### Summary

You searched for: inst=-399

1

New Number: 7.12 |  AESZ:  |  Superseeker: -21 -7941  |  Hash: 0841b278bc566a089b643bbe2460fe8b

Degree: 7

$\theta^4+3 x\left(99\theta^4+162\theta^3+139\theta^2+58\theta+10\right)+2 3^{4} x^{2}\left(135\theta^4+738\theta^3+945\theta^2+518\theta+116\right)-2^{2} 3^{7} x^{3}\left(117\theta^4-738\theta^3-2010\theta^2-1493\theta-406\right)-2^{3} 3^{10} x^{4}\left(333\theta^4+774\theta^3-898\theta^2-1269\theta-454\right)-2^{4} 3^{13} x^{5}\left(54\theta^4+1224\theta^3+1179\theta^2+347\theta-22\right)+2^{5} 3^{16} x^{6}\left(180\theta^4+72\theta^3-327\theta^2-359\theta-106\right)+2^{7} 3^{19} x^{7}(\theta+1)^2(6\theta+5)(6\theta+7)$

Maple   LaTex

Coefficients of the holomorphic solution: 1, -30, 1458, -89076, 6250050, ...
--> OEIS
Normalized instanton numbers (n0=1): -21, -399, -7941, -986355/4, -8179455, ... ; Common denominator:...

#### Discriminant

$(27z+1)(54z+1)(54z-1)^2(108z+1)^3$

#### Local exponents

$-\frac{ 1}{ 27}$$-\frac{ 1}{ 54}$$-\frac{ 1}{ 108}$$0$$\frac{ 1}{ 54}$$\infty$
$0$$0$$0$$0$$0$$\frac{ 5}{ 6}$
$1$$1$$\frac{ 1}{ 2}$$0$$1$$1$
$1$$1$$\frac{ 3}{ 2}$$0$$3$$1$
$2$$2$$2$$0$$4$$\frac{ 7}{ 6}$

#### Note:

This is operator "7.12" from ...

2

New Number: 8.78 |  AESZ:  |  Superseeker: 52 48732  |  Hash: 2fb524ad6efb19e0117ae7acbd9f67b9

Degree: 8

$\theta^4-2^{2} x\left(184\theta^4+224\theta^3+175\theta^2+63\theta+9\right)+2^{4} 3 x^{2}\left(3472\theta^4+9664\theta^3+9864\theta^2+4264\theta+705\right)-2^{8} 3^{2} x^{3}\left(1936\theta^4+27936\theta^3+43336\theta^2+21528\theta+3933\right)-2^{16} 3^{3} x^{4}\left(1384\theta^4+524\theta^3-4555\theta^2-3404\theta-753\right)+2^{19} 3^{4} x^{5}\left(3440\theta^4+13712\theta^3-58\theta^2-3774\theta-1161\right)+2^{22} 3^{5} x^{6}\left(11312\theta^4-9888\theta^3-10808\theta^2-1608\theta+459\right)-2^{26} 3^{7} x^{7}(2\theta+1)(1336\theta^3+2772\theta^2+2234\theta+663)-2^{32} 3^{9} x^{8}(2\theta+1)(4\theta+3)(4\theta+5)(2\theta+3)$

Maple   LaTex

Coefficients of the holomorphic solution: 1, 36, 3780, 555120, 95199300, ...
--> OEIS
Normalized instanton numbers (n0=1): 52, -399, 48732, -992750, 98106208, ... ; Common denominator:...

#### Discriminant

$-(256z-1)(110592z^3+6912z^2-288z+1)(-1+96z+13824z^2)^2$

#### Local exponents

≈$-0.091906$$-\frac{ 1}{ 288}-\frac{ 1}{ 288}\sqrt{ 7}$$0$ ≈$0.00385$$\frac{ 1}{ 256}$$-\frac{ 1}{ 288}+\frac{ 1}{ 288}\sqrt{ 7}$ ≈$0.025556$$\infty$
$0$$0$$0$$0$$0$$0$$0$$\frac{ 1}{ 2}$
$1$$1$$0$$1$$1$$1$$1$$\frac{ 3}{ 4}$
$1$$3$$0$$1$$1$$3$$1$$\frac{ 5}{ 4}$
$2$$4$$0$$2$$2$$4$$2$$\frac{ 3}{ 2}$

#### Note:

This is operator "8.78" from ...