31
New Number: 5.69 | AESZ: 280 | Superseeker: -117 -844872 | Hash: 5083c4e9f432302302c564ba554e3bcd
Degree: 5
\(\theta^4-3^{2} x\left(123\theta^4-60\theta^3-39\theta^2-9\theta-1\right)+3^{5} x^{2}\left(1521\theta^4-1260\theta^3+30\theta^2-21\theta-10\right)-3^{8} x^{3}\left(4110\theta^4-5634\theta^3-4353\theta^2-1629\theta-220\right)-3^{12} 17 x^{4}\left(286\theta^4+410\theta^3+170\theta^2-35\theta-30\right)-3^{18} 17^{2} x^{5}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -9, 81, 1017, -93231, ... --> OEIS Normalized instanton numbers (n0=1): -117, -28899/4, -844872, -131189436, -23932952667, ... ; Common denominator:...
\(-(531441z^3+14580z^2+189z-1)(-1+459z)^2\)
| ≈\(-0.015682-0.015263I\) | ≈\(-0.015682+0.015263I\) | \(0\) | \(\frac{ 1}{ 459}\) | ≈\(0.003929\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) |
| \(1\) | \(1\) | \(0\) | \(3\) | \(1\) | \(1\) |
| \(2\) | \(2\) | \(0\) | \(4\) | \(2\) | \(1\) |
32
New Number: 5.6 | AESZ: 23 | Superseeker: 4/3 44/3 | Hash: 65760d446ba9c3da587ce5bd9912745e
Degree: 5
\(3^{2} \theta^4-2^{2} 3 x\left(64\theta^4+80\theta^3+73\theta^2+33\theta+6\right)+2^{7} x^{2}\left(194\theta^4+440\theta^3+527\theta^2+315\theta+75\right)-2^{12} x^{3}\left(94\theta^4+288\theta^3+397\theta^2+261\theta+66\right)+2^{17} x^{4}\left(22\theta^4+80\theta^3+117\theta^2+77\theta+19\right)-2^{23} x^{5}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 8, 104, 1664, 30376, ... --> OEIS Normalized instanton numbers (n0=1): 4/3, 13/3, 44/3, 278/3, 2336/3, ... ; Common denominator:...
\(-(-1+32z)(16z-1)^2(32z-3)^2\)
| \(0\) | \(\frac{ 1}{ 32}\) | \(\frac{ 1}{ 16}\) | \(\frac{ 3}{ 32}\) | \(\infty\) |
|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(0\) | \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) |
| \(0\) | \(1\) | \(\frac{ 1}{ 2}\) | \(3\) | \(1\) |
| \(0\) | \(2\) | \(1\) | \(4\) | \(1\) |
33
New Number: 5.71 | AESZ: 290 | Superseeker: 162 751026 | Hash: 5552195a371df176b84ac2c2d791be7e
Degree: 5
\(\theta^4+3 x\left(279\theta^4-252\theta^3-160\theta^2-34\theta-3\right)+2 3^{5} x^{2}\left(423\theta^4-468\theta^3+457\theta^2+215\theta+37\right)+2 3^{9} x^{3}\left(531\theta^4+1296\theta^3+1243\theta^2+567\theta+104\right)+3^{15} 5 x^{4}\left(51\theta^4+120\theta^3+126\theta^2+66\theta+14\right)+3^{20} 5^{2} x^{5}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 9, -837, -32553, 4787019, ... --> OEIS Normalized instanton numbers (n0=1): 162, -8829, 751026, -163125009/2, 10343901204, ... ; Common denominator:...
\((27z+1)(19683z^2+1)(1+405z)^2\)
| \(-\frac{ 1}{ 27}\) | \(-\frac{ 1}{ 405}\) | \(0-\frac{ 1}{ 243}\sqrt{ 3}I\) | \(0\) | \(0+\frac{ 1}{ 243}\sqrt{ 3}I\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) |
| \(1\) | \(3\) | \(1\) | \(0\) | \(1\) | \(1\) |
| \(2\) | \(4\) | \(2\) | \(0\) | \(2\) | \(1\) |
34
New Number: 5.72 | AESZ: 291 | Superseeker: -28 -37768 | Hash: cbc8242a8fecc72056e6e36b4864b868
Degree: 5
\(\theta^4-x\left(566\theta^4+34\theta^3+62\theta^2+45\theta+9\right)+3 x^{2}\left(39370\theta^4+17302\theta^3+22493\theta^2+8369\theta+1140\right)-3^{2} x^{3}\left(1215215\theta^4+1432728\theta^3+1274122\theta^2+538245\theta+93222\right)+3^{7} 61 x^{4}\left(3029\theta^4+6544\theta^3+6135\theta^2+2863\theta+548\right)-3^{12} 61^{2} x^{5}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 9, 189, 3375, -159651, ... --> OEIS Normalized instanton numbers (n0=1): -28, -809, -37768, -2185213, -143204777, ... ; Common denominator:...
\(-(59049z^3-11421z^2+200z-1)(-1+183z)^2\)
| \(0\) | \(\frac{ 1}{ 183}\) | ≈\(0.009423-0.002866I\) | ≈\(0.009423+0.002866I\) | ≈\(0.174569\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(0\) | \(3\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(0\) | \(4\) | \(2\) | \(2\) | \(2\) | \(1\) |
35
New Number: 5.7 | AESZ: 27 | Superseeker: 14/3 910/3 | Hash: 3671a1760894e9030e36de89070612e8
Degree: 5
\(3^{2} \theta^4-3 x\left(173\theta^4+340\theta^3+272\theta^2+102\theta+15\right)-2 x^{2}\left(1129\theta^4+5032\theta^3+7597\theta^2+4773\theta+1083\right)+2 x^{3}\left(843\theta^4+2628\theta^3+2353\theta^2+675\theta+6\right)-x^{4}\left(295\theta^4+608\theta^3+478\theta^2+174\theta+26\right)+x^{5}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 5, 109, 3317, 121501, ... --> OEIS Normalized instanton numbers (n0=1): 14/3, 175/6, 910/3, 14147/3, 265496/3, ... ; Common denominator:...
\((z^3-289z^2-57z+1)(z-3)^2\)
| ≈\(-0.213297\) | \(0\) | ≈\(0.016211\) | \(3\) | ≈\(289.197085\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(1\) | \(0\) | \(1\) | \(3\) | \(1\) | \(1\) |
| \(2\) | \(0\) | \(2\) | \(4\) | \(2\) | \(1\) |
36
New Number: 5.84 | AESZ: 318 | Superseeker: 46/5 1126 | Hash: 3fa38f629ecd5f39b585ce0c1bd88463
Degree: 5
\(5^{2} \theta^4-5 x\left(473\theta^4+892\theta^3+696\theta^2+250\theta+35\right)+2 x^{2}\left(1973\theta^4-4636\theta^3-14417\theta^2-10895\theta-2745\right)+2 3^{2} x^{3}\left(343\theta^4+1920\theta^3+1147\theta^2-345\theta-320\right)-3^{4} x^{4}\left(83\theta^4-104\theta^3-458\theta^2-406\theta-114\right)-3^{8} x^{5}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 7, 219, 9961, 546379, ... --> OEIS Normalized instanton numbers (n0=1): 46/5, 717/10, 1126, 51481/2, 3609772/5, ... ; Common denominator:...
\(-(z+1)(81z^2+92z-1)(-5+9z)^2\)
| \(-\frac{ 46}{ 81}-\frac{ 13}{ 81}\sqrt{ 13}\) | \(-1\) | \(0\) | \(-\frac{ 46}{ 81}+\frac{ 13}{ 81}\sqrt{ 13}\) | \(\frac{ 5}{ 9}\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(3\) | \(1\) |
| \(2\) | \(2\) | \(0\) | \(2\) | \(4\) | \(1\) |
37
New Number: 5.85 | AESZ: 319 | Superseeker: -26 -14942/3 | Hash: 40a034330b9ad40ec865803f0a601932
Degree: 5
\(\theta^4+x\left(83\theta^4+436\theta^3+352\theta^2+134\theta+21\right)-2 3^{2} x^{2}\left(343\theta^4-548\theta^3-2555\theta^2-1749\theta-405\right)-2 3^{4} x^{3}\left(1973\theta^4+12528\theta^3+11329\theta^2+3861\theta+342\right)+3^{8} 5 x^{4}\left(473\theta^4+1000\theta^3+858\theta^2+358\theta+62\right)-3^{12} 5^{2} x^{5}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -21, 891, -48027, 2920779, ... --> OEIS Normalized instanton numbers (n0=1): -26, -475/2, -14942/3, -244479/2, -3574404, ... ; Common denominator:...
\(-(81z+1)(81z^2-92z-1)(-1+45z)^2\)
| \(-\frac{ 1}{ 81}\) | \(\frac{ 46}{ 81}-\frac{ 13}{ 81}\sqrt{ 13}\) | \(0\) | \(\frac{ 1}{ 45}\) | \(\frac{ 46}{ 81}+\frac{ 13}{ 81}\sqrt{ 13}\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) |
| \(1\) | \(1\) | \(0\) | \(3\) | \(1\) | \(1\) |
| \(2\) | \(2\) | \(0\) | \(4\) | \(2\) | \(1\) |
38
New Number: 5.9 | AESZ: 56 | Superseeker: -16 -3280 | Hash: 58a7f24bf18cb98b526885069667f9f0
Degree: 5
\(\theta^4-2^{4} x\left(22\theta^4+8\theta^3+9\theta^2+5\theta+1\right)+2^{9} x^{2}\left(94\theta^4+88\theta^3+97\theta^2+45\theta+8\right)-2^{14} x^{3}\left(194\theta^4+336\theta^3+371\theta^2+195\theta+41\right)+2^{19} 3 x^{4}\left(64\theta^4+176\theta^3+217\theta^2+129\theta+30\right)-2^{27} 3^{2} x^{5}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 16, 464, 17152, 725776, ... --> OEIS Normalized instanton numbers (n0=1): -16, -178, -3280, -76197, -2046896, ... ; Common denominator:...
\(-(-1+32z)(96z-1)^2(64z-1)^2\)
| \(0\) | \(\frac{ 1}{ 96}\) | \(\frac{ 1}{ 64}\) | \(\frac{ 1}{ 32}\) | \(\infty\) |
|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(0\) | \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) |
| \(0\) | \(3\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) |
| \(0\) | \(4\) | \(1\) | \(2\) | \(1\) |
39
New Number: 11.14 | AESZ: | Superseeker: 10 13958/9 | Hash: 0a4e6572e1bb29d996fd62dc404c2446
Degree: 11
\(3^{6} \theta^4-3^{6} x\left(111\theta^4+180\theta^3+140\theta^2+50\theta+7\right)+3^{3} x^{2}\left(31925\theta^4+11480\theta^3-42466\theta^2-34182\theta-7560\right)+3^{3} x^{3}\left(4877\theta^4+370644\theta^3+409430\theta^2+199476\theta+42297\right)-2 x^{4}\left(10348339\theta^4+26540048\theta^3+42009388\theta^2+29955528\theta+7880058\right)+2 x^{5}\left(9831565\theta^4+67438924\theta^3+143690304\theta^2+116711926\theta+33599143\right)+2 x^{6}\left(14540887\theta^4-5897448\theta^3-129216202\theta^2-158647410\theta-56400514\right)-2 x^{7}\left(20947985\theta^4+93882580\theta^3+71337738\theta^2-9343940\theta-17269525\right)+x^{8}\left(1325117\theta^4+114002144\theta^3+209338120\theta^2+141064960\theta+32960772\right)+3^{4} x^{9}\left(254941\theta^4+471612\theta^3+445052\theta^2+300870\theta+101457\right)-3^{8} x^{10}\left(1621\theta^4+5816\theta^3+8326\theta^2+5418\theta+1332\right)+3^{13} x^{11}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 7, 231, 11185, 654199, ... --> OEIS Normalized instanton numbers (n0=1): 10, 2591/27, 13958/9, 1037839/27, 3535478/3, ... ; Common denominator:...
\((z-1)(243z^4-520z^3+310z^2+96z-1)(27-189z-143z^2+81z^3)^2\)
| ≈\(-0.97581\) | \(0\) | ≈\(0.130861\) | \(1\) | ≈\(2.610381\) | \(#ND+#NDI\) | \(\infty\) |
|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(3\) | \(0\) | \(3\) | \(1\) | \(3\) | \(1\) | \(1\) |
| \(4\) | \(0\) | \(4\) | \(2\) | \(4\) | \(2\) | \(1\) |
40
New Number: 11.15 | AESZ: | Superseeker: 26 1205094 | Hash: 3569012dbdb9fd87263426cf2bb6fc1e
Degree: 11
\(\theta^4+x\left(1621\theta^4+668\theta^3+604\theta^2+270\theta+45\right)+3 x^{2}\left(254941\theta^4+548152\theta^3+559862\theta^2+194162\theta+28968\right)-3^{2} x^{3}\left(1325117\theta^4-108701676\theta^3-124717610\theta^2-59094684\theta-11443095\right)-2 3^{7} x^{4}\left(20947985\theta^4-10090640\theta^3-84622092\theta^2-45836384\theta-9522442\right)-2 3^{12} x^{5}\left(14540887\theta^4+64060996\theta^3-24278536\theta^2-23929102\theta-6530971\right)+2 3^{17} x^{6}\left(9831565\theta^4-28112664\theta^3+362922\theta^2+7678170\theta+2970162\right)+2 3^{22} x^{7}\left(10348339\theta^4+14853308\theta^3+24479278\theta^2+15836460\theta+3742209\right)+3^{30} x^{8}\left(4877\theta^4-351136\theta^3-673240\theta^2-473040\theta-113516\right)-3^{35} x^{9}\left(31925\theta^4+116220\theta^3+114644\theta^2+42510\theta+4601\right)-3^{43} x^{10}\left(111\theta^4+264\theta^3+266\theta^2+134\theta+28\right)-3^{48} x^{11}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -45, 3591, -147771, -62088201, ... --> OEIS Normalized instanton numbers (n0=1): 26, -15173, 1205094, -256830529, 38564264386, ... ; Common denominator:...
\(-(243z+1)(14348907z^4+5668704z^3-75330z^2-520z-1)(-1-429z+137781z^2+4782969z^3)^2\)
| ≈\(-0.031447\) | \(-\frac{ 1}{ 243}\) | ≈\(-0.001576\) | \(0\) | ≈\(0.004217\) | \(#ND+#NDI\) | \(\infty\) |
|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) |
| \(3\) | \(1\) | \(3\) | \(0\) | \(3\) | \(1\) | \(1\) |
| \(4\) | \(2\) | \(4\) | \(0\) | \(4\) | \(2\) | \(1\) |
41
New Number: 11.16 | AESZ: | Superseeker: 211/35 19279/35 | Hash: dc993c4f73af62a0915341e2b6d1f81f
Degree: 11
\(5^{2} 7^{2} \theta^4-5 7 x\left(2658\theta^4+4272\theta^3+3361\theta^2+1225\theta+175\right)-x^{2}\left(482475+2058700\theta+2927049\theta^2+1102432\theta^3-364211\theta^4\right)+x^{3}\left(1107645+7584675\theta+17848802\theta^2+16891206\theta^3+3547267\theta^4\right)-x^{4}\left(5628891+26546780\theta+46592338\theta^2+38194636\theta^3+16110878\theta^4\right)-3 x^{5}\left(2019469\theta^4+2698822\theta^3+453746\theta^2+985337\theta+832575\right)+3^{2} x^{6}\left(3186847\theta^4+10570488\theta^3+13101727\theta^2+7620366\theta+1780951\right)+3^{3} x^{7}\left(515831\theta^4+2708278\theta^3+5879206\theta^2+4986803\theta+1463799\right)-3^{4} x^{8}\left(94081\theta^4+60208\theta^3-440794\theta^2-635338\theta-240009\right)-3^{6} x^{9}\left(4919\theta^4+23958\theta^3+26539\theta^2+8334\theta-480\right)+2 3^{6} x^{10}\left(392\theta^4-674\theta^3-2747\theta^2-2410\theta-663\right)+2^{2} 3^{10} x^{11}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 5, 129, 4523, 191329, ... --> OEIS Normalized instanton numbers (n0=1): 211/35, 1643/35, 19279/35, 69901/7, 7789913/35, ... ; Common denominator:...
\((1-66z-379z^2+427z^3+439z^4+81z^5)(35-174z-81z^2+54z^3)^2\)
| ≈\(-1.31797\) | \(0\) | ≈\(0.186913\) | ≈\(2.631057\) | \(#ND+#NDI\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(3\) | \(0\) | \(3\) | \(3\) | \(1\) | \(1\) |
| \(4\) | \(0\) | \(4\) | \(4\) | \(2\) | \(1\) |
42
New Number: 11.17 | AESZ: | Superseeker: -263/2 -218434 | Hash: 8aa8ad0296efe97c979c0336a2ec2312
Degree: 11
\(2^{2} \theta^4+2 x\left(392\theta^4+2242\theta^3+1627\theta^2+506\theta+66\right)-3^{4} x^{2}\left(4919\theta^4-4282\theta^3-15821\theta^2-7454\theta-1314\right)-3^{6} x^{3}\left(94081\theta^4+316116\theta^3-56932\theta^2-50550\theta-11592\right)+3^{9} x^{4}\left(515831\theta^4-644954\theta^3+849358\theta^2+710099\theta+163755\right)+3^{12} x^{5}\left(3186847\theta^4+2176900\theta^3+511345\theta^2-380988\theta-121329\right)-3^{15} x^{6}\left(2019469\theta^4+5379054\theta^3+4474094\theta^2-96435\theta-378369\right)-3^{18} x^{7}\left(16110878\theta^4+26248876\theta^3+28673698\theta^2+16497500\theta+3590691\right)+3^{22} x^{8}\left(3547267\theta^4-2702138\theta^3-11541214\theta^2-8371621\theta-1972167\right)+3^{26} x^{9}\left(364211\theta^4+2559276\theta^3+2565513\theta^2+968742\theta+115819\right)-3^{30} 5 7 x^{10}\left(2658\theta^4+6360\theta^3+6493\theta^2+3313\theta+697\right)+3^{34} 5^{2} 7^{2} x^{11}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -33, 3321, -480255, 82588329, ... --> OEIS Normalized instanton numbers (n0=1): -263/2, -21293/8, -218434, -32618595/2, -1709392950, ... ; Common denominator:...
\((43046721z^5-35075106z^4-2486619z^3+34587z^2+439z+1)(2-243z-42282z^2+688905z^3)^2\)
| ≈\(-0.009367\) | \(0\) | ≈\(0.004692\) | ≈\(0.066051\) | \(#ND+#NDI\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(3\) | \(0\) | \(3\) | \(3\) | \(1\) | \(1\) |
| \(4\) | \(0\) | \(4\) | \(4\) | \(2\) | \(1\) |
43
New Number: 11.18 | AESZ: | Superseeker: -343/26 -27836/13 | Hash: 7fd9e473da9a826dea365ad9c234d2b1
Degree: 11
\(2^{2} 13^{2} \theta^4+2 13 x\left(2902\theta^4+6146\theta^3+4763\theta^2+1690\theta+234\right)-3 x^{2}\left(96469\theta^4+49486\theta^3-135373\theta^2-115726\theta-26754\right)+3 x^{3}\left(107658\theta^4-7866\theta^3+142429\theta^2+209352\theta+70434\right)+3^{2} x^{4}\left(27312\theta^4-323430\theta^3-1054064\theta^2-786941\theta-191951\right)-3^{4} x^{5}\left(1180\theta^4-103322\theta^3-143955\theta^2-85327\theta-20494\right)-3^{5} x^{6}\left(2379\theta^4+12696\theta^3+45266\theta^2+49297\theta+16562\right)-3^{6} x^{7}\left(929\theta^4+13156\theta^3-15355\theta^2-25877\theta-8920\right)+3^{7} x^{8}\left(1318\theta^4+2950\theta^3+2915\theta^2+772\theta-131\right)+3^{7} x^{9}\left(315\theta^4-3006\theta^3-5005\theta^2-2784\theta-504\right)-2^{2} 3^{8} x^{10}\left(42\theta^4+66\theta^3+25\theta^2-8\theta-5\right)+2^{4} 3^{10} x^{11}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -9, 333, -18639, 1264509, ... --> OEIS Normalized instanton numbers (n0=1): -343/26, 11207/104, -27836/13, 764852/13, -52338075/26, ... ; Common denominator:...
\((1+116z+75z^2+162z^3-108z^4+81z^5)(26-57z+9z^2+108z^3)^2\)
| ≈\(-0.92963\) | \(0\) | ≈\(0.423148-0.282683I\) | ≈\(0.423148+0.282683I\) | \(#ND+#NDI\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(3\) | \(0\) | \(3\) | \(3\) | \(1\) | \(1\) |
| \(4\) | \(0\) | \(4\) | \(4\) | \(2\) | \(1\) |
44
New Number: 11.19 | AESZ: | Superseeker: 21/4 -1045/6 | Hash: acf903f94ac2a08b9f2b26dff65a52ff
Degree: 11
\(2^{4} \theta^4-2^{2} 3 x\left(42\theta^4+102\theta^3+79\theta^2+28\theta+4\right)+3^{3} x^{2}\left(315\theta^4+4266\theta^3+5903\theta^2+3052\theta+596\right)+3^{6} x^{3}\left(1318\theta^4+2322\theta^3+1973\theta^2+1480\theta+380\right)-3^{8} x^{4}\left(929\theta^4-9440\theta^3-49249\theta^2-40585\theta-10625\right)-3^{10} x^{5}\left(2379\theta^4-3180\theta^3+21452\theta^2+12663\theta+2214\right)-3^{12} x^{6}\left(1180\theta^4+108042\theta^3+173091\theta^2+112103\theta+25380\right)+3^{13} x^{7}\left(27312\theta^4+432678\theta^3+80098\theta^2-241649\theta-108332\right)+3^{15} x^{8}\left(107658\theta^4+438498\theta^3+811975\theta^2+529736\theta+119035\right)-3^{18} x^{9}\left(96469\theta^4+336390\theta^3+294983\theta^2+82398\theta+582\right)+2 3^{20} 13 x^{10}\left(2902\theta^4+5462\theta^3+3737\theta^2+1006\theta+63\right)+2^{2} 3^{23} 13^{2} x^{11}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 3, -27, -1563, -40491, ... --> OEIS Normalized instanton numbers (n0=1): 21/4, -969/16, -1045/6, -35199/4, 536619/4, ... ; Common denominator:...
\((1-36z+1458z^2+18225z^3+761076z^4+177147z^5)(4+9z-1539z^2+18954z^3)^2\)
| ≈\(-4.272671\) | ≈\(-0.039841\) | ≈\(-0.024843\) | ≈\(-0.024843\) | \(0\) | ≈\(0.01303\) | ≈\(0.01303\) | ≈\(0.060519-0.040429I\) | ≈\(0.060519+0.040429I\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(1\) | \(3\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(3\) | \(3\) | \(1\) |
| \(2\) | \(4\) | \(2\) | \(2\) | \(0\) | \(2\) | \(2\) | \(4\) | \(4\) | \(1\) |
45
New Number: 11.20 | AESZ: | Superseeker: 21/4 1285/2 | Hash: b07e191c8c5d8b6a2c25e842f85fcaf0
Degree: 11
\(2^{4} \theta^4-2^{2} x\left(278\theta^4+394\theta^3+309\theta^2+112\theta+16\right)-x^{2}\left(11952+57616\theta+96951\theta^2+56722\theta^3+4615\theta^4\right)+2 x^{3}\left(129366\theta^4+473682\theta^3+531879\theta^2+282576\theta+62656\right)-x^{4}\left(1430728+5365104\theta+7153953\theta^2+3814866\theta^3+1139565\theta^4\right)-2 3 x^{5}\left(286602\theta^4-694990\theta^3-3072025\theta^2-2917584\theta-895328\right)+2^{2} x^{6}\left(1338547\theta^4+4488552\theta^3+821964\theta^2-3171240\theta-1633306\right)+2^{4} x^{7}\left(17380\theta^4-1361536\theta^3-2049918\theta^2-1043692\theta-152703\right)-2^{6} x^{8}\left(106051\theta^4+123172\theta^3+23589\theta^2-28382\theta-10873\right)+2^{10} x^{9}\left(4885\theta^4+15033\theta^3+20559\theta^2+13908\theta+3737\right)-2^{12} x^{10}\left(335\theta^4+1270\theta^3+1875\theta^2+1240\theta+307\right)+2^{17} x^{11}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 4, 116, 3856, 163636, ... --> OEIS Normalized instanton numbers (n0=1): 21/4, 1965/32, 1285/2, 103095/8, 1157421/4, ... ; Common denominator:...
\((z-1)(16z^2-16z-1)(32z^2-71z+1)(4-27z-50z^2+16z^3)^2\)
| ≈\(-0.573963\) | \(\frac{ 1}{ 2}-\frac{ 1}{ 4}\sqrt{ 5}\) | \(0\) | \(\frac{ 71}{ 64}-\frac{ 17}{ 64}\sqrt{ 17}\) | ≈\(0.121762\) | \(1\) | \(\frac{ 1}{ 2}+\frac{ 1}{ 4}\sqrt{ 5}\) | \(\frac{ 71}{ 64}+\frac{ 17}{ 64}\sqrt{ 17}\) | ≈\(3.577201\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(3\) | \(1\) | \(0\) | \(1\) | \(3\) | \(1\) | \(1\) | \(1\) | \(3\) | \(1\) |
| \(4\) | \(2\) | \(0\) | \(2\) | \(4\) | \(2\) | \(2\) | \(2\) | \(4\) | \(1\) |
46
New Number: 11.21 | AESZ: | Superseeker: 240 31333936 | Hash: 9a8c2dbc999179b3ef13a33cce17dc01
Degree: 11
\(\theta^4+2^{4} x\left(335\theta^4+70\theta^3+75\theta^2+40\theta+7\right)+2^{11} x^{2}\left(4885\theta^4+4507\theta^3+4770\theta^2+1651\theta+240\right)+2^{16} x^{3}\left(106051\theta^4+301032\theta^3+290379\theta^2+130248\theta+23977\right)+2^{23} x^{4}\left(17380\theta^4+1431056\theta^3+2138970\theta^2+1097984\theta+219987\right)-2^{30} x^{5}\left(1338547\theta^4+865636\theta^3-4612410\theta^2-3296300\theta-790107\right)-2^{38} 3 x^{6}\left(286602\theta^4+1841398\theta^3+732557\theta^2+4912\theta-68177\right)+2^{46} x^{7}\left(1139565\theta^4+743394\theta^3+2546745\theta^2+2056464\theta+544276\right)+2^{56} x^{8}\left(129366\theta^4+43782\theta^3-112971\theta^2-122400\theta-32357\right)+2^{64} x^{9}\left(4615\theta^4-38262\theta^3-45525\theta^2-15420\theta-820\right)-2^{75} x^{10}\left(278\theta^4+718\theta^3+795\theta^2+436\theta+97\right)-2^{86} x^{11}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -112, 28304, -9202432, 3381592336, ... --> OEIS Normalized instanton numbers (n0=1): 240, -95082, 31333936, -15748488666, 8901200955216, ... ; Common denominator:...
\(-(512z+1)(8192z^2+1136z+1)(16384z^2-512z-1)(-1-1600z+442368z^2+33554432z^3)^2\)
| \(-\frac{ 71}{ 1024}-\frac{ 17}{ 1024}\sqrt{ 17}\) | ≈\(-0.01604\) | \(-\frac{ 1}{ 512}\) | \(\frac{ 1}{ 64}-\frac{ 1}{ 128}\sqrt{ 5}\) | \(-\frac{ 71}{ 1024}+\frac{ 17}{ 1024}\sqrt{ 17}\) | ≈\(-0.000546\) | \(0\) | ≈\(0.003403\) | \(\frac{ 1}{ 64}+\frac{ 1}{ 128}\sqrt{ 5}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) |
| \(1\) | \(3\) | \(1\) | \(1\) | \(1\) | \(3\) | \(0\) | \(3\) | \(1\) | \(1\) |
| \(2\) | \(4\) | \(2\) | \(2\) | \(2\) | \(4\) | \(0\) | \(4\) | \(2\) | \(1\) |
47
New Number: 11.4 | AESZ: | Superseeker: 116/5 29628/5 | Hash: 4222cdacde3dbaf06ed32adadb70f0d6
Degree: 11
\(5^{2} \theta^4-2^{2} 5 x\left(197\theta^4+418\theta^3+319\theta^2+110\theta+15\right)+2^{4} x^{2}\left(181\theta^4+5068\theta^3+10291\theta^2+6750\theta+1585\right)-2^{6} x^{3}\left(1727\theta^4-4758\theta^3-11365\theta^2-4560\theta-345\right)+2^{9} x^{4}\left(2351\theta^4+4552\theta^3-11125\theta^2-12552\theta-3833\right)-2^{12} x^{5}\left(527\theta^4+1448\theta^3+16\theta^2-1811\theta-887\right)+2^{15} x^{6}\left(493\theta^4-1527\theta^3-789\theta^2-363\theta-116\right)-2^{17} x^{7}\left(780\theta^4-282\theta^3+865\theta^2+1459\theta+563\right)+2^{20} x^{8}\left(151\theta^4-104\theta^3-291\theta^2-239\theta-65\right)-2^{22} x^{9}\left(23\theta^4+24\theta^3+85\theta^2+132\theta+55\right)+2^{25} x^{10}(\theta+1)(7\theta^3+31\theta^2+35\theta+12)-2^{28} x^{11}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 12, 572, 42960, 3944556, ... --> OEIS Normalized instanton numbers (n0=1): 116/5, 1059/5, 29628/5, 2227181/10, 51562768/5, ... ; Common denominator:...
\(-(-1+156z+160z^2+256z^3)(4z-1)^2(256z^3-128z^2-16z-5)^2\)
| ≈\(-0.315684-0.716756I\) | ≈\(-0.315684+0.716756I\) | ≈\(-0.072055-0.158527I\) | ≈\(-0.072055+0.158527I\) | \(0\) | ≈\(0.006368\) | \(\frac{ 1}{ 4}\) | ≈\(0.64411\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) |
| \(1\) | \(1\) | \(3\) | \(3\) | \(0\) | \(1\) | \(\frac{ 1}{ 2}\) | \(3\) | \(1\) |
| \(2\) | \(2\) | \(4\) | \(4\) | \(0\) | \(2\) | \(1\) | \(4\) | \(1\) |
48
New Number: 11.5 | AESZ: | Superseeker: -32 608 | Hash: f5f2274632f5544ebf559c6c512159d1
Degree: 11
\(\theta^4-2^{4} x\theta(7\theta^3-10\theta^2-6\theta-1)+2^{8} x^{2}\left(23\theta^4+68\theta^3+151\theta^2+58\theta+7\right)-2^{13} x^{3}\left(151\theta^4+708\theta^3+927\theta^2+573\theta+138\right)+2^{17} x^{4}\left(780\theta^4+3402\theta^3+6391\theta^2+4237\theta+1031\right)-2^{22} x^{5}\left(493\theta^4+3499\theta^3+6750\theta^2+5338\theta+1478\right)+2^{26} x^{6}\left(527\theta^4+660\theta^3-1166\theta^2-393\theta+19\right)-2^{30} x^{7}\left(2351\theta^4+4852\theta^3-10675\theta^2-13950\theta-4607\right)+2^{34} x^{8}\left(1727\theta^4+11666\theta^3+13271\theta^2+3012\theta-665\right)-2^{39} x^{9}\left(181\theta^4-4344\theta^3-3827\theta^2-648\theta+239\right)+2^{44} 5 x^{10}\left(197\theta^4+370\theta^3+247\theta^2+62\theta+3\right)-2^{49} 5^{2} x^{11}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, -112, 13824, -136944, ... --> OEIS Normalized instanton numbers (n0=1): -32, -616, 608, -21270, -15181664, ... ; Common denominator:...
\(-(-1-80z-9984z^2+8192z^3)(32z-1)^2(40960z^3+1024z^2+64z-1)^2\)
| ≈\(-0.018565-0.040844I\) | ≈\(-0.018565+0.040844I\) | ≈\(-0.004021-0.009129I\) | ≈\(-0.004021+0.009129I\) | \(0\) | ≈\(0.012129\) | \(\frac{ 1}{ 32}\) | ≈\(1.226791\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) |
| \(3\) | \(3\) | \(1\) | \(1\) | \(0\) | \(3\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) |
| \(4\) | \(4\) | \(2\) | \(2\) | \(0\) | \(4\) | \(1\) | \(2\) | \(1\) |
49
New Number: 7.18 | AESZ: | Superseeker: 352 26115552 | Hash: df2c3b4e6a3366531b24bb05809eb1a4
Degree: 7
\(\theta^4-2^{4} x\left(144\theta^4-192\theta^3-172\theta^2-76\theta-11\right)+2^{14} x^{2}\left(100\theta^4-320\theta^3-25\theta^2+155\theta+36\right)-2^{21} x^{3}\left(72\theta^4-1248\theta^3+628\theta^2-180\theta-97\right)-2^{30} x^{4}\left(212\theta^4+256\theta^3-14\theta^2+86\theta+15\right)+2^{36} 3 x^{5}\left(240\theta^4-320\theta^3-332\theta^2-380\theta-119\right)+2^{46} 3^{2} x^{6}\left(12\theta^4+64\theta^3+99\theta^2+67\theta+17\right)-2^{56} 3^{3} x^{7}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -176, 17168, -4715264, 653856016, ... --> OEIS Normalized instanton numbers (n0=1): 352, 60664, 26115552, 16623590600, 13165993300256, ... ; Common denominator:...
\(-(256z-1)^2(256z+1)^2(768z-1)^3\)
| \(-\frac{ 1}{ 256}\) | \(0\) | \(\frac{ 1}{ 768}\) | \(\frac{ 1}{ 256}\) | \(\infty\) |
|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(0\) | \(0\) | \(2\) | \(\frac{ 1}{ 2}\) | \(1\) |
| \(1\) | \(0\) | \(3\) | \(\frac{ 1}{ 2}\) | \(1\) |
| \(1\) | \(0\) | \(5\) | \(1\) | \(1\) |
50
New Number: 7.19 | AESZ: | Superseeker: 4/3 -124/81 | Hash: f7f0f5d883101c38ed22cb74c80c8f5c
Degree: 7
\(3^{3} \theta^4-2^{2} 3^{2} x\left(12\theta^4-16\theta^3-21\theta^2-13\theta-3\right)-2^{4} 3 x^{2}\left(240\theta^4+1280\theta^3+2068\theta^2+1636\theta+489\right)+2^{10} x^{3}\left(212\theta^4+592\theta^3+490\theta^2-34\theta-129\right)+2^{13} x^{4}\left(72\theta^4+1536\theta^3+4804\theta^2+5468\theta+2031\right)-2^{18} x^{5}\left(100\theta^4+720\theta^3+1535\theta^2+1155\theta+276\right)+2^{20} x^{6}\left(144\theta^4+768\theta^3+1268\theta^2+884\theta+229\right)-2^{28} x^{7}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -4, 68, -496, 9796, ... --> OEIS Normalized instanton numbers (n0=1): 4/3, -14/9, -124/81, -4498/243, 37024/729, ... ; Common denominator:...
\(-(16z-1)^2(16z+1)^2(16z-3)^3\)
| \(-\frac{ 1}{ 16}\) | \(0\) | \(\frac{ 1}{ 16}\) | \(\frac{ 3}{ 16}\) | \(\infty\) |
|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(0\) | \(0\) | \(\frac{ 1}{ 2}\) | \(2\) | \(1\) |
| \(1\) | \(0\) | \(\frac{ 1}{ 2}\) | \(3\) | \(1\) |
| \(1\) | \(0\) | \(1\) | \(5\) | \(1\) |
51
New Number: 7.1 | AESZ: | Superseeker: 10/7 508/7 | Hash: 08ab3cb496250adfa30bc3e24ac63c4f
Degree: 7
\(7^{2} \theta^4-2 7 x\theta(46\theta^3+52\theta^2+33\theta+7)-2^{2} x^{2}\left(7332\theta^4+28848\theta^3+42633\theta^2+26670\theta+6272\right)-2^{4} x^{3}\left(2860\theta^4+44760\theta^3+120483\theta^2+111279\theta+35098\right)+2^{9} x^{4}\left(2230\theta^4+5920\theta^3-741\theta^2-6509\theta-3049\right)+2^{14} x^{5}\left(174\theta^4+1320\theta^3+1971\theta^2+1095\theta+190\right)-2^{19} x^{6}\left(22\theta^4+24\theta^3-9\theta^2-21\theta-7\right)-2^{25} x^{7}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, 32, 288, 7776, ... --> OEIS Normalized instanton numbers (n0=1): 10/7, 100/7, 508/7, 808, 59910/7, ... ; Common denominator:...
\(-(16z+1)(32z-1)(32z-7)^2(4z+1)^3\)
| \(-\frac{ 1}{ 4}\) | \(-\frac{ 1}{ 16}\) | \(0\) | \(\frac{ 1}{ 32}\) | \(\frac{ 7}{ 32}\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(\frac{ 1}{ 2}\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) |
| \(\frac{ 3}{ 2}\) | \(1\) | \(0\) | \(1\) | \(3\) | \(1\) |
| \(2\) | \(2\) | \(0\) | \(2\) | \(4\) | \(1\) |
52
New Number: 7.2 | AESZ: | Superseeker: -80 -249872 | Hash: 341389ebf4ab0242c5b70d9a8fd7a1d9
Degree: 7
\(\theta^4+2^{4} x\left(22\theta^4+64\theta^3+51\theta^2+19\theta+3\right)-2^{9} x^{2}\left(174\theta^4-624\theta^3-945\theta^2-417\theta-80\right)-2^{14} x^{3}\left(2230\theta^4+3000\theta^3-5121\theta^2-3813\theta-971\right)+2^{19} x^{4}\left(2860\theta^4-33320\theta^3+3363\theta^2+6847\theta+2402\right)+2^{27} x^{5}\left(7332\theta^4+480\theta^3+81\theta^2+1380\theta+719\right)+2^{36} 7 x^{6}(\theta+1)(46\theta^3+86\theta^2+67\theta+20)-2^{45} 7^{2} x^{7}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -48, 5072, -733440, 124117776, ... --> OEIS Normalized instanton numbers (n0=1): -80, -4202, -249872, -22251117, -2195810928, ... ; Common denominator:...
\(-(64z+1)(32z-1)(224z-1)^2(256z+1)^3\)
| \(-\frac{ 1}{ 64}\) | \(-\frac{ 1}{ 256}\) | \(0\) | \(\frac{ 1}{ 224}\) | \(\frac{ 1}{ 32}\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(\frac{ 1}{ 2}\) | \(0\) | \(1\) | \(1\) | \(1\) |
| \(1\) | \(\frac{ 3}{ 2}\) | \(0\) | \(3\) | \(1\) | \(1\) |
| \(2\) | \(2\) | \(0\) | \(4\) | \(2\) | \(1\) |
53
New Number: 8.10 | AESZ: 123 | Superseeker: 12 1828/3 | Hash: f0d76ab2b6b8808f4faa4ab8ecadff2c
Degree: 8
\(\theta^4-2^{2} x(3\theta^2+3\theta+1)(10\theta^2+10\theta+3)+2^{4} x^{2}\left(209\theta^4+1052\theta^3+1471\theta^2+838\theta+183\right)+2^{7} 3^{2} x^{3}\left(30\theta^4-180\theta^3-551\theta^2-417\theta-111\right)-2^{10} 3^{2} x^{4}\left(227\theta^4+454\theta^3-550\theta^2-777\theta-261\right)+2^{12} 3^{4} x^{5}\left(30\theta^4+300\theta^3+169\theta^2-25\theta-35\right)+2^{14} 3^{4} x^{6}\left(209\theta^4-216\theta^3-431\theta^2-216\theta-27\right)-2^{17} 3^{6} x^{7}(3\theta^2+3\theta+1)(10\theta^2+10\theta+3)+2^{20} 3^{8} x^{8}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 12, 300, 10416, 431964, ... --> OEIS Normalized instanton numbers (n0=1): 12, -47/2, 1828/3, -10813/4, 127948, ... ; Common denominator:...
\((36z-1)(8z-1)(72z-1)(4z-1)(-1+288z^2)^2\)
| \(-\frac{ 1}{ 24}\sqrt{ 2}\) | \(0\) | \(\frac{ 1}{ 72}\) | \(\frac{ 1}{ 36}\) | \(\frac{ 1}{ 24}\sqrt{ 2}\) | \(\frac{ 1}{ 8}\) | \(\frac{ 1}{ 4}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(3\) | \(0\) | \(1\) | \(1\) | \(3\) | \(1\) | \(1\) | \(1\) |
| \(4\) | \(0\) | \(2\) | \(2\) | \(4\) | \(2\) | \(2\) | \(1\) |
54
New Number: 8.11 | AESZ: 162 | Superseeker: 9 242/3 | Hash: 542708b59b898c35f43e00120897ff8d
Degree: 8
\(\theta^4-3 x(3\theta^2+3\theta+1)(10\theta^2+10\theta+3)+3^{3} x^{2}\left(91\theta^4+472\theta^3+659\theta^2+374\theta+81\right)+3^{6} x^{3}\left(30\theta^4-180\theta^3-551\theta^2-417\theta-111\right)-3^{8} x^{4}\left(200\theta^4+400\theta^3-514\theta^2-714\theta-237\right)+3^{11} x^{5}\left(30\theta^4+300\theta^3+169\theta^2-25\theta-35\right)+3^{13} x^{6}\left(91\theta^4-108\theta^3-211\theta^2-108\theta-15\right)-3^{16} x^{7}(3\theta^2+3\theta+1)(10\theta^2+10\theta+3)+3^{20} x^{8}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 9, 135, 1953, 5751, ... --> OEIS Normalized instanton numbers (n0=1): 9, -153/4, 242/3, -4923, 34245, ... ; Common denominator:...
\((27z^2-9z+1)(2187z^2-81z+1)(-1+243z^2)^2\)
| \(-\frac{ 1}{ 27}\sqrt{ 3}\) | \(0\) | \(\frac{ 1}{ 54}-\frac{ 1}{ 162}\sqrt{ 3}I\) | \(\frac{ 1}{ 54}+\frac{ 1}{ 162}\sqrt{ 3}I\) | \(\frac{ 1}{ 27}\sqrt{ 3}\) | \(\frac{ 1}{ 6}-\frac{ 1}{ 18}\sqrt{ 3}I\) | \(\frac{ 1}{ 6}+\frac{ 1}{ 18}\sqrt{ 3}I\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(3\) | \(0\) | \(1\) | \(1\) | \(3\) | \(1\) | \(1\) | \(1\) |
| \(4\) | \(0\) | \(2\) | \(2\) | \(4\) | \(2\) | \(2\) | \(1\) |
55
New Number: 8.12 | AESZ: 175 | Superseeker: 17 1387 | Hash: f6db11b5e593983f455489d5bb1003c5
Degree: 8
\(\theta^4-x(10\theta^2+10\theta+3)(17\theta^2+17\theta+6)+3^{4} x^{2}\left(89\theta^4+452\theta^3+633\theta^2+362\theta+80\right)+2^{3} 3^{4} x^{3}\left(170\theta^4-1020\theta^3-3119\theta^2-2373\theta-648\right)-2^{4} 3^{8} x^{4}\left(97\theta^4+194\theta^3-238\theta^2-335\theta-114\right)+2^{6} 3^{8} x^{5}\left(170\theta^4+1700\theta^3+961\theta^2-125\theta-204\right)+2^{6} 3^{12} x^{6}\left(89\theta^4-96\theta^3-189\theta^2-96\theta-12\right)-2^{9} 3^{12} x^{7}(10\theta^2+10\theta+3)(17\theta^2+17\theta+6)+2^{12} 3^{16} x^{8}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 18, 630, 29016, 1529766, ... --> OEIS Normalized instanton numbers (n0=1): 17, -299/4, 1387, -47623/2, 500282, ... ; Common denominator:...
\((81z-1)(8z-1)(72z-1)(9z-1)(-1+648z^2)^2\)
| \(-\frac{ 1}{ 36}\sqrt{ 2}\) | \(0\) | \(\frac{ 1}{ 81}\) | \(\frac{ 1}{ 72}\) | \(\frac{ 1}{ 36}\sqrt{ 2}\) | \(\frac{ 1}{ 9}\) | \(\frac{ 1}{ 8}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(3\) | \(0\) | \(1\) | \(1\) | \(3\) | \(1\) | \(1\) | \(1\) |
| \(4\) | \(0\) | \(2\) | \(2\) | \(4\) | \(2\) | \(2\) | \(1\) |
56
New Number: 8.13 | AESZ: 163 | Superseeker: 12 3020/3 | Hash: e21fd830a9dca03305deb8363a26fcf2
Degree: 8
\(\theta^4-2^{2} 3 x\left((3\theta^2+3\theta+1)^2\right)+2^{4} 3^{2} x^{2}\left(21\theta^4+156\theta^3+219\theta^2+126\theta+29\right)+2^{7} 3^{4} x^{3}(3\theta^2+3\theta+1)(3\theta^2-21\theta-35)-2^{10} 3^{5} x^{4}\left(27\theta^4+54\theta^3-114\theta^2-141\theta-49\right)+2^{12} 3^{7} x^{5}(3\theta^2+3\theta+1)(3\theta^2+27\theta-11)+2^{14} 3^{8} x^{6}\left(21\theta^4-72\theta^3-123\theta^2-72\theta-13\right)-2^{17} 3^{10} x^{7}\left((3\theta^2+3\theta+1)^2\right)+2^{20} 3^{12} x^{8}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 12, 180, 2352, 6084, ... --> OEIS Normalized instanton numbers (n0=1): 12, -96, 3020/3, -71493/4, 319584, ... ; Common denominator:...
\((1728z^2-72z+1)(432z^2-36z+1)(-1+864z^2)^2\)
| \(-\frac{ 1}{ 72}\sqrt{ 6}\) | \(0\) | \(\frac{ 1}{ 48}-\frac{ 1}{ 144}\sqrt{ 3}I\) | \(\frac{ 1}{ 48}+\frac{ 1}{ 144}\sqrt{ 3}I\) | \(\frac{ 1}{ 72}\sqrt{ 6}\) | \(\frac{ 1}{ 24}-\frac{ 1}{ 72}\sqrt{ 3}I\) | \(\frac{ 1}{ 24}+\frac{ 1}{ 72}\sqrt{ 3}I\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(3\) | \(0\) | \(1\) | \(1\) | \(3\) | \(1\) | \(1\) | \(1\) |
| \(4\) | \(0\) | \(2\) | \(2\) | \(4\) | \(2\) | \(2\) | \(1\) |
57
New Number: 8.14 | AESZ: 176 | Superseeker: 24 15448/3 | Hash: e2a40a57f7e88dba6655d936b4abe327
Degree: 8
\(\theta^4-2^{2} x(3\theta^2+3\theta+1)(17\theta^2+17\theta+6)+2^{5} x^{2}\left(325\theta^4+2164\theta^3+3053\theta^2+1778\theta+420\right)+2^{10} 3^{2} x^{3}\left(51\theta^4-306\theta^3-934\theta^2-717\theta-204\right)-2^{14} 3^{2} x^{4}\left(397\theta^4+794\theta^3-1454\theta^2-1851\theta-666\right)+2^{18} 3^{4} x^{5}\left(51\theta^4+510\theta^3+290\theta^2-29\theta-64\right)+2^{21} 3^{4} x^{6}\left(325\theta^4-864\theta^3-1489\theta^2-864\theta-144\right)-2^{26} 3^{6} x^{7}(3\theta^2+3\theta+1)(17\theta^2+17\theta+6)+2^{32} 3^{8} x^{8}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 24, 840, 34944, 1618344, ... --> OEIS Normalized instanton numbers (n0=1): 24, -509/2, 15448/3, -128530, 3746624, ... ; Common denominator:...
\((72z-1)(36z-1)(64z-1)(32z-1)(48z-1)^2(48z+1)^2\)
| \(-\frac{ 1}{ 48}\) | \(0\) | \(\frac{ 1}{ 72}\) | \(\frac{ 1}{ 64}\) | \(\frac{ 1}{ 48}\) | \(\frac{ 1}{ 36}\) | \(\frac{ 1}{ 32}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(3\) | \(0\) | \(1\) | \(1\) | \(3\) | \(1\) | \(1\) | \(1\) |
| \(4\) | \(0\) | \(2\) | \(2\) | \(4\) | \(2\) | \(2\) | \(1\) |
58
New Number: 8.15 | AESZ: 178 | Superseeker: 18 9799/3 | Hash: e748913f322a008ae5c350f96f1cd860
Degree: 8
\(\theta^4-3 x(3\theta^2+3\theta+1)(17\theta^2+17\theta+6)+3^{3} x^{2}\left(217\theta^4+1732\theta^3+2441\theta^2+1418\theta+336\right)+2^{3} 3^{6} x^{3}\left(51\theta^4-306\theta^3-934\theta^2-717\theta-204\right)-2^{4} 3^{8} x^{4}\left(289\theta^4+578\theta^3-1310\theta^2-1599\theta-570\right)+2^{6} 3^{11} x^{5}\left(51\theta^4+510\theta^3+290\theta^2-29\theta-64\right)+2^{6} 3^{13} x^{6}\left(217\theta^4-864\theta^3-1453\theta^2-864\theta-156\right)-2^{9} 3^{16} x^{7}(3\theta^2+3\theta+1)(17\theta^2+17\theta+6)+2^{12} 3^{20} x^{8}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 18, 378, 6552, 21546, ... --> OEIS Normalized instanton numbers (n0=1): 18, -423/2, 9799/3, -150003/2, 1914237, ... ; Common denominator:...
\((1728z^2-72z+1)(2187z^2-81z+1)(-1+1944z^2)^2\)
| \(-\frac{ 1}{ 108}\sqrt{ 6}\) | \(0\) | \(\frac{ 1}{ 54}-\frac{ 1}{ 162}\sqrt{ 3}I\) | \(\frac{ 1}{ 54}+\frac{ 1}{ 162}\sqrt{ 3}I\) | \(\frac{ 1}{ 48}-\frac{ 1}{ 144}\sqrt{ 3}I\) | \(\frac{ 1}{ 48}+\frac{ 1}{ 144}\sqrt{ 3}I\) | \(\frac{ 1}{ 108}\sqrt{ 6}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(3\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(3\) | \(1\) |
| \(4\) | \(0\) | \(2\) | \(2\) | \(2\) | \(2\) | \(4\) | \(1\) |
59
New Number: 8.16 | AESZ: 196 | Superseeker: 189/47 9277/47 | Hash: fdeee36c14d9c003b59c1738c024d479
Degree: 8
\(47^{2} \theta^4-47 x\left(2489\theta^4+4984\theta^3+4043\theta^2+1551\theta+235\right)-x^{2}\left(161022+701851\theta+1135848\theta^2+790072\theta^3+208867\theta^4\right)+x^{3}\left(38352+149319\theta+383912\theta^2+637644\theta^3+370857\theta^4\right)-x^{4}\left(1770676+5161283\theta+4424049\theta^2+511820\theta^3-291161\theta^4\right)+x^{5}\left(2151-260936\theta-750755\theta^2-749482\theta^3-406192\theta^4\right)+3^{3} x^{6}\left(5305\theta^4+90750\theta^3+152551\theta^2+91194\theta+17914\right)+2 3^{6} x^{7}\left(106\theta^4+230\theta^3+197\theta^2+82\theta+15\right)-2^{2} 3^{10} x^{8}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 5, 93, 2507, 81229, ... --> OEIS Normalized instanton numbers (n0=1): 189/47, 979/47, 9277/47, 124795/47, 2049020/47, ... ; Common denominator:...
\(-(-1+53z+90z^2-50z^3+81z^4)(-47-z+54z^2)^2\)
| \(\frac{ 1}{ 108}-\frac{ 1}{ 108}\sqrt{ 10153}\) | \(0\) | \(\frac{ 1}{ 108}+\frac{ 1}{ 108}\sqrt{ 10153}\) | \(#ND+#NDI\) | \(\infty\) |
|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(0\) | \(1\) | \(1\) | \(1\) |
| \(3\) | \(0\) | \(3\) | \(1\) | \(1\) |
| \(4\) | \(0\) | \(4\) | \(2\) | \(1\) |
60
New Number: 8.17 | AESZ: 200 | Superseeker: 19/2 -99607/18 | Hash: e970fa76e74543660fe271b31c8ad485
Degree: 8
\(2^{2} \theta^4-2 x\left(106\theta^4+194\theta^3+143\theta^2+46\theta+6\right)-3 x^{2}\left(5305\theta^4-69530\theta^3-87869\theta^2-37122\theta-6174\right)+3^{2} x^{3}\left(406192\theta^4+875286\theta^3+939461\theta^2+616896\theta+144378\right)-3^{6} x^{4}\left(291161\theta^4+1676464\theta^3-1141623\theta^2-986711\theta-230461\right)-3^{10} x^{5}\left(370857\theta^4+845784\theta^3+696122\theta^2+189001\theta+6158\right)+3^{14} x^{6}\left(208867\theta^4+45396\theta^3+18834\theta^2+35097\theta+13814\right)+3^{18} 47 x^{7}\left(2489\theta^4+4972\theta^3+4025\theta^2+1539\theta+232\right)-3^{22} 47^{2} x^{8}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 3, -243, -15315, -55971, ... --> OEIS Normalized instanton numbers (n0=1): 19/2, -5195/8, -99607/18, -217650, 23603349/2, ... ; Common denominator:...
\(-(531441z^4-347733z^3-7290z^2+50z-1)(-2+3z+11421z^2)^2\)
| \(-\frac{ 1}{ 7614}-\frac{ 1}{ 7614}\sqrt{ 10153}\) | \(0\) | \(-\frac{ 1}{ 7614}+\frac{ 1}{ 7614}\sqrt{ 10153}\) | \(#ND+#NDI\) | \(\infty\) |
|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(0\) | \(1\) | \(1\) | \(1\) |
| \(3\) | \(0\) | \(3\) | \(1\) | \(1\) |
| \(4\) | \(0\) | \(4\) | \(2\) | \(1\) |