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You searched for: inst=2790

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1

New Number: 10.5 |  AESZ:  |  Superseeker: 8 -830/9  |  Hash: 26cb7b62aea8fead9548cb08c510d8cc  

Degree: 10

\(\theta^4-x\left(5+36\theta+102\theta^2+132\theta^3+42\theta^4\right)+x^{2}\left(321+2500\theta+5078\theta^2+2676\theta^3-126\theta^4\right)+x^{3}\left(58511+193314\theta+255284\theta^2+165228\theta^3+36750\theta^4\right)+3 x^{4}\left(149076\theta^4+788140\theta^3+1818454\theta^2+1636604\theta+537147\right)+x^{5}\left(18978161+48287282\theta+41352784\theta^2+10485348\theta^3-282726\theta^4\right)+x^{6}\left(75240839+129474252\theta+18361102\theta^2-64936644\theta^3-20164434\theta^4\right)-x^{7}\left(192652267+790586058\theta+1080753300\theta^2+555817116\theta^3+53729334\theta^4\right)-x^{8}\left(1469856277+3396870740\theta+2385867946\theta^2+267688500\theta^3-184083363\theta^4\right)+2 5 13 x^{9}(2\theta+3)(3678542\theta^3+13483935\theta^2+14333215\theta+4727112)+2^{2} 3 5^{2} 13^{2} 73^{2} x^{10}(\theta+1)(2\theta+5)(2\theta+3)(\theta+3)\)

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Coefficients of the holomorphic solution: 1, 5, 79, 791, -9329, ...
--> OEIS
Normalized instanton numbers (n0=1): 8, -45/2, -830/9, -5301/2, 2790, ... ; Common denominator:...

Discriminant

\((3z+1)(5329z^3+1587z^2-69z+1)(13z+1)^2(4z+1)^2(5z-1)^2\)

Local exponents

≈\(-0.337782\)\(-\frac{ 1}{ 3}\)\(-\frac{ 1}{ 4}\)\(-\frac{ 1}{ 13}\)\(0\) ≈\(0.019989-0.01249I\) ≈\(0.019989+0.01249I\)\(\frac{ 1}{ 5}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(\frac{ 1}{ 2}\)\(1\)\(0\)\(1\)\(1\)\(1\)\(\frac{ 3}{ 2}\)
\(1\)\(1\)\(\frac{ 1}{ 2}\)\(3\)\(0\)\(1\)\(1\)\(3\)\(\frac{ 5}{ 2}\)
\(2\)\(2\)\(1\)\(4\)\(0\)\(2\)\(2\)\(4\)\(3\)

Note:

This is operator "10.5" from ...

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2

New Number: 13.8 |  AESZ:  |  Superseeker: 8 -830/9  |  Hash: bcea3fff557004b4da26e9aa34caac6c  

Degree: 13

\(\theta^4-x\left(55\theta^4+142\theta^3+112\theta^2+41\theta+6\right)+x^{2}\left(456\theta^4+4668\theta^3+7455\theta^2+3958\theta+696\right)+x^{3}\left(35078\theta^4+127188\theta^3+175671\theta^2+133507\theta+41718\right)+x^{4}\left(82753\theta^4+664768\theta^3+2450839\theta^2+2316756\theta+736812\right)-3 x^{5}\left(885105\theta^4+1342938\theta^3-883331\theta^2-2706576\theta-1350228\right)-2 3^{2} x^{6}\left(345501\theta^4+3334206\theta^3+4969485\theta^2+2964744\theta+630748\right)+2^{2} 3^{3} x^{7}\left(459939\theta^4+270666\theta^3-1625381\theta^2-2377792\theta-962956\right)+2^{4} 3^{4} x^{8}\left(112581\theta^4+699447\theta^3+1277449\theta^2+1022649\theta+314494\right)-2^{4} 3^{5} x^{9}\left(34101\theta^4-33864\theta^3-473835\theta^2-744726\theta-350272\right)-2^{5} 3^{6} x^{10}(\theta+1)(20847\theta^3+146325\theta^2+303230\theta+217616)+2^{6} 3^{7} x^{11}(\theta+1)(\theta+2)(1791\theta^2-1173\theta-14800)+2^{9} 3^{9} x^{12}(\theta+3)(\theta+2)(\theta+1)(52\theta+257)-2^{10} 3^{9} 17 x^{13}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)

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Coefficients of the holomorphic solution: 1, 6, 90, 1044, -5670, ...
--> OEIS
Normalized instanton numbers (n0=1): 8, -45/2, -830/9, -5301/2, 2790, ... ; Common denominator:...

Discriminant

\(-(2z+1)(3672z^3+1728z^2-72z+1)(6z-1)^2(12z+1)^2(3z+1)^2(z-1)^3\)

Local exponents

≈\(-0.510076\)\(-\frac{ 1}{ 2}\)\(-\frac{ 1}{ 3}\)\(-\frac{ 1}{ 12}\)\(0\) ≈\(0.019744-0.012003I\) ≈\(0.019744+0.012003I\)\(\frac{ 1}{ 6}\)\(1\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(\frac{ 1}{ 2}\)\(1\)\(0\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)\(2\)
\(1\)\(1\)\(\frac{ 1}{ 2}\)\(3\)\(0\)\(1\)\(1\)\(3\)\(\frac{ 3}{ 2}\)\(3\)
\(2\)\(2\)\(1\)\(4\)\(0\)\(2\)\(2\)\(4\)\(2\)\(4\)

Note:

This is operator "13.8" from ...

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