Summary

You searched for: Spectrum0=3/2,7/4,9/4,5/2

Your search produced 6 matches

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1

New Number: 4.13 |  AESZ: ~37  |  Superseeker: -128 -1546624/3  |  Hash: c03e4e4ca58f9f1f76c98c8616bc2cbd  

Degree: 4

\(\theta^4-2^{2} x\left(640\theta^4+1280\theta^3+1534\theta^2+894\theta+201\right)+2^{4} 3 x^{2}\left(45056\theta^4+180224\theta^3+308352\theta^2+256256\theta+86363\right)-2^{19} x^{3}(320\theta^2+960\theta+957)(2\theta+3)^2+2^{30} x^{4}(2\theta+3)(2\theta+5)(4\theta+7)(4\theta+9)\)

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Coefficients of the holomorphic solution: 1, 804, 655260, 563879792, 505573095132, ...
--> OEIS
Normalized instanton numbers (n0=1): -128, -5232, -1546624/3, -64705008, -7960717440, ... ; Common denominator:...

Discriminant

\((1024z-1)^2(256z-1)^2\)

Local exponents

\(0\)\(\frac{ 1}{ 1024}\)\(\frac{ 1}{ 256}\)\(\infty\)
\(0\)\(0\)\(0\)\(\frac{ 3}{ 2}\)
\(0\)\(-\frac{ 1}{ 2}\)\(-\frac{ 1}{ 2}\)\(\frac{ 7}{ 4}\)
\(0\)\(1\)\(1\)\(\frac{ 9}{ 4}\)
\(0\)\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(\frac{ 5}{ 2}\)

Note:

YY-Operator equivalent to AESZ 37$=C \ast \alpha ~tilde c \ast i$

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2

New Number: 4.14 |  AESZ:  |  Superseeker: -340 -15174100/3  |  Hash: a961869d91c2f73091913e8f8c4b5fa0  

Degree: 4

\(\theta^4-2^{2} x\left(1088\theta^4+2176\theta^3+2579\theta^2+1491\theta+330\right)+2^{7} 3 x^{2}\left(12352\theta^4+49408\theta^3+74070\theta^2+49324\theta+12325\right)-2^{12} x^{3}(1088\theta^2+3264\theta+3225)(2\theta+3)^2+2^{18} x^{4}(2\theta+3)(2\theta+5)(4\theta+7)(4\theta+9)\)

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Coefficients of the holomorphic solution: 1, 1320, 2233320, 4108451200, 7880762169000, ...
--> OEIS
Normalized instanton numbers (n0=1): -340, -31985, -15174100/3, -1036481610, -246612212640, ... ; Common denominator:...

Discriminant

\((1-2176z+4096z^2)^2\)

Local exponents

\(0\)\(s_1\)\(s_2\)\(\frac{ 17}{ 64}-\frac{ 3}{ 16}\sqrt{ 2}\)\(\frac{ 17}{ 64}+\frac{ 3}{ 16}\sqrt{ 2}\)\(\infty\)
\(0\)\(-\frac{ 1}{ 2}\)\(-\frac{ 1}{ 2}\)\(0\)\(0\)\(\frac{ 3}{ 2}\)
\(0\)\(0\)\(0\)\(-\frac{ 1}{ 2}\)\(-\frac{ 1}{ 2}\)\(\frac{ 7}{ 4}\)
\(0\)\(1\)\(1\)\(1\)\(1\)\(\frac{ 9}{ 4}\)
\(0\)\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(\frac{ 5}{ 2}\)

Note:

YY-Operator equivalent to AESZ 52 $=C \ast \gamma \tilde g \ast i$

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3

New Number: 4.15 |  AESZ:  |  Superseeker: -76 415420  |  Hash: d8c866a60b2b4edb0c88e03315fa2a7b  

Degree: 4

\(\theta^4-2^{2} x\left(448\theta^4+896\theta^3+1077\theta^2+629\theta+142\right)+2^{7} x^{2}\left(11456\theta^4+45824\theta^3+86434\theta^2+81220\theta+30693\right)-2^{12} 3^{4} x^{3}(448\theta^2+1344\theta+1343)(2\theta+3)^2+2^{18} 3^{8} x^{4}(2\theta+3)(2\theta+5)(4\theta+7)(4\theta+9)\)

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Coefficients of the holomorphic solution: 1, 568, 207720, 25669504, -32774007128, ...
--> OEIS
Normalized instanton numbers (n0=1): -76, 2958, 415420, 17891650, -1211214176, ... ; Common denominator:...

Discriminant

\((331776z^2-896z+1)^2\)

Local exponents

\(0\)\(s_1\)\(s_2\)\(\frac{ 7}{ 5184}-\frac{ 1}{ 1296}\sqrt{ 2}I\)\(\frac{ 7}{ 5184}+\frac{ 1}{ 1296}\sqrt{ 2}I\)\(\infty\)
\(0\)\(-\frac{ 1}{ 2}\)\(-\frac{ 1}{ 2}\)\(0\)\(0\)\(\frac{ 3}{ 2}\)
\(0\)\(0\)\(0\)\(-\frac{ 1}{ 2}\)\(-\frac{ 1}{ 2}\)\(\frac{ 7}{ 4}\)
\(0\)\(1\)\(1\)\(1\)\(1\)\(\frac{ 9}{ 4}\)
\(0\)\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(\frac{ 5}{ 2}\)

Note:

YY-Operator equivalent to AESZ 152 $=C \ast \delta ~tilde \alpha \ast i$

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4

New Number: 4.16 |  AESZ:  |  Superseeker: -208 -1863312  |  Hash: ff22b96c1af3d06292a97d4dee085628  

Degree: 4

\(\theta^4-2^{4} x\left(192\theta^4+384\theta^3+457\theta^2+265\theta+59\right)+2^{9} x^{2}\left(4864\theta^4+19456\theta^3+30088\theta^2+21264\theta+5849\right)-2^{18} x^{3}(192\theta^2+576\theta+571)(2\theta+3)^2+2^{26} x^{4}(2\theta+3)(2\theta+5)(4\theta+7)(4\theta+9)\)

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Coefficients of the holomorphic solution: 1, 944, 1093840, 1379945728, 1816122981136, ...
--> OEIS
Normalized instanton numbers (n0=1): -208, -15098, -1863312, -284211001, -50414626800, ... ; Common denominator:...

Discriminant

\((1-1536z+65536z^2)^2\)

Local exponents

\(0\)\(s_1\)\(s_2\)\(\frac{ 3}{ 256}-\frac{ 1}{ 128}\sqrt{ 2}\)\(\frac{ 3}{ 256}+\frac{ 1}{ 128}\sqrt{ 2}\)\(\infty\)
\(0\)\(-\frac{ 1}{ 2}\)\(-\frac{ 1}{ 2}\)\(0\)\(0\)\(\frac{ 3}{ 2}\)
\(0\)\(0\)\(0\)\(-\frac{ 1}{ 2}\)\(-\frac{ 1}{ 2}\)\(\frac{ 7}{ 4}\)
\(0\)\(1\)\(1\)\(1\)\(1\)\(\frac{ 9}{ 4}\)
\(0\)\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(\frac{ 5}{ 2}\)

Note:

YY-Operator equivalent to $C \ast \epsilon ~d \ast i$

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5

New Number: 4.17 |  AESZ:  |  Superseeker: -156 -1229332  |  Hash: 245e2566c8da93abbfc4296923ccba12  

Degree: 4

\(\theta^4-2^{2} 3 x\left(192\theta^4+384\theta^3+457\theta^2+265\theta+59\right)+2^{4} 3^{2} x^{2}\left(7680\theta^4+30720\theta^3+41040\theta^2+20640\theta+2203\right)+2^{12} 3^{4} x^{3}(192\theta^2+576\theta+571)(2\theta+3)^2+2^{18} 3^{6} x^{4}(2\theta+3)(2\theta+5)(4\theta+7)(4\theta+9)\)

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Coefficients of the holomorphic solution: 1, 708, 700740, 738956400, 811309522500, ...
--> OEIS
Normalized instanton numbers (n0=1): -156, -12549, -1229332, -175559052, -27542017056, ... ; Common denominator:...

Discriminant

\((-1+1152z+110592z^2)^2\)

Local exponents

\(-\frac{ 1}{ 192}-\frac{ 1}{ 288}\sqrt{ 3}\)\(0\)\(s_1\)\(s_2\)\(-\frac{ 1}{ 192}+\frac{ 1}{ 288}\sqrt{ 3}\)\(\infty\)
\(0\)\(0\)\(-\frac{ 1}{ 2}\)\(-\frac{ 1}{ 2}\)\(0\)\(\frac{ 3}{ 2}\)
\(-\frac{ 1}{ 2}\)\(0\)\(0\)\(0\)\(-\frac{ 1}{ 2}\)\(\frac{ 7}{ 4}\)
\(1\)\(0\)\(1\)\(1\)\(1\)\(\frac{ 9}{ 4}\)
\(\frac{ 3}{ 2}\)\(0\)\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(\frac{ 5}{ 2}\)

Note:

YY-Operator equivalent to $C \ast \zeta ~tilde f \ast i$

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6

New Number: 4.18 |  AESZ:  |  Superseeker: -100 126580  |  Hash: 3ab4956c5da76dad5e104e338e7c0128  

Degree: 4

\(\theta^4-2^{2} x\left(704\theta^4+1408\theta^3+1697\theta^2+993\theta+225\right)+2^{4} x^{2}\left(187904\theta^4+751616\theta^3+1350224\theta^2+1197216\theta+429975\right)-2^{12} 5^{3} x^{3}(704\theta^2+2112\theta+2115)(2\theta+3)^2+2^{18} 5^{6} x^{4}(2\theta+3)(2\theta+5)(4\theta+7)(4\theta+9)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 900, 701100, 515510800, 365497137900, ...
--> OEIS
Normalized instanton numbers (n0=1): -100, -1260, 126580, 12033300, 1211646512, ... ; Common denominator:...

Discriminant

\((512000z^2-1408z+1)^2\)

Local exponents

\(0\)\(s_1\)\(s_2\)\(\frac{ 11}{ 8000}-\frac{ 1}{ 4000}I\)\(\frac{ 11}{ 8000}+\frac{ 1}{ 4000}I\)\(\infty\)
\(0\)\(-\frac{ 1}{ 2}\)\(-\frac{ 1}{ 2}\)\(0\)\(0\)\(\frac{ 3}{ 2}\)
\(0\)\(0\)\(0\)\(-\frac{ 1}{ 2}\)\(-\frac{ 1}{ 2}\)\(\frac{ 7}{ 4}\)
\(0\)\(1\)\(1\)\(1\)\(1\)\(\frac{ 9}{ 4}\)
\(0\)\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(\frac{ 5}{ 2}\)

Note:

YY-Operator equivalent to $C \ast \eta ~b \ast i$

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