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You searched for: superseeker=9,2564/3

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1

New Number: 11.7 |  AESZ:  |  Superseeker: 9 2564/3  |  Hash: 3933e1482d30ea8bca1e5e5f914286e2  

Degree: 11

\(\theta^4+3 x\left(60\theta^4+12\theta^3+19\theta^2+13\theta+3\right)+3^{3} x^{2}\left(463\theta^4+304\theta^3+405\theta^2+184\theta+27\right)+3^{5} x^{3}\left(1710\theta^4+2268\theta^3+2450\theta^2+1080\theta+153\right)+3^{7} x^{4}\left(2870\theta^4+5344\theta^3+4044\theta^2-188\theta-981\right)+3^{9} x^{5}\left(560\theta^4-4552\theta^3-20650\theta^2-29130\theta-13389\right)-3^{11} x^{6}\left(5114\theta^4+37440\theta^3+101098\theta^2+119700\theta+51219\right)-3^{13} x^{7}\left(6620\theta^4+48712\theta^3+130868\theta^2+152172\theta+63981\right)-3^{16} x^{8}(\theta+1)(83\theta^3-2739\theta^2-16257\theta-20563)+3^{17} x^{9}(\theta+1)(\theta+2)(4676\theta^2+42864\theta+94887)+3^{20} x^{10}(\theta+3)(\theta+2)(\theta+1)(505\theta+2522)+2 3^{23} 7 x^{11}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)

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Coefficients of the holomorphic solution: 1, -9, 135, -2115, 38799, ...
--> OEIS
Normalized instanton numbers (n0=1): 9, -72, 2564/3, -12924, 228024, ... ; Common denominator:...

Discriminant

\((18z+1)(189z^2+18z+1)(27z+1)^2(9z-1)^2(81z^2+54z+1)^2\)

Local exponents

\(-\frac{ 1}{ 3}-\frac{ 2}{ 9}\sqrt{ 2}\)\(-\frac{ 1}{ 18}\)\(-\frac{ 1}{ 21}-\frac{ 2}{ 63}\sqrt{ 3}I\)\(-\frac{ 1}{ 21}+\frac{ 2}{ 63}\sqrt{ 3}I\)\(-\frac{ 1}{ 27}\)\(-\frac{ 1}{ 3}+\frac{ 2}{ 9}\sqrt{ 2}\)\(0\)\(\frac{ 1}{ 9}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)\(1\)\(0\)\(\frac{ 1}{ 2}\)\(2\)
\(3\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)\(3\)\(0\)\(\frac{ 1}{ 2}\)\(3\)
\(4\)\(2\)\(2\)\(2\)\(1\)\(4\)\(0\)\(1\)\(4\)

Note:

This is operator "11.7" from ...

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2

New Number: 9.7 |  AESZ:  |  Superseeker: 9 2564/3  |  Hash: 9bb7a7f3a3d5f66018396173696c194c  

Degree: 9

\(\theta^4+3 x\left(93\theta^4+42\theta^3+49\theta^2+28\theta+6\right)+2^{2} 3^{3} x^{2}\left(307\theta^4+328\theta^3+401\theta^2+230\theta+53\right)+2^{2} 3^{5} x^{3}\left(2268\theta^4+4128\theta^3+5443\theta^2+3525\theta+932\right)+2^{4} 3^{7} x^{4}\left(2588\theta^4+6880\theta^3+10145\theta^2+7398\theta+2167\right)+2^{6} 3^{9} x^{5}\left(1897\theta^4+6694\theta^3+11167\theta^2+9015\theta+2853\right)+2^{8} 3^{11} x^{6}\left(895\theta^4+3912\theta^3+7309\theta^2+6408\theta+2150\right)+2^{8} 3^{13} x^{7}\left(1048\theta^4+5360\theta^3+10939\theta^2+10155\theta+3534\right)+2^{10} 3^{15} x^{8}(\theta+1)(172\theta^3+804\theta^2+1295\theta+699)+2^{12} 3^{18} x^{9}(\theta+2)(\theta+1)(2\theta+3)^2\)

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Coefficients of the holomorphic solution: 1, -18, 378, -8676, 213354, ...
--> OEIS
Normalized instanton numbers (n0=1): 9, -72, 2564/3, -12924, 228024, ... ; Common denominator:...

Discriminant

\((27z+1)(432z^2+36z+1)(36z+1)^2(648z^2+72z+1)^2\)

Local exponents

\(-\frac{ 1}{ 18}-\frac{ 1}{ 36}\sqrt{ 2}\)\(-\frac{ 1}{ 24}-\frac{ 1}{ 72}\sqrt{ 3}I\)\(-\frac{ 1}{ 24}+\frac{ 1}{ 72}\sqrt{ 3}I\)\(-\frac{ 1}{ 27}\)\(-\frac{ 1}{ 36}\)\(-\frac{ 1}{ 18}+\frac{ 1}{ 36}\sqrt{ 2}\)\(0\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)\(1\)\(0\)\(\frac{ 3}{ 2}\)
\(3\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)\(3\)\(0\)\(\frac{ 3}{ 2}\)
\(4\)\(2\)\(2\)\(2\)\(1\)\(4\)\(0\)\(2\)

Note:

This is operator "9.7" from ...

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