Summary

You searched for: sol=784

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1

New Number: 4.43 |  AESZ: 225  |  Superseeker: 93984 25265152551072  |  Hash: 5993002ccf811247be9232b089dd8e3a  

Degree: 4

\(\theta^4+2^{4} x\left(22192\theta^4-17056\theta^3-9576\theta^2-1048\theta-49\right)+2^{20} x^{2}\left(33648\theta^4-44688\theta^3+16224\theta^2+1764\theta+17\right)+2^{34} 5 x^{3}\left(6512\theta^4-6144\theta^3-4440\theta^2-1536\theta-193\right)-2^{55} 5^{2} x^{4}\left((2\theta+1)^4\right)\)

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Coefficients of the holomorphic solution: 1, 784, 3226896, 20413907200, 157477179235600, ...
--> OEIS
Normalized instanton numbers (n0=1): 93984, -1084521600, 25265152551072, -787700706860008320, 28889437619654310485088, ... ; Common denominator:...

Discriminant

\(-(536870912z^2-27392z-1)(1+163840z)^2\)

Local exponents

≈\(-2.5e-05\)\(-\frac{ 1}{ 163840}\)\(0\)\(s_2\)\(s_1\) ≈\(7.6e-05\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)
\(1\)\(3\)\(0\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)
\(2\)\(4\)\(0\)\(2\)\(2\)\(2\)\(\frac{ 1}{ 2}\)

Note:

Sporadic Operator. There is a second MUM-point
hiding at infinity, corresponding to Operator
AESZ 222/4.42

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2

New Number: 13.2 |  AESZ:  |  Superseeker: 288 -8252768  |  Hash: ad47c122958add1c452a9858793ef177  

Degree: 13

\(\theta^4-2^{4} x\left(192\theta^4+352\theta^3+392\theta^2+216\theta+49\right)+2^{12} x^{2}\left(1312\theta^4+2912\theta^3+5328\theta^2+4968\theta+1777\right)-2^{21} x^{3}\left(3336\theta^4+7360\theta^3+12252\theta^2+14040\theta+6269\right)+2^{28} x^{4}\left(26000\theta^4+61440\theta^3+92496\theta^2+79216\theta+30659\right)-2^{38} x^{5}\left(19848\theta^4+49192\theta^3+87106\theta^2+61486\theta+15137\right)+2^{46} x^{6}\left(48464\theta^4+126184\theta^3+248968\theta^2+204418\theta+60711\right)-2^{52} x^{7}\left(370576\theta^4+1125248\theta^3+2210040\theta^2+2071840\theta+776313\right)+2^{64} x^{8}\left(32992\theta^4+127280\theta^3+257876\theta^2+261776\theta+109291\right)-2^{71} x^{9}\left(66640\theta^4+329440\theta^3+743448\theta^2+827560\theta+373765\right)+2^{81} x^{10}\left(11376\theta^4+70016\theta^3+181088\theta^2+224296\theta+110253\right)-2^{88} x^{11}\left(9872\theta^4+73152\theta^3+216216\theta^2+297488\theta+159121\right)+2^{99} x^{12}\left(304\theta^4+2640\theta^3+8824\theta^2+13396\theta+7763\right)-2^{108} x^{13}\left((2\theta+5)^4\right)\)

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Coefficients of the holomorphic solution: 1, 784, 486672, 279216384, 154637278480, ...
--> OEIS
Normalized instanton numbers (n0=1): 288, 59200, -8252768, -1223488576, 585571467872, ... ; Common denominator:...

Discriminant

\(-(1-768z+65536z^2)(512z-1)^2(134217728z^3-655360z^2+256z-1)^2(256z-1)^3\)

Local exponents

\(0\) ≈\(3.7e-05-0.001244I\) ≈\(3.7e-05+0.001244I\)\(\frac{ 3}{ 512}-\frac{ 1}{ 512}\sqrt{ 5}\)\(\frac{ 1}{ 512}\)\(\frac{ 1}{ 256}\) ≈\(0.004808\)\(\frac{ 3}{ 512}+\frac{ 1}{ 512}\sqrt{ 5}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 5}{ 2}\)
\(0\)\(1\)\(1\)\(1\)\(0\)\(0\)\(1\)\(1\)\(\frac{ 5}{ 2}\)
\(0\)\(3\)\(3\)\(1\)\(-1\)\(0\)\(3\)\(1\)\(\frac{ 5}{ 2}\)
\(0\)\(4\)\(4\)\(2\)\(1\)\(0\)\(4\)\(2\)\(\frac{ 5}{ 2}\)

Note:

This is operator "13.2" from ...

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