Summary

You searched for: Spectrum0=5/6,1,1,7/6

Your search produced 6 matches

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1

New Number: 2.41 |  AESZ:  |  Superseeker: -522 -9879192  |  Hash: 73d9f98b2c49f1c35df531f020cf1721  

Degree: 2

\(\theta^4-2 3^{2} x\left(324\theta^4+648\theta^3+765\theta^2+441\theta+97\right)+2^{2} 3^{10} x^{2}(\theta+1)^2(6\theta+5)(6\theta+7)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 1746, 3951990, 9740271348, 25043989159350, ...
--> OEIS
Normalized instanton numbers (n0=1): -522, -105291/2, -9879192, -2420127936, -689420749716, ... ; Common denominator:...

Discriminant

\((2916z-1)^2\)

Local exponents

\(0\)\(\frac{ 1}{ 2916}\)\(\infty\)
\(0\)\(0\)\(\frac{ 5}{ 6}\)
\(0\)\(-\frac{ 1}{ 2}\)\(1\)
\(0\)\(1\)\(1\)
\(0\)\(\frac{ 3}{ 2}\)\(\frac{ 7}{ 6}\)

Note:

Operator equivalent to $\hat{4}$

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2

New Number: 2.64 |  AESZ: 182  |  Superseeker: 1 7  |  Hash: 89ba4729efa82413b33fe6928ff8d2c9  

Degree: 2

\(\theta^4-x\left(43\theta^4+86\theta^3+77\theta^2+34\theta+6\right)+2^{2} 3 x^{2}(\theta+1)^2(6\theta+5)(6\theta+7)\)

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Coefficients of the holomorphic solution: 1, 6, 66, 924, 14850, ...
--> OEIS
Normalized instanton numbers (n0=1): 1, 7/4, 7, 40, 270, ... ; Common denominator:...

Discriminant

\((27z-1)(16z-1)\)

Local exponents

\(0\)\(\frac{ 1}{ 27}\)\(\frac{ 1}{ 16}\)\(\infty\)
\(0\)\(0\)\(0\)\(\frac{ 5}{ 6}\)
\(0\)\(1\)\(1\)\(1\)
\(0\)\(1\)\(1\)\(1\)
\(0\)\(2\)\(2\)\(\frac{ 7}{ 6}\)

Note:

This is operator "2.64" from ...

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3

New Number: 5.111 |  AESZ: 380  |  Superseeker: 12 2320  |  Hash: 85214e3836a67470a05358a4d38fb124  

Degree: 5

\(\theta^4-2 x\left(60\theta^4+90\theta^3+68\theta^2+23\theta+3\right)+2^{2} x^{2}\left(313\theta^4-398\theta^3-1417\theta^2-1033\theta-252\right)+2^{3} x^{3}\left(654\theta^4+5064\theta^3+3574\theta^2+129\theta-405\right)-2^{4} 5 x^{4}\left(628\theta^4-40\theta^3-1699\theta^2-1661\theta-480\right)-2^{6} 3 5^{2} x^{5}(\theta+1)^2(6\theta+5)(6\theta+7)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 6, 246, 13020, 832950, ...
--> OEIS
Normalized instanton numbers (n0=1): 12, 511/4, 2320, 63507, 2180312, ... ; Common denominator:...

Discriminant

\(-(108z-1)(4z+1)^2(10z-1)^2\)

Local exponents

\(-\frac{ 1}{ 4}\)\(0\)\(\frac{ 1}{ 108}\)\(\frac{ 1}{ 10}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(\frac{ 5}{ 6}\)
\(\frac{ 1}{ 2}\)\(0\)\(1\)\(1\)\(1\)
\(\frac{ 1}{ 2}\)\(0\)\(1\)\(3\)\(1\)
\(1\)\(0\)\(2\)\(4\)\(\frac{ 7}{ 6}\)

Note:

This is operator "5.111" from ...

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4

New Number: 5.81 |  AESZ: 312  |  Superseeker: 5/7 48/7  |  Hash: 767262575f8b1458839c1e9a8beacf0a  

Degree: 5

\(7^{2} \theta^4-7 x\left(39\theta^4+234\theta^3+201\theta^2+84\theta+14\right)-2 x^{2}\left(12073\theta^4+43222\theta^3+57461\theta^2+34328\theta+7756\right)-2^{2} x^{3}\left(28923\theta^4+48426\theta^3-33393\theta^2-80976\theta-32032\right)+2^{3} 13 x^{4}\left(359\theta^4+9790\theta^3+20805\theta^2+15784\theta+4124\right)+2^{5} 3 13^{2} x^{5}(\theta+1)^2(6\theta+5)(6\theta+7)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 2, 30, 308, 5950, ...
--> OEIS
Normalized instanton numbers (n0=1): 5/7, 239/28, 48/7, 4451/14, 5888/7, ... ; Common denominator:...

Discriminant

\((16z+1)(2z-1)(27z-1)(7+26z)^2\)

Local exponents

\(-\frac{ 7}{ 26}\)\(-\frac{ 1}{ 16}\)\(0\)\(\frac{ 1}{ 27}\)\(\frac{ 1}{ 2}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 5}{ 6}\)
\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)
\(3\)\(1\)\(0\)\(1\)\(1\)\(1\)
\(4\)\(2\)\(0\)\(2\)\(2\)\(\frac{ 7}{ 6}\)

Note:

This is operator "5.81" from ...

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5

New Number: 7.12 |  AESZ:  |  Superseeker: -21 -7941  |  Hash: 0841b278bc566a089b643bbe2460fe8b  

Degree: 7

\(\theta^4+3 x\left(99\theta^4+162\theta^3+139\theta^2+58\theta+10\right)+2 3^{4} x^{2}\left(135\theta^4+738\theta^3+945\theta^2+518\theta+116\right)-2^{2} 3^{7} x^{3}\left(117\theta^4-738\theta^3-2010\theta^2-1493\theta-406\right)-2^{3} 3^{10} x^{4}\left(333\theta^4+774\theta^3-898\theta^2-1269\theta-454\right)-2^{4} 3^{13} x^{5}\left(54\theta^4+1224\theta^3+1179\theta^2+347\theta-22\right)+2^{5} 3^{16} x^{6}\left(180\theta^4+72\theta^3-327\theta^2-359\theta-106\right)+2^{7} 3^{19} x^{7}(\theta+1)^2(6\theta+5)(6\theta+7)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, -30, 1458, -89076, 6250050, ...
--> OEIS
Normalized instanton numbers (n0=1): -21, -399, -7941, -986355/4, -8179455, ... ; Common denominator:...

Discriminant

\((27z+1)(54z+1)(54z-1)^2(108z+1)^3\)

Local exponents

\(-\frac{ 1}{ 27}\)\(-\frac{ 1}{ 54}\)\(-\frac{ 1}{ 108}\)\(0\)\(\frac{ 1}{ 54}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 5}{ 6}\)
\(1\)\(1\)\(\frac{ 1}{ 2}\)\(0\)\(1\)\(1\)
\(1\)\(1\)\(\frac{ 3}{ 2}\)\(0\)\(3\)\(1\)
\(2\)\(2\)\(2\)\(0\)\(4\)\(\frac{ 7}{ 6}\)

Note:

This is operator "7.12" from ...

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6

New Number: 8.71 |  AESZ:  |  Superseeker: -15 14044/3  |  Hash: de469dbb89801caa07ec523e3b0e4772  

Degree: 8

\(\theta^4+3 x\left(111\theta^4+186\theta^3+169\theta^2+76\theta+14\right)+2 3^{2} x^{2}\left(2529\theta^4+6930\theta^3+9483\theta^2+6096\theta+1508\right)+2^{2} 3^{4} x^{3}\left(11367\theta^4+32886\theta^3+47658\theta^2+36099\theta+10084\right)+2^{3} 3^{6} x^{4}\left(37017\theta^4+100278\theta^3+103626\theta^2+56025\theta+11582\right)+2^{4} 3^{9} x^{5}\left(29160\theta^4+80676\theta^3+84897\theta^2+27261\theta-568\right)+2^{5} 3^{12} x^{6}\left(16200\theta^4+40824\theta^3+53991\theta^2+31131\theta+6578\right)+2^{7} 3^{17} x^{7}\left(360\theta^4+936\theta^3+1056\theta^2+585\theta+131\right)+2^{9} 3^{20} x^{8}(\theta+1)^2(6\theta+5)(6\theta+7)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, -42, 2682, -200436, 16310250, ...
--> OEIS
Normalized instanton numbers (n0=1): -15, 39, 14044/3, 213069/2, 462576, ... ; Common denominator:...

Discriminant

\((27z+1)(54z+1)(108z+1)^2(1944z^2+18z+1)^2\)

Local exponents

\(-\frac{ 1}{ 27}\)\(-\frac{ 1}{ 54}\)\(-\frac{ 1}{ 108}\)\(-\frac{ 1}{ 216}-\frac{ 1}{ 216}\sqrt{ 23}I\)\(-\frac{ 1}{ 216}+\frac{ 1}{ 216}\sqrt{ 23}I\)\(0\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 5}{ 6}\)
\(1\)\(1\)\(\frac{ 1}{ 6}\)\(1\)\(1\)\(0\)\(1\)
\(1\)\(1\)\(\frac{ 5}{ 6}\)\(3\)\(3\)\(0\)\(1\)
\(2\)\(2\)\(1\)\(4\)\(4\)\(0\)\(\frac{ 7}{ 6}\)

Note:

This is operator "8.71" from ...

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