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You searched for: inst=284/29

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1

New Number: 6.23 |  AESZ:  |  Superseeker: 24/29 284/29  |  Hash: 83e67651e4ea5ee123354c2989ff7460  

Degree: 6

\(29^{6} \theta^4-2 29^{5} x(2\theta^2+2\theta+1)(152\theta^2+152\theta+41)-2^{2} 29^{4} x^{2}\left(4104\theta^4+16416\theta^3+23786\theta^2+14740\theta+3267\right)+2^{2} 29^{3} x^{3}\left(517492\theta^4+3104952\theta^3+6923513\theta^2+6798255\theta+2465928\right)-2^{4} 3 29^{2} x^{4}\left(3104764\theta^4+24838112\theta^3+70273625\theta^2+82389604\theta+33870303\right)+2^{8} 3^{2} 19 23 29 x^{5}(\theta+4)(\theta+1)(5408\theta^2+27040\theta+30585)-2^{12} 3^{4} 19^{2} 23^{2} x^{6}(\theta+5)(\theta+4)(\theta+2)(\theta+1)\)

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Coefficients of the holomorphic solution: 1, 82/29, 18498/841, 5789116/24389, 2183601010/707281, ...
--> OEIS
Normalized instanton numbers (n0=1): 24/29, 72/29, 284/29, 1616/29, 10632/29, ... ; Common denominator:...

Discriminant

\(-(92z+29)(1195632z^3-467248z^2+548332z-24389)(24z-29)^2\)

Local exponents

\(-\frac{ 29}{ 92}\)\(0\) ≈\(0.046074\) ≈\(0.172361-0.642668I\) ≈\(0.172361+0.642668I\)\(\frac{ 29}{ 24}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(0\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)\(2\)
\(1\)\(0\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)\(4\)
\(2\)\(0\)\(2\)\(2\)\(2\)\(1\)\(5\)

Note:

This is operator "6.23" from ...

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2

New Number: 8.36 |  AESZ: 327  |  Superseeker: 24/29 284/29  |  Hash: 586c1906112cbba9b2d54c57ce2add99  

Degree: 8

\(29^{2} \theta^4+2 29 x\theta(24\theta^3-198\theta^2-128\theta-29)-2^{2} x^{2}\left(44284\theta^4+172954\theta^3+248589\theta^2+172057\theta+47096\right)-2^{2} x^{3}\left(525708\theta^4+2414772\theta^3+4447643\theta^2+3839049\theta+1275594\right)-2^{3} x^{4}\left(1415624\theta^4+7911004\theta^3+17395449\theta^2+17396359\theta+6496262\right)-2^{4} x^{5}(\theta+1)(2152040\theta^3+12186636\theta^2+24179373\theta+16560506)-2^{5} x^{6}(\theta+1)(\theta+2)(1912256\theta^2+9108540\theta+11349571)-2^{8} 41 x^{7}(\theta+3)(\theta+2)(\theta+1)(5671\theta+16301)-2^{8} 3 19 41^{2} x^{8}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)

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Coefficients of the holomorphic solution: 1, 0, 14, 96, 1266, ...
--> OEIS
Normalized instanton numbers (n0=1): 24/29, 72/29, 284/29, 1616/29, 10632/29, ... ; Common denominator:...

Discriminant

\(-(6z+1)(152z^3+84z^2+14z-1)(2z+1)^2(82z+29)^2\)

Local exponents

\(-\frac{ 1}{ 2}\)\(-\frac{ 29}{ 82}\) ≈\(-0.302804-0.180271I\) ≈\(-0.302804+0.180271I\)\(-\frac{ 1}{ 6}\)\(0\) ≈\(0.052976\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(\frac{ 1}{ 2}\)\(1\)\(1\)\(1\)\(1\)\(0\)\(1\)\(2\)
\(\frac{ 1}{ 2}\)\(3\)\(1\)\(1\)\(1\)\(0\)\(1\)\(3\)
\(1\)\(4\)\(2\)\(2\)\(2\)\(0\)\(2\)\(4\)

Note:

This operator is reducible to operator 6.23

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