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You searched for: inst=-855952448

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1

New Number: 12.10 |  AESZ:  |  Superseeker: 224 4999008  |  Hash: d0e84951fc25cf38a32ec7fba5893d59  

Degree: 12

\(\theta^4+2^{4} x\left(160\theta^4+32\theta^3+56\theta^2+40\theta+9\right)+2^{13} x^{2}\left(328\theta^4+304\theta^3+442\theta^2+240\theta+57\right)+2^{22} x^{3}\left(416\theta^4+696\theta^3+939\theta^2+738\theta+225\right)+2^{28} 3 x^{4}\left(1120\theta^4+1856\theta^3+3196\theta^2+2832\theta+959\right)+2^{39} 3^{2} x^{5}\left(76\theta^4+128\theta^3+168\theta^2+168\theta+61\right)+2^{45} 3 x^{6}\left(1232\theta^4+2160\theta^3+2420\theta^2+1344\theta+273\right)+2^{54} 3 x^{7}\left(696\theta^4+1272\theta^3+1781\theta^2+554\theta-109\right)+2^{60} 3 x^{8}\left(2608\theta^4+4960\theta^3+8764\theta^2+4440\theta+423\right)+2^{68} 5 x^{9}\left(1216\theta^4+2592\theta^3+4596\theta^2+3456\theta+999\right)+2^{76} 5 x^{10}\left(736\theta^4+2048\theta^3+3128\theta^2+2536\theta+867\right)+2^{84} 5^{2} x^{11}\left(64\theta^4+256\theta^3+412\theta^2+312\theta+93\right)+2^{92} 5^{2} x^{12}\left((2\theta+3)^4\right)\)

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Coefficients of the holomorphic solution: 1, -144, 13584, -80128, -173794032, ...
--> OEIS
Normalized instanton numbers (n0=1): 224, -22712, 4999008, -855952448, 199163179936, ... ; Common denominator:...

Discriminant

\((256z+1)^2(65536z^2+256z+1)^2(83886080z^3+768z+1)^2\)

Local exponents

\(-\frac{ 1}{ 256}\)\(-\frac{ 1}{ 512}-\frac{ 1}{ 512}\sqrt{ 3}I\)\(-\frac{ 1}{ 512}+\frac{ 1}{ 512}\sqrt{ 3}I\) ≈\(-0.00114\)\(0\) ≈\(0.00057-0.003183I\) ≈\(0.00057+0.003183I\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 3}{ 2}\)
\(\frac{ 1}{ 2}\)\(\frac{ 1}{ 2}\)\(\frac{ 1}{ 2}\)\(1\)\(0\)\(1\)\(1\)\(\frac{ 3}{ 2}\)
\(\frac{ 1}{ 2}\)\(\frac{ 1}{ 2}\)\(\frac{ 1}{ 2}\)\(3\)\(0\)\(3\)\(3\)\(\frac{ 3}{ 2}\)
\(1\)\(1\)\(1\)\(4\)\(0\)\(4\)\(4\)\(\frac{ 3}{ 2}\)

Note:

This is operator "12.10" from ...

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2

New Number: 13.5 |  AESZ:  |  Superseeker: 224 4999008  |  Hash: 6d924b9c12ee7379761d409ee75e42ab  

Degree: 13

\(\theta^4-2^{4} x\left(80\theta^4+160\theta^3+152\theta^2+72\theta+15\right)+2^{14} x^{2}\left(24\theta^4+240\theta^3+355\theta^2+230\theta+69\right)+2^{20} x^{3}\left(416\theta^4-2400\theta^3-6216\theta^2-4824\theta-1773\right)-2^{28} x^{4}\left(1840\theta^4-544\theta^3-15328\theta^2-15056\theta-6525\right)+2^{38} 3 x^{5}\left(236\theta^4+1040\theta^3-1629\theta^2-2248\theta-1208\right)+2^{47} 3 x^{6}\left(8\theta^4-1512\theta^3+192\theta^2+951\theta+786\right)-2^{53} 3 x^{7}\left(1568\theta^4-7952\theta^3-4278\theta^2-740\theta+1981\right)+2^{60} 3 x^{8}\left(6976\theta^4-6656\theta^3-9268\theta^2-7912\theta-55\right)-2^{70} x^{9}\left(6680\theta^4+8856\theta^3+8397\theta^2+3060\theta+1017\right)+2^{76} x^{10}\left(22672\theta^4+71840\theta^3+113068\theta^2+90072\theta+30483\right)-2^{84} x^{11}\left(12912\theta^4+62592\theta^3+128336\theta^2+126736\theta+49707\right)+2^{93} 7 x^{12}(2\theta+3)(164\theta^3+810\theta^2+1434\theta+891)-2^{102} 7^{2} x^{13}(\theta+2)^2(2\theta+3)(2\theta+5)\)

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Coefficients of the holomorphic solution: 1, 240, 44304, 7503616, 1459723536, ...
--> OEIS
Normalized instanton numbers (n0=1): 224, -22712, 4999008, -855952448, 199163179936, ... ; Common denominator:...

Discriminant

\(-(65536z^2-256z+1)^2(117440512z^3-196608z^2+1)^2(256z-1)^3\)

Local exponents

≈\(-0.00161\)\(0\) ≈\(0.001642-0.00161I\) ≈\(0.001642+0.00161I\)\(\frac{ 1}{ 512}-\frac{ 1}{ 512}\sqrt{ 3}I\)\(\frac{ 1}{ 512}+\frac{ 1}{ 512}\sqrt{ 3}I\)\(\frac{ 1}{ 256}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 3}{ 2}\)
\(1\)\(0\)\(1\)\(1\)\(\frac{ 1}{ 2}\)\(\frac{ 1}{ 2}\)\(0\)\(2\)
\(3\)\(0\)\(3\)\(3\)\(\frac{ 1}{ 2}\)\(\frac{ 1}{ 2}\)\(0\)\(2\)
\(4\)\(0\)\(4\)\(4\)\(1\)\(1\)\(0\)\(\frac{ 5}{ 2}\)

Note:

This is operator "13.5" from ...

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