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You searched for: sol=76

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1

New Number: 13.15 |  AESZ:  |  Superseeker: 6 626/3  |  Hash: 3e24fdfe8119ac950ce846460f109e44  

Degree: 13

\(\theta^4-2 x\left(16\theta^4+50\theta^3+39\theta^2+14\theta+2\right)-2^{2} x^{2}\left(219\theta^4+390\theta^3+335\theta^2+214\theta+62\right)-2^{4} x^{3}\left(115\theta^4+1068\theta^3+2660\theta^2+2022\theta+582\right)+2^{6} x^{4}\left(122\theta^4-788\theta^3+151\theta^2-913\theta-696\right)-2^{8} 3 x^{5}\left(303\theta^4-1488\theta^3-2955\theta^2-2550\theta-827\right)-2^{10} 3 x^{6}\left(37\theta^4+714\theta^3-5760\theta^2-8319\theta-3550\right)-2^{13} 3 x^{7}\left(101\theta^4+82\theta^3+102\theta^2-1679\theta-1322\right)+2^{15} 3 x^{8}\left(48\theta^4+948\theta^3-461\theta^2-1447\theta-628\right)-2^{17} x^{9}\left(89\theta^4-4392\theta^3-6123\theta^2-450\theta+1902\right)-2^{20} x^{10}\left(121\theta^4-532\theta^3-3072\theta^2-3697\theta-1348\right)+2^{23} 5 x^{11}(\theta+1)(21\theta^3+63\theta^2+206\theta+218)+2^{25} 5^{2} x^{12}(\theta+2)(\theta+1)(2\theta^2-12\theta-27)+2^{27} 5^{3} x^{13}(\theta+1)(\theta+2)^2(\theta+3)\)

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Coefficients of the holomorphic solution: 1, 4, 76, 1936, 57820, ...
--> OEIS
Normalized instanton numbers (n0=1): 6, 41/4, 626/3, 12349/8, 33062, ... ; Common denominator:...

Discriminant

\((4z-1)(4z+1)(16z^2+4z+1)(640z^3+96z^2+48z-1)(1+6z-48z^2+320z^3)^2\)

Local exponents

\(-\frac{ 1}{ 4}\)\(-\frac{ 1}{ 8}-\frac{ 1}{ 8}\sqrt{ 3}I\)\(-\frac{ 1}{ 8}+\frac{ 1}{ 8}\sqrt{ 3}I\) ≈\(-0.084967-0.266773I\) ≈\(-0.084967+0.266773I\) ≈\(-0.082432\)\(0\) ≈\(0.019933\) ≈\(0.116216-0.156217I\) ≈\(0.116216+0.156217I\)\(\frac{ 1}{ 4}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(1\)\(1\)\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)\(1\)\(2\)
\(1\)\(1\)\(1\)\(1\)\(1\)\(3\)\(0\)\(1\)\(3\)\(3\)\(1\)\(2\)
\(2\)\(2\)\(2\)\(2\)\(2\)\(4\)\(0\)\(2\)\(4\)\(4\)\(2\)\(3\)

Note:

This is operator "13.15" from ...

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2

New Number: 14.11 |  AESZ:  |  Superseeker: 52/5 13436/5  |  Hash: c3784675984d5e6eac952e2484ce5404  

Degree: 14

\(5^{2} \theta^4-2^{2} 5 x\left(104\theta^4+256\theta^3+483\theta^2+355\theta+95\right)-2^{4} x^{2}\left(416\theta^4-4672\theta^3+2816\theta^2+12600\theta+7865\right)+2^{10} x^{3}\left(3248\theta^4+17808\theta^3+48534\theta^2+70980\theta+43885\right)-2^{12} x^{4}\left(1024\theta^4+36416\theta^3+105744\theta^2+110264\theta+16363\right)-2^{18} x^{5}\left(8760\theta^4+76704\theta^3+282893\theta^2+513127\theta+376109\right)-2^{21} 3 x^{6}\left(888\theta^4+896\theta^3-8544\theta^2-17976\theta-2111\right)+2^{28} x^{7}\left(2848\theta^4+34496\theta^3+165049\theta^2+366072\theta+314912\right)+2^{29} x^{8}\left(10216\theta^4+125440\theta^3+627568\theta^2+1479624\theta+1370831\right)-2^{34} x^{9}\left(5720\theta^4+84576\theta^3+485065\theta^2+1262925\theta+1248247\right)-2^{36} x^{10}\left(16640\theta^4+273472\theta^3+1728064\theta^2+4911896\theta+5256897\right)+2^{42} x^{11}\left(336\theta^4+1392\theta^3-16378\theta^2-112292\theta-182997\right)+2^{44} x^{12}\left(2720\theta^4+43584\theta^3+258352\theta^2+671784\theta+646989\right)+2^{50} 3 x^{13}\left(8\theta^4+256\theta^3+2199\theta^2+7393\theta+8717\right)-2^{56} 3^{2} x^{14}\left((\theta+4)^4\right)\)

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Coefficients of the holomorphic solution: 1, 76, 5228, 322224, 18933228, ...
--> OEIS
Normalized instanton numbers (n0=1): 52/5, 115, 13436/5, 89632, 18465296/5, ... ; Common denominator:...

Discriminant

\(-(-1+16z)(48z-1)^2(256z^2-32z-5)^2(256z^2+16z-1)^2(16z+1)^3\)

Local exponents

\(-\frac{ 1}{ 32}-\frac{ 1}{ 32}\sqrt{ 5}\)\(\frac{ 1}{ 16}-\frac{ 1}{ 16}\sqrt{ 6}\)\(-\frac{ 1}{ 16}\)\(0\)\(\frac{ 1}{ 48}\)\(-\frac{ 1}{ 32}+\frac{ 1}{ 32}\sqrt{ 5}\)\(\frac{ 1}{ 16}\)\(\frac{ 1}{ 16}+\frac{ 1}{ 16}\sqrt{ 6}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(4\)
\(\frac{ 1}{ 2}\)\(1\)\(0\)\(0\)\(1\)\(\frac{ 1}{ 2}\)\(1\)\(1\)\(4\)
\(\frac{ 1}{ 2}\)\(3\)\(0\)\(0\)\(-2\)\(\frac{ 1}{ 2}\)\(1\)\(3\)\(4\)
\(1\)\(4\)\(0\)\(0\)\(3\)\(1\)\(2\)\(4\)\(4\)

Note:

This is operator "14.11" from ...

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