Summary

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1

New Number: 5.95 |  AESZ: 338  |  Superseeker: -140/3 -66092  |  Hash: eb4f6d6e59fafa4e794fb664dbdeab3f  

Degree: 5

\(3^{2} \theta^4+2^{2} 3 x\left(278\theta^4+424\theta^3+311\theta^2+99\theta+12\right)+2^{5} x^{2}\left(5210\theta^4+3944\theta^3-2635\theta^2-2433\theta-492\right)+2^{8} x^{3}\left(8190\theta^4-3528\theta^3-3991\theta^2-585\theta+114\right)-2^{11} 11 x^{4}(2\theta+1)(86\theta^3+57\theta^2-39\theta-32)+2^{15} 11^{2} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)\)

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Coefficients of the holomorphic solution: 1, -16, 1608, -243520, 44810920, ...
--> OEIS
Normalized instanton numbers (n0=1): -140/3, 1293, -66092, 5236719, -1553321056/3, ... ; Common denominator:...

Discriminant

\((2048z^3-640z^2+312z+1)(3+88z)^2\)

Local exponents

\(-\frac{ 3}{ 88}\) ≈\(-0.003184\)\(0\) ≈\(0.157842-0.358378I\) ≈\(0.157842+0.358378I\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)
\(3\)\(1\)\(0\)\(1\)\(1\)\(1\)
\(4\)\(2\)\(0\)\(2\)\(2\)\(\frac{ 3}{ 2}\)

Note:

This is operator "5.95" from ...

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2

New Number: 8.30 |  AESZ: 314  |  Superseeker: 229/4 297111/4  |  Hash: 893692ba7eb3effcbc0c3b48d405456a  

Degree: 8

\(2^{4} \theta^4-2^{2} x\left(1282\theta^4+2618\theta^3+1909\theta^2+600\theta+72\right)-3^{2} x^{2}\left(9503\theta^4+26810\theta^3+31755\theta^2+15944\theta+2936\right)+3^{4} x^{3}\left(15627\theta^4-18288\theta^3-91412\theta^2-53256\theta-9688\right)+2 3^{6} x^{4}\left(15106\theta^4+20300\theta^3-20421\theta^2-23443\theta-5907\right)-2^{2} 3^{8} x^{5}\left(2072\theta^4-18256\theta^3-2563\theta^2+4626\theta+1495\right)-2^{2} 3^{10} x^{6}\left(6204\theta^4+360\theta^3-281\theta^2+1017\theta+434\right)-2^{5} 3^{12} x^{7}(2\theta+1)(100\theta^3+162\theta^2+95\theta+21)+2^{8} 3^{14} x^{8}(2\theta+1)(\theta+1)^2(2\theta+3)\)

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Coefficients of the holomorphic solution: 1, 18, 1926, 310860, 61060230, ...
--> OEIS
Normalized instanton numbers (n0=1): 229/4, 1293, 297111/4, 6150238, 2540085295/4, ... ; Common denominator:...

Discriminant

\((z-1)(11664z^3+3888z^2+324z-1)(-4-9z+648z^2)^2\)

Local exponents

≈\(-0.168156-0.022431I\) ≈\(-0.168156+0.022431I\)\(\frac{ 1}{ 144}-\frac{ 1}{ 144}\sqrt{ 129}\)\(0\)\(\frac{ 1}{ 18}2^(\frac{ 1}{ 3})+\frac{ 1}{ 36}2^(\frac{ 2}{ 3})-\frac{ 1}{ 9}\)\(\frac{ 1}{ 144}+\frac{ 1}{ 144}\sqrt{ 129}\)\(1\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)\(1\)
\(1\)\(1\)\(3\)\(0\)\(1\)\(3\)\(1\)\(1\)
\(2\)\(2\)\(4\)\(0\)\(2\)\(4\)\(2\)\(\frac{ 3}{ 2}\)

Note:

This is operator "8.30" from ...

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