1
New Number: 5.69 | AESZ: 280 | Superseeker: -117 -844872 | Hash: 5083c4e9f432302302c564ba554e3bcd
Degree: 5
\(\theta^4-3^{2} x\left(123\theta^4-60\theta^3-39\theta^2-9\theta-1\right)+3^{5} x^{2}\left(1521\theta^4-1260\theta^3+30\theta^2-21\theta-10\right)-3^{8} x^{3}\left(4110\theta^4-5634\theta^3-4353\theta^2-1629\theta-220\right)-3^{12} 17 x^{4}\left(286\theta^4+410\theta^3+170\theta^2-35\theta-30\right)-3^{18} 17^{2} x^{5}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -9, 81, 1017, -93231, ... --> OEIS Normalized instanton numbers (n0=1): -117, -28899/4, -844872, -131189436, -23932952667, ... ; Common denominator:...
\(-(531441z^3+14580z^2+189z-1)(-1+459z)^2\)
≈\(-0.015682-0.015263I\) | ≈\(-0.015682+0.015263I\) | \(0\) | \(\frac{ 1}{ 459}\) | ≈\(0.003929\) | \(\infty\) |
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\(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
\(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) |
\(1\) | \(1\) | \(0\) | \(3\) | \(1\) | \(1\) |
\(2\) | \(2\) | \(0\) | \(4\) | \(2\) | \(1\) |
2
New Number: 11.18 | AESZ: | Superseeker: -343/26 -27836/13 | Hash: 7fd9e473da9a826dea365ad9c234d2b1
Degree: 11
\(2^{2} 13^{2} \theta^4+2 13 x\left(2902\theta^4+6146\theta^3+4763\theta^2+1690\theta+234\right)-3 x^{2}\left(96469\theta^4+49486\theta^3-135373\theta^2-115726\theta-26754\right)+3 x^{3}\left(107658\theta^4-7866\theta^3+142429\theta^2+209352\theta+70434\right)+3^{2} x^{4}\left(27312\theta^4-323430\theta^3-1054064\theta^2-786941\theta-191951\right)-3^{4} x^{5}\left(1180\theta^4-103322\theta^3-143955\theta^2-85327\theta-20494\right)-3^{5} x^{6}\left(2379\theta^4+12696\theta^3+45266\theta^2+49297\theta+16562\right)-3^{6} x^{7}\left(929\theta^4+13156\theta^3-15355\theta^2-25877\theta-8920\right)+3^{7} x^{8}\left(1318\theta^4+2950\theta^3+2915\theta^2+772\theta-131\right)+3^{7} x^{9}\left(315\theta^4-3006\theta^3-5005\theta^2-2784\theta-504\right)-2^{2} 3^{8} x^{10}\left(42\theta^4+66\theta^3+25\theta^2-8\theta-5\right)+2^{4} 3^{10} x^{11}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -9, 333, -18639, 1264509, ... --> OEIS Normalized instanton numbers (n0=1): -343/26, 11207/104, -27836/13, 764852/13, -52338075/26, ... ; Common denominator:...
\((1+116z+75z^2+162z^3-108z^4+81z^5)(26-57z+9z^2+108z^3)^2\)
≈\(-0.92963\) | \(0\) | ≈\(0.423148-0.282683I\) | ≈\(0.423148+0.282683I\) | \(#ND+#NDI\) | \(\infty\) |
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\(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
\(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) |
\(3\) | \(0\) | \(3\) | \(3\) | \(1\) | \(1\) |
\(4\) | \(0\) | \(4\) | \(4\) | \(2\) | \(1\) |
3
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:...
\((18z+1)(189z^2+18z+1)(27z+1)^2(9z-1)^2(81z^2+54z+1)^2\)
\(-\frac{ 1}{ 3}-\frac{ 2}{ 9}\sqrt{ 2}\) | \(-\frac{ 1}{ 18}\) | \(-\frac{ 1}{ 21}-\frac{ 2}{ 63}\sqrt{ 3}I\) | \(-\frac{ 1}{ 21}+\frac{ 2}{ 63}\sqrt{ 3}I\) | \(-\frac{ 1}{ 27}\) | \(-\frac{ 1}{ 3}+\frac{ 2}{ 9}\sqrt{ 2}\) | \(0\) | \(\frac{ 1}{ 9}\) | \(\infty\) |
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\(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
\(1\) | \(1\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(0\) | \(\frac{ 1}{ 2}\) | \(2\) |
\(3\) | \(1\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(3\) | \(0\) | \(\frac{ 1}{ 2}\) | \(3\) |
\(4\) | \(2\) | \(2\) | \(2\) | \(1\) | \(4\) | \(0\) | \(1\) | \(4\) |
4
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:...
\((9z+1)(z+1)(324z^2-18z+1)(81z^2+9z+1)^2(486z^2-27z-2)^2\)
\(-1\) | \(-\frac{ 1}{ 9}\) | \(-\frac{ 1}{ 18}-\frac{ 1}{ 18}\sqrt{ 3}I\) | \(-\frac{ 1}{ 18}+\frac{ 1}{ 18}\sqrt{ 3}I\) | \(\frac{ 1}{ 36}-\frac{ 1}{ 108}\sqrt{ 57}\) | \(0\) | \(\frac{ 1}{ 36}-\frac{ 1}{ 36}\sqrt{ 3}I\) | \(\frac{ 1}{ 36}+\frac{ 1}{ 36}\sqrt{ 3}I\) | \(\frac{ 1}{ 36}+\frac{ 1}{ 108}\sqrt{ 57}\) | \(\infty\) |
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\(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(3\) |
\(1\) | \(1\) | \(0\) | \(0\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(4\) |
\(1\) | \(1\) | \(-1\) | \(-1\) | \(3\) | \(0\) | \(1\) | \(1\) | \(3\) | \(4\) |
\(2\) | \(2\) | \(1\) | \(1\) | \(4\) | \(0\) | \(2\) | \(2\) | \(4\) | \(5\) |
5
New Number: 8.59 | AESZ: | Superseeker: -26/5 -234/5 | Hash: 53885e46a1519d98ee4697de1c109214
Degree: 8
\(5^{2} \theta^4+5 x\left(278\theta^4+772\theta^3+656\theta^2+270\theta+45\right)+x^{2}\left(19406\theta^4+145988\theta^3+259366\theta^2+172540\theta+41745\right)-3^{2} x^{3}\left(30338\theta^4+30636\theta^3-177680\theta^2-235350\theta-80565\right)-3^{2} x^{4}\left(189512\theta^4+1676428\theta^3+3050258\theta^2+2136012\theta+525339\right)+3^{4} x^{5}\left(173242\theta^4+651964\theta^3+972352\theta^2+649458\theta+161507\right)+3^{4} x^{6}\left(85922\theta^4+248940\theta^3+209506\theta^2+37044\theta-12717\right)+3^{6} x^{7}\left(1114\theta^4+2012\theta^3+1056\theta^2+50\theta-57\right)-3^{8} x^{8}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -9, 123, -1719, 17739, ... --> OEIS Normalized instanton numbers (n0=1): -26/5, -177/10, -234/5, -1837/2, -27716/5, ... ; Common denominator:...
\(-(9z+1)(9z^3-1187z^2-61z-1)(-5+36z+9z^2)^2\)
\(-2-\frac{ 1}{ 3}\sqrt{ 41}\) | \(-\frac{ 1}{ 9}\) | ≈\(-0.025688-0.0135I\) | ≈\(-0.025688+0.0135I\) | \(0\) | \(-2+\frac{ 1}{ 3}\sqrt{ 41}\) | ≈\(131.940265\) | \(\infty\) |
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\(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
\(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) |
\(3\) | \(1\) | \(1\) | \(1\) | \(0\) | \(3\) | \(1\) | \(1\) |
\(4\) | \(2\) | \(2\) | \(2\) | \(0\) | \(4\) | \(2\) | \(1\) |