### Summary

You searched for: superseeker=-64,-64320

Your search produced exactly one match

1

New Number: 8.53 |  AESZ:  |  Superseeker: -64 -64320  |  Hash: 0714a480e1c587ebada71771f7e3b555

Degree: 8

$\theta^4-2^{5} x\left(2\theta^4-20\theta^3-16\theta^2-6\theta-1\right)-2^{8} x^{2}\left(80\theta^4+32\theta^3-472\theta^2-336\theta-91\right)-2^{14} x^{3}\left(32\theta^4+576\theta^3-52\theta^2-300\theta-141\right)+2^{20} x^{4}\left(116\theta^4-560\theta^3-768\theta^2-464\theta-91\right)+2^{26} x^{5}\left(220\theta^4+232\theta^3-28\theta^2-220\theta-95\right)+2^{30} x^{6}\left(640\theta^4+2304\theta^3+3752\theta^2+2928\theta+867\right)+2^{36} x^{7}\left(176\theta^4+736\theta^3+1156\theta^2+788\theta+197\right)+2^{46} x^{8}\left((\theta+1)^4\right)$

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Coefficients of the holomorphic solution: 1, -32, 1168, -43520, 1777936, ...
--> OEIS
Normalized instanton numbers (n0=1): -64, -1604, -64320, -3255802, -191614656, ... ; Common denominator:...

#### Discriminant

$(1+64z+4096z^2)(64z+1)^2(2048z^2+128z-1)^2$

#### Local exponents

$-\frac{ 1}{ 32}-\frac{ 1}{ 64}\sqrt{ 6}$$-\frac{ 1}{ 64}$$-\frac{ 1}{ 128}-\frac{ 1}{ 128}\sqrt{ 3}I$$-\frac{ 1}{ 128}+\frac{ 1}{ 128}\sqrt{ 3}I$$0$$-\frac{ 1}{ 32}+\frac{ 1}{ 64}\sqrt{ 6}$$\infty$
$0$$0$$0$$0$$0$$0$$1$
$1$$\frac{ 1}{ 2}$$1$$1$$0$$1$$1$
$3$$\frac{ 1}{ 2}$$1$$1$$0$$3$$1$
$4$$1$$2$$2$$0$$4$$1$

#### Note:

This is operator "8.53" from ...