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1

New Number: 11.14 |  AESZ:  |  Superseeker: 10 13958/9  |  Hash: 0a4e6572e1bb29d996fd62dc404c2446  

Degree: 11

\(3^{6} \theta^4-3^{6} x\left(111\theta^4+180\theta^3+140\theta^2+50\theta+7\right)+3^{3} x^{2}\left(31925\theta^4+11480\theta^3-42466\theta^2-34182\theta-7560\right)+3^{3} x^{3}\left(4877\theta^4+370644\theta^3+409430\theta^2+199476\theta+42297\right)-2 x^{4}\left(10348339\theta^4+26540048\theta^3+42009388\theta^2+29955528\theta+7880058\right)+2 x^{5}\left(9831565\theta^4+67438924\theta^3+143690304\theta^2+116711926\theta+33599143\right)+2 x^{6}\left(14540887\theta^4-5897448\theta^3-129216202\theta^2-158647410\theta-56400514\right)-2 x^{7}\left(20947985\theta^4+93882580\theta^3+71337738\theta^2-9343940\theta-17269525\right)+x^{8}\left(1325117\theta^4+114002144\theta^3+209338120\theta^2+141064960\theta+32960772\right)+3^{4} x^{9}\left(254941\theta^4+471612\theta^3+445052\theta^2+300870\theta+101457\right)-3^{8} x^{10}\left(1621\theta^4+5816\theta^3+8326\theta^2+5418\theta+1332\right)+3^{13} x^{11}\left((\theta+1)^4\right)\)

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Coefficients of the holomorphic solution: 1, 7, 231, 11185, 654199, ...
--> OEIS
Normalized instanton numbers (n0=1): 10, 2591/27, 13958/9, 1037839/27, 3535478/3, ... ; Common denominator:...

Discriminant

\((z-1)(243z^4-520z^3+310z^2+96z-1)(27-189z-143z^2+81z^3)^2\)

Local exponents

≈\(-0.97581\)\(0\) ≈\(0.130861\)\(1\) ≈\(2.610381\)\(#ND+#NDI\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(0\)\(1\)\(1\)\(1\)\(1\)\(1\)
\(3\)\(0\)\(3\)\(1\)\(3\)\(1\)\(1\)
\(4\)\(0\)\(4\)\(2\)\(4\)\(2\)\(1\)

Note:

This is operator "11.14" from ...

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2

New Number: 14.4 |  AESZ:  |  Superseeker: 10 13958/9  |  Hash: 0091fcfec3692ae6ced2f585ef96177c  

Degree: 14

\(3^{6} \theta^4-3^{6} x\theta(15+70\theta+110\theta^2+13\theta^3)-3^{3} x^{2}\left(120409\theta^4+434560\theta^3+542371\theta^2+323352\theta+78624\right)-3^{3} x^{3}\left(5396953\theta^4+22626666\theta^3+37042425\theta^2+28217556\theta+8482968\right)-2 x^{4}\left(1704421489\theta^4+8538160718\theta^3+16779519205\theta^2+14919147216\theta+5077251288\right)-2^{2} 3 x^{5}\left(4201278867\theta^4+24797778110\theta^3+56302322281\theta^2+56325956066\theta+20967103728\right)-2^{3} x^{6}\left(63154319213\theta^4+432278933514\theta^3+1110085421927\theta^2+1224810967950\theta+489654799596\right)-2^{5} 3 x^{7}\left(36597277323\theta^4+286904817870\theta^3+822690934223\theta^2+989019393562\theta+419959932336\right)-2^{6} x^{8}\left(263122045911\theta^4+2344932626130\theta^3+7455815983415\theta^2+9696396501490\theta+4343347545434\right)-2^{7} 5 x^{9}\left(83257168289\theta^4+843955668354\theta^3+2974370084181\theta^2+4174636770342\theta+1965917099796\right)-2^{9} 5 x^{10}\left(38447331387\theta^4+453440983815\theta^3+1797507529325\theta^2+2740147614260\theta+1358896159983\right)-2^{8} 5^{2} 23 x^{11}(\theta+1)(421574469\theta^3+6597293181\theta^2+28022760832\theta+32033938840)+2^{9} 5^{2} 7 23^{2} x^{12}(\theta+2)(\theta+1)(2012137\theta^2+10160979\theta-151326)+2^{10} 5^{3} 7^{2} 23^{3} x^{13}(1525\theta+10484)(\theta+3)(\theta+2)(\theta+1)-2^{11} 3 5^{3} 7^{3} 23^{4} x^{14}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)

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Coefficients of the holomorphic solution: 1, 0, 182, 7020, 401730, ...
--> OEIS
Normalized instanton numbers (n0=1): 10, 2591/27, 13958/9, 1037839/27, 3535478/3, ... ; Common denominator:...

Discriminant

\(-(6z+1)(42320z^4+16560z^3+2032z^2+68z-1)(920z^3-1180z^2-378z-27)^2(7z+1)^3\)

Local exponents

\(-\frac{ 1}{ 6}\) ≈\(-0.157194\) ≈\(-0.157194\) ≈\(-0.151128\)\(-\frac{ 1}{ 7}\) ≈\(-0.124614\) ≈\(-0.087777\)\(0\) ≈\(0.010861\) ≈\(1.55835\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(1\)\(1\)\(0\)\(1\)\(1\)\(0\)\(1\)\(1\)\(2\)
\(1\)\(1\)\(1\)\(3\)\(0\)\(3\)\(1\)\(0\)\(1\)\(3\)\(3\)
\(2\)\(2\)\(2\)\(4\)\(0\)\(4\)\(2\)\(0\)\(2\)\(4\)\(4\)

Note:

This is operator "14.4" from ...

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