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

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1

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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2

New Number: 13.3 |  AESZ:  |  Superseeker: 4 52  |  Hash: 9127ce057848ca38f220a7bb67e245a2  

Degree: 13

\(\theta^4-2^{2} x\left(38\theta^4+50\theta^3+53\theta^2+28\theta+6\right)+2^{4} x^{2}\left(617\theta^4+1598\theta^3+2361\theta^2+1812\theta+586\right)-2^{8} x^{3}\left(1422\theta^4+5468\theta^3+10321\theta^2+9918\theta+3961\right)+2^{11} x^{4}\left(4165\theta^4+21060\theta^3+48228\theta^2+54855\theta+25440\right)-2^{14} x^{5}\left(8248\theta^4+50660\theta^3+135119\theta^2+175776\theta+91644\right)+2^{16} x^{6}\left(23161\theta^4+161282\theta^3+479205\theta^2+690060\theta+393943\right)-2^{20} x^{7}\left(12116\theta^4+89614\theta^3+279997\theta^2+425868\theta+256804\right)+2^{23} x^{8}\left(9924\theta^4+74644\theta^3+231233\theta^2+346097\theta+206261\right)-2^{27} x^{9}\left(3250\theta^4+24820\theta^3+75837\theta^2+107033\theta+58293\right)+2^{28} x^{10}\left(6672\theta^4+52000\theta^3+164304\theta^2+235440\theta+126113\right)-2^{32} x^{11}\left(1312\theta^4+10208\theta^3+32688\theta^2+49072\theta+28407\right)+2^{36} x^{12}\left(192\theta^4+1568\theta^3+4952\theta^2+7144\theta+3959\right)-2^{40} x^{13}\left((2\theta+5)^4\right)\)

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Coefficients of the holomorphic solution: 1, 24, 464, 8832, 178960, ...
--> OEIS
Normalized instanton numbers (n0=1): 4, 7/2, 52, 500, 2796, ... ; Common denominator:...

Discriminant

\(-(1-48z+256z^2)(8z-1)^2(512z^3-32z^2+20z-1)^2(16z-1)^3\)

Local exponents

\(0\) ≈\(0.005863-0.196043I\) ≈\(0.005863+0.196043I\)\(\frac{ 3}{ 32}-\frac{ 1}{ 32}\sqrt{ 5}\) ≈\(0.050774\)\(\frac{ 1}{ 16}\)\(\frac{ 1}{ 8}\)\(\frac{ 3}{ 32}+\frac{ 1}{ 32}\sqrt{ 5}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 5}{ 2}\)
\(0\)\(1\)\(1\)\(1\)\(1\)\(0\)\(0\)\(1\)\(\frac{ 5}{ 2}\)
\(0\)\(3\)\(3\)\(1\)\(3\)\(0\)\(-1\)\(1\)\(\frac{ 5}{ 2}\)
\(0\)\(4\)\(4\)\(2\)\(4\)\(0\)\(1\)\(2\)\(\frac{ 5}{ 2}\)

Note:

This is operator "13.3" from ...

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