### Summary

You searched for: Spectrum0=1/2,3/2,3/2,5/2

1

New Number: 3.24 |  AESZ:  |  Superseeker: -2 -108  |  Hash: 3c89cc2017daa2eba88c016b8ae5865c

Degree: 3

$\theta^4+2 x(2\theta+1)^2(3\theta^2+3\theta+1)-2^{2} x^{2}(2\theta+1)(2\theta+3)(47\theta^2+94\theta+51)+2^{4} 7 x^{3}(2\theta+1)(2\theta+3)^2(2\theta+5)$

Maple   LaTex

Coefficients of the holomorphic solution: 1, -2, 54, -980, 26950, ...
--> OEIS
Normalized instanton numbers (n0=1): -2, 17, -108, 1498, -19630, ... ; Common denominator:...

#### Discriminant

$(16z-1)(112z^2-40z-1)$

#### Local exponents

$\frac{ 5}{ 28}-\frac{ 1}{ 7}\sqrt{ 2}$$0$$\frac{ 1}{ 16}$$\frac{ 5}{ 28}+\frac{ 1}{ 7}\sqrt{ 2}$$\infty$
$0$$0$$0$$0$$\frac{ 1}{ 2}$
$1$$0$$1$$1$$\frac{ 3}{ 2}$
$1$$0$$1$$1$$\frac{ 3}{ 2}$
$2$$0$$2$$2$$\frac{ 5}{ 2}$

#### Note:

This is operator $\tilde{C_9}$

2

New Number: 3.25 |  AESZ:  |  Superseeker: -2 -308/3  |  Hash: 287da3a26b0da679d81da411b46958d1

Degree: 3

$\theta^4+2 x(2\theta+1)^2(7\theta^2+7\theta+3)+2^{2} x^{2}(2\theta+1)(2\theta+3)(29\theta^2+58\theta+33)+2^{4} 3 5 x^{3}(2\theta+1)(2\theta+3)^2(2\theta+5)$

Maple   LaTex

Coefficients of the holomorphic solution: 1, -6, 90, -2100, 59850, ...
--> OEIS
Normalized instanton numbers (n0=1): -2, 12, -308/3, 1058, -71158/5, ... ; Common denominator:...

#### Discriminant

$(48z+1)(80z^2+8z+1)$

#### Local exponents

$-\frac{ 1}{ 20}-\frac{ 1}{ 10}I$$-\frac{ 1}{ 20}+\frac{ 1}{ 10}I$$-\frac{ 1}{ 48}$$0$$\infty$
$0$$0$$0$$0$$\frac{ 1}{ 2}$
$1$$1$$1$$0$$\frac{ 3}{ 2}$
$1$$1$$1$$0$$\frac{ 3}{ 2}$
$2$$2$$2$$0$$\frac{ 5}{ 2}$

#### Note:

This is operator $\tilde{C_17}$