Summary

You searched for: Spectrum0=0,1/2,1/2,1

Your search produced 116 matches
 1-30  31-60  61-90  91-116 

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91

New Number: 6.7 |  AESZ:  |  Superseeker: -9 217/3  |  Hash: 9492f991c909a6774f5546668ff53b6a  

Degree: 6

\(\theta^4-3 x\left(42\theta^4+84\theta^3+77\theta^2+35\theta+6\right)+3^{3} x^{2}\left(291\theta^4+1164\theta^3+1747\theta^2+1166\theta+264\right)-2^{2} 3^{5} x^{3}\left(360\theta^4+2160\theta^3+4553\theta^2+3939\theta+1035\right)+2^{3} 3^{8} x^{4}\left(204\theta^4+1632\theta^3+4449\theta^2+4740\theta+1400\right)-2^{4} 3^{11} x^{5}(16\theta^2+80\theta+35)(2\theta+5)^2+2^{4} 3^{14} x^{6}(2\theta+11)(2\theta+7)(2\theta+5)(2\theta+1)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 18, 378, 8820, 266490, ...
--> OEIS
Normalized instanton numbers (n0=1): -9, 18, 217/3, -9, -146079, ... ; Common denominator:...

Discriminant

\((27z-1)(34992z^3-1944z^2+27z-1)(-1+36z)^2\)

Local exponents

\(0\) ≈\(0.002095-0.023494I\) ≈\(0.002095+0.023494I\)\(\frac{ 1}{ 36}\)\(\frac{ 1}{ 27}\) ≈\(0.051365\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(0\)\(1\)\(1\)\(\frac{ 1}{ 2}\)\(1\)\(1\)\(\frac{ 5}{ 2}\)
\(0\)\(1\)\(1\)\(\frac{ 1}{ 2}\)\(1\)\(1\)\(\frac{ 7}{ 2}\)
\(0\)\(2\)\(2\)\(1\)\(2\)\(2\)\(\frac{ 11}{ 2}\)

Note:

This is operator "6.7" from ...

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92

New Number: 6.8 |  AESZ:  |  Superseeker: 567/13 512341/13  |  Hash: 00104510dfaa4ae75940f08df0a52bf5  

Degree: 6

\(13^{2} \theta^4-13 x\left(5041\theta^4+7634\theta^3+5767\theta^2+1950\theta+260\right)+2^{3} x^{2}\left(744635\theta^4+1560842\theta^3+1510101\theta^2+768170\theta+156078\right)-2^{6} 3 x^{3}\left(1232985\theta^4+3409302\theta^3+4189688\theta^2+2419209\theta+518414\right)+2^{9} x^{4}\left(9225025\theta^4+33675338\theta^3+49289090\theta^2+31849807\theta+7296732\right)-2^{12} 3 17 x^{5}(\theta+1)(222704\theta^3+833160\theta^2+989659\theta+317310)+2^{15} 3^{2} 17^{2} 23^{2} x^{6}(\theta+1)(\theta+2)(2\theta+1)(2\theta+5)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 20, 1524, 196400, 31587220, ...
--> OEIS
Normalized instanton numbers (n0=1): 567/13, 11392/13, 512341/13, 34191454/13, 2850663840/13, ... ; Common denominator:...

Discriminant

\((1-293z+4232z^2)(408z-13)^2(16z-1)^2\)

Local exponents

\(0\)\(\frac{ 293}{ 8464}-\frac{ 41}{ 8464}\sqrt{ 41}\)\(\frac{ 13}{ 408}\)\(\frac{ 1}{ 16}\)\(\frac{ 293}{ 8464}+\frac{ 41}{ 8464}\sqrt{ 41}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(0\)\(1\)\(1\)\(\frac{ 1}{ 2}\)\(1\)\(1\)
\(0\)\(1\)\(3\)\(\frac{ 1}{ 2}\)\(1\)\(2\)
\(0\)\(2\)\(4\)\(1\)\(2\)\(\frac{ 5}{ 2}\)

Note:

This is operator "6.8" from ...

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93

New Number: 7.10 |  AESZ:  |  Superseeker: 1 11  |  Hash: b1c277f62ba740f9f7e0371ba53e4194  

Degree: 7

\(\theta^4-x\left(76\theta^4+80\theta^3+73\theta^2+33\theta+6\right)+x^{2}\left(2209\theta^4+4228\theta^3+4745\theta^2+2726\theta+648\right)-2 3^{2} x^{3}\left(1735\theta^4+4646\theta^3+6099\theta^2+4072\theta+1124\right)+2^{2} 3^{3} x^{4}\left(2085\theta^4+7388\theta^3+11695\theta^2+9140\theta+2844\right)-2^{3} 3^{3} x^{5}(\theta+1)(3707\theta^3+14055\theta^2+20242\theta+10704)+2^{6} 3^{5} x^{6}(\theta+1)(\theta+2)(86\theta^2+285\theta+262)-2^{7} 3^{8} x^{7}(\theta+1)(\theta+2)^2(\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 6, 60, 816, 13104, ...
--> OEIS
Normalized instanton numbers (n0=1): 1, 13/4, 11, 50, 1674/5, ... ; Common denominator:...

Discriminant

\(-(3z-1)(18z-1)(27z-1)(12z-1)^2(-1+2z)^2\)

Local exponents

\(0\)\(\frac{ 1}{ 27}\)\(\frac{ 1}{ 18}\)\(\frac{ 1}{ 12}\)\(\frac{ 1}{ 3}\)\(\frac{ 1}{ 2}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(0\)\(1\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)\(2\)
\(0\)\(1\)\(1\)\(3\)\(1\)\(\frac{ 1}{ 2}\)\(2\)
\(0\)\(2\)\(2\)\(4\)\(2\)\(1\)\(3\)

Note:

This is operator "7.10" from ...

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94

New Number: 7.16 |  AESZ:  |  Superseeker: 22/5 68  |  Hash: 660211ce6175f36772066594bfc33cbb  

Degree: 7

\(5^{2} \theta^4-2 5 x\theta(15+71\theta+112\theta^2+38\theta^3)-2^{2} x^{2}\left(4364\theta^4+15872\theta^3+24679\theta^2+19360\theta+6000\right)-2^{4} 3^{2} 5 x^{3}\left(92\theta^4+224\theta^3+103\theta^2-176\theta-165\right)+2^{6} 3^{2} x^{4}\left(1228\theta^4+10496\theta^3+30154\theta^2+35736\theta+14715\right)+2^{9} 3^{4} x^{5}(\theta+1)(38\theta^3+74\theta^2-304\theta-495)-2^{10} 3^{4} x^{6}(2\theta+13)(2\theta+3)(17\theta+39)(\theta+1)-2^{12} 3^{6} x^{7}(\theta+1)(2\theta+5)(2\theta+3)(\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 0, 60, 480, 16524, ...
--> OEIS
Normalized instanton numbers (n0=1): 22/5, 8, 68, 3292/5, 38826/5, ... ; Common denominator:...

Discriminant

\(-(-1+36z)(12z+5)^2(12z+1)^2(4z-1)^2\)

Local exponents

\(-\frac{ 5}{ 12}\)\(-\frac{ 1}{ 12}\)\(0\)\(\frac{ 1}{ 36}\)\(\frac{ 1}{ 4}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(0\)\(0\)\(1\)\(\frac{ 1}{ 2}\)\(\frac{ 3}{ 2}\)
\(3\)\(1\)\(0\)\(1\)\(\frac{ 1}{ 2}\)\(\frac{ 5}{ 2}\)
\(4\)\(1\)\(0\)\(2\)\(1\)\(3\)

Note:

This is operator "7.16" from ...

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95

New Number: 7.17 |  AESZ:  |  Superseeker: 0 18  |  Hash: c248fd7c807d0aae71ef687a9ee40c80  

Degree: 7

\(\theta^4+3 x\left(87\theta^4+84\theta^3+86\theta^2+44\theta+9\right)+2 3^{3} x^{2}\left(539\theta^4+1076\theta^3+1366\theta^2+880\theta+233\right)+2 3^{5} x^{3}\left(3699\theta^4+11424\theta^3+17579\theta^2+13389\theta+4088\right)+3^{7} x^{4}\left(30367\theta^4+128696\theta^3+235722\theta^2+205070\theta+69226\right)+3^{9} x^{5}\left(74547\theta^4+405660\theta^3+871096\theta^2+848930\theta+310507\right)+2 3^{11} 5 x^{6}(2\theta+3)(5066\theta^3+26325\theta^2+44815\theta+23766)+2^{2} 3^{14} 5^{2} 7^{2} x^{7}(\theta+1)(2\theta+5)(2\theta+3)(\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, -27, 783, -23481, 717903, ...
--> OEIS
Normalized instanton numbers (n0=1): 0, -27/2, 18, -999/2, 1566, ... ; Common denominator:...

Discriminant

\((27z+1)(1323z^2+72z+1)(36z+1)^2(45z+1)^2\)

Local exponents

\(-\frac{ 1}{ 27}\)\(-\frac{ 1}{ 36}\)\(-\frac{ 4}{ 147}-\frac{ 1}{ 441}\sqrt{ 3}I\)\(-\frac{ 4}{ 147}+\frac{ 1}{ 441}\sqrt{ 3}I\)\(-\frac{ 1}{ 45}\)\(0\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(\frac{ 1}{ 2}\)\(1\)\(1\)\(1\)\(0\)\(\frac{ 3}{ 2}\)
\(1\)\(\frac{ 1}{ 2}\)\(1\)\(1\)\(3\)\(0\)\(\frac{ 5}{ 2}\)
\(2\)\(1\)\(2\)\(2\)\(4\)\(0\)\(3\)

Note:

This is operator "7.17" from ...

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96

New Number: 7.18 |  AESZ:  |  Superseeker: 352 26115552  |  Hash: df2c3b4e6a3366531b24bb05809eb1a4  

Degree: 7

\(\theta^4-2^{4} x\left(144\theta^4-192\theta^3-172\theta^2-76\theta-11\right)+2^{14} x^{2}\left(100\theta^4-320\theta^3-25\theta^2+155\theta+36\right)-2^{21} x^{3}\left(72\theta^4-1248\theta^3+628\theta^2-180\theta-97\right)-2^{30} x^{4}\left(212\theta^4+256\theta^3-14\theta^2+86\theta+15\right)+2^{36} 3 x^{5}\left(240\theta^4-320\theta^3-332\theta^2-380\theta-119\right)+2^{46} 3^{2} x^{6}\left(12\theta^4+64\theta^3+99\theta^2+67\theta+17\right)-2^{56} 3^{3} x^{7}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, -176, 17168, -4715264, 653856016, ...
--> OEIS
Normalized instanton numbers (n0=1): 352, 60664, 26115552, 16623590600, 13165993300256, ... ; Common denominator:...

Discriminant

\(-(256z-1)^2(256z+1)^2(768z-1)^3\)

Local exponents

\(-\frac{ 1}{ 256}\)\(0\)\(\frac{ 1}{ 768}\)\(\frac{ 1}{ 256}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(1\)
\(0\)\(0\)\(2\)\(\frac{ 1}{ 2}\)\(1\)
\(1\)\(0\)\(3\)\(\frac{ 1}{ 2}\)\(1\)
\(1\)\(0\)\(5\)\(1\)\(1\)

Note:

This is operator "7.18" from ...

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97

New Number: 7.19 |  AESZ:  |  Superseeker: 4/3 -124/81  |  Hash: f7f0f5d883101c38ed22cb74c80c8f5c  

Degree: 7

\(3^{3} \theta^4-2^{2} 3^{2} x\left(12\theta^4-16\theta^3-21\theta^2-13\theta-3\right)-2^{4} 3 x^{2}\left(240\theta^4+1280\theta^3+2068\theta^2+1636\theta+489\right)+2^{10} x^{3}\left(212\theta^4+592\theta^3+490\theta^2-34\theta-129\right)+2^{13} x^{4}\left(72\theta^4+1536\theta^3+4804\theta^2+5468\theta+2031\right)-2^{18} x^{5}\left(100\theta^4+720\theta^3+1535\theta^2+1155\theta+276\right)+2^{20} x^{6}\left(144\theta^4+768\theta^3+1268\theta^2+884\theta+229\right)-2^{28} x^{7}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, -4, 68, -496, 9796, ...
--> OEIS
Normalized instanton numbers (n0=1): 4/3, -14/9, -124/81, -4498/243, 37024/729, ... ; Common denominator:...

Discriminant

\(-(16z-1)^2(16z+1)^2(16z-3)^3\)

Local exponents

\(-\frac{ 1}{ 16}\)\(0\)\(\frac{ 1}{ 16}\)\(\frac{ 3}{ 16}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(1\)
\(0\)\(0\)\(\frac{ 1}{ 2}\)\(2\)\(1\)
\(1\)\(0\)\(\frac{ 1}{ 2}\)\(3\)\(1\)
\(1\)\(0\)\(1\)\(5\)\(1\)

Note:

This is operator "7.19" from ...

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98

New Number: 8.25 |  AESZ: 299  |  Superseeker: -54 -197216/3  |  Hash: c9e3907e21d64cf5564bf2d00992459e  

Degree: 8

\(\theta^4-2 3 x\left(144\theta^4+36\theta^3+47\theta^2+29\theta+6\right)+2^{2} 3^{2} x^{2}\left(8376\theta^4+6648\theta^3+8157\theta^2+3900\theta+724\right)-2^{4} 3^{4} x^{3}\left(42672\theta^4+68616\theta^3+81056\theta^2+44841\theta+9964\right)+2^{6} 3^{5} x^{4}\left(374028\theta^4+962040\theta^3+1262091\theta^2+794463\theta+195335\right)-2^{8} 3^{7} x^{5}\left(633840\theta^4+2243328\theta^3+3405968\theta^2+2385208\theta+629129\right)+2^{12} 3^{8} x^{6}\left(438960\theta^4+1884384\theta^3+3176664\theta^2+2380392\theta+652943\right)-2^{19} 3^{10} x^{7}\left(5760\theta^4+25128\theta^3+39548\theta^2+26606\theta+6517\right)+2^{22} 3^{11} x^{8}(6\theta+5)^2(6\theta+7)^2\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 36, 1908, 116496, 7816500, ...
--> OEIS
Normalized instanton numbers (n0=1): -54, -1530, -197216/3, -3553920, -222887448, ... ; Common denominator:...

Discriminant

\((1-144z+6912z^2)(108z-1)^2(3456z^2-252z+1)^2\)

Local exponents

\(0\)\(\frac{ 7}{ 192}-\frac{ 1}{ 576}\sqrt{ 345}\)\(\frac{ 1}{ 108}\)\(\frac{ 1}{ 96}-\frac{ 1}{ 288}\sqrt{ 3}I\)\(\frac{ 1}{ 96}+\frac{ 1}{ 288}\sqrt{ 3}I\)\(\frac{ 7}{ 192}+\frac{ 1}{ 576}\sqrt{ 345}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 5}{ 6}\)
\(0\)\(1\)\(\frac{ 1}{ 2}\)\(1\)\(1\)\(1\)\(\frac{ 5}{ 6}\)
\(0\)\(3\)\(\frac{ 1}{ 2}\)\(1\)\(1\)\(3\)\(\frac{ 7}{ 6}\)
\(0\)\(4\)\(1\)\(2\)\(2\)\(4\)\(\frac{ 7}{ 6}\)

Note:

This is operator "8.25" from ...

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99

New Number: 8.26 |  AESZ: 301  |  Superseeker: 193/11 48570/11  |  Hash: a91db18876a9dfbf42b88f8d64c55d85  

Degree: 8

\(11^{2} \theta^4-11 x\left(1517\theta^4+3136\theta^3+2393\theta^2+825\theta+110\right)-x^{2}\left(24266+106953\theta+202166\theta^2+207620\theta^3+90362\theta^4\right)-x^{3}\left(53130+217437\theta+415082\theta^2+507996\theta^3+245714\theta^4\right)-x^{4}\left(15226+183269\theta+564786\theta^2+785972\theta^3+407863\theta^4\right)-x^{5}\left(25160+279826\theta+728323\theta^2+790148\theta^3+434831\theta^4\right)-2^{3} x^{6}\left(36361\theta^4+70281\theta^3+73343\theta^2+37947\theta+7644\right)-2^{4} 5 x^{7}\left(1307\theta^4+3430\theta^3+3877\theta^2+2162\theta+488\right)-2^{9} 5^{2} x^{8}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 10, 466, 32392, 2727826, ...
--> OEIS
Normalized instanton numbers (n0=1): 193/11, 1973/11, 48570/11, 1689283/11, 72444183/11, ... ; Common denominator:...

Discriminant

\(-(-1+143z+32z^2)(z+1)^2(20z^2+17z+11)^2\)

Local exponents

\(-\frac{ 143}{ 64}-\frac{ 19}{ 64}\sqrt{ 57}\)\(-1\)\(-\frac{ 17}{ 40}-\frac{ 1}{ 40}\sqrt{ 591}I\)\(-\frac{ 17}{ 40}+\frac{ 1}{ 40}\sqrt{ 591}I\)\(0\)\(-\frac{ 143}{ 64}+\frac{ 19}{ 64}\sqrt{ 57}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(\frac{ 1}{ 2}\)\(1\)\(1\)\(0\)\(1\)\(1\)
\(1\)\(\frac{ 1}{ 2}\)\(3\)\(3\)\(0\)\(1\)\(1\)
\(2\)\(1\)\(4\)\(4\)\(0\)\(2\)\(1\)

Note:

This operator has a second MUM-point at infinity corresponding to operator 8.27.

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100

New Number: 8.27 |  AESZ: 302  |  Superseeker: 109/5 16777/5  |  Hash: e18ddbe4d66a3648b349130bcf119dc7  

Degree: 8

\(5^{2} \theta^4-5 x\left(1307\theta^4+1798\theta^3+1429\theta^2+530\theta+80\right)+2^{4} x^{2}\left(36361\theta^4+75163\theta^3+80666\theta^2+43340\theta+9120\right)-2^{6} x^{3}\left(434831\theta^4+949176\theta^3+966865\theta^2+545700\theta+118340\right)+2^{11} x^{4}\left(407863\theta^4+845480\theta^3+654048\theta^2+219839\theta+18634\right)-2^{16} x^{5}\left(245714\theta^4+474860\theta^3+365378\theta^2+71595\theta-11507\right)+2^{21} x^{6}\left(90362\theta^4+153828\theta^3+121478\theta^2+35967\theta+2221\right)-2^{26} 11 x^{7}\left(1517\theta^4+2932\theta^3+2087\theta^2+621\theta+59\right)-2^{31} 11^{2} x^{8}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 16, 664, 41920, 3350776, ...
--> OEIS
Normalized instanton numbers (n0=1): 109/5, 867/4, 16777/5, 662976/5, 26339071/5, ... ; Common denominator:...

Discriminant

\(-(-1+143z+32z^2)(32z-1)^2(2816z^2-136z+5)^2\)

Local exponents

\(-\frac{ 143}{ 64}-\frac{ 19}{ 64}\sqrt{ 57}\)\(0\)\(-\frac{ 143}{ 64}+\frac{ 19}{ 64}\sqrt{ 57}\)\(\frac{ 17}{ 704}-\frac{ 1}{ 704}\sqrt{ 591}I\)\(\frac{ 17}{ 704}+\frac{ 1}{ 704}\sqrt{ 591}I\)\(\frac{ 1}{ 32}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(0\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)\(1\)
\(1\)\(0\)\(1\)\(3\)\(3\)\(\frac{ 1}{ 2}\)\(1\)
\(2\)\(0\)\(2\)\(4\)\(4\)\(1\)\(1\)

Note:

This operator has a second MUM-point at infinity corresponding to operator 8.26

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101

New Number: 8.36 |  AESZ: 327  |  Superseeker: 24/29 284/29  |  Hash: 586c1906112cbba9b2d54c57ce2add99  

Degree: 8

\(29^{2} \theta^4+2 29 x\theta(24\theta^3-198\theta^2-128\theta-29)-2^{2} x^{2}\left(44284\theta^4+172954\theta^3+248589\theta^2+172057\theta+47096\right)-2^{2} x^{3}\left(525708\theta^4+2414772\theta^3+4447643\theta^2+3839049\theta+1275594\right)-2^{3} x^{4}\left(1415624\theta^4+7911004\theta^3+17395449\theta^2+17396359\theta+6496262\right)-2^{4} x^{5}(\theta+1)(2152040\theta^3+12186636\theta^2+24179373\theta+16560506)-2^{5} x^{6}(\theta+1)(\theta+2)(1912256\theta^2+9108540\theta+11349571)-2^{8} 41 x^{7}(\theta+3)(\theta+2)(\theta+1)(5671\theta+16301)-2^{8} 3 19 41^{2} x^{8}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 0, 14, 96, 1266, ...
--> OEIS
Normalized instanton numbers (n0=1): 24/29, 72/29, 284/29, 1616/29, 10632/29, ... ; Common denominator:...

Discriminant

\(-(6z+1)(152z^3+84z^2+14z-1)(2z+1)^2(82z+29)^2\)

Local exponents

\(-\frac{ 1}{ 2}\)\(-\frac{ 29}{ 82}\) ≈\(-0.302804-0.180271I\) ≈\(-0.302804+0.180271I\)\(-\frac{ 1}{ 6}\)\(0\) ≈\(0.052976\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(\frac{ 1}{ 2}\)\(1\)\(1\)\(1\)\(1\)\(0\)\(1\)\(2\)
\(\frac{ 1}{ 2}\)\(3\)\(1\)\(1\)\(1\)\(0\)\(1\)\(3\)
\(1\)\(4\)\(2\)\(2\)\(2\)\(0\)\(2\)\(4\)

Note:

This operator is reducible to operator 6.23

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102

New Number: 8.43 |  AESZ:  |  Superseeker: 66/7 8716/7  |  Hash: 923554dba37f79c41bf0f67b875c36f7  

Degree: 8

\(7^{2} \theta^4-2 7 x\left(452\theta^4+640\theta^3+509\theta^2+189\theta+28\right)+2^{2} x^{2}\left(47156\theta^4+78224\theta^3+63963\theta^2+31010\theta+7000\right)-2^{5} x^{3}\left(77224\theta^4+150936\theta^3+155876\theta^2+86751\theta+19838\right)+2^{8} x^{4}\left(65988\theta^4+160584\theta^3+193653\theta^2+117501\theta+28198\right)-2^{12} x^{5}\left(15712\theta^4+46888\theta^3+63382\theta^2+41163\theta+10338\right)+2^{16} x^{6}\left(2088\theta^4+7272\theta^3+10589\theta^2+7140\theta+1828\right)-2^{22} x^{7}\left(36\theta^4+138\theta^3+206\theta^2+137\theta+34\right)+2^{26} x^{8}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 8, 224, 10016, 547936, ...
--> OEIS
Normalized instanton numbers (n0=1): 66/7, 573/7, 8716/7, 197852/7, 5617614/7, ... ; Common denominator:...

Discriminant

\((1-96z+256z^2)(4z-1)^2(128z^2-88z+7)^2\)

Local exponents

\(0\)\(\frac{ 3}{ 16}-\frac{ 1}{ 8}\sqrt{ 2}\)\(\frac{ 11}{ 32}-\frac{ 1}{ 32}\sqrt{ 65}\)\(\frac{ 1}{ 4}\)\(\frac{ 3}{ 16}+\frac{ 1}{ 8}\sqrt{ 2}\)\(\frac{ 11}{ 32}+\frac{ 1}{ 32}\sqrt{ 65}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(0\)\(1\)\(1\)\(\frac{ 1}{ 2}\)\(1\)\(1\)\(1\)
\(0\)\(1\)\(3\)\(\frac{ 1}{ 2}\)\(1\)\(3\)\(1\)
\(0\)\(2\)\(4\)\(1\)\(2\)\(4\)\(1\)

Note:

This is operator "8.43" from ...

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103

New Number: 8.44 |  AESZ:  |  Superseeker: -64 -131904  |  Hash: 2d570a3dc1cbc5b6596272f33b48fc98  

Degree: 8

\(\theta^4-2^{5} x\left(36\theta^4+6\theta^3+8\theta^2+5\theta+1\right)+2^{8} x^{2}\left(2088\theta^4+1080\theta^3+1301\theta^2+574\theta+93\right)-2^{13} x^{3}\left(15712\theta^4+15960\theta^3+16990\theta^2+7785\theta+1381\right)+2^{18} x^{4}\left(65988\theta^4+103368\theta^3+107829\theta^2+52005\theta+9754\right)-2^{24} x^{5}\left(77224\theta^4+157960\theta^3+166412\theta^2+81089\theta+15251\right)+2^{30} x^{6}\left(47156\theta^4+110400\theta^3+112227\theta^2+50868\theta+8885\right)-2^{38} 7 x^{7}\left(452\theta^4+1168\theta^3+1301\theta^2+717\theta+160\right)+2^{46} 7^{2} x^{8}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 32, 2096, 172544, 15870736, ...
--> OEIS
Normalized instanton numbers (n0=1): -64, -2084, -131904, -10745878, -1015115456, ... ; Common denominator:...

Discriminant

\((1-192z+1024z^2)(128z-1)^2(14336z^2-352z+1)^2\)

Local exponents

\(0\)\(\frac{ 11}{ 896}-\frac{ 1}{ 896}\sqrt{ 65}\)\(\frac{ 3}{ 32}-\frac{ 1}{ 16}\sqrt{ 2}\)\(\frac{ 1}{ 128}\)\(\frac{ 11}{ 896}+\frac{ 1}{ 896}\sqrt{ 65}\)\(\frac{ 3}{ 32}+\frac{ 1}{ 16}\sqrt{ 2}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(0\)\(1\)\(1\)\(\frac{ 1}{ 2}\)\(1\)\(1\)\(1\)
\(0\)\(3\)\(1\)\(\frac{ 1}{ 2}\)\(3\)\(1\)\(1\)
\(0\)\(4\)\(2\)\(1\)\(4\)\(2\)\(1\)

Note:

This is operator "8.44" from ...

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104

New Number: 8.51 |  AESZ:  |  Superseeker: 58/43 1024/43  |  Hash: 85b9064701880ae8e0518e47cff1b030  

Degree: 8

\(43^{2} \theta^4-43 x\theta(142\theta^3+890\theta^2+574\theta+129)-x^{2}\left(647269\theta^4+2441818\theta^3+3538503\theta^2+2423953\theta+650848\right)-x^{3}\left(7200000\theta^4+34423908\theta^3+65337898\theta^2+57379329\theta+19251960\right)-x^{4}\left(37610765\theta^4+220029964\theta^3+499781264\theta^2+511393545\theta+194039928\right)-2 x^{5}(\theta+1)(54978121\theta^3+324737370\theta^2+665066226\theta+466789876)-x^{6}(\theta+1)(\theta+2)(185181547\theta^2+915931425\theta+1176131796)-2^{2} 3 101 x^{7}(\theta+3)(\theta+2)(\theta+1)(138979\theta+413408)-2^{2} 3^{2} 5^{2} 7 101^{2} x^{8}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 0, 22, 204, 3474, ...
--> OEIS
Normalized instanton numbers (n0=1): 58/43, 211/43, 1024/43, 7544/43, 64880/43, ... ; Common denominator:...

Discriminant

\(-(7z+1)(25z-1)(2z+1)^2(101z+43)^2(3z+1)^2\)

Local exponents

\(-\frac{ 1}{ 2}\)\(-\frac{ 43}{ 101}\)\(-\frac{ 1}{ 3}\)\(-\frac{ 1}{ 7}\)\(0\)\(\frac{ 1}{ 25}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(\frac{ 1}{ 3}\)\(1\)\(\frac{ 1}{ 2}\)\(1\)\(0\)\(1\)\(2\)
\(\frac{ 2}{ 3}\)\(3\)\(\frac{ 1}{ 2}\)\(1\)\(0\)\(1\)\(3\)
\(1\)\(4\)\(1\)\(2\)\(0\)\(2\)\(4\)

Note:

This is operator "8.51" from ...

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105

New Number: 8.52 |  AESZ:  |  Superseeker: 416 9734432  |  Hash: 87729f275f24cb2daf88133571476576  

Degree: 8

\(\theta^4+2^{4} x\left(176\theta^4-32\theta^3+4\theta^2+20\theta+5\right)+2^{12} x^{2}\left(640\theta^4+256\theta^3+680\theta^2+224\theta+27\right)+2^{22} x^{3}\left(220\theta^4+648\theta^3+596\theta^2+348\theta+85\right)+2^{30} x^{4}\left(116\theta^4+1024\theta^3+1608\theta^2+1072\theta+281\right)-2^{38} x^{5}\left(32\theta^4-448\theta^3-1588\theta^2-1404\theta-437\right)-2^{46} x^{6}\left(80\theta^4+288\theta^3-88\theta^2-384\theta-179\right)-2^{57} x^{7}\left(2\theta^4+28\theta^3+56\theta^2+42\theta+11\right)+2^{66} x^{8}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, -80, 6928, -597248, 95243536, ...
--> OEIS
Normalized instanton numbers (n0=1): 416, -52752, 9734432, -2404009688, 687625871328, ... ; Common denominator:...

Discriminant

\((1+256z+65536z^2)(256z+1)^2(131072z^2-1024z-1)^2\)

Local exponents

\(-\frac{ 1}{ 256}\)\(-\frac{ 1}{ 512}-\frac{ 1}{ 512}\sqrt{ 3}I\)\(-\frac{ 1}{ 512}+\frac{ 1}{ 512}\sqrt{ 3}I\)\(\frac{ 1}{ 256}-\frac{ 1}{ 512}\sqrt{ 6}\)\(0\)\(\frac{ 1}{ 256}+\frac{ 1}{ 512}\sqrt{ 6}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(\frac{ 1}{ 2}\)\(1\)\(1\)\(1\)\(0\)\(1\)\(1\)
\(\frac{ 1}{ 2}\)\(1\)\(1\)\(3\)\(0\)\(3\)\(1\)
\(1\)\(2\)\(2\)\(4\)\(0\)\(4\)\(1\)

Note:

This is operator "8.52" from ...

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106

New Number: 8.53 |  AESZ:  |  Superseeker: -64 -64320  |  Hash: 0714a480e1c587ebada71771f7e3b555  

Degree: 8

\(\theta^4-2^{5} x\left(2\theta^4-20\theta^3-16\theta^2-6\theta-1\right)-2^{8} x^{2}\left(80\theta^4+32\theta^3-472\theta^2-336\theta-91\right)-2^{14} x^{3}\left(32\theta^4+576\theta^3-52\theta^2-300\theta-141\right)+2^{20} x^{4}\left(116\theta^4-560\theta^3-768\theta^2-464\theta-91\right)+2^{26} x^{5}\left(220\theta^4+232\theta^3-28\theta^2-220\theta-95\right)+2^{30} x^{6}\left(640\theta^4+2304\theta^3+3752\theta^2+2928\theta+867\right)+2^{36} x^{7}\left(176\theta^4+736\theta^3+1156\theta^2+788\theta+197\right)+2^{46} x^{8}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, -32, 1168, -43520, 1777936, ...
--> OEIS
Normalized instanton numbers (n0=1): -64, -1604, -64320, -3255802, -191614656, ... ; Common denominator:...

Discriminant

\((1+64z+4096z^2)(64z+1)^2(2048z^2+128z-1)^2\)

Local exponents

\(-\frac{ 1}{ 32}-\frac{ 1}{ 64}\sqrt{ 6}\)\(-\frac{ 1}{ 64}\)\(-\frac{ 1}{ 128}-\frac{ 1}{ 128}\sqrt{ 3}I\)\(-\frac{ 1}{ 128}+\frac{ 1}{ 128}\sqrt{ 3}I\)\(0\)\(-\frac{ 1}{ 32}+\frac{ 1}{ 64}\sqrt{ 6}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(\frac{ 1}{ 2}\)\(1\)\(1\)\(0\)\(1\)\(1\)
\(3\)\(\frac{ 1}{ 2}\)\(1\)\(1\)\(0\)\(3\)\(1\)
\(4\)\(1\)\(2\)\(2\)\(0\)\(4\)\(1\)

Note:

This is operator "8.53" from ...

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107

New Number: 8.54 |  AESZ:  |  Superseeker: 0 1/3  |  Hash: bb80872017d0578a4ae56172666b807c  

Degree: 8

\(\theta^4+x\theta(3\theta^3-6\theta^2-4\theta-1)-x^{2}\left(211\theta^4+856\theta^3+1433\theta^2+1184\theta+384\right)-2 x^{3}\left(761\theta^4+3288\theta^3+6477\theta^2+6654\theta+2700\right)+2^{2} x^{4}(\theta+1)(2013\theta^3+17379\theta^2+40726\theta+28548)+2^{3} x^{5}(\theta+1)(15719\theta^3+126105\theta^2+325408\theta+269508)+2^{5} 3^{2} x^{6}(\theta+1)(\theta+2)(1817\theta^2+11967\theta+19631)+2^{7} 3^{4} x^{7}(\theta+3)(\theta+2)(\theta+1)(89\theta+350)+2^{9} 3^{3} 43 x^{8}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 0, 24, 72, 1296, ...
--> OEIS
Normalized instanton numbers (n0=1): 0, 1/2, 1/3, -1, 2, ... ; Common denominator:...

Discriminant

\((4z+1)(6z+1)(43z^2+13z+1)(2z+1)^2(12z-1)^2\)

Local exponents

\(-\frac{ 1}{ 2}\)\(-\frac{ 1}{ 4}\)\(-\frac{ 1}{ 6}\)\(-\frac{ 13}{ 86}-\frac{ 1}{ 86}\sqrt{ 3}I\)\(-\frac{ 13}{ 86}+\frac{ 1}{ 86}\sqrt{ 3}I\)\(0\)\(\frac{ 1}{ 12}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(1\)\(1\)\(1\)\(0\)\(\frac{ 1}{ 2}\)\(2\)
\(3\)\(1\)\(1\)\(1\)\(1\)\(0\)\(\frac{ 1}{ 2}\)\(3\)
\(4\)\(2\)\(2\)\(2\)\(2\)\(0\)\(1\)\(4\)

Note:

This is operator "8.54" from ...

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108

New Number: 8.68 |  AESZ:  |  Superseeker: 6/17 33/17  |  Hash: 0c0662f5b46ac6cb0bd298a63cf364c7  

Degree: 8

\(17^{2} \theta^4+17 x\theta(165\theta^3-114\theta^2-74\theta-17)-x^{2}\left(20619\theta^4+122880\theta^3+175353\theta^2+126480\theta+36992\right)-2 x^{3}\left(201857\theta^4+853944\theta^3+1437673\theta^2+1174122\theta+375972\right)-2^{2} x^{4}\left(571275\theta^4+2711616\theta^3+5301571\theta^2+4856674\theta+1694372\right)-2^{3} 3 x^{5}(\theta+1)(295815\theta^3+1523993\theta^2+2924668\theta+1983212)-2^{5} x^{6}(\theta+1)(\theta+2)(558823\theta^2+2951265\theta+4136951)-2^{7} 3 37 x^{7}(\theta+3)(\theta+2)(\theta+1)(2797\theta+9878)-2^{9} 3^{2} 7 37^{2} x^{8}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 0, 8, 24, 288, ...
--> OEIS
Normalized instanton numbers (n0=1): 6/17, 25/34, 33/17, 157/17, 577/17, ... ; Common denominator:...

Discriminant

\(-(12z-1)(6z+1)(7z^2-z+1)(4z+1)^2(74z+17)^2\)

Local exponents

\(-\frac{ 1}{ 4}\)\(-\frac{ 17}{ 74}\)\(-\frac{ 1}{ 6}\)\(0\)\(\frac{ 1}{ 14}-\frac{ 3}{ 14}\sqrt{ 3}I\)\(\frac{ 1}{ 14}+\frac{ 3}{ 14}\sqrt{ 3}I\)\(\frac{ 1}{ 12}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(\frac{ 1}{ 2}\)\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)\(2\)
\(\frac{ 1}{ 2}\)\(3\)\(1\)\(0\)\(1\)\(1\)\(1\)\(3\)
\(1\)\(4\)\(2\)\(0\)\(2\)\(2\)\(2\)\(4\)

Note:

This is operator "8.68" from ...

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109

New Number: 8.74 |  AESZ:  |  Superseeker: 4 436  |  Hash: a0fbd8561e58a032d489a1dabee1e026  

Degree: 8

\(\theta^4-2^{2} x\theta(22\theta^3+14\theta^2+9\theta+2)+2^{4} x^{2}\left(109\theta^4-74\theta^3-293\theta^2-258\theta-80\right)+2^{8} x^{3}\left(39\theta^4+414\theta^3+674\theta^2+504\theta+144\right)-2^{10} x^{4}\left(405\theta^4+1170\theta^3+1321\theta^2+424\theta-104\right)-2^{14} x^{5}(\theta+1)(12\theta^3+558\theta^2+1495\theta+1255)+2^{16} x^{6}(\theta+1)(\theta+2)(467\theta^2+1593\theta+1540)-2^{20} 5 x^{7}(\theta+3)(\theta+2)(\theta+1)(\theta-40)-2^{22} 5^{2} 7 x^{8}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 0, 80, 1536, 56592, ...
--> OEIS
Normalized instanton numbers (n0=1): 4, 71/2, 436, 6728, 127212, ... ; Common denominator:...

Discriminant

\(-(-1+56z)(20z-1)^2(8z-1)^2(8z+1)^3\)

Local exponents

\(-\frac{ 1}{ 8}\)\(0\)\(\frac{ 1}{ 56}\)\(\frac{ 1}{ 20}\)\(\frac{ 1}{ 8}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(0\)\(0\)\(1\)\(1\)\(\frac{ 1}{ 2}\)\(2\)
\(-\frac{ 1}{ 4}\)\(0\)\(1\)\(3\)\(\frac{ 1}{ 2}\)\(3\)
\(\frac{ 1}{ 4}\)\(0\)\(2\)\(4\)\(1\)\(4\)

Note:

This is operator "8.74" from ...

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110

New Number: 8.79 |  AESZ:  |  Superseeker: 22/5 68  |  Hash: 064e5b590dd8b6a4daa1e905fbe693c2  

Degree: 8

\(5^{2} \theta^4-2 5 x\left(338\theta^4+412\theta^3+371\theta^2+165\theta+30\right)+2^{2} x^{2}\left(46396\theta^4+103408\theta^3+125291\theta^2+76370\theta+19080\right)-2^{4} 3 x^{3}\left(115508\theta^4+357896\theta^3+524149\theta^2+375205\theta+106530\right)+2^{6} 3^{2} x^{4}\left(173456\theta^4+669024\theta^3+1118292\theta^2+883484\theta+269049\right)-2^{11} 3^{3} x^{5}\left(20272\theta^4+91616\theta^3+168594\theta^2+142006\theta+45053\right)+2^{14} 3^{4} x^{6}\left(5792\theta^4+29504\theta^3+58300\theta^2+51220\theta+16641\right)-2^{21} 3^{5} x^{7}(\theta+1)^2(58\theta^2+208\theta+201)+2^{26} 3^{6} x^{8}(\theta+1)^2(\theta+2)^2\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 12, 204, 4368, 112140, ...
--> OEIS
Normalized instanton numbers (n0=1): 22/5, 8, 68, 3292/5, 38826/5, ... ; Common denominator:...

Discriminant

\((-1+48z)(16z-1)^2(48z-5)^2(12z-1)^3\)

Local exponents

\(0\)\(\frac{ 1}{ 48}\)\(\frac{ 1}{ 16}\)\(\frac{ 1}{ 12}\)\(\frac{ 5}{ 48}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(0\)\(1\)\(\frac{ 1}{ 2}\)\(\frac{ 1}{ 2}\)\(1\)\(1\)
\(0\)\(1\)\(\frac{ 1}{ 2}\)\(\frac{ 3}{ 2}\)\(3\)\(2\)
\(0\)\(2\)\(1\)\(2\)\(4\)\(2\)

Note:

This is operator "8.79" from ...

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111

New Number: 8.80 |  AESZ:  |  Superseeker: -28/3 2764/3  |  Hash: 01b1872abfd55652952ae535920a40fe  

Degree: 8

\(3^{2} \theta^4+2^{2} 3 x\left(148\theta^4+248\theta^3+223\theta^2+99\theta+18\right)+2^{7} x^{2}\left(1124\theta^4+3080\theta^3+4211\theta^2+2709\theta+675\right)+2^{12} x^{3}\left(1684\theta^4+4872\theta^3+7059\theta^2+5373\theta+1530\right)+2^{17} x^{4}\left(1828\theta^4+4952\theta^3+5125\theta^2+2799\theta+599\right)+2^{23} x^{5}\left(720\theta^4+1992\theta^3+2102\theta^2+691\theta-13\right)+2^{29} x^{6}\left(200\theta^4+504\theta^3+669\theta^2+390\theta+83\right)+2^{35} x^{7}\left(40\theta^4+104\theta^3+118\theta^2+66\theta+15\right)+2^{43} x^{8}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, -24, 872, -37248, 1740456, ...
--> OEIS
Normalized instanton numbers (n0=1): -28/3, 49/3, 2764/3, 13414, 44384, ... ; Common denominator:...

Discriminant

\((16z+1)(32z+1)(64z+1)^2(2048z^2+32z+3)^2\)

Local exponents

\(-\frac{ 1}{ 16}\)\(-\frac{ 1}{ 32}\)\(-\frac{ 1}{ 64}\)\(-\frac{ 1}{ 128}-\frac{ 1}{ 128}\sqrt{ 23}I\)\(-\frac{ 1}{ 128}+\frac{ 1}{ 128}\sqrt{ 23}I\)\(0\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(\frac{ 1}{ 2}\)\(1\)\(1\)\(0\)\(1\)
\(1\)\(1\)\(\frac{ 1}{ 2}\)\(3\)\(3\)\(0\)\(1\)
\(2\)\(2\)\(1\)\(4\)\(4\)\(0\)\(1\)

Note:

This is operator "8.80" from ...

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112

New Number: 8.81 |  AESZ:  |  Superseeker: -64 54464  |  Hash: 3cc4cfea037192a297dc29928555ed1d  

Degree: 8

\(\theta^4+2^{4} x\left(40\theta^4+56\theta^3+46\theta^2+18\theta+3\right)+2^{10} x^{2}\left(200\theta^4+296\theta^3+357\theta^2+236\theta+58\right)+2^{16} x^{3}\left(720\theta^4+888\theta^3+446\theta^2+417\theta+126\right)+2^{22} x^{4}\left(1828\theta^4+2360\theta^3+1237\theta^2-93\theta-199\right)+2^{29} x^{5}\left(1684\theta^4+1864\theta^3+2547\theta^2+865\theta+28\right)+2^{36} x^{6}\left(1124\theta^4+1416\theta^3+1715\theta^2+969\theta+221\right)+2^{43} 3 x^{7}\left(148\theta^4+344\theta^3+367\theta^2+195\theta+42\right)+2^{53} 3^{2} x^{8}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, -48, 4112, -470784, 65066256, ...
--> OEIS
Normalized instanton numbers (n0=1): -64, 2380, 54464, -1677212, -279711424, ... ; Common denominator:...

Discriminant

\((128z+1)(256z+1)(64z+1)^2(24576z^2+64z+1)^2\)

Local exponents

\(-\frac{ 1}{ 64}\)\(-\frac{ 1}{ 128}\)\(-\frac{ 1}{ 256}\)\(-\frac{ 1}{ 768}-\frac{ 1}{ 768}\sqrt{ 23}I\)\(-\frac{ 1}{ 768}+\frac{ 1}{ 768}\sqrt{ 23}I\)\(0\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(\frac{ 1}{ 2}\)\(1\)\(1\)\(1\)\(1\)\(0\)\(1\)
\(\frac{ 1}{ 2}\)\(1\)\(1\)\(3\)\(3\)\(0\)\(1\)
\(1\)\(2\)\(2\)\(4\)\(4\)\(0\)\(1\)

Note:

This is operator "8.81" from ...

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113

New Number: 8.82 |  AESZ:  |  Superseeker: 0 -1/3  |  Hash: 8bab1ddc8b31cb2c21f01402f27895ce  

Degree: 8

\(\theta^4-x\theta(3\theta^3-6\theta^2-4\theta-1)-x^{2}\left(211\theta^4+856\theta^3+1433\theta^2+1184\theta+384\right)+2 x^{3}\left(761\theta^4+3288\theta^3+6477\theta^2+6654\theta+2700\right)+2^{2} x^{4}(\theta+1)(2013\theta^3+17379\theta^2+40726\theta+28548)-2^{3} x^{5}(\theta+1)(15719\theta^3+126105\theta^2+325408\theta+269508)+2^{5} 3^{2} x^{6}(\theta+1)(\theta+2)(1817\theta^2+11967\theta+19631)-2^{7} 3^{4} x^{7}(\theta+3)(\theta+2)(\theta+1)(89\theta+350)+2^{9} 3^{3} 43 x^{8}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)

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Coefficients of the holomorphic solution: 1, 0, 24, -72, 1296, ...
--> OEIS
Normalized instanton numbers (n0=1): 0, 1/2, -1/3, -1, -2, ... ; Common denominator:...

Discriminant

\((6z-1)(4z-1)(43z^2-13z+1)(12z+1)^2(-1+2z)^2\)

Local exponents

\(-\frac{ 1}{ 12}\)\(0\)\(\frac{ 13}{ 86}-\frac{ 1}{ 86}\sqrt{ 3}I\)\(\frac{ 13}{ 86}+\frac{ 1}{ 86}\sqrt{ 3}I\)\(\frac{ 1}{ 6}\)\(\frac{ 1}{ 4}\)\(\frac{ 1}{ 2}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(\frac{ 1}{ 2}\)\(0\)\(1\)\(1\)\(1\)\(1\)\(1\)\(2\)
\(\frac{ 1}{ 2}\)\(0\)\(1\)\(1\)\(1\)\(1\)\(3\)\(3\)
\(1\)\(0\)\(2\)\(2\)\(2\)\(2\)\(4\)\(4\)

Note:

This is operator "8.82" from ...

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114

New Number: 9.7 |  AESZ:  |  Superseeker: 9 2564/3  |  Hash: 9bb7a7f3a3d5f66018396173696c194c  

Degree: 9

\(\theta^4+3 x\left(93\theta^4+42\theta^3+49\theta^2+28\theta+6\right)+2^{2} 3^{3} x^{2}\left(307\theta^4+328\theta^3+401\theta^2+230\theta+53\right)+2^{2} 3^{5} x^{3}\left(2268\theta^4+4128\theta^3+5443\theta^2+3525\theta+932\right)+2^{4} 3^{7} x^{4}\left(2588\theta^4+6880\theta^3+10145\theta^2+7398\theta+2167\right)+2^{6} 3^{9} x^{5}\left(1897\theta^4+6694\theta^3+11167\theta^2+9015\theta+2853\right)+2^{8} 3^{11} x^{6}\left(895\theta^4+3912\theta^3+7309\theta^2+6408\theta+2150\right)+2^{8} 3^{13} x^{7}\left(1048\theta^4+5360\theta^3+10939\theta^2+10155\theta+3534\right)+2^{10} 3^{15} x^{8}(\theta+1)(172\theta^3+804\theta^2+1295\theta+699)+2^{12} 3^{18} x^{9}(\theta+2)(\theta+1)(2\theta+3)^2\)

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Coefficients of the holomorphic solution: 1, -18, 378, -8676, 213354, ...
--> OEIS
Normalized instanton numbers (n0=1): 9, -72, 2564/3, -12924, 228024, ... ; Common denominator:...

Discriminant

\((27z+1)(432z^2+36z+1)(36z+1)^2(648z^2+72z+1)^2\)

Local exponents

\(-\frac{ 1}{ 18}-\frac{ 1}{ 36}\sqrt{ 2}\)\(-\frac{ 1}{ 24}-\frac{ 1}{ 72}\sqrt{ 3}I\)\(-\frac{ 1}{ 24}+\frac{ 1}{ 72}\sqrt{ 3}I\)\(-\frac{ 1}{ 27}\)\(-\frac{ 1}{ 36}\)\(-\frac{ 1}{ 18}+\frac{ 1}{ 36}\sqrt{ 2}\)\(0\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)\(1\)\(0\)\(\frac{ 3}{ 2}\)
\(3\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)\(3\)\(0\)\(\frac{ 3}{ 2}\)
\(4\)\(2\)\(2\)\(2\)\(1\)\(4\)\(0\)\(2\)

Note:

This is operator "9.7" from ...

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115

New Number: 9.9 |  AESZ:  |  Superseeker: 256/31 28062/31  |  Hash: 924a831431fc249044fe63cfea0eb535  

Degree: 9

\(31^{2} \theta^4-31 x\left(2836\theta^4+4790\theta^3+3728\theta^2+1333\theta+186\right)-x^{2}\left(1539241\theta^2+1291677\theta+342550-558095\theta^4+131134\theta^3\right)+x^{3}\left(6495560\theta^2+387046\theta^4+6264048\theta^3+558+2100591\theta\right)+x^{4}\left(3388169\theta-7521396\theta^3-5037573\theta^4+2030450-2351908\theta^2\right)-2 x^{5}\left(2014896\theta^4+11047341\theta^3+24693967\theta^2+23008058\theta+7682256\right)+x^{6}\left(37321692\theta+8697364+6817193\theta^4+33832842\theta^3+56561513\theta^2\right)+2 11 x^{7}\left(351229\theta^4+2420534\theta^3+6030705\theta^2+6243956\theta+2275780\right)+2^{2} 11^{2} x^{8}(3667\theta^2+17036\theta+18316)(\theta+1)^2+2^{3} 11^{4} x^{9}(\theta+1)^2(\theta+2)^2\)

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Coefficients of the holomorphic solution: 1, 6, 178, 7404, 370674, ...
--> OEIS
Normalized instanton numbers (n0=1): 256/31, 1982/31, 28062/31, 591475/31, 15400630/31, ... ; Common denominator:...

Discriminant

\((2z+1)(121z^2-86z+1)(z+1)^2(22z^2+147z-31)^2\)

Local exponents

\(-\frac{ 147}{ 44}-\frac{ 1}{ 44}\sqrt{ 24337}\)\(-1\)\(-\frac{ 1}{ 2}\)\(0\)\(\frac{ 43}{ 121}-\frac{ 24}{ 121}\sqrt{ 3}\)\(-\frac{ 147}{ 44}+\frac{ 1}{ 44}\sqrt{ 24337}\)\(\frac{ 43}{ 121}+\frac{ 24}{ 121}\sqrt{ 3}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(\frac{ 1}{ 2}\)\(1\)\(0\)\(1\)\(1\)\(1\)\(1\)
\(3\)\(\frac{ 1}{ 2}\)\(1\)\(0\)\(1\)\(3\)\(1\)\(2\)
\(4\)\(1\)\(2\)\(0\)\(2\)\(4\)\(2\)\(2\)

Note:

This is operator "9.9" from ...

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116

New Number: 32.1 |  AESZ:  |  Superseeker: 13 1275  |  Hash: 5c2e3e1d3e85022a77a9136d2272db2f  

Degree: 32

\(\theta^4+x\left(52\theta^4-36\theta-142\theta^3-5-107\theta^2\right)-x^{2}\left(620\theta+8686\theta^3+170+2477\theta^2+1603\theta^4\right)-2 x^{3}\left(57842\theta^4+88182\theta^3+89923\theta^2+53586\theta+14064\right)-x^{4}\left(2697348\theta^3+3016956\theta+1218741\theta^4+4034478\theta^2+1011862\right)+x^{5}\left(4154284\theta^4-36611635\theta^2-9502094\theta^3-20359939-44530432\theta\right)-x^{6}\left(337605744\theta-48775967\theta^4+194246629\theta^2-5346306\theta^3+193227408\right)-2^{2} x^{7}\left(20258471\theta^4-183191522\theta^3-458704813\theta^2-332600094\theta-41903870\right)-2^{3} x^{8}\left(66325647\theta^4-411353730\theta^3-1541171000\theta^2-2130504013\theta-1105449340\right)+2^{5} 3 x^{9}\left(1066771\theta^4-131777420\theta^3+79983198\theta^2+543150745\theta+463708954\right)-2^{4} x^{10}\left(143783659\theta^4+4053640514\theta^3+9858746999\theta^2+7077509476\theta-502326500\right)+2^{7} x^{11}\left(138368083\theta^4+183238033\theta^3-3310018192\theta^2-6653286340\theta-3889203872\right)+2^{7} x^{12}\left(496481718\theta^4+4322462304\theta^3+199787519\theta^2-15317512629\theta-16640068710\right)-2^{8} x^{13}\left(289743462\theta^4-4401242298\theta^3-13355918183\theta^2-7397020754\theta+6375065509\right)-2^{10} x^{14}\left(396133743\theta^4-1333996518\theta^3-15885985865\theta^2-33541445647\theta-23107708481\right)-2^{11} x^{15}\left(453981938\theta^4+4435638750\theta^3+3949663684\theta^2-11263025013\theta-17739853167\right)-2^{12} x^{16}\left(227785391\theta^4+9832817848\theta^3+42310236910\theta^2+74461395968\theta+49621401789\right)+2^{15} x^{17}\left(198897592\theta^4+11771212\theta^3-3867168178\theta^2-11297299537\theta-10235944704\right)+2^{16} x^{18}\left(383086368\theta^4+3420815388\theta^3+11952116012\theta^2+20508953472\theta+14439167835\right)+2^{17} x^{19}\left(190788296\theta^4+2425061392\theta^3+10401497028\theta^2+20606177314\theta+16211593657\right)-2^{19} x^{20}\left(54126314\theta^4+419989028\theta^3+1520710075\theta^2+2841733138\theta+2156782988\right)-2^{21} 3 x^{21}\left(13401434\theta^4+146502422\theta^3+639965165\theta^2+1327396637\theta+1086335005\right)-2^{22} x^{22}\left(10981880\theta^4+141779260\theta^3+691712182\theta^2+1569642590\theta+1393845167\right)+2^{23} x^{23}\left(6721988\theta^4+71373164\theta^3+305959012\theta^2+607082692\theta+457859591\right)+2^{24} x^{24}\left(5172254\theta^4+63781560\theta^3+312564510\theta^2+712915992\theta+628949703\right)+2^{27} x^{25}\left(151244\theta^4+2505628\theta^3+15500094\theta^2+43116865\theta+45072668\right)-2^{28} x^{26}\left(133829\theta^4+1536890\theta^3+6680129\theta^2+12566244\theta+8313095\right)-2^{29} x^{27}\left(54212\theta^4+746052\theta^3+3929140\theta^2+9277842\theta+8249757\right)-2^{31} x^{28}\left(1640\theta^4+35404\theta^3+249484\theta^2+728729\theta+767131\right)+2^{32} x^{29}\left(1266\theta^4+15354\theta^3+69999\theta^2+141732\theta+107131\right)+2^{34} x^{30}\left(187\theta^4+2670\theta^3+14509\theta^2+35511\theta+32982\right)+2^{35} x^{31}\left(22\theta^4+338\theta^3+1960\theta^2+5079\theta+4958\right)+2^{36} x^{32}\left((\theta+4)^4\right)\)

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Coefficients of the holomorphic solution: 1, 5, 85, 2033, 56701, ...
--> OEIS
Normalized instanton numbers (n0=1): 13, -305/4, 1275, -82705/4, 456346, ... ; Common denominator:...

Discriminant

\((2z+1)(z+1)(8z^2+16z+1)(8z^3+28z^2+46z-1)(8z^3+8z^2+z-1)(z-1)^2(8z^2+1)^2(1024z^8+2560z^7-1792z^6-3520z^5-1616z^4+920z^3+36z^2-41z-1)^2\)

Local exponents

\(-1\)\(-\frac{ 1}{ 2}\)\(0\)\(s_18\)\(s_15\)\(s_14\)\(s_17\)\(s_16\)\(s_11\)\(s_10\)\(s_13\)\(s_12\)\(s_1\)\(s_3\)\(s_2\)\(s_5\)\(s_4\)\(s_7\)\(s_6\)\(s_9\)\(s_8\)\(1\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(4\)
\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)\(1\)\(1\)\(1\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)\(1\)\(\frac{ 1}{ 2}\)\(1\)\(1\)\(1\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)\(4\)
\(1\)\(1\)\(0\)\(3\)\(3\)\(3\)\(3\)\(3\)\(3\)\(1\)\(3\)\(3\)\(\frac{ 1}{ 2}\)\(1\)\(\frac{ 1}{ 2}\)\(1\)\(1\)\(1\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)\(4\)
\(2\)\(2\)\(0\)\(4\)\(4\)\(4\)\(4\)\(4\)\(4\)\(2\)\(4\)\(4\)\(1\)\(2\)\(1\)\(2\)\(2\)\(2\)\(2\)\(2\)\(2\)\(1\)\(4\)

Note:

This is operator "32.1" from ...

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