### Summary

You searched for: sol=32

1

New Number: 5.14 |  AESZ: 116  |  Superseeker: 64 23360  |  Hash: 0b366ad8c78b6697205c5a7fff270f5b

Degree: 5

$\theta^4-2^{5} x\left(10\theta^4+26\theta^3+20\theta^2+7\theta+1\right)+2^{8} x^{2}\left(52\theta^4+472\theta^3+832\theta^2+492\theta+103\right)+2^{16} x^{3}\left(14\theta^4+12\theta^3-96\theta^2-105\theta-29\right)-2^{18} x^{4}(2\theta+1)(56\theta^3+468\theta^2+646\theta+249)-2^{24} x^{5}(2\theta+1)(4\theta+3)(4\theta+5)(2\theta+3)$

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Coefficients of the holomorphic solution: 1, 32, 2448, 273920, 38525200, ...
--> OEIS
Normalized instanton numbers (n0=1): 64, 12, 23360, 654490, 53956288, ... ; Common denominator:...

#### Discriminant

$-(-1+256z)(32z+1)^2(64z-1)^2$

#### Local exponents

$-\frac{ 1}{ 32}$$0$$\frac{ 1}{ 256}$$\frac{ 1}{ 64}$$\infty$
$0$$0$$0$$0$$\frac{ 1}{ 2}$
$1$$0$$1$$\frac{ 1}{ 2}$$\frac{ 3}{ 4}$
$3$$0$$1$$\frac{ 1}{ 2}$$\frac{ 5}{ 4}$
$4$$0$$2$$1$$\frac{ 3}{ 2}$

#### Note:

This is operator "5.14" from ...

2

New Number: 7.1 |  AESZ:  |  Superseeker: 10/7 508/7  |  Hash: 08ab3cb496250adfa30bc3e24ac63c4f

Degree: 7

$7^{2} \theta^4-2 7 x\theta(46\theta^3+52\theta^2+33\theta+7)-2^{2} x^{2}\left(7332\theta^4+28848\theta^3+42633\theta^2+26670\theta+6272\right)-2^{4} x^{3}\left(2860\theta^4+44760\theta^3+120483\theta^2+111279\theta+35098\right)+2^{9} x^{4}\left(2230\theta^4+5920\theta^3-741\theta^2-6509\theta-3049\right)+2^{14} x^{5}\left(174\theta^4+1320\theta^3+1971\theta^2+1095\theta+190\right)-2^{19} x^{6}\left(22\theta^4+24\theta^3-9\theta^2-21\theta-7\right)-2^{25} x^{7}\left((\theta+1)^4\right)$

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Coefficients of the holomorphic solution: 1, 0, 32, 288, 7776, ...
--> OEIS
Normalized instanton numbers (n0=1): 10/7, 100/7, 508/7, 808, 59910/7, ... ; Common denominator:...

#### Discriminant

$-(16z+1)(32z-1)(32z-7)^2(4z+1)^3$

#### Local exponents

$-\frac{ 1}{ 4}$$-\frac{ 1}{ 16}$$0$$\frac{ 1}{ 32}$$\frac{ 7}{ 32}$$\infty$
$0$$0$$0$$0$$0$$1$
$\frac{ 1}{ 2}$$1$$0$$1$$1$$1$
$\frac{ 3}{ 2}$$1$$0$$1$$3$$1$
$2$$2$$0$$2$$4$$1$

#### Note:

This is operator "7.1" from ...

3

New Number: 8.44 |  AESZ:  |  Superseeker: -64 -131904  |  Hash: 2d570a3dc1cbc5b6596272f33b48fc98

Degree: 8

$\theta^4-2^{5} x\left(36\theta^4+6\theta^3+8\theta^2+5\theta+1\right)+2^{8} x^{2}\left(2088\theta^4+1080\theta^3+1301\theta^2+574\theta+93\right)-2^{13} x^{3}\left(15712\theta^4+15960\theta^3+16990\theta^2+7785\theta+1381\right)+2^{18} x^{4}\left(65988\theta^4+103368\theta^3+107829\theta^2+52005\theta+9754\right)-2^{24} x^{5}\left(77224\theta^4+157960\theta^3+166412\theta^2+81089\theta+15251\right)+2^{30} x^{6}\left(47156\theta^4+110400\theta^3+112227\theta^2+50868\theta+8885\right)-2^{38} 7 x^{7}\left(452\theta^4+1168\theta^3+1301\theta^2+717\theta+160\right)+2^{46} 7^{2} x^{8}\left((\theta+1)^4\right)$

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Coefficients of the holomorphic solution: 1, 32, 2096, 172544, 15870736, ...
--> OEIS
Normalized instanton numbers (n0=1): -64, -2084, -131904, -10745878, -1015115456, ... ; Common denominator:...

#### Discriminant

$(1-192z+1024z^2)(128z-1)^2(14336z^2-352z+1)^2$

#### Local exponents

$0$$\frac{ 11}{ 896}-\frac{ 1}{ 896}\sqrt{ 65}$$\frac{ 3}{ 32}-\frac{ 1}{ 16}\sqrt{ 2}$$\frac{ 1}{ 128}$$\frac{ 11}{ 896}+\frac{ 1}{ 896}\sqrt{ 65}$$\frac{ 3}{ 32}+\frac{ 1}{ 16}\sqrt{ 2}$$\infty$
$0$$0$$0$$0$$0$$0$$1$
$0$$1$$1$$\frac{ 1}{ 2}$$1$$1$$1$
$0$$3$$1$$\frac{ 1}{ 2}$$3$$1$$1$
$0$$4$$2$$1$$4$$2$$1$

#### Note:

This is operator "8.44" from ...

4

New Number: 8.46 |  AESZ:  |  Superseeker: 192 616896  |  Hash: e38642e59fc2f9e3117437fcdbfe450e

Degree: 8

$\theta^4-2^{5} x\left(11\theta^4+46\theta^3+32\theta^2+9\theta+1\right)-2^{8} x^{2}\left(613\theta^4+892\theta^3-29\theta^2-66\theta-7\right)-2^{13} x^{3}\left(1315\theta^4+978\theta^3+2243\theta^2+1068\theta+179\right)+2^{18} x^{4}\left(949\theta^4-2986\theta^3-3302\theta^2-1569\theta-313\right)+2^{23} x^{5}\left(420\theta^4+1566\theta^3-1116\theta^2-1290\theta-353\right)-2^{26} x^{6}\left(709\theta^4-1416\theta^3-1163\theta^2-72\theta+131\right)-2^{31} 5 x^{7}\left(19\theta^4-10\theta^3-71\theta^2-66\theta-19\right)-2^{36} 5^{2} x^{8}\left((\theta+1)^4\right)$

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Coefficients of the holomorphic solution: 1, 32, 6224, 1859072, 679223056, ...
--> OEIS
Normalized instanton numbers (n0=1): 192, 3108, 616896, 73692781, 15330708544, ... ; Common denominator:...

#### Discriminant

$-(16z+1)(16384z^3+2560z^2+624z-1)(-1-128z+2560z^2)^2$

#### Local exponents

≈$-0.078921-0.179189I$ ≈$-0.078921+0.179189I$$-\frac{ 1}{ 16}$$\frac{ 1}{ 40}-\frac{ 1}{ 160}\sqrt{ 26}$$0$ ≈$0.001592$$\frac{ 1}{ 40}+\frac{ 1}{ 160}\sqrt{ 26}$$\infty$
$0$$0$$0$$0$$0$$0$$0$$1$
$1$$1$$1$$1$$0$$1$$1$$1$
$1$$1$$1$$3$$0$$1$$3$$1$
$2$$2$$2$$4$$0$$2$$4$$1$

#### Note:

This is operator "8.46" from ...

5

New Number: 2.71 |  AESZ:  |  Superseeker: 0 0  |  Hash: 757b011780c5986bd45a5bf434c76c28

Degree: 2

$\theta^4-2^{5} x(2\theta+1)^2(2\theta^2+2\theta+1)+2^{8} x^{2}(2\theta+1)(4\theta+3)(4\theta+5)(2\theta+3)$

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Coefficients of the holomorphic solution: 1, 32, 2160, 181760, 17021200, ...
--> OEIS
Normalized instanton numbers (n0=1): 0, -20, 0, -865, 0, ... ; Common denominator:...

#### Discriminant

$(-1+128z)^2$

#### Local exponents

$0$$\frac{ 1}{ 128}$$\infty$
$0$$0$$\frac{ 1}{ 2}$
$0$$\frac{ 1}{ 4}$$\frac{ 3}{ 4}$
$0$$\frac{ 3}{ 4}$$\frac{ 5}{ 4}$
$0$$1$$\frac{ 3}{ 2}$

#### Note:

This is operator is equivalent to [2.33]. Transformation:.....