Summary

You searched for: inst=5150

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1

New Number: 11.8 |  AESZ:  |  Superseeker: 6/17 688/17  |  Hash: a0a3e346d09b91b8ad96e54854c136ad  

Degree: 11

\(17^{2} \theta^4-2 3 17 x\theta^2(117\theta^2+2\theta+1)+2^{2} x^{2}\left(8475\theta^4-64176\theta^3-97010\theta^2-63580\theta-16184\right)+2^{2} x^{3}\left(717094\theta^4+1400796\theta^3+1493367\theta^2+893571\theta+254082\right)-2^{4} x^{4}\left(464294\theta^4-1133264\theta^3-1648391\theta^2-1200310\theta-375336\right)-2^{4} x^{5}\left(18282700\theta^4+46995928\theta^3+83098711\theta^2+73517673\theta+25685438\right)-2^{6} 3 x^{6}\left(2709886\theta^4+7353008\theta^3+18175093\theta^2+18787708\theta+5966228\right)+2^{6} x^{7}\left(154368940\theta^4+947965400\theta^3+2363187035\theta^2+2646307981\theta+1071488886\right)+2^{8} x^{8}(\theta+1)(119648213\theta^3+399067803\theta^2+77665606\theta-498465144)-2^{8} 3 x^{9}(\theta+1)(\theta+2)(120410834\theta^2+865960638\theta+1188072247)-2^{10} 3^{2} 107 x^{10}(\theta+3)(\theta+2)(\theta+1)(218683\theta-39394)+2^{11} 3^{3} 5 107^{2} 137 x^{11}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)

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Coefficients of the holomorphic solution: 1, 0, 14, 72, 1554, ...
--> OEIS
Normalized instanton numbers (n0=1): 6/17, 83/17, 688/17, 7350/17, 5150, ... ; Common denominator:...

Discriminant

\((10z+1)(6z-1)(1096z^3+228z^2+14z-1)(2z-1)^2(1284z^2+232z-17)^2\)

Local exponents

\(-\frac{ 29}{ 321}-\frac{ 1}{ 642}\sqrt{ 8821}\) ≈\(-0.124082-0.085658I\) ≈\(-0.124082+0.085658I\)\(-\frac{ 1}{ 10}\)\(0\) ≈\(0.040135\)\(-\frac{ 29}{ 321}+\frac{ 1}{ 642}\sqrt{ 8821}\)\(\frac{ 1}{ 6}\)\(\frac{ 1}{ 2}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)\(0\)\(2\)
\(3\)\(1\)\(1\)\(1\)\(0\)\(1\)\(3\)\(1\)\(1\)\(3\)
\(4\)\(2\)\(2\)\(2\)\(0\)\(2\)\(4\)\(2\)\(1\)\(4\)

Note:

This is operator "11.8" from ...

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2

New Number: 9.8 |  AESZ:  |  Superseeker: 6/17 688/17  |  Hash: 0574d9effd306eb6c9288752b7670904  

Degree: 9

\(17^{2} \theta^4-2 17 x\left(164\theta^4-164\theta^3-167\theta^2-85\theta-17\right)-2^{2} x^{2}\left(35300\theta^4+95864\theta^3+121575\theta^2+70856\theta+16235\right)+2^{2} x^{3}\left(427984\theta^4-277824\theta^3-1460293\theta^2-1490475\theta-492694\right)+2^{4} x^{4}\left(2088512\theta^4+6692704\theta^3+7319011\theta^2+3820745\theta+794302\right)-2^{6} x^{5}\left(1379872\theta^4-6413120\theta^3-11843583\theta^2-9110135\theta-2589134\right)-2^{8} x^{6}\left(13237904\theta^4+37140384\theta^3+64254239\theta^2+57084594\theta+19379105\right)-2^{10} 3^{2} 5 x^{7}\left(255072\theta^4+803200\theta^3+1114259\theta^2+709496\theta+167515\right)+2^{12} 3^{3} 5^{2} 7 x^{8}(2224\theta^2+11008\theta+12225)(\theta+1)^2+2^{18} 3^{3} 5^{4} 7^{2} x^{9}(\theta+1)^2(\theta+2)^2\)

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Coefficients of the holomorphic solution: 1, -2, 18, -20, 1330, ...
--> OEIS
Normalized instanton numbers (n0=1): 6/17, 83/17, 688/17, 7350/17, 5150, ... ; Common denominator:...

Discriminant

\((4z-1)(12z+1)(1600z^3+272z^2+8z-1)(-17+164z+1680z^2)^2\)

Local exponents

\(-\frac{ 41}{ 840}-\frac{ 1}{ 840}\sqrt{ 8821}\) ≈\(-0.106819-0.053966I\) ≈\(-0.106819+0.053966I\)\(-\frac{ 1}{ 12}\)\(0\) ≈\(0.043637\)\(-\frac{ 41}{ 840}+\frac{ 1}{ 840}\sqrt{ 8821}\)\(\frac{ 1}{ 4}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)\(1\)
\(3\)\(1\)\(1\)\(1\)\(0\)\(1\)\(3\)\(1\)\(2\)
\(4\)\(2\)\(2\)\(2\)\(0\)\(2\)\(4\)\(2\)\(2\)

Note:

This is operator "9.8" from ...

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