1
New Number: 14.10 | AESZ: | Superseeker: 2 38 | Hash: 364dddcd3359111a8e01be8efc1de60c
Degree: 14
\(\theta^4+2 x\left(72\theta^4+48\theta^3+59\theta^2+35\theta+8\right)+2^{2} x^{2}\left(2277\theta^4+3252\theta^3+4573\theta^2+3266\theta+992\right)+2^{4} x^{3}\left(20907\theta^4+47634\theta^3+77375\theta^2+65724\theta+24022\right)+2^{7} x^{4}\left(62171\theta^4+199492\theta^3+375946\theta^2+371450\theta+156488\right)+2^{9} x^{5}\left(253302\theta^4+1066440\theta^3+2327568\theta^2+2630202\theta+1250623\right)+2^{10} x^{6}\left(1459436\theta^4+7698000\theta^3+19344508\theta^2+24706800\theta+13098093\right)+2^{12} x^{7}\left(3024300\theta^4+19348248\theta^3+55554208\theta^2+79484188\theta+46581901\right)+2^{15} x^{8}\left(2268548\theta^4+17191376\theta^3+55960360\theta^2+89050336\theta+57303573\right)+2^{18} x^{9}\left(1227744\theta^4+10826688\theta^3+39662704\theta^2+69775740\theta+49021017\right)+2^{20} x^{10}\left(945104\theta^4+9566080\theta^3+39177592\theta^2+75788768\theta+57836847\right)+2^{22} x^{11}\left(502368\theta^4+5772864\theta^3+26266668\theta^2+55590540\theta+45853745\right)+2^{25} x^{12}\left(87264\theta^4+1128192\theta^3+5668024\theta^2+13052400\theta+11573495\right)+2^{30} 5 x^{13}\left(444\theta^4+6408\theta^3+35315\theta^2+87905\theta+83203\right)+2^{35} 5^{2} x^{14}\left((\theta+4)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -16, 196, -2352, 29920, ... --> OEIS Normalized instanton numbers (n0=1): 2, -29/4, 38, -2077/8, 2034, ... ; Common denominator:...
\((4z+1)(2z+1)^2(64z^2+24z+1)^2(160z^2+32z+1)^2(8z+1)^3\)
| \(-\frac{ 1}{ 2}\) | \(-\frac{ 3}{ 16}-\frac{ 1}{ 16}\sqrt{ 5}\) | \(-\frac{ 1}{ 4}\) | \(-\frac{ 1}{ 10}-\frac{ 1}{ 40}\sqrt{ 6}\) | \(-\frac{ 1}{ 8}\) | \(-\frac{ 3}{ 16}+\frac{ 1}{ 16}\sqrt{ 5}\) | \(-\frac{ 1}{ 10}+\frac{ 1}{ 40}\sqrt{ 6}\) | \(0\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(4\) |
| \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(0\) | \(\frac{ 1}{ 2}\) | \(1\) | \(0\) | \(4\) |
| \(-2\) | \(\frac{ 1}{ 2}\) | \(1\) | \(3\) | \(0\) | \(\frac{ 1}{ 2}\) | \(3\) | \(0\) | \(4\) |
| \(3\) | \(1\) | \(2\) | \(4\) | \(0\) | \(1\) | \(4\) | \(0\) | \(4\) |
2
New Number: 14.11 | AESZ: | Superseeker: 52/5 13436/5 | Hash: c3784675984d5e6eac952e2484ce5404
Degree: 14
\(5^{2} \theta^4-2^{2} 5 x\left(104\theta^4+256\theta^3+483\theta^2+355\theta+95\right)-2^{4} x^{2}\left(416\theta^4-4672\theta^3+2816\theta^2+12600\theta+7865\right)+2^{10} x^{3}\left(3248\theta^4+17808\theta^3+48534\theta^2+70980\theta+43885\right)-2^{12} x^{4}\left(1024\theta^4+36416\theta^3+105744\theta^2+110264\theta+16363\right)-2^{18} x^{5}\left(8760\theta^4+76704\theta^3+282893\theta^2+513127\theta+376109\right)-2^{21} 3 x^{6}\left(888\theta^4+896\theta^3-8544\theta^2-17976\theta-2111\right)+2^{28} x^{7}\left(2848\theta^4+34496\theta^3+165049\theta^2+366072\theta+314912\right)+2^{29} x^{8}\left(10216\theta^4+125440\theta^3+627568\theta^2+1479624\theta+1370831\right)-2^{34} x^{9}\left(5720\theta^4+84576\theta^3+485065\theta^2+1262925\theta+1248247\right)-2^{36} x^{10}\left(16640\theta^4+273472\theta^3+1728064\theta^2+4911896\theta+5256897\right)+2^{42} x^{11}\left(336\theta^4+1392\theta^3-16378\theta^2-112292\theta-182997\right)+2^{44} x^{12}\left(2720\theta^4+43584\theta^3+258352\theta^2+671784\theta+646989\right)+2^{50} 3 x^{13}\left(8\theta^4+256\theta^3+2199\theta^2+7393\theta+8717\right)-2^{56} 3^{2} x^{14}\left((\theta+4)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 76, 5228, 322224, 18933228, ... --> OEIS Normalized instanton numbers (n0=1): 52/5, 115, 13436/5, 89632, 18465296/5, ... ; Common denominator:...
\(-(-1+16z)(48z-1)^2(256z^2-32z-5)^2(256z^2+16z-1)^2(16z+1)^3\)
| \(-\frac{ 1}{ 32}-\frac{ 1}{ 32}\sqrt{ 5}\) | \(\frac{ 1}{ 16}-\frac{ 1}{ 16}\sqrt{ 6}\) | \(-\frac{ 1}{ 16}\) | \(0\) | \(\frac{ 1}{ 48}\) | \(-\frac{ 1}{ 32}+\frac{ 1}{ 32}\sqrt{ 5}\) | \(\frac{ 1}{ 16}\) | \(\frac{ 1}{ 16}+\frac{ 1}{ 16}\sqrt{ 6}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(4\) |
| \(\frac{ 1}{ 2}\) | \(1\) | \(0\) | \(0\) | \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(4\) |
| \(\frac{ 1}{ 2}\) | \(3\) | \(0\) | \(0\) | \(-2\) | \(\frac{ 1}{ 2}\) | \(1\) | \(3\) | \(4\) |
| \(1\) | \(4\) | \(0\) | \(0\) | \(3\) | \(1\) | \(2\) | \(4\) | \(4\) |
3
New Number: 14.1 | AESZ: | Superseeker: 0 0 | Hash: a8cf56492aecc07971e82c9104785180
Degree: 14
\(\theta^4-x\left(13\theta^4+14\theta^3+16\theta^2+9\theta+2\right)+x^{2}\left(33\theta^4-88\theta^3-265\theta^2-324\theta-148\right)+x^{3}\left(217\theta^4+2362\theta^3+6403\theta^2+8178\theta+4160\right)-2 x^{4}\left(677\theta^4+4134\theta^3+8089\theta^2+6210\theta+360\right)+2^{2} 3 x^{5}\left(151\theta^4-1266\theta^3-11610\theta^2-28955\theta-25110\right)+2^{2} x^{6}\left(1895\theta^4+37302\theta^3+176991\theta^2+355848\theta+268836\right)-2^{2} x^{7}\left(9635\theta^4+89170\theta^3+185885\theta^2-107394\theta-522464\right)+2^{3} x^{8}\left(5907\theta^4-10636\theta^3-416125\theta^2-1666326\theta-2051920\right)+2^{5} x^{9}\left(2947\theta^4+80284\theta^3+519934\theta^2+1328475\theta+1205150\right)-2^{6} x^{10}\left(6122\theta^4+84852\theta^3+397555\theta^2+722745\theta+356430\right)+2^{6} 3 x^{11}\left(2259\theta^4+13398\theta^3-46549\theta^2-456244\theta-796656\right)+2^{7} 3^{2} x^{12}(\theta+4)(371\theta^3+8580\theta^2+53325\theta+101564)-2^{10} 3^{3} x^{13}(\theta+4)(\theta+5)(51\theta^2+519\theta+1330)+2^{11} 3^{4} 5 x^{14}(\theta+4)(\theta+5)^2(\theta+6)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 2, 16, 48, 264, ... --> OEIS Normalized instanton numbers (n0=1): 0, 1/4, 0, -1/2, 0, ... ; Common denominator:...
\((z-1)(6z-1)(4z-1)(3z+1)(4z+1)(5z-1)(2z+1)^2(2z-1)^2(6z^2-2z+1)^2\)
| \(-\frac{ 1}{ 2}\) | \(-\frac{ 1}{ 3}\) | \(-\frac{ 1}{ 4}\) | \(0\) | \(\frac{ 1}{ 6}-\frac{ 1}{ 6}\sqrt{ 5}I\) | \(\frac{ 1}{ 6}\) | \(\frac{ 1}{ 6}+\frac{ 1}{ 6}\sqrt{ 5}I\) | \(\frac{ 1}{ 5}\) | \(\frac{ 1}{ 4}\) | \(\frac{ 1}{ 2}\) | \(1\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(4\) |
| \(0\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(5\) |
| \(-1\) | \(1\) | \(1\) | \(0\) | \(3\) | \(1\) | \(3\) | \(1\) | \(1\) | \(-1\) | \(1\) | \(5\) |
| \(1\) | \(2\) | \(2\) | \(0\) | \(4\) | \(2\) | \(4\) | \(2\) | \(2\) | \(1\) | \(2\) | \(6\) |
4
New Number: 14.2 | AESZ: | Superseeker: 27/5 1619/5 | Hash: c0f6d85270164c8c5a63d1bb2deaba83
Degree: 14
\(5^{2} \theta^4+3^{2} 5 x\theta(6\theta^3-36\theta^2-23\theta-5)-x^{2}\left(43856\theta^4+189068\theta^3+226691\theta^2+135510\theta+33600\right)-3^{2} x^{3}\left(224236\theta^4+916896\theta^3+1403247\theta^2+1048995\theta+313920\right)-x^{4}\left(44621090\theta^4+199900036\theta^3+357072757\theta^2+304636250\theta+101358144\right)-3^{2} x^{5}\left(69593744\theta^4+347076728\theta^3+696076003\theta^2+653370139\theta+234075456\right)-3^{2} x^{6}\left(681084088\theta^4+3766244020\theta^3+8299124637\theta^2+8400442322\theta+3184811840\right)-3^{3} x^{7}\left(1616263276\theta^4+9835107968\theta^3+23484467027\theta^2+25311872719\theta+10046134656\right)-3^{3} x^{8}\left(8527956293\theta^4+56671723156\theta^3+145225420081\theta^2+165230257706\theta+68152357440\right)-2 3^{4} x^{9}\left(5575274615\theta^4+40185448970\theta^3+109721715457\theta^2+130944512374\theta+55834822464\right)-2^{3} 3^{3} x^{10}\left(12062719219\theta^4+93737716664\theta^3+271167874625\theta^2+337796659588\theta+148305175248\right)-2^{5} 3^{5} x^{11}(\theta+1)(691573543\theta^3+5071601663\theta^2+12510902832\theta+10260936720)-2^{7} 3^{6} x^{12}(\theta+1)(\theta+2)(80620421\theta^2+475174733\theta+711172676)-2^{14} 3^{6} 5 x^{13}(\theta+3)(\theta+2)(\theta+1)(107069\theta+369433)-2^{19} 3^{8} 5^{2} 29 x^{14}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, 84, 1944, 70476, ... --> OEIS Normalized instanton numbers (n0=1): 27/5, 158/5, 1619/5, 51193/10, 485082/5, ... ; Common denominator:...
\(-(9z+1)(6z+1)(348z^2+51z-1)(5z+1)^2(4z+1)^2(576z^3+357z^2+72z+5)^2\)
| ≈\(-0.298314\) | \(-\frac{ 1}{ 4}\) | \(-\frac{ 1}{ 5}\) | \(-\frac{ 1}{ 6}\) | \(-\frac{ 17}{ 232}-\frac{ 11}{ 696}\sqrt{ 33}\) | ≈\(-0.160739-0.057112I\) | ≈\(-0.160739+0.057112I\) | \(-\frac{ 1}{ 9}\) | \(0\) | \(-\frac{ 17}{ 232}+\frac{ 11}{ 696}\sqrt{ 33}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(\frac{ 1}{ 2}\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(2\) |
| \(3\) | \(\frac{ 1}{ 2}\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(3\) | \(3\) | \(1\) | \(0\) | \(1\) | \(3\) |
| \(4\) | \(1\) | \(1\) | \(2\) | \(2\) | \(4\) | \(4\) | \(2\) | \(0\) | \(2\) | \(4\) |
5
New Number: 14.3 | AESZ: | Superseeker: 21/4 1285/2 | Hash: fed06deb794f226dc9bf5119acb5fcf2
Degree: 14
\(2^{4} \theta^4-2^{2} x\theta(32+149\theta+234\theta^2+54\theta^3)-x^{2}\left(39143\theta^4+143570\theta^3+193959\theta^2+113504\theta+25600\right)-2 x^{3}\left(488914\theta^4+2366790\theta^3+4293033\theta^2+3346032\theta+1000416\right)-x^{4}\left(10882749\theta^4+71055186\theta^3+164405289\theta^2+154949112\theta+53930896\right)-2 x^{5}\left(27668482\theta^4+276475198\theta^3+837116993\theta^2+935359976\theta+366972272\right)+2^{2} x^{6}\left(417907\theta^4-460236984\theta^3-2273346630\theta^2-3128567370\theta-1388917916\right)+2^{4} x^{7}\left(101741100\theta^4+252571782\theta^3-1076988014\theta^2-2508674129\theta-1362925766\right)+2^{6} x^{8}\left(136151221\theta^4+982924270\theta^3+1322951772\theta^2+257785345\theta-274176968\right)+2^{8} x^{9}\left(54403942\theta^4+889245288\theta^3+2318053632\theta^2+2306501340\theta+802166039\right)-2^{10} 3 x^{10}\left(16110621\theta^4-52456644\theta^3-344061634\theta^2-516147274\theta-239510540\right)-2^{12} x^{11}(\theta+1)(75181760\theta^3+257537898\theta^2+246848548\theta+22104519)-2^{14} 3 x^{12}(\theta+1)(\theta+2)(14369939\theta^2+55966221\theta+56991175)-2^{17} 3^{3} 5 x^{13}(\theta+3)(\theta+2)(\theta+1)(45377\theta+116950)-2^{20} 3^{5} 5^{2} 59 x^{14}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, 100, 2592, 112308, ... --> OEIS Normalized instanton numbers (n0=1): 21/4, 1965/32, 1285/2, 103095/8, 1157421/4, ... ; Common denominator:...
\(-(3z+1)(64z^2+24z+1)(236z^2+63z-1)(360z^3+74z^2-21z-4)^2(4z+1)^3\)
| \(-\frac{ 1}{ 3}\) | \(-\frac{ 3}{ 16}-\frac{ 1}{ 16}\sqrt{ 5}\) | \(-\frac{ 63}{ 472}-\frac{ 17}{ 472}\sqrt{ 17}\) | ≈\(-0.268785\) | \(-\frac{ 1}{ 4}\) | ≈\(-0.174147\) | \(-\frac{ 3}{ 16}+\frac{ 1}{ 16}\sqrt{ 5}\) | \(0\) | \(-\frac{ 63}{ 472}+\frac{ 17}{ 472}\sqrt{ 17}\) | ≈\(0.237376\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(2\) |
| \(1\) | \(1\) | \(1\) | \(3\) | \(0\) | \(3\) | \(1\) | \(0\) | \(1\) | \(3\) | \(3\) |
| \(2\) | \(2\) | \(2\) | \(4\) | \(0\) | \(4\) | \(2\) | \(0\) | \(2\) | \(4\) | \(4\) |
6
New Number: 14.4 | AESZ: | Superseeker: 10 13958/9 | Hash: 0091fcfec3692ae6ced2f585ef96177c
Degree: 14
\(3^{6} \theta^4-3^{6} x\theta(15+70\theta+110\theta^2+13\theta^3)-3^{3} x^{2}\left(120409\theta^4+434560\theta^3+542371\theta^2+323352\theta+78624\right)-3^{3} x^{3}\left(5396953\theta^4+22626666\theta^3+37042425\theta^2+28217556\theta+8482968\right)-2 x^{4}\left(1704421489\theta^4+8538160718\theta^3+16779519205\theta^2+14919147216\theta+5077251288\right)-2^{2} 3 x^{5}\left(4201278867\theta^4+24797778110\theta^3+56302322281\theta^2+56325956066\theta+20967103728\right)-2^{3} x^{6}\left(63154319213\theta^4+432278933514\theta^3+1110085421927\theta^2+1224810967950\theta+489654799596\right)-2^{5} 3 x^{7}\left(36597277323\theta^4+286904817870\theta^3+822690934223\theta^2+989019393562\theta+419959932336\right)-2^{6} x^{8}\left(263122045911\theta^4+2344932626130\theta^3+7455815983415\theta^2+9696396501490\theta+4343347545434\right)-2^{7} 5 x^{9}\left(83257168289\theta^4+843955668354\theta^3+2974370084181\theta^2+4174636770342\theta+1965917099796\right)-2^{9} 5 x^{10}\left(38447331387\theta^4+453440983815\theta^3+1797507529325\theta^2+2740147614260\theta+1358896159983\right)-2^{8} 5^{2} 23 x^{11}(\theta+1)(421574469\theta^3+6597293181\theta^2+28022760832\theta+32033938840)+2^{9} 5^{2} 7 23^{2} x^{12}(\theta+2)(\theta+1)(2012137\theta^2+10160979\theta-151326)+2^{10} 5^{3} 7^{2} 23^{3} x^{13}(1525\theta+10484)(\theta+3)(\theta+2)(\theta+1)-2^{11} 3 5^{3} 7^{3} 23^{4} x^{14}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, 182, 7020, 401730, ... --> OEIS Normalized instanton numbers (n0=1): 10, 2591/27, 13958/9, 1037839/27, 3535478/3, ... ; Common denominator:...
\(-(6z+1)(42320z^4+16560z^3+2032z^2+68z-1)(920z^3-1180z^2-378z-27)^2(7z+1)^3\)
| \(-\frac{ 1}{ 6}\) | ≈\(-0.157194\) | ≈\(-0.157194\) | ≈\(-0.151128\) | \(-\frac{ 1}{ 7}\) | ≈\(-0.124614\) | ≈\(-0.087777\) | \(0\) | ≈\(0.010861\) | ≈\(1.55835\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(2\) |
| \(1\) | \(1\) | \(1\) | \(3\) | \(0\) | \(3\) | \(1\) | \(0\) | \(1\) | \(3\) | \(3\) |
| \(2\) | \(2\) | \(2\) | \(4\) | \(0\) | \(4\) | \(2\) | \(0\) | \(2\) | \(4\) | \(4\) |
7
New Number: 14.5 | AESZ: | Superseeker: 211/35 19279/35 | Hash: f3806aa0de676048470ecaa401cb173e
Degree: 14
\(5^{2} 7^{2} \theta^4-5 7 x\theta(208\theta^3+2522\theta^2+1611\theta+350)-x^{2}\left(2895864\theta^4+10743882\theta^3+13787199\theta^2+8373750\theta+2038400\right)-x^{3}\left(100271073\theta^4+431892504\theta^3+723680933\theta^2+561181425\theta+170041830\right)-x^{4}\left(1779494918\theta^4+9127622236\theta^3+18290497093\theta^2+16539531755\theta+5684071466\right)-x^{5}\left(19827182682\theta^4+119162684736\theta^3+274771737213\theta^2+279000299901\theta+104851723790\right)-x^{6}\left(149204258817\theta^4+1032818408748\theta^3+2681116117542\theta^2+2993600486151\theta+1206564891326\right)-x^{7}\left(778822250193\theta^4+6126161719824\theta^3+17659178255613\theta^2+21402250647384\theta+9142529120612\right)-x^{8}\left(2812797944541\theta^4+24913922595768\theta^3+79078287326181\theta^2+103186060627602\theta+46367068712696\right)-2 x^{9}\left(3396806566178\theta^4+33765210209691\theta^3+117624369015258\theta^2+164571138801333\theta+77449742958250\right)-x^{10}\left(10000008656989\theta^4+112554410392382\theta^3+432872666762301\theta^2+650564904626120\theta+320443815723404\right)-2^{2} 3 x^{11}(\theta+1)(551266200382\theta^3+6974826522501\theta^2+26399880418886\theta+28678364691672)+2^{2} 5 x^{12}(\theta+1)(\theta+2)(92480406417\theta^2+96008519961\theta-1687668183707)+2^{3} 5^{2} 163 x^{13}(\theta+3)(\theta+2)(\theta+1)(106246927\theta+649964324)-2^{2} 3^{3} 5^{3} 163^{2} 2687 x^{14}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, 104, 2838, 118344, ... --> OEIS Normalized instanton numbers (n0=1): 211/35, 1643/35, 19279/35, 69901/7, 7789913/35, ... ; Common denominator:...
\(-(-1+41z+1449z^2+13908z^3+53591z^4+72549z^5)(326z^3-804z^2-351z-35)^2(5z+1)^3\)
| ≈\(-0.216454\) | \(-\frac{ 1}{ 5}\) | ≈\(-0.173649\) | \(0\) | ≈\(2.85636\) | \(#ND+#NDI\) | \(\infty\) |
|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(0\) | \(1\) | \(0\) | \(1\) | \(1\) | \(2\) |
| \(3\) | \(0\) | \(3\) | \(0\) | \(3\) | \(1\) | \(3\) |
| \(4\) | \(0\) | \(4\) | \(0\) | \(4\) | \(2\) | \(4\) |
8
New Number: 14.6 | AESZ: | Superseeker: 343/26 27836/13 | Hash: b419826ae9a841fd2485cf17a33e3c82
Degree: 14
\(2^{2} 13^{2} \theta^4+2 13 x\theta(374\theta^3-3806\theta^2-2423\theta-520)-3 x^{2}\left(1378165\theta^4+5692942\theta^3+6262109\theta^2+3632408\theta+908544\right)-3 x^{3}\left(109634670\theta^4+414665370\theta^3+585954355\theta^2+424721388\theta+125838648\right)-3^{2} x^{4}\left(1430057388\theta^4+5835126030\theta^3+9693559559\theta^2+7980072398\theta+2602285652\right)-3^{4} x^{5}\left(3973724102\theta^4+18016019762\theta^3+33809871817\theta^2+30548046888\theta+10682005352\right)-3^{5} x^{6}\left(23181342780\theta^4+117157350210\theta^3+242997310916\theta^2+236792965009\theta+87556639706\right)-3^{6} x^{7}\left(98661453307\theta^4+553704139946\theta^3+1252095727942\theta^2+1301834765069\theta+504487460698\right)-3^{7} x^{8}\left(312059119661\theta^4+1933538622170\theta^3+4722871403800\theta^2+5200539067181\theta+2098928967026\right)-3^{7} x^{9}\left(2207453009832\theta^4+15008943280014\theta^3+39332490555167\theta^2+45616623444051\theta+19085482478826\right)-3^{8} x^{10}\left(3839323955127\theta^4+28479004361040\theta^3+79653137355055\theta^2+96880903986262\theta+41867518152496\right)-3^{10} x^{11}(\theta+1)(1597618239529\theta^3+11261457267015\theta^2+26962321719782\theta+21625438724040)-3^{12} x^{12}(\theta+1)(\theta+2)(452183900223\theta^2+2573271558279\theta+3747021993116)-2^{4} 3^{16} 109 x^{13}(\theta+3)(\theta+2)(\theta+1)(4973417\theta+16619273)-2^{6} 3^{16} 109^{2} 8167 x^{14}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, 252, 11106, 735660, ... --> OEIS Normalized instanton numbers (n0=1): 343/26, 1358/13, 27836/13, 764852/13, 52338075/26, ... ; Common denominator:...
\(-(661527z^5+290250z^4+47223z^3+3291z^2+71z-1)(23544z^3+7353z^2+759z+26)^2(9z+1)^3\)
| ≈\(-0.126194\) | \(-\frac{ 1}{ 9}\) | ≈\(-0.093057-0.009552I\) | ≈\(-0.093057+0.009552I\) | \(0\) | \(#ND+#NDI\) | \(\infty\) |
|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(0\) | \(1\) | \(1\) | \(0\) | \(1\) | \(2\) |
| \(3\) | \(0\) | \(3\) | \(3\) | \(0\) | \(1\) | \(3\) |
| \(4\) | \(0\) | \(4\) | \(4\) | \(0\) | \(2\) | \(4\) |
9
New Number: 14.7 | AESZ: | Superseeker: 48 3184 | Hash: 9e304ff532f3cfafc29dfac77fdff067
Degree: 14
\(\theta^4-2^{4} x\left(35\theta^4+50\theta^3+49\theta^2+24\theta+5\right)+2^{9} x^{2}\left(255\theta^4+722\theta^3+1027\theta^2+740\theta+227\right)-2^{14} x^{3}\left(1033\theta^4+4298\theta^3+7994\theta^2+7243\theta+2695\right)+2^{19} x^{4}\left(2699\theta^4+13730\theta^3+30984\theta^2+33699\theta+14443\right)-2^{24} x^{5}\left(5407\theta^4+26718\theta^3+63946\theta^2+80619\theta+38786\right)+2^{29} x^{6}\left(10081\theta^4+39658\theta^3+68604\theta^2+85851\theta+43438\right)-2^{34} x^{7}\left(17583\theta^4+63666\theta^3+51252\theta^2-1045\theta-18966\right)+2^{39} x^{8}\left(25019\theta^4+98594\theta^3+101972\theta^2-44371\theta-87630\right)-2^{44} x^{9}\left(29162\theta^4+103060\theta^3+189337\theta^2+75677\theta-39871\right)+2^{49} x^{10}\left(32428\theta^4+78424\theta^3+166293\theta^2+155877\theta+49943\right)-2^{54} x^{11}\left(33248\theta^4+85104\theta^3+119906\theta^2+105882\theta+49279\right)+2^{59} x^{12}\left(24144\theta^4+97280\theta^3+159468\theta^2+125460\theta+41819\right)-2^{67} 5 x^{13}\left(244\theta^4+1456\theta^3+3353\theta^2+3523\theta+1423\right)+2^{75} 5^{2} x^{14}\left((\theta+2)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 80, 5776, 422144, 32579856, ... --> OEIS Normalized instanton numbers (n0=1): 48, 46, 3184, 409910, -3351792, ... ; Common denominator:...
\((16z-1)(32z-1)(4096z^2-192z+1)(163840z^3+1024z^2+32z-1)^2(64z-1)^4\)
| ≈\(-0.009802-0.019I\) | ≈\(-0.009802+0.019I\) | \(0\) | \(\frac{ 3}{ 128}-\frac{ 1}{ 128}\sqrt{ 5}\) | ≈\(0.013353\) | \(\frac{ 1}{ 64}\) | \(\frac{ 1}{ 32}\) | \(\frac{ 3}{ 128}+\frac{ 1}{ 128}\sqrt{ 5}\) | \(\frac{ 1}{ 16}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(-\frac{ 1}{ 2}\) | \(0\) | \(0\) | \(0\) | \(2\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(-\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(1\) | \(2\) |
| \(3\) | \(3\) | \(0\) | \(1\) | \(3\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(1\) | \(2\) |
| \(4\) | \(4\) | \(0\) | \(2\) | \(4\) | \(\frac{ 1}{ 2}\) | \(2\) | \(2\) | \(2\) | \(2\) |
10
New Number: 14.8 | AESZ: | Superseeker: 92/5 -76/5 | Hash: a787adbb87527c14af9a5f2508991317
Degree: 14
\(5^{2} \theta^4-2^{2} 5 x\left(244\theta^4+496\theta^3+473\theta^2+225\theta+45\right)+2^{4} x^{2}\left(24144\theta^4+95872\theta^3+155244\theta^2+117660\theta+36835\right)-2^{9} x^{3}\left(33248\theta^4+180880\theta^3+407234\theta^2+416430\theta+168275\right)+2^{14} x^{4}\left(32428\theta^4+181000\theta^3+474021\theta^2+605903\theta+294817\right)-2^{19} x^{5}\left(29162\theta^4+130236\theta^3+270865\theta^2+378135\theta+208235\right)+2^{24} x^{6}\left(25019\theta^4+101558\theta^3+110864\theta^2+69739\theta+20552\right)-2^{29} x^{7}\left(17583\theta^4+76998\theta^3+91248\theta^2+4717\theta-39868\right)+2^{34} x^{8}\left(10081\theta^4+40990\theta^3+72600\theta^2+35261\theta-9816\right)-2^{39} x^{9}\left(5407\theta^4+16538\theta^3+33406\theta^2+27573\theta+6100\right)+2^{44} x^{10}\left(2699\theta^4+7862\theta^3+13380\theta^2+11845\theta+4325\right)-2^{49} x^{11}\left(1033\theta^4+3966\theta^3+6998\theta^2+6213\theta+2329\right)+2^{54} x^{12}\left(255\theta^4+1318\theta^3+2815\theta^2+2864\theta+1159\right)-2^{59} x^{13}\left(35\theta^4+230\theta^3+589\theta^2+692\theta+313\right)+2^{65} x^{14}\left((\theta+2)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 36, 1196, 41488, 1543916, ... --> OEIS Normalized instanton numbers (n0=1): 92/5, -342/5, -76/5, 75394/5, -2156752/5, ... ; Common denominator:...
\((64z-1)(32z-1)(256z^2-48z+1)(32768z^3-1024z^2-5-32z)^2(16z-1)^4\)
| ≈\(-0.020941-0.040594I\) | ≈\(-0.020941+0.040594I\) | \(0\) | \(\frac{ 1}{ 64}\) | \(\frac{ 3}{ 32}-\frac{ 1}{ 32}\sqrt{ 5}\) | \(\frac{ 1}{ 32}\) | \(\frac{ 1}{ 16}\) | ≈\(0.073133\) | \(\frac{ 3}{ 32}+\frac{ 1}{ 32}\sqrt{ 5}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(-\frac{ 1}{ 2}\) | \(0\) | \(0\) | \(2\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(-\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(2\) |
| \(3\) | \(3\) | \(0\) | \(1\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(3\) | \(1\) | \(2\) |
| \(4\) | \(4\) | \(0\) | \(2\) | \(2\) | \(2\) | \(\frac{ 1}{ 2}\) | \(4\) | \(2\) | \(2\) |
11
New Number: 14.9 | AESZ: | Superseeker: 44/3 220588/81 | Hash: 32527b63e2e6c7ca027dfb5cb9afac16
Degree: 14
\(3^{2} \theta^4+2^{2} 3 x\left(8\theta^4-128\theta^3-105\theta^2-41\theta-7\right)-2^{4} x^{2}\left(2720\theta^4-64\theta^3-3536\theta^2-680\theta+429\right)+2^{10} x^{3}\left(336\theta^4+3984\theta^3-826\theta^2+468\theta+1051\right)+2^{12} x^{4}\left(16640\theta^4-7232\theta^3+43840\theta^2+45800\theta+15969\right)-2^{18} x^{5}\left(5720\theta^4+6944\theta^3+19273\theta^2+22267\theta+9043\right)-2^{21} x^{6}\left(10216\theta^4+38016\theta^3+103024\theta^2+135096\theta+80559\right)+2^{28} x^{7}\left(2848\theta^4+11072\theta^3+24505\theta^2+27600\theta+12752\right)+2^{29} 3 x^{8}\left(888\theta^4+13312\theta^3+65952\theta^2+133944\theta+103073\right)-2^{34} x^{9}\left(8760\theta^4+63456\theta^3+203405\theta^2+310785\theta+183393\right)+2^{36} x^{10}\left(1024\theta^4-20032\theta^3-232944\theta^2-750136\theta-801269\right)+2^{42} x^{11}\left(3248\theta^4+34160\theta^3+146646\theta^2+293996\theta+228285\right)+2^{44} x^{12}\left(416\theta^4+11328\theta^3+98816\theta^2+340680\theta+408025\right)-2^{50} 5 x^{13}\left(104\theta^4+1408\theta^3+7395\theta^2+17845\theta+16643\right)-2^{56} 5^{2} x^{14}\left((\theta+4)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 28/3, 260, 116240/27, 7153796/81, ... --> OEIS Normalized instanton numbers (n0=1): 44/3, -1421/9, 220588/81, -14752264/243, 1138508000/729, ... ; Common denominator:...
\(-(1+16z)(16z+3)^2(1280z^2-32z-1)^2(256z^2+16z-1)^2(16z-1)^3\)
| \(-\frac{ 3}{ 16}\) | \(-\frac{ 1}{ 32}-\frac{ 1}{ 32}\sqrt{ 5}\) | \(-\frac{ 1}{ 16}\) | \(\frac{ 1}{ 80}-\frac{ 1}{ 80}\sqrt{ 6}\) | \(0\) | \(-\frac{ 1}{ 32}+\frac{ 1}{ 32}\sqrt{ 5}\) | \(\frac{ 1}{ 80}+\frac{ 1}{ 80}\sqrt{ 6}\) | \(\frac{ 1}{ 16}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(4\) |
| \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(0\) | \(\frac{ 1}{ 2}\) | \(1\) | \(0\) | \(4\) |
| \(-2\) | \(\frac{ 1}{ 2}\) | \(1\) | \(3\) | \(0\) | \(\frac{ 1}{ 2}\) | \(3\) | \(0\) | \(4\) |
| \(3\) | \(1\) | \(2\) | \(4\) | \(0\) | \(1\) | \(4\) | \(0\) | \(4\) |