1
New Number: 4.37 | AESZ: 206 | Superseeker: 4 284 | Hash: bd5dae321e1369e7fae153775f84a351
Degree: 4
\(\theta^4-2^{2} x\theta(\theta+1)(2\theta+1)^2-2^{5} x^{2}(2\theta+1)(2\theta+3)(11\theta^2+22\theta+12)-2^{4} 3 5^{2} x^{3}(2\theta+1)(2\theta+3)^2(2\theta+5)-2^{8} 19 x^{4}(2\theta+1)(2\theta+3)(2\theta+5)(2\theta+7)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, 72, 1200, 44520, ... --> OEIS Normalized instanton numbers (n0=1): 4, 27, 284, 4368, 80968, ... ; Common denominator:...
\(-(16z+1)(4864z^3+896z^2+32z-1)\)
| ≈\(-0.10185-0.013248I\) | ≈\(-0.10185+0.013248I\) | \(-\frac{ 1}{ 16}\) | \(0\) | \(s_1\) | \(s_3\) | \(s_2\) | ≈\(0.019489\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(\frac{ 3}{ 2}\) |
| \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(\frac{ 5}{ 2}\) |
| \(2\) | \(2\) | \(2\) | \(0\) | \(2\) | \(2\) | \(2\) | \(2\) | \(\frac{ 7}{ 2}\) |
2
New Number: 5.112 | AESZ: 395 | Superseeker: 4 940 | Hash: 2d13c01eaf16983977dfb0325c5f376e
Degree: 5
\(\theta^4-2^{2} x\theta(22\theta^3+8\theta^2+5\theta+1)+2^{5} x^{2}\left(34\theta^4-152\theta^3-265\theta^2-163\theta-36\right)+2^{8} x^{3}\left(142\theta^4+600\theta^3+335\theta^2-39\theta-54\right)-2^{11} 3 x^{4}\left(68\theta^4-56\theta^3-295\theta^2-261\theta-72\right)-2^{15} 3^{2} x^{5}(4\theta+3)(\theta+1)^2(4\theta+5)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, 72, 1728, 72360, ... --> OEIS Normalized instanton numbers (n0=1): 4, 60, 940, 19091, 463904, ... ; Common denominator:...
\(-(16z+1)(8z+1)(64z-1)(-1+24z)^2\)
| \(-\frac{ 1}{ 8}\) | \(-\frac{ 1}{ 16}\) | \(0\) | \(\frac{ 1}{ 64}\) | \(\frac{ 1}{ 24}\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 3}{ 4}\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(3\) | \(1\) |
| \(2\) | \(2\) | \(0\) | \(2\) | \(4\) | \(\frac{ 5}{ 4}\) |
3
New Number: 5.28 | AESZ: 203 | Superseeker: -13/5 -6729/5 | Hash: dfab012366b4bc6f7af83dc79f28b802
Degree: 5
\(5^{2} \theta^4+5 x\theta(499\theta^3+86\theta^2+53\theta+10)+2^{4} x^{2}\left(1649\theta^4-13183\theta^3-19776\theta^2-11020\theta-2200\right)-2^{6} x^{3}\left(39521\theta^4+162000\theta^3+142095\theta^2+51540\theta+6540\right)-2^{11} 19 x^{4}\left(1370\theta^4+2860\theta^3+2449\theta^2+1019\theta+174\right)-2^{16} 19^{2} x^{5}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, 88, -1728, 99576, ... --> OEIS Normalized instanton numbers (n0=1): -13/5, 427/5, -6729/5, 173044/5, -952275, ... ; Common denominator:...
\(-(32z-1)(32z^2+71z+1)(5+152z)^2\)
| \(-\frac{ 71}{ 64}-\frac{ 17}{ 64}\sqrt{ 17}\) | \(-\frac{ 5}{ 152}\) | \(-\frac{ 71}{ 64}+\frac{ 17}{ 64}\sqrt{ 17}\) | \(0\) | \(\frac{ 1}{ 32}\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) |
| \(1\) | \(3\) | \(1\) | \(0\) | \(1\) | \(1\) |
| \(2\) | \(4\) | \(2\) | \(0\) | \(2\) | \(1\) |
4
New Number: 5.33 | AESZ: 216 | Superseeker: 9 14201/3 | Hash: af7027bf24acce4fd0ed5b09e575e2a5
Degree: 5
\(\theta^4-3 x\theta(2+11\theta+18\theta^2+27\theta^3)-2 3^{3} x^{2}\left(72\theta^4+414\theta^3+603\theta^2+330\theta+64\right)+2^{2} 3^{5} x^{3}\left(93\theta^4-720\theta^2-708\theta-184\right)+2^{3} 3^{7} x^{4}(2\theta+1)(54\theta^3+405\theta^2+544\theta+200)-2^{4} 3^{10} x^{5}(2\theta+1)(3\theta+2)(3\theta+4)(2\theta+3)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, 216, 7200, 567000, ... --> OEIS Normalized instanton numbers (n0=1): 9, 225, 14201/3, 154800, 6298596, ... ; Common denominator:...
\(-(27z+1)(108z-1)(36z+1)(-1+18z)^2\)
| \(-\frac{ 1}{ 27}\) | \(-\frac{ 1}{ 36}\) | \(0\) | \(\frac{ 1}{ 108}\) | \(\frac{ 1}{ 18}\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(\frac{ 2}{ 3}\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(3\) | \(\frac{ 4}{ 3}\) |
| \(2\) | \(2\) | \(0\) | \(2\) | \(4\) | \(\frac{ 3}{ 2}\) |
5
New Number: 5.34 | AESZ: 217 | Superseeker: 17/7 5095/21 | Hash: e8743aeac19deca699ff90aaef6b8ea7
Degree: 5
\(7^{2} \theta^4+7 x\theta(-14-73\theta-118\theta^2+13\theta^3)-2^{3} 3 x^{2}\left(3378\theta^4+13446\theta^3+18869\theta^2+11158\theta+2352\right)-2^{4} 3^{3} x^{3}\left(3628\theta^4+17920\theta^3+31668\theta^2+22596\theta+5383\right)-2^{8} 3^{3} x^{4}(2\theta+1)(572\theta^3+2370\theta^2+2896\theta+1095)-2^{10} 3^{4} x^{5}(2\theta+1)(6\theta+5)(6\theta+7)(2\theta+3)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, 72, 720, 37800, ... --> OEIS Normalized instanton numbers (n0=1): 17/7, 254/7, 5095/21, 29600/7, 491991/7, ... ; Common denominator:...
\(-(16z+1)(27z+1)(48z-1)(7+24z)^2\)
| \(-\frac{ 7}{ 24}\) | \(-\frac{ 1}{ 16}\) | \(-\frac{ 1}{ 27}\) | \(0\) | \(\frac{ 1}{ 48}\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(\frac{ 5}{ 6}\) |
| \(3\) | \(1\) | \(1\) | \(0\) | \(1\) | \(\frac{ 7}{ 6}\) |
| \(4\) | \(2\) | \(2\) | \(0\) | \(2\) | \(\frac{ 3}{ 2}\) |
6
New Number: 5.38 | AESZ: 223 | Superseeker: 18 64744/3 | Hash: e3ab25cffe4a0968b175bd9e98c96427
Degree: 5
\(\theta^4+2 3 x\theta(48\theta^3-12\theta^2-7\theta-1)+2^{2} 3^{3} x^{2}\left(392\theta^4+488\theta^3+775\theta^2+376\theta+64\right)+2^{4} 3^{5} x^{3}\left(1184\theta^4+3288\theta^3+3512\theta^2+1635\theta+278\right)+2^{6} 3^{8} x^{4}(169\theta^2+361\theta+238)(2\theta+1)^2+2^{11} 3^{11} x^{5}(2\theta+1)^2(2\theta+3)^2\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, -432, 7200, 1587600, ... --> OEIS Normalized instanton numbers (n0=1): 18, -873, 64744/3, -229968, -1628892, ... ; Common denominator:...
\((36z+1)(13824z^2+36z+1)(1+108z)^2\)
| \(-\frac{ 1}{ 36}\) | \(-\frac{ 1}{ 108}\) | \(-\frac{ 1}{ 768}-\frac{ 5}{ 2304}\sqrt{ 15}I\) | \(-\frac{ 1}{ 768}+\frac{ 5}{ 2304}\sqrt{ 15}I\) | \(0\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(1\) | \(3\) | \(1\) | \(1\) | \(0\) | \(\frac{ 3}{ 2}\) |
| \(2\) | \(4\) | \(2\) | \(2\) | \(0\) | \(\frac{ 3}{ 2}\) |
7
New Number: 5.43 | AESZ: 234 | Superseeker: 18/7 5676/7 | Hash: 3e70b30959c0c3bd799b435b9c842186
Degree: 5
\(7^{2} \theta^4-2 7 x\theta(192\theta^3+60\theta^2+37\theta+7)-2^{2} x^{2}\left(17608\theta^4+115144\theta^3+166715\theta^2+94556\theta+18816\right)+2^{4} 3^{2} x^{3}\left(20288\theta^4+57288\theta^3+27524\theta^2-7455\theta-5026\right)-2^{6} 3^{5} x^{4}(2\theta+1)(458\theta^3-657\theta^2-1799\theta-846)-2^{12} 3^{8} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, 96, 1440, 90720, ... --> OEIS Normalized instanton numbers (n0=1): 18/7, 515/7, 5676/7, 133796/7, 2929726/7, ... ; Common denominator:...
\(-(64z-1)(36z+1)(4z+1)(-7+108z)^2\)
| \(-\frac{ 1}{ 4}\) | \(-\frac{ 1}{ 36}\) | \(0\) | \(\frac{ 1}{ 64}\) | \(\frac{ 7}{ 108}\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(3\) | \(1\) |
| \(2\) | \(2\) | \(0\) | \(2\) | \(4\) | \(\frac{ 3}{ 2}\) |
8
New Number: 5.74 | AESZ: 297 | Superseeker: 26/7 55644/7 | Hash: cd0b6008fa6b70d89e004100b5698063
Degree: 5
\(7^{2} \theta^4-2 7 x\theta(520\theta^3+68\theta^2+41\theta+7)-2^{2} 3 x^{2}\left(9480\theta^4+153912\theta^3+212893\theta^2+108080\theta+18816\right)+2^{4} 3^{3} 7 x^{3}\left(13424\theta^4+48792\theta^3+45656\theta^2+17979\theta+2606\right)-2^{6} 3^{7} x^{4}(2\theta+1)^2(2257\theta^2+3601\theta+1942)+2^{11} 3^{11} x^{5}(2\theta+1)^2(2\theta+3)^2\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, 288, 7200, 1058400, ... --> OEIS Normalized instanton numbers (n0=1): 26/7, 2594/7, 55644/7, 2996576/7, 135364470/7, ... ; Common denominator:...
\((128z-1)(432z^2-72z-1)(-7+324z)^2\)
| \(\frac{ 1}{ 12}-\frac{ 1}{ 18}\sqrt{ 3}\) | \(0\) | \(\frac{ 1}{ 128}\) | \(\frac{ 7}{ 324}\) | \(\frac{ 1}{ 12}+\frac{ 1}{ 18}\sqrt{ 3}\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) |
| \(1\) | \(0\) | \(1\) | \(3\) | \(1\) | \(\frac{ 3}{ 2}\) |
| \(2\) | \(0\) | \(2\) | \(4\) | \(2\) | \(\frac{ 3}{ 2}\) |
9
New Number: 5.93 | AESZ: 333 | Superseeker: 1 2668/3 | Hash: dc274781605ee4262d8745e3fa3a8057
Degree: 5
\(\theta^4+x\theta^2(71\theta^2-2\theta-1)+2^{3} 3 x^{2}\left(154\theta^4+334\theta^3+461\theta^2+248\theta+48\right)+2^{6} 3^{2} x^{3}(5\theta+3)(31\theta^3+39\theta^2-25\theta-21)+2^{9} 3^{4} x^{4}(2\theta+1)(2\theta^3-33\theta^2-56\theta-24)-2^{12} 3^{6} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, -72, 1440, 22680, ... --> OEIS Normalized instanton numbers (n0=1): 1, -66, 2668/3, -2774, -167786, ... ; Common denominator:...
\(-(9z-1)(2304z^2+32z+1)(1+24z)^2\)
| \(-\frac{ 1}{ 24}\) | \(-\frac{ 1}{ 144}-\frac{ 1}{ 72}\sqrt{ 2}I\) | \(-\frac{ 1}{ 144}+\frac{ 1}{ 72}\sqrt{ 2}I\) | \(0\) | \(\frac{ 1}{ 9}\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) |
| \(3\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) |
| \(4\) | \(2\) | \(2\) | \(0\) | \(2\) | \(\frac{ 3}{ 2}\) |
10
New Number: 5.96 | AESZ: 339 | Superseeker: 12 28 | Hash: 41593acc689cf76c174442db98218947
Degree: 5
\(\theta^4-2^{2} x\left(10\theta^4+50\theta^3+39\theta^2+14\theta+2\right)+2^{4} x^{2}\left(177\theta^4+1158\theta^3+2007\theta^2+1158\theta+230\right)+2^{8} x^{3}\left(539\theta^4+1344\theta^3-300\theta^2-1068\theta-340\right)+2^{10} 5 x^{4}(2\theta+1)(4\theta^3-642\theta^2-1002\theta-385)-2^{13} 3 5^{2} x^{5}(2\theta+1)(3\theta+2)(3\theta+4)(2\theta+3)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 8, 0, -6400, -249200, ... --> OEIS Normalized instanton numbers (n0=1): 12, -339/2, 28, 27639/2, 634692, ... ; Common denominator:...
\(-(55296z^3-5632z^2+80z-1)(1+20z)^2\)
| \(-\frac{ 1}{ 20}\) | \(0\) | ≈\(0.007072-0.012497I\) | ≈\(0.007072+0.012497I\) | ≈\(0.087707\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(\frac{ 2}{ 3}\) |
| \(3\) | \(0\) | \(1\) | \(1\) | \(1\) | \(\frac{ 4}{ 3}\) |
| \(4\) | \(0\) | \(2\) | \(2\) | \(2\) | \(\frac{ 3}{ 2}\) |
11
New Number: 11.10 | AESZ: | Superseeker: 307/31 30366/31 | Hash: 4af67003a52ef978f182204bfaff3b67
Degree: 11
\(31^{2} \theta^4-31 x\theta(37\theta^3+3404\theta^2+2167\theta+465)-x^{2}\left(3584242\theta^4+13193680\theta^3+15543050\theta^2+9592175\theta+2490912\right)-3^{2} x^{3}\left(19107317\theta^4+73205086\theta^3+112285993\theta^2+86123611\theta+26445852\right)-3 x^{4}\left(1372729742\theta^4+6047894734\theta^3+11016338393\theta^2+9650491725\theta+3283335324\right)-x^{5}\left(61079790533\theta^4+312026249948\theta^3+649293087145\theta^2+630130831252\theta+231606447564\right)-2 3^{2} x^{6}\left(33534165907\theta^4+196973375042\theta^3+458528416805\theta^2+484791515686\theta+189712671726\right)-3^{2} 7 x^{7}\left(64606565117\theta^4+431259053450\theta^3+1107908854519\theta^2+1261805762830\theta+520567245048\right)-3^{4} 7^{2} x^{8}(\theta+1)(4683541363\theta^3+30431977551\theta^2+68128269606\theta+51768680224)-2^{2} 3^{3} 7^{3} x^{9}(\theta+1)(\theta+2)(1489780280\theta^2+7942046183\theta+10944040794)-2^{2} 3^{4} 7^{4} 53 x^{10}(\theta+3)(\theta+2)(\theta+1)(2336627\theta+7400894)-2^{5} 3^{3} 7^{5} 19 53^{2} 97 x^{11}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, 162, 5472, 282366, ... --> OEIS Normalized instanton numbers (n0=1): 307/31, 1814/31, 30366/31, 639686/31, 17126962/31, ... ; Common denominator:...
\(-(8z+1)(679z^2+74z-1)(57z^2+15z+1)(7z+1)^2(2226z^2+555z+31)^2\)
| \(-\frac{ 185}{ 1484}-\frac{ 1}{ 4452}\sqrt{ 32001}\) | \(-\frac{ 1}{ 7}\) | \(-\frac{ 5}{ 38}-\frac{ 1}{ 114}\sqrt{ 3}I\) | \(-\frac{ 5}{ 38}+\frac{ 1}{ 114}\sqrt{ 3}I\) | \(-\frac{ 1}{ 8}\) | \(-\frac{ 37}{ 679}-\frac{ 32}{ 679}\sqrt{ 2}\) | \(-\frac{ 185}{ 1484}+\frac{ 1}{ 4452}\sqrt{ 32001}\) | \(0\) | \(-\frac{ 37}{ 679}+\frac{ 32}{ 679}\sqrt{ 2}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(2\) |
| \(3\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(1\) | \(1\) | \(3\) | \(0\) | \(1\) | \(3\) |
| \(4\) | \(1\) | \(2\) | \(2\) | \(2\) | \(2\) | \(4\) | \(0\) | \(2\) | \(4\) |
12
New Number: 11.11 | AESZ: | Superseeker: 256/31 28062/31 | Hash: dbd551a4eb6b44b1575c949fe3158ad8
Degree: 11
\(31^{2} \theta^4-31 x\theta(790\theta^3+2930\theta^2+1868\theta+403)-x^{2}\left(2814085\theta^4+9964954\theta^3+13382605\theta^2+8541027\theta+2183392\right)-x^{3}\left(77649704\theta^4+350426364\theta^3+626329390\theta^2+517109481\theta+165295596\right)-x^{4}\left(1130950485\theta^4+6282081612\theta^3+13577302372\theta^2+13176194701\theta+4791500140\right)-2 x^{5}\left(5087102169\theta^4+33490353027\theta^3+83662730413\theta^2+91498335797\theta+36413643210\right)-x^{6}\left(59691820411\theta^4+451633384578\theta^3+1266886011283\theta^2+1521913712448\theta+648339514868\right)-2^{2} x^{7}\left(57682690343\theta^4+488627614012\theta^3+1504693262559\theta^2+1947925954210\theta+874695283544\right)-2^{2} x^{8}(\theta+1)(143617960931\theta^3+1184948771451\theta^2+3211500965214\theta+2815433689448)-2^{5} x^{9}(\theta+1)(\theta+2)(27089561480\theta^2+184897066731\theta+314481835312)-2^{6} 3 7 53 x^{10}(\theta+3)(\theta+2)(\theta+1)(9822371\theta+40000042)-2^{9} 3^{2} 7^{2} 53^{2} 359 x^{11}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, 142, 4632, 227538, ... --> OEIS Normalized instanton numbers (n0=1): 256/31, 1982/31, 28062/31, 591475/31, 15400630/31, ... ; Common denominator:...
\(-(8z+1)(359z^2+74z-1)(7z+1)^2(6z+1)^2(212z^2+225z+31)^2\)
| \(-\frac{ 225}{ 424}-\frac{ 1}{ 424}\sqrt{ 24337}\) | \(-\frac{ 37}{ 359}-\frac{ 24}{ 359}\sqrt{ 3}\) | \(-\frac{ 1}{ 6}\) | \(-\frac{ 225}{ 424}+\frac{ 1}{ 424}\sqrt{ 24337}\) | \(-\frac{ 1}{ 7}\) | \(-\frac{ 1}{ 8}\) | \(0\) | \(-\frac{ 37}{ 359}+\frac{ 24}{ 359}\sqrt{ 3}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(0\) | \(1\) | \(2\) |
| \(3\) | \(1\) | \(1\) | \(3\) | \(\frac{ 1}{ 2}\) | \(1\) | \(0\) | \(1\) | \(3\) |
| \(4\) | \(2\) | \(1\) | \(4\) | \(1\) | \(2\) | \(0\) | \(2\) | \(4\) |
13
New Number: 11.12 | AESZ: | Superseeker: 226/35 3959/7 | Hash: dea88e564bf3d9a3c445795800a932fd
Degree: 11
\(5^{2} 7^{2} \theta^4-5 7 x\theta(913\theta^3+2762\theta^2+1766\theta+385)-x^{2}\left(2524749\theta^4+9069852\theta^3+12659629\theta^2+8291990\theta+2156000\right)-2 3 x^{3}\left(8810271\theta^4+42507742\theta^3+80155619\theta^2+68498780\theta+22423100\right)-2^{3} x^{4}\left(72233462\theta^4+442878292\theta^3+1027312839\theta^2+1042690171\theta+390711800\right)-2^{4} 3 x^{5}\left(78678044\theta^4+588264556\theta^3+1609189009\theta^2+1863445805\theta+769363148\right)-2^{5} x^{6}\left(472939267\theta^4+4201829760\theta^3+13245452180\theta^2+17123706057\theta+7634545706\right)-2^{6} x^{7}\left(551391703\theta^4+5765755514\theta^3+20753496824\theta^2+29644168669\theta+14122329342\right)-2^{7} x^{8}(\theta+1)(299511992\theta^3+3514696980\theta^2+12474987717\theta+12944991068)+2^{8} 3 x^{9}(\theta+1)(\theta+2)(3500769\theta^2-93979701\theta-505363628)+2^{8} 3^{5} 17 x^{10}(\theta+3)(\theta+2)(\theta+1)(25977\theta+154654)-2^{9} 3^{3} 5^{2} 17^{2} 79 x^{11}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, 110, 3084, 130914, ... --> OEIS Normalized instanton numbers (n0=1): 226/35, 1599/35, 3959/7, 51101/5, 8052703/35, ... ; Common denominator:...
\(-(-1+53z+919z^2+4792z^3+7900z^4)(34z+7)^2(2z-5)^2(6z+1)^3\)
| \(-\frac{ 7}{ 34}\) | \(-\frac{ 1}{ 6}\) | \(0\) | \(\frac{ 5}{ 2}\) | \(#ND+#NDI\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(0\) | \(0\) | \(1\) | \(1\) | \(2\) |
| \(3\) | \(0\) | \(0\) | \(3\) | \(1\) | \(3\) |
| \(4\) | \(0\) | \(0\) | \(4\) | \(2\) | \(4\) |
14
New Number: 11.2 | AESZ: | Superseeker: 136/97 1768/97 | Hash: 940a6a9fb87fe9b9613bd73b990374c1
Degree: 11
\(97^{2} \theta^4+97 x\theta(1727\theta^3-2018\theta^2-1300\theta-291)-x^{2}\left(1652135\theta^4+13428812\theta^3+16174393\theta^2+10216234\theta+2709792\right)-3 x^{3}\left(27251145\theta^4+121375398\theta^3+189546499\theta^2+147705198\theta+46000116\right)-2 x^{4}\left(587751431\theta^4+2711697232\theta^3+5003189285\theta^2+4434707760\theta+1524637512\right)-x^{5}\left(9726250397\theta^4+50507429234\theta^3+106108023451\theta^2+103964102350\theta+38537290992\right)-2 3 x^{6}\left(8793822649\theta^4+52062405804\theta^3+122175610025\theta^2+130254629814\theta+51340027968\right)-2^{2} 3^{2} x^{7}\left(5429262053\theta^4+36477756530\theta^3+94431307279\theta^2+108363704338\theta+44982230808\right)-2^{4} 3^{2} x^{8}(\theta+1)(3432647479\theta^3+22487363787\theta^2+50808614711\theta+38959393614)-2^{4} 3^{3} x^{9}(\theta+1)(\theta+2)(1903493629\theta^2+10262864555\theta+14314039440)-2^{5} 3^{4} 13^{2} x^{10}(\theta+3)(\theta+2)(\theta+1)(1862987\theta+5992902)-2^{6} 3^{3} 13^{4} 7457 x^{11}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, 18, 168, 2430, ... --> OEIS Normalized instanton numbers (n0=1): 136/97, 292/97, 1768/97, 10128/97, 83387/97, ... ; Common denominator:...
\(-(12z^2+6z+1)(7457z^5+6100z^4+1929z^3+257z^2+7z-1)(97+912z+2028z^2)^2\)
| \(-\frac{ 38}{ 169}-\frac{ 1}{ 1014}\sqrt{ 2805}\) | \(-\frac{ 1}{ 4}-\frac{ 1}{ 12}\sqrt{ 3}I\) | \(-\frac{ 1}{ 4}+\frac{ 1}{ 12}\sqrt{ 3}I\) | \(-\frac{ 38}{ 169}+\frac{ 1}{ 1014}\sqrt{ 2805}\) | \(0\) | \(#ND+#NDI\) | \(\infty\) |
|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(2\) |
| \(3\) | \(1\) | \(1\) | \(3\) | \(0\) | \(1\) | \(3\) |
| \(4\) | \(2\) | \(2\) | \(4\) | \(0\) | \(2\) | \(4\) |
15
New Number: 11.3 | AESZ: | Superseeker: 118/91 268/13 | Hash: 082df0c6e37c18b98ea10260e3e1c195
Degree: 11
\(7^{2} 13^{2} \theta^4+7 13 x\theta(782\theta^3-1874\theta^2-1210\theta-273)-x^{2}\left(2515785\theta^4+11622522\theta^3+15227939\theta^2+9962953\theta+2649920\right)-x^{3}\left(59827597\theta^4+258678126\theta^3+432607868\theta^2+348819198\theta+110445426\right)-2 x^{4}\left(306021521\theta^4+1499440609\theta^3+2950997910\theta^2+2719866190\theta+957861945\right)-3 x^{5}\left(1254280114\theta^4+7075609686\theta^3+15834414271\theta^2+16174233521\theta+6159865002\right)-x^{6}\left(15265487382\theta^4+98210309094\theta^3+244753624741\theta^2+271941545379\theta+110147546634\right)-2 x^{7}\left(21051636001\theta^4+152243816141\theta^3+415982528557\theta^2+495914741301\theta+211134581226\right)-2 x^{8}(\theta+1)(39253400626\theta^3+275108963001\theta^2+654332416678\theta+521254338620)-x^{9}(\theta+1)(\theta+2)(94987355417\theta^2+545340710193\theta+799002779040)-2^{2} 5 7 11 x^{10}(\theta+3)(\theta+2)(\theta+1)(43765159\theta+149264765)-2^{2} 3 5^{2} 7^{2} 11^{2} 11971 x^{11}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, 20, 186, 2940, ... --> OEIS Normalized instanton numbers (n0=1): 118/91, 373/91, 268/13, 12732/91, 105020/91, ... ; Common denominator:...
\(-(3z+1)(11971z^6+16085z^5+8704z^4+2334z^3+289z^2+7z-1)(91+573z+770z^2)^2\)
| \(-\frac{ 573}{ 1540}-\frac{ 1}{ 1540}\sqrt{ 48049}\) | \(-\frac{ 1}{ 3}\) | \(-\frac{ 573}{ 1540}+\frac{ 1}{ 1540}\sqrt{ 48049}\) | \(0\) | \(#ND+#NDI\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(2\) |
| \(3\) | \(1\) | \(3\) | \(0\) | \(1\) | \(3\) |
| \(4\) | \(2\) | \(4\) | \(0\) | \(2\) | \(4\) |
16
New Number: 11.5 | AESZ: | Superseeker: -32 608 | Hash: f5f2274632f5544ebf559c6c512159d1
Degree: 11
\(\theta^4-2^{4} x\theta(7\theta^3-10\theta^2-6\theta-1)+2^{8} x^{2}\left(23\theta^4+68\theta^3+151\theta^2+58\theta+7\right)-2^{13} x^{3}\left(151\theta^4+708\theta^3+927\theta^2+573\theta+138\right)+2^{17} x^{4}\left(780\theta^4+3402\theta^3+6391\theta^2+4237\theta+1031\right)-2^{22} x^{5}\left(493\theta^4+3499\theta^3+6750\theta^2+5338\theta+1478\right)+2^{26} x^{6}\left(527\theta^4+660\theta^3-1166\theta^2-393\theta+19\right)-2^{30} x^{7}\left(2351\theta^4+4852\theta^3-10675\theta^2-13950\theta-4607\right)+2^{34} x^{8}\left(1727\theta^4+11666\theta^3+13271\theta^2+3012\theta-665\right)-2^{39} x^{9}\left(181\theta^4-4344\theta^3-3827\theta^2-648\theta+239\right)+2^{44} 5 x^{10}\left(197\theta^4+370\theta^3+247\theta^2+62\theta+3\right)-2^{49} 5^{2} x^{11}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, -112, 13824, -136944, ... --> OEIS Normalized instanton numbers (n0=1): -32, -616, 608, -21270, -15181664, ... ; Common denominator:...
\(-(-1-80z-9984z^2+8192z^3)(32z-1)^2(40960z^3+1024z^2+64z-1)^2\)
| ≈\(-0.018565-0.040844I\) | ≈\(-0.018565+0.040844I\) | ≈\(-0.004021-0.009129I\) | ≈\(-0.004021+0.009129I\) | \(0\) | ≈\(0.012129\) | \(\frac{ 1}{ 32}\) | ≈\(1.226791\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) |
| \(3\) | \(3\) | \(1\) | \(1\) | \(0\) | \(3\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) |
| \(4\) | \(4\) | \(2\) | \(2\) | \(0\) | \(4\) | \(1\) | \(2\) | \(1\) |
17
New Number: 11.6 | AESZ: | Superseeker: 95/102 1421/102 | Hash: e79a3108441c74cdc23a53a603a6181e
Degree: 11
\(2^{2} 3^{2} 17^{2} \theta^4-2 3 17 x\theta(116\theta^3+1414\theta^2+911\theta+204)-x^{2}\left(2596259\theta^4+9892670\theta^3+14508941\theta^2+9947652\theta+2663424\right)-3 x^{3}\left(8561767\theta^4+41744696\theta^3+79668236\theta^2+68977704\theta+22655832\right)-2^{2} x^{4}\left(28089475\theta^4+171762758\theta^3+396877187\theta^2+402013525\theta+149622901\right)-2 x^{5}\left(127339346\theta^4+963856934\theta^3+2636877099\theta^2+3042828449\theta+1247694978\right)-x^{6}\left(283337071\theta^4+2758627602\theta^3+9101625228\theta^2+11995897911\theta+5385015134\right)-2 x^{7}\left(43252385\theta^4+777895672\theta^3+3537873325\theta^2+5604936458\theta+2806067360\right)+2^{2} 3 x^{8}(\theta+1)(7613560\theta^3+27844427\theta^2-51849552\theta-134696600)+x^{9}(\theta+1)(\theta+2)(60585089\theta^2+495871401\theta+595115780)-2^{3} 3 5^{2} x^{10}(\theta+3)(\theta+2)(\theta+1)(10279\theta-113205)-2^{4} 5^{4} 7 97 x^{11}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, 16, 114, 1680, ... --> OEIS Normalized instanton numbers (n0=1): 95/102, 58/17, 1421/102, 1451/17, 31474/51, ... ; Common denominator:...
\(-(-1+7z+219z^2+1115z^3+1934z^4+679z^5)(z+1)^2(100z^2-197z-102)^2\)
| \(-1\) | \(\frac{ 197}{ 200}-\frac{ 1}{ 200}\sqrt{ 79609}\) | \(0\) | \(\frac{ 197}{ 200}+\frac{ 1}{ 200}\sqrt{ 79609}\) | \(#ND+#NDI\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(\frac{ 1}{ 3}\) | \(1\) | \(0\) | \(1\) | \(1\) | \(2\) |
| \(\frac{ 2}{ 3}\) | \(3\) | \(0\) | \(3\) | \(1\) | \(3\) |
| \(1\) | \(4\) | \(0\) | \(4\) | \(2\) | \(4\) |
18
New Number: 11.8 | AESZ: | Superseeker: 6/17 688/17 | Hash: a0a3e346d09b91b8ad96e54854c136ad
Degree: 11
\(17^{2} \theta^4-2 3 17 x\theta^2(117\theta^2+2\theta+1)+2^{2} x^{2}\left(8475\theta^4-64176\theta^3-97010\theta^2-63580\theta-16184\right)+2^{2} x^{3}\left(717094\theta^4+1400796\theta^3+1493367\theta^2+893571\theta+254082\right)-2^{4} x^{4}\left(464294\theta^4-1133264\theta^3-1648391\theta^2-1200310\theta-375336\right)-2^{4} x^{5}\left(18282700\theta^4+46995928\theta^3+83098711\theta^2+73517673\theta+25685438\right)-2^{6} 3 x^{6}\left(2709886\theta^4+7353008\theta^3+18175093\theta^2+18787708\theta+5966228\right)+2^{6} x^{7}\left(154368940\theta^4+947965400\theta^3+2363187035\theta^2+2646307981\theta+1071488886\right)+2^{8} x^{8}(\theta+1)(119648213\theta^3+399067803\theta^2+77665606\theta-498465144)-2^{8} 3 x^{9}(\theta+1)(\theta+2)(120410834\theta^2+865960638\theta+1188072247)-2^{10} 3^{2} 107 x^{10}(\theta+3)(\theta+2)(\theta+1)(218683\theta-39394)+2^{11} 3^{3} 5 107^{2} 137 x^{11}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, 14, 72, 1554, ... --> OEIS Normalized instanton numbers (n0=1): 6/17, 83/17, 688/17, 7350/17, 5150, ... ; Common denominator:...
\((10z+1)(6z-1)(1096z^3+228z^2+14z-1)(2z-1)^2(1284z^2+232z-17)^2\)
| \(-\frac{ 29}{ 321}-\frac{ 1}{ 642}\sqrt{ 8821}\) | ≈\(-0.124082-0.085658I\) | ≈\(-0.124082+0.085658I\) | \(-\frac{ 1}{ 10}\) | \(0\) | ≈\(0.040135\) | \(-\frac{ 29}{ 321}+\frac{ 1}{ 642}\sqrt{ 8821}\) | \(\frac{ 1}{ 6}\) | \(\frac{ 1}{ 2}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(0\) | \(2\) |
| \(3\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(3\) | \(1\) | \(1\) | \(3\) |
| \(4\) | \(2\) | \(2\) | \(2\) | \(0\) | \(2\) | \(4\) | \(2\) | \(1\) | \(4\) |
19
New Number: 11.9 | AESZ: | Superseeker: 17/3 4127/9 | Hash: fa7c260e6f07cef5d727e6af380a6373
Degree: 11
\(3^{2} \theta^4-3 x\theta(20\theta^3+196\theta^2+125\theta+27)-x^{2}\left(19127\theta^4+69044\theta^3+89705\theta^2+54504\theta+13248\right)-2 x^{3}\left(285799\theta^4+1251420\theta^3+2142633\theta^2+1678248\theta+511560\right)-2^{2} x^{4}\left(2058125\theta^4+11190220\theta^3+23374875\theta^2+21658060\theta+7556504\right)-2^{3} x^{5}\left(8570685\theta^4+57030456\theta^3+140934413\theta^2+149627146\theta+57858760\right)-2^{6} x^{6}\left(5382486\theta^4+43183593\theta^3+124360784\theta^2+148979343\theta+62839586\right)-2^{7} x^{7}\left(7897671\theta^4+75745098\theta^3+252663545\theta^2+339244430\theta+154810568\right)-2^{10} x^{8}(\theta+1)(1454893\theta^3+15409953\theta^2+50286726\theta+48898444)-2^{11} x^{9}(\theta+1)(\theta+2)(227963\theta^2+3375435\theta+10342960)+2^{14} x^{10}(\theta+3)(\theta+2)(\theta+1)(48476\theta+271867)-2^{15} 3 5 13 23 x^{11}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, 92, 2328, 91212, ... --> OEIS Normalized instanton numbers (n0=1): 17/3, 257/6, 4127/9, 23827/3, 496999/3, ... ; Common denominator:...
\(-(5z+1)(13z+1)(6z+1)(368z^2+56z-1)(4z+1)^2(8z^2-26z-3)^2\)
| \(-\frac{ 1}{ 4}\) | \(-\frac{ 1}{ 5}\) | \(-\frac{ 7}{ 92}-\frac{ 3}{ 46}\sqrt{ 2}\) | \(-\frac{ 1}{ 6}\) | \(\frac{ 13}{ 8}-\frac{ 1}{ 8}\sqrt{ 193}\) | \(-\frac{ 1}{ 13}\) | \(0\) | \(-\frac{ 7}{ 92}+\frac{ 3}{ 46}\sqrt{ 2}\) | \(\frac{ 13}{ 8}+\frac{ 1}{ 8}\sqrt{ 193}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(2\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(3\) | \(1\) | \(0\) | \(1\) | \(3\) | \(3\) |
| \(1\) | \(2\) | \(2\) | \(2\) | \(4\) | \(2\) | \(0\) | \(2\) | \(4\) | \(4\) |
20
New Number: 12.2 | AESZ: | Superseeker: 64 39744 | Hash: b92032007ecbbf3af5801c4b1e4cf97a
Degree: 12
\(\theta^4+2^{5} x\theta(4\theta^3-10\theta^2-6\theta-1)-2^{8} x^{2}\left(92\theta^4+248\theta^3+200\theta^2+228\theta+89\right)-2^{14} x^{3}\left(84\theta^4+336\theta^3+664\theta^2+132\theta-51\right)+2^{18} x^{4}\left(944\theta^4+1312\theta^3+8928\theta^2+7384\theta+2567\right)-2^{26} x^{5}\left(176\theta^4-1456\theta^3-3477\theta^2-3814\theta-1741\right)-2^{32} x^{6}\left(216\theta^4+1200\theta^3+576\theta^2+1314\theta+697\right)+2^{38} x^{7}\left(456\theta^4+624\theta^3-3085\theta^2-5590\theta-3089\right)-2^{43} x^{8}\left(176\theta^4-3616\theta^3-2404\theta^2-288\theta+1027\right)-2^{50} x^{9}\left(208\theta^4+1824\theta^3+2581\theta^2+1434\theta+73\right)+2^{57} x^{10}\left(122\theta^4-44\theta^3-718\theta^2-1005\theta-410\right)-2^{62} 5 x^{11}\left(4\theta^4-32\theta^3-145\theta^2-190\theta-82\right)-2^{66} 5^{2} x^{12}\left((2\theta+3)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, 1424, 13312, 4213008, ... --> OEIS Normalized instanton numbers (n0=1): 64, -692, 39744, -2001358, 95440576, ... ; Common denominator:...
\(-(-1+64z+4096z^2)(64z-1)^2(64z+1)^2(655360z^3-4096z^2+96z+1)^2\)
| \(-\frac{ 1}{ 128}-\frac{ 1}{ 128}\sqrt{ 5}\) | \(-\frac{ 1}{ 64}\) | ≈\(-0.006598\) | \(0\) | ≈\(0.006424-0.013784I\) | ≈\(0.006424+0.013784I\) | \(-\frac{ 1}{ 128}+\frac{ 1}{ 128}\sqrt{ 5}\) | \(\frac{ 1}{ 64}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 3}{ 2}\) |
| \(1\) | \(0\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(\frac{ 3}{ 2}\) |
| \(1\) | \(1\) | \(3\) | \(0\) | \(3\) | \(3\) | \(1\) | \(\frac{ 1}{ 2}\) | \(\frac{ 3}{ 2}\) |
| \(2\) | \(1\) | \(4\) | \(0\) | \(4\) | \(4\) | \(2\) | \(1\) | \(\frac{ 3}{ 2}\) |
21
New Number: 12.6 | AESZ: | Superseeker: 5 953/3 | Hash: 4ea78627bfc56ef9555d9b6b3c949e7a
Degree: 12
\(\theta^4-x\theta(5\theta^3+46\theta^2+29\theta+6)-2 3 x^{2}\left(258\theta^4+1038\theta^3+1387\theta^2+818\theta+192\right)-2^{2} 3^{3} x^{3}\left(381\theta^4+1664\theta^3+2804\theta^2+2126\theta+624\right)-2^{4} 3^{3} x^{4}\left(1231\theta^4+5927\theta^3+11019\theta^2+9266\theta+3000\right)-2^{4} 3^{4} x^{5}\left(2621\theta^4+16730\theta^3+39069\theta^2+35141\theta+11748\right)-2^{5} 3^{5} x^{6}\left(150\theta^4+11268\theta^3+45560\theta^2+50253\theta+18756\right)+2^{6} 3^{7} x^{7}\left(1024\theta^4+800\theta^3-8483\theta^2-13641\theta-6108\right)+2^{8} 3^{7} x^{8}\left(1724\theta^4+6608\theta^3+1047\theta^2-7027\theta-4488\right)+2^{11} 3^{8} x^{9}\left(74\theta^4+1416\theta^3+1889\theta^2+687\theta-81\right)-2^{13} 3^{10} x^{10}\left(26\theta^4-16\theta^3-125\theta^2-128\theta-39\right)-2^{14} 3^{11} x^{11}(\theta+1)(16\theta^3+40\theta^2+31\theta+6)-2^{16} 3^{11} x^{12}(\theta+2)(\theta+1)(2\theta+3)^2\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, 72, 1344, 48600, ... --> OEIS Normalized instanton numbers (n0=1): 5, 83/2, 953/3, 5319, 97812, ... ; Common denominator:...
\(-(4z+1)(12z+1)(3z+1)(1728z^3+864z^2+36z-1)(-1-6z-36z^2+432z^3)^2\)
| ≈\(-0.450956\) | \(-\frac{ 1}{ 3}\) | \(-\frac{ 1}{ 4}\) | \(-\frac{ 1}{ 12}\) | ≈\(-0.067934\) | ≈\(-0.061146-0.08671I\) | ≈\(-0.061146+0.08671I\) | \(0\) | ≈\(0.01889\) | ≈\(0.205625\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(\frac{ 3}{ 2}\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(3\) | \(3\) | \(0\) | \(1\) | \(3\) | \(\frac{ 3}{ 2}\) |
| \(2\) | \(2\) | \(2\) | \(2\) | \(2\) | \(4\) | \(4\) | \(0\) | \(2\) | \(4\) | \(2\) |
22
New Number: 13.9 | AESZ: | Superseeker: 8 2200/9 | Hash: 31ff3b7bd4c8fed070ee43b6903d3752
Degree: 13
\(\theta^4+2^{3} x\theta(4\theta^3-8\theta^2-5\theta-1)-2^{4} x^{2}\left(48\theta^4+120\theta^3+45\theta^2+74\theta+36\right)-2^{7} x^{3}\left(101\theta^4-342\theta^3-387\theta^2-410\theta-171\right)+2^{8} x^{4}\left(3121\theta^4+14104\theta^3+30889\theta^2+27720\theta+9351\right)+2^{11} 3^{2} x^{5}\left(655\theta^4+4062\theta^3+10081\theta^2+10272\theta+3856\right)-2^{12} 3^{2} x^{6}\left(2272\theta^4+2816\theta^3-9950\theta^2-18768\theta-8813\right)-2^{15} 3^{3} x^{7}\left(1546\theta^4+12172\theta^3+30708\theta^2+33880\theta+13843\right)+2^{16} 3^{4} x^{8}\left(1099\theta^4+1344\theta^3-11134\theta^2-23964\theta-13063\right)+2^{19} 3^{5} x^{9}\left(458\theta^4+4828\theta^3+15325\theta^2+19721\theta+8830\right)-2^{20} 3^{6} x^{10}(\theta+1)(368\theta^3+1752\theta^2+1297\theta-1035)-2^{23} 3^{7} x^{11}(\theta+1)(\theta+2)(39\theta^2+513\theta+1172)+2^{24} 3^{9} x^{12}(\theta+3)(\theta+2)(\theta+1)(17\theta+82)-2^{27} 3^{10} x^{13}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, 36, -192, -4284, ... --> OEIS Normalized instanton numbers (n0=1): 8, -75/2, 2200/9, -8117/2, 47936, ... ; Common denominator:...
\(-(8z+1)(5184z^3+432z^2-36z+1)(12z+1)^2(144z^2-24z-1)^2(4z-1)^3\)
| ≈\(-0.141868\) | \(-\frac{ 1}{ 8}\) | \(-\frac{ 1}{ 12}\) | \(\frac{ 1}{ 12}-\frac{ 1}{ 12}\sqrt{ 2}\) | \(0\) | ≈\(0.029267-0.022431I\) | ≈\(0.029267+0.022431I\) | \(\frac{ 1}{ 12}+\frac{ 1}{ 12}\sqrt{ 2}\) | \(\frac{ 1}{ 4}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(2\) |
| \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(3\) | \(0\) | \(1\) | \(1\) | \(3\) | \(\frac{ 3}{ 2}\) | \(3\) |
| \(2\) | \(2\) | \(1\) | \(4\) | \(0\) | \(2\) | \(2\) | \(4\) | \(2\) | \(4\) |
23
New Number: 14.2 | AESZ: | Superseeker: 27/5 1619/5 | Hash: c0f6d85270164c8c5a63d1bb2deaba83
Degree: 14
\(5^{2} \theta^4+3^{2} 5 x\theta(6\theta^3-36\theta^2-23\theta-5)-x^{2}\left(43856\theta^4+189068\theta^3+226691\theta^2+135510\theta+33600\right)-3^{2} x^{3}\left(224236\theta^4+916896\theta^3+1403247\theta^2+1048995\theta+313920\right)-x^{4}\left(44621090\theta^4+199900036\theta^3+357072757\theta^2+304636250\theta+101358144\right)-3^{2} x^{5}\left(69593744\theta^4+347076728\theta^3+696076003\theta^2+653370139\theta+234075456\right)-3^{2} x^{6}\left(681084088\theta^4+3766244020\theta^3+8299124637\theta^2+8400442322\theta+3184811840\right)-3^{3} x^{7}\left(1616263276\theta^4+9835107968\theta^3+23484467027\theta^2+25311872719\theta+10046134656\right)-3^{3} x^{8}\left(8527956293\theta^4+56671723156\theta^3+145225420081\theta^2+165230257706\theta+68152357440\right)-2 3^{4} x^{9}\left(5575274615\theta^4+40185448970\theta^3+109721715457\theta^2+130944512374\theta+55834822464\right)-2^{3} 3^{3} x^{10}\left(12062719219\theta^4+93737716664\theta^3+271167874625\theta^2+337796659588\theta+148305175248\right)-2^{5} 3^{5} x^{11}(\theta+1)(691573543\theta^3+5071601663\theta^2+12510902832\theta+10260936720)-2^{7} 3^{6} x^{12}(\theta+1)(\theta+2)(80620421\theta^2+475174733\theta+711172676)-2^{14} 3^{6} 5 x^{13}(\theta+3)(\theta+2)(\theta+1)(107069\theta+369433)-2^{19} 3^{8} 5^{2} 29 x^{14}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, 84, 1944, 70476, ... --> OEIS Normalized instanton numbers (n0=1): 27/5, 158/5, 1619/5, 51193/10, 485082/5, ... ; Common denominator:...
\(-(9z+1)(6z+1)(348z^2+51z-1)(5z+1)^2(4z+1)^2(576z^3+357z^2+72z+5)^2\)
| ≈\(-0.298314\) | \(-\frac{ 1}{ 4}\) | \(-\frac{ 1}{ 5}\) | \(-\frac{ 1}{ 6}\) | \(-\frac{ 17}{ 232}-\frac{ 11}{ 696}\sqrt{ 33}\) | ≈\(-0.160739-0.057112I\) | ≈\(-0.160739+0.057112I\) | \(-\frac{ 1}{ 9}\) | \(0\) | \(-\frac{ 17}{ 232}+\frac{ 11}{ 696}\sqrt{ 33}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(\frac{ 1}{ 2}\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(2\) |
| \(3\) | \(\frac{ 1}{ 2}\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(3\) | \(3\) | \(1\) | \(0\) | \(1\) | \(3\) |
| \(4\) | \(1\) | \(1\) | \(2\) | \(2\) | \(4\) | \(4\) | \(2\) | \(0\) | \(2\) | \(4\) |
24
New Number: 14.3 | AESZ: | Superseeker: 21/4 1285/2 | Hash: fed06deb794f226dc9bf5119acb5fcf2
Degree: 14
\(2^{4} \theta^4-2^{2} x\theta(32+149\theta+234\theta^2+54\theta^3)-x^{2}\left(39143\theta^4+143570\theta^3+193959\theta^2+113504\theta+25600\right)-2 x^{3}\left(488914\theta^4+2366790\theta^3+4293033\theta^2+3346032\theta+1000416\right)-x^{4}\left(10882749\theta^4+71055186\theta^3+164405289\theta^2+154949112\theta+53930896\right)-2 x^{5}\left(27668482\theta^4+276475198\theta^3+837116993\theta^2+935359976\theta+366972272\right)+2^{2} x^{6}\left(417907\theta^4-460236984\theta^3-2273346630\theta^2-3128567370\theta-1388917916\right)+2^{4} x^{7}\left(101741100\theta^4+252571782\theta^3-1076988014\theta^2-2508674129\theta-1362925766\right)+2^{6} x^{8}\left(136151221\theta^4+982924270\theta^3+1322951772\theta^2+257785345\theta-274176968\right)+2^{8} x^{9}\left(54403942\theta^4+889245288\theta^3+2318053632\theta^2+2306501340\theta+802166039\right)-2^{10} 3 x^{10}\left(16110621\theta^4-52456644\theta^3-344061634\theta^2-516147274\theta-239510540\right)-2^{12} x^{11}(\theta+1)(75181760\theta^3+257537898\theta^2+246848548\theta+22104519)-2^{14} 3 x^{12}(\theta+1)(\theta+2)(14369939\theta^2+55966221\theta+56991175)-2^{17} 3^{3} 5 x^{13}(\theta+3)(\theta+2)(\theta+1)(45377\theta+116950)-2^{20} 3^{5} 5^{2} 59 x^{14}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, 100, 2592, 112308, ... --> OEIS Normalized instanton numbers (n0=1): 21/4, 1965/32, 1285/2, 103095/8, 1157421/4, ... ; Common denominator:...
\(-(3z+1)(64z^2+24z+1)(236z^2+63z-1)(360z^3+74z^2-21z-4)^2(4z+1)^3\)
| \(-\frac{ 1}{ 3}\) | \(-\frac{ 3}{ 16}-\frac{ 1}{ 16}\sqrt{ 5}\) | \(-\frac{ 63}{ 472}-\frac{ 17}{ 472}\sqrt{ 17}\) | ≈\(-0.268785\) | \(-\frac{ 1}{ 4}\) | ≈\(-0.174147\) | \(-\frac{ 3}{ 16}+\frac{ 1}{ 16}\sqrt{ 5}\) | \(0\) | \(-\frac{ 63}{ 472}+\frac{ 17}{ 472}\sqrt{ 17}\) | ≈\(0.237376\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(2\) |
| \(1\) | \(1\) | \(1\) | \(3\) | \(0\) | \(3\) | \(1\) | \(0\) | \(1\) | \(3\) | \(3\) |
| \(2\) | \(2\) | \(2\) | \(4\) | \(0\) | \(4\) | \(2\) | \(0\) | \(2\) | \(4\) | \(4\) |
25
New Number: 14.4 | AESZ: | Superseeker: 10 13958/9 | Hash: 0091fcfec3692ae6ced2f585ef96177c
Degree: 14
\(3^{6} \theta^4-3^{6} x\theta(15+70\theta+110\theta^2+13\theta^3)-3^{3} x^{2}\left(120409\theta^4+434560\theta^3+542371\theta^2+323352\theta+78624\right)-3^{3} x^{3}\left(5396953\theta^4+22626666\theta^3+37042425\theta^2+28217556\theta+8482968\right)-2 x^{4}\left(1704421489\theta^4+8538160718\theta^3+16779519205\theta^2+14919147216\theta+5077251288\right)-2^{2} 3 x^{5}\left(4201278867\theta^4+24797778110\theta^3+56302322281\theta^2+56325956066\theta+20967103728\right)-2^{3} x^{6}\left(63154319213\theta^4+432278933514\theta^3+1110085421927\theta^2+1224810967950\theta+489654799596\right)-2^{5} 3 x^{7}\left(36597277323\theta^4+286904817870\theta^3+822690934223\theta^2+989019393562\theta+419959932336\right)-2^{6} x^{8}\left(263122045911\theta^4+2344932626130\theta^3+7455815983415\theta^2+9696396501490\theta+4343347545434\right)-2^{7} 5 x^{9}\left(83257168289\theta^4+843955668354\theta^3+2974370084181\theta^2+4174636770342\theta+1965917099796\right)-2^{9} 5 x^{10}\left(38447331387\theta^4+453440983815\theta^3+1797507529325\theta^2+2740147614260\theta+1358896159983\right)-2^{8} 5^{2} 23 x^{11}(\theta+1)(421574469\theta^3+6597293181\theta^2+28022760832\theta+32033938840)+2^{9} 5^{2} 7 23^{2} x^{12}(\theta+2)(\theta+1)(2012137\theta^2+10160979\theta-151326)+2^{10} 5^{3} 7^{2} 23^{3} x^{13}(1525\theta+10484)(\theta+3)(\theta+2)(\theta+1)-2^{11} 3 5^{3} 7^{3} 23^{4} x^{14}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, 182, 7020, 401730, ... --> OEIS Normalized instanton numbers (n0=1): 10, 2591/27, 13958/9, 1037839/27, 3535478/3, ... ; Common denominator:...
\(-(6z+1)(42320z^4+16560z^3+2032z^2+68z-1)(920z^3-1180z^2-378z-27)^2(7z+1)^3\)
| \(-\frac{ 1}{ 6}\) | ≈\(-0.157194\) | ≈\(-0.157194\) | ≈\(-0.151128\) | \(-\frac{ 1}{ 7}\) | ≈\(-0.124614\) | ≈\(-0.087777\) | \(0\) | ≈\(0.010861\) | ≈\(1.55835\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(2\) |
| \(1\) | \(1\) | \(1\) | \(3\) | \(0\) | \(3\) | \(1\) | \(0\) | \(1\) | \(3\) | \(3\) |
| \(2\) | \(2\) | \(2\) | \(4\) | \(0\) | \(4\) | \(2\) | \(0\) | \(2\) | \(4\) | \(4\) |
26
New Number: 14.5 | AESZ: | Superseeker: 211/35 19279/35 | Hash: f3806aa0de676048470ecaa401cb173e
Degree: 14
\(5^{2} 7^{2} \theta^4-5 7 x\theta(208\theta^3+2522\theta^2+1611\theta+350)-x^{2}\left(2895864\theta^4+10743882\theta^3+13787199\theta^2+8373750\theta+2038400\right)-x^{3}\left(100271073\theta^4+431892504\theta^3+723680933\theta^2+561181425\theta+170041830\right)-x^{4}\left(1779494918\theta^4+9127622236\theta^3+18290497093\theta^2+16539531755\theta+5684071466\right)-x^{5}\left(19827182682\theta^4+119162684736\theta^3+274771737213\theta^2+279000299901\theta+104851723790\right)-x^{6}\left(149204258817\theta^4+1032818408748\theta^3+2681116117542\theta^2+2993600486151\theta+1206564891326\right)-x^{7}\left(778822250193\theta^4+6126161719824\theta^3+17659178255613\theta^2+21402250647384\theta+9142529120612\right)-x^{8}\left(2812797944541\theta^4+24913922595768\theta^3+79078287326181\theta^2+103186060627602\theta+46367068712696\right)-2 x^{9}\left(3396806566178\theta^4+33765210209691\theta^3+117624369015258\theta^2+164571138801333\theta+77449742958250\right)-x^{10}\left(10000008656989\theta^4+112554410392382\theta^3+432872666762301\theta^2+650564904626120\theta+320443815723404\right)-2^{2} 3 x^{11}(\theta+1)(551266200382\theta^3+6974826522501\theta^2+26399880418886\theta+28678364691672)+2^{2} 5 x^{12}(\theta+1)(\theta+2)(92480406417\theta^2+96008519961\theta-1687668183707)+2^{3} 5^{2} 163 x^{13}(\theta+3)(\theta+2)(\theta+1)(106246927\theta+649964324)-2^{2} 3^{3} 5^{3} 163^{2} 2687 x^{14}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, 104, 2838, 118344, ... --> OEIS Normalized instanton numbers (n0=1): 211/35, 1643/35, 19279/35, 69901/7, 7789913/35, ... ; Common denominator:...
\(-(-1+41z+1449z^2+13908z^3+53591z^4+72549z^5)(326z^3-804z^2-351z-35)^2(5z+1)^3\)
| ≈\(-0.216454\) | \(-\frac{ 1}{ 5}\) | ≈\(-0.173649\) | \(0\) | ≈\(2.85636\) | \(#ND+#NDI\) | \(\infty\) |
|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(0\) | \(1\) | \(0\) | \(1\) | \(1\) | \(2\) |
| \(3\) | \(0\) | \(3\) | \(0\) | \(3\) | \(1\) | \(3\) |
| \(4\) | \(0\) | \(4\) | \(0\) | \(4\) | \(2\) | \(4\) |
27
New Number: 14.6 | AESZ: | Superseeker: 343/26 27836/13 | Hash: b419826ae9a841fd2485cf17a33e3c82
Degree: 14
\(2^{2} 13^{2} \theta^4+2 13 x\theta(374\theta^3-3806\theta^2-2423\theta-520)-3 x^{2}\left(1378165\theta^4+5692942\theta^3+6262109\theta^2+3632408\theta+908544\right)-3 x^{3}\left(109634670\theta^4+414665370\theta^3+585954355\theta^2+424721388\theta+125838648\right)-3^{2} x^{4}\left(1430057388\theta^4+5835126030\theta^3+9693559559\theta^2+7980072398\theta+2602285652\right)-3^{4} x^{5}\left(3973724102\theta^4+18016019762\theta^3+33809871817\theta^2+30548046888\theta+10682005352\right)-3^{5} x^{6}\left(23181342780\theta^4+117157350210\theta^3+242997310916\theta^2+236792965009\theta+87556639706\right)-3^{6} x^{7}\left(98661453307\theta^4+553704139946\theta^3+1252095727942\theta^2+1301834765069\theta+504487460698\right)-3^{7} x^{8}\left(312059119661\theta^4+1933538622170\theta^3+4722871403800\theta^2+5200539067181\theta+2098928967026\right)-3^{7} x^{9}\left(2207453009832\theta^4+15008943280014\theta^3+39332490555167\theta^2+45616623444051\theta+19085482478826\right)-3^{8} x^{10}\left(3839323955127\theta^4+28479004361040\theta^3+79653137355055\theta^2+96880903986262\theta+41867518152496\right)-3^{10} x^{11}(\theta+1)(1597618239529\theta^3+11261457267015\theta^2+26962321719782\theta+21625438724040)-3^{12} x^{12}(\theta+1)(\theta+2)(452183900223\theta^2+2573271558279\theta+3747021993116)-2^{4} 3^{16} 109 x^{13}(\theta+3)(\theta+2)(\theta+1)(4973417\theta+16619273)-2^{6} 3^{16} 109^{2} 8167 x^{14}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, 252, 11106, 735660, ... --> OEIS Normalized instanton numbers (n0=1): 343/26, 1358/13, 27836/13, 764852/13, 52338075/26, ... ; Common denominator:...
\(-(661527z^5+290250z^4+47223z^3+3291z^2+71z-1)(23544z^3+7353z^2+759z+26)^2(9z+1)^3\)
| ≈\(-0.126194\) | \(-\frac{ 1}{ 9}\) | ≈\(-0.093057-0.009552I\) | ≈\(-0.093057+0.009552I\) | \(0\) | \(#ND+#NDI\) | \(\infty\) |
|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(0\) | \(1\) | \(1\) | \(0\) | \(1\) | \(2\) |
| \(3\) | \(0\) | \(3\) | \(3\) | \(0\) | \(1\) | \(3\) |
| \(4\) | \(0\) | \(4\) | \(4\) | \(0\) | \(2\) | \(4\) |
28
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 LaTexCoefficients 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:...
\(-(-1+36z)(12z+5)^2(12z+1)^2(4z-1)^2\)
| \(-\frac{ 5}{ 12}\) | \(-\frac{ 1}{ 12}\) | \(0\) | \(\frac{ 1}{ 36}\) | \(\frac{ 1}{ 4}\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(0\) | \(0\) | \(1\) | \(\frac{ 1}{ 2}\) | \(\frac{ 3}{ 2}\) |
| \(3\) | \(1\) | \(0\) | \(1\) | \(\frac{ 1}{ 2}\) | \(\frac{ 5}{ 2}\) |
| \(4\) | \(1\) | \(0\) | \(2\) | \(1\) | \(3\) |
29
New Number: 7.1 | AESZ: | Superseeker: 10/7 508/7 | Hash: 08ab3cb496250adfa30bc3e24ac63c4f
Degree: 7
\(7^{2} \theta^4-2 7 x\theta(46\theta^3+52\theta^2+33\theta+7)-2^{2} x^{2}\left(7332\theta^4+28848\theta^3+42633\theta^2+26670\theta+6272\right)-2^{4} x^{3}\left(2860\theta^4+44760\theta^3+120483\theta^2+111279\theta+35098\right)+2^{9} x^{4}\left(2230\theta^4+5920\theta^3-741\theta^2-6509\theta-3049\right)+2^{14} x^{5}\left(174\theta^4+1320\theta^3+1971\theta^2+1095\theta+190\right)-2^{19} x^{6}\left(22\theta^4+24\theta^3-9\theta^2-21\theta-7\right)-2^{25} x^{7}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, 32, 288, 7776, ... --> OEIS Normalized instanton numbers (n0=1): 10/7, 100/7, 508/7, 808, 59910/7, ... ; Common denominator:...
\(-(16z+1)(32z-1)(32z-7)^2(4z+1)^3\)
| \(-\frac{ 1}{ 4}\) | \(-\frac{ 1}{ 16}\) | \(0\) | \(\frac{ 1}{ 32}\) | \(\frac{ 7}{ 32}\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(\frac{ 1}{ 2}\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) |
| \(\frac{ 3}{ 2}\) | \(1\) | \(0\) | \(1\) | \(3\) | \(1\) |
| \(2\) | \(2\) | \(0\) | \(2\) | \(4\) | \(1\) |
30
New Number: 7.3 | AESZ: | Superseeker: 3 64 | Hash: 8413250555ca536f1bdccfeed506ea4e
Degree: 7
\(\theta^4+x\theta(39\theta^3-30\theta^2-19\theta-4)+2 x^{2}\left(16\theta^4-1070\theta^3-1057\theta^2-676\theta-192\right)-2^{2} 3^{2} x^{3}(3\theta+2)(171\theta^3+566\theta^2+600\theta+316)-2^{5} 3^{3} x^{4}\left(384\theta^4+1542\theta^3+2635\theta^2+2173\theta+702\right)-2^{6} 3^{3} x^{5}(\theta+1)(1393\theta^3+5571\theta^2+8378\theta+4584)-2^{10} 3^{5} x^{6}(\theta+1)(\theta+2)(31\theta^2+105\theta+98)-2^{12} 3^{7} x^{7}(\theta+1)(\theta+2)^2(\theta+3)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, 24, 192, 3384, ... --> OEIS Normalized instanton numbers (n0=1): 3, -4, 64, -253, 4292, ... ; Common denominator:...
\(-(8z+1)(24z-1)(3z+1)(4z+1)(12z+1)(1+18z)^2\)
| \(-\frac{ 1}{ 3}\) | \(-\frac{ 1}{ 4}\) | \(-\frac{ 1}{ 8}\) | \(-\frac{ 1}{ 12}\) | \(-\frac{ 1}{ 18}\) | \(0\) | \(\frac{ 1}{ 24}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(2\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(3\) | \(0\) | \(1\) | \(2\) |
| \(2\) | \(2\) | \(2\) | \(2\) | \(4\) | \(0\) | \(2\) | \(3\) |