{ 12}\sqrt{ 19}\) | ≈\(-0.020821-0.049733I\) | ≈\(-0.020821+0.049733I\) | \(0\) | \(\frac{ 1}{ 9}\) | \(\frac{ 1}{ 4}+\frac{ 1}{ 12}\sqrt{ 19}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) |
| \(1\) | \(3\) | \(1\) | \(1\) | \(0\) | \(1\) | \(3\) | \(1\) |
| \(2\) | \(4\) | \(2\) | \(2\) | \(0\) | \(2\) | \(4\) | \(1\) |
44
New Number: 9.1 | AESZ: | Superseeker: -4/7 955/63 | Hash: d32eab6005ac34ecc01a9db7675daa24
Degree: 9
\(7^{2} \theta^4-7 x\theta(-7-32\theta-50\theta^2+29\theta^3)+3 x^{2}\theta(532+1165\theta+512\theta^2+1235\theta^3)-2 3^{2} x^{3}\left(5373\theta^4+29040\theta^3+61493\theta^2+51786\theta+15876\right)+2^{2} 3^{3} x^{4}\left(10813\theta^4+68120\theta^3+160529\theta^2+154570\theta+53396\right)-2^{3} 3^{4} x^{5}\left(13929\theta^4+84348\theta^3+181015\theta^2+171080\theta+59172\right)+2^{5} 3^{5} x^{6}\left(6160\theta^4+35964\theta^3+69935\theta^2+58677\theta+18110\right)-2^{8} 3^{6} x^{7}\left(944\theta^4+5308\theta^3+10916\theta^2+9657\theta+3109\right)+2^{11} 3^{7} x^{8}(96\theta^2+300\theta+265)(\theta+1)^2-2^{15} 3^{9} x^{9}(\theta+1)^2(\theta+2)^2\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, 0, 72, -432, ... --> OEIS Normalized instanton numbers (n0=1): -4/7, -4/7, 955/63, -262/7, -1002/7, ... ; Common denominator:...
\(-(6z-1)(27z^2-9z+1)(192z^2+16z+1)(7-18z+144z^2)^2\)
| \(-\frac{ 1}{ 24}-\frac{ 1}{ 24}\sqrt{ 2}I\) | \(-\frac{ 1}{ 24}+\frac{ 1}{ 24}\sqrt{ 2}I\) | \(0\) | \(\frac{ 1}{ 16}-\frac{ 1}{ 48}\sqrt{ 103}I\) | \(\frac{ 1}{ 16}+\frac{ 1}{ 48}\sqrt{ 103}I\) | \(\frac{ 1}{ 6}-\frac{ 1}{ 18}\sqrt{ 3}I\) | \(\frac{ 1}{ 6}\) | \(\frac{ 1}{ 6}+\frac{ 1}{ 18}\sqrt{ 3}I\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(1\) | \(1\) | \(0\) | \(3\) | \(3\) | \(1\) | \(1\) | \(1\) | \(2\) |
| \(2\) | \(2\) | \(0\) | \(4\) | \(4\) | \(2\) | \(2\) | \(2\) | \(2\) |
45
New Number: 9.2 | AESZ: | Superseeker: 9/7 49/3 | Hash: 356d4564e48d7a04e815fa223b6ccc46
Degree: 9
\(7^{2} \theta^4+7 x\theta(165\theta^3-102\theta^2-65\theta-14)-2^{3} x^{2}\left(920\theta^4+11726\theta^3+15277\theta^2+9478\theta+2352\right)-2^{4} 3^{2} x^{3}\left(4035\theta^4+19554\theta^3+29157\theta^2+20706\theta+5761\right)-2^{8} 3^{2} x^{4}\left(4156\theta^4+17951\theta^3+28198\theta^2+21045\theta+6096\right)-2^{11} 3^{3} x^{5}\left(1538\theta^4+6560\theta^3+10755\theta^2+8234\theta+2420\right)-2^{13} 3^{4} x^{6}\left(695\theta^4+3051\theta^3+5285\theta^2+4191\theta+1259\right)-2^{14} 3^{5} x^{7}\left(385\theta^4+1802\theta^3+3319\theta^2+2754\theta+855\right)-2^{18} 3^{6} x^{8}(\theta+1)^2(15\theta^2+48\theta+43)-2^{20} 3^{7} x^{9}(\theta+1)^2(\theta+2)^2\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, 24, 144, 3240, ... --> OEIS Normalized instanton numbers (n0=1): 9/7, 47/7, 49/3, 1370/7, 10063/7, ... ; Common denominator:...
\(-(8z+1)(24z-1)(3z+1)(4z+1)(12z+1)(7+72z+288z^2)^2\)
| \(-\frac{ 1}{ 3}\) | \(-\frac{ 1}{ 4}\) | \(-\frac{ 1}{ 8}-\frac{ 1}{ 24}\sqrt{ 5}I\) | \(-\frac{ 1}{ 8}\) | \(-\frac{ 1}{ 8}+\frac{ 1}{ 24}\sqrt{ 5}I\) | \(-\frac{ 1}{ 12}\) | \(0\) | \(\frac{ 1}{ 24}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) |
| \(1\) | \(1\) | \(3\) | \(1\) | \(3\) | \(1\) | \(0\) | \(1\) | \(2\) |
| \(2\) | \(2\) | \(4\) | \(2\) | \(4\) | \(2\) | \(0\) | \(2\) | \(2\) |
46
New Number: 8.87 | AESZ: | Superseeker: 10 18994/9 | Hash: 038b62cbc5b6e43ac232ededcc3b6a59
Degree: 8
\(\theta^4+2 x\theta(-2-13\theta-22\theta^2+88\theta^3)+2^{2} x^{2}\left(3323\theta^4+722\theta^3+2365\theta^2+1306\theta+256\right)+2^{4} 3 x^{3}\left(12903\theta^4+16874\theta^3+21943\theta^2+11164\theta+2164\right)+2^{5} x^{4}\left(618707\theta^4+1367710\theta^3+1570347\theta^2+801712\theta+157652\right)+2^{9} 3 x^{5}\left(248985\theta^4+660583\theta^3+726977\theta^2+362865\theta+69886\right)+2^{11} x^{6}\left(1818051\theta^4+4794576\theta^3+4692593\theta^2+2080392\theta+357884\right)+2^{17} 5 7 x^{7}\left(3223\theta^4+8030\theta^3+8618\theta^2+4603\theta+1002\right)+2^{23} 5^{2} 7^{2} x^{8}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, -64, 576, 22716, ... --> OEIS Normalized instanton numbers (n0=1): 10, -581/4, 18994/9, -274969/8, 3458142/5, ... ; Common denominator:...
\((1+44z+2008z^2+39424z^3+32768z^4)(10z+1)^2(56z+1)^2\)
| \(-\frac{ 1}{ 10}\) | \(-\frac{ 1}{ 56}\) | \(0\) | \(s_1\) | \(s_3\) | \(s_2\) | \(s_4\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(3\) | \(3\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(4\) | \(4\) | \(0\) | \(2\) | \(2\) | \(2\) | \(2\) | \(1\) |
47
New Number: 24.11 | AESZ: | Superseeker: 53/5 -309836/1215 | Hash: 682b45ff9c4177035e08e594ea968a40
Degree: 24
\(5^{2} \theta^4-5 x\theta(780\theta^3+233\theta+45)+x^{2}\left(29459\theta^4+155852\theta^3+133609\theta^2+27010\theta-6000\right)-3^{2} x^{3}\left(170942\theta^4+5388\theta^3+123841\theta^2+538965\theta+289950\right)-2^{2} 3^{3} x^{4}\left(299324\theta^4+1917922\theta^3+2469992\theta^2+1887645\theta+792630\right)+3^{4} x^{5}\left(13371098\theta^4-15702340\theta^3-56878373\theta^2-21939359\theta-1565760\right)+3^{7} x^{6}\left(10056623\theta^4+51572556\theta^3+34820569\theta^2+76534814\theta+46490824\right)-3^{7} x^{7}\left(235027408\theta^4-62481208\theta^3-620667755\theta^2-694808037\theta-436763790\right)-3^{8} x^{8}\left(1103983063\theta^4+6898242712\theta^3+5618673632\theta^2+8342492360\theta+4306904496\right)+2 3^{10} x^{9}\left(1567811420\theta^4+1125299280\theta^3+2679400693\theta^2+929271741\theta-931458972\right)+2 3^{12} x^{10}\left(1091890963\theta^4+8818792004\theta^3+14797099953\theta^2+16119935558\theta+6720833160\right)-2 3^{14} x^{11}\left(4132995702\theta^4+11210477796\theta^3+22335304201\theta^2+21391532585\theta+7680128002\right)-2^{3} 3^{16} x^{12}\left(36094918\theta^4+2244000840\theta^3+5817619373\theta^2+7236866988\theta+3390157938\right)+2 3^{18} x^{13}\left(5245867146\theta^4+28750482372\theta^3+67038993743\theta^2+76465169633\theta+33958775428\right)-2 3^{20} x^{14}\left(2325299271\theta^4+9056959668\theta^3+15535709593\theta^2+13710343706\theta+4772169024\right)-2 3^{22} x^{15}\left(1937917032\theta^4+18692730384\theta^3+60632460723\theta^2+83153628009\theta+41806101938\right)+3^{24} x^{16}\left(3589458339\theta^4+31443345792\theta^3+101210591864\theta^2+140988740840\theta+71945494016\right)-3^{26} x^{17}\left(917154124\theta^4+7902286936\theta^3+25304271327\theta^2+35059224115\theta+17843355880\right)+3^{28} x^{18}\left(32843719\theta^4+454332780\theta^3+2174878229\theta^2+3835061490\theta+2302959008\right)+3^{30} x^{19}\left(28756154\theta^4+169682932\theta^3+218616787\theta^2-103588009\theta-230015838\right)-2^{2} 3^{32} x^{20}\left(1138248\theta^4+7399434\theta^3+14543734\theta^2+8831609\theta-443286\right)-3^{34} x^{21}\left(15470\theta^4-742908\theta^3-2759711\theta^2-3300309\theta-1216344\right)+3^{37} x^{22}\left(19299\theta^4+100277\theta^2+123674\theta+5048\right)-3^{40} x^{23}(12\theta^2+37\theta+29)(20\theta^2+59\theta+46)+3^{43} x^{24}\left((\theta+2)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, 15, 48296/27, 23854513/240, ... --> OEIS Normalized instanton numbers (n0=1): 53/5, 53/10, -309836/1215, -73952369/345600, 209793337409497/1687500000, ... ; Common denominator:...
\(25-3900z+8690029099790358108537z^22-2917839710173662912240z^23+328256967394537077627z^24+21993834501z^6-514004941296z^7-7243232876343z^8+185155393079160z^9+1160551250535366z^10+1013769054901630165059z^16-2331282727106618378796z^17+29459z^2-1538478z^3-32326992z^4+1083058938z^5+751358943012059239959z^18-39535980639598476z^11-12430142917311024z^12+4064712829864708788z^13-16215634451558943342z^14-121627779796976720976z^15+5920637101748069219946z^19-8436786095680921258272z^20-257996000893841822430z^21\)
No data for singularities
48
New Number: 24.1 | AESZ: | Superseeker: 3 1322/9 | Hash: d77f5cce80101a4e8f097ff7dc1cac1f
Degree: 24
\(\theta^4-3 x\theta(8\theta^2+5\theta+1)-3^{2} x^{2}\left(141\theta^4-76\theta^3-53\theta^2+74\theta+48\right)+3^{3} x^{3}\left(350\theta^4+268\theta^3-911\theta^2+193\theta+366\right)+2^{2} 3^{4} x^{4}\left(1536\theta^4-210\theta^3+5498\theta^2+3259\theta+432\right)-3^{6} x^{5}\left(9982\theta^4-4940\theta^3+26473\theta^2+14567\theta+72\right)-3^{7} x^{6}\left(13329\theta^4+128212\theta^3+141347\theta^2+176702\theta+93936\right)+3^{8} x^{7}\left(179988\theta^4+489272\theta^3+581261\theta^2+545387\theta+236754\right)-3^{9} x^{8}\left(473261\theta^4-322200\theta^3-1952576\theta^2-2540184\theta-1052928\right)+2 3^{11} x^{9}\left(89272\theta^4-647728\theta^3-1032101\theta^2-477573\theta+275604\right)+2 3^{12} x^{10}\left(380267\theta^4+3534580\theta^3+6813301\theta^2+7672754\theta+3370032\right)-2 3^{13} x^{11}\left(2824394\theta^4+21447564\theta^3+70086871\theta^2+111632667\theta+67101174\right)+2^{3} 3^{15} x^{12}\left(604658\theta^4+4211064\theta^3+13816867\theta^2+20606976\theta+11731242\right)-2 3^{16} x^{13}\left(2513086\theta^4-1029540\theta^3-71899267\theta^2-199754241\theta-151321716\right)-2 3^{17} x^{14}\left(4936477\theta^4+113054700\theta^3+624917375\theta^2+1236797682\theta+810302688\right)+2 3^{19} x^{15}\left(10447060\theta^4+141814160\theta^3+623159411\theta^2+1236797682\theta+658549626\right)-3^{21} x^{16}\left(15883703\theta^4+190281632\theta^3+7662783992\theta^2+1272288312\theta+742283280\right)+3^{24} x^{17}\left(2257088\theta^4+24107672\theta^3+94611213\theta^2+157783505\theta+93169704\right)-3^{25} x^{18}\left(1409659\theta^4+13667804\theta^3+60904285\theta^2+118238478\theta+79019856\right)-3^{27} x^{19}\left(372282\theta^4+2964756\theta^3+4412579\theta^2-3409349\theta-6851134\right)+2^{2} 3^{29} x^{20}\left(79892\theta^4+648390\theta^3+1698852\theta^2+1619127\theta+396380\right)-3^{31} x^{21}\left(42578\theta^4+351292\theta^3+908415\theta^2+928057\theta+321472\right)-3^{33} x^{22}\left(10861\theta^4+68980\theta^3+157607\theta^2+161390\theta+65296\right)+3^{35} 5 x^{23}\left(444\theta^4+2616\theta^3+5783\theta^2+5673\theta+2078\right)+3^{37} 5^{2} x^{24}\left((\theta+2)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, 27, -36, 891, ... --> OEIS Normalized instanton numbers (n0=1): 3, -24, 1322/9, -1824, 19551, ... ; Common denominator:...
\((9z-1)(81z^2-9z-1)(6561z^6+66339z^5-16767z^4+2106z^3-297z^2+27z-1)(9z+1)^2(32805z^5+12393z^4-324z^3+432z^2-9z-1)^2(3z-1)^3\)
No data for singularities