You searched for: Spectrum0=0,0,0,0
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361
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:...
\(-(-1+16z)(16z-3)^2(16z+1)^2(3072z^2-48z-1)^2(1024z^2-48z+1)^2\)
| \(-\frac{ 1}{ 16}\) | \(\frac{ 1}{ 128}-\frac{ 1}{ 384}\sqrt{ 57}\) | \(0\) | \(\frac{ 3}{ 128}-\frac{ 1}{ 128}\sqrt{ 7}I\) | \(\frac{ 3}{ 128}+\frac{ 1}{ 128}\sqrt{ 7}I\) | \(\frac{ 1}{ 128}+\frac{ 1}{ 384}\sqrt{ 57}\) | \(\frac{ 1}{ 16}\) | \(\frac{ 3}{ 16}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 13}{ 4}\) |
| \(\frac{ 1}{ 2}\) | \(1\) | \(0\) | \(\frac{ 1}{ 2}\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(1\) | \(\frac{ 13}{ 4}\) |
| \(\frac{ 1}{ 2}\) | \(3\) | \(0\) | \(\frac{ 1}{ 2}\) | \(\frac{ 1}{ 2}\) | \(3\) | \(1\) | \(-2\) | \(\frac{ 15}{ 4}\) |
| \(1\) | \(4\) | \(0\) | \(1\) | \(1\) | \(4\) | \(2\) | \(3\) | \(\frac{ 15}{ 4}\) |
362
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:...
\(-(16z-1)(262144z^4-8192z^3+2304z^2-256z+1)(48z-1)^2(16z+1)^2(512z^2+128z-1)^2\)
| \(-\frac{ 1}{ 8}-\frac{ 3}{ 32}\sqrt{ 2}\) | \(-\frac{ 1}{ 16}\) | ≈\(-0.024399\) | ≈\(-0.024399\) | \(0\) | ≈\(0.004052\) | \(-\frac{ 1}{ 8}+\frac{ 3}{ 32}\sqrt{ 2}\) | \(\frac{ 1}{ 48}\) | \(\frac{ 1}{ 16}\) | ≈\(0.075996\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 7}{ 2}\) |
| \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(\frac{ 7}{ 2}\) |
| \(3\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(0\) | \(1\) | \(3\) | \(-2\) | \(1\) | \(1\) | \(\frac{ 7}{ 2}\) |
| \(4\) | \(1\) | \(2\) | \(2\) | \(0\) | \(2\) | \(4\) | \(3\) | \(2\) | \(2\) | \(\frac{ 7}{ 2}\) |
363
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:...
\(-(8z-1)(1024z^4-2048z^3+144z^2-4z+1)(8z-3)^2(8z+1)^2(32z^2-32z-1)^2\)
| \(-\frac{ 1}{ 8}\) | \(\frac{ 1}{ 2}-\frac{ 3}{ 8}\sqrt{ 2}\) | ≈\(-0.015388\) | ≈\(-0.015388\) | \(0\) | ≈\(0.102801\) | \(\frac{ 1}{ 8}\) | \(\frac{ 3}{ 8}\) | \(\frac{ 1}{ 2}+\frac{ 3}{ 8}\sqrt{ 2}\) | ≈\(1.927975\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 7}{ 2}\) |
| \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(\frac{ 7}{ 2}\) |
| \(\frac{ 1}{ 2}\) | \(3\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(-2\) | \(3\) | \(1\) | \(\frac{ 7}{ 2}\) |
| \(1\) | \(4\) | \(2\) | \(2\) | \(0\) | \(2\) | \(2\) | \(3\) | \(4\) | \(2\) | \(\frac{ 7}{ 2}\) |
364
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:...
\((4z-1)(4z+1)(16z^2+4z+1)(640z^3+96z^2+48z-1)(1+6z-48z^2+320z^3)^2\)
| \(-\frac{ 1}{ 4}\) | \(-\frac{ 1}{ 8}-\frac{ 1}{ 8}\sqrt{ 3}I\) | \(-\frac{ 1}{ 8}+\frac{ 1}{ 8}\sqrt{ 3}I\) | ≈\(-0.084967-0.266773I\) | ≈\(-0.084967+0.266773I\) | ≈\(-0.082432\) | \(0\) | ≈\(0.019933\) | ≈\(0.116216-0.156217I\) | ≈\(0.116216+0.156217I\) | \(\frac{ 1}{ 4}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(2\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(3\) | \(0\) | \(1\) | \(3\) | \(3\) | \(1\) | \(2\) |
| \(2\) | \(2\) | \(2\) | \(2\) | \(2\) | \(4\) | \(0\) | \(2\) | \(4\) | \(4\) | \(2\) | \(3\) |
365
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:...
\(-(9z-1)(8z-1)(4672z^3-840z^2+57z-1)(64z^2-8z+1)(1-12z-192z^2+2336z^3)^2\)
| ≈\(-0.071938\) | \(0\) | ≈\(0.026164\) | \(\frac{ 1}{ 16}-\frac{ 1}{ 16}\sqrt{ 3}I\) | \(\frac{ 1}{ 16}+\frac{ 1}{ 16}\sqrt{ 3}I\) | ≈\(0.076815-0.047751I\) | ≈\(0.076815+0.047751I\) | ≈\(0.077065-0.003429I\) | ≈\(0.077065+0.003429I\) | \(\frac{ 1}{ 9}\) | \(\frac{ 1}{ 8}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(2\) |
| \(3\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(3\) | \(3\) | \(1\) | \(1\) | \(2\) |
| \(4\) | \(0\) | \(2\) | \(2\) | \(2\) | \(2\) | \(2\) | \(4\) | \(4\) | \(2\) | \(2\) | \(3\) |
366
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:...
\(-(512z+1)(65536z^2-256z-1)(256z+1)^2(67108864z^3+1792z+1)^2(256z-1)^4\)
| \(-\frac{ 1}{ 256}\) | \(\frac{ 1}{ 512}-\frac{ 1}{ 512}\sqrt{ 5}\) | \(-\frac{ 1}{ 512}\) | ≈\(-0.000552\) | \(0\) | ≈\(0.000276-0.00519I\) | ≈\(0.000276+0.00519I\) | \(\frac{ 1}{ 256}\) | \(\frac{ 1}{ 512}+\frac{ 1}{ 512}\sqrt{ 5}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(3\) | \(0\) | \(3\) | \(3\) | \(1\) | \(1\) | \(2\) |
| \(1\) | \(2\) | \(2\) | \(4\) | \(0\) | \(4\) | \(4\) | \(2\) | \(2\) | \(2\) |
367
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:...
\(-(1-768z+65536z^2)(512z-1)^2(134217728z^3-655360z^2+256z-1)^2(256z-1)^3\)
| \(0\) | ≈\(3.7e-05-0.001244I\) | ≈\(3.7e-05+0.001244I\) | \(\frac{ 3}{ 512}-\frac{ 1}{ 512}\sqrt{ 5}\) | \(\frac{ 1}{ 512}\) | \(\frac{ 1}{ 256}\) | ≈\(0.004808\) | \(\frac{ 3}{ 512}+\frac{ 1}{ 512}\sqrt{ 5}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 5}{ 2}\) |
| \(0\) | \(1\) | \(1\) | \(1\) | \(0\) | \(0\) | \(1\) | \(1\) | \(\frac{ 5}{ 2}\) |
| \(0\) | \(3\) | \(3\) | \(1\) | \(-1\) | \(0\) | \(3\) | \(1\) | \(\frac{ 5}{ 2}\) |
| \(0\) | \(4\) | \(4\) | \(2\) | \(1\) | \(0\) | \(4\) | \(2\) | \(\frac{ 5}{ 2}\) |
368
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:...
\(-(1-48z+256z^2)(8z-1)^2(512z^3-32z^2+20z-1)^2(16z-1)^3\)
| \(0\) | ≈\(0.005863-0.196043I\) | ≈\(0.005863+0.196043I\) | \(\frac{ 3}{ 32}-\frac{ 1}{ 32}\sqrt{ 5}\) | ≈\(0.050774\) | \(\frac{ 1}{ 16}\) | \(\frac{ 1}{ 8}\) | \(\frac{ 3}{ 32}+\frac{ 1}{ 32}\sqrt{ 5}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 5}{ 2}\) |
| \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(0\) | \(1\) | \(\frac{ 5}{ 2}\) |
| \(0\) | \(3\) | \(3\) | \(1\) | \(3\) | \(0\) | \(-1\) | \(1\) | \(\frac{ 5}{ 2}\) |
| \(0\) | \(4\) | \(4\) | \(2\) | \(4\) | \(0\) | \(1\) | \(2\) | \(\frac{ 5}{ 2}\) |
369
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:...
\((128z-1)(4096z^2+64z-1)(1048576z^3-28672z^2+160z+1)^2(64z-1)^4\)
| \(-\frac{ 1}{ 128}-\frac{ 1}{ 128}\sqrt{ 5}\) | ≈\(-0.003609\) | \(0\) | \(\frac{ 1}{ 128}\) | \(-\frac{ 1}{ 128}+\frac{ 1}{ 128}\sqrt{ 5}\) | ≈\(0.015476-0.004977I\) | ≈\(0.015476+0.004977I\) | \(\frac{ 1}{ 64}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 3}{ 2}\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(\frac{ 3}{ 2}\) |
| \(1\) | \(3\) | \(0\) | \(1\) | \(1\) | \(3\) | \(3\) | \(0\) | \(\frac{ 3}{ 2}\) |
| \(2\) | \(4\) | \(0\) | \(2\) | \(2\) | \(4\) | \(4\) | \(0\) | \(\frac{ 3}{ 2}\) |
370
New Number: 13.5 | AESZ: | Superseeker: 224 4999008 | Hash: 6d924b9c12ee7379761d409ee75e42ab
Degree: 13
\(\theta^4-2^{4} x\left(80\theta^4+160\theta^3+152\theta^2+72\theta+15\right)+2^{14} x^{2}\left(24\theta^4+240\theta^3+355\theta^2+230\theta+69\right)+2^{20} x^{3}\left(416\theta^4-2400\theta^3-6216\theta^2-4824\theta-1773\right)-2^{28} x^{4}\left(1840\theta^4-544\theta^3-15328\theta^2-15056\theta-6525\right)+2^{38} 3 x^{5}\left(236\theta^4+1040\theta^3-1629\theta^2-2248\theta-1208\right)+2^{47} 3 x^{6}\left(8\theta^4-1512\theta^3+192\theta^2+951\theta+786\right)-2^{53} 3 x^{7}\left(1568\theta^4-7952\theta^3-4278\theta^2-740\theta+1981\right)+2^{60} 3 x^{8}\left(6976\theta^4-6656\theta^3-9268\theta^2-7912\theta-55\right)-2^{70} x^{9}\left(6680\theta^4+8856\theta^3+8397\theta^2+3060\theta+1017\right)+2^{76} x^{10}\left(22672\theta^4+71840\theta^3+113068\theta^2+90072\theta+30483\right)-2^{84} x^{11}\left(12912\theta^4+62592\theta^3+128336\theta^2+126736\theta+49707\right)+2^{93} 7 x^{12}(2\theta+3)(164\theta^3+810\theta^2+1434\theta+891)-2^{102} 7^{2} x^{13}(\theta+2)^2(2\theta+3)(2\theta+5)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 240, 44304, 7503616, 1459723536, ... --> OEIS Normalized instanton numbers (n0=1): 224, -22712, 4999008, -855952448, 199163179936, ... ; Common denominator:...
\(-(65536z^2-256z+1)^2(117440512z^3-196608z^2+1)^2(256z-1)^3\)
| ≈\(-0.00161\) | \(0\) | ≈\(0.001642-0.00161I\) | ≈\(0.001642+0.00161I\) | \(\frac{ 1}{ 512}-\frac{ 1}{ 512}\sqrt{ 3}I\) | \(\frac{ 1}{ 512}+\frac{ 1}{ 512}\sqrt{ 3}I\) | \(\frac{ 1}{ 256}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 3}{ 2}\) |
| \(1\) | \(0\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(\frac{ 1}{ 2}\) | \(0\) | \(2\) |
| \(3\) | \(0\) | \(3\) | \(3\) | \(\frac{ 1}{ 2}\) | \(\frac{ 1}{ 2}\) | \(0\) | \(2\) |
| \(4\) | \(0\) | \(4\) | \(4\) | \(1\) | \(1\) | \(0\) | \(\frac{ 5}{ 2}\) |
371
New Number: 13.6 | AESZ: | Superseeker: 2 421/9 | Hash: 679aa37a05aafe03e8d68785d566fcfb
Degree: 13
\(\theta^4-x\left(217\theta^4+178\theta^3+178\theta^2+89\theta+18\right)+x^{2}\left(6192+24334\theta+39795\theta^2+33324\theta^3+20643\theta^4\right)-2^{3} x^{3}\left(139307\theta^4+333558\theta^3+457560\theta^2+315505\theta+89244\right)+2^{4} x^{4}\left(2283535\theta^4+7259062\theta^3+11103058\theta^2+8192571\theta+2419362\right)-2^{6} 3 x^{5}\left(3630237\theta^4+14551206\theta^3+23954402\theta^2+17624013\theta+4953960\right)+2^{6} 3^{2} x^{6}\left(9379387\theta^4+48172928\theta^3+74157721\theta^2+31932048\theta-1833876\right)+2^{9} 3^{5} x^{7}\left(495945\theta^4+2307886\theta^3+6892788\theta^2+10676039\theta+5452406\right)-2^{12} 3^{4} x^{8}\left(5269994\theta^4+31826568\theta^3+83327461\theta^2+106595346\theta+49104855\right)+2^{15} 3^{7} x^{9}\left(129774\theta^4+976140\theta^3+2673571\theta^2+3442327\theta+1597000\right)+2^{18} 3^{10} x^{10}(\theta+1)(6759\theta^3+40481\theta^2+97855\theta+79397)-2^{21} 3^{9} x^{11}(\theta+1)(\theta+2)(29107\theta^2+160713\theta+251822)-2^{27} 3^{12} x^{12}(\theta+3)(\theta+2)(\theta+1)(17\theta+4)+2^{29} 3^{15} 5 x^{13}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 18, 378, 8280, 187434, ... --> OEIS Normalized instanton numbers (n0=1): 2, -3/2, 421/9, -519/2, 285, ... ; Common denominator:...
\((16z-1)(19440z^3-2187z^2+81z-1)(24z-1)^2(648z^2-48z+1)^2(8z+1)^3\)
| \(-\frac{ 1}{ 8}\) | \(0\) | ≈\(0.032165-0.005771I\) | ≈\(0.032165+0.005771I\) | \(\frac{ 1}{ 27}-\frac{ 1}{ 108}\sqrt{ 2}I\) | \(\frac{ 1}{ 27}+\frac{ 1}{ 108}\sqrt{ 2}I\) | \(\frac{ 1}{ 24}\) | ≈\(0.04817\) | \(\frac{ 1}{ 16}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(\frac{ 1}{ 2}\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(2\) |
| \(\frac{ 3}{ 2}\) | \(0\) | \(1\) | \(1\) | \(3\) | \(3\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(3\) |
| \(2\) | \(0\) | \(2\) | \(2\) | \(4\) | \(4\) | \(1\) | \(2\) | \(2\) | \(4\) |
372
New Number: 13.7 | AESZ: | Superseeker: 10 7709/9 | Hash: 47093f7f3b7ab4544ef6b418bdae778b
Degree: 13
\(\theta^4+x\left(127\theta^4-2\theta^3+22\theta^2+23\theta+6\right)+x^{2}\left(4803\theta^4+1644\theta^3+3459\theta^2+430\theta-384\right)+2^{3} x^{3}\left(2507\theta^4+8118\theta^3-2448\theta^2-7127\theta-2940\right)-2^{4} x^{4}\left(94175\theta^4+88358\theta^3+133418\theta^2+111507\theta+38898\right)+2^{6} 3 x^{5}\left(22347\theta^4+197706\theta^3+783766\theta^2+893091\theta+359952\right)+2^{6} 3^{2} x^{6}\left(869067\theta^4+4718208\theta^3+11162457\theta^2+11758320\theta+4583500\right)-2^{9} 3^{3} x^{7}\left(245985\theta^4+1338174\theta^3+3414812\theta^2+4418167\theta+2103502\right)-2^{12} 3^{4} x^{8}\left(234234\theta^4+2167368\theta^3+7012373\theta^2+9416514\theta+4375751\right)+2^{15} 3^{5} x^{9}\left(81234\theta^4+643380\theta^3+1815861\theta^2+2193249\theta+947968\right)+2^{18} 3^{6} x^{10}(\theta+1)(15879\theta^3+214401\theta^2+816191\theta+896789)-2^{21} 3^{7} x^{11}(\theta+1)(\theta+2)(8037\theta^2+71103\theta+151546)+2^{27} 3^{9} x^{12}(\theta+3)(\theta+2)(\theta+1)(31\theta+152)-2^{29} 3^{9} 5 x^{13}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -6, 90, -1368, 21546, ... --> OEIS Normalized instanton numbers (n0=1): 10, -149/2, 7709/9, -27333/2, 242829, ... ; Common denominator:...
\(-(16z+1)(2160z^3+27z^2-9z+1)(24z+1)^2(72z^2-48z-1)^2(8z-1)^3\)
| ≈\(-0.100198\) | \(-\frac{ 1}{ 16}\) | \(-\frac{ 1}{ 24}\) | \(\frac{ 1}{ 3}-\frac{ 1}{ 4}\sqrt{ 2}\) | \(0\) | ≈\(0.043849-0.05194I\) | ≈\(0.043849+0.05194I\) | \(\frac{ 1}{ 8}\) | \(\frac{ 1}{ 3}+\frac{ 1}{ 4}\sqrt{ 2}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(0\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(2\) |
| \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(3\) | \(0\) | \(1\) | \(1\) | \(\frac{ 3}{ 2}\) | \(3\) | \(3\) |
| \(2\) | \(2\) | \(1\) | \(4\) | \(0\) | \(2\) | \(2\) | \(2\) | \(4\) | \(4\) |
373
New Number: 13.8 | AESZ: | Superseeker: 8 -830/9 | Hash: bcea3fff557004b4da26e9aa34caac6c
Degree: 13
\(\theta^4-x\left(55\theta^4+142\theta^3+112\theta^2+41\theta+6\right)+x^{2}\left(456\theta^4+4668\theta^3+7455\theta^2+3958\theta+696\right)+x^{3}\left(35078\theta^4+127188\theta^3+175671\theta^2+133507\theta+41718\right)+x^{4}\left(82753\theta^4+664768\theta^3+2450839\theta^2+2316756\theta+736812\right)-3 x^{5}\left(885105\theta^4+1342938\theta^3-883331\theta^2-2706576\theta-1350228\right)-2 3^{2} x^{6}\left(345501\theta^4+3334206\theta^3+4969485\theta^2+2964744\theta+630748\right)+2^{2} 3^{3} x^{7}\left(459939\theta^4+270666\theta^3-1625381\theta^2-2377792\theta-962956\right)+2^{4} 3^{4} x^{8}\left(112581\theta^4+699447\theta^3+1277449\theta^2+1022649\theta+314494\right)-2^{4} 3^{5} x^{9}\left(34101\theta^4-33864\theta^3-473835\theta^2-744726\theta-350272\right)-2^{5} 3^{6} x^{10}(\theta+1)(20847\theta^3+146325\theta^2+303230\theta+217616)+2^{6} 3^{7} x^{11}(\theta+1)(\theta+2)(1791\theta^2-1173\theta-14800)+2^{9} 3^{9} x^{12}(\theta+3)(\theta+2)(\theta+1)(52\theta+257)-2^{10} 3^{9} 17 x^{13}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 6, 90, 1044, -5670, ... --> OEIS Normalized instanton numbers (n0=1): 8, -45/2, -830/9, -5301/2, 2790, ... ; Common denominator:...
\(-(2z+1)(3672z^3+1728z^2-72z+1)(6z-1)^2(12z+1)^2(3z+1)^2(z-1)^3\)
| ≈\(-0.510076\) | \(-\frac{ 1}{ 2}\) | \(-\frac{ 1}{ 3}\) | \(-\frac{ 1}{ 12}\) | \(0\) | ≈\(0.019744-0.012003I\) | ≈\(0.019744+0.012003I\) | \(\frac{ 1}{ 6}\) | \(1\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(2\) |
| \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(3\) | \(0\) | \(1\) | \(1\) | \(3\) | \(\frac{ 3}{ 2}\) | \(3\) |
| \(2\) | \(2\) | \(1\) | \(4\) | \(0\) | \(2\) | \(2\) | \(4\) | \(2\) | \(4\) |
374
New Number: 13.9 | AESZ: | Superseeker: 8 2200/9 | Hash: 31ff3b7bd4c8fed070ee43b6903d3752
Degree: 13
\(\theta^4+2^{3} x\theta(4\theta^3-8\theta^2-5\theta-1)-2^{4} x^{2}\left(48\theta^4+120\theta^3+45\theta^2+74\theta+36\right)-2^{7} x^{3}\left(101\theta^4-342\theta^3-387\theta^2-410\theta-171\right)+2^{8} x^{4}\left(3121\theta^4+14104\theta^3+30889\theta^2+27720\theta+9351\right)+2^{11} 3^{2} x^{5}\left(655\theta^4+4062\theta^3+10081\theta^2+10272\theta+3856\right)-2^{12} 3^{2} x^{6}\left(2272\theta^4+2816\theta^3-9950\theta^2-18768\theta-8813\right)-2^{15} 3^{3} x^{7}\left(1546\theta^4+12172\theta^3+30708\theta^2+33880\theta+13843\right)+2^{16} 3^{4} x^{8}\left(1099\theta^4+1344\theta^3-11134\theta^2-23964\theta-13063\right)+2^{19} 3^{5} x^{9}\left(458\theta^4+4828\theta^3+15325\theta^2+19721\theta+8830\right)-2^{20} 3^{6} x^{10}(\theta+1)(368\theta^3+1752\theta^2+1297\theta-1035)-2^{23} 3^{7} x^{11}(\theta+1)(\theta+2)(39\theta^2+513\theta+1172)+2^{24} 3^{9} x^{12}(\theta+3)(\theta+2)(\theta+1)(17\theta+82)-2^{27} 3^{10} x^{13}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, 36, -192, -4284, ... --> OEIS Normalized instanton numbers (n0=1): 8, -75/2, 2200/9, -8117/2, 47936, ... ; Common denominator:...
\(-(8z+1)(5184z^3+432z^2-36z+1)(12z+1)^2(144z^2-24z-1)^2(4z-1)^3\)
| ≈\(-0.141868\) | \(-\frac{ 1}{ 8}\) | \(-\frac{ 1}{ 12}\) | \(\frac{ 1}{ 12}-\frac{ 1}{ 12}\sqrt{ 2}\) | \(0\) | ≈\(0.029267-0.022431I\) | ≈\(0.029267+0.022431I\) | \(\frac{ 1}{ 12}+\frac{ 1}{ 12}\sqrt{ 2}\) | \(\frac{ 1}{ 4}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(2\) |
| \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(3\) | \(0\) | \(1\) | \(1\) | \(3\) | \(\frac{ 3}{ 2}\) | \(3\) |
| \(2\) | \(2\) | \(1\) | \(4\) | \(0\) | \(2\) | \(2\) | \(4\) | \(2\) | \(4\) |
375
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:...
\((4z+1)(2z+1)^2(64z^2+24z+1)^2(160z^2+32z+1)^2(8z+1)^3\)
| \(-\frac{ 1}{ 2}\) | \(-\frac{ 3}{ 16}-\frac{ 1}{ 16}\sqrt{ 5}\) | \(-\frac{ 1}{ 4}\) | \(-\frac{ 1}{ 10}-\frac{ 1}{ 40}\sqrt{ 6}\) | \(-\frac{ 1}{ 8}\) | \(-\frac{ 3}{ 16}+\frac{ 1}{ 16}\sqrt{ 5}\) | \(-\frac{ 1}{ 10}+\frac{ 1}{ 40}\sqrt{ 6}\) | \(0\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(4\) |
| \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(0\) | \(\frac{ 1}{ 2}\) | \(1\) | \(0\) | \(4\) |
| \(-2\) | \(\frac{ 1}{ 2}\) | \(1\) | \(3\) | \(0\) | \(\frac{ 1}{ 2}\) | \(3\) | \(0\) | \(4\) |
| \(3\) | \(1\) | \(2\) | \(4\) | \(0\) | \(1\) | \(4\) | \(0\) | \(4\) |
376
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:...
\(-(-1+16z)(48z-1)^2(256z^2-32z-5)^2(256z^2+16z-1)^2(16z+1)^3\)
| \(-\frac{ 1}{ 32}-\frac{ 1}{ 32}\sqrt{ 5}\) | \(\frac{ 1}{ 16}-\frac{ 1}{ 16}\sqrt{ 6}\) | \(-\frac{ 1}{ 16}\) | \(0\) | \(\frac{ 1}{ 48}\) | \(-\frac{ 1}{ 32}+\frac{ 1}{ 32}\sqrt{ 5}\) | \(\frac{ 1}{ 16}\) | \(\frac{ 1}{ 16}+\frac{ 1}{ 16}\sqrt{ 6}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(4\) |
| \(\frac{ 1}{ 2}\) | \(1\) | \(0\) | \(0\) | \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(4\) |
| \(\frac{ 1}{ 2}\) | \(3\) | \(0\) | \(0\) | \(-2\) | \(\frac{ 1}{ 2}\) | \(1\) | \(3\) | \(4\) |
| \(1\) | \(4\) | \(0\) | \(0\) | \(3\) | \(1\) | \(2\) | \(4\) | \(4\) |
377
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:...
\((z-1)(6z-1)(4z-1)(3z+1)(4z+1)(5z-1)(2z+1)^2(2z-1)^2(6z^2-2z+1)^2\)
| \(-\frac{ 1}{ 2}\) | \(-\frac{ 1}{ 3}\) | \(-\frac{ 1}{ 4}\) | \(0\) | \(\frac{ 1}{ 6}-\frac{ 1}{ 6}\sqrt{ 5}I\) | \(\frac{ 1}{ 6}\) | \(\frac{ 1}{ 6}+\frac{ 1}{ 6}\sqrt{ 5}I\) | \(\frac{ 1}{ 5}\) | \(\frac{ 1}{ 4}\) | \(\frac{ 1}{ 2}\) | \(1\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(4\) |
| \(0\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(5\) |
| \(-1\) | \(1\) | \(1\) | \(0\) | \(3\) | \(1\) | \(3\) | \(1\) | \(1\) | \(-1\) | \(1\) | \(5\) |
| \(1\) | \(2\) | \(2\) | \(0\) | \(4\) | \(2\) | \(4\) | \(2\) | \(2\) | \(1\) | \(2\) | \(6\) |
378
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:...
\(-(9z+1)(6z+1)(348z^2+51z-1)(5z+1)^2(4z+1)^2(576z^3+357z^2+72z+5)^2\)
| ≈\(-0.298314\) | \(-\frac{ 1}{ 4}\) | \(-\frac{ 1}{ 5}\) | \(-\frac{ 1}{ 6}\) | \(-\frac{ 17}{ 232}-\frac{ 11}{ 696}\sqrt{ 33}\) | ≈\(-0.160739-0.057112I\) | ≈\(-0.160739+0.057112I\) | \(-\frac{ 1}{ 9}\) | \(0\) | \(-\frac{ 17}{ 232}+\frac{ 11}{ 696}\sqrt{ 33}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(\frac{ 1}{ 2}\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(2\) |
| \(3\) | \(\frac{ 1}{ 2}\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(3\) | \(3\) | \(1\) | \(0\) | \(1\) | \(3\) |
| \(4\) | \(1\) | \(1\) | \(2\) | \(2\) | \(4\) | \(4\) | \(2\) | \(0\) | \(2\) | \(4\) |
379
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:...
\(-(3z+1)(64z^2+24z+1)(236z^2+63z-1)(360z^3+74z^2-21z-4)^2(4z+1)^3\)
| \(-\frac{ 1}{ 3}\) | \(-\frac{ 3}{ 16}-\frac{ 1}{ 16}\sqrt{ 5}\) | \(-\frac{ 63}{ 472}-\frac{ 17}{ 472}\sqrt{ 17}\) | ≈\(-0.268785\) | \(-\frac{ 1}{ 4}\) | ≈\(-0.174147\) | \(-\frac{ 3}{ 16}+\frac{ 1}{ 16}\sqrt{ 5}\) | \(0\) | \(-\frac{ 63}{ 472}+\frac{ 17}{ 472}\sqrt{ 17}\) | ≈\(0.237376\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(2\) |
| \(1\) | \(1\) | \(1\) | \(3\) | \(0\) | \(3\) | \(1\) | \(0\) | \(1\) | \(3\) | \(3\) |
| \(2\) | \(2\) | \(2\) | \(4\) | \(0\) | \(4\) | \(2\) | \(0\) | \(2\) | \(4\) | \(4\) |
380
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:...
\(-(6z+1)(42320z^4+16560z^3+2032z^2+68z-1)(920z^3-1180z^2-378z-27)^2(7z+1)^3\)
| \(-\frac{ 1}{ 6}\) | ≈\(-0.157194\) | ≈\(-0.157194\) | ≈\(-0.151128\) | \(-\frac{ 1}{ 7}\) | ≈\(-0.124614\) | ≈\(-0.087777\) | \(0\) | ≈\(0.010861\) | ≈\(1.55835\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(2\) |
| \(1\) | \(1\) | \(1\) | \(3\) | \(0\) | \(3\) | \(1\) | \(0\) | \(1\) | \(3\) | \(3\) |
| \(2\) | \(2\) | \(2\) | \(4\) | \(0\) | \(4\) | \(2\) | \(0\) | \(2\) | \(4\) | \(4\) |
381
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:...
\(-(-1+41z+1449z^2+13908z^3+53591z^4+72549z^5)(326z^3-804z^2-351z-35)^2(5z+1)^3\)
| ≈\(-0.216454\) | \(-\frac{ 1}{ 5}\) | ≈\(-0.173649\) | \(0\) | ≈\(2.85636\) | \(#ND+#NDI\) | \(\infty\) |
|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(0\) | \(1\) | \(0\) | \(1\) | \(1\) | \(2\) |
| \(3\) | \(0\) | \(3\) | \(0\) | \(3\) | \(1\) | \(3\) |
| \(4\) | \(0\) | \(4\) | \(0\) | \(4\) | \(2\) | \(4\) |
382
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:...
\(-(661527z^5+290250z^4+47223z^3+3291z^2+71z-1)(23544z^3+7353z^2+759z+26)^2(9z+1)^3\)
| ≈\(-0.126194\) | \(-\frac{ 1}{ 9}\) | ≈\(-0.093057-0.009552I\) | ≈\(-0.093057+0.009552I\) | \(0\) | \(#ND+#NDI\) | \(\infty\) |
|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(0\) | \(1\) | \(1\) | \(0\) | \(1\) | \(2\) |
| \(3\) | \(0\) | \(3\) | \(3\) | \(0\) | \(1\) | \(3\) |
| \(4\) | \(0\) | \(4\) | \(4\) | \(0\) | \(2\) | \(4\) |
383
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:...
\((16z-1)(32z-1)(4096z^2-192z+1)(163840z^3+1024z^2+32z-1)^2(64z-1)^4\)
| ≈\(-0.009802-0.019I\) | ≈\(-0.009802+0.019I\) | \(0\) | \(\frac{ 3}{ 128}-\frac{ 1}{ 128}\sqrt{ 5}\) | ≈\(0.013353\) | \(\frac{ 1}{ 64}\) | \(\frac{ 1}{ 32}\) | \(\frac{ 3}{ 128}+\frac{ 1}{ 128}\sqrt{ 5}\) | \(\frac{ 1}{ 16}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(-\frac{ 1}{ 2}\) | \(0\) | \(0\) | \(0\) | \(2\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(-\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(1\) | \(2\) |
| \(3\) | \(3\) | \(0\) | \(1\) | \(3\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(1\) | \(2\) |
| \(4\) | \(4\) | \(0\) | \(2\) | \(4\) | \(\frac{ 1}{ 2}\) | \(2\) | \(2\) | \(2\) | \(2\) |
384
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:...
\((64z-1)(32z-1)(256z^2-48z+1)(32768z^3-1024z^2-5-32z)^2(16z-1)^4\)
| ≈\(-0.020941-0.040594I\) | ≈\(-0.020941+0.040594I\) | \(0\) | \(\frac{ 1}{ 64}\) | \(\frac{ 3}{ 32}-\frac{ 1}{ 32}\sqrt{ 5}\) | \(\frac{ 1}{ 32}\) | \(\frac{ 1}{ 16}\) | ≈\(0.073133\) | \(\frac{ 3}{ 32}+\frac{ 1}{ 32}\sqrt{ 5}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(-\frac{ 1}{ 2}\) | \(0\) | \(0\) | \(2\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(-\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(2\) |
| \(3\) | \(3\) | \(0\) | \(1\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(3\) | \(1\) | \(2\) |
| \(4\) | \(4\) | \(0\) | \(2\) | \(2\) | \(2\) | \(\frac{ 1}{ 2}\) | \(4\) | \(2\) | \(2\) |
385
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:...
\(-(1+16z)(16z+3)^2(1280z^2-32z-1)^2(256z^2+16z-1)^2(16z-1)^3\)
| \(-\frac{ 3}{ 16}\) | \(-\frac{ 1}{ 32}-\frac{ 1}{ 32}\sqrt{ 5}\) | \(-\frac{ 1}{ 16}\) | \(\frac{ 1}{ 80}-\frac{ 1}{ 80}\sqrt{ 6}\) | \(0\) | \(-\frac{ 1}{ 32}+\frac{ 1}{ 32}\sqrt{ 5}\) | \(\frac{ 1}{ 80}+\frac{ 1}{ 80}\sqrt{ 6}\) | \(\frac{ 1}{ 16}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(4\) |
| \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(0\) | \(\frac{ 1}{ 2}\) | \(1\) | \(0\) | \(4\) |
| \(-2\) | \(\frac{ 1}{ 2}\) | \(1\) | \(3\) | \(0\) | \(\frac{ 1}{ 2}\) | \(3\) | \(0\) | \(4\) |
| \(3\) | \(1\) | \(2\) | \(4\) | \(0\) | \(1\) | \(4\) | \(0\) | \(4\) |
386
New Number: 15.1 | AESZ: | Superseeker: 7/2 237/2 | Hash: df146e1b37d7a257f905c6707b923620
Degree: 15
\(2^{2} 5^{30} \theta^4-2 5^{28} x\left(3640\theta^4+11006\theta^3+13879\theta^2+8376\theta+1980\right)+3^{2} 5^{26} x^{2}\left(538345\theta^4+4434106\theta^3+9865547\theta^2+10318472\theta+4308060\right)-3^{4} 5^{24} x^{3}\left(6742465\theta^4+323187588\theta^3+1293374270\theta^2+2006832192\theta+1174440960\right)-3^{7} 5^{22} x^{4}\left(526873995\theta^4-1668961078\theta^3-24223747379\theta^2-58879161136\theta-47787749580\right)+3^{8} 5^{20} x^{5}\left(112183726219\theta^4+702881575498\theta^3-655695079267\theta^2-6796301255992\theta-8645676874410\right)-3^{10} 5^{18} x^{6}\left(2728176480430\theta^4+50098509218682\theta^3+140700841079393\theta^2+45277394357802\theta-187513884611415\right)-3^{12} 5^{16} x^{7}\left(34762414267630\theta^4-1334642903889766\theta^3-8286651788306957\theta^2-15990739837380612\theta-8287376192342010\right)+3^{15} 5^{14} x^{8}\left(1629579653924345\theta^4+954388085050194\theta^3-55618872802839705\theta^2-207693840516161754\theta-214442659712419520\right)-3^{17} 5^{12} x^{9}\left(65369060331963795\theta^4+512595644471686042\theta^3+992825405643594911\theta^2-1201538784520100286\theta-4009291166039086080\right)+3^{20} 5^{10} x^{10}\left(534261782717034863\theta^4+6643553399420804992\theta^3+30007608488826895812\theta^2+55818610344670779952\theta+32009410686899411085\right)-3^{22} 5^{8} x^{11}\left(8440215529571954655\theta^4+138165063547130806682\theta^3+847930452008770373373\theta^2+2305208800672476166582\theta+2332526675705017692360\right)+2^{2} 3^{25} 5^{6} x^{12}(\theta+5)(6822457746356194860\theta^3+105594221828043028718\theta^2+542119266560031019991\theta+926555809752183305931)-2^{2} 3^{27} 5^{4} x^{13}(\theta+5)(\theta+6)(15337273149232082245\theta^2+289665397258229241319\theta+1092956642701689252996)-2^{5} 3^{30} 5^{2} 7 163 4447 x^{14}(\theta+5)(\theta+6)(\theta+7)(4612345059685\theta+22748051972446)+2^{12} 3^{33} 7^{2} 17 163^{2} 1213 4447^{2} x^{15}(\theta+5)(\theta+6)(\theta+7)(\theta+8)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 198/5, 119412/125, 59226669/3125, 27037427724/78125, ... --> OEIS Normalized instanton numbers (n0=1): 7/2, -193/8, 237/2, -6119/4, 16307, ... ; Common denominator:...
\((128z-25)(72z+25)(153z-25)(294759z^2-18900z+625)(378z-25)^2(39609z^2-2025z+625)^2(360207z^2-1575z-1250)^2\)
| \(-\frac{ 25}{ 72}\) | \(\frac{ 175}{ 80046}-\frac{ 625}{ 80046}\sqrt{ 57}\) | \(0\) | \(\frac{ 25}{ 978}-\frac{ 625}{ 8802}\sqrt{ 3}I\) | \(\frac{ 25}{ 978}+\frac{ 625}{ 8802}\sqrt{ 3}I\) | \(\frac{ 350}{ 10917}-\frac{ 625}{ 32751}\sqrt{ 3}I\) | \(\frac{ 350}{ 10917}+\frac{ 625}{ 32751}\sqrt{ 3}I\) | \(\frac{ 175}{ 80046}+\frac{ 625}{ 80046}\sqrt{ 57}\) | \(\frac{ 25}{ 378}\) | \(\frac{ 25}{ 153}\) | \(\frac{ 25}{ 128}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(5\) |
| \(1\) | \(1\) | \(0\) | \(0\) | \(0\) | \(1\) | \(1\) | \(1\) | \(-1\) | \(1\) | \(1\) | \(6\) |
| \(1\) | \(3\) | \(0\) | \(-1\) | \(-1\) | \(1\) | \(1\) | \(3\) | \(1\) | \(1\) | \(1\) | \(7\) |
| \(2\) | \(4\) | \(0\) | \(1\) | \(1\) | \(2\) | \(2\) | \(4\) | \(-2\) | \(2\) | \(2\) | \(8\) |
387
New Number: 15.2 | AESZ: | Superseeker: 2 38 | Hash: 76d5c5e186c39f14d8f32dfa0f13e22a
Degree: 15
\(\theta^4+2 x\left(73\theta^4+40\theta^3+47\theta^2+27\theta+6\right)+2^{2} x^{2}\left(2349\theta^4+2724\theta^3+3516\theta^2+2273\theta+614\right)+2^{3} x^{3}\left(44091\theta^4+80304\theta^3+115043\theta^2+84574\theta+26356\right)+2^{5} x^{4}\left(269591\theta^4+678346\theta^3+1084179\theta^2+893856\theta+309842\right)+2^{8} x^{5}\left(568775\theta^4+1835004\theta^3+3266314\theta^2+2971734\theta+1120498\right)+2^{11} x^{6}\left(856369\theta^4+3369012\theta^3+6631886\theta^2+6564309\theta+2651780\right)+2^{11} x^{7}\left(7508036\theta^4+34719008\theta^3+74840604\theta^2+79593816\theta+34039943\right)+2^{13} x^{8}\left(12098492\theta^4+63919352\theta^3+149239952\theta^2+168641212\theta+75569097\right)+2^{16} x^{9}\left(7179524\theta^4+42349744\theta^3+105902696\theta^2+125838704\theta+58525593\right)+2^{19} x^{10}\left(3117952\theta^4+20136896\theta^3+53326176\theta^2+65967996\theta+31556287\right)+2^{21} x^{11}\left(1949840\theta^4+13550976\theta^3+37571920\theta^2+47915544\theta+23371681\right)+2^{23} x^{12}\left(851424\theta^4+6266688\theta^3+17985676\theta^2+23424156\theta+11560933\right)+2^{26} x^{13}\left(122784\theta^4+942720\theta^3+2770088\theta^2+3654240\theta+1815239\right)+2^{31} 5 x^{14}\left(524\theta^4+4136\theta^3+12323\theta^2+16373\theta+8173\right)+2^{36} 5^{2} x^{15}\left((\theta+2)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -12, 136, -1632, 21296, ... --> OEIS Normalized instanton numbers (n0=1): 2, -29/4, 38, -2077/8, 2034, ... ; Common denominator:...
\((4z+1)(64z^2+24z+1)^2(160z^2+32z+1)^2(2z+1)^3(8z+1)^3\)
| \(-\frac{ 1}{ 2}\) | \(-\frac{ 3}{ 16}-\frac{ 1}{ 16}\sqrt{ 5}\) | \(-\frac{ 1}{ 4}\) | \(-\frac{ 1}{ 10}-\frac{ 1}{ 40}\sqrt{ 6}\) | \(-\frac{ 1}{ 8}\) | \(-\frac{ 3}{ 16}+\frac{ 1}{ 16}\sqrt{ 5}\) | \(-\frac{ 1}{ 10}+\frac{ 1}{ 40}\sqrt{ 6}\) | \(0\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(2\) |
| \(2\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(0\) | \(\frac{ 1}{ 2}\) | \(1\) | \(0\) | \(2\) |
| \(3\) | \(\frac{ 1}{ 2}\) | \(1\) | \(3\) | \(0\) | \(\frac{ 1}{ 2}\) | \(3\) | \(0\) | \(2\) |
| \(5\) | \(1\) | \(2\) | \(4\) | \(0\) | \(1\) | \(4\) | \(0\) | \(2\) |
388
New Number: 15.3 | AESZ: | Superseeker: 44/3 220588/81 | Hash: ae51313cd958206bb1b7a3c8ae23e509
Degree: 15
\(3^{3} \theta^4+2^{2} 3^{2} x\left(12\theta^4-160\theta^3-153\theta^2-73\theta-15\right)-2^{4} 3 x^{2}\left(2688\theta^4+704\theta^3-6380\theta^2-6164\theta-2343\right)+2^{8} x^{3}\left(1312\theta^4+69632\theta^3+26456\theta^2+3928\theta-4305\right)+2^{12} x^{4}\left(51264\theta^4-16512\theta^3-16360\theta^2-16088\theta-1785\right)-2^{16} x^{5}\left(52000\theta^4+223680\theta^3+316652\theta^2+308700\theta+133179\right)-2^{21} x^{6}\left(42088\theta^4+36416\theta^3+31682\theta^2-15530\theta-24313\right)+2^{25} x^{7}\left(58136\theta^4+309440\theta^3+666728\theta^2+761160\theta+351769\right)+2^{29} x^{8}\left(30776\theta^4+26112\theta^3-81496\theta^2-231912\theta-165231\right)-2^{33} 3 x^{9}\left(16632\theta^4+120704\theta^3+332890\theta^2+441546\theta+227145\right)-2^{36} x^{10}\left(31968\theta^4+33600\theta^3-297916\theta^2-852260\theta-648637\right)+2^{40} x^{11}\left(40000\theta^4+381696\theta^3+1258584\theta^2+1813272\theta+964287\right)+2^{44} x^{12}\left(14240\theta^4+66688\theta^3+44952\theta^2-163928\theta-198345\right)-2^{48} x^{13}\left(5824\theta^4+76480\theta^3+307828\theta^2+490020\theta+272659\right)-2^{54} 5 x^{14}\left(164\theta^4+1536\theta^3+5043\theta^2+7113\theta+3693\right)-2^{60} 5^{2} x^{15}\left((\theta+2)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 20, 388, 7344, 141636, ... --> OEIS Normalized instanton numbers (n0=1): 44/3, -1421/9, 220588/81, -14752264/243, 1138508000/729, ... ; Common denominator:...
\(-(1+16z)(1280z^2-32z-1)^2(256z^2+16z-1)^2(16z+3)^3(16z-1)^3\)
| \(-\frac{ 3}{ 16}\) | \(-\frac{ 1}{ 32}-\frac{ 1}{ 32}\sqrt{ 5}\) | \(-\frac{ 1}{ 16}\) | \(\frac{ 1}{ 80}-\frac{ 1}{ 80}\sqrt{ 6}\) | \(0\) | \(-\frac{ 1}{ 32}+\frac{ 1}{ 32}\sqrt{ 5}\) | \(\frac{ 1}{ 80}+\frac{ 1}{ 80}\sqrt{ 6}\) | \(\frac{ 1}{ 16}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(2\) |
| \(2\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(0\) | \(\frac{ 1}{ 2}\) | \(1\) | \(0\) | \(2\) |
| \(3\) | \(\frac{ 1}{ 2}\) | \(1\) | \(3\) | \(0\) | \(\frac{ 1}{ 2}\) | \(3\) | \(0\) | \(2\) |
| \(5\) | \(1\) | \(2\) | \(4\) | \(0\) | \(1\) | \(4\) | \(0\) | \(2\) |
389
New Number: 15.4 | AESZ: | Superseeker: 52/5 13436/5 | Hash: 2306e85a3af0a97d616dedf03cc93f69
Degree: 15
\(5^{2} \theta^4-2^{2} 5 x\left(524\theta^4+56\theta^3+83\theta^2+55\theta+15\right)+2^{4} x^{2}\left(122784\theta^4+39552\theta^3+60584\theta^2+42560\theta+9895\right)-2^{8} x^{3}\left(851424\theta^4+544704\theta^3+819724\theta^2+563860\theta+144605\right)+2^{13} x^{4}\left(1949840\theta^4+2047744\theta^3+3062224\theta^2+2155304\theta+617905\right)-2^{18} x^{5}\left(3117952\theta^4+4806720\theta^3+7335648\theta^2+5468420\theta+1717063\right)+2^{22} x^{6}\left(7179524\theta^4+15086448\theta^3+24112808\theta^2+19319920\theta+6533401\right)-2^{26} x^{7}\left(12098492\theta^4+32868584\theta^3+56087648\theta^2+48438116\theta+17467537\right)+2^{31} x^{8}\left(7508036\theta^4+25345280\theta^3+46719420\theta^2+43397656\theta+16591239\right)-2^{38} x^{9}\left(856369\theta^4+3481940\theta^3+6970670\theta^2+6938899\theta+2800514\right)+2^{42} x^{10}\left(568775\theta^4+2715196\theta^3+5906890\theta^2+6274274\theta+2662654\right)-2^{46} x^{11}\left(269591\theta^4+1478382\theta^3+3484287\theta^2+3929620\theta+1745534\right)+2^{51} x^{12}\left(44091\theta^4+272424\theta^3+691403\theta^2+822862\theta+380404\right)-2^{57} x^{13}\left(2349\theta^4+16068\theta^3+43548\theta^2+54271\theta+25924\right)+2^{63} x^{14}\left(73\theta^4+544\theta^3+1559\theta^2+2017\theta+988\right)-2^{69} x^{15}\left((\theta+2)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 12, 44, -3792, -207124, ... --> OEIS Normalized instanton numbers (n0=1): 52/5, 115, 13436/5, 89632, 18465296/5, ... ; Common denominator:...
\(-(-1+32z)(256z^2-48z+1)^2(512z^2-128z+5)^2(64z-1)^3(16z-1)^3\)
| \(0\) | \(\frac{ 1}{ 64}\) | \(\frac{ 3}{ 32}-\frac{ 1}{ 32}\sqrt{ 5}\) | \(\frac{ 1}{ 32}\) | \(\frac{ 1}{ 8}-\frac{ 1}{ 32}\sqrt{ 6}\) | \(\frac{ 1}{ 16}\) | \(\frac{ 3}{ 32}+\frac{ 1}{ 32}\sqrt{ 5}\) | \(\frac{ 1}{ 8}+\frac{ 1}{ 32}\sqrt{ 6}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(2\) |
| \(0\) | \(2\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(0\) | \(\frac{ 1}{ 2}\) | \(1\) | \(2\) |
| \(0\) | \(3\) | \(\frac{ 1}{ 2}\) | \(1\) | \(3\) | \(0\) | \(\frac{ 1}{ 2}\) | \(3\) | \(2\) |
| \(0\) | \(5\) | \(1\) | \(2\) | \(4\) | \(0\) | \(1\) | \(4\) | \(2\) |
390
New Number: 6.10 | AESZ: | Superseeker: 23 16723 | Hash: 23025d094839fb9d8e76076bd9a0bfa7
Degree: 6
\(\theta^4-x\left(254\theta^4+508\theta^3+391\theta^2+137\theta+18\right)+x^{2}\left(4657\theta^4+18628\theta^3+27265\theta^2+17274\theta+3672\right)-2^{2} 3 x^{3}\left(2920\theta^4+17520\theta^3+36833\theta^2+31659\theta+8235\right)+2^{3} 3^{4} x^{4}\left(204\theta^4+1632\theta^3+4449\theta^2+4740\theta+1400\right)-2^{4} 3^{5} x^{5}(16\theta^2+80\theta+35)(2\theta+5)^2+2^{4} 3^{6} x^{6}(2\theta+11)(2\theta+7)(2\theta+5)(2\theta+1)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 18, 1242, 138420, 18954810, ... --> OEIS Normalized instanton numbers (n0=1): 23, 462, 16723, 923487, 61874817, ... ; Common denominator:...
\((3z-1)(3888z^3-1944z^2+243z-1)(4z-1)^2\)
| \(0\) | ≈\(0.004259\) | ≈\(0.215449\) | \(\frac{ 1}{ 4}\) | ≈\(0.280292\) | \(\frac{ 1}{ 3}\) | \(\infty\) |
|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(0\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(\frac{ 5}{ 2}\) |
| \(0\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(\frac{ 7}{ 2}\) |
| \(0\) | \(2\) | \(2\) | \(1\) | \(2\) | \(2\) | \(\frac{ 11}{ 2}\) |