You searched for: Spectrum0=0,1,1,2
Your search produced 482 matches
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61
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:...
\(-(144z-1)(-1+128z)^2\)
| \(0\) | \(\frac{ 1}{ 144}\) | \(\frac{ 1}{ 128}\) | \(\infty\) |
|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(0\) | \(1\) | \(\frac{ 1}{ 2}\) | \(1\) |
| \(0\) | \(1\) | \(\frac{ 1}{ 2}\) | \(2\) |
| \(0\) | \(2\) | \(1\) | \(\frac{ 5}{ 2}\) |
62
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:...
\((192z+1)(1+256z)^2\)
| \(-\frac{ 1}{ 192}\) | \(-\frac{ 1}{ 256}\) | \(0\) | \(\infty\) |
|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(1\) | \(\frac{ 1}{ 2}\) | \(0\) | \(\frac{ 3}{ 4}\) |
| \(1\) | \(\frac{ 1}{ 2}\) | \(0\) | \(\frac{ 9}{ 4}\) |
| \(2\) | \(1\) | \(0\) | \(\frac{ 5}{ 2}\) |
63
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:...
\((81z+1)(1+108z)^2\)
| \(-\frac{ 1}{ 81}\) | \(-\frac{ 1}{ 108}\) | \(0\) | \(\infty\) |
|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(1\) | \(\frac{ 1}{ 2}\) | \(0\) | \(1\) |
| \(1\) | \(\frac{ 1}{ 2}\) | \(0\) | \(2\) |
| \(2\) | \(1\) | \(0\) | \(\frac{ 5}{ 2}\) |
64
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:...
\(-(196z-1)(4z-1)^2\)
| \(0\) | \(\frac{ 1}{ 196}\) | \(\frac{ 1}{ 4}\) | \(\infty\) |
|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(0\) | \(1\) | \(\frac{ 1}{ 4}\) | \(1\) |
| \(0\) | \(1\) | \(\frac{ 3}{ 4}\) | \(2\) |
| \(0\) | \(2\) | \(1\) | \(\frac{ 5}{ 2}\) |
65
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:...
\(-(784z-1)(1+512z)^2\)
| \(-\frac{ 1}{ 512}\) | \(0\) | \(\frac{ 1}{ 784}\) | \(\infty\) |
|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 4}\) |
| \(\frac{ 1}{ 2}\) | \(0\) | \(1\) | \(\frac{ 3}{ 4}\) |
| \(1\) | \(0\) | \(1\) | \(\frac{ 7}{ 4}\) |
| \(\frac{ 3}{ 2}\) | \(0\) | \(2\) | \(\frac{ 9}{ 4}\) |
66
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:...
\(-(324z-1)(1+108z)^2\)
| \(-\frac{ 1}{ 108}\) | \(0\) | \(\frac{ 1}{ 324}\) | \(\infty\) |
|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(0\) | \(0\) | \(1\) | \(1\) |
| \(1\) | \(0\) | \(1\) | \(2\) |
| \(1\) | \(0\) | \(2\) | \(\frac{ 5}{ 2}\) |
67
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:...
\(-(49z-1)(1+32z)^2\)
| \(-\frac{ 1}{ 32}\) | \(0\) | \(\frac{ 1}{ 49}\) | \(\infty\) |
|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(\frac{ 1}{ 2}\) | \(0\) | \(1\) | \(1\) |
| \(\frac{ 1}{ 2}\) | \(0\) | \(1\) | \(2\) |
| \(1\) | \(0\) | \(2\) | \(\frac{ 5}{ 2}\) |
68
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:...
\(-(121z-1)(4z+1)^2\)
| \(-\frac{ 1}{ 4}\) | \(0\) | \(\frac{ 1}{ 121}\) | \(\infty\) |
|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(\frac{ 1}{ 2}\) | \(0\) | \(1\) | \(1\) |
| \(\frac{ 1}{ 2}\) | \(0\) | \(1\) | \(2\) |
| \(1\) | \(0\) | \(2\) | \(\frac{ 5}{ 2}\) |
69
New Number: 4.33 | AESZ: 55 | Superseeker: 76/3 144196/3 | Hash: 7e88cd5b7dc1c51022b66ac6f009218f
Degree: 4
\(3^{2} \theta^4-2^{2} 3 x\left(208\theta^4+224\theta^3+163\theta^2+51\theta+6\right)+2^{9} x^{2}\left(32\theta^4-928\theta^3-1606\theta^2-837\theta-141\right)+2^{16} x^{3}\left(144\theta^4+576\theta^3+467\theta^2+144\theta+15\right)-2^{24} x^{4}\left((2\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 8, 936, 108800, 16748200, ... --> OEIS Normalized instanton numbers (n0=1): 76/3, 3476/3, 144196/3, 3563196, 309069600, ... ; Common denominator:...
\(-(64z+1)(256z-1)(-3+128z)^2\)
| \(-\frac{ 1}{ 64}\) | \(0\) | \(\frac{ 1}{ 256}\) | \(\frac{ 3}{ 128}\) | \(\infty\) |
|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(1\) | \(0\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) |
| \(1\) | \(0\) | \(1\) | \(3\) | \(\frac{ 1}{ 2}\) |
| \(2\) | \(0\) | \(2\) | \(4\) | \(\frac{ 1}{ 2}\) |
70
New Number: 4.34 | AESZ: 99 | Superseeker: 647/13 942613/13 | Hash: f6c6b846edc829f336d8e4ae1dcb5618
Degree: 4
\(13^{2} \theta^4-13 x\left(4569\theta^4+9042\theta^3+6679\theta^2+2158\theta+260\right)+2^{4} x^{2}\left(6386\theta^4-1774\theta^3-17898\theta^2-11596\theta-2119\right)+2^{8} x^{3}\left(67\theta^4+1248\theta^3+1091\theta^2+312\theta+26\right)-2^{12} x^{4}\left((2\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 20, 2196, 369200, 75562900, ... --> OEIS Normalized instanton numbers (n0=1): 647/13, 16166/13, 942613/13, 80218296/13, 8418215008/13, ... ; Common denominator:...
\(-(256z^2+349z-1)(-13+16z)^2\)
| \(-\frac{ 349}{ 512}-\frac{ 85}{ 512}\sqrt{ 17}\) | \(0\) | \(s_1\) | \(s_2\) | \(-\frac{ 349}{ 512}+\frac{ 85}{ 512}\sqrt{ 17}\) | \(\frac{ 13}{ 16}\) | \(\infty\) |
|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) |
| \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(3\) | \(\frac{ 1}{ 2}\) |
| \(2\) | \(0\) | \(2\) | \(2\) | \(2\) | \(4\) | \(\frac{ 1}{ 2}\) |
71
New Number: 4.35 | AESZ: | Superseeker: -16 -1744 | Hash: cd392ce4c33f242f5d17e59976d0ea4f
Degree: 4
\(\theta^4-2^{4} x\left(23\theta^4+14\theta^3+13\theta^2+6\theta+1\right)+2^{11} x^{2}\theta(21\theta^3+24\theta^2+18\theta+4)-2^{16} x^{3}(2\theta+1)(10\theta^3+7\theta^2-5\theta-4)-2^{23} x^{4}(2\theta+1)(\theta+1)^2(2\theta+3)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 16, 912, 67840, 5839120, ... --> OEIS Normalized instanton numbers (n0=1): -16, -106, -1744, -29526, -644016, ... ; Common denominator:...
\(-(16z+1)(128z-1)^3\)
| \(-\frac{ 1}{ 16}\) | \(0\) | \(\frac{ 1}{ 128}\) | \(\infty\) |
|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(1\) | \(0\) | \(\frac{ 1}{ 2}\) | \(1\) |
| \(1\) | \(0\) | \(\frac{ 3}{ 2}\) | \(1\) |
| \(2\) | \(0\) | \(2\) | \(\frac{ 3}{ 2}\) |
72
New Number: 4.36 | AESZ: 109 | Superseeker: 1434/7 18676572/7 | Hash: bca2938ac7fa09f5bdc395cab75caf82
Degree: 4
\(7^{2} \theta^4-2 3 7 x\left(1272\theta^4+2508\theta^3+1779\theta^2+525\theta+56\right)+2^{2} 3 x^{2}\left(43704\theta^4+38088\theta^3-25757\theta^2-20608\theta-3360\right)-2^{4} 3^{3} x^{3}\left(2736\theta^4-1512\theta^3-1672\theta^2-357\theta-14\right)-2^{6} 3^{5} x^{4}(3\theta+1)(2\theta+1)^2(3\theta+2)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 48, 15840, 8148000, 5126536800, ... --> OEIS Normalized instanton numbers (n0=1): 1434/7, 14718, 18676572/7, 4988009280/7, 1646787631350/7, ... ; Common denominator:...
\(-(432z^2+1080z-1)(-7+36z)^2\)
| \(-\frac{ 5}{ 4}-\frac{ 13}{ 18}\sqrt{ 3}\) | \(0\) | \(s_1\) | \(s_2\) | \(-\frac{ 5}{ 4}+\frac{ 13}{ 18}\sqrt{ 3}\) | \(\frac{ 7}{ 36}\) | \(\infty\) |
|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 3}\) |
| \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) |
| \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(3\) | \(\frac{ 1}{ 2}\) |
| \(2\) | \(0\) | \(2\) | \(2\) | \(2\) | \(4\) | \(\frac{ 2}{ 3}\) |
73
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:...
\(-(16z+1)(4864z^3+896z^2+32z-1)\)
| ≈\(-0.10185-0.013248I\) | ≈\(-0.10185+0.013248I\) | \(-\frac{ 1}{ 16}\) | \(0\) | \(s_1\) | \(s_3\) | \(s_2\) | ≈\(0.019489\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(\frac{ 3}{ 2}\) |
| \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(\frac{ 5}{ 2}\) |
| \(2\) | \(2\) | \(2\) | \(0\) | \(2\) | \(2\) | \(2\) | \(2\) | \(\frac{ 7}{ 2}\) |
74
New Number: 4.38 | AESZ: 207 | Superseeker: -70944 -3707752060576 | Hash: eadc0882a9bf59840ef2b4a602f586e8
Degree: 4
\(\theta^4-2^{4} x\left(1072\theta^4-17824\theta^3-10888\theta^2-1976\theta-145\right)-2^{17} x^{2}\left(51088\theta^4+116368\theta^3-45264\theta^2-14228\theta-1397\right)+2^{28} 13 x^{3}\left(73104\theta^4+1536\theta^3-488\theta^2+384\theta+97\right)-2^{44} 13^{2} x^{4}\left((2\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -2320, 57601296, -2373661139200, 121665506430000400, ... --> OEIS Normalized instanton numbers (n0=1): -70944, 107317768, -3707752060576, 66327758316665792, -1970671594871618215520, ... ; Common denominator:...
\(-(16777216z^2-89344z-1)(-1+53248z)^2\)
| \(\frac{ 349}{ 131072}-\frac{ 85}{ 131072}\sqrt{ 17}\) | \(0\) | \(s_2\) | \(s_1\) | \(\frac{ 1}{ 53248}\) | \(\frac{ 349}{ 131072}+\frac{ 85}{ 131072}\sqrt{ 17}\) | \(\infty\) |
|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) |
| \(1\) | \(0\) | \(1\) | \(1\) | \(3\) | \(1\) | \(\frac{ 1}{ 2}\) |
| \(2\) | \(0\) | \(2\) | \(2\) | \(4\) | \(2\) | \(\frac{ 1}{ 2}\) |
75
New Number: 4.39 | AESZ: 210 | Superseeker: -444/5 -1501908/5 | Hash: 155d0198a5b26de08a0c2caf680f0786
Degree: 4
\(5^{2} \theta^4+2^{2} 5 x\left(688\theta^4+1352\theta^3+981\theta^2+305\theta+35\right)+2^{4} x^{2}\left(5856\theta^4+7008\theta^3+96\theta^2-1260\theta-265\right)+2^{10} x^{3}\left(176\theta^4+120\theta^3+69\theta^2+30\theta+5\right)+2^{12} x^{4}\left((2\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -28, 4716, -1226800, 389349100, ... --> OEIS Normalized instanton numbers (n0=1): -444/5, 16653/5, -1501908/5, 199965534/5, -6573697776, ... ; Common denominator:...
\((256z^2+544z+1)(5+16z)^2\)
| \(-\frac{ 17}{ 16}-\frac{ 3}{ 4}\sqrt{ 2}\) | \(-\frac{ 5}{ 16}\) | \(-\frac{ 17}{ 16}+\frac{ 3}{ 4}\sqrt{ 2}\) | \(0\) | \(s_1\) | \(s_2\) | \(\infty\) |
|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) |
| \(1\) | \(3\) | \(1\) | \(0\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) |
| \(2\) | \(4\) | \(2\) | \(0\) | \(2\) | \(2\) | \(\frac{ 1}{ 2}\) |
76
New Number: 4.40 | AESZ: 211 | Superseeker: -2400 -2956977632 | Hash: c923c78e33e72a3a2b294bf3f2749298
Degree: 4
\(\theta^4+2^{4} x\left(704\theta^4+928\theta^3+612\theta^2+148\theta+13\right)+2^{12} x^{2}\left(5856\theta^4+4704\theta^3-1632\theta^2-972\theta-121\right)+2^{20} 5 x^{3}\left(2752\theta^4+96\theta^3-60\theta^2+24\theta+7\right)+2^{28} 5^{2} x^{4}\left((2\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -208, 531216, -2168300800, 10900554288400, ... --> OEIS Normalized instanton numbers (n0=1): -2400, 1830480, -2956977632, 7117422755016, -21319886408804640, ... ; Common denominator:...
\((65536z^2+8704z+1)(1+1280z)^2\)
| \(-\frac{ 17}{ 256}-\frac{ 3}{ 64}\sqrt{ 2}\) | \(-\frac{ 1}{ 1280}\) | \(-\frac{ 17}{ 256}+\frac{ 3}{ 64}\sqrt{ 2}\) | \(0\) | \(s_1\) | \(s_2\) | \(\infty\) |
|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) |
| \(1\) | \(3\) | \(1\) | \(0\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) |
| \(2\) | \(4\) | \(2\) | \(0\) | \(2\) | \(2\) | \(\frac{ 1}{ 2}\) |
77
New Number: 4.41 | AESZ: 220 | Superseeker: 128 382592 | Hash: 671a1aa788ead53985e13ad6774d0189
Degree: 4
\(\theta^4-2^{4} x\left(20\theta^4+56\theta^3+38\theta^2+10\theta+1\right)-2^{10} x^{2}\left(84\theta^4+240\theta^3+261\theta^2+134\theta+25\right)-2^{16} x^{3}(2\theta+1)^2(23\theta^2+55\theta+39)-2^{23} x^{4}(2\theta+1)^2(2\theta+3)^2\)
Maple LaTexCoefficients of the holomorphic solution: 1, 16, 3600, 851200, 257328400, ... --> OEIS Normalized instanton numbers (n0=1): 128, 4084, 382592, 51510860, 8644861312, ... ; Common denominator:...
\(-(512z-1)(64z+1)^3\)
| \(-\frac{ 1}{ 64}\) | \(0\) | \(\frac{ 1}{ 512}\) | \(\infty\) |
|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(\frac{ 1}{ 2}\) | \(0\) | \(1\) | \(\frac{ 1}{ 2}\) |
| \(\frac{ 3}{ 2}\) | \(0\) | \(1\) | \(\frac{ 3}{ 2}\) |
| \(2\) | \(0\) | \(2\) | \(\frac{ 3}{ 2}\) |
78
New Number: 4.42 | AESZ: 222 | Superseeker: 69/5 29081/5 | Hash: aad7a72e711c9c463396d319e0bf7603
Degree: 4
\(5^{2} \theta^4-5 x\left(407\theta^4+1198\theta^3+909\theta^2+310\theta+40\right)-2^{7} x^{2}\left(2103\theta^4+6999\theta^3+8358\theta^2+4050\theta+680\right)-2^{12} x^{3}\left(1387\theta^4+3840\theta^3+3081\theta^2+960\theta+100\right)-2^{21} x^{4}\left((2\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 8, 504, 36800, 3518200, ... --> OEIS Normalized instanton numbers (n0=1): 69/5, 1383/4, 29081/5, 346080, 72023607/5, ... ; Common denominator:...
\(-(8192z^2+107z-1)(5+64z)^2\)
| \(-\frac{ 5}{ 64}\) | \(-\frac{ 107}{ 16384}-\frac{ 51}{ 16384}\sqrt{ 17}\) | \(0\) | \(s_1\) | \(s_2\) | \(-\frac{ 107}{ 16384}+\frac{ 51}{ 16384}\sqrt{ 17}\) | \(\infty\) |
|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) |
| \(3\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) |
| \(4\) | \(2\) | \(0\) | \(2\) | \(2\) | \(2\) | \(\frac{ 1}{ 2}\) |
79
New Number: 4.43 | AESZ: 225 | Superseeker: 93984 25265152551072 | Hash: 5993002ccf811247be9232b089dd8e3a
Degree: 4
\(\theta^4+2^{4} x\left(22192\theta^4-17056\theta^3-9576\theta^2-1048\theta-49\right)+2^{20} x^{2}\left(33648\theta^4-44688\theta^3+16224\theta^2+1764\theta+17\right)+2^{34} 5 x^{3}\left(6512\theta^4-6144\theta^3-4440\theta^2-1536\theta-193\right)-2^{55} 5^{2} x^{4}\left((2\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 784, 3226896, 20413907200, 157477179235600, ... --> OEIS Normalized instanton numbers (n0=1): 93984, -1084521600, 25265152551072, -787700706860008320, 28889437619654310485088, ... ; Common denominator:...
\(-(536870912z^2-27392z-1)(1+163840z)^2\)
| ≈\(-2.5e-05\) | \(-\frac{ 1}{ 163840}\) | \(0\) | \(s_2\) | \(s_1\) | ≈\(7.6e-05\) | \(\infty\) |
|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) |
| \(1\) | \(3\) | \(0\) | \(1\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) |
| \(2\) | \(4\) | \(0\) | \(2\) | \(2\) | \(2\) | \(\frac{ 1}{ 2}\) |
80
New Number: 4.44 | AESZ: 232 | Superseeker: 379/5 1364199/5 | Hash: 8d5ff690c87757ed51a092dee764eede
Degree: 4
\(5^{2} \theta^4-5 x\left(2617\theta^4+4658\theta^3+3379\theta^2+1050\theta+120\right)+2^{6} 3 x^{2}\left(673\theta^4-4871\theta^3-10282\theta^2-5410\theta-860\right)+2^{10} 3^{2} x^{3}\left(955\theta^4+4320\theta^3+3477\theta^2+1020\theta+100\right)-2^{17} 3^{3} x^{4}(3\theta+1)(2\theta+1)^2(3\theta+2)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 24, 3960, 974400, 292030200, ... --> OEIS Normalized instanton numbers (n0=1): 379/5, 3346, 1364199/5, 177727432/5, 5658116533, ... ; Common denominator:...
\(-(27z+1)(512z-1)(-5+96z)^2\)
| \(-\frac{ 1}{ 27}\) | \(0\) | \(\frac{ 1}{ 512}\) | \(\frac{ 5}{ 96}\) | \(\infty\) |
|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 3}\) |
| \(1\) | \(0\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) |
| \(1\) | \(0\) | \(1\) | \(3\) | \(\frac{ 1}{ 2}\) |
| \(2\) | \(0\) | \(2\) | \(4\) | \(\frac{ 2}{ 3}\) |
81
New Number: 4.45 | AESZ: 233 | Superseeker: 80 104976 | Hash: 03f67459f6d678669f766c99281b1e79
Degree: 4
\(\theta^4-2^{4} x\left(83\theta^4+94\theta^3+71\theta^2+24\theta+3\right)+2^{11} 3 x^{2}\left(101\theta^4+191\theta^3+174\theta^2+71\theta+10\right)-2^{16} 3^{2} x^{3}\left(203\theta^4+432\theta^3+333\theta^2+102\theta+11\right)+2^{23} 3^{3} x^{4}(3\theta+1)(2\theta+1)^2(3\theta+2)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 48, 9360, 2553600, 813027600, ... --> OEIS Normalized instanton numbers (n0=1): 80, 2794, 104976, 5367454, 508265072, ... ; Common denominator:...
\((512z-1)(432z-1)(-1+192z)^2\)
| \(0\) | \(\frac{ 1}{ 512}\) | \(\frac{ 1}{ 432}\) | \(\frac{ 1}{ 192}\) | \(\infty\) |
|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 3}\) |
| \(0\) | \(1\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) |
| \(0\) | \(1\) | \(1\) | \(3\) | \(\frac{ 1}{ 2}\) |
| \(0\) | \(2\) | \(2\) | \(4\) | \(\frac{ 2}{ 3}\) |
82
New Number: 4.46 | AESZ: 237 | Superseeker: 208 1218192 | Hash: 52c18dd4477f6548dd3b185e97b94c20
Degree: 4
\(\theta^4-2^{4} x\left(46\theta^4+128\theta^3+91\theta^2+27\theta+3\right)-2^{9} 3 x^{2}\left(74\theta^4-16\theta^3-231\theta^2-127\theta-20\right)+2^{14} 3^{2} x^{3}\left(14\theta^4+216\theta^3+175\theta^2+51\theta+5\right)+2^{19} 3^{3} x^{4}(3\theta+1)(2\theta+1)^2(3\theta+2)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 48, 12240, 4972800, 2489533200, ... --> OEIS Normalized instanton numbers (n0=1): 208, 5874, 1218192, 220754467, 56417503216, ... ; Common denominator:...
\((864z-1)(64z-1)(1+96z)^2\)
| \(-\frac{ 1}{ 96}\) | \(0\) | \(\frac{ 1}{ 864}\) | \(\frac{ 1}{ 64}\) | \(\infty\) |
|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 3}\) |
| \(1\) | \(0\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) |
| \(3\) | \(0\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) |
| \(4\) | \(0\) | \(2\) | \(2\) | \(\frac{ 2}{ 3}\) |
83
New Number: 4.47 | AESZ: 239 | Superseeker: 1584 171534960 | Hash: 8e610c3437d7f38e552038bc55399495
Degree: 4
\(\theta^4+2^{4} 3 x\left(9\theta^4-198\theta^3-131\theta^2-32\theta-3\right)-2^{11} 3^{2} x^{2}\left(486\theta^4+1215\theta^3+81\theta^2-27\theta-5\right)-2^{16} 3^{5} x^{3}\left(891\theta^4+972\theta^3+675\theta^2+216\theta+25\right)-2^{23} 3^{8} x^{4}(3\theta+1)^2(3\theta+2)^2\)
Maple LaTexCoefficients of the holomorphic solution: 1, 144, 147600, 239904000, 479672701200, ... --> OEIS Normalized instanton numbers (n0=1): 1584, -17874, 171534960, 30012731550, 105934107802896, ... ; Common denominator:...
\(-(432z+1)(3456z-1)(1+1728z)^2\)
| \(-\frac{ 1}{ 432}\) | \(-\frac{ 1}{ 1728}\) | \(0\) | \(\frac{ 1}{ 3456}\) | \(\infty\) |
|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 3}\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(\frac{ 1}{ 3}\) |
| \(1\) | \(3\) | \(0\) | \(1\) | \(\frac{ 2}{ 3}\) |
| \(2\) | \(4\) | \(0\) | \(2\) | \(\frac{ 2}{ 3}\) |
84
New Number: 4.48 | AESZ: 241 | Superseeker: 320 19748928 | Hash: b4d16d8dd1eb7839630ecf8e8d242023
Degree: 4
\(\theta^4-2^{4} x\left(152\theta^4+160\theta^3+110\theta^2+30\theta+3\right)+2^{10} 3 x^{2}\left(428\theta^4+176\theta^3-299\theta^2-170\theta-25\right)-2^{17} 3^{2} x^{3}\left(136\theta^4-216\theta^3-180\theta^2-51\theta-5\right)-2^{24} 3^{3} x^{4}(3\theta+1)(2\theta+1)^2(3\theta+2)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 48, 26640, 21907200, 22048765200, ... --> OEIS Normalized instanton numbers (n0=1): 320, 61084, 19748928, 9428973876, 5618509433280, ... ; Common denominator:...
\(-(64z+1)(1728z-1)(-1+384z)^2\)
| \(-\frac{ 1}{ 64}\) | \(0\) | \(\frac{ 1}{ 1728}\) | \(\frac{ 1}{ 384}\) | \(\infty\) |
|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 3}\) |
| \(1\) | \(0\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) |
| \(1\) | \(0\) | \(1\) | \(3\) | \(\frac{ 1}{ 2}\) |
| \(2\) | \(0\) | \(2\) | \(4\) | \(\frac{ 2}{ 3}\) |
85
New Number: 4.49 | AESZ: 254 | Superseeker: -5408 -22147077792 | Hash: 2539c1ff260271c9f7de53e267e2e8cf
Degree: 4
\(\theta^4-2^{4} x\left(2608\theta^4-544\theta^3-200\theta^2+72\theta+15\right)+2^{15} 3 x^{2}\left(6128\theta^4-208\theta^3+2328\theta^2+452\theta+25\right)-2^{24} 3^{2} 5 x^{3}\left(4592\theta^4+3456\theta^3+2632\theta^2+816\theta+95\right)+2^{38} 3^{3} 5^{2} x^{4}(3\theta+1)(2\theta+1)^2(3\theta+2)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 240, 314640, 627244800, 1516001533200, ... --> OEIS Normalized instanton numbers (n0=1): -5408, -8033784, -22147077792, -80392290665536, -341267541912723040, ... ; Common denominator:...
\((6912z-1)(4096z-1)(-1+15360z)^2\)
| \(0\) | \(\frac{ 1}{ 15360}\) | \(\frac{ 1}{ 6912}\) | \(\frac{ 1}{ 4096}\) | \(\infty\) |
|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 3}\) |
| \(0\) | \(1\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) |
| \(0\) | \(3\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) |
| \(0\) | \(4\) | \(2\) | \(2\) | \(\frac{ 2}{ 3}\) |
86
New Number: 4.50 | AESZ: 256 | Superseeker: -128 -800384 | Hash: 05e172cfdecc836685981a2b01b75d1d
Degree: 4
\(\theta^4+2^{5} x\left(24\theta^4+42\theta^3+30\theta^2+9\theta+1\right)+2^{8} x^{2}\left(164\theta^4+104\theta^3-144\theta^2-100\theta-17\right)+2^{14} x^{3}\left(28\theta^4-48\theta^3-44\theta^2-12\theta-1\right)-2^{18} x^{4}\left((2\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -32, 7056, -2393600, 991152400, ... --> OEIS Normalized instanton numbers (n0=1): -128, 6884, -800384, 143245314, -31691939200, ... ; Common denominator:...
\(-(4096z^2-704z-1)(1+32z)^2\)
| \(-\frac{ 1}{ 32}\) | \(\frac{ 11}{ 128}-\frac{ 5}{ 128}\sqrt{ 5}\) | \(0\) | \(s_1\) | \(s_2\) | \(\frac{ 11}{ 128}+\frac{ 5}{ 128}\sqrt{ 5}\) | \(\infty\) |
|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) |
| \(3\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) |
| \(4\) | \(2\) | \(0\) | \(2\) | \(2\) | \(2\) | \(\frac{ 1}{ 2}\) |
87
New Number: 4.51 | AESZ: | Superseeker: 992 63721056 | Hash: 1d45a05c9bcf007b5042b0f7a5672551
Degree: 4
\(\theta^4-2^{4} x\left(112\theta^4+416\theta^3+280\theta^2+72\theta+7\right)-2^{12} x^{2}\left(656\theta^4+896\theta^3-216\theta^2-160\theta-23\right)-2^{23} x^{3}\left(96\theta^4+24\theta^3+12\theta^2+6\theta+1\right)-2^{30} x^{4}\left((2\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 112, 93456, 124614400, 204621667600, ... --> OEIS Normalized instanton numbers (n0=1): 992, 98792, 63721056, 40943244128, 36122052633760, ... ; Common denominator:...
\(-(65536z^2+2816z-1)(1+512z)^2\)
| \(-\frac{ 11}{ 512}-\frac{ 5}{ 512}\sqrt{ 5}\) | \(-\frac{ 1}{ 512}\) | \(0\) | \(s_2\) | \(s_1\) | \(-\frac{ 11}{ 512}+\frac{ 5}{ 512}\sqrt{ 5}\) | \(\infty\) |
|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) |
| \(1\) | \(3\) | \(0\) | \(1\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) |
| \(2\) | \(4\) | \(0\) | \(2\) | \(2\) | \(2\) | \(\frac{ 1}{ 2}\) |
88
New Number: 4.52 | AESZ: 258 | Superseeker: 480 4215904 | Hash: bfb9f01124fd9980817cbf1b50f789c3
Degree: 4
\(\theta^4-2^{4} x\left(16\theta^4+224\theta^3+156\theta^2+44\theta+5\right)-2^{14} x^{2}\left(48\theta^4+48\theta^3-120\theta^2-66\theta-11\right)-2^{22} x^{3}\left(16\theta^4-192\theta^3-156\theta^2-48\theta-5\right)+2^{32} x^{4}\left((2\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 80, 24336, 11398400, 6632189200, ... --> OEIS Normalized instanton numbers (n0=1): 480, -16536, 4215904, -242723592, 151800032928, ... ; Common denominator:...
\((1024z-1)(256z-1)(1+512z)^2\)
| \(-\frac{ 1}{ 512}\) | \(0\) | \(\frac{ 1}{ 1024}\) | \(\frac{ 1}{ 256}\) | \(\infty\) |
|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(1\) | \(0\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) |
| \(3\) | \(0\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) |
| \(4\) | \(0\) | \(2\) | \(2\) | \(\frac{ 1}{ 2}\) |
89
New Number: 4.53 | AESZ: 264 | Superseeker: 37216 464865119712 | Hash: 625990ef22ba977bc3dd247ccc791780
Degree: 4
\(\theta^4+2^{4} x\left(3392\theta^4-9344\theta^3-5764\theta^2-1092\theta-93\right)-2^{17} 3 x^{2}\left(1952\theta^4+15200\theta^3-7758\theta^2-2593\theta-323\right)-2^{26} 3^{2} 7 x^{3}\left(11584\theta^4-6912\theta^3-5364\theta^2-1632\theta-167\right)+2^{42} 3^{3} 7^{2} x^{4}(3\theta+1)(2\theta+1)^2(3\theta+2)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 1488, 11258640, 139962144000, 2191135140810000, ... --> OEIS Normalized instanton numbers (n0=1): 37216, -75619080, 464865119712, -2749454414283384, 24030314100181942560, ... ; Common denominator:...
\((27648z-1)(4096z-1)(1+43008z)^2\)
| \(-\frac{ 1}{ 43008}\) | \(0\) | \(\frac{ 1}{ 27648}\) | \(\frac{ 1}{ 4096}\) | \(\infty\) |
|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 3}\) |
| \(1\) | \(0\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) |
| \(3\) | \(0\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) |
| \(4\) | \(0\) | \(2\) | \(2\) | \(\frac{ 2}{ 3}\) |
90
New Number: 4.54 | AESZ: 265 | Superseeker: 1056 138459552 | Hash: fad89ac60b7ab4118edfed4cf6350d0c
Degree: 4
\(\theta^4+2^{4} 3 x\left(96\theta^4-96\theta^3-60\theta^2-12\theta-1\right)+2^{13} 3 x^{2}\left(288\theta^4-144\theta^3+526\theta^2+206\theta+27\right)+2^{20} 3^{3} x^{3}\left(288\theta^4+864\theta^3+652\theta^2+204\theta+23\right)+2^{30} 3^{5} x^{4}(3\theta+1)(2\theta+1)^2(3\theta+2)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 48, -30960, -11961600, 15342742800, ... --> OEIS Normalized instanton numbers (n0=1): 1056, -360672, 138459552, -50965971720, 20236543243104, ... ; Common denominator:...
\((1769472z^2+1)(1+2304z)^2\)
| \(-\frac{ 1}{ 2304}\) | \(0-\frac{ 1}{ 2304}\sqrt{ 3}I\) | \(0\) | \(s_1\) | \(s_2\) | \(0+\frac{ 1}{ 2304}\sqrt{ 3}I\) | \(\infty\) |
|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 3}\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) |
| \(3\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) |
| \(4\) | \(2\) | \(0\) | \(2\) | \(2\) | \(2\) | \(\frac{ 2}{ 3}\) |