You searched for: Spectrum0=0,1,3,4
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151
New Number: 5.7 | AESZ: 27 | Superseeker: 14/3 910/3 | Hash: 3671a1760894e9030e36de89070612e8
Degree: 5
\(3^{2} \theta^4-3 x\left(173\theta^4+340\theta^3+272\theta^2+102\theta+15\right)-2 x^{2}\left(1129\theta^4+5032\theta^3+7597\theta^2+4773\theta+1083\right)+2 x^{3}\left(843\theta^4+2628\theta^3+2353\theta^2+675\theta+6\right)-x^{4}\left(295\theta^4+608\theta^3+478\theta^2+174\theta+26\right)+x^{5}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 5, 109, 3317, 121501, ... --> OEIS Normalized instanton numbers (n0=1): 14/3, 175/6, 910/3, 14147/3, 265496/3, ... ; Common denominator:...
\((z^3-289z^2-57z+1)(z-3)^2\)
| ≈\(-0.213297\) | \(0\) | ≈\(0.016211\) | \(3\) | ≈\(289.197085\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(1\) | \(0\) | \(1\) | \(3\) | \(1\) | \(1\) |
| \(2\) | \(0\) | \(2\) | \(4\) | \(2\) | \(1\) |
152
New Number: 5.80 | AESZ: 311 | Superseeker: 25/13 875/13 | Hash: 8219f3f4bd56f6c2b2cc3ab9093b65d1
Degree: 5
\(13^{2} \theta^4-13 x\left(327\theta^4+1038\theta^3+857\theta^2+338\theta+52\right)-2^{4} x^{2}\left(12848\theta^4+42008\theta^3+52082\theta^2+28548\theta+5707\right)-2^{11} x^{3}\left(122\theta^4-1872\theta^3-6341\theta^2-5772\theta-1547\right)+2^{16} x^{4}(2\theta+1)(76\theta^3+426\theta^2+570\theta+227)+2^{23} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 4, 84, 1840, 56980, ... --> OEIS Normalized instanton numbers (n0=1): 25/13, 1359/52, 875/13, 36572/13, 256800/13, ... ; Common denominator:...
\((8192z^3-896z^2-35z+1)(13+64z)^2\)
| \(-\frac{ 13}{ 64}\) | ≈\(-0.045147\) | \(0\) | ≈\(0.020117\) | ≈\(0.134405\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) |
| \(3\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) |
| \(4\) | \(2\) | \(0\) | \(2\) | \(2\) | \(\frac{ 3}{ 2}\) |
153
New Number: 5.81 | AESZ: 312 | Superseeker: 5/7 48/7 | Hash: 767262575f8b1458839c1e9a8beacf0a
Degree: 5
\(7^{2} \theta^4-7 x\left(39\theta^4+234\theta^3+201\theta^2+84\theta+14\right)-2 x^{2}\left(12073\theta^4+43222\theta^3+57461\theta^2+34328\theta+7756\right)-2^{2} x^{3}\left(28923\theta^4+48426\theta^3-33393\theta^2-80976\theta-32032\right)+2^{3} 13 x^{4}\left(359\theta^4+9790\theta^3+20805\theta^2+15784\theta+4124\right)+2^{5} 3 13^{2} x^{5}(\theta+1)^2(6\theta+5)(6\theta+7)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 2, 30, 308, 5950, ... --> OEIS Normalized instanton numbers (n0=1): 5/7, 239/28, 48/7, 4451/14, 5888/7, ... ; Common denominator:...
\((16z+1)(2z-1)(27z-1)(7+26z)^2\)
| \(-\frac{ 7}{ 26}\) | \(-\frac{ 1}{ 16}\) | \(0\) | \(\frac{ 1}{ 27}\) | \(\frac{ 1}{ 2}\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 5}{ 6}\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) |
| \(3\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) |
| \(4\) | \(2\) | \(0\) | \(2\) | \(2\) | \(\frac{ 7}{ 6}\) |
154
New Number: 5.82 | AESZ: 313 | Superseeker: 45 43531 | Hash: f8bfe82988e14680bdb775a3ce956216
Degree: 5
\(\theta^4-x(\theta+1)(285\theta^3+321\theta^2+128\theta+18)-2 x^{2}\left(1640\theta^4+1322\theta^3-1337\theta^2-1178\theta-240\right)-2^{2} 3^{2} x^{3}\left(213\theta^4-256\theta^3-286\theta^2-80\theta-5\right)+2^{3} 3^{3} x^{4}(2\theta+1)(22\theta^3+37\theta^2+24\theta+6)+2^{4} 3^{3} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 18, 1662, 236340, 40943070, ... --> OEIS Normalized instanton numbers (n0=1): 45, 845, 43531, 3091112, 273471538, ... ; Common denominator:...
\((z-1)(48z^2+296z-1)(6z+1)^2\)
| \(-\frac{ 37}{ 12}-\frac{ 7}{ 6}\sqrt{ 7}\) | \(-\frac{ 1}{ 6}\) | \(0\) | \(-\frac{ 37}{ 12}+\frac{ 7}{ 6}\sqrt{ 7}\) | \(1\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) |
| \(1\) | \(3\) | \(0\) | \(1\) | \(1\) | \(1\) |
| \(2\) | \(4\) | \(0\) | \(2\) | \(2\) | \(\frac{ 3}{ 2}\) |
155
New Number: 5.83 | AESZ: 316 | Superseeker: 852/11 1678156/11 | Hash: b8201d587a016cc013e2477aadb5c1ff
Degree: 5
\(11^{2} \theta^4-2^{2} 3 11 x\left(364\theta^4+824\theta^3+599\theta^2+187\theta+22\right)-2^{5} x^{2}\left(62164\theta^4+84496\theta^3+12499\theta^2-6402\theta-1584\right)-2^{4} 3 x^{3}\left(484016\theta^4+474144\theta^3+366952\theta^2+161832\theta+27027\right)-2^{11} 3^{2} x^{4}(964\theta^2+1360\theta+669)(2\theta+1)^2-2^{16} 3^{4} x^{5}(2\theta+1)^2(2\theta+3)^2\)
Maple LaTexCoefficients of the holomorphic solution: 1, 24, 3240, 675600, 171901800, ... --> OEIS Normalized instanton numbers (n0=1): 852/11, 21572/11, 1678156/11, 15912512, 22956446184/11, ... ; Common denominator:...
\(-(2304z^3+1664z^2+432z-1)(11+192z)^2\)
| ≈\(-0.362258-0.240689I\) | ≈\(-0.362258+0.240689I\) | \(-\frac{ 11}{ 192}\) | \(0\) | ≈\(0.002294\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(\frac{ 1}{ 2}\) |
| \(1\) | \(1\) | \(3\) | \(0\) | \(1\) | \(\frac{ 3}{ 2}\) |
| \(2\) | \(2\) | \(4\) | \(0\) | \(2\) | \(\frac{ 3}{ 2}\) |
156
New Number: 5.84 | AESZ: 318 | Superseeker: 46/5 1126 | Hash: 3fa38f629ecd5f39b585ce0c1bd88463
Degree: 5
\(5^{2} \theta^4-5 x\left(473\theta^4+892\theta^3+696\theta^2+250\theta+35\right)+2 x^{2}\left(1973\theta^4-4636\theta^3-14417\theta^2-10895\theta-2745\right)+2 3^{2} x^{3}\left(343\theta^4+1920\theta^3+1147\theta^2-345\theta-320\right)-3^{4} x^{4}\left(83\theta^4-104\theta^3-458\theta^2-406\theta-114\right)-3^{8} x^{5}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 7, 219, 9961, 546379, ... --> OEIS Normalized instanton numbers (n0=1): 46/5, 717/10, 1126, 51481/2, 3609772/5, ... ; Common denominator:...
\(-(z+1)(81z^2+92z-1)(-5+9z)^2\)
| \(-\frac{ 46}{ 81}-\frac{ 13}{ 81}\sqrt{ 13}\) | \(-1\) | \(0\) | \(-\frac{ 46}{ 81}+\frac{ 13}{ 81}\sqrt{ 13}\) | \(\frac{ 5}{ 9}\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(3\) | \(1\) |
| \(2\) | \(2\) | \(0\) | \(2\) | \(4\) | \(1\) |
157
New Number: 5.85 | AESZ: 319 | Superseeker: -26 -14942/3 | Hash: 40a034330b9ad40ec865803f0a601932
Degree: 5
\(\theta^4+x\left(83\theta^4+436\theta^3+352\theta^2+134\theta+21\right)-2 3^{2} x^{2}\left(343\theta^4-548\theta^3-2555\theta^2-1749\theta-405\right)-2 3^{4} x^{3}\left(1973\theta^4+12528\theta^3+11329\theta^2+3861\theta+342\right)+3^{8} 5 x^{4}\left(473\theta^4+1000\theta^3+858\theta^2+358\theta+62\right)-3^{12} 5^{2} x^{5}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -21, 891, -48027, 2920779, ... --> OEIS Normalized instanton numbers (n0=1): -26, -475/2, -14942/3, -244479/2, -3574404, ... ; Common denominator:...
\(-(81z+1)(81z^2-92z-1)(-1+45z)^2\)
| \(-\frac{ 1}{ 81}\) | \(\frac{ 46}{ 81}-\frac{ 13}{ 81}\sqrt{ 13}\) | \(0\) | \(\frac{ 1}{ 45}\) | \(\frac{ 46}{ 81}+\frac{ 13}{ 81}\sqrt{ 13}\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) |
| \(1\) | \(1\) | \(0\) | \(3\) | \(1\) | \(1\) |
| \(2\) | \(2\) | \(0\) | \(4\) | \(2\) | \(1\) |
158
New Number: 5.86 | AESZ: 320 | Superseeker: 741/11 138745 | Hash: d19e7569ce62abdd5393977835e411a9
Degree: 5
\(11^{2} \theta^4-11 x\left(4843\theta^4+8918\theta^3+6505\theta^2+2046\theta+242\right)+2^{2} x^{2}\left(312184\theta^4+343456\theta^3-23371\theta^2-73942\theta-14883\right)-2^{4} x^{3}\left(511972\theta^4+256344\theta^3+144969\theta^2+78639\theta+15642\right)+2^{11} x^{4}(2\theta+1)(1964\theta^3+3078\theta^2+1853\theta+419)-2^{18} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 22, 2850, 568300, 138119170, ... --> OEIS Normalized instanton numbers (n0=1): 741/11, 22232/11, 138745, 157326644/11, 19999995398/11, ... ; Common denominator:...
\(-(z-1)(64z^2-416z+1)(-11+128z)^2\)
| \(0\) | \(\frac{ 13}{ 4}-\frac{ 15}{ 8}\sqrt{ 3}\) | \(\frac{ 11}{ 128}\) | \(1\) | \(\frac{ 13}{ 4}+\frac{ 15}{ 8}\sqrt{ 3}\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(0\) | \(1\) | \(3\) | \(1\) | \(1\) | \(1\) |
| \(0\) | \(2\) | \(4\) | \(2\) | \(2\) | \(\frac{ 3}{ 2}\) |
159
New Number: 5.87 | AESZ: 321 | Superseeker: 35/9 3002/9 | Hash: b786027c217dd5d5c5abac7b1ecc570b
Degree: 5
\(3^{4} \theta^4-3^{2} x\left(191\theta^4+862\theta^3+683\theta^2+252\theta+36\right)-2^{5} x^{2}\left(7225\theta^4+24835\theta^3+30634\theta^2+16173\theta+3069\right)-2^{8} x^{3}\left(13251\theta^4+35856\theta^3+27641\theta^2+6966\theta+180\right)-2^{12} 5 x^{4}(2\theta+1)(314\theta^3+363\theta^2+68\theta-31)+2^{16} 5^{2} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 4, 132, 4000, 179620, ... --> OEIS Normalized instanton numbers (n0=1): 35/9, 261/4, 3002/9, 126800/9, 1727129/9, ... ; Common denominator:...
\((32z+1)(32z^2-71z+1)(9+80z)^2\)
| \(-\frac{ 9}{ 80}\) | \(-\frac{ 1}{ 32}\) | \(0\) | \(\frac{ 71}{ 64}-\frac{ 17}{ 64}\sqrt{ 17}\) | \(\frac{ 71}{ 64}+\frac{ 17}{ 64}\sqrt{ 17}\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) |
| \(3\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) |
| \(4\) | \(2\) | \(0\) | \(2\) | \(2\) | \(\frac{ 3}{ 2}\) |
160
New Number: 5.88 | AESZ: 324 | Superseeker: 148/11 44108/11 | Hash: 7f84d776cf00ff399b20865542185f87
Degree: 5
\(11^{2} \theta^4-2^{2} 11 x\left(432\theta^4+624\theta^3+477\theta^2+165\theta+22\right)+2^{5} x^{2}\left(12944\theta^4+4736\theta^3-15491\theta^2-12914\theta-2860\right)-2^{4} 5 x^{3}\left(10688\theta^4-114048\theta^3-159132\theta^2-83028\theta-15455\right)-2^{11} 5^{2} x^{4}(2\theta+1)(4\theta+3)(76\theta^2+189\theta+125)+2^{14} 5^{3} x^{5}(2\theta+1)(4\theta+3)(4\theta+5)(2\theta+3)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 8, 360, 23120, 1796200, ... --> OEIS Normalized instanton numbers (n0=1): 148/11, 2044/11, 44108/11, 1459636/11, 60212712/11, ... ; Common denominator:...
\((5120z^3-512z^2-128z+1)(-11+160z)^2\)
| ≈\(-0.120643\) | \(0\) | ≈\(0.007599\) | \(\frac{ 11}{ 160}\) | ≈\(0.213044\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(\frac{ 3}{ 4}\) |
| \(1\) | \(0\) | \(1\) | \(3\) | \(1\) | \(\frac{ 5}{ 4}\) |
| \(2\) | \(0\) | \(2\) | \(4\) | \(2\) | \(\frac{ 3}{ 2}\) |
161
New Number: 5.89 | AESZ: 329 | Superseeker: 48 25200 | Hash: 8c526b3b825d5ad6a3d0fb83ee4e6059
Degree: 5
\(\theta^4-2^{4} x\left(8\theta^4+34\theta^3+25\theta^2+8\theta+1\right)-2^{8} x^{2}\left(87\theta^4+150\theta^3+32\theta^2-2\theta-1\right)-2^{12} x^{3}\left(202\theta^4+240\theta^3+211\theta^2+102\theta+19\right)-2^{16} 3 x^{4}(2\theta+1)(22\theta^3+45\theta^2+38\theta+12)-2^{20} 3^{2} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 16, 1200, 136960, 19010320, ... --> OEIS Normalized instanton numbers (n0=1): 48, 270, 25200, 968066, 80892688, ... ; Common denominator:...
\(-(16384z^3+3072z^2+224z-1)(1+48z)^2\)
| ≈\(-0.095858-0.072741I\) | ≈\(-0.095858+0.072741I\) | \(-\frac{ 1}{ 48}\) | \(0\) | ≈\(0.004215\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) |
| \(1\) | \(1\) | \(3\) | \(0\) | \(1\) | \(1\) |
| \(2\) | \(2\) | \(4\) | \(0\) | \(2\) | \(\frac{ 3}{ 2}\) |
162
New Number: 5.8 | AESZ: | Superseeker: 84 1522388/3 | Hash: f4b2a154823e983e64682b48f6254a15
Degree: 5
\(\theta^4-2^{2} 3 x\left(192\theta^4+240\theta^3+191\theta^2+71\theta+10\right)+2^{7} 3^{2} x^{2}\left(1746\theta^4+3960\theta^3+4323\theta^2+2247\theta+395\right)-2^{12} 3^{4} x^{3}\left(2538\theta^4+7776\theta^3+9915\theta^2+5643\theta+1030\right)+2^{17} 3^{6} x^{4}\left(1782\theta^4+6480\theta^3+8793\theta^2+4905\theta+875\right)-2^{23} 3^{11} x^{5}(\theta+1)^2(3\theta+1)(3\theta+5)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 120, 34920, 13157760, 5790070440, ... --> OEIS Normalized instanton numbers (n0=1): 84, 9210, 1522388/3, 120348978, 19186016160, ... ; Common denominator:...
\(-(-1+864z)(432z-1)^2(288z-1)^2\)
| \(0\) | \(\frac{ 1}{ 864}\) | \(\frac{ 1}{ 432}\) | \(\frac{ 1}{ 288}\) | \(\infty\) |
|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 3}\) |
| \(0\) | \(1\) | \(\frac{ 1}{ 6}\) | \(1\) | \(1\) |
| \(0\) | \(1\) | \(\frac{ 5}{ 6}\) | \(3\) | \(1\) |
| \(0\) | \(2\) | \(1\) | \(4\) | \(\frac{ 5}{ 3}\) |
163
New Number: 5.90 | AESZ: 330 | Superseeker: 352 3284448 | Hash: ba5b66d5fe92237e6416a117563571e9
Degree: 5
\(\theta^4+2^{4} x\left(112\theta^4-64\theta^3-32\theta^2+1\right)+2^{14} x^{2}\left(56\theta^4-64\theta^3+3\theta^2-10\theta-4\right)+2^{20} x^{3}\left(32\theta^4-384\theta^3-436\theta^2-264\theta-55\right)-2^{29} 3 x^{4}(2\theta+1)(10\theta+7)(2\theta^2+4\theta+3)-2^{38} 3^{2} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -16, 4368, -344320, 107445520, ... --> OEIS Normalized instanton numbers (n0=1): 352, -23368, 3284448, -578330224, 120252731680, ... ; Common denominator:...
\(-(-1+256z)(256z+1)^2(768z+1)^2\)
| \(-\frac{ 1}{ 256}\) | \(-\frac{ 1}{ 768}\) | \(0\) | \(\frac{ 1}{ 256}\) | \(\infty\) |
|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(\frac{ 1}{ 2}\) | \(1\) | \(0\) | \(1\) | \(1\) |
| \(\frac{ 1}{ 2}\) | \(3\) | \(0\) | \(1\) | \(1\) |
| \(1\) | \(4\) | \(0\) | \(2\) | \(\frac{ 3}{ 2}\) |
164
New Number: 5.91 | AESZ: 331 | Superseeker: 112 186800 | Hash: a30093d8c1ab2f66122cef8935b79efb
Degree: 5
\(\theta^4+2^{4} x\left(18\theta^4-48\theta^3-33\theta^2-9\theta-1\right)-2^{9} x^{2}\left(86\theta^4+512\theta^3+125\theta^2+45\theta+10\right)-2^{14} x^{3}\left(1138\theta^4+2040\theta^3+1883\theta^2+879\theta+157\right)-2^{19} 7 x^{4}(2\theta+1)(186\theta^3+375\theta^2+317\theta+100)-2^{27} 7^{2} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 16, 1488, 183040, 27611920, ... --> OEIS Normalized instanton numbers (n0=1): 112, -2242, 186800, -11675813, 1250599376, ... ; Common denominator:...
\(-(32z+1)(256z-1)(64z+1)(1+224z)^2\)
| \(-\frac{ 1}{ 32}\) | \(-\frac{ 1}{ 64}\) | \(-\frac{ 1}{ 224}\) | \(0\) | \(\frac{ 1}{ 256}\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) |
| \(1\) | \(1\) | \(3\) | \(0\) | \(1\) | \(1\) |
| \(2\) | \(2\) | \(4\) | \(0\) | \(2\) | \(\frac{ 3}{ 2}\) |
165
New Number: 5.92 | AESZ: 332 | Superseeker: -16/3 208/3 | Hash: f788b099648b78746af9d38e85874401
Degree: 5
\(3^{2} \theta^4+2^{2} 3 x\left(67\theta^4+122\theta^3+100\theta^2+39\theta+6\right)+2^{5} x^{2}\left(1172\theta^4+4298\theta^3+5831\theta^2+3315\theta+678\right)+2^{8} x^{3}\left(3021\theta^4+15912\theta^3+29314\theta^2+20925\theta+4926\right)+2^{11} x^{4}(2\theta+1)(826\theta^3+3543\theta^2+4321\theta+1594)+2^{16} x^{5}(2\theta+1)(4\theta+3)(4\theta+5)(2\theta+3)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -8, 72, 640, -51800, ... --> OEIS Normalized instanton numbers (n0=1): -16/3, -257/6, 208/3, 10444/3, -116608/3, ... ; Common denominator:...
\((32z+1)(2048z^2+52z+1)(8z+3)^2\)
| \(-\frac{ 3}{ 8}\) | \(-\frac{ 1}{ 32}\) | \(-\frac{ 13}{ 1024}-\frac{ 7}{ 1024}\sqrt{ 7}I\) | \(-\frac{ 13}{ 1024}+\frac{ 7}{ 1024}\sqrt{ 7}I\) | \(0\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(\frac{ 3}{ 4}\) |
| \(3\) | \(1\) | \(1\) | \(1\) | \(0\) | \(\frac{ 5}{ 4}\) |
| \(4\) | \(2\) | \(2\) | \(2\) | \(0\) | \(\frac{ 3}{ 2}\) |
166
New Number: 5.93 | AESZ: 333 | Superseeker: 1 2668/3 | Hash: dc274781605ee4262d8745e3fa3a8057
Degree: 5
\(\theta^4+x\theta^2(71\theta^2-2\theta-1)+2^{3} 3 x^{2}\left(154\theta^4+334\theta^3+461\theta^2+248\theta+48\right)+2^{6} 3^{2} x^{3}(5\theta+3)(31\theta^3+39\theta^2-25\theta-21)+2^{9} 3^{4} x^{4}(2\theta+1)(2\theta^3-33\theta^2-56\theta-24)-2^{12} 3^{6} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, -72, 1440, 22680, ... --> OEIS Normalized instanton numbers (n0=1): 1, -66, 2668/3, -2774, -167786, ... ; Common denominator:...
\(-(9z-1)(2304z^2+32z+1)(1+24z)^2\)
| \(-\frac{ 1}{ 24}\) | \(-\frac{ 1}{ 144}-\frac{ 1}{ 72}\sqrt{ 2}I\) | \(-\frac{ 1}{ 144}+\frac{ 1}{ 72}\sqrt{ 2}I\) | \(0\) | \(\frac{ 1}{ 9}\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) |
| \(3\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) |
| \(4\) | \(2\) | \(2\) | \(0\) | \(2\) | \(\frac{ 3}{ 2}\) |
167
New Number: 5.94 | AESZ: 334 | Superseeker: 7/3 -4843/81 | Hash: 1ab1dce2847b14dd89a8f8f48ddc7214
Degree: 5
\(3^{2} \theta^4-3 x\left(166\theta^4+320\theta^3+271\theta^2+111\theta+18\right)+x^{2}\left(11155\theta^4+42652\theta^3+60463\theta^2+36876\theta+8172\right)-3^{2} x^{3}\left(4705\theta^4+23418\theta^3+42217\theta^2+31152\theta+7932\right)+2^{2} 3 x^{4}\left(3514\theta^4+16403\theta^3+25581\theta^2+16442\theta+3744\right)-2^{2} 5 x^{5}(5\theta+3)(5\theta+4)(5\theta+6)(5\theta+7)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 6, 54, 240, -9450, ... --> OEIS Normalized instanton numbers (n0=1): 7/3, -79/12, -4843/81, -1058/3, 3620/3, ... ; Common denominator:...
\(-(3125z^3-1167z^2+54z-1)(2z-3)^2\)
| \(0\) | ≈\(0.025215-0.018839I\) | ≈\(0.025215+0.018839I\) | ≈\(0.32301\) | \(\frac{ 3}{ 2}\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 3}{ 5}\) |
| \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(\frac{ 4}{ 5}\) |
| \(0\) | \(1\) | \(1\) | \(1\) | \(3\) | \(\frac{ 6}{ 5}\) |
| \(0\) | \(2\) | \(2\) | \(2\) | \(4\) | \(\frac{ 7}{ 5}\) |
168
New Number: 5.95 | AESZ: 338 | Superseeker: -140/3 -66092 | Hash: eb4f6d6e59fafa4e794fb664dbdeab3f
Degree: 5
\(3^{2} \theta^4+2^{2} 3 x\left(278\theta^4+424\theta^3+311\theta^2+99\theta+12\right)+2^{5} x^{2}\left(5210\theta^4+3944\theta^3-2635\theta^2-2433\theta-492\right)+2^{8} x^{3}\left(8190\theta^4-3528\theta^3-3991\theta^2-585\theta+114\right)-2^{11} 11 x^{4}(2\theta+1)(86\theta^3+57\theta^2-39\theta-32)+2^{15} 11^{2} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -16, 1608, -243520, 44810920, ... --> OEIS Normalized instanton numbers (n0=1): -140/3, 1293, -66092, 5236719, -1553321056/3, ... ; Common denominator:...
\((2048z^3-640z^2+312z+1)(3+88z)^2\)
| \(-\frac{ 3}{ 88}\) | ≈\(-0.003184\) | \(0\) | ≈\(0.157842-0.358378I\) | ≈\(0.157842+0.358378I\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) |
| \(3\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) |
| \(4\) | \(2\) | \(0\) | \(2\) | \(2\) | \(\frac{ 3}{ 2}\) |
169
New Number: 5.96 | AESZ: 339 | Superseeker: 12 28 | Hash: 41593acc689cf76c174442db98218947
Degree: 5
\(\theta^4-2^{2} x\left(10\theta^4+50\theta^3+39\theta^2+14\theta+2\right)+2^{4} x^{2}\left(177\theta^4+1158\theta^3+2007\theta^2+1158\theta+230\right)+2^{8} x^{3}\left(539\theta^4+1344\theta^3-300\theta^2-1068\theta-340\right)+2^{10} 5 x^{4}(2\theta+1)(4\theta^3-642\theta^2-1002\theta-385)-2^{13} 3 5^{2} x^{5}(2\theta+1)(3\theta+2)(3\theta+4)(2\theta+3)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 8, 0, -6400, -249200, ... --> OEIS Normalized instanton numbers (n0=1): 12, -339/2, 28, 27639/2, 634692, ... ; Common denominator:...
\(-(55296z^3-5632z^2+80z-1)(1+20z)^2\)
| \(-\frac{ 1}{ 20}\) | \(0\) | ≈\(0.007072-0.012497I\) | ≈\(0.007072+0.012497I\) | ≈\(0.087707\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(\frac{ 2}{ 3}\) |
| \(3\) | \(0\) | \(1\) | \(1\) | \(1\) | \(\frac{ 4}{ 3}\) |
| \(4\) | \(0\) | \(2\) | \(2\) | \(2\) | \(\frac{ 3}{ 2}\) |
170
New Number: 5.97 | AESZ: 340 | Superseeker: 484/3 819404/3 | Hash: 2775f87d96d6e9710faad170157dd033
Degree: 5
\(3^{2} \theta^4-2^{2} 3 x\left(124\theta^4+1064\theta^3+769\theta^2+237\theta+30\right)-2^{7} x^{2}\left(8092\theta^4+5848\theta^3-22175\theta^2-13869\theta-2751\right)-2^{12} x^{3}\left(5412\theta^4-92376\theta^3-67609\theta^2-15615\theta-96\right)+2^{17} 17 x^{4}(2\theta+1)(2242\theta^3+1419\theta^2-1047\theta-733)-2^{23} 3 17^{2} x^{5}(2\theta+1)(3\theta+2)(3\theta+4)(2\theta+3)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 40, 4968, 976000, 240389800, ... --> OEIS Normalized instanton numbers (n0=1): 484/3, -2053, 819404/3, -14598094/3, 5541353504/3, ... ; Common denominator:...
\(-(432z-1)(64z-1)(32z-1)(3+544z)^2\)
| \(-\frac{ 3}{ 544}\) | \(0\) | \(\frac{ 1}{ 432}\) | \(\frac{ 1}{ 64}\) | \(\frac{ 1}{ 32}\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(\frac{ 2}{ 3}\) |
| \(3\) | \(0\) | \(1\) | \(1\) | \(1\) | \(\frac{ 4}{ 3}\) |
| \(4\) | \(0\) | \(2\) | \(2\) | \(2\) | \(\frac{ 3}{ 2}\) |
171
New Number: 5.98 | AESZ: 341 | Superseeker: 87/13 21589/13 | Hash: eed12a307d671fcf681b9d108c5e4c9e
Degree: 5
\(13^{2} \theta^4-13 x\left(1217\theta^4+1474\theta^3+1127\theta^2+390\theta+52\right)-2^{4} x^{2}\left(5134\theta^4+83956\theta^3+142024\theta^2+83616\theta+16575\right)+2^{6} x^{3}\left(142492\theta^4+565032\theta^3+604615\theta^2+269841\theta+44070\right)-2^{11} 5 x^{4}(2\theta+1)(4324\theta^3+10698\theta^2+9903\theta+3110)+2^{16} 3 5^{2} x^{5}(2\theta+1)(3\theta+2)(3\theta+4)(2\theta+3)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 4, 180, 7600, 433300, ... --> OEIS Normalized instanton numbers (n0=1): 87/13, 1532/13, 21589/13, 589110/13, 17749920/13, ... ; Common denominator:...
\((27z+1)(256z^2-96z+1)(-13+160z)^2\)
| \(-\frac{ 1}{ 27}\) | \(0\) | \(\frac{ 3}{ 16}-\frac{ 1}{ 8}\sqrt{ 2}\) | \(\frac{ 13}{ 160}\) | \(\frac{ 3}{ 16}+\frac{ 1}{ 8}\sqrt{ 2}\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(\frac{ 2}{ 3}\) |
| \(1\) | \(0\) | \(1\) | \(3\) | \(1\) | \(\frac{ 4}{ 3}\) |
| \(2\) | \(0\) | \(2\) | \(4\) | \(2\) | \(\frac{ 3}{ 2}\) |
172
New Number: 5.99 | AESZ: 342 | Superseeker: -4 3856/9 | Hash: 009a00efdd065ef9ea58db999d777786
Degree: 5
\(\theta^4+2 x\left(50\theta^4+64\theta^3+52\theta^2+20\theta+3\right)+2^{2} 3 x^{2}\left(380\theta^4+992\theta^3+1166\theta^2+612\theta+117\right)+2^{2} 3^{2} x^{3}\left(2140\theta^4+5832\theta^3+5651\theta^2+2349\theta+360\right)+2^{4} 3^{6} x^{4}(2\theta+1)(20\theta^3+42\theta^2+35\theta+11)+2^{6} 3^{7} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -6, 54, 660, -69930, ... --> OEIS Normalized instanton numbers (n0=1): -4, -16, 3856/9, -3864, -20784, ... ; Common denominator:...
\((3888z^3+2592z^2+76z+1)(1+12z)^2\)
| ≈\(-0.636595\) | \(-\frac{ 1}{ 12}\) | ≈\(-0.015036-0.01334I\) | ≈\(-0.015036+0.01334I\) | \(0\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) |
| \(1\) | \(3\) | \(1\) | \(1\) | \(0\) | \(1\) |
| \(2\) | \(4\) | \(2\) | \(2\) | \(0\) | \(\frac{ 3}{ 2}\) |
173
New Number: 5.9 | AESZ: 56 | Superseeker: -16 -3280 | Hash: 58a7f24bf18cb98b526885069667f9f0
Degree: 5
\(\theta^4-2^{4} x\left(22\theta^4+8\theta^3+9\theta^2+5\theta+1\right)+2^{9} x^{2}\left(94\theta^4+88\theta^3+97\theta^2+45\theta+8\right)-2^{14} x^{3}\left(194\theta^4+336\theta^3+371\theta^2+195\theta+41\right)+2^{19} 3 x^{4}\left(64\theta^4+176\theta^3+217\theta^2+129\theta+30\right)-2^{27} 3^{2} x^{5}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 16, 464, 17152, 725776, ... --> OEIS Normalized instanton numbers (n0=1): -16, -178, -3280, -76197, -2046896, ... ; Common denominator:...
\(-(-1+32z)(96z-1)^2(64z-1)^2\)
| \(0\) | \(\frac{ 1}{ 96}\) | \(\frac{ 1}{ 64}\) | \(\frac{ 1}{ 32}\) | \(\infty\) |
|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(0\) | \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) |
| \(0\) | \(3\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) |
| \(0\) | \(4\) | \(1\) | \(2\) | \(1\) |
174
New Number: 10.10 | AESZ: | Superseeker: 28/3 83612/81 | Hash: 8270c1ecc701d7cbd422a656c6118587
Degree: 10
\(3^{2} \theta^4+2^{2} 3 x\left(220\theta^4+152\theta^3+207\theta^2+131\theta+31\right)+2^{4} x^{2}\left(20608\theta^4+32896\theta^3+50132\theta^2+37496\theta+11991\right)+2^{8} x^{3}\left(89936\theta^4+243168\theta^3+429080\theta^2+391080\theta+152645\right)+2^{12} x^{4}\left(242448\theta^4+966912\theta^3+2030168\theta^2+2199488\theta+1002377\right)+2^{20} x^{5}\left(26320\theta^4+142696\theta^3+359216\theta^2+454946\theta+237357\right)+2^{23} x^{6}\left(59600\theta^4+415872\theta^3+1247376\theta^2+1826640\theta+1079063\right)+2^{28} x^{7}\left(21712\theta^4+187424\theta^3+661000\theta^2+1107048\theta+733353\right)+2^{32} x^{8}\left(9744\theta^4+100992\theta^3+412312\theta^2+779936\theta+572857\right)+2^{39} x^{9}\left(304\theta^4+3696\theta^3+17208\theta^2+36300\theta+29211\right)+2^{44} x^{10}\left((2\theta+7)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -124/3, 1220, -872528/27, 67351172/81, ... --> OEIS Normalized instanton numbers (n0=1): 28/3, -695/9, 83612/81, -4447894/243, 274874464/729, ... ; Common denominator:...
\((1+48z+256z^2)(32z+1)^2(16z+1)^2(32z+3)^2(64z+1)^2\)
| \(-\frac{ 3}{ 32}-\frac{ 1}{ 32}\sqrt{ 5}\) | \(-\frac{ 3}{ 32}\) | \(-\frac{ 1}{ 16}\) | \(-\frac{ 1}{ 32}\) | \(-\frac{ 3}{ 32}+\frac{ 1}{ 32}\sqrt{ 5}\) | \(-\frac{ 1}{ 64}\) | \(0\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 7}{ 2}\) |
| \(1\) | \(1\) | \(0\) | \(0\) | \(1\) | \(1\) | \(0\) | \(\frac{ 7}{ 2}\) |
| \(1\) | \(-2\) | \(1\) | \(1\) | \(1\) | \(3\) | \(0\) | \(\frac{ 7}{ 2}\) |
| \(2\) | \(3\) | \(1\) | \(1\) | \(2\) | \(4\) | \(0\) | \(\frac{ 7}{ 2}\) |
175
New Number: 10.1 | AESZ: | Superseeker: 118/91 268/13 | Hash: 9708eba070b10afbba48d1f539423c22
Degree: 10
\(7^{2} 13^{2} \theta^4-7 13 x\left(2221\theta^4+4604\theta^3+3940\theta^2+1638\theta+273\right)-2 x^{2}\left(275775\theta^4+850032\theta^3+1167211\theta^2+754481\theta+190918\right)+x^{3}\left(27353\theta^4-6829166\theta^2-6586125\theta-2489994\theta^3-2242968\right)-x^{4}\left(46728731\theta+12063734\theta^3+18386820+508804\theta^4+40173426\theta^2\right)+3 x^{5}\left(33450\theta^4+319414\theta^3-766536\theta^2-1551527\theta-668977\right)+x^{6}\left(2892684+47526449\theta^2+4076796\theta^4+26519901\theta+28614978\theta^3\right)-2 x^{7}\left(96271\theta^4+1136261\theta^3+4541506\theta^2+6411261\theta+2925345\right)-13 x^{8}(\theta+1)(257369\theta^3+699321\theta^2+523184\theta+25156)+2^{2} 5 13^{2} x^{9}(\theta+2)(\theta+1)(227\theta^2+762\theta+681)-2^{2} 5^{2} 13^{3} x^{10}(\theta+1)(\theta+2)^2(\theta+3)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 3, 29, 393, 6333, ... --> OEIS Normalized instanton numbers (n0=1): 118/91, 373/91, 268/13, 12732/91, 105020/91, ... ; Common denominator:...
\(-(-1+25z+49z^2+36z^3+199z^4-40z^5+13z^6)(-91-27z+130z^2)^2\)
| \(\frac{ 27}{ 260}-\frac{ 1}{ 260}\sqrt{ 48049}\) | \(0\) | \(\frac{ 27}{ 260}+\frac{ 1}{ 260}\sqrt{ 48049}\) | \(#ND+#NDI\) | \(\infty\) |
|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(0\) | \(1\) | \(1\) | \(2\) |
| \(3\) | \(0\) | \(3\) | \(1\) | \(2\) |
| \(4\) | \(0\) | \(4\) | \(2\) | \(3\) |
176
New Number: 10.2 | AESZ: | Superseeker: 4 2252/9 | Hash: 4a65f8c6ad1f8eaf4aa56879ebb94205
Degree: 10
\(\theta^4+2^{2} x\left(69\theta^4+42\theta^3+45\theta^2+24\theta+5\right)+2^{4} x^{2}\left(2097\theta^4+2748\theta^3+3311\theta^2+1990\theta+489\right)+2^{8} x^{3}\left(9240\theta^4+19254\theta^3+26269\theta^2+17979\theta+5020\right)+2^{10} 3 x^{4}\left(34845\theta^4+101230\theta^3+156798\theta^2+120187\theta+36857\right)+2^{12} x^{5}\left(792225\theta^4+2972406\theta^3+5205467\theta^2+4394830\theta+1449907\right)+2^{14} x^{6}\left(4064601\theta^4+18714936\theta^3+36737137\theta^2+33711480\theta+11807867\right)+2^{18} x^{7}\left(3474333\theta^4+18927498\theta^3+41213301\theta^2+40674636\theta+14985820\right)+2^{20} x^{8}\left(7544547\theta^4+47365644\theta^3+113299226\theta^2+119329996\theta+45950951\right)+2^{24} 23 x^{9}(2\theta+3)(50786\theta^3+284985\theta^2+515497\theta+282264)+2^{28} 3 7^{2} 23^{2} x^{10}(\theta+1)(2\theta+5)(2\theta+3)(\theta+3)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -20, 436, -9872, 228292, ... --> OEIS Normalized instanton numbers (n0=1): 4, -31, 2252/9, -11109/4, 33312, ... ; Common denominator:...
\((24z+1)(8z+1)(784z^2+52z+1)(32z+1)^2(736z^2+64z+1)^2\)
| \(-\frac{ 1}{ 8}\) | \(-\frac{ 1}{ 23}-\frac{ 3}{ 184}\sqrt{ 2}\) | \(-\frac{ 1}{ 24}\) | \(-\frac{ 13}{ 392}-\frac{ 3}{ 392}\sqrt{ 3}I\) | \(-\frac{ 13}{ 392}+\frac{ 3}{ 392}\sqrt{ 3}I\) | \(-\frac{ 1}{ 32}\) | \(-\frac{ 1}{ 23}+\frac{ 3}{ 184}\sqrt{ 2}\) | \(0\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(0\) | \(\frac{ 3}{ 2}\) |
| \(1\) | \(3\) | \(1\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(3\) | \(0\) | \(\frac{ 5}{ 2}\) |
| \(2\) | \(4\) | \(2\) | \(2\) | \(2\) | \(1\) | \(4\) | \(0\) | \(3\) |
177
New Number: 10.3 | AESZ: | Superseeker: 2 421/9 | Hash: 5219414e025733d8e128028821370b4b
Degree: 10
\(\theta^4-x\left(321\theta^4+258\theta^3+258\theta^2+129\theta+26\right)+x^{2}\left(74028\theta^3+14112+55150\theta+89219\theta^2+46467\theta^4\right)-2^{3} x^{3}\left(499260\theta^4+1184748\theta^3+1665809\theta^2+1187841\theta+345452\right)+2^{4} 3 x^{4}\left(4702665\theta^4+14805730\theta^3+23754818\theta^2+18867201\theta+5979118\right)-2^{6} x^{5}\left(136927125\theta^4+537349854\theta^3+968406086\theta^2+839579917\theta+283906432\right)+2^{6} x^{6}\left(3697617171\theta^4+17401686816\theta^3+34821823585\theta^2+32540314464\theta+11600569724\right)-2^{9} x^{7}\left(8571324186\theta^4+47135706036\theta^3+103830096399\theta^2+103713883221\theta+38684901782\right)+2^{12} x^{8}\left(13055773347\theta^4+82367586444\theta^3+198438600506\theta^2+210671505052\theta+81797663483\right)-2^{16} 137 x^{9}(2\theta+3)(21527774\theta^3+121431015\theta^2+220937755\theta+121634574)+2^{20} 3 73^{2} 137^{2} x^{10}(\theta+1)(2\theta+5)(2\theta+3)(\theta+3)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 26, 730, 21320, 638506, ... --> OEIS Normalized instanton numbers (n0=1): 2, -3/2, 421/9, -519/2, 285, ... ; Common denominator:...
\((24z-1)(42632z^3-3675z^2+105z-1)(32z-1)^2(1096z^2-64z+1)^2\)
| \(0\) | ≈\(0.025716-0.003646I\) | ≈\(0.025716+0.003646I\) | \(\frac{ 4}{ 137}-\frac{ 3}{ 548}\sqrt{ 2}I\) | \(\frac{ 4}{ 137}+\frac{ 3}{ 548}\sqrt{ 2}I\) | \(\frac{ 1}{ 32}\) | ≈\(0.034771\) | \(\frac{ 1}{ 24}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(\frac{ 3}{ 2}\) |
| \(0\) | \(1\) | \(1\) | \(3\) | \(3\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(\frac{ 5}{ 2}\) |
| \(0\) | \(2\) | \(2\) | \(4\) | \(4\) | \(1\) | \(2\) | \(2\) | \(3\) |
178
New Number: 10.4 | AESZ: | Superseeker: 10 7709/9 | Hash: 6162ae56594cb4ca6830174a8ed00300
Degree: 10
\(\theta^4+x\left(14+63\theta+102\theta^2+78\theta^3+231\theta^4\right)+x^{2}\left(2832+13390\theta+24563\theta^2+19308\theta^3+21987\theta^4\right)+2^{3} x^{3}\left(140700\theta^4+225708\theta^3+290537\theta^2+177465\theta+44084\right)+2^{4} 3 x^{4}\left(713295\theta^4+1769710\theta^3+2523886\theta^2+1767335\theta+499986\right)+2^{6} x^{5}\left(10296675\theta^4+36211314\theta^3+60921650\theta^2+49433683\theta+15811528\right)+2^{6} x^{6}\left(137088291\theta^4+659829216\theta^3+1356977569\theta^2+1291863456\theta+467669756\right)+2^{9} x^{7}\left(179375706\theta^4+1143044916\theta^3+2845532295\theta^2+3114799053\theta+1242790862\right)+2^{12} x^{8}\left(184827267\theta^4+1416425484\theta^3+3980381306\theta^2+4736268700\theta+1991273435\right)+2^{16} 47 x^{9}(2\theta+3)(622034\theta^3+4130865\theta^2+8390461\theta+4891218)+2^{20} 3 17^{2} 47^{2} x^{10}(\theta+1)(2\theta+5)(2\theta+3)(\theta+3)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -14, 250, -5192, 116266, ... --> OEIS Normalized instanton numbers (n0=1): 10, -149/2, 7709/9, -27333/2, 242829, ... ; Common denominator:...
\((24z+1)(2312z^3+75z^2+15z+1)(32z+1)^2(376z^2+64z+1)^2\)
| \(-\frac{ 4}{ 47}-\frac{ 9}{ 188}\sqrt{ 2}\) | ≈\(-0.055617\) | \(-\frac{ 1}{ 24}\) | \(-\frac{ 1}{ 32}\) | \(-\frac{ 4}{ 47}+\frac{ 9}{ 188}\sqrt{ 2}\) | \(0\) | ≈\(0.011589-0.087422I\) | ≈\(0.011589+0.087422I\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(0\) | \(1\) | \(1\) | \(\frac{ 3}{ 2}\) |
| \(3\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(3\) | \(0\) | \(1\) | \(1\) | \(\frac{ 5}{ 2}\) |
| \(4\) | \(2\) | \(2\) | \(1\) | \(4\) | \(0\) | \(2\) | \(2\) | \(3\) |
179
New Number: 10.5 | AESZ: | Superseeker: 8 -830/9 | Hash: 26cb7b62aea8fead9548cb08c510d8cc
Degree: 10
\(\theta^4-x\left(5+36\theta+102\theta^2+132\theta^3+42\theta^4\right)+x^{2}\left(321+2500\theta+5078\theta^2+2676\theta^3-126\theta^4\right)+x^{3}\left(58511+193314\theta+255284\theta^2+165228\theta^3+36750\theta^4\right)+3 x^{4}\left(149076\theta^4+788140\theta^3+1818454\theta^2+1636604\theta+537147\right)+x^{5}\left(18978161+48287282\theta+41352784\theta^2+10485348\theta^3-282726\theta^4\right)+x^{6}\left(75240839+129474252\theta+18361102\theta^2-64936644\theta^3-20164434\theta^4\right)-x^{7}\left(192652267+790586058\theta+1080753300\theta^2+555817116\theta^3+53729334\theta^4\right)-x^{8}\left(1469856277+3396870740\theta+2385867946\theta^2+267688500\theta^3-184083363\theta^4\right)+2 5 13 x^{9}(2\theta+3)(3678542\theta^3+13483935\theta^2+14333215\theta+4727112)+2^{2} 3 5^{2} 13^{2} 73^{2} x^{10}(\theta+1)(2\theta+5)(2\theta+3)(\theta+3)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 5, 79, 791, -9329, ... --> OEIS Normalized instanton numbers (n0=1): 8, -45/2, -830/9, -5301/2, 2790, ... ; Common denominator:...
\((3z+1)(5329z^3+1587z^2-69z+1)(13z+1)^2(4z+1)^2(5z-1)^2\)
| ≈\(-0.337782\) | \(-\frac{ 1}{ 3}\) | \(-\frac{ 1}{ 4}\) | \(-\frac{ 1}{ 13}\) | \(0\) | ≈\(0.019989-0.01249I\) | ≈\(0.019989+0.01249I\) | \(\frac{ 1}{ 5}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(\frac{ 3}{ 2}\) |
| \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(3\) | \(0\) | \(1\) | \(1\) | \(3\) | \(\frac{ 5}{ 2}\) |
| \(2\) | \(2\) | \(1\) | \(4\) | \(0\) | \(2\) | \(2\) | \(4\) | \(3\) |
180
New Number: 10.6 | AESZ: | Superseeker: 8 2200/9 | Hash: b5aa0abf76ddfbd280ec220a43822aa4
Degree: 10
\(\theta^4+2^{2} x\left(21\theta^4-6\theta^3+3\theta+1\right)+2^{4} x^{2}\left(126\theta^4-96\theta^3-16\theta^2-56\theta-33\right)+2^{6} x^{3}\left(84\theta^4-336\theta^3-226\theta^2-366\theta-163\right)+2^{11} 3 x^{4}\left(39\theta^4+500\theta^3+1230\theta^2+1160\theta+407\right)+2^{12} x^{5}\left(7029\theta^4+50118\theta^3+125086\theta^2+129149\theta+48902\right)+2^{14} x^{6}\left(38550\theta^4+294456\theta^3+806428\theta^2+911232\theta+368273\right)+2^{16} x^{7}\left(77544\theta^4+708720\theta^3+2233434\theta^2+2804346\theta+1214177\right)+2^{20} x^{8}\left(9171\theta^4+117228\theta^3+467444\theta^2+684316\theta+324572\right)-2^{23} x^{9}(2\theta+3)(2114\theta^3+16713\theta^2+37111\theta+22497)+2^{26} 3 5^{2} x^{10}(\theta+1)(2\theta+5)(2\theta+3)(\theta+3)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -4, 52, -688, 2500, ... --> OEIS Normalized instanton numbers (n0=1): 8, -75/2, 2200/9, -8117/2, 47936, ... ; Common denominator:...
\((12z+1)(6400z^3+192z^2-24z+1)(16z+1)^2(32z^2-32z-1)^2\)
| ≈\(-0.090507\) | \(-\frac{ 1}{ 12}\) | \(-\frac{ 1}{ 16}\) | \(\frac{ 1}{ 2}-\frac{ 3}{ 8}\sqrt{ 2}\) | \(0\) | ≈\(0.030254-0.02848I\) | ≈\(0.030254+0.02848I\) | \(\frac{ 1}{ 2}+\frac{ 3}{ 8}\sqrt{ 2}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(\frac{ 3}{ 2}\) |
| \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(3\) | \(0\) | \(1\) | \(1\) | \(3\) | \(\frac{ 5}{ 2}\) |
| \(2\) | \(2\) | \(1\) | \(4\) | \(0\) | \(2\) | \(2\) | \(4\) | \(3\) |