You searched for: Spectrum0=0,1,1,2
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271
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:...
\(-(-1+156z+160z^2+256z^3)(4z-1)^2(256z^3-128z^2-16z-5)^2\)
| ≈\(-0.315684-0.716756I\) | ≈\(-0.315684+0.716756I\) | ≈\(-0.072055-0.158527I\) | ≈\(-0.072055+0.158527I\) | \(0\) | ≈\(0.006368\) | \(\frac{ 1}{ 4}\) | ≈\(0.64411\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) |
| \(1\) | \(1\) | \(3\) | \(3\) | \(0\) | \(1\) | \(\frac{ 1}{ 2}\) | \(3\) | \(1\) |
| \(2\) | \(2\) | \(4\) | \(4\) | \(0\) | \(2\) | \(1\) | \(4\) | \(1\) |
272
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:...
\(-(-1-80z-9984z^2+8192z^3)(32z-1)^2(40960z^3+1024z^2+64z-1)^2\)
| ≈\(-0.018565-0.040844I\) | ≈\(-0.018565+0.040844I\) | ≈\(-0.004021-0.009129I\) | ≈\(-0.004021+0.009129I\) | \(0\) | ≈\(0.012129\) | \(\frac{ 1}{ 32}\) | ≈\(1.226791\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) |
| \(3\) | \(3\) | \(1\) | \(1\) | \(0\) | \(3\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) |
| \(4\) | \(4\) | \(2\) | \(2\) | \(0\) | \(4\) | \(1\) | \(2\) | \(1\) |
273
New Number: 11.6 | AESZ: | Superseeker: 95/102 1421/102 | Hash: e79a3108441c74cdc23a53a603a6181e
Degree: 11
\(2^{2} 3^{2} 17^{2} \theta^4-2 3 17 x\theta(116\theta^3+1414\theta^2+911\theta+204)-x^{2}\left(2596259\theta^4+9892670\theta^3+14508941\theta^2+9947652\theta+2663424\right)-3 x^{3}\left(8561767\theta^4+41744696\theta^3+79668236\theta^2+68977704\theta+22655832\right)-2^{2} x^{4}\left(28089475\theta^4+171762758\theta^3+396877187\theta^2+402013525\theta+149622901\right)-2 x^{5}\left(127339346\theta^4+963856934\theta^3+2636877099\theta^2+3042828449\theta+1247694978\right)-x^{6}\left(283337071\theta^4+2758627602\theta^3+9101625228\theta^2+11995897911\theta+5385015134\right)-2 x^{7}\left(43252385\theta^4+777895672\theta^3+3537873325\theta^2+5604936458\theta+2806067360\right)+2^{2} 3 x^{8}(\theta+1)(7613560\theta^3+27844427\theta^2-51849552\theta-134696600)+x^{9}(\theta+1)(\theta+2)(60585089\theta^2+495871401\theta+595115780)-2^{3} 3 5^{2} x^{10}(\theta+3)(\theta+2)(\theta+1)(10279\theta-113205)-2^{4} 5^{4} 7 97 x^{11}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, 16, 114, 1680, ... --> OEIS Normalized instanton numbers (n0=1): 95/102, 58/17, 1421/102, 1451/17, 31474/51, ... ; Common denominator:...
\(-(-1+7z+219z^2+1115z^3+1934z^4+679z^5)(z+1)^2(100z^2-197z-102)^2\)
| \(-1\) | \(\frac{ 197}{ 200}-\frac{ 1}{ 200}\sqrt{ 79609}\) | \(0\) | \(\frac{ 197}{ 200}+\frac{ 1}{ 200}\sqrt{ 79609}\) | \(#ND+#NDI\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(\frac{ 1}{ 3}\) | \(1\) | \(0\) | \(1\) | \(1\) | \(2\) |
| \(\frac{ 2}{ 3}\) | \(3\) | \(0\) | \(3\) | \(1\) | \(3\) |
| \(1\) | \(4\) | \(0\) | \(4\) | \(2\) | \(4\) |
274
New Number: 11.7 | AESZ: | Superseeker: 9 2564/3 | Hash: 3933e1482d30ea8bca1e5e5f914286e2
Degree: 11
\(\theta^4+3 x\left(60\theta^4+12\theta^3+19\theta^2+13\theta+3\right)+3^{3} x^{2}\left(463\theta^4+304\theta^3+405\theta^2+184\theta+27\right)+3^{5} x^{3}\left(1710\theta^4+2268\theta^3+2450\theta^2+1080\theta+153\right)+3^{7} x^{4}\left(2870\theta^4+5344\theta^3+4044\theta^2-188\theta-981\right)+3^{9} x^{5}\left(560\theta^4-4552\theta^3-20650\theta^2-29130\theta-13389\right)-3^{11} x^{6}\left(5114\theta^4+37440\theta^3+101098\theta^2+119700\theta+51219\right)-3^{13} x^{7}\left(6620\theta^4+48712\theta^3+130868\theta^2+152172\theta+63981\right)-3^{16} x^{8}(\theta+1)(83\theta^3-2739\theta^2-16257\theta-20563)+3^{17} x^{9}(\theta+1)(\theta+2)(4676\theta^2+42864\theta+94887)+3^{20} x^{10}(\theta+3)(\theta+2)(\theta+1)(505\theta+2522)+2 3^{23} 7 x^{11}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -9, 135, -2115, 38799, ... --> OEIS Normalized instanton numbers (n0=1): 9, -72, 2564/3, -12924, 228024, ... ; Common denominator:...
\((18z+1)(189z^2+18z+1)(27z+1)^2(9z-1)^2(81z^2+54z+1)^2\)
| \(-\frac{ 1}{ 3}-\frac{ 2}{ 9}\sqrt{ 2}\) | \(-\frac{ 1}{ 18}\) | \(-\frac{ 1}{ 21}-\frac{ 2}{ 63}\sqrt{ 3}I\) | \(-\frac{ 1}{ 21}+\frac{ 2}{ 63}\sqrt{ 3}I\) | \(-\frac{ 1}{ 27}\) | \(-\frac{ 1}{ 3}+\frac{ 2}{ 9}\sqrt{ 2}\) | \(0\) | \(\frac{ 1}{ 9}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(0\) | \(\frac{ 1}{ 2}\) | \(2\) |
| \(3\) | \(1\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(3\) | \(0\) | \(\frac{ 1}{ 2}\) | \(3\) |
| \(4\) | \(2\) | \(2\) | \(2\) | \(1\) | \(4\) | \(0\) | \(1\) | \(4\) |
275
New Number: 11.8 | AESZ: | Superseeker: 6/17 688/17 | Hash: a0a3e346d09b91b8ad96e54854c136ad
Degree: 11
\(17^{2} \theta^4-2 3 17 x\theta^2(117\theta^2+2\theta+1)+2^{2} x^{2}\left(8475\theta^4-64176\theta^3-97010\theta^2-63580\theta-16184\right)+2^{2} x^{3}\left(717094\theta^4+1400796\theta^3+1493367\theta^2+893571\theta+254082\right)-2^{4} x^{4}\left(464294\theta^4-1133264\theta^3-1648391\theta^2-1200310\theta-375336\right)-2^{4} x^{5}\left(18282700\theta^4+46995928\theta^3+83098711\theta^2+73517673\theta+25685438\right)-2^{6} 3 x^{6}\left(2709886\theta^4+7353008\theta^3+18175093\theta^2+18787708\theta+5966228\right)+2^{6} x^{7}\left(154368940\theta^4+947965400\theta^3+2363187035\theta^2+2646307981\theta+1071488886\right)+2^{8} x^{8}(\theta+1)(119648213\theta^3+399067803\theta^2+77665606\theta-498465144)-2^{8} 3 x^{9}(\theta+1)(\theta+2)(120410834\theta^2+865960638\theta+1188072247)-2^{10} 3^{2} 107 x^{10}(\theta+3)(\theta+2)(\theta+1)(218683\theta-39394)+2^{11} 3^{3} 5 107^{2} 137 x^{11}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, 14, 72, 1554, ... --> OEIS Normalized instanton numbers (n0=1): 6/17, 83/17, 688/17, 7350/17, 5150, ... ; Common denominator:...
\((10z+1)(6z-1)(1096z^3+228z^2+14z-1)(2z-1)^2(1284z^2+232z-17)^2\)
| \(-\frac{ 29}{ 321}-\frac{ 1}{ 642}\sqrt{ 8821}\) | ≈\(-0.124082-0.085658I\) | ≈\(-0.124082+0.085658I\) | \(-\frac{ 1}{ 10}\) | \(0\) | ≈\(0.040135\) | \(-\frac{ 29}{ 321}+\frac{ 1}{ 642}\sqrt{ 8821}\) | \(\frac{ 1}{ 6}\) | \(\frac{ 1}{ 2}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(0\) | \(2\) |
| \(3\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(3\) | \(1\) | \(1\) | \(3\) |
| \(4\) | \(2\) | \(2\) | \(2\) | \(0\) | \(2\) | \(4\) | \(2\) | \(1\) | \(4\) |
276
New Number: 11.9 | AESZ: | Superseeker: 17/3 4127/9 | Hash: fa7c260e6f07cef5d727e6af380a6373
Degree: 11
\(3^{2} \theta^4-3 x\theta(20\theta^3+196\theta^2+125\theta+27)-x^{2}\left(19127\theta^4+69044\theta^3+89705\theta^2+54504\theta+13248\right)-2 x^{3}\left(285799\theta^4+1251420\theta^3+2142633\theta^2+1678248\theta+511560\right)-2^{2} x^{4}\left(2058125\theta^4+11190220\theta^3+23374875\theta^2+21658060\theta+7556504\right)-2^{3} x^{5}\left(8570685\theta^4+57030456\theta^3+140934413\theta^2+149627146\theta+57858760\right)-2^{6} x^{6}\left(5382486\theta^4+43183593\theta^3+124360784\theta^2+148979343\theta+62839586\right)-2^{7} x^{7}\left(7897671\theta^4+75745098\theta^3+252663545\theta^2+339244430\theta+154810568\right)-2^{10} x^{8}(\theta+1)(1454893\theta^3+15409953\theta^2+50286726\theta+48898444)-2^{11} x^{9}(\theta+1)(\theta+2)(227963\theta^2+3375435\theta+10342960)+2^{14} x^{10}(\theta+3)(\theta+2)(\theta+1)(48476\theta+271867)-2^{15} 3 5 13 23 x^{11}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, 92, 2328, 91212, ... --> OEIS Normalized instanton numbers (n0=1): 17/3, 257/6, 4127/9, 23827/3, 496999/3, ... ; Common denominator:...
\(-(5z+1)(13z+1)(6z+1)(368z^2+56z-1)(4z+1)^2(8z^2-26z-3)^2\)
| \(-\frac{ 1}{ 4}\) | \(-\frac{ 1}{ 5}\) | \(-\frac{ 7}{ 92}-\frac{ 3}{ 46}\sqrt{ 2}\) | \(-\frac{ 1}{ 6}\) | \(\frac{ 13}{ 8}-\frac{ 1}{ 8}\sqrt{ 193}\) | \(-\frac{ 1}{ 13}\) | \(0\) | \(-\frac{ 7}{ 92}+\frac{ 3}{ 46}\sqrt{ 2}\) | \(\frac{ 13}{ 8}+\frac{ 1}{ 8}\sqrt{ 193}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(2\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(3\) | \(1\) | \(0\) | \(1\) | \(3\) | \(3\) |
| \(1\) | \(2\) | \(2\) | \(2\) | \(4\) | \(2\) | \(0\) | \(2\) | \(4\) | \(4\) |
277
New Number: 12.12 | AESZ: | Superseeker: 48 3184 | Hash: 2b1c995b5f2826ce90fc016ad86fd66f
Degree: 12
\(\theta^4-2^{4} x\left(27\theta^4+42\theta^3+37\theta^2+16\theta+3\right)+2^{9} x^{2}\left(139\theta^4+430\theta^3+579\theta^2+376\theta+103\right)-2^{14} x^{3}\left(369\theta^4+1638\theta^3+2992\theta^2+2481\theta+819\right)+2^{19} x^{4}\left(667\theta^4+2870\theta^3+6158\theta^2+6571\theta+2559\right)-2^{24} x^{5}\left(1263\theta^4+3066\theta^3+2692\theta^2+4295\theta+2110\right)+2^{29} 3 x^{6}\left(787\theta^4+1842\theta^3-1598\theta^2-3339\theta-1652\right)-2^{34} x^{7}\left(3087\theta^4+9750\theta^3+2942\theta^2-13117\theta-9816\right)+2^{39} x^{8}\left(3227\theta^4+6254\theta^3+14286\theta^2+4793\theta-1948\right)-2^{44} x^{9}\left(3906\theta^4+1440\theta^3+5279\theta^2+7593\theta+3747\right)+2^{49} x^{10}\left(3896\theta^4+6208\theta^3+3391\theta^2+725\theta+525\right)-2^{54} 5 x^{11}\left(408\theta^4+1536\theta^3+2230\theta^2+1460\theta+361\right)+2^{59} 5^{2} x^{12}\left((2\theta+3)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 48, 2704, 179968, 14147856, ... --> OEIS Normalized instanton numbers (n0=1): 48, 46, 3184, 409910, -3351792, ... ; Common denominator:...
\((16z-1)(32z-1)(4096z^2-192z+1)(64z-1)^2(163840z^3+1024z^2+32z-1)^2\)
| ≈\(-0.009802-0.019I\) | ≈\(-0.009802+0.019I\) | \(0\) | \(\frac{ 3}{ 128}-\frac{ 1}{ 128}\sqrt{ 5}\) | ≈\(0.013353\) | \(\frac{ 1}{ 64}\) | \(\frac{ 1}{ 32}\) | \(\frac{ 3}{ 128}+\frac{ 1}{ 128}\sqrt{ 5}\) | \(\frac{ 1}{ 16}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 3}{ 2}\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(\frac{ 3}{ 2}\) |
| \(3\) | \(3\) | \(0\) | \(1\) | \(3\) | \(1\) | \(1\) | \(1\) | \(1\) | \(\frac{ 3}{ 2}\) |
| \(4\) | \(4\) | \(0\) | \(2\) | \(4\) | \(1\) | \(2\) | \(2\) | \(2\) | \(\frac{ 3}{ 2}\) |
278
New Number: 12.13 | AESZ: | Superseeker: 92/5 -76/5 | Hash: dba247c75acfa39c7b95fa5054ec0315
Degree: 12
\(5^{2} \theta^4-2^{2} 5 x\left(204\theta^4+456\theta^3+413\theta^2+185\theta+35\right)+2^{4} x^{2}\left(15584\theta^4+68672\theta^3+112204\theta^2+80560\theta+23355\right)-2^{8} x^{3}\left(31248\theta^4+175968\theta^3+412240\theta^2+410040\theta+153195\right)+2^{12} x^{4}\left(51632\theta^4+209728\theta^3+475320\theta^2+630640\theta+291767\right)-2^{17} x^{5}\left(49392\theta^4+140352\theta^3+11864\theta^2-35120\theta-12789\right)+2^{22} 3 x^{6}\left(12592\theta^4+46080\theta^3+11800\theta^2-52224\theta-39545\right)-2^{27} x^{7}\left(20208\theta^4+72192\theta^3+95128\theta^2+2176\theta-35669\right)+2^{32} x^{8}\left(10672\theta^4+18112\theta^3+35960\theta^2+24560\theta+3975\right)-2^{37} x^{9}\left(5904\theta^4+9216\theta^3+9640\theta^2+6720\theta+2709\right)+2^{42} x^{10}\left(2224\theta^4+6464\theta^3+8328\theta^2+5360\theta+1507\right)-2^{47} x^{11}\left(432\theta^4+1920\theta^3+3400\theta^2+2816\theta+915\right)+2^{53} x^{12}\left((2\theta+3)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 28, 876, 30512, 1161964, ... --> OEIS Normalized instanton numbers (n0=1): 92/5, -342/5, -76/5, 75394/5, -2156752/5, ... ; Common denominator:...
\((64z-1)(32z-1)(256z^2-48z+1)(16z-1)^2(32768z^3-1024z^2-32z-5)^2\)
| ≈\(-0.020941-0.040594I\) | ≈\(-0.020941+0.040594I\) | \(0\) | \(\frac{ 1}{ 64}\) | \(\frac{ 3}{ 32}-\frac{ 1}{ 32}\sqrt{ 5}\) | \(\frac{ 1}{ 32}\) | \(\frac{ 1}{ 16}\) | ≈\(0.073133\) | \(\frac{ 3}{ 32}+\frac{ 1}{ 32}\sqrt{ 5}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 3}{ 2}\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(\frac{ 3}{ 2}\) |
| \(3\) | \(3\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(3\) | \(1\) | \(\frac{ 3}{ 2}\) |
| \(4\) | \(4\) | \(0\) | \(2\) | \(2\) | \(2\) | \(1\) | \(4\) | \(2\) | \(\frac{ 3}{ 2}\) |
279
New Number: 12.14 | AESZ: | Superseeker: 7/2 237/2 | Hash: 614b95fc4275078df0800c7546870e7f
Degree: 12
\(2^{2} \theta^4+2 x\left(74\theta^4+22\theta^3+77\theta^2+66\theta+18\right)+3^{2} x^{2}\left(97\theta^4+1206\theta^3+2235\theta^2+1750\theta+642\right)+3^{4} x^{3}\left(126\theta^4+3910\theta^3+7341\theta^2+8588\theta+3750\right)+3^{6} x^{4}\left(832\theta^4+6078\theta^3+26372\theta^2+37719\theta+21825\right)+3^{8} x^{5}\left(442\theta^4+12544\theta^3+62654\theta^2+116087\theta+78828\right)-3^{10} x^{6}\left(1032\theta^4-5126\theta^3-73629\theta^2-192529\theta-165306\right)-2 3^{12} x^{7}\left(1432\theta^4+11737\theta^3+11907\theta^2-41634\theta-71496\right)-3^{14} x^{8}\left(1871\theta^4+35422\theta^3+145979\theta^2+220752\theta+99504\right)+2 3^{17} x^{9}\left(151\theta^4-2094\theta^3-20341\theta^2-54972\theta-48672\right)+2^{3} 3^{19} x^{10}(\theta+3)(86\theta^3+414\theta^2+181\theta-936)+2^{3} 3^{22} x^{11}(\theta+4)(\theta+3)(21\theta^2+137\theta+224)+2^{4} 3^{24} x^{12}(\theta+3)(\theta+5)(\theta+4)^2\)
Maple LaTexCoefficients of the holomorphic solution: 1, -9, -18, 747, -5751, ... --> OEIS Normalized instanton numbers (n0=1): 7/2, -193/8, 237/2, -6119/4, 16307, ... ; Common denominator:...
\((9z+1)(z+1)(324z^2-18z+1)(81z^2+9z+1)^2(486z^2-27z-2)^2\)
| \(-1\) | \(-\frac{ 1}{ 9}\) | \(-\frac{ 1}{ 18}-\frac{ 1}{ 18}\sqrt{ 3}I\) | \(-\frac{ 1}{ 18}+\frac{ 1}{ 18}\sqrt{ 3}I\) | \(\frac{ 1}{ 36}-\frac{ 1}{ 108}\sqrt{ 57}\) | \(0\) | \(\frac{ 1}{ 36}-\frac{ 1}{ 36}\sqrt{ 3}I\) | \(\frac{ 1}{ 36}+\frac{ 1}{ 36}\sqrt{ 3}I\) | \(\frac{ 1}{ 36}+\frac{ 1}{ 108}\sqrt{ 57}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(3\) |
| \(1\) | \(1\) | \(0\) | \(0\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(4\) |
| \(1\) | \(1\) | \(-1\) | \(-1\) | \(3\) | \(0\) | \(1\) | \(1\) | \(3\) | \(4\) |
| \(2\) | \(2\) | \(1\) | \(1\) | \(4\) | \(0\) | \(2\) | \(2\) | \(4\) | \(5\) |
280
New Number: 12.15 | AESZ: | Superseeker: 27/5 1619/5 | Hash: f7297f2850190f8613d1cbc3a7363a23
Degree: 12
\(5^{2} \theta^4-5 x\left(296\theta^4+574\theta^3+457\theta^2+170\theta+25\right)-x^{2}\left(4531\theta^4+24118\theta^3+37791\theta^2+23710\theta+5550\right)+2^{2} x^{3}\left(559\theta^4+9744\theta^3+19448\theta^2+14280\theta+4055\right)+x^{4}\left(1455\theta^4-636\theta^3+151398\theta^2+254100\theta+114136\right)+x^{5}\left(80304\theta^4+79818\theta^3-776517\theta^2-952026\theta-338569\right)-x^{6}\left(18597\theta^4-67050\theta^3-680097\theta^2-608202\theta-164470\right)-2 x^{7}\left(19086\theta^4+454818\theta^3+525507\theta^2-112266\theta-235189\right)-2^{2} x^{8}\left(52779\theta^4-252492\theta^3-39867\theta^2+316368\theta+192050\right)-2^{3} x^{9}\left(27325\theta^4+45630\theta^3-118827\theta^2-223839\theta-101599\right)+2^{2} 17 x^{10}\left(8047\theta^4+9182\theta^3-8905\theta^2-20876\theta-9476\right)+2^{5} 17^{2} x^{11}(\theta+1)(19\theta^3+129\theta^2+246\theta+145)-2^{4} 17^{3} x^{12}(\theta+2)(\theta+1)(2\theta+3)^2\)
Maple LaTexCoefficients of the holomorphic solution: 1, 5, 109, 3329, 122581, ... --> OEIS Normalized instanton numbers (n0=1): 27/5, 158/5, 1619/5, 51193/10, 485082/5, ... ; Common denominator:...
\(-(4z+1)(z+1)(68z^2+61z-1)(z-1)^2(34z^3-12z^2+3z-5)^2\)
| \(-1\) | \(-\frac{ 61}{ 136}-\frac{ 11}{ 136}\sqrt{ 33}\) | \(-\frac{ 1}{ 4}\) | ≈\(-0.126959-0.475615I\) | ≈\(-0.126959+0.475615I\) | \(0\) | \(-\frac{ 61}{ 136}+\frac{ 11}{ 136}\sqrt{ 33}\) | ≈\(0.606859\) | \(1\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(\frac{ 3}{ 2}\) |
| \(1\) | \(1\) | \(1\) | \(3\) | \(3\) | \(0\) | \(1\) | \(3\) | \(\frac{ 1}{ 2}\) | \(\frac{ 3}{ 2}\) |
| \(2\) | \(2\) | \(2\) | \(4\) | \(4\) | \(0\) | \(2\) | \(4\) | \(1\) | \(2\) |
281
New Number: 12.16 | AESZ: | Superseeker: 288 -8252768 | Hash: e5412f8624ff9afc10459abda2d297d0
Degree: 12
\(\theta^4-2^{4} x\left(160\theta^4+224\theta^3+200\theta^2+88\theta+17\right)+2^{12} x^{2}\left(992\theta^4+1184\theta^3+1664\theta^2+1368\theta+399\right)-2^{22} x^{3}\left(1172\theta^4+1104\theta^3+542\theta^2+912\theta+331\right)+2^{28} x^{4}\left(16624\theta^4+15104\theta^3+5408\theta^2-752\theta-1829\right)-2^{37} x^{5}\left(23072\theta^4+16784\theta^3+23748\theta^2+1100\theta-4281\right)+2^{47} x^{6}\left(12696\theta^4+8556\theta^3+18218\theta^2+6591\theta+144\right)-2^{52} x^{7}\left(167440\theta^4+175808\theta^3+289048\theta^2+160176\theta+37033\right)+2^{61} x^{8}\left(96496\theta^4+172672\theta^3+241896\theta^2+158752\theta+44823\right)-2^{70} x^{9}\left(36784\theta^4+100224\theta^3+148008\theta^2+108576\theta+32891\right)+2^{79} x^{10}\left(8720\theta^4+32704\theta^3+54968\theta^2+44784\theta+14529\right)-2^{91} x^{11}\left(144\theta^4+696\theta^3+1352\theta^2+1222\theta+427\right)+2^{99} x^{12}\left((2\theta+3)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 272, 85264, 30040320, 11678489872, ... --> OEIS Normalized instanton numbers (n0=1): 288, 59200, -8252768, -1223488576, 585571467872, ... ; Common denominator:...
\((512z-1)(65536z^2-768z+1)(134217728z^3-655360z^2+256z-1)^2(256z-1)^3\)
| \(0\) | ≈\(3.7e-05-0.001244I\) | ≈\(3.7e-05+0.001244I\) | \(\frac{ 3}{ 512}-\frac{ 1}{ 512}\sqrt{ 5}\) | \(\frac{ 1}{ 512}\) | \(\frac{ 1}{ 256}\) | ≈\(0.004808\) | \(\frac{ 3}{ 512}+\frac{ 1}{ 512}\sqrt{ 5}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 3}{ 2}\) |
| \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(\frac{ 3}{ 2}\) |
| \(0\) | \(3\) | \(3\) | \(1\) | \(1\) | \(0\) | \(3\) | \(1\) | \(\frac{ 3}{ 2}\) |
| \(0\) | \(4\) | \(4\) | \(2\) | \(2\) | \(0\) | \(4\) | \(2\) | \(\frac{ 3}{ 2}\) |
282
New Number: 12.17 | AESZ: | Superseeker: 4 52 | Hash: e65be092d4832d3740d2a3078755f447
Degree: 12
\(\theta^4+2^{2} x\left(24\theta^4+6\theta^3+11\theta^2+8\theta+2\right)+2^{4} x^{2}\left(209\theta^4+2\theta^3+23\theta^2-10\right)+2^{7} x^{3}\left(223\theta^4-1218\theta^3-2225\theta^2-2088\theta-776\right)-2^{10} x^{4}\left(1409\theta^4+9634\theta^3+19337\theta^2+18420\theta+6872\right)-2^{13} x^{5}\left(6527\theta^4+35858\theta^3+78357\theta^2+78428\theta+30414\right)-2^{17} x^{6}\left(6276\theta^4+37704\theta^3+91143\theta^2+97914\theta+40036\right)-2^{21} x^{7}\left(2923\theta^4+22130\theta^3+61939\theta^2+73401\theta+32138\right)-2^{24} x^{8}\left(602\theta^4+10928\theta^3+42765\theta^2+60182\theta+29287\right)+2^{26} x^{9}\left(2352\theta^4+7392\theta^3-7024\theta^2-31968\theta-21891\right)+2^{29} x^{10}\left(1584\theta^4+11904\theta^3+24696\theta^2+19776\theta+4915\right)-2^{35} x^{11}\left(16\theta^4-176\theta^3-784\theta^2-1036\theta-449\right)-2^{39} x^{12}\left((2\theta+3)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -8, 112, -1152, 19216, ... --> OEIS Normalized instanton numbers (n0=1): 4, 7/2, 52, 500, 2796, ... ; Common denominator:...
\(-(8z+1)(256z^2+16z-1)(1024z^3-160z^2-28z-1)^2(16z+1)^3\)
| \(-\frac{ 1}{ 8}\) | \(-\frac{ 1}{ 32}-\frac{ 1}{ 32}\sqrt{ 5}\) | \(-\frac{ 1}{ 16}\) | ≈\(-0.057187-0.018391I\) | ≈\(-0.057187+0.018391I\) | \(0\) | \(-\frac{ 1}{ 32}+\frac{ 1}{ 32}\sqrt{ 5}\) | ≈\(0.270624\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 3}{ 2}\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(\frac{ 3}{ 2}\) |
| \(1\) | \(1\) | \(0\) | \(3\) | \(3\) | \(0\) | \(1\) | \(3\) | \(\frac{ 3}{ 2}\) |
| \(2\) | \(2\) | \(0\) | \(4\) | \(4\) | \(0\) | \(2\) | \(4\) | \(\frac{ 3}{ 2}\) |
283
New Number: 12.7 | AESZ: | Superseeker: -24/7 117 | Hash: fedf397077a0af56af404f5156e1b5c0
Degree: 12
\(7^{2} \theta^4+2 3 7 x\left(111\theta^4+120\theta^3+102\theta^2+42\theta+7\right)+2^{2} 3 x^{2}\left(16827\theta^4+34008\theta^3+38464\theta^2+20846\theta+4494\right)+3^{3} x^{3}\left(178553\theta^4+439878\theta^3+528099\theta^2+313502\theta+74536\right)+2 3^{3} x^{4}\left(1355053\theta^4+3438698\theta^3+3854711\theta^2+2221354\theta+519896\right)+2^{2} 3^{4} x^{5}\left(2406561\theta^4+5708802\theta^3+5082043\theta^2+2161754\theta+336752\right)+2^{3} 3^{5} x^{6}\left(3133411\theta^4+6625998\theta^3+4266961\theta^2+238710\theta-485736\right)+2^{6} 3^{6} x^{7}\left(746186\theta^4+1366021\theta^3+743388\theta^2-203279\theta-212552\right)+2^{7} 3^{7} x^{8}\left(506499\theta^4+760668\theta^3+404459\theta^2-112958\theta-117216\right)+2^{11} 3^{8} x^{9}\left(27992\theta^4+34962\theta^3+7197\theta^2-14685\theta-7604\right)+2^{14} 3^{9} x^{10}\left(1381\theta^4+1244\theta^3-2460\theta^2-4030\theta-1571\right)-2^{18} 3^{10} x^{11}(22\theta^2+98\theta+105)(\theta+1)^2-2^{22} 3^{11} x^{12}(\theta+1)^2(\theta+2)^2\)
Maple LaTexCoefficients of the holomorphic solution: 1, -6, 54, -276, -8442, ... --> OEIS Normalized instanton numbers (n0=1): -24/7, -24/7, 117, -564, 948/7, ... ; Common denominator:...
\(-(6z+1)(10368z^5-864z^4-7371z^3-1440z^2-60z-1)(7+102z+648z^2+3456z^3)^2\)
| \(-\frac{ 1}{ 6}\) | ≈\(-0.097659\) | ≈\(-0.04492-0.136829I\) | ≈\(-0.04492+0.136829I\) | \(0\) | \(#ND+#NDI\) | \(\infty\) |
|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) |
| \(1\) | \(3\) | \(3\) | \(3\) | \(0\) | \(1\) | \(2\) |
| \(2\) | \(4\) | \(4\) | \(4\) | \(0\) | \(2\) | \(2\) |
284
New Number: 12.2 | AESZ: | Superseeker: 64 39744 | Hash: b92032007ecbbf3af5801c4b1e4cf97a
Degree: 12
\(\theta^4+2^{5} x\theta(4\theta^3-10\theta^2-6\theta-1)-2^{8} x^{2}\left(92\theta^4+248\theta^3+200\theta^2+228\theta+89\right)-2^{14} x^{3}\left(84\theta^4+336\theta^3+664\theta^2+132\theta-51\right)+2^{18} x^{4}\left(944\theta^4+1312\theta^3+8928\theta^2+7384\theta+2567\right)-2^{26} x^{5}\left(176\theta^4-1456\theta^3-3477\theta^2-3814\theta-1741\right)-2^{32} x^{6}\left(216\theta^4+1200\theta^3+576\theta^2+1314\theta+697\right)+2^{38} x^{7}\left(456\theta^4+624\theta^3-3085\theta^2-5590\theta-3089\right)-2^{43} x^{8}\left(176\theta^4-3616\theta^3-2404\theta^2-288\theta+1027\right)-2^{50} x^{9}\left(208\theta^4+1824\theta^3+2581\theta^2+1434\theta+73\right)+2^{57} x^{10}\left(122\theta^4-44\theta^3-718\theta^2-1005\theta-410\right)-2^{62} 5 x^{11}\left(4\theta^4-32\theta^3-145\theta^2-190\theta-82\right)-2^{66} 5^{2} x^{12}\left((2\theta+3)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, 1424, 13312, 4213008, ... --> OEIS Normalized instanton numbers (n0=1): 64, -692, 39744, -2001358, 95440576, ... ; Common denominator:...
\(-(-1+64z+4096z^2)(64z-1)^2(64z+1)^2(655360z^3-4096z^2+96z+1)^2\)
| \(-\frac{ 1}{ 128}-\frac{ 1}{ 128}\sqrt{ 5}\) | \(-\frac{ 1}{ 64}\) | ≈\(-0.006598\) | \(0\) | ≈\(0.006424-0.013784I\) | ≈\(0.006424+0.013784I\) | \(-\frac{ 1}{ 128}+\frac{ 1}{ 128}\sqrt{ 5}\) | \(\frac{ 1}{ 64}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 3}{ 2}\) |
| \(1\) | \(0\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(\frac{ 3}{ 2}\) |
| \(1\) | \(1\) | \(3\) | \(0\) | \(3\) | \(3\) | \(1\) | \(\frac{ 1}{ 2}\) | \(\frac{ 3}{ 2}\) |
| \(2\) | \(1\) | \(4\) | \(0\) | \(4\) | \(4\) | \(2\) | \(1\) | \(\frac{ 3}{ 2}\) |
285
New Number: 12.3 | AESZ: | Superseeker: -12/5 444/5 | Hash: 45726409a4c817f929c9e6e49b33a941
Degree: 12
\(5^{2} \theta^4+2^{2} 5 x\left(4\theta^4+56\theta^3+53\theta^2+25\theta+5\right)-2^{4} x^{2}\left(976\theta^4+6208\theta^3+9016\theta^2+6360\theta+1985\right)+2^{8} x^{3}\left(832\theta^4-2304\theta^3-11276\theta^2-12780\theta-5495\right)+2^{13} x^{4}\left(176\theta^4+4672\theta^3+16244\theta^2+19860\theta+9145\right)-2^{16} x^{5}\left(1824\theta^4+8448\theta^3+1052\theta^2-6884\theta-5771\right)+2^{21} x^{6}\left(432\theta^4+192\theta^3-3816\theta^2-9540\theta-5869\right)+2^{24} x^{7}\left(704\theta^4+10048\theta^3+21804\theta^2+22348\theta+7847\right)-2^{29} x^{8}\left(472\theta^4+2176\theta^3+7884\theta^2+11644\theta+5965\right)+2^{32} x^{9}\left(336\theta^4+672\theta^3+1144\theta^2+2904\theta+2145\right)+2^{36} x^{10}\left(368\theta^4+1216\theta^3+1304\theta^2-240\theta-697\right)-2^{44} x^{11}(2\theta+3)(4\theta^3+28\theta^2+51\theta+28)-2^{46} x^{12}\left((2\theta+3)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -4, 108, -912, 21484, ... --> OEIS Normalized instanton numbers (n0=1): -12/5, 103/5, 444/5, 1148/5, -6704, ... ; Common denominator:...
\(-(-1-16z+256z^2)(16z+1)^2(16z-1)^2(8192z^3+768z^2-32z+5)^2\)
| ≈\(-0.148005\) | \(-\frac{ 1}{ 16}\) | \(\frac{ 1}{ 32}-\frac{ 1}{ 32}\sqrt{ 5}\) | \(0\) | ≈\(0.027128-0.058206I\) | ≈\(0.027128+0.058206I\) | \(\frac{ 1}{ 16}\) | \(\frac{ 1}{ 32}+\frac{ 1}{ 32}\sqrt{ 5}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 3}{ 2}\) |
| \(1\) | \(0\) | \(1\) | \(0\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(\frac{ 3}{ 2}\) |
| \(3\) | \(1\) | \(1\) | \(0\) | \(3\) | \(3\) | \(\frac{ 1}{ 2}\) | \(1\) | \(\frac{ 3}{ 2}\) |
| \(4\) | \(1\) | \(2\) | \(0\) | \(4\) | \(4\) | \(1\) | \(2\) | \(\frac{ 3}{ 2}\) |
286
New Number: 12.5 | AESZ: | Superseeker: 4 2252/9 | Hash: bb257a283455fdd1fa17fef9649505e3
Degree: 12
\(\theta^4+2^{2} x\left(43\theta^4+22\theta^3+25\theta^2+14\theta+3\right)+2^{4} x^{2}\left(753\theta^4+924\theta^3+1107\theta^2+622\theta+141\right)+2^{7} x^{3}\left(3377\theta^4+7218\theta^3+9261\theta^2+5764\theta+1455\right)+2^{10} x^{4}\left(7570\theta^4+24718\theta^3+34375\theta^2+21933\theta+5310\right)+2^{12} 3^{2} x^{5}\left(901\theta^4+5118\theta^3+5777\theta^2-84\theta-1829\right)-2^{14} 3^{2} x^{6}\left(7783\theta^4+33872\theta^3+83851\theta^2+107556\theta+49489\right)-2^{17} 3^{3} x^{7}\left(4895\theta^4+28154\theta^3+69267\theta^2+83564\theta+36929\right)-2^{20} 3^{4} x^{8}\left(44\theta^4+528\theta^3+247\theta^2+240\theta+274\right)+2^{23} 3^{5} x^{9}\left(664\theta^4+4760\theta^3+13781\theta^2+17353\theta+7679\right)+2^{26} 3^{6} x^{10}(\theta+1)(109\theta^3+651\theta^2+1373\theta+933)-2^{29} 3^{7} x^{11}(\theta+1)(\theta+2)(27\theta^2+153\theta+199)-2^{33} 3^{9} x^{12}(\theta+1)(\theta+2)^2(\theta+3)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -12, 180, -2736, 42948, ... --> OEIS Normalized instanton numbers (n0=1): 4, -31, 2252/9, -11109/4, 33312, ... ; Common denominator:...
\(-(16z+1)(432z^2+36z+1)(24z+1)^2(288z^2+48z+1)^2(8z-1)^3\)
| \(-\frac{ 1}{ 12}-\frac{ 1}{ 24}\sqrt{ 2}\) | \(-\frac{ 1}{ 16}\) | \(-\frac{ 1}{ 24}-\frac{ 1}{ 72}\sqrt{ 3}I\) | \(-\frac{ 1}{ 24}\) | \(-\frac{ 1}{ 24}+\frac{ 1}{ 72}\sqrt{ 3}I\) | \(-\frac{ 1}{ 12}+\frac{ 1}{ 24}\sqrt{ 2}\) | \(0\) | \(\frac{ 1}{ 8}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(0\) | \(\frac{ 1}{ 2}\) | \(2\) |
| \(3\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(3\) | \(0\) | \(\frac{ 3}{ 2}\) | \(2\) |
| \(4\) | \(2\) | \(2\) | \(1\) | \(2\) | \(4\) | \(0\) | \(2\) | \(3\) |
287
New Number: 12.6 | AESZ: | Superseeker: 5 953/3 | Hash: 4ea78627bfc56ef9555d9b6b3c949e7a
Degree: 12
\(\theta^4-x\theta(5\theta^3+46\theta^2+29\theta+6)-2 3 x^{2}\left(258\theta^4+1038\theta^3+1387\theta^2+818\theta+192\right)-2^{2} 3^{3} x^{3}\left(381\theta^4+1664\theta^3+2804\theta^2+2126\theta+624\right)-2^{4} 3^{3} x^{4}\left(1231\theta^4+5927\theta^3+11019\theta^2+9266\theta+3000\right)-2^{4} 3^{4} x^{5}\left(2621\theta^4+16730\theta^3+39069\theta^2+35141\theta+11748\right)-2^{5} 3^{5} x^{6}\left(150\theta^4+11268\theta^3+45560\theta^2+50253\theta+18756\right)+2^{6} 3^{7} x^{7}\left(1024\theta^4+800\theta^3-8483\theta^2-13641\theta-6108\right)+2^{8} 3^{7} x^{8}\left(1724\theta^4+6608\theta^3+1047\theta^2-7027\theta-4488\right)+2^{11} 3^{8} x^{9}\left(74\theta^4+1416\theta^3+1889\theta^2+687\theta-81\right)-2^{13} 3^{10} x^{10}\left(26\theta^4-16\theta^3-125\theta^2-128\theta-39\right)-2^{14} 3^{11} x^{11}(\theta+1)(16\theta^3+40\theta^2+31\theta+6)-2^{16} 3^{11} x^{12}(\theta+2)(\theta+1)(2\theta+3)^2\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, 72, 1344, 48600, ... --> OEIS Normalized instanton numbers (n0=1): 5, 83/2, 953/3, 5319, 97812, ... ; Common denominator:...
\(-(4z+1)(12z+1)(3z+1)(1728z^3+864z^2+36z-1)(-1-6z-36z^2+432z^3)^2\)
| ≈\(-0.450956\) | \(-\frac{ 1}{ 3}\) | \(-\frac{ 1}{ 4}\) | \(-\frac{ 1}{ 12}\) | ≈\(-0.067934\) | ≈\(-0.061146-0.08671I\) | ≈\(-0.061146+0.08671I\) | \(0\) | ≈\(0.01889\) | ≈\(0.205625\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(\frac{ 3}{ 2}\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(3\) | \(3\) | \(0\) | \(1\) | \(3\) | \(\frac{ 3}{ 2}\) |
| \(2\) | \(2\) | \(2\) | \(2\) | \(2\) | \(4\) | \(4\) | \(0\) | \(2\) | \(4\) | \(2\) |
288
New Number: 12.8 | AESZ: | Superseeker: 288 12718752 | Hash: 3373bbe821cc39369e8ba8c46ec88532
Degree: 12
\(\theta^4+2^{4} 3 x\left(112\theta^4+32\theta^3+40\theta^2+24\theta+5\right)+2^{13} x^{2}\left(1408\theta^4+1312\theta^3+1596\theta^2+784\theta+165\right)+2^{22} 3 x^{3}\left(988\theta^4+2088\theta^3+2591\theta^2+1485\theta+372\right)+2^{28} x^{4}\left(24464\theta^4+111040\theta^3+165136\theta^2+111992\theta+31983\right)+2^{38} 3^{2} x^{5}\left(288\theta^4+6544\theta^3+13980\theta^2+11216\theta+3605\right)-2^{46} x^{6}\left(14528\theta^4-36480\theta^3-205340\theta^2-205716\theta-76023\right)-2^{55} 3 x^{7}\left(4848\theta^4+13680\theta^3-20224\theta^2-34444\theta-16035\right)-2^{64} 3^{2} x^{8}\left(384\theta^4+4704\theta^3+2868\theta^2-852\theta-1307\right)+2^{74} 3 x^{9}\left(388\theta^4-1800\theta^3-3283\theta^2-2097\theta-333\right)+2^{80} 3^{2} x^{10}\left(784\theta^4+1184\theta^3+240\theta^2-592\theta-297\right)+2^{93} 3^{3} x^{11}(4\theta^2+8\theta+5)(\theta+1)^2+2^{100} 3^{2} x^{12}(\theta+2)(\theta+1)(2\theta+3)^2\)
Maple LaTexCoefficients of the holomorphic solution: 1, -240, 68880, -22281984, 7875829008, ... --> OEIS Normalized instanton numbers (n0=1): 288, -71872, 12718752, -4499223616, 1510063178336, ... ; Common denominator:...
\((1+768z+65536z^2)(256z+1)^2(512z+1)^2(201326592z^3-1536z-1)^2\)
| \(-\frac{ 3}{ 512}-\frac{ 1}{ 512}\sqrt{ 5}\) | \(-\frac{ 1}{ 256}\) | ≈\(-0.002348\) | \(-\frac{ 1}{ 512}\) | \(-\frac{ 3}{ 512}+\frac{ 1}{ 512}\sqrt{ 5}\) | ≈\(-0.000695\) | \(0\) | ≈\(0.003043\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(0\) | \(1\) | \(\frac{ 3}{ 2}\) |
| \(1\) | \(\frac{ 1}{ 2}\) | \(3\) | \(\frac{ 1}{ 2}\) | \(1\) | \(3\) | \(0\) | \(3\) | \(\frac{ 3}{ 2}\) |
| \(2\) | \(1\) | \(4\) | \(1\) | \(2\) | \(4\) | \(0\) | \(4\) | \(2\) |
289
New Number: 12.9 | AESZ: | Superseeker: 800 38825120 | Hash: 7e2f8423069147eb36cfd1d714d1996a
Degree: 12
\(\theta^4+2^{4} x\left(288\theta^4-96\theta^3-24\theta^2+24\theta+7\right)+2^{13} x^{2}\left(864\theta^4-240\theta^3+438\theta^2+96\theta-7\right)+2^{20} x^{3}\left(3856\theta^4+1152\theta^3+1036\theta^2+192\theta-53\right)+2^{30} x^{4}\left(636\theta^4-1440\theta^3-2303\theta^2-1988\theta-672\right)-2^{38} x^{5}\left(320\theta^4+7928\theta^3+14109\theta^2+11270\theta+3517\right)-2^{48} x^{6}\left(134\theta^4+1830\theta^3+3688\theta^2+3585\theta+1195\right)-2^{56} x^{7}\left(187\theta^4+356\theta^3-2355\theta^2-2866\theta-1199\right)-2^{65} x^{8}\left(91\theta^4+202\theta^3-1069\theta^2-2020\theta-948\right)-2^{74} x^{9}\left(2\theta^4-120\theta^3-211\theta^2-198\theta-69\right)+2^{84} x^{10}\left(\theta^4+44\theta^3+122\theta^2+121\theta+41\right)+2^{92} x^{11}(\theta^2+2\theta+2)(\theta+1)^2+2^{101} x^{12}(\theta+1)^2(\theta+2)^2\)
Maple LaTexCoefficients of the holomorphic solution: 1, -112, 25872, -5691136, 1522998544, ... --> OEIS Normalized instanton numbers (n0=1): 800, -121088, 38825120, -15641910336, 7303803435104, ... ; Common denominator:...
\((256z-1)(512z+1)(65536z^2-256z-1)(256z+1)^2(67108864z^3+1792z+1)^2\)
| \(-\frac{ 1}{ 256}\) | \(\frac{ 1}{ 512}-\frac{ 1}{ 512}\sqrt{ 5}\) | \(-\frac{ 1}{ 512}\) | ≈\(-0.000552\) | \(0\) | ≈\(0.000276-0.00519I\) | ≈\(0.000276+0.00519I\) | \(\frac{ 1}{ 256}\) | \(\frac{ 1}{ 512}+\frac{ 1}{ 512}\sqrt{ 5}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(3\) | \(0\) | \(3\) | \(3\) | \(1\) | \(1\) | \(2\) |
| \(1\) | \(2\) | \(2\) | \(4\) | \(0\) | \(4\) | \(4\) | \(2\) | \(2\) | \(2\) |
290
New Number: 13.10 | AESZ: | Superseeker: 4 -628/9 | Hash: 2a9fda379889eb2fd218bd01f2520f7a
Degree: 13
\(\theta^4-2^{2} x\left(35\theta^4+38\theta^3+35\theta^2+16\theta+3\right)+2^{4} x^{2}\left(546\theta^4+1068\theta^3+1287\theta^2+790\theta+201\right)-2^{6} x^{3}\left(4928\theta^4+12888\theta^3+17829\theta^2+12673\theta+3693\right)+2^{8} x^{4}\left(28123\theta^4+88408\theta^3+131977\theta^2+98226\theta+29511\right)-2^{10} 3^{2} x^{5}\left(11315\theta^4+41094\theta^3+65088\theta^2+47691\theta+13532\right)+2^{13} 3^{2} x^{6}\left(11674\theta^4+48674\theta^3+79399\theta^2+52683\theta+11716\right)-2^{15} 3^{3} x^{7}\left(2063\theta^4+11102\theta^3+11184\theta^2-9217\theta-10762\right)-2^{17} 3^{4} x^{8}\left(3277\theta^4+16284\theta^3+42329\theta^2+57018\theta+27266\right)+2^{20} 3^{5} x^{9}\left(1124\theta^4+7114\theta^3+18121\theta^2+22265\theta+10018\right)+2^{24} 3^{6} x^{10}(\theta+1)(\theta^3-105\theta^2-277\theta-267)-2^{25} 3^{7} x^{11}(\theta+1)(\theta+2)(93\theta^2+441\theta+607)+2^{27} 3^{10} x^{12}(\theta+3)(\theta+2)(\theta+1)(\theta+6)+2^{30} 3^{10} x^{13}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 12, 180, 2928, 47556, ... --> OEIS Normalized instanton numbers (n0=1): 4, 5, -628/9, -2823/4, 672, ... ; Common denominator:...
\((8z-1)(10368z^3-1728z^2+72z-1)(12z-1)^2(288z^2-24z+1)^2(4z+1)^3\)
| \(-\frac{ 1}{ 4}\) | \(0\) | ≈\(0.027033-0.011216I\) | ≈\(0.027033+0.011216I\) | \(\frac{ 1}{ 24}-\frac{ 1}{ 24}I\) | \(\frac{ 1}{ 24}+\frac{ 1}{ 24}I\) | \(\frac{ 1}{ 12}\) | ≈\(0.112601\) | \(\frac{ 1}{ 8}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(\frac{ 1}{ 2}\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(2\) |
| \(\frac{ 3}{ 2}\) | \(0\) | \(1\) | \(1\) | \(3\) | \(3\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(3\) |
| \(2\) | \(0\) | \(2\) | \(2\) | \(4\) | \(4\) | \(1\) | \(2\) | \(2\) | \(4\) |
291
New Number: 13.11 | AESZ: | Superseeker: 7 -2044/9 | Hash: d6e183df7853fe5068c8b8cdeb3f63cb
Degree: 13
\(\theta^4-x\left(98\theta^4+164\theta^3+137\theta^2+55\theta+9\right)+x^{2}\left(3822\theta^4+11400\theta^3+14901\theta^2+8746\theta+2007\right)-x^{3}\left(64148\theta^4+196344\theta^3+271665\theta^2+199855\theta+60354\right)+x^{4}\left(802771\theta^4+2242504\theta^3+2203855\theta^2+1316868\theta+390636\right)-2 3 x^{5}\left(1040145\theta^4+2982426\theta^3+3578912\theta^2+1897395\theta+345411\right)+2 3^{2} x^{6}\left(1927994\theta^4+4917832\theta^3+7329041\theta^2+5154630\theta+1338003\right)-2 3^{5} x^{7}\left(219316\theta^4+761432\theta^3+1064075\theta^2+703129\theta+181966\right)+3^{4} x^{8}\left(754759\theta^4+7471824\theta^3+13904030\theta^2+8830464\theta+1544112\right)+3^{7} x^{9}\left(174966\theta^4+736236\theta^3+1307237\theta^2+1340471\theta+568265\right)-3^{10} x^{10}(\theta+1)(8018\theta^3+62342\theta^2+139257\theta+108861)-3^{9} x^{11}(\theta+1)(\theta+2)(28988\theta^2+81396\theta+36331)+3^{12} x^{12}(\theta+3)(\theta+2)(\theta+1)(1061\theta+5386)+2 3^{15} 17 x^{13}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 9, 135, 2115, 18063, ... --> OEIS Normalized instanton numbers (n0=1): 7, -31/4, -2044/9, -1380, -8520, ... ; Common denominator:...
\((2z-1)(4131z^3-2187z^2+81z-1)(3z-1)^2(81z^2-6z+1)^2(z+1)^3\)
| \(-1\) | \(0\) | ≈\(0.019487-0.01067I\) | ≈\(0.019487+0.01067I\) | \(\frac{ 1}{ 27}-\frac{ 2}{ 27}\sqrt{ 2}I\) | \(\frac{ 1}{ 27}+\frac{ 2}{ 27}\sqrt{ 2}I\) | \(\frac{ 1}{ 3}\) | ≈\(0.490438\) | \(\frac{ 1}{ 2}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(\frac{ 1}{ 2}\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(2\) |
| \(\frac{ 3}{ 2}\) | \(0\) | \(1\) | \(1\) | \(3\) | \(3\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(3\) |
| \(2\) | \(0\) | \(2\) | \(2\) | \(4\) | \(4\) | \(1\) | \(2\) | \(2\) | \(4\) |
292
New Number: 13.12 | AESZ: | Superseeker: 76/3 746444/81 | Hash: fec1670f7378fb309308803574ce2a00
Degree: 13
\(3^{2} \theta^4+2^{2} 3 x\left(4\theta^4-208\theta^3-189\theta^2-85\theta-17\right)-2^{4} x^{2}\left(5120\theta^4-7168\theta^3-21704\theta^2-15788\theta-5307\right)+2^{9} x^{3}\left(6080\theta^4+28992\theta^3-21720\theta^2-27270\theta-13529\right)+2^{12} x^{4}\left(40096\theta^4-258688\theta^3-41760\theta^2+16820\theta+38071\right)-2^{17} x^{5}\left(123088\theta^4-63104\theta^3+45236\theta^2+55562\theta+46257\right)+2^{21} x^{6}\left(219712\theta^4+380352\theta^3+753688\theta^2+810222\theta+409897\right)-2^{24} x^{7}\left(107008\theta^4+264320\theta^3+651536\theta^2+1298596\theta+1113327\right)-2^{28} x^{8}\left(704944\theta^4+3925888\theta^3+9920672\theta^2+12076292\theta+5776605\right)+2^{34} x^{9}\left(220796\theta^4+1480752\theta^3+4427225\theta^2+6675624\theta+4170854\right)-2^{36} 3 x^{10}\left(9216\theta^4-66432\theta^3-131864\theta^2+696808\theta+1370197\right)-2^{40} 3 x^{11}\left(168448\theta^4+1796608\theta^3+7226400\theta^2+13138336\theta+9227347\right)+2^{47} 3^{2} x^{12}\left(3584\theta^4+43776\theta^3+208688\theta^2+457392\theta+385875\right)-2^{52} 3^{2} x^{13}(4\theta+15)^2(4\theta+13)^2\)
Maple LaTexCoefficients of the holomorphic solution: 1, 68/3, 1036/3, 44464/27, -8491132/81, ... --> OEIS Normalized instanton numbers (n0=1): 76/3, -3641/9, 746444/81, -69221068/243, 7315935712/729, ... ; Common denominator:...
\(-(-1+16z)(16z-3)^2(16z+1)^2(3072z^2-48z-1)^2(1024z^2-48z+1)^2\)
| \(-\frac{ 1}{ 16}\) | \(\frac{ 1}{ 128}-\frac{ 1}{ 384}\sqrt{ 57}\) | \(0\) | \(\frac{ 3}{ 128}-\frac{ 1}{ 128}\sqrt{ 7}I\) | \(\frac{ 3}{ 128}+\frac{ 1}{ 128}\sqrt{ 7}I\) | \(\frac{ 1}{ 128}+\frac{ 1}{ 384}\sqrt{ 57}\) | \(\frac{ 1}{ 16}\) | \(\frac{ 3}{ 16}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 13}{ 4}\) |
| \(\frac{ 1}{ 2}\) | \(1\) | \(0\) | \(\frac{ 1}{ 2}\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(1\) | \(\frac{ 13}{ 4}\) |
| \(\frac{ 1}{ 2}\) | \(3\) | \(0\) | \(\frac{ 1}{ 2}\) | \(\frac{ 1}{ 2}\) | \(3\) | \(1\) | \(-2\) | \(\frac{ 15}{ 4}\) |
| \(1\) | \(4\) | \(0\) | \(1\) | \(1\) | \(4\) | \(2\) | \(3\) | \(\frac{ 15}{ 4}\) |
293
New Number: 13.13 | AESZ: | Superseeker: 32 74144 | Hash: e20067c633b6371dc19f760a1140f0e4
Degree: 13
\(\theta^4-2^{3} x\left(74\theta^4+52\theta^3+70\theta^2+44\theta+11\right)+2^{6} x^{2}\left(1948\theta^4+2320\theta^3+3750\theta^2+3244\theta+1117\right)-2^{11} x^{3}\left(5498\theta^4+9708\theta^3+17699\theta^2+12099\theta+2024\right)+2^{12} x^{4}\left(90192\theta^4+243456\theta^3+317216\theta^2-2080\theta-132883\right)+2^{16} x^{5}\left(35024\theta^4+171680\theta^3+1168736\theta^2+2029296\theta+1162051\right)-2^{20} x^{6}\left(249200\theta^4+1529280\theta^3+3887240\theta^2+5111280\theta+2830091\right)+2^{24} x^{7}\left(6224\theta^4+297952\theta^3+1078344\theta^2+1331848\theta+442349\right)+2^{29} x^{8}\left(78896\theta^4+725696\theta^3+2501496\theta^2+3908720\theta+2314163\right)+2^{34} x^{9}\left(9584\theta^4+62208\theta^3+120960\theta^2+36216\theta-71103\right)+2^{38} x^{10}\left(2864\theta^4+44992\theta^3+291624\theta^2+843472\theta+893907\right)-2^{42} x^{11}\left(8176\theta^4+131296\theta^3+780536\theta^2+2035976\theta+1968867\right)-2^{47} 3 x^{12}\left(752\theta^4+11328\theta^3+62952\theta^2+153648\theta+139383\right)-2^{52} 3^{2} x^{13}\left((2\theta+7)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 88, 6576, 475776, 37804816, ... --> OEIS Normalized instanton numbers (n0=1): 32, 1048, 74144, 7046865, 788076384, ... ; Common denominator:...
\(-(16z-1)(262144z^4-8192z^3+2304z^2-256z+1)(48z-1)^2(16z+1)^2(512z^2+128z-1)^2\)
| \(-\frac{ 1}{ 8}-\frac{ 3}{ 32}\sqrt{ 2}\) | \(-\frac{ 1}{ 16}\) | ≈\(-0.024399\) | ≈\(-0.024399\) | \(0\) | ≈\(0.004052\) | \(-\frac{ 1}{ 8}+\frac{ 3}{ 32}\sqrt{ 2}\) | \(\frac{ 1}{ 48}\) | \(\frac{ 1}{ 16}\) | ≈\(0.075996\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 7}{ 2}\) |
| \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(\frac{ 7}{ 2}\) |
| \(3\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(0\) | \(1\) | \(3\) | \(-2\) | \(1\) | \(1\) | \(\frac{ 7}{ 2}\) |
| \(4\) | \(1\) | \(2\) | \(2\) | \(0\) | \(2\) | \(4\) | \(3\) | \(2\) | \(2\) | \(\frac{ 7}{ 2}\) |
294
New Number: 13.14 | AESZ: | Superseeker: 20/3 36340/81 | Hash: 4b391bfc7d7d7a60edd430907aff9fae
Degree: 13
\(3^{2} \theta^4+2^{2} 3 x\left(47\theta^4-50\theta^3-45\theta^2-20\theta-4\right)+2^{4} x^{2}\left(511\theta^4-1052\theta^3+179\theta^2+302\theta+132\right)-2^{7} x^{3}\left(179\theta^4-306\theta^3+1857\theta^2+2226\theta+931\right)-2^{8} x^{4}\left(2396\theta^4+17992\theta^3+43050\theta^2+42004\theta+13733\right)-2^{10} x^{5}\left(19724\theta^4+94712\theta^3+170136\theta^2+115772\theta+521\right)-2^{12} x^{6}\left(1556\theta^4-52704\theta^3-398172\theta^2-916440\theta-712527\right)+2^{15} x^{7}\left(62300\theta^4+489880\theta^3+1536500\theta^2+2159040\theta+1096749\right)-2^{18} x^{8}\left(8756\theta^4+79664\theta^3+485090\theta^2+1462308\theta+1567885\right)-2^{20} x^{9}\left(45096\theta^4+509616\theta^3+2195020\theta^2+4371756\theta+3428277\right)+2^{22} x^{10}\left(43984\theta^4+538112\theta^3+2558944\theta^2+5583456\theta+4682427\right)-2^{25} x^{11}\left(7792\theta^4+99808\theta^3+490272\theta^2+1087312\theta+914209\right)+2^{28} x^{12}\left(592\theta^4+7872\theta^3+39704\theta^2+89808\theta+76717\right)-2^{31} x^{13}\left((2\theta+7)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 16/3, 52/3, 3200/27, 129668/81, ... --> OEIS Normalized instanton numbers (n0=1): 20/3, -410/9, 36340/81, -5386783/972, 57719264/729, ... ; Common denominator:...
\(-(8z-1)(1024z^4-2048z^3+144z^2-4z+1)(8z-3)^2(8z+1)^2(32z^2-32z-1)^2\)
| \(-\frac{ 1}{ 8}\) | \(\frac{ 1}{ 2}-\frac{ 3}{ 8}\sqrt{ 2}\) | ≈\(-0.015388\) | ≈\(-0.015388\) | \(0\) | ≈\(0.102801\) | \(\frac{ 1}{ 8}\) | \(\frac{ 3}{ 8}\) | \(\frac{ 1}{ 2}+\frac{ 3}{ 8}\sqrt{ 2}\) | ≈\(1.927975\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 7}{ 2}\) |
| \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(\frac{ 7}{ 2}\) |
| \(\frac{ 1}{ 2}\) | \(3\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(-2\) | \(3\) | \(1\) | \(\frac{ 7}{ 2}\) |
| \(1\) | \(4\) | \(2\) | \(2\) | \(0\) | \(2\) | \(2\) | \(3\) | \(4\) | \(2\) | \(\frac{ 7}{ 2}\) |
295
New Number: 13.15 | AESZ: | Superseeker: 6 626/3 | Hash: 3e24fdfe8119ac950ce846460f109e44
Degree: 13
\(\theta^4-2 x\left(16\theta^4+50\theta^3+39\theta^2+14\theta+2\right)-2^{2} x^{2}\left(219\theta^4+390\theta^3+335\theta^2+214\theta+62\right)-2^{4} x^{3}\left(115\theta^4+1068\theta^3+2660\theta^2+2022\theta+582\right)+2^{6} x^{4}\left(122\theta^4-788\theta^3+151\theta^2-913\theta-696\right)-2^{8} 3 x^{5}\left(303\theta^4-1488\theta^3-2955\theta^2-2550\theta-827\right)-2^{10} 3 x^{6}\left(37\theta^4+714\theta^3-5760\theta^2-8319\theta-3550\right)-2^{13} 3 x^{7}\left(101\theta^4+82\theta^3+102\theta^2-1679\theta-1322\right)+2^{15} 3 x^{8}\left(48\theta^4+948\theta^3-461\theta^2-1447\theta-628\right)-2^{17} x^{9}\left(89\theta^4-4392\theta^3-6123\theta^2-450\theta+1902\right)-2^{20} x^{10}\left(121\theta^4-532\theta^3-3072\theta^2-3697\theta-1348\right)+2^{23} 5 x^{11}(\theta+1)(21\theta^3+63\theta^2+206\theta+218)+2^{25} 5^{2} x^{12}(\theta+2)(\theta+1)(2\theta^2-12\theta-27)+2^{27} 5^{3} x^{13}(\theta+1)(\theta+2)^2(\theta+3)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 4, 76, 1936, 57820, ... --> OEIS Normalized instanton numbers (n0=1): 6, 41/4, 626/3, 12349/8, 33062, ... ; Common denominator:...
\((4z-1)(4z+1)(16z^2+4z+1)(640z^3+96z^2+48z-1)(1+6z-48z^2+320z^3)^2\)
| \(-\frac{ 1}{ 4}\) | \(-\frac{ 1}{ 8}-\frac{ 1}{ 8}\sqrt{ 3}I\) | \(-\frac{ 1}{ 8}+\frac{ 1}{ 8}\sqrt{ 3}I\) | ≈\(-0.084967-0.266773I\) | ≈\(-0.084967+0.266773I\) | ≈\(-0.082432\) | \(0\) | ≈\(0.019933\) | ≈\(0.116216-0.156217I\) | ≈\(0.116216+0.156217I\) | \(\frac{ 1}{ 4}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(2\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(3\) | \(0\) | \(1\) | \(3\) | \(3\) | \(1\) | \(2\) |
| \(2\) | \(2\) | \(2\) | \(2\) | \(2\) | \(4\) | \(0\) | \(2\) | \(4\) | \(4\) | \(2\) | \(3\) |
296
New Number: 13.16 | AESZ: | Superseeker: 5 581/3 | Hash: 2ab5512d2cfda3cde6ee0ea98a12d6fb
Degree: 13
\(\theta^4-x\left(106\theta^4+140\theta^3+125\theta^2+55\theta+10\right)+x^{2}\left(2472+4265\theta^4+12596\theta^3+15925\theta^2+9718\theta\right)-2^{3} x^{3}\left(9346\theta^4+58443\theta^3+105118\theta^2+80373\theta+24412\right)+2^{4} 3 x^{4}\left(1747\theta^4+173306\theta^3+488163\theta^2+460544\theta+161900\right)+2^{6} 3 x^{5}\left(108841\theta^4-198029\theta^3-1835967\theta^2-2248271\theta-919518\right)-2^{8} 3 x^{6}\left(510411\theta^4+1710438\theta^3-2652339\theta^2-5816622\theta-2956384\right)+2^{12} 3 x^{7}\left(213944\theta^4+2327365\theta^3+1622852\theta^2-837189\theta-1027734\right)+2^{10} 3 x^{8}\left(4640003\theta^4-76516006\theta^3-140342311\theta^2-92680566\theta-16297224\right)-2^{13} x^{9}\left(56543147\theta^4-21416544\theta^3-251991507\theta^2-314165376\theta-118113840\right)+2^{16} x^{10}\left(70691941\theta^4+213840362\theta^3+253613996\theta^2+121602823\theta+15102754\right)-2^{19} 73 x^{11}(\theta+1)(680053\theta^3+2794143\theta^2+4238129\theta+2311527)+2^{22} 73^{2} x^{12}(\theta+2)(\theta+1)(3707\theta^2+13713\theta+13693)-2^{25} 3^{2} 73^{3} x^{13}(\theta+1)(\theta+2)^2(\theta+3)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 10, 118, 1864, 38566, ... --> OEIS Normalized instanton numbers (n0=1): 5, -53/4, 581/3, -1231, 19810, ... ; Common denominator:...
\(-(9z-1)(8z-1)(4672z^3-840z^2+57z-1)(64z^2-8z+1)(1-12z-192z^2+2336z^3)^2\)
| ≈\(-0.071938\) | \(0\) | ≈\(0.026164\) | \(\frac{ 1}{ 16}-\frac{ 1}{ 16}\sqrt{ 3}I\) | \(\frac{ 1}{ 16}+\frac{ 1}{ 16}\sqrt{ 3}I\) | ≈\(0.076815-0.047751I\) | ≈\(0.076815+0.047751I\) | ≈\(0.077065-0.003429I\) | ≈\(0.077065+0.003429I\) | \(\frac{ 1}{ 9}\) | \(\frac{ 1}{ 8}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(2\) |
| \(3\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(3\) | \(3\) | \(1\) | \(1\) | \(2\) |
| \(4\) | \(0\) | \(2\) | \(2\) | \(2\) | \(2\) | \(2\) | \(4\) | \(4\) | \(2\) | \(2\) | \(3\) |
297
New Number: 15.1 | AESZ: | Superseeker: 800 38825120 | Hash: c26e6797c51f4c09c1dfbc9e354ce168
Degree: 15
\(\theta^4+2^{4} x\left(240\theta^4-96\theta^3-24\theta^2+24\theta+7\right)+2^{12} x^{2}\left(912\theta^4-192\theta^3+948\theta^2+120\theta-35\right)-2^{21} x^{3}\left(240\theta^4-1152\theta^3+832\theta^2+156\theta-5\right)-2^{29} x^{4}\left(2064\theta^4+5280\theta^3+4834\theta^2+3988\theta+1289\right)+2^{36} x^{5}\left(928\theta^4-10496\theta^3-26568\theta^2-20840\theta-6149\right)+2^{44} x^{6}\left(5472\theta^4+47424\theta^3+81628\theta^2+53832\theta+15073\right)-2^{54} x^{7}\left(736\theta^4+1808\theta^3-13652\theta^2-22662\theta-9257\right)+2^{62} x^{8}\left(228\theta^4-11376\theta^3-49855\theta^2-49982\theta-17627\right)+2^{72} x^{9}\left(111\theta^4+2454\theta^3+5183\theta^2+855\theta-620\right)-2^{80} x^{10}\left(319\theta^4+1592\theta^3-3479\theta^2-8814\theta-4317\right)+2^{89} x^{11}\left(63\theta^4-102\theta^3-2675\theta^2-3688\theta-1502\right)+2^{98} x^{12}\left(10\theta^4+408\theta^3+1273\theta^2+1278\theta+431\right)-2^{108} x^{13}\left(4\theta^4+68\theta^3+179\theta^2+175\theta+59\right)+2^{116} x^{14}(5\theta^2+22\theta+22)(\theta+1)^2-2^{125} x^{15}(\theta+1)^2(\theta+2)^2\)
Maple LaTexCoefficients of the holomorphic solution: 1, -112, 25872, -5691136, 1522998544, ... --> OEIS Normalized instanton numbers (n0=1): 800, -121088, 38825120, -15641910336, 7303803435104, ... ; Common denominator:...
\(-(512z+1)(65536z^2-256z-1)(256z+1)^2(67108864z^3+1792z+1)^2(256z-1)^4\)
| \(-\frac{ 1}{ 256}\) | \(\frac{ 1}{ 512}-\frac{ 1}{ 512}\sqrt{ 5}\) | \(-\frac{ 1}{ 512}\) | ≈\(-0.000552\) | \(0\) | ≈\(0.000276-0.00519I\) | ≈\(0.000276+0.00519I\) | \(\frac{ 1}{ 256}\) | \(\frac{ 1}{ 512}+\frac{ 1}{ 512}\sqrt{ 5}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(3\) | \(0\) | \(3\) | \(3\) | \(1\) | \(1\) | \(2\) |
| \(1\) | \(2\) | \(2\) | \(4\) | \(0\) | \(4\) | \(4\) | \(2\) | \(2\) | \(2\) |
298
New Number: 13.2 | AESZ: | Superseeker: 288 -8252768 | Hash: ad47c122958add1c452a9858793ef177
Degree: 13
\(\theta^4-2^{4} x\left(192\theta^4+352\theta^3+392\theta^2+216\theta+49\right)+2^{12} x^{2}\left(1312\theta^4+2912\theta^3+5328\theta^2+4968\theta+1777\right)-2^{21} x^{3}\left(3336\theta^4+7360\theta^3+12252\theta^2+14040\theta+6269\right)+2^{28} x^{4}\left(26000\theta^4+61440\theta^3+92496\theta^2+79216\theta+30659\right)-2^{38} x^{5}\left(19848\theta^4+49192\theta^3+87106\theta^2+61486\theta+15137\right)+2^{46} x^{6}\left(48464\theta^4+126184\theta^3+248968\theta^2+204418\theta+60711\right)-2^{52} x^{7}\left(370576\theta^4+1125248\theta^3+2210040\theta^2+2071840\theta+776313\right)+2^{64} x^{8}\left(32992\theta^4+127280\theta^3+257876\theta^2+261776\theta+109291\right)-2^{71} x^{9}\left(66640\theta^4+329440\theta^3+743448\theta^2+827560\theta+373765\right)+2^{81} x^{10}\left(11376\theta^4+70016\theta^3+181088\theta^2+224296\theta+110253\right)-2^{88} x^{11}\left(9872\theta^4+73152\theta^3+216216\theta^2+297488\theta+159121\right)+2^{99} x^{12}\left(304\theta^4+2640\theta^3+8824\theta^2+13396\theta+7763\right)-2^{108} x^{13}\left((2\theta+5)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 784, 486672, 279216384, 154637278480, ... --> OEIS Normalized instanton numbers (n0=1): 288, 59200, -8252768, -1223488576, 585571467872, ... ; Common denominator:...
\(-(1-768z+65536z^2)(512z-1)^2(134217728z^3-655360z^2+256z-1)^2(256z-1)^3\)
| \(0\) | ≈\(3.7e-05-0.001244I\) | ≈\(3.7e-05+0.001244I\) | \(\frac{ 3}{ 512}-\frac{ 1}{ 512}\sqrt{ 5}\) | \(\frac{ 1}{ 512}\) | \(\frac{ 1}{ 256}\) | ≈\(0.004808\) | \(\frac{ 3}{ 512}+\frac{ 1}{ 512}\sqrt{ 5}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 5}{ 2}\) |
| \(0\) | \(1\) | \(1\) | \(1\) | \(0\) | \(0\) | \(1\) | \(1\) | \(\frac{ 5}{ 2}\) |
| \(0\) | \(3\) | \(3\) | \(1\) | \(-1\) | \(0\) | \(3\) | \(1\) | \(\frac{ 5}{ 2}\) |
| \(0\) | \(4\) | \(4\) | \(2\) | \(1\) | \(0\) | \(4\) | \(2\) | \(\frac{ 5}{ 2}\) |
299
New Number: 13.3 | AESZ: | Superseeker: 4 52 | Hash: 9127ce057848ca38f220a7bb67e245a2
Degree: 13
\(\theta^4-2^{2} x\left(38\theta^4+50\theta^3+53\theta^2+28\theta+6\right)+2^{4} x^{2}\left(617\theta^4+1598\theta^3+2361\theta^2+1812\theta+586\right)-2^{8} x^{3}\left(1422\theta^4+5468\theta^3+10321\theta^2+9918\theta+3961\right)+2^{11} x^{4}\left(4165\theta^4+21060\theta^3+48228\theta^2+54855\theta+25440\right)-2^{14} x^{5}\left(8248\theta^4+50660\theta^3+135119\theta^2+175776\theta+91644\right)+2^{16} x^{6}\left(23161\theta^4+161282\theta^3+479205\theta^2+690060\theta+393943\right)-2^{20} x^{7}\left(12116\theta^4+89614\theta^3+279997\theta^2+425868\theta+256804\right)+2^{23} x^{8}\left(9924\theta^4+74644\theta^3+231233\theta^2+346097\theta+206261\right)-2^{27} x^{9}\left(3250\theta^4+24820\theta^3+75837\theta^2+107033\theta+58293\right)+2^{28} x^{10}\left(6672\theta^4+52000\theta^3+164304\theta^2+235440\theta+126113\right)-2^{32} x^{11}\left(1312\theta^4+10208\theta^3+32688\theta^2+49072\theta+28407\right)+2^{36} x^{12}\left(192\theta^4+1568\theta^3+4952\theta^2+7144\theta+3959\right)-2^{40} x^{13}\left((2\theta+5)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 24, 464, 8832, 178960, ... --> OEIS Normalized instanton numbers (n0=1): 4, 7/2, 52, 500, 2796, ... ; Common denominator:...
\(-(1-48z+256z^2)(8z-1)^2(512z^3-32z^2+20z-1)^2(16z-1)^3\)
| \(0\) | ≈\(0.005863-0.196043I\) | ≈\(0.005863+0.196043I\) | \(\frac{ 3}{ 32}-\frac{ 1}{ 32}\sqrt{ 5}\) | ≈\(0.050774\) | \(\frac{ 1}{ 16}\) | \(\frac{ 1}{ 8}\) | \(\frac{ 3}{ 32}+\frac{ 1}{ 32}\sqrt{ 5}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 5}{ 2}\) |
| \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(0\) | \(1\) | \(\frac{ 5}{ 2}\) |
| \(0\) | \(3\) | \(3\) | \(1\) | \(3\) | \(0\) | \(-1\) | \(1\) | \(\frac{ 5}{ 2}\) |
| \(0\) | \(4\) | \(4\) | \(2\) | \(4\) | \(0\) | \(1\) | \(2\) | \(\frac{ 5}{ 2}\) |
300
New Number: 13.4 | AESZ: | Superseeker: 128 341632 | Hash: e2189010cb583bd9f4eab25b75b409cf
Degree: 13
\(\theta^4-2^{5} x\left(4\theta^4+34\theta^3+28\theta^2+11\theta+2\right)-2^{8} x^{2}\left(380\theta^4-872\theta^3-2096\theta^2-1252\theta-351\right)+2^{14} x^{3}\left(1572\theta^4+2760\theta^3-6140\theta^2-4788\theta-1727\right)+2^{18} x^{4}\left(112\theta^4-71968\theta^3+30800\theta^2+34304\theta+16775\right)-2^{25} x^{5}\left(25792\theta^4-66000\theta^3+21380\theta^2+29896\theta+17669\right)+2^{30} x^{6}\left(147184\theta^4-74240\theta^3+128248\theta^2+131808\theta+68259\right)-2^{36} x^{7}\left(204848\theta^4+52096\theta^3+180984\theta^2+135280\theta+61687\right)+2^{42} x^{8}\left(149520\theta^4+15104\theta^3-78056\theta^2-161888\theta-66647\right)-2^{49} x^{9}\left(15408\theta^4-100672\theta^3-280440\theta^2-315312\theta-124965\right)-2^{56} x^{10}\left(10256\theta^4+80960\theta^3+191000\theta^2+198384\theta+76409\right)+2^{63} x^{11}\left(4880\theta^4+28864\theta^3+65080\theta^2+65776\theta+24913\right)-2^{73} x^{12}\left(112\theta^4+648\theta^3+1448\theta^2+1450\theta+545\right)+2^{79} x^{13}\left((2\theta+3)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 64, 4496, 339968, 27330832, ... --> OEIS Normalized instanton numbers (n0=1): 128, -4796, 341632, -31623118, 3395329408, ... ; Common denominator:...
\((128z-1)(4096z^2+64z-1)(1048576z^3-28672z^2+160z+1)^2(64z-1)^4\)
| \(-\frac{ 1}{ 128}-\frac{ 1}{ 128}\sqrt{ 5}\) | ≈\(-0.003609\) | \(0\) | \(\frac{ 1}{ 128}\) | \(-\frac{ 1}{ 128}+\frac{ 1}{ 128}\sqrt{ 5}\) | ≈\(0.015476-0.004977I\) | ≈\(0.015476+0.004977I\) | \(\frac{ 1}{ 64}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 3}{ 2}\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(\frac{ 3}{ 2}\) |
| \(1\) | \(3\) | \(0\) | \(1\) | \(1\) | \(3\) | \(3\) | \(0\) | \(\frac{ 3}{ 2}\) |
| \(2\) | \(4\) | \(0\) | \(2\) | \(2\) | \(4\) | \(4\) | \(0\) | \(\frac{ 3}{ 2}\) |