You searched for: Spectrum0=0,0,0,0
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91
New Number: 3.2 | AESZ: 227 | Superseeker: -900 8364884 | Hash: 2e00a51fe0c232d13a452380f44c79da
Degree: 3
\(\theta^4+2^{2} 3^{2} x\left(132\theta^4+264\theta^3+201\theta^2+69\theta+10\right)+2^{9} 3^{6} x^{2}\left(20\theta^4+80\theta^3+107\theta^2+54\theta+10\right)+2^{12} 3^{10} x^{3}(2\theta+5)^2(2\theta+1)^2\)
Maple LaTexCoefficients of the holomorphic solution: 1, -360, 314280, -348076800, 431342188200, ... --> OEIS Normalized instanton numbers (n0=1): -900, -27387, 8364884, 2066389488, -208833104160, ... ; Common denominator:...
\((1296z+1)(1+1728z)^2\)
| \(-\frac{ 1}{ 1296}\) | \(-\frac{ 1}{ 1728}\) | \(0\) | \(\infty\) |
|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(1\) | \(\frac{ 1}{ 2}\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(1\) | \(\frac{ 1}{ 2}\) | \(0\) | \(\frac{ 5}{ 2}\) |
| \(2\) | \(1\) | \(0\) | \(\frac{ 5}{ 2}\) |
92
New Number: 3.30 | AESZ: 422 | Superseeker: 124 2152276/9 | Hash: b37ac82ae57415849cb59beac4cd6adf
Degree: 3
\(\theta^4+2^{2} x\left(380\theta^4+760\theta^3+907\theta^2+527\theta+117\right)+2^{4} 3 x^{2}(8\theta+7)(8\theta+9)(184\theta^2+368\theta+183)-2^{8} 3^{2} x^{3}(8\theta+7)(8\theta+9)(8\theta+15)(8\theta+17)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -468, 280260, -182276400, 123566444100, ... --> OEIS Normalized instanton numbers (n0=1): 124, -3752, 2152276/9, -18042588, 1647569184, ... ; Common denominator:...
\(-(16z-1)(1+768z)^2\)
| \(-\frac{ 1}{ 768}\) | \(0\) | \(\frac{ 1}{ 16}\) | \(\infty\) |
|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(\frac{ 7}{ 8}\) |
| \(-\frac{ 1}{ 2}\) | \(0\) | \(1\) | \(\frac{ 9}{ 8}\) |
| \(1\) | \(0\) | \(1\) | \(\frac{ 15}{ 8}\) |
| \(\frac{ 3}{ 2}\) | \(0\) | \(2\) | \(\frac{ 17}{ 8}\) |
93
New Number: 3.32 | AESZ: | Superseeker: 128 382592 | Hash: 9b39b616939718654c472dbfb37cdd4e
Degree: 3
\(\theta^4-2^{4} x(6\theta^2+6\theta-1)(2\theta+1)^2-2^{10} x^{2}(60\theta^2+120\theta+97)(\theta+1)^2-2^{21} x^{3}(\theta+1)^2(\theta+2)^2\)
Maple LaTexCoefficients of the holomorphic solution: 1, -16, 4624, 678656, 238896400, ... --> OEIS Normalized instanton numbers (n0=1): 128, 4084, 382592, 51510860, 8644861312, ... ; Common denominator:...
\(-(512z-1)(1+64z)^2\)
| \(-\frac{ 1}{ 64}\) | \(0\) | \(\frac{ 1}{ 512}\) | \(\infty\) |
|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(1\) |
| \(-\frac{ 1}{ 2}\) | \(0\) | \(1\) | \(1\) |
| \(1\) | \(0\) | \(1\) | \(2\) |
| \(\frac{ 3}{ 2}\) | \(0\) | \(2\) | \(2\) |
94
New Number: 3.33 | AESZ: | Superseeker: 4 1580/9 | Hash: da01a7b2dfcebe6e332be6c29ed2a8e5
Degree: 3
\(\theta^4+2^{2} x\left(36\theta^4+72\theta^3+85\theta^2+49\theta+11\right)+2^{4} x^{2}(8\theta^2+16\theta+11)(48\theta^2+96\theta+49)+2^{8} x^{3}(4\theta+7)^2(4\theta+5)^2\)
Maple LaTexCoefficients of the holomorphic solution: 1, -44, 2244, -122576, 6952516, ... --> OEIS Normalized instanton numbers (n0=1): 4, -25, 1580/9, -1580, 17120, ... ; Common denominator:...
\((16z+1)(1+64z)^2\)
| \(-\frac{ 1}{ 16}\) | \(-\frac{ 1}{ 64}\) | \(0\) | \(\infty\) |
|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(\frac{ 5}{ 4}\) |
| \(1\) | \(-\frac{ 1}{ 2}\) | \(0\) | \(\frac{ 5}{ 4}\) |
| \(1\) | \(1\) | \(0\) | \(\frac{ 7}{ 4}\) |
| \(2\) | \(\frac{ 3}{ 2}\) | \(0\) | \(\frac{ 7}{ 4}\) |
95
New Number: 3.34 | AESZ: | Superseeker: 16 1744 | Hash: 931a876bfe4d4aa192c6e18e74047640
Degree: 3
\(\theta^4-2^{4} x\left(25\theta^4+50\theta^3+43\theta^2+18\theta+3\right)+2^{11} x^{2}(26\theta^2+52\theta+21)(\theta+1)^2-2^{16} 3^{2} x^{3}(\theta+1)(\theta+2)(2\theta+1)(2\theta+5)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 48, 3984, 387840, 40818960, ... --> OEIS Normalized instanton numbers (n0=1): 16, -110, 1744, -29526, 644016, ... ; Common denominator:...
\(-(144z-1)(-1+128z)^2\)
| \(0\) | \(\frac{ 1}{ 144}\) | \(\frac{ 1}{ 128}\) | \(\infty\) |
|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(0\) | \(1\) | \(\frac{ 1}{ 2}\) | \(1\) |
| \(0\) | \(1\) | \(\frac{ 1}{ 2}\) | \(2\) |
| \(0\) | \(2\) | \(1\) | \(\frac{ 5}{ 2}\) |
96
New Number: 3.3 | AESZ: 228 | Superseeker: -68 -18628/3 | Hash: b15f49e2c20021dbc50eaf05a6fd3126
Degree: 3
\(\theta^4+2^{2} x\left(176\theta^4+352\theta^3+289\theta^2+113\theta+18\right)+2^{11} x^{2}\left(80\theta^4+320\theta^3+449\theta^2+258\theta+54\right)+2^{16} 3 x^{3}(2\theta+5)(2\theta+1)(4\theta+3)(4\theta+9)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -72, 10152, -1739520, 327839400, ... --> OEIS Normalized instanton numbers (n0=1): -68, -835, -18628/3, 359052, 23710944, ... ; Common denominator:...
\((192z+1)(1+256z)^2\)
| \(-\frac{ 1}{ 192}\) | \(-\frac{ 1}{ 256}\) | \(0\) | \(\infty\) |
|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(1\) | \(\frac{ 1}{ 2}\) | \(0\) | \(\frac{ 3}{ 4}\) |
| \(1\) | \(\frac{ 1}{ 2}\) | \(0\) | \(\frac{ 9}{ 4}\) |
| \(2\) | \(1\) | \(0\) | \(\frac{ 5}{ 2}\) |
97
New Number: 3.4 | AESZ: | Superseeker: -9 -748 | Hash: 350ef7c6e038467a3f50bfbe164fa73a
Degree: 3
\(\theta^4+3^{2} x\left(33\theta^4+66\theta^3+57\theta^2+24\theta+4\right)+2^{3} 3^{6} x^{2}(\theta+1)^2(5\theta^2+10\theta+4)+2^{2} 3^{10} x^{3}(\theta+1)(\theta+2)(2\theta+1)(2\theta+5)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -36, 2268, -168840, 13664700, ... --> OEIS Normalized instanton numbers (n0=1): -9, -279/4, -748, -9612, -155448, ... ; Common denominator:...
\((81z+1)(1+108z)^2\)
| \(-\frac{ 1}{ 81}\) | \(-\frac{ 1}{ 108}\) | \(0\) | \(\infty\) |
|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(1\) | \(\frac{ 1}{ 2}\) | \(0\) | \(1\) |
| \(1\) | \(\frac{ 1}{ 2}\) | \(0\) | \(2\) |
| \(2\) | \(1\) | \(0\) | \(\frac{ 5}{ 2}\) |
98
New Number: 3.5 | AESZ: | Superseeker: 26 103520/9 | Hash: 4ed9bc316d49a71649da0a1148f7ea9d
Degree: 3
\(\theta^4-2 x\left(102\theta^4+204\theta^3+155\theta^2+53\theta+7\right)+2^{2} x^{2}(\theta+1)^2(396\theta^2+792\theta+311)-2^{4} 7^{2} x^{3}(\theta+1)(\theta+2)(2\theta+1)(2\theta+5)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 14, 834, 78260, 8970850, ... --> OEIS Normalized instanton numbers (n0=1): 26, 348, 103520/9, 539764, 31290280, ... ; Common denominator:...
\(-(196z-1)(4z-1)^2\)
| \(0\) | \(\frac{ 1}{ 196}\) | \(\frac{ 1}{ 4}\) | \(\infty\) |
|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(0\) | \(1\) | \(\frac{ 1}{ 4}\) | \(1\) |
| \(0\) | \(1\) | \(\frac{ 3}{ 4}\) | \(2\) |
| \(0\) | \(2\) | \(1\) | \(\frac{ 5}{ 2}\) |
99
New Number: 3.6 | AESZ: ~33 | Superseeker: 196 2993772 | Hash: 29aeacb8c7e91c8c2838e65ce2750b5a
Degree: 3
\(\theta^4+2^{2} x\left(60\theta^4-8\theta^3+31\theta^2+35\theta+6\right)-2^{10} x^{2}(4\theta+3)(132\theta^3+395\theta^2+363\theta+69)-2^{14} 7^{2} x^{3}(4\theta+1)(4\theta+3)(4\theta+7)(4\theta+9)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -24, 13992, -920832, 1808021160, ... --> OEIS Normalized instanton numbers (n0=1): 196, 17212, 2993772, 789858520, 260782261024, ... ; Common denominator:...
\(-(784z-1)(1+512z)^2\)
| \(-\frac{ 1}{ 512}\) | \(0\) | \(\frac{ 1}{ 784}\) | \(\infty\) |
|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 4}\) |
| \(\frac{ 1}{ 2}\) | \(0\) | \(1\) | \(\frac{ 3}{ 4}\) |
| \(1\) | \(0\) | \(1\) | \(\frac{ 7}{ 4}\) |
| \(\frac{ 3}{ 2}\) | \(0\) | \(2\) | \(\frac{ 9}{ 4}\) |
100
New Number: 3.7 | AESZ: ~73 | Superseeker: 90 151648 | Hash: 9f672e1168859bdcc8ddc7a201c57968
Degree: 3
\(\theta^4-2 3^{2} x\left(6\theta^4+12\theta^3+3\theta^2-3\theta-1\right)-2^{2} 3^{6} x^{2}(\theta+1)^2(20\theta^2+40\theta+17)-2^{4} 3^{10} x^{3}(\theta+1)(\theta+2)(2\theta+1)(2\theta+5)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -18, 2754, 37620, 43789410, ... --> OEIS Normalized instanton numbers (n0=1): 90, 2196, 151648, 14813388, 1820806056, ... ; Common denominator:...
\(-(324z-1)(1+108z)^2\)
| \(-\frac{ 1}{ 108}\) | \(0\) | \(\frac{ 1}{ 324}\) | \(\infty\) |
|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(0\) | \(0\) | \(1\) | \(1\) |
| \(1\) | \(0\) | \(1\) | \(2\) |
| \(1\) | \(0\) | \(2\) | \(\frac{ 5}{ 2}\) |
101
New Number: 3.8 | AESZ: ~100 | Superseeker: 5 454 | Hash: 82a1ac6ac6fb9ab2e4d6b5d5790d1d9b
Degree: 3
\(\theta^4+x\left(15\theta^4+30\theta^3+35\theta^2+20\theta+4\right)-2^{5} x^{2}(\theta+1)^2(66\theta^2+132\theta+53)-2^{8} 7^{2} x^{3}(\theta+1)(\theta+2)(2\theta+1)(2\theta+5)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -4, 132, -1120, 72100, ... --> OEIS Normalized instanton numbers (n0=1): 5, 42, 454, 7498, 154351, ... ; Common denominator:...
\(-(49z-1)(1+32z)^2\)
| \(-\frac{ 1}{ 32}\) | \(0\) | \(\frac{ 1}{ 49}\) | \(\infty\) |
|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(\frac{ 1}{ 2}\) | \(0\) | \(1\) | \(1\) |
| \(\frac{ 1}{ 2}\) | \(0\) | \(1\) | \(2\) |
| \(1\) | \(0\) | \(2\) | \(\frac{ 5}{ 2}\) |
102
New Number: 3.9 | AESZ: ~101 | Superseeker: 13 2650 | Hash: a6878d847acf199583e8168a33967174
Degree: 3
\(\theta^4-x\left(113\theta^4+226\theta^3+173\theta^2+60\theta+8\right)-2^{3} x^{2}(\theta+1)^2(119\theta^2+238\theta+92)-2^{2} 11^{2} x^{3}(\theta+1)(\theta+2)(2\theta+1)(2\theta+5)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 8, 336, 19880, 1420720, ... --> OEIS Normalized instanton numbers (n0=1): 13, 128, 2650, 79400, 2921395, ... ; Common denominator:...
\(-(121z-1)(4z+1)^2\)
| \(-\frac{ 1}{ 4}\) | \(0\) | \(\frac{ 1}{ 121}\) | \(\infty\) |
|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(\frac{ 1}{ 2}\) | \(0\) | \(1\) | \(1\) |
| \(\frac{ 1}{ 2}\) | \(0\) | \(1\) | \(2\) |
| \(1\) | \(0\) | \(2\) | \(\frac{ 5}{ 2}\) |
103
New Number: 4.10 | AESZ: | Superseeker: -84 -148820 | Hash: fc2837f1001e57a5cc53749a08d4f2bf
Degree: 4
\(\theta^4-2 3 x\left(216\theta^4+432\theta^3+516\theta^2+300\theta+67\right)+2^{2} 3^{2} x^{2}\left(12312\theta^4+49248\theta^3+76374\theta^2+54252\theta+15017\right)-2^{6} 3^{10} x^{3}(\theta^2+3\theta+3)(2\theta+3)^2+2^{4} 3^{10} x^{4}(2\theta+3)(2\theta+5)(6\theta+11)(6\theta+13)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 402, 197010, 104962956, 58311249066, ... --> OEIS Normalized instanton numbers (n0=1): -84, -5271/2, -148820, -41373213/4, -836813460, ... ; Common denominator:...
\((1-648z+11664z^2)^2\)
| \(0\) | \(s_1\) | \(s_2\) | \(\frac{ 1}{ 36}-\frac{ 1}{ 54}\sqrt{ 2}\) | \(\frac{ 1}{ 36}+\frac{ 1}{ 54}\sqrt{ 2}\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(-\frac{ 1}{ 2}\) | \(-\frac{ 1}{ 2}\) | \(0\) | \(0\) | \(\frac{ 3}{ 2}\) |
| \(0\) | \(0\) | \(0\) | \(-\frac{ 1}{ 2}\) | \(-\frac{ 1}{ 2}\) | \(\frac{ 11}{ 6}\) |
| \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(\frac{ 13}{ 6}\) |
| \(0\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 5}{ 2}\) |
104
New Number: 4.11 | AESZ: | Superseeker: -63 -96866 | Hash: 39ed55f37672c58e7ce182c4c33d4a66
Degree: 4
\(\theta^4-x\left(972\theta^4+1944\theta^3+2322\theta^2+1350\theta+603/2\right)+x^{2}\left(196830\theta^4+787320\theta^3+2110455/2\theta^2+535815\theta+237897/4\right)+3^{14} x^{3}(\theta^2+3\theta+3)(2\theta+3)^2+x^{4}43046721/16(2\theta+3)(2\theta+5)(6\theta+11)(6\theta+13)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 603/2, 1008855/8, 898513875/16, 3331190162475/128, ... --> OEIS Normalized instanton numbers (n0=1): -63, -8757/4, -96866, -6253821, -446217723, ... ; Common denominator:...
\((-1+486z+19683z^2)^2\)
| \(-\frac{ 1}{ 81}-\frac{ 2}{ 243}\sqrt{ 3}\) | \(0\) | \(s_1\) | \(s_2\) | \(-\frac{ 1}{ 81}+\frac{ 2}{ 243}\sqrt{ 3}\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(-\frac{ 1}{ 2}\) | \(-\frac{ 1}{ 2}\) | \(0\) | \(\frac{ 3}{ 2}\) |
| \(-\frac{ 1}{ 2}\) | \(0\) | \(0\) | \(0\) | \(-\frac{ 1}{ 2}\) | \(\frac{ 11}{ 6}\) |
| \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(\frac{ 13}{ 6}\) |
| \(\frac{ 3}{ 2}\) | \(0\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 5}{ 2}\) |
105
New Number: 4.12 | AESZ: | Superseeker: -45 7080 | Hash: 6c95cb50a57e8a1c96a5a4e3e353cb85
Degree: 4
\(\theta^4-x\left(1188\theta^4+2376\theta^3+2874\theta^2+1686\theta+765/2\right)+x^{2}\left(535086\theta^4+2140344\theta^3+7708527/2\theta^2+3427839\theta+4938345/4\right)-3^{8} 5^{3} x^{3}(33\theta^2+99\theta+100)(2\theta+3)^2+x^{4}922640625/16(2\theta+3)(2\theta+5)(6\theta+11)(6\theta+13)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 765/2, 1009575/8, 627988725/16, 1505754528075/128, ... --> OEIS Normalized instanton numbers (n0=1): -45, -135, 7080, 406035, 17168436, ... ; Common denominator:...
\((1-594z+91125z^2)^2\)
| \(0\) | \(s_1\) | \(s_2\) | \(\frac{ 11}{ 3375}-\frac{ 2}{ 3375}I\) | \(\frac{ 11}{ 3375}+\frac{ 2}{ 3375}I\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(-\frac{ 1}{ 2}\) | \(-\frac{ 1}{ 2}\) | \(0\) | \(0\) | \(\frac{ 3}{ 2}\) |
| \(0\) | \(0\) | \(0\) | \(-\frac{ 1}{ 2}\) | \(-\frac{ 1}{ 2}\) | \(\frac{ 11}{ 6}\) |
| \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(\frac{ 13}{ 6}\) |
| \(0\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 5}{ 2}\) |
106
New Number: 4.13 | AESZ: ~37 | Superseeker: -128 -1546624/3 | Hash: c03e4e4ca58f9f1f76c98c8616bc2cbd
Degree: 4
\(\theta^4-2^{2} x\left(640\theta^4+1280\theta^3+1534\theta^2+894\theta+201\right)+2^{4} 3 x^{2}\left(45056\theta^4+180224\theta^3+308352\theta^2+256256\theta+86363\right)-2^{19} x^{3}(320\theta^2+960\theta+957)(2\theta+3)^2+2^{30} x^{4}(2\theta+3)(2\theta+5)(4\theta+7)(4\theta+9)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 804, 655260, 563879792, 505573095132, ... --> OEIS Normalized instanton numbers (n0=1): -128, -5232, -1546624/3, -64705008, -7960717440, ... ; Common denominator:...
\((1024z-1)^2(256z-1)^2\)
| \(0\) | \(\frac{ 1}{ 1024}\) | \(\frac{ 1}{ 256}\) | \(\infty\) |
|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(\frac{ 3}{ 2}\) |
| \(0\) | \(-\frac{ 1}{ 2}\) | \(-\frac{ 1}{ 2}\) | \(\frac{ 7}{ 4}\) |
| \(0\) | \(1\) | \(1\) | \(\frac{ 9}{ 4}\) |
| \(0\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 5}{ 2}\) |
107
New Number: 4.14 | AESZ: | Superseeker: -340 -15174100/3 | Hash: a961869d91c2f73091913e8f8c4b5fa0
Degree: 4
\(\theta^4-2^{2} x\left(1088\theta^4+2176\theta^3+2579\theta^2+1491\theta+330\right)+2^{7} 3 x^{2}\left(12352\theta^4+49408\theta^3+74070\theta^2+49324\theta+12325\right)-2^{12} x^{3}(1088\theta^2+3264\theta+3225)(2\theta+3)^2+2^{18} x^{4}(2\theta+3)(2\theta+5)(4\theta+7)(4\theta+9)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 1320, 2233320, 4108451200, 7880762169000, ... --> OEIS Normalized instanton numbers (n0=1): -340, -31985, -15174100/3, -1036481610, -246612212640, ... ; Common denominator:...
\((1-2176z+4096z^2)^2\)
| \(0\) | \(s_1\) | \(s_2\) | \(\frac{ 17}{ 64}-\frac{ 3}{ 16}\sqrt{ 2}\) | \(\frac{ 17}{ 64}+\frac{ 3}{ 16}\sqrt{ 2}\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(-\frac{ 1}{ 2}\) | \(-\frac{ 1}{ 2}\) | \(0\) | \(0\) | \(\frac{ 3}{ 2}\) |
| \(0\) | \(0\) | \(0\) | \(-\frac{ 1}{ 2}\) | \(-\frac{ 1}{ 2}\) | \(\frac{ 7}{ 4}\) |
| \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(\frac{ 9}{ 4}\) |
| \(0\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 5}{ 2}\) |
108
New Number: 4.15 | AESZ: | Superseeker: -76 415420 | Hash: d8c866a60b2b4edb0c88e03315fa2a7b
Degree: 4
\(\theta^4-2^{2} x\left(448\theta^4+896\theta^3+1077\theta^2+629\theta+142\right)+2^{7} x^{2}\left(11456\theta^4+45824\theta^3+86434\theta^2+81220\theta+30693\right)-2^{12} 3^{4} x^{3}(448\theta^2+1344\theta+1343)(2\theta+3)^2+2^{18} 3^{8} x^{4}(2\theta+3)(2\theta+5)(4\theta+7)(4\theta+9)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 568, 207720, 25669504, -32774007128, ... --> OEIS Normalized instanton numbers (n0=1): -76, 2958, 415420, 17891650, -1211214176, ... ; Common denominator:...
\((331776z^2-896z+1)^2\)
| \(0\) | \(s_1\) | \(s_2\) | \(\frac{ 7}{ 5184}-\frac{ 1}{ 1296}\sqrt{ 2}I\) | \(\frac{ 7}{ 5184}+\frac{ 1}{ 1296}\sqrt{ 2}I\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(-\frac{ 1}{ 2}\) | \(-\frac{ 1}{ 2}\) | \(0\) | \(0\) | \(\frac{ 3}{ 2}\) |
| \(0\) | \(0\) | \(0\) | \(-\frac{ 1}{ 2}\) | \(-\frac{ 1}{ 2}\) | \(\frac{ 7}{ 4}\) |
| \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(\frac{ 9}{ 4}\) |
| \(0\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 5}{ 2}\) |
109
New Number: 4.16 | AESZ: | Superseeker: -208 -1863312 | Hash: ff22b96c1af3d06292a97d4dee085628
Degree: 4
\(\theta^4-2^{4} x\left(192\theta^4+384\theta^3+457\theta^2+265\theta+59\right)+2^{9} x^{2}\left(4864\theta^4+19456\theta^3+30088\theta^2+21264\theta+5849\right)-2^{18} x^{3}(192\theta^2+576\theta+571)(2\theta+3)^2+2^{26} x^{4}(2\theta+3)(2\theta+5)(4\theta+7)(4\theta+9)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 944, 1093840, 1379945728, 1816122981136, ... --> OEIS Normalized instanton numbers (n0=1): -208, -15098, -1863312, -284211001, -50414626800, ... ; Common denominator:...
\((1-1536z+65536z^2)^2\)
| \(0\) | \(s_1\) | \(s_2\) | \(\frac{ 3}{ 256}-\frac{ 1}{ 128}\sqrt{ 2}\) | \(\frac{ 3}{ 256}+\frac{ 1}{ 128}\sqrt{ 2}\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(-\frac{ 1}{ 2}\) | \(-\frac{ 1}{ 2}\) | \(0\) | \(0\) | \(\frac{ 3}{ 2}\) |
| \(0\) | \(0\) | \(0\) | \(-\frac{ 1}{ 2}\) | \(-\frac{ 1}{ 2}\) | \(\frac{ 7}{ 4}\) |
| \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(\frac{ 9}{ 4}\) |
| \(0\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 5}{ 2}\) |
110
New Number: 4.17 | AESZ: | Superseeker: -156 -1229332 | Hash: 245e2566c8da93abbfc4296923ccba12
Degree: 4
\(\theta^4-2^{2} 3 x\left(192\theta^4+384\theta^3+457\theta^2+265\theta+59\right)+2^{4} 3^{2} x^{2}\left(7680\theta^4+30720\theta^3+41040\theta^2+20640\theta+2203\right)+2^{12} 3^{4} x^{3}(192\theta^2+576\theta+571)(2\theta+3)^2+2^{18} 3^{6} x^{4}(2\theta+3)(2\theta+5)(4\theta+7)(4\theta+9)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 708, 700740, 738956400, 811309522500, ... --> OEIS Normalized instanton numbers (n0=1): -156, -12549, -1229332, -175559052, -27542017056, ... ; Common denominator:...
\((-1+1152z+110592z^2)^2\)
| \(-\frac{ 1}{ 192}-\frac{ 1}{ 288}\sqrt{ 3}\) | \(0\) | \(s_1\) | \(s_2\) | \(-\frac{ 1}{ 192}+\frac{ 1}{ 288}\sqrt{ 3}\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(-\frac{ 1}{ 2}\) | \(-\frac{ 1}{ 2}\) | \(0\) | \(\frac{ 3}{ 2}\) |
| \(-\frac{ 1}{ 2}\) | \(0\) | \(0\) | \(0\) | \(-\frac{ 1}{ 2}\) | \(\frac{ 7}{ 4}\) |
| \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(\frac{ 9}{ 4}\) |
| \(\frac{ 3}{ 2}\) | \(0\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 5}{ 2}\) |
111
New Number: 4.18 | AESZ: | Superseeker: -100 126580 | Hash: 3ab4956c5da76dad5e104e338e7c0128
Degree: 4
\(\theta^4-2^{2} x\left(704\theta^4+1408\theta^3+1697\theta^2+993\theta+225\right)+2^{4} x^{2}\left(187904\theta^4+751616\theta^3+1350224\theta^2+1197216\theta+429975\right)-2^{12} 5^{3} x^{3}(704\theta^2+2112\theta+2115)(2\theta+3)^2+2^{18} 5^{6} x^{4}(2\theta+3)(2\theta+5)(4\theta+7)(4\theta+9)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 900, 701100, 515510800, 365497137900, ... --> OEIS Normalized instanton numbers (n0=1): -100, -1260, 126580, 12033300, 1211646512, ... ; Common denominator:...
\((512000z^2-1408z+1)^2\)
| \(0\) | \(s_1\) | \(s_2\) | \(\frac{ 11}{ 8000}-\frac{ 1}{ 4000}I\) | \(\frac{ 11}{ 8000}+\frac{ 1}{ 4000}I\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(-\frac{ 1}{ 2}\) | \(-\frac{ 1}{ 2}\) | \(0\) | \(0\) | \(\frac{ 3}{ 2}\) |
| \(0\) | \(0\) | \(0\) | \(-\frac{ 1}{ 2}\) | \(-\frac{ 1}{ 2}\) | \(\frac{ 7}{ 4}\) |
| \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(\frac{ 9}{ 4}\) |
| \(0\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 5}{ 2}\) |
112
New Number: 4.19 | AESZ: ~66 | Superseeker: -864 -147560800 | Hash: b9b85f803521c6af3b5f7572d309f89a
Degree: 4
\(\theta^4-2^{2} 3 x\left(1440\theta^4+2880\theta^3+3434\theta^2+1994\theta+447\right)+2^{4} 3^{4} x^{2}\left(76032\theta^4+304128\theta^3+518496\theta^2+428736\theta+143785\right)-2^{15} 3^{8} x^{3}(240\theta^2+720\theta+709)(2\theta+3)^2+2^{26} 3^{10} x^{4}(2\theta+3)(2\theta+5)(3\theta+5)(3\theta+7)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 5364, 29367900, 170217457200, 1029027458497500, ... --> OEIS Normalized instanton numbers (n0=1): -864, -261684, -147560800, -120568926924, -88009904955744, ... ; Common denominator:...
\((6912z-1)^2(1728z-1)^2\)
| \(0\) | \(\frac{ 1}{ 6912}\) | \(\frac{ 1}{ 1728}\) | \(\infty\) |
|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(\frac{ 3}{ 2}\) |
| \(0\) | \(-\frac{ 1}{ 2}\) | \(-\frac{ 1}{ 2}\) | \(\frac{ 5}{ 3}\) |
| \(0\) | \(1\) | \(1\) | \(\frac{ 7}{ 3}\) |
| \(0\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 5}{ 2}\) |
113
New Number: 4.1 | AESZ: ~39 | Superseeker: -32 -8736 | Hash: 462066f711fc3742db1ea9befa2fe01b
Degree: 4
\(\theta^4-2^{2} x\left(160\theta^4+320\theta^3+386\theta^2+226\theta+51\right)+2^{4} 3 x^{2}\left(2816\theta^4+11264\theta^3+19360\theta^2+16192\theta+5491\right)-2^{15} x^{3}(80\theta^2+240\theta+243)(2\theta+3)^2+2^{26} x^{4}(\theta+2)^2(2\theta+3)(2\theta+5)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 204, 41820, 9022160, 2025179100, ... --> OEIS Normalized instanton numbers (n0=1): -32, -284, -8736, -283900, -10041888, ... ; Common denominator:...
\((256z-1)^2(64z-1)^2\)
| \(0\) | \(\frac{ 1}{ 256}\) | \(\frac{ 1}{ 64}\) | \(\infty\) |
|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(\frac{ 3}{ 2}\) |
| \(0\) | \(-\frac{ 1}{ 2}\) | \(-\frac{ 1}{ 2}\) | \(2\) |
| \(0\) | \(1\) | \(1\) | \(2\) |
| \(0\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 5}{ 2}\) |
114
New Number: 4.20 | AESZ: | Superseeker: -2484 -1327731388 | Hash: 80035e90a6f24cd6da3d4c5adc98379f
Degree: 4
\(\theta^4-2^{2} 3 x\left(2448\theta^4+4896\theta^3+5773\theta^2+3325\theta+732\right)+2^{6} 3^{4} x^{2}\left(41688\theta^4+166752\theta^3+248973\theta^2+164442\theta+40616\right)-2^{8} 3^{8} x^{3}(816\theta^2+2448\theta+2389)(2\theta+3)^2+2^{14} 3^{10} x^{4}(2\theta+3)(2\theta+5)(3\theta+5)(3\theta+7)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 8784, 99982728, 1239742123200, 16039070549564328, ... --> OEIS Normalized instanton numbers (n0=1): -2484, -1446309, -1327731388, -1580284433106, -2187358898922144, ... ; Common denominator:...
\((1-14688z+186624z^2)^2\)
| \(0\) | \(s_1\) | \(s_2\) | \(\frac{ 17}{ 432}-\frac{ 1}{ 36}\sqrt{ 2}\) | \(\frac{ 17}{ 432}+\frac{ 1}{ 36}\sqrt{ 2}\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(-\frac{ 1}{ 2}\) | \(-\frac{ 1}{ 2}\) | \(0\) | \(0\) | \(\frac{ 3}{ 2}\) |
| \(0\) | \(0\) | \(0\) | \(-\frac{ 1}{ 2}\) | \(-\frac{ 1}{ 2}\) | \(\frac{ 5}{ 3}\) |
| \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(\frac{ 7}{ 3}\) |
| \(0\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 5}{ 2}\) |
115
New Number: 4.21 | AESZ: | Superseeker: -492 136094428 | Hash: 595707be6cb20abc1dfeecf72492ae5f
Degree: 4
\(\theta^4-2^{2} 3 x\left(1008\theta^4+2016\theta^3+2411\theta^2+1403\theta+316\right)+2^{6} 3^{2} x^{2}\left(115992\theta^4+463968\theta^3+872325\theta^2+816714\theta+307516\right)-2^{8} 3^{12} x^{3}(336\theta^2+1008\theta+995)(2\theta+3)^2+2^{14} 3^{18} x^{4}(2\theta+3)(2\theta+5)(3\theta+5)(3\theta+7)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 3792, 9275400, 7430606400, -68166524583000, ... --> OEIS Normalized instanton numbers (n0=1): -492, 128514, 136094428, 32416215738, -16919954920032, ... ; Common denominator:...
\((15116544z^2-6048z+1)^2\)
| \(0\) | \(s_1\) | \(s_2\) | \(\frac{ 7}{ 34992}-\frac{ 1}{ 8748}\sqrt{ 2}I\) | \(\frac{ 7}{ 34992}+\frac{ 1}{ 8748}\sqrt{ 2}I\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(-\frac{ 1}{ 2}\) | \(-\frac{ 1}{ 2}\) | \(0\) | \(0\) | \(\frac{ 3}{ 2}\) |
| \(0\) | \(0\) | \(0\) | \(-\frac{ 1}{ 2}\) | \(-\frac{ 1}{ 2}\) | \(\frac{ 5}{ 3}\) |
| \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(\frac{ 7}{ 3}\) |
| \(0\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 5}{ 2}\) |
116
New Number: 4.22 | AESZ: | Superseeker: -1488 -517984144 | Hash: 7d70f749f0fd6381c088f4c1fac4d6df
Degree: 4
\(\theta^4-2^{4} 3 x\left(432\theta^4+864\theta^3+1023\theta^2+591\theta+131\right)+2^{9} 3^{2} x^{2}\left(24624\theta^4+98496\theta^3+151722\theta^2+106452\theta+29023\right)-2^{14} 3^{10} x^{3}(16\theta^2+48\theta+47)(2\theta+3)^2+2^{22} 3^{10} x^{4}(2\theta+3)(2\theta+5)(3\theta+5)(3\theta+7)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 6288, 49006800, 416705452800, 3698851729136400, ... --> OEIS Normalized instanton numbers (n0=1): -1488, -704730, -517984144, -469396561641, -493072108113648, ... ; Common denominator:...
\((2985984z^2-10368z+1)^2\)
| \(0\) | \(s_1\) | \(s_2\) | \(\frac{ 1}{ 576}-\frac{ 1}{ 864}\sqrt{ 2}\) | \(\frac{ 1}{ 576}+\frac{ 1}{ 864}\sqrt{ 2}\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(-\frac{ 1}{ 2}\) | \(-\frac{ 1}{ 2}\) | \(0\) | \(0\) | \(\frac{ 3}{ 2}\) |
| \(0\) | \(0\) | \(0\) | \(-\frac{ 1}{ 2}\) | \(-\frac{ 1}{ 2}\) | \(\frac{ 5}{ 3}\) |
| \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(\frac{ 7}{ 3}\) |
| \(0\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 5}{ 2}\) |
117
New Number: 4.23 | AESZ: | Superseeker: -1116 -349462868 | Hash: 4cde44ecce8658b2c2ca6b3c279f4e62
Degree: 4
\(\theta^4-2^{2} 3^{2} x\left(432\theta^4+864\theta^3+1023\theta^2+591\theta+131\right)+2^{4} 3^{5} 5 x^{2}\left(2592\theta^4+10368\theta^3+13788\theta^2+6840\theta+689\right)+2^{8} 3^{14} x^{3}(16\theta^2+48\theta+47)(2\theta+3)^2+2^{14} 3^{16} x^{4}(2\theta+3)(2\theta+5)(3\theta+5)(3\theta+7)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 4716, 31430916, 223425214992, 1654537886846532, ... --> OEIS Normalized instanton numbers (n0=1): -1116, -586989, -349462868, -300569202144, -280354383814176, ... ; Common denominator:...
\((5038848z^2+7776z-1)^2\)
| \(-\frac{ 1}{ 1296}-\frac{ 1}{ 1944}\sqrt{ 3}\) | \(0\) | \(s_1\) | \(s_2\) | \(-\frac{ 1}{ 1296}+\frac{ 1}{ 1944}\sqrt{ 3}\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(-\frac{ 1}{ 2}\) | \(-\frac{ 1}{ 2}\) | \(0\) | \(\frac{ 3}{ 2}\) |
| \(-\frac{ 1}{ 2}\) | \(0\) | \(0\) | \(0\) | \(-\frac{ 1}{ 2}\) | \(\frac{ 5}{ 3}\) |
| \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(\frac{ 7}{ 3}\) |
| \(\frac{ 3}{ 2}\) | \(0\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 5}{ 2}\) |
118
New Number: 4.24 | AESZ: | Superseeker: -612 51318900 | Hash: dc90e303db3462d0c0bd472762000ad5
Degree: 4
\(\theta^4-2^{2} 3 x\left(1584\theta^4+3168\theta^3+3799\theta^2+2215\theta+501\right)+2^{4} 3^{2} x^{2}\left(951264\theta^4+3805056\theta^3+6812388\theta^2+6014664\theta+2151443\right)-2^{8} 3^{8} 5^{3} x^{3}(528\theta^2+1584\theta+1567)(2\theta+3)^2+2^{14} 3^{10} 5^{6} x^{4}(2\theta+3)(2\theta+5)(3\theta+5)(3\theta+7)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 6012, 31439916, 155468925360, 741919701370860, ... --> OEIS Normalized instanton numbers (n0=1): -612, -87372, 51318900, 24336059400, 14111081636400, ... ; Common denominator:...
\((23328000z^2-9504z+1)^2\)
| \(0\) | \(s_1\) | \(s_2\) | \(\frac{ 11}{ 54000}-\frac{ 1}{ 27000}I\) | \(\frac{ 11}{ 54000}+\frac{ 1}{ 27000}I\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(-\frac{ 1}{ 2}\) | \(-\frac{ 1}{ 2}\) | \(0\) | \(0\) | \(\frac{ 3}{ 2}\) |
| \(0\) | \(0\) | \(0\) | \(-\frac{ 1}{ 2}\) | \(-\frac{ 1}{ 2}\) | \(\frac{ 5}{ 3}\) |
| \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(\frac{ 7}{ 3}\) |
| \(0\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 5}{ 2}\) |
119
New Number: 4.25 | AESZ: 32 | Superseeker: -33 -13051 | Hash: bf53401dcbe0436fb67761f590ee3295
Degree: 4
\(\theta^4-x\left(540\theta^4+1080\theta^3+1296\theta^2+756\theta+339/2\right)+x^{2}\left(72846\theta^4+291384\theta^3+881067/2\theta^2+298299\theta+305217/4\right)+x^{3}\left(14580\theta^4+87480\theta^3+209547\theta^2+234981\theta+205497/2\right)+x^{4}9/16(6\theta+11)^2(6\theta+13)^2\)
Maple LaTexCoefficients of the holomorphic solution: 1, 339/2, 287415/8, 131845323/16, 251852894379/128, ... --> OEIS Normalized instanton numbers (n0=1): -33, -1995/4, -13051, -435975, -16838124, ... ; Common denominator:...
\((-1+270z+27z^2)^2\)
| \(-5-\frac{ 26}{ 9}\sqrt{ 3}\) | \(0\) | \(s_1\) | \(s_2\) | \(-5+\frac{ 26}{ 9}\sqrt{ 3}\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(-\frac{ 1}{ 2}\) | \(-\frac{ 1}{ 2}\) | \(0\) | \(\frac{ 11}{ 6}\) |
| \(-\frac{ 1}{ 2}\) | \(0\) | \(0\) | \(0\) | \(-\frac{ 1}{ 2}\) | \(\frac{ 11}{ 6}\) |
| \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(\frac{ 13}{ 6}\) |
| \(\frac{ 3}{ 2}\) | \(0\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 13}{ 6}\) |
120
New Number: 4.26 | AESZ: 60 | Superseeker: -10 -870 | Hash: 033b6632bf7cbbfe2a70e1f1eee4bf04
Degree: 4
\(\theta^4-x\left(248\theta^4+496\theta^3+604\theta^2+356\theta+81\right)+x^{2}\left(18832\theta^4+75328\theta^3+126798\theta^2+102940\theta+33889\right)-2^{3} 3 x^{3}\left(17856\theta^4+107136\theta^3+256985\theta^2+288843\theta+126617\right)+3^{2} x^{4}(24\theta+41)(24\theta+47)(24\theta+49)(24\theta+55)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 81, 13837/2, 1263327/2, 480917043/8, ... --> OEIS Normalized instanton numbers (n0=1): -10, -65, -870, -13905, -248910, ... ; Common denominator:...
\((108z-1)^2(16z-1)^2\)
| \(0\) | \(\frac{ 1}{ 108}\) | \(\frac{ 1}{ 16}\) | \(\infty\) |
|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(\frac{ 41}{ 24}\) |
| \(0\) | \(-\frac{ 1}{ 2}\) | \(-\frac{ 1}{ 2}\) | \(\frac{ 47}{ 24}\) |
| \(0\) | \(1\) | \(1\) | \(\frac{ 49}{ 24}\) |
| \(0\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 55}{ 24}\) |