### Summary

You searched for: superseeker=0,1/3

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1

New Number: 8.54 |  AESZ:  |  Superseeker: 0 1/3  |  Hash: bb80872017d0578a4ae56172666b807c

Degree: 8

$\theta^4+x\theta(3\theta^3-6\theta^2-4\theta-1)-x^{2}\left(211\theta^4+856\theta^3+1433\theta^2+1184\theta+384\right)-2 x^{3}\left(761\theta^4+3288\theta^3+6477\theta^2+6654\theta+2700\right)+2^{2} x^{4}(\theta+1)(2013\theta^3+17379\theta^2+40726\theta+28548)+2^{3} x^{5}(\theta+1)(15719\theta^3+126105\theta^2+325408\theta+269508)+2^{5} 3^{2} x^{6}(\theta+1)(\theta+2)(1817\theta^2+11967\theta+19631)+2^{7} 3^{4} x^{7}(\theta+3)(\theta+2)(\theta+1)(89\theta+350)+2^{9} 3^{3} 43 x^{8}(\theta+1)(\theta+2)(\theta+3)(\theta+4)$

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Coefficients of the holomorphic solution: 1, 0, 24, 72, 1296, ...
--> OEIS
Normalized instanton numbers (n0=1): 0, 1/2, 1/3, -1, 2, ... ; Common denominator:...

#### Discriminant

$(4z+1)(6z+1)(43z^2+13z+1)(2z+1)^2(12z-1)^2$

#### Local exponents

$-\frac{ 1}{ 2}$$-\frac{ 1}{ 4}$$-\frac{ 1}{ 6}$$-\frac{ 13}{ 86}-\frac{ 1}{ 86}\sqrt{ 3}I$$-\frac{ 13}{ 86}+\frac{ 1}{ 86}\sqrt{ 3}I$$0$$\frac{ 1}{ 12}$$\infty$
$0$$0$$0$$0$$0$$0$$0$$1$
$1$$1$$1$$1$$1$$0$$\frac{ 1}{ 2}$$2$
$3$$1$$1$$1$$1$$0$$\frac{ 1}{ 2}$$3$
$4$$2$$2$$2$$2$$0$$1$$4$

#### Note:

This is operator "8.54" from ...