You searched for: Spectrum0=0,1,1,2
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421
New Number: 8.56 | AESZ: | Superseeker: 80 266256 | Hash: b561c9f1501dce5c055c95391a2176d3
Degree: 8
\(\theta^4-2^{4} x\left(34\theta^4+44\theta^3+31\theta^2+9\theta+1\right)+2^{9} x^{2}\left(94\theta^4-14\theta^3-168\theta^2-98\theta-19\right)-2^{12} x^{3}\left(368\theta^4-1104\theta^3-1505\theta^2-549\theta-60\right)+2^{16} x^{4}\left(28\theta^4-2740\theta^3-154\theta^2+928\theta+331\right)+2^{20} x^{5}\left(678\theta^4+1116\theta^3-2997\theta^2-2295\theta-505\right)-2^{26} x^{6}\left(94\theta^4-561\theta^3-508\theta^2-132\theta+6\right)-2^{28} 5 x^{7}\left(92\theta^4+160\theta^3+97\theta^2+17\theta-2\right)-2^{32} 5^{2} x^{8}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 16, 2512, 533248, 138259216, ... --> OEIS Normalized instanton numbers (n0=1): 80, 3554, 266256, 31532007, 4663446128, ... ; Common denominator:...
\(-(16z+1)(4096z^3+4864z^2+432z-1)(1-64z+1280z^2)^2\)
| ≈\(-1.090586\) | ≈\(-0.099171\) | \(-\frac{ 1}{ 16}\) | \(0\) | ≈\(0.002257\) | \(\frac{ 1}{ 40}-\frac{ 1}{ 80}I\) | \(\frac{ 1}{ 40}+\frac{ 1}{ 80}I\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(3\) | \(3\) | \(1\) |
| \(2\) | \(2\) | \(2\) | \(0\) | \(2\) | \(4\) | \(4\) | \(1\) |
422
New Number: 8.57 | AESZ: | Superseeker: -36/5 -380 | Hash: c2a931d298755811a60b7f8e5dd3afbe
Degree: 8
\(5^{2} \theta^4+2^{2} 5 x\left(92\theta^4+208\theta^3+169\theta^2+65\theta+10\right)+2^{6} x^{2}\left(94\theta^4+937\theta^3+1739\theta^2+1175\theta+285\right)-2^{6} x^{3}\left(678\theta^4+1596\theta^3-2277\theta^2-4335\theta-1645\right)-2^{8} x^{4}\left(28\theta^4+2852\theta^3+8234\theta^2+7096\theta+2017\right)+2^{10} x^{5}\left(368\theta^4+2576\theta^3+4015\theta^2+2323\theta+456\right)-2^{13} x^{6}\left(94\theta^4+390\theta^3+438\theta^2+180\theta+19\right)+2^{14} x^{7}\left(34\theta^4+92\theta^3+103\theta^2+57\theta+13\right)-2^{16} x^{8}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -8, 172, -5696, 231916, ... --> OEIS Normalized instanton numbers (n0=1): -36/5, 132/5, -380, 112043/20, -560656/5, ... ; Common denominator:...
\(-(4z+1)(64z^3-432z^2-76z-1)(5-16z+16z^2)^2\)
| \(-\frac{ 1}{ 4}\) | ≈\(-0.157556\) | ≈\(-0.014327\) | \(0\) | \(\frac{ 1}{ 2}-\frac{ 1}{ 4}I\) | \(\frac{ 1}{ 2}+\frac{ 1}{ 4}I\) | ≈\(6.921883\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(0\) | \(3\) | \(3\) | \(1\) | \(1\) |
| \(2\) | \(2\) | \(2\) | \(0\) | \(4\) | \(4\) | \(2\) | \(1\) |
423
New Number: 8.58 | AESZ: | Superseeker: 286 12179050/3 | Hash: 870f2e78b48eb5ee8f5de2f6a438f2b8
Degree: 8
\(\theta^4-x\left(1114\theta^4+2444\theta^3+1704\theta^2+482\theta+51\right)-x^{2}\left(85922\theta^4+94748\theta^3-21782\theta^2-21164\theta-3273\right)-3^{2} x^{3}\left(173242\theta^4+41004\theta^3+55912\theta^2+32322\theta+5679\right)+3^{2} x^{4}\left(189512\theta^4-918380\theta^3-841954\theta^2-306732\theta-47331\right)+3^{4} x^{5}\left(30338\theta^4+90716\theta^3-87560\theta^2-90566\theta-23193\right)-3^{4} x^{6}\left(19406\theta^4-68364\theta^3-62162\theta^2-14148\theta+1989\right)-3^{6} 5 x^{7}\left(278\theta^4+340\theta^3+8\theta^2-162\theta-63\right)-3^{8} 5^{2} x^{8}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 51, 18267, 10280301, 7092708939, ... --> OEIS Normalized instanton numbers (n0=1): 286, 38919/2, 12179050/3, 2393489451/2, 439227114444, ... ; Common denominator:...
\(-(z+1)(81z^3+549z^2+1187z-1)(-1-36z+45z^2)^2\)
| ≈\(-3.38931-1.781181I\) | ≈\(-3.38931+1.781181I\) | \(-1\) | \(\frac{ 2}{ 5}-\frac{ 1}{ 15}\sqrt{ 41}\) | \(0\) | ≈\(0.000842\) | \(\frac{ 2}{ 5}+\frac{ 1}{ 15}\sqrt{ 41}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(3\) | \(0\) | \(1\) | \(3\) | \(1\) |
| \(2\) | \(2\) | \(2\) | \(4\) | \(0\) | \(2\) | \(4\) | \(1\) |
424
New Number: 8.59 | AESZ: | Superseeker: -26/5 -234/5 | Hash: 53885e46a1519d98ee4697de1c109214
Degree: 8
\(5^{2} \theta^4+5 x\left(278\theta^4+772\theta^3+656\theta^2+270\theta+45\right)+x^{2}\left(19406\theta^4+145988\theta^3+259366\theta^2+172540\theta+41745\right)-3^{2} x^{3}\left(30338\theta^4+30636\theta^3-177680\theta^2-235350\theta-80565\right)-3^{2} x^{4}\left(189512\theta^4+1676428\theta^3+3050258\theta^2+2136012\theta+525339\right)+3^{4} x^{5}\left(173242\theta^4+651964\theta^3+972352\theta^2+649458\theta+161507\right)+3^{4} x^{6}\left(85922\theta^4+248940\theta^3+209506\theta^2+37044\theta-12717\right)+3^{6} x^{7}\left(1114\theta^4+2012\theta^3+1056\theta^2+50\theta-57\right)-3^{8} x^{8}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -9, 123, -1719, 17739, ... --> OEIS Normalized instanton numbers (n0=1): -26/5, -177/10, -234/5, -1837/2, -27716/5, ... ; Common denominator:...
\(-(9z+1)(9z^3-1187z^2-61z-1)(-5+36z+9z^2)^2\)
| \(-2-\frac{ 1}{ 3}\sqrt{ 41}\) | \(-\frac{ 1}{ 9}\) | ≈\(-0.025688-0.0135I\) | ≈\(-0.025688+0.0135I\) | \(0\) | \(-2+\frac{ 1}{ 3}\sqrt{ 41}\) | ≈\(131.940265\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) |
| \(3\) | \(1\) | \(1\) | \(1\) | \(0\) | \(3\) | \(1\) | \(1\) |
| \(4\) | \(2\) | \(2\) | \(2\) | \(0\) | \(4\) | \(2\) | \(1\) |
425
New Number: 8.5 | AESZ: 173 | Superseeker: 11 -2434/3 | Hash: afa82ed9ee239bb5fcac960f8884db01
Degree: 8
\(\theta^4-x(7\theta^2+7\theta+2)(17\theta^2+17\theta+6)+2^{6} x^{2}\left(55\theta^4+112\theta^3+155\theta^2+86\theta+15\right)-2^{6} 3^{2} x^{3}\left(119\theta^4-714\theta^3-2185\theta^2-1656\theta-444\right)+2^{12} 3^{2} x^{4}\left(92\theta^4+184\theta^3+98\theta^2+6\theta+9\right)+2^{12} 3^{4} x^{5}\left(119\theta^4+1190\theta^3+671\theta^2-96\theta-140\right)+2^{18} 3^{4} x^{6}\left(55\theta^4+108\theta^3+149\theta^2+108\theta+27\right)+2^{18} 3^{6} x^{7}(7\theta^2+7\theta+2)(17\theta^2+17\theta+6)+2^{24} 3^{8} x^{8}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 12, 420, 17472, 828324, ... --> OEIS Normalized instanton numbers (n0=1): 11, 229/4, -2434/3, 7512, 54801, ... ; Common denominator:...
\((72z-1)(8z+1)(64z-1)(9z+1)(1+576z^2)^2\)
| \(-\frac{ 1}{ 8}\) | \(-\frac{ 1}{ 9}\) | \(0-\frac{ 1}{ 24}I\) | \(0\) | \(0+\frac{ 1}{ 24}I\) | \(\frac{ 1}{ 72}\) | \(\frac{ 1}{ 64}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(1\) | \(1\) | \(3\) | \(0\) | \(3\) | \(1\) | \(1\) | \(1\) |
| \(2\) | \(2\) | \(4\) | \(0\) | \(4\) | \(2\) | \(2\) | \(1\) |
426
New Number: 8.60 | AESZ: | Superseeker: 247 3584909 | Hash: 540ab51629d98ae18b7d061824bd258b
Degree: 8
\(\theta^4-x\left(1182\theta^4+2172\theta^3+1519\theta^2+433\theta+46\right)+x^{2}\left(70937\theta^4+62468\theta^3-34151\theta^2-26294\theta-4528\right)-2^{3} x^{3}\left(140935\theta^4-41718\theta^3-83276\theta^2-29367\theta-3376\right)+2^{4} 3 x^{4}\left(21007\theta^4-134418\theta^3-100578\theta^2-26137\theta-1974\right)+2^{6} x^{5}\left(29420\theta^4+79292\theta^3-91933\theta^2-88917\theta-22012\right)-2^{6} x^{6}\left(17519\theta^4-73056\theta^3-66923\theta^2-16512\theta+1436\right)-2^{9} 5 x^{7}\left(351\theta^4+510\theta^3+176\theta^2-79\theta-46\right)-2^{12} 5^{2} x^{8}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 46, 15670, 8332840, 5425831846, ... --> OEIS Normalized instanton numbers (n0=1): 247, 38017/2, 3584909, 2039721503/2, 359173241174, ... ; Common denominator:...
\(-(z+1)(64z^3+600z^2+1119z-1)(1-32z+40z^2)^2\)
| ≈\(-6.805514\) | ≈\(-2.570379\) | \(-1\) | \(0\) | ≈\(0.000893\) | \(\frac{ 2}{ 5}-\frac{ 3}{ 20}\sqrt{ 6}\) | \(\frac{ 2}{ 5}+\frac{ 3}{ 20}\sqrt{ 6}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(3\) | \(3\) | \(1\) |
| \(2\) | \(2\) | \(2\) | \(0\) | \(2\) | \(4\) | \(4\) | \(1\) |
427
New Number: 8.61 | AESZ: | Superseeker: -32/5 -863/5 | Hash: 9699709447380eb1373469a1cf5a9586
Degree: 8
\(5^{2} \theta^4+5 x\left(351\theta^4+894\theta^3+752\theta^2+305\theta+50\right)+x^{2}\left(17519\theta^4+143132\theta^3+257359\theta^2+171910\theta+41600\right)-2^{3} x^{3}\left(29420\theta^4+38388\theta^3-153289\theta^2-215145\theta-74900\right)-2^{4} 3 x^{4}\left(21007\theta^4+218446\theta^3+428718\theta^2+312263\theta+79010\right)+2^{6} x^{5}\left(140935\theta^4+605458\theta^3+887488\theta^2+551709\theta+125368\right)-2^{6} x^{6}\left(70937\theta^4+221280\theta^3+204067\theta^2+54336\theta-3916\right)+2^{9} x^{7}\left(1182\theta^4+2556\theta^3+2095\theta^2+817\theta+142\right)-2^{12} x^{8}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -10, 190, -4888, 151246, ... --> OEIS Normalized instanton numbers (n0=1): -32/5, -33/10, -863/5, 715/2, -83882/5, ... ; Common denominator:...
\(-(8z+1)(8z^3-1119z^2-75z-1)(5-32z+8z^2)^2\)
| \(-\frac{ 1}{ 8}\) | ≈\(-0.048631\) | ≈\(-0.018367\) | \(0\) | \(2-\frac{ 3}{ 4}\sqrt{ 6}\) | \(2+\frac{ 3}{ 4}\sqrt{ 6}\) | ≈\(139.941998\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(0\) | \(3\) | \(3\) | \(1\) | \(1\) |
| \(2\) | \(2\) | \(2\) | \(0\) | \(4\) | \(4\) | \(2\) | \(1\) |
428
New Number: 8.62 | AESZ: | Superseeker: 127 1566863/3 | Hash: 4165325308c2b65daacebc1d19717e13
Degree: 8
\(\theta^4+x\left(578\theta^4-572\theta^3-359\theta^2-73\theta-6\right)+3^{2} x^{2}\left(4673\theta^4+1892\theta^3+31601\theta^2+11514\theta+1728\right)-2^{3} 3^{4} x^{3}\left(9185\theta^4-134298\theta^3-35420\theta^2-22329\theta-5544\right)+2^{4} 3^{8} x^{4}\left(19051\theta^4+11846\theta^3+114678\theta^2+65939\theta+14290\right)-2^{6} 3^{12} x^{5}\left(7540\theta^4+8068\theta^3-6459\theta^2-7907\theta-2300\right)-2^{6} 3^{16} x^{6}\left(3919\theta^4+27744\theta^3+29957\theta^2+14208\theta+2556\right)+2^{9} 3^{20} 5 x^{7}\left(199\theta^4+590\theta^3+744\theta^2+449\theta+106\right)-2^{12} 3^{24} 5^{2} x^{8}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 6, -810, -47784, 3354534, ... --> OEIS Normalized instanton numbers (n0=1): 127, -14353/2, 1566863/3, -106847355/2, 6507370854, ... ; Common denominator:...
\(-(81z+1)(419904z^3-22680z^2+79z-1)(-1-288z+29160z^2)^2\)
| \(-\frac{ 1}{ 81}\) | \(\frac{ 2}{ 405}-\frac{ 1}{ 1620}\sqrt{ 154}\) | \(0\) | ≈\(0.001382-0.006675I\) | ≈\(0.001382+0.006675I\) | \(\frac{ 2}{ 405}+\frac{ 1}{ 1620}\sqrt{ 154}\) | ≈\(0.051248\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(1\) | \(3\) | \(0\) | \(1\) | \(1\) | \(3\) | \(1\) | \(1\) |
| \(2\) | \(4\) | \(0\) | \(2\) | \(2\) | \(4\) | \(2\) | \(1\) |
429
New Number: 8.63 | AESZ: | Superseeker: 8/5 67 | Hash: 2c5f91dca73abc39f5d6eb00b9c4ea16
Degree: 8
\(5^{2} \theta^4-5 x\left(199\theta^4+206\theta^3+168\theta^2+65\theta+10\right)+x^{2}\left(3919\theta^4-12068\theta^3-29761\theta^2-21850\theta-5520\right)+2^{3} x^{3}\left(7540\theta^4+22092\theta^3+14577\theta^2+945\theta-1380\right)-2^{4} x^{4}\left(19051\theta^4+64358\theta^3+193446\theta^2+204083\theta+70234\right)+2^{6} x^{5}\left(9185\theta^4+171038\theta^3+422584\theta^2+391123\theta+124848\right)-2^{6} 3^{2} x^{6}\left(4673\theta^4+16800\theta^3+53963\theta^2+64704\theta+24596\right)-2^{9} 3^{4} x^{7}\left(578\theta^4+2884\theta^3+4825\theta^2+3383\theta+858\right)-2^{12} 3^{8} x^{8}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 2, 30, 488, 9934, ... --> OEIS Normalized instanton numbers (n0=1): 8/5, 101/10, 67, 6197/10, 32978/5, ... ; Common denominator:...
\(-(8z+1)(648z^3-79z^2+35z-1)(-5+32z+72z^2)^2\)
| \(-\frac{ 2}{ 9}-\frac{ 1}{ 36}\sqrt{ 154}\) | \(-\frac{ 1}{ 8}\) | \(0\) | ≈\(0.030113\) | ≈\(0.0459-0.221678I\) | ≈\(0.0459+0.221678I\) | \(-\frac{ 2}{ 9}+\frac{ 1}{ 36}\sqrt{ 154}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(3\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(3\) | \(1\) |
| \(4\) | \(2\) | \(0\) | \(2\) | \(2\) | \(2\) | \(4\) | \(1\) |
430
New Number: 8.64 | AESZ: | Superseeker: 0 -32768 | Hash: 00b5810e4a2d21fec464e4e87169df86
Degree: 8
\(\theta^4-2^{4} x\left(32\theta^4+16\theta^3+14\theta^2+6\theta+1\right)+2^{10} x^{2}\left(86\theta^4+176\theta^3+184\theta^2+76\theta+13\right)-2^{16} x^{3}\left(61\theta^4+510\theta^3+620\theta^2+327\theta+68\right)-2^{22} x^{4}\left(110\theta^4-260\theta^3-942\theta^2-608\theta-141\right)+2^{26} x^{5}\left(708\theta^4+2160\theta^3-666\theta^2-1230\theta-397\right)+2^{32} x^{6}\left(134\theta^4-1536\theta^3-1488\theta^2-492\theta-29\right)-2^{38} 5 x^{7}\left(73\theta^4+170\theta^3+168\theta^2+83\theta+17\right)-2^{44} 5^{2} x^{8}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 16, 272, -15104, -2814704, ... --> OEIS Normalized instanton numbers (n0=1): 0, -1116, -32768, -2011784, -92274688, ... ; Common denominator:...
\(-(64z-1)(65536z^3+14336z^2-192z+1)(-1+128z+10240z^2)^2\)
| ≈\(-0.23168\) | \(-\frac{ 1}{ 160}-\frac{ 1}{ 320}\sqrt{ 14}\) | \(0\) | \(-\frac{ 1}{ 160}+\frac{ 1}{ 320}\sqrt{ 14}\) | ≈\(0.006465-0.004906I\) | ≈\(0.006465+0.004906I\) | \(\frac{ 1}{ 64}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(1\) | \(3\) | \(0\) | \(3\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(2\) | \(4\) | \(0\) | \(4\) | \(2\) | \(2\) | \(2\) | \(1\) |
431
New Number: 8.65 | AESZ: | Superseeker: -24/5 -1608/5 | Hash: 5e457fa5807a784e24220c973aeceba8
Degree: 8
\(5^{2} \theta^4+2^{2} 5 x\left(73\theta^4+122\theta^3+96\theta^2+35\theta+5\right)-2^{4} x^{2}\left(134\theta^4+2072\theta^3+3924\theta^2+2660\theta+645\right)-2^{6} x^{3}\left(708\theta^4+672\theta^3-2898\theta^2-3750\theta-1285\right)+2^{10} x^{4}\left(110\theta^4+700\theta^3+498\theta^2-56\theta-105\right)+2^{12} x^{5}\left(61\theta^4-266\theta^3-544\theta^2-373\theta-88\right)-2^{14} x^{6}\left(86\theta^4+168\theta^3+172\theta^2+108\theta+31\right)+2^{16} x^{7}\left(32\theta^4+112\theta^3+158\theta^2+102\theta+25\right)-2^{20} x^{8}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -4, 92, -2704, 95596, ... --> OEIS Normalized instanton numbers (n0=1): -24/5, 329/10, -1608/5, 48409/10, -455264/5, ... ; Common denominator:...
\(-(4z-1)(256z^3-192z^2+56z+1)(-5-16z+32z^2)^2\)
| \(\frac{ 1}{ 4}-\frac{ 1}{ 8}\sqrt{ 14}\) | ≈\(-0.016861\) | \(0\) | \(\frac{ 1}{ 4}\) | ≈\(0.38343-0.290965I\) | ≈\(0.38343+0.290965I\) | \(\frac{ 1}{ 4}+\frac{ 1}{ 8}\sqrt{ 14}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(3\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(3\) | \(1\) |
| \(4\) | \(2\) | \(0\) | \(2\) | \(2\) | \(2\) | \(4\) | \(1\) |
432
New Number: 8.66 | AESZ: | Superseeker: 4 12332 | Hash: d941d8e5d41f2e7285be47b4fbc81023
Degree: 8
\(\theta^4-2^{2} x\left(12\theta^4-24\theta^3-23\theta^2-11\theta-2\right)-2^{7} x^{2}\left(32\theta^4+392\theta^3+484\theta^2+223\theta+41\right)+2^{12} x^{3}\left(31\theta^4-30\theta^3-872\theta^2-801\theta-217\right)-2^{16} 3 x^{4}\left(140\theta^4+60\theta^3-1332\theta^2-971\theta-231\right)-2^{20} x^{5}\left(772\theta^4+7960\theta^3+7483\theta^2+1509\theta-266\right)+2^{26} x^{6}\left(46\theta^4+2766\theta^3+2333\theta^2+672\theta+19\right)-2^{30} 5 x^{7}\left(477\theta^4+930\theta^3+697\theta^2+232\theta+28\right)-2^{36} 5^{2} x^{8}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -8, 424, -6272, 859816, ... --> OEIS Normalized instanton numbers (n0=1): 4, 500, 12332, 358180, 15491360, ... ; Common denominator:...
\(-(64z+1)(4096z^3+6144z^2+48z-1)(1-32z+2560z^2)^2\)
| ≈\(-1.492036\) | ≈\(-0.017379\) | \(-\frac{ 1}{ 64}\) | \(0\) | \(\frac{ 1}{ 160}-\frac{ 3}{ 160}I\) | \(\frac{ 1}{ 160}+\frac{ 3}{ 160}I\) | ≈\(0.009415\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(0\) | \(3\) | \(3\) | \(1\) | \(1\) |
| \(2\) | \(2\) | \(2\) | \(0\) | \(4\) | \(4\) | \(2\) | \(1\) |
433
New Number: 8.67 | AESZ: | Superseeker: -49/5 -5776/5 | Hash: 807c6166f3d1991fadc5a93fdf4671e8
Degree: 8
\(5^{2} \theta^4+5 x\left(477\theta^4+978\theta^3+769\theta^2+280\theta+40\right)-2^{2} x^{2}\left(46\theta^4-2582\theta^3-5689\theta^2-4120\theta-1040\right)+2^{2} x^{3}\left(772\theta^4-4872\theta^3-11765\theta^2-7335\theta-1480\right)+2^{4} 3 x^{4}\left(140\theta^4+500\theta^3-672\theta^2-1313\theta-512\right)-2^{6} x^{5}\left(31\theta^4+154\theta^3-596\theta^2-729\theta-227\right)+2^{7} x^{6}\left(32\theta^4-264\theta^3-500\theta^2-303\theta-58\right)+2^{8} x^{7}\left(12\theta^4+72\theta^3+121\theta^2+85\theta+22\right)-2^{12} x^{8}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -8, 244, -11312, 635716, ... --> OEIS Normalized instanton numbers (n0=1): -49/5, 1441/20, -5776/5, 26480, -748058, ... ; Common denominator:...
\(-(z+1)(64z^3-48z^2-96z-1)(5-4z+8z^2)^2\)
| \(-1\) | ≈\(-0.899067\) | ≈\(-0.010472\) | \(0\) | \(\frac{ 1}{ 4}-\frac{ 3}{ 4}I\) | \(\frac{ 1}{ 4}+\frac{ 3}{ 4}I\) | ≈\(1.659539\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(0\) | \(3\) | \(3\) | \(1\) | \(1\) |
| \(2\) | \(2\) | \(2\) | \(0\) | \(4\) | \(4\) | \(2\) | \(1\) |
434
New Number: 8.68 | AESZ: | Superseeker: 6/17 33/17 | Hash: 0c0662f5b46ac6cb0bd298a63cf364c7
Degree: 8
\(17^{2} \theta^4+17 x\theta(165\theta^3-114\theta^2-74\theta-17)-x^{2}\left(20619\theta^4+122880\theta^3+175353\theta^2+126480\theta+36992\right)-2 x^{3}\left(201857\theta^4+853944\theta^3+1437673\theta^2+1174122\theta+375972\right)-2^{2} x^{4}\left(571275\theta^4+2711616\theta^3+5301571\theta^2+4856674\theta+1694372\right)-2^{3} 3 x^{5}(\theta+1)(295815\theta^3+1523993\theta^2+2924668\theta+1983212)-2^{5} x^{6}(\theta+1)(\theta+2)(558823\theta^2+2951265\theta+4136951)-2^{7} 3 37 x^{7}(\theta+3)(\theta+2)(\theta+1)(2797\theta+9878)-2^{9} 3^{2} 7 37^{2} x^{8}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, 8, 24, 288, ... --> OEIS Normalized instanton numbers (n0=1): 6/17, 25/34, 33/17, 157/17, 577/17, ... ; Common denominator:...
\(-(12z-1)(6z+1)(7z^2-z+1)(4z+1)^2(74z+17)^2\)
| \(-\frac{ 1}{ 4}\) | \(-\frac{ 17}{ 74}\) | \(-\frac{ 1}{ 6}\) | \(0\) | \(\frac{ 1}{ 14}-\frac{ 3}{ 14}\sqrt{ 3}I\) | \(\frac{ 1}{ 14}+\frac{ 3}{ 14}\sqrt{ 3}I\) | \(\frac{ 1}{ 12}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(2\) |
| \(\frac{ 1}{ 2}\) | \(3\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(3\) |
| \(1\) | \(4\) | \(2\) | \(0\) | \(2\) | \(2\) | \(2\) | \(4\) |
435
New Number: 8.69 | AESZ: | Superseeker: 4 52 | Hash: e303d10e77a367612be2fb706f37b895
Degree: 8
\(\theta^4-2^{2} x\left(20\theta^4+34\theta^3+29\theta^2+12\theta+2\right)+2^{4} x^{2}\left(125\theta^4+362\theta^3+471\theta^2+284\theta+66\right)-2^{7} x^{3}\left(191\theta^4+606\theta^3+855\theta^2+588\theta+154\right)+2^{10} x^{4}\left(192\theta^4+552\theta^3+562\theta^2+268\theta+49\right)-2^{13} x^{5}\left(134\theta^4+380\theta^3+373\theta^2+124\theta+3\right)+2^{16} x^{6}\left(61\theta^4+150\theta^3+173\theta^2+93\theta+19\right)-2^{19} x^{7}\left(19\theta^4+50\theta^3+56\theta^2+31\theta+7\right)+2^{23} x^{8}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 8, 128, 2816, 74896, ... --> OEIS Normalized instanton numbers (n0=1): 4, 15/2, 52, 1563/2, 7276, ... ; Common denominator:...
\((16z-1)(8z-1)(64z^2-48z+1)(1-4z+32z^2)^2\)
| \(0\) | \(\frac{ 3}{ 8}-\frac{ 1}{ 4}\sqrt{ 2}\) | \(\frac{ 1}{ 16}-\frac{ 1}{ 16}\sqrt{ 7}I\) | \(\frac{ 1}{ 16}\) | \(\frac{ 1}{ 16}+\frac{ 1}{ 16}\sqrt{ 7}I\) | \(\frac{ 1}{ 8}\) | \(\frac{ 3}{ 8}+\frac{ 1}{ 4}\sqrt{ 2}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(0\) | \(1\) | \(3\) | \(1\) | \(3\) | \(1\) | \(1\) | \(1\) |
| \(0\) | \(2\) | \(4\) | \(2\) | \(4\) | \(2\) | \(2\) | \(1\) |
436
New Number: 8.6 | AESZ: 113 | Superseeker: 11 1200 | Hash: 3754b3cce7930e99efa8acb802e524bb
Degree: 8
\(\theta^4-x(10\theta^2+10\theta+3)(11\theta^2+11\theta+3)+x^{2}\left(1025\theta^4+3992\theta^3+5533\theta^2+3082\theta+615\right)-3^{2} x^{3}\left(110\theta^4-660\theta^3-2027\theta^2-1509\theta-369\right)+3^{2} x^{4}\left(2032\theta^4+4064\theta^3-2726\theta^2-4758\theta-1431\right)+3^{4} x^{5}\left(110\theta^4+1100\theta^3+613\theta^2-125\theta-117\right)+3^{4} x^{6}\left(1025\theta^4+108\theta^3-293\theta^2+108\theta+99\right)+3^{6} x^{7}(10\theta^2+10\theta+3)(11\theta^2+11\theta+3)+3^{8} x^{8}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 9, 285, 13671, 799389, ... --> OEIS Normalized instanton numbers (n0=1): 11, 66, 1200, 28201, 802124, ... ; Common denominator:...
\((81z^2+99z-1)(z^2+11z-1)(1+9z^2)^2\)
| \(-\frac{ 11}{ 2}-\frac{ 5}{ 2}\sqrt{ 5}\) | \(-\frac{ 11}{ 18}-\frac{ 5}{ 18}\sqrt{ 5}\) | \(0-\frac{ 1}{ 3}I\) | \(0\) | \(0+\frac{ 1}{ 3}I\) | \(-\frac{ 11}{ 18}+\frac{ 5}{ 18}\sqrt{ 5}\) | \(-\frac{ 11}{ 2}+\frac{ 5}{ 2}\sqrt{ 5}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(1\) | \(1\) | \(3\) | \(0\) | \(3\) | \(1\) | \(1\) | \(1\) |
| \(2\) | \(2\) | \(4\) | \(0\) | \(4\) | \(2\) | \(2\) | \(1\) |
437
New Number: 8.70 | AESZ: | Superseeker: 32 8608 | Hash: 664bcad4360eb63fde0fdd3018aed2f2
Degree: 8
\(\theta^4-2^{4} x\left(19\theta^4+26\theta^3+20\theta^2+7\theta+1\right)+2^{9} x^{2}\left(61\theta^4+94\theta^3+89\theta^2+47\theta+10\right)-2^{14} x^{3}\left(134\theta^4+156\theta^3+37\theta^2+18\theta+6\right)+2^{19} x^{4}\left(192\theta^4+216\theta^3+58\theta^2-32\theta-17\right)-2^{24} x^{5}\left(191\theta^4+158\theta^3+183\theta^2+68\theta+6\right)+2^{29} x^{6}\left(125\theta^4+138\theta^3+135\theta^2+72\theta+16\right)-2^{35} x^{7}\left(20\theta^4+46\theta^3+47\theta^2+24\theta+5\right)+2^{41} x^{8}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 16, 848, 72448, 7745296, ... --> OEIS Normalized instanton numbers (n0=1): 32, 504, 8608, 475061, 28268384, ... ; Common denominator:...
\((16z-1)(32z-1)(1024z^2-192z+1)(1-32z+2048z^2)^2\)
| \(0\) | \(\frac{ 3}{ 32}-\frac{ 1}{ 16}\sqrt{ 2}\) | \(\frac{ 1}{ 128}-\frac{ 1}{ 128}\sqrt{ 7}I\) | \(\frac{ 1}{ 128}+\frac{ 1}{ 128}\sqrt{ 7}I\) | \(\frac{ 1}{ 32}\) | \(\frac{ 1}{ 16}\) | \(\frac{ 3}{ 32}+\frac{ 1}{ 16}\sqrt{ 2}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(0\) | \(1\) | \(3\) | \(3\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(0\) | \(2\) | \(4\) | \(4\) | \(2\) | \(2\) | \(2\) | \(1\) |
438
New Number: 8.71 | AESZ: | Superseeker: -15 14044/3 | Hash: de469dbb89801caa07ec523e3b0e4772
Degree: 8
\(\theta^4+3 x\left(111\theta^4+186\theta^3+169\theta^2+76\theta+14\right)+2 3^{2} x^{2}\left(2529\theta^4+6930\theta^3+9483\theta^2+6096\theta+1508\right)+2^{2} 3^{4} x^{3}\left(11367\theta^4+32886\theta^3+47658\theta^2+36099\theta+10084\right)+2^{3} 3^{6} x^{4}\left(37017\theta^4+100278\theta^3+103626\theta^2+56025\theta+11582\right)+2^{4} 3^{9} x^{5}\left(29160\theta^4+80676\theta^3+84897\theta^2+27261\theta-568\right)+2^{5} 3^{12} x^{6}\left(16200\theta^4+40824\theta^3+53991\theta^2+31131\theta+6578\right)+2^{7} 3^{17} x^{7}\left(360\theta^4+936\theta^3+1056\theta^2+585\theta+131\right)+2^{9} 3^{20} x^{8}(\theta+1)^2(6\theta+5)(6\theta+7)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -42, 2682, -200436, 16310250, ... --> OEIS Normalized instanton numbers (n0=1): -15, 39, 14044/3, 213069/2, 462576, ... ; Common denominator:...
\((27z+1)(54z+1)(108z+1)^2(1944z^2+18z+1)^2\)
| \(-\frac{ 1}{ 27}\) | \(-\frac{ 1}{ 54}\) | \(-\frac{ 1}{ 108}\) | \(-\frac{ 1}{ 216}-\frac{ 1}{ 216}\sqrt{ 23}I\) | \(-\frac{ 1}{ 216}+\frac{ 1}{ 216}\sqrt{ 23}I\) | \(0\) | \(\infty\) |
|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 5}{ 6}\) |
| \(1\) | \(1\) | \(\frac{ 1}{ 6}\) | \(1\) | \(1\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(\frac{ 5}{ 6}\) | \(3\) | \(3\) | \(0\) | \(1\) |
| \(2\) | \(2\) | \(1\) | \(4\) | \(4\) | \(0\) | \(\frac{ 7}{ 6}\) |
439
New Number: 8.72 | AESZ: | Superseeker: 32/3 14279/9 | Hash: d1b06e21c273cae807016268cd540d98
Degree: 8
\(3^{2} \theta^4-2 3 x\theta(85\theta^3+176\theta^2+112\theta+24)-2^{2} x^{2}\left(6581\theta^4+25808\theta^3+38672\theta^2+26184\theta+6912\right)-x^{3}\left(433513\theta^4+2497158\theta^3+5333997\theta^2+4967532\theta+1724868\right)-2 x^{4}\left(1751393\theta^4+13178758\theta^3+35803021\theta^2+40983788\theta+16698948\right)-2^{2} x^{5}(\theta+1)(3719315\theta^3+30248511\theta^2+79801768\theta+66666732)-2^{3} 3^{3} x^{6}(\theta+1)(\theta+2)(144041\theta^2+1060683\theta+1963346)-2^{7} 3^{4} x^{7}(\theta+3)(\theta+2)(\theta+1)(2449\theta+10862)-2^{9} 3^{3} 7 71 x^{8}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, 192, 7524, 438912, ... --> OEIS Normalized instanton numbers (n0=1): 32/3, 284/3, 14279/9, 118940/3, 1226784, ... ; Common denominator:...
\(-(7z+1)(6z+1)(639z^2+87z-1)(2z+3)^2(8z+1)^2\)
| \(-\frac{ 3}{ 2}\) | \(-\frac{ 1}{ 6}\) | \(-\frac{ 29}{ 426}-\frac{ 5}{ 142}\sqrt{ 5}\) | \(-\frac{ 1}{ 7}\) | \(-\frac{ 1}{ 8}\) | \(0\) | \(-\frac{ 29}{ 426}+\frac{ 5}{ 142}\sqrt{ 5}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(0\) | \(1\) | \(2\) |
| \(3\) | \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(3\) |
| \(4\) | \(2\) | \(2\) | \(2\) | \(1\) | \(0\) | \(2\) | \(4\) |
440
New Number: 8.73 | AESZ: | Superseeker: 161/13 26946/13 | Hash: 13db5d8c98a3d4f31589970217896191
Degree: 8
\(13^{2} \theta^4-13 x\theta(614\theta^3+1804\theta^2+1149\theta+247)-x^{2}\left(775399\theta^4+2692636\theta^3+3693483\theta^2+2450110\theta+648960\right)-2^{2} x^{3}\left(5408420\theta^4+24616488\theta^3+45163287\theta^2+38795913\theta+12838410\right)-2^{5} x^{4}\left(9763642\theta^4+55386224\theta^3+123097843\theta^2+124066416\theta+46600563\right)-2^{9} 3 x^{5}(\theta+1)(1717504\theta^3+9940776\theta^2+20063523\theta+13933966)-2^{13} 3^{2} x^{6}(\theta+1)(\theta+2)(178975\theta^2+874119\theta+1112486)-2^{19} 3^{4} x^{7}(\theta+3)(\theta+2)(\theta+1)(857\theta+2533)-2^{23} 3^{6} 7 x^{8}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, 240, 10440, 679104, ... --> OEIS Normalized instanton numbers (n0=1): 161/13, 1406/13, 26946/13, 742982/13, 25168759/13, ... ; Common denominator:...
\(-(-1+96z+896z^2)(9z+1)^2(96z+13)^2(8z+1)^2\)
| \(-\frac{ 13}{ 96}\) | \(-\frac{ 1}{ 8}\) | \(-\frac{ 3}{ 56}-\frac{ 5}{ 112}\sqrt{ 2}\) | \(-\frac{ 1}{ 9}\) | \(0\) | \(-\frac{ 3}{ 56}+\frac{ 5}{ 112}\sqrt{ 2}\) | \(\infty\) |
|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(0\) | \(1\) | \(0\) | \(0\) | \(1\) | \(2\) |
| \(3\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(3\) |
| \(4\) | \(1\) | \(2\) | \(1\) | \(0\) | \(2\) | \(4\) |
441
New Number: 8.74 | AESZ: | Superseeker: 4 436 | Hash: a0fbd8561e58a032d489a1dabee1e026
Degree: 8
\(\theta^4-2^{2} x\theta(22\theta^3+14\theta^2+9\theta+2)+2^{4} x^{2}\left(109\theta^4-74\theta^3-293\theta^2-258\theta-80\right)+2^{8} x^{3}\left(39\theta^4+414\theta^3+674\theta^2+504\theta+144\right)-2^{10} x^{4}\left(405\theta^4+1170\theta^3+1321\theta^2+424\theta-104\right)-2^{14} x^{5}(\theta+1)(12\theta^3+558\theta^2+1495\theta+1255)+2^{16} x^{6}(\theta+1)(\theta+2)(467\theta^2+1593\theta+1540)-2^{20} 5 x^{7}(\theta+3)(\theta+2)(\theta+1)(\theta-40)-2^{22} 5^{2} 7 x^{8}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, 80, 1536, 56592, ... --> OEIS Normalized instanton numbers (n0=1): 4, 71/2, 436, 6728, 127212, ... ; Common denominator:...
\(-(-1+56z)(20z-1)^2(8z-1)^2(8z+1)^3\)
| \(-\frac{ 1}{ 8}\) | \(0\) | \(\frac{ 1}{ 56}\) | \(\frac{ 1}{ 20}\) | \(\frac{ 1}{ 8}\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(0\) | \(0\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(2\) |
| \(-\frac{ 1}{ 4}\) | \(0\) | \(1\) | \(3\) | \(\frac{ 1}{ 2}\) | \(3\) |
| \(\frac{ 1}{ 4}\) | \(0\) | \(2\) | \(4\) | \(1\) | \(4\) |
442
New Number: 8.75 | AESZ: | Superseeker: -100/3 66364 | Hash: 76a0af78cc3434c7a78f3edc406baa61
Degree: 8
\(3^{2} \theta^4+2^{2} 3 x\left(592\theta^4+992\theta^3+913\theta^2+417\theta+78\right)+2^{7} x^{2}\left(17984\theta^4+49280\theta^3+67508\theta^2+43356\theta+10623\right)+2^{15} x^{3}\left(13472\theta^4+38976\theta^3+56498\theta^2+42534\theta+11589\right)+2^{21} x^{4}\left(29248\theta^4+79232\theta^3+81724\theta^2+43620\theta+8603\right)+2^{30} x^{5}\left(5760\theta^4+15936\theta^3+16712\theta^2+5206\theta-123\right)+2^{37} x^{6}\left(3200\theta^4+8064\theta^3+10616\theta^2+6036\theta+1263\right)+2^{47} x^{7}\left(160\theta^4+416\theta^3+466\theta^2+255\theta+56\right)+2^{55} x^{8}(4\theta+3)(\theta+1)^2(4\theta+5)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -104, 16488, -3037568, 605558440, ... --> OEIS Normalized instanton numbers (n0=1): -100/3, 538/3, 66364, 9836374/3, 67135456/3, ... ; Common denominator:...
\((64z+1)(128z+1)(256z+1)^2(32768z^2+128z+3)^2\)
| \(-\frac{ 1}{ 64}\) | \(-\frac{ 1}{ 128}\) | \(-\frac{ 1}{ 256}\) | \(-\frac{ 1}{ 512}-\frac{ 1}{ 512}\sqrt{ 23}I\) | \(-\frac{ 1}{ 512}+\frac{ 1}{ 512}\sqrt{ 23}I\) | \(0\) | \(\infty\) |
|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 3}{ 4}\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(3\) | \(3\) | \(0\) | \(1\) |
| \(2\) | \(2\) | \(1\) | \(4\) | \(4\) | \(0\) | \(\frac{ 5}{ 4}\) |
443
New Number: 8.76 | AESZ: | Superseeker: -204 66054580/3 | Hash: a1b606169a188129e64002b152d24330
Degree: 8
\(\theta^4+2^{2} 3 x\left(444\theta^4+744\theta^3+697\theta^2+325\theta+62\right)+2^{7} 3^{2} x^{2}\left(10116\theta^4+27720\theta^3+38031\theta^2+24393\theta+5891\right)+2^{12} 3^{4} x^{3}\left(45468\theta^4+131544\theta^3+190749\theta^2+142371\theta+37390\right)+2^{17} 3^{6} x^{4}\left(148068\theta^4+401112\theta^3+412641\theta^2+216243\theta+39599\right)+2^{23} 3^{9} x^{5}\left(58320\theta^4+161352\theta^3+168390\theta^2+50175\theta-1409\right)+2^{29} 3^{12} x^{6}\left(16200\theta^4+40824\theta^3+53397\theta^2+29754\theta+6131\right)+2^{35} 3^{17} x^{7}\left(360\theta^4+936\theta^3+1038\theta^2+558\theta+119\right)+2^{43} 3^{20} x^{8}(\theta+1)^2(3\theta+2)(3\theta+4)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -744, 843624, -1099121280, 1536242069160, ... --> OEIS Normalized instanton numbers (n0=1): -204, 6654, 66054580/3, 6573546582, 118182295200, ... ; Common denominator:...
\((432z+1)(864z+1)(1728z+1)^2(497664z^2+288z+1)^2\)
| \(-\frac{ 1}{ 432}\) | \(-\frac{ 1}{ 864}\) | \(-\frac{ 1}{ 1728}\) | \(-\frac{ 1}{ 3456}-\frac{ 1}{ 3456}\sqrt{ 23}I\) | \(-\frac{ 1}{ 3456}+\frac{ 1}{ 3456}\sqrt{ 23}I\) | \(0\) | \(\infty\) |
|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 2}{ 3}\) |
| \(1\) | \(1\) | \(-\frac{ 1}{ 6}\) | \(1\) | \(1\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(3\) | \(3\) | \(0\) | \(1\) |
| \(2\) | \(2\) | \(\frac{ 7}{ 6}\) | \(4\) | \(4\) | \(0\) | \(\frac{ 4}{ 3}\) |
444
New Number: 8.77 | AESZ: | Superseeker: 91/5 25991/5 | Hash: fa37d863a8d0cc4b7a34e7d9b5e3a1a5
Degree: 8
\(5^{2} \theta^4-5 x\left(693\theta^4+1242\theta^3+931\theta^2+310\theta+40\right)-2^{4} x^{2}\left(659\theta^4+9977\theta^3+17174\theta^2+10200\theta+2160\right)-2^{5} x^{3}\left(7235\theta^4-19374\theta^3-34715\theta^2-7290\theta+1560\right)-2^{8} x^{4}\left(14861\theta^4+40168\theta^3-70511\theta^2-88342\theta-26424\right)-2^{10} x^{5}\left(6973\theta^4+29386\theta^3+99859\theta^2+58446\theta+9864\right)-2^{14} x^{6}\left(6951\theta^4-25713\theta^3-34544\theta^2-14472\theta-1680\right)-2^{15} 11 x^{7}\left(2029\theta^4+5030\theta^3+5139\theta^2+2570\theta+520\right)+2^{18} 3 11^{2} x^{8}(\theta+1)^2(3\theta+2)(3\theta+4)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 8, 408, 28160, 2360440, ... --> OEIS Normalized instanton numbers (n0=1): 91/5, 1158/5, 25991/5, 192163, 42855113/5, ... ; Common denominator:...
\((z-1)(8z+1)(864z^2+136z-1)(5-24z+352z^2)^2\)
| \(-\frac{ 17}{ 216}-\frac{ 7}{ 216}\sqrt{ 7}\) | \(-\frac{ 1}{ 8}\) | \(0\) | \(-\frac{ 17}{ 216}+\frac{ 7}{ 216}\sqrt{ 7}\) | \(\frac{ 3}{ 88}-\frac{ 1}{ 88}\sqrt{ 101}I\) | \(\frac{ 3}{ 88}+\frac{ 1}{ 88}\sqrt{ 101}I\) | \(1\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 2}{ 3}\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(3\) | \(3\) | \(1\) | \(1\) |
| \(2\) | \(2\) | \(0\) | \(2\) | \(4\) | \(4\) | \(2\) | \(\frac{ 4}{ 3}\) |
445
New Number: 8.78 | AESZ: | Superseeker: 52 48732 | Hash: 2fb524ad6efb19e0117ae7acbd9f67b9
Degree: 8
\(\theta^4-2^{2} x\left(184\theta^4+224\theta^3+175\theta^2+63\theta+9\right)+2^{4} 3 x^{2}\left(3472\theta^4+9664\theta^3+9864\theta^2+4264\theta+705\right)-2^{8} 3^{2} x^{3}\left(1936\theta^4+27936\theta^3+43336\theta^2+21528\theta+3933\right)-2^{16} 3^{3} x^{4}\left(1384\theta^4+524\theta^3-4555\theta^2-3404\theta-753\right)+2^{19} 3^{4} x^{5}\left(3440\theta^4+13712\theta^3-58\theta^2-3774\theta-1161\right)+2^{22} 3^{5} x^{6}\left(11312\theta^4-9888\theta^3-10808\theta^2-1608\theta+459\right)-2^{26} 3^{7} x^{7}(2\theta+1)(1336\theta^3+2772\theta^2+2234\theta+663)-2^{32} 3^{9} x^{8}(2\theta+1)(4\theta+3)(4\theta+5)(2\theta+3)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 36, 3780, 555120, 95199300, ... --> OEIS Normalized instanton numbers (n0=1): 52, -399, 48732, -992750, 98106208, ... ; Common denominator:...
\(-(256z-1)(110592z^3+6912z^2-288z+1)(-1+96z+13824z^2)^2\)
| ≈\(-0.091906\) | \(-\frac{ 1}{ 288}-\frac{ 1}{ 288}\sqrt{ 7}\) | \(0\) | ≈\(0.00385\) | \(\frac{ 1}{ 256}\) | \(-\frac{ 1}{ 288}+\frac{ 1}{ 288}\sqrt{ 7}\) | ≈\(0.025556\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(\frac{ 3}{ 4}\) |
| \(1\) | \(3\) | \(0\) | \(1\) | \(1\) | \(3\) | \(1\) | \(\frac{ 5}{ 4}\) |
| \(2\) | \(4\) | \(0\) | \(2\) | \(2\) | \(4\) | \(2\) | \(\frac{ 3}{ 2}\) |
446
New Number: 8.79 | AESZ: | Superseeker: 22/5 68 | Hash: 064e5b590dd8b6a4daa1e905fbe693c2
Degree: 8
\(5^{2} \theta^4-2 5 x\left(338\theta^4+412\theta^3+371\theta^2+165\theta+30\right)+2^{2} x^{2}\left(46396\theta^4+103408\theta^3+125291\theta^2+76370\theta+19080\right)-2^{4} 3 x^{3}\left(115508\theta^4+357896\theta^3+524149\theta^2+375205\theta+106530\right)+2^{6} 3^{2} x^{4}\left(173456\theta^4+669024\theta^3+1118292\theta^2+883484\theta+269049\right)-2^{11} 3^{3} x^{5}\left(20272\theta^4+91616\theta^3+168594\theta^2+142006\theta+45053\right)+2^{14} 3^{4} x^{6}\left(5792\theta^4+29504\theta^3+58300\theta^2+51220\theta+16641\right)-2^{21} 3^{5} x^{7}(\theta+1)^2(58\theta^2+208\theta+201)+2^{26} 3^{6} x^{8}(\theta+1)^2(\theta+2)^2\)
Maple LaTexCoefficients of the holomorphic solution: 1, 12, 204, 4368, 112140, ... --> OEIS Normalized instanton numbers (n0=1): 22/5, 8, 68, 3292/5, 38826/5, ... ; Common denominator:...
\((-1+48z)(16z-1)^2(48z-5)^2(12z-1)^3\)
| \(0\) | \(\frac{ 1}{ 48}\) | \(\frac{ 1}{ 16}\) | \(\frac{ 1}{ 12}\) | \(\frac{ 5}{ 48}\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(0\) | \(1\) | \(\frac{ 1}{ 2}\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) |
| \(0\) | \(1\) | \(\frac{ 1}{ 2}\) | \(\frac{ 3}{ 2}\) | \(3\) | \(2\) |
| \(0\) | \(2\) | \(1\) | \(2\) | \(4\) | \(2\) |
447
New Number: 8.7 | AESZ: 106 | Superseeker: 12 356 | Hash: fe1c90929d18b81637eaaa93366409ed
Degree: 8
\(\theta^4-2^{2} x(3\theta^2+3\theta+1)(11\theta^2+11\theta+3)+2^{4} x^{2}\left(241\theta^4+940\theta^3+1303\theta^2+726\theta+145\right)-2^{7} x^{3}\left(33\theta^4-198\theta^3-607\theta^2-456\theta-117\right)+2^{10} x^{4}\left(239\theta^4+478\theta^3-322\theta^2-561\theta-169\right)+2^{12} x^{5}\left(33\theta^4+330\theta^3+185\theta^2-32\theta-37\right)+2^{14} x^{6}\left(241\theta^4+24\theta^3-71\theta^2+24\theta+23\right)+2^{17} x^{7}(3\theta^2+3\theta+1)(11\theta^2+11\theta+3)+2^{20} x^{8}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 12, 380, 16464, 845676, ... --> OEIS Normalized instanton numbers (n0=1): 12, 20, 356, 34561/4, 161840, ... ; Common denominator:...
\((64z^2+88z-1)(16z^2+44z-1)(1+32z^2)^2\)
| \(-\frac{ 11}{ 8}-\frac{ 5}{ 8}\sqrt{ 5}\) | \(-\frac{ 11}{ 16}-\frac{ 5}{ 16}\sqrt{ 5}\) | \(0-\frac{ 1}{ 8}\sqrt{ 2}I\) | \(0\) | \(0+\frac{ 1}{ 8}\sqrt{ 2}I\) | \(-\frac{ 11}{ 16}+\frac{ 5}{ 16}\sqrt{ 5}\) | \(-\frac{ 11}{ 8}+\frac{ 5}{ 8}\sqrt{ 5}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(1\) | \(1\) | \(3\) | \(0\) | \(3\) | \(1\) | \(1\) | \(1\) |
| \(2\) | \(2\) | \(4\) | \(0\) | \(4\) | \(2\) | \(2\) | \(1\) |
448
New Number: 8.80 | AESZ: | Superseeker: -28/3 2764/3 | Hash: 01b1872abfd55652952ae535920a40fe
Degree: 8
\(3^{2} \theta^4+2^{2} 3 x\left(148\theta^4+248\theta^3+223\theta^2+99\theta+18\right)+2^{7} x^{2}\left(1124\theta^4+3080\theta^3+4211\theta^2+2709\theta+675\right)+2^{12} x^{3}\left(1684\theta^4+4872\theta^3+7059\theta^2+5373\theta+1530\right)+2^{17} x^{4}\left(1828\theta^4+4952\theta^3+5125\theta^2+2799\theta+599\right)+2^{23} x^{5}\left(720\theta^4+1992\theta^3+2102\theta^2+691\theta-13\right)+2^{29} x^{6}\left(200\theta^4+504\theta^3+669\theta^2+390\theta+83\right)+2^{35} x^{7}\left(40\theta^4+104\theta^3+118\theta^2+66\theta+15\right)+2^{43} x^{8}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -24, 872, -37248, 1740456, ... --> OEIS Normalized instanton numbers (n0=1): -28/3, 49/3, 2764/3, 13414, 44384, ... ; Common denominator:...
\((16z+1)(32z+1)(64z+1)^2(2048z^2+32z+3)^2\)
| \(-\frac{ 1}{ 16}\) | \(-\frac{ 1}{ 32}\) | \(-\frac{ 1}{ 64}\) | \(-\frac{ 1}{ 128}-\frac{ 1}{ 128}\sqrt{ 23}I\) | \(-\frac{ 1}{ 128}+\frac{ 1}{ 128}\sqrt{ 23}I\) | \(0\) | \(\infty\) |
|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(3\) | \(3\) | \(0\) | \(1\) |
| \(2\) | \(2\) | \(1\) | \(4\) | \(4\) | \(0\) | \(1\) |
449
New Number: 8.81 | AESZ: | Superseeker: -64 54464 | Hash: 3cc4cfea037192a297dc29928555ed1d
Degree: 8
\(\theta^4+2^{4} x\left(40\theta^4+56\theta^3+46\theta^2+18\theta+3\right)+2^{10} x^{2}\left(200\theta^4+296\theta^3+357\theta^2+236\theta+58\right)+2^{16} x^{3}\left(720\theta^4+888\theta^3+446\theta^2+417\theta+126\right)+2^{22} x^{4}\left(1828\theta^4+2360\theta^3+1237\theta^2-93\theta-199\right)+2^{29} x^{5}\left(1684\theta^4+1864\theta^3+2547\theta^2+865\theta+28\right)+2^{36} x^{6}\left(1124\theta^4+1416\theta^3+1715\theta^2+969\theta+221\right)+2^{43} 3 x^{7}\left(148\theta^4+344\theta^3+367\theta^2+195\theta+42\right)+2^{53} 3^{2} x^{8}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -48, 4112, -470784, 65066256, ... --> OEIS Normalized instanton numbers (n0=1): -64, 2380, 54464, -1677212, -279711424, ... ; Common denominator:...
\((128z+1)(256z+1)(64z+1)^2(24576z^2+64z+1)^2\)
| \(-\frac{ 1}{ 64}\) | \(-\frac{ 1}{ 128}\) | \(-\frac{ 1}{ 256}\) | \(-\frac{ 1}{ 768}-\frac{ 1}{ 768}\sqrt{ 23}I\) | \(-\frac{ 1}{ 768}+\frac{ 1}{ 768}\sqrt{ 23}I\) | \(0\) | \(\infty\) |
|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) |
| \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(3\) | \(3\) | \(0\) | \(1\) |
| \(1\) | \(2\) | \(2\) | \(4\) | \(4\) | \(0\) | \(1\) |
450
New Number: 8.82 | AESZ: | Superseeker: 0 -1/3 | Hash: 8bab1ddc8b31cb2c21f01402f27895ce
Degree: 8
\(\theta^4-x\theta(3\theta^3-6\theta^2-4\theta-1)-x^{2}\left(211\theta^4+856\theta^3+1433\theta^2+1184\theta+384\right)+2 x^{3}\left(761\theta^4+3288\theta^3+6477\theta^2+6654\theta+2700\right)+2^{2} x^{4}(\theta+1)(2013\theta^3+17379\theta^2+40726\theta+28548)-2^{3} x^{5}(\theta+1)(15719\theta^3+126105\theta^2+325408\theta+269508)+2^{5} 3^{2} x^{6}(\theta+1)(\theta+2)(1817\theta^2+11967\theta+19631)-2^{7} 3^{4} x^{7}(\theta+3)(\theta+2)(\theta+1)(89\theta+350)+2^{9} 3^{3} 43 x^{8}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, 24, -72, 1296, ... --> OEIS Normalized instanton numbers (n0=1): 0, 1/2, -1/3, -1, -2, ... ; Common denominator:...
\((6z-1)(4z-1)(43z^2-13z+1)(12z+1)^2(-1+2z)^2\)
| \(-\frac{ 1}{ 12}\) | \(0\) | \(\frac{ 13}{ 86}-\frac{ 1}{ 86}\sqrt{ 3}I\) | \(\frac{ 13}{ 86}+\frac{ 1}{ 86}\sqrt{ 3}I\) | \(\frac{ 1}{ 6}\) | \(\frac{ 1}{ 4}\) | \(\frac{ 1}{ 2}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(\frac{ 1}{ 2}\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(2\) |
| \(\frac{ 1}{ 2}\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(3\) | \(3\) |
| \(1\) | \(0\) | \(2\) | \(2\) | \(2\) | \(2\) | \(4\) | \(4\) |