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You searched for: Spectrum0=-1/2,-1/2,1/2,1/2

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1

New Number: 14.7 |  AESZ:  |  Superseeker: 48 3184  |  Hash: 9e304ff532f3cfafc29dfac77fdff067  

Degree: 14

\(\theta^4-2^{4} x\left(35\theta^4+50\theta^3+49\theta^2+24\theta+5\right)+2^{9} x^{2}\left(255\theta^4+722\theta^3+1027\theta^2+740\theta+227\right)-2^{14} x^{3}\left(1033\theta^4+4298\theta^3+7994\theta^2+7243\theta+2695\right)+2^{19} x^{4}\left(2699\theta^4+13730\theta^3+30984\theta^2+33699\theta+14443\right)-2^{24} x^{5}\left(5407\theta^4+26718\theta^3+63946\theta^2+80619\theta+38786\right)+2^{29} x^{6}\left(10081\theta^4+39658\theta^3+68604\theta^2+85851\theta+43438\right)-2^{34} x^{7}\left(17583\theta^4+63666\theta^3+51252\theta^2-1045\theta-18966\right)+2^{39} x^{8}\left(25019\theta^4+98594\theta^3+101972\theta^2-44371\theta-87630\right)-2^{44} x^{9}\left(29162\theta^4+103060\theta^3+189337\theta^2+75677\theta-39871\right)+2^{49} x^{10}\left(32428\theta^4+78424\theta^3+166293\theta^2+155877\theta+49943\right)-2^{54} x^{11}\left(33248\theta^4+85104\theta^3+119906\theta^2+105882\theta+49279\right)+2^{59} x^{12}\left(24144\theta^4+97280\theta^3+159468\theta^2+125460\theta+41819\right)-2^{67} 5 x^{13}\left(244\theta^4+1456\theta^3+3353\theta^2+3523\theta+1423\right)+2^{75} 5^{2} x^{14}\left((\theta+2)^4\right)\)

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Coefficients of the holomorphic solution: 1, 80, 5776, 422144, 32579856, ...
--> OEIS
Normalized instanton numbers (n0=1): 48, 46, 3184, 409910, -3351792, ... ; Common denominator:...

Discriminant

\((16z-1)(32z-1)(4096z^2-192z+1)(163840z^3+1024z^2+32z-1)^2(64z-1)^4\)

Local exponents

≈\(-0.009802-0.019I\) ≈\(-0.009802+0.019I\)\(0\)\(\frac{ 3}{ 128}-\frac{ 1}{ 128}\sqrt{ 5}\) ≈\(0.013353\)\(\frac{ 1}{ 64}\)\(\frac{ 1}{ 32}\)\(\frac{ 3}{ 128}+\frac{ 1}{ 128}\sqrt{ 5}\)\(\frac{ 1}{ 16}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(-\frac{ 1}{ 2}\)\(0\)\(0\)\(0\)\(2\)
\(1\)\(1\)\(0\)\(1\)\(1\)\(-\frac{ 1}{ 2}\)\(1\)\(1\)\(1\)\(2\)
\(3\)\(3\)\(0\)\(1\)\(3\)\(\frac{ 1}{ 2}\)\(1\)\(1\)\(1\)\(2\)
\(4\)\(4\)\(0\)\(2\)\(4\)\(\frac{ 1}{ 2}\)\(2\)\(2\)\(2\)\(2\)

Note:

This is operator "14.7" from ...

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2

New Number: 14.8 |  AESZ:  |  Superseeker: 92/5 -76/5  |  Hash: a787adbb87527c14af9a5f2508991317  

Degree: 14

\(5^{2} \theta^4-2^{2} 5 x\left(244\theta^4+496\theta^3+473\theta^2+225\theta+45\right)+2^{4} x^{2}\left(24144\theta^4+95872\theta^3+155244\theta^2+117660\theta+36835\right)-2^{9} x^{3}\left(33248\theta^4+180880\theta^3+407234\theta^2+416430\theta+168275\right)+2^{14} x^{4}\left(32428\theta^4+181000\theta^3+474021\theta^2+605903\theta+294817\right)-2^{19} x^{5}\left(29162\theta^4+130236\theta^3+270865\theta^2+378135\theta+208235\right)+2^{24} x^{6}\left(25019\theta^4+101558\theta^3+110864\theta^2+69739\theta+20552\right)-2^{29} x^{7}\left(17583\theta^4+76998\theta^3+91248\theta^2+4717\theta-39868\right)+2^{34} x^{8}\left(10081\theta^4+40990\theta^3+72600\theta^2+35261\theta-9816\right)-2^{39} x^{9}\left(5407\theta^4+16538\theta^3+33406\theta^2+27573\theta+6100\right)+2^{44} x^{10}\left(2699\theta^4+7862\theta^3+13380\theta^2+11845\theta+4325\right)-2^{49} x^{11}\left(1033\theta^4+3966\theta^3+6998\theta^2+6213\theta+2329\right)+2^{54} x^{12}\left(255\theta^4+1318\theta^3+2815\theta^2+2864\theta+1159\right)-2^{59} x^{13}\left(35\theta^4+230\theta^3+589\theta^2+692\theta+313\right)+2^{65} x^{14}\left((\theta+2)^4\right)\)

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Coefficients of the holomorphic solution: 1, 36, 1196, 41488, 1543916, ...
--> OEIS
Normalized instanton numbers (n0=1): 92/5, -342/5, -76/5, 75394/5, -2156752/5, ... ; Common denominator:...

Discriminant

\((64z-1)(32z-1)(256z^2-48z+1)(32768z^3-1024z^2-5-32z)^2(16z-1)^4\)

Local exponents

≈\(-0.020941-0.040594I\) ≈\(-0.020941+0.040594I\)\(0\)\(\frac{ 1}{ 64}\)\(\frac{ 3}{ 32}-\frac{ 1}{ 32}\sqrt{ 5}\)\(\frac{ 1}{ 32}\)\(\frac{ 1}{ 16}\) ≈\(0.073133\)\(\frac{ 3}{ 32}+\frac{ 1}{ 32}\sqrt{ 5}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(-\frac{ 1}{ 2}\)\(0\)\(0\)\(2\)
\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)\(-\frac{ 1}{ 2}\)\(1\)\(1\)\(2\)
\(3\)\(3\)\(0\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)\(3\)\(1\)\(2\)
\(4\)\(4\)\(0\)\(2\)\(2\)\(2\)\(\frac{ 1}{ 2}\)\(4\)\(2\)\(2\)

Note:

This is operator "14.8" from ...

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