You searched for: Spectrum0=0,1,1,2
Your search produced 482 matches
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391
New Number: 8.29 | AESZ: 304 | Superseeker: -5 -641 | Hash: cf055a245b1537ed4f2609fa56cf67aa
Degree: 8
\(\theta^4+x\left(82\theta^4+98\theta^3+77\theta^2+28\theta+4\right)-x^{2}\left(636+2916\theta+4463\theta^2+1850\theta^3-553\theta^4\right)-2^{2} x^{3}\left(6087\theta^4+22542\theta^3+27199\theta^2+14916\theta+3136\right)-2^{5} x^{4}\left(7241\theta^4+22750\theta^3+42326\theta^2+29943\theta+7272\right)+2^{7} x^{5}\left(7524\theta^4+1998\theta^3-23019\theta^2-24627\theta-7186\right)+2^{8} x^{6}\left(22961\theta^4+93930\theta^3+88283\theta^2+28194\theta+1624\right)-2^{10} 13 x^{7}\left(1505\theta^4+3274\theta^3+2919\theta^2+1282\theta+236\right)+2^{14} 13^{2} x^{8}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -4, 112, -3712, 155536, ... --> OEIS Normalized instanton numbers (n0=1): -5, 469/8, -641, 50173/4, -276231, ... ; Common denominator:...
\((16z-1)(64z^3-432z^2-76z-1)(-1-11z+52z^2)^2\)
| ≈\(-0.157556\) | \(\frac{ 11}{ 104}-\frac{ 1}{ 104}\sqrt{ 329}\) | ≈\(-0.014327\) | \(0\) | \(\frac{ 1}{ 16}\) | \(\frac{ 11}{ 104}+\frac{ 1}{ 104}\sqrt{ 329}\) | ≈\(6.921883\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(1\) | \(3\) | \(1\) | \(0\) | \(1\) | \(3\) | \(1\) | \(1\) |
| \(2\) | \(4\) | \(2\) | \(0\) | \(2\) | \(4\) | \(2\) | \(1\) |
392
New Number: 8.2 | AESZ: 104 | Superseeker: 7 1271/3 | Hash: d6bd0d1524954c8ce0a6421d295e9795
Degree: 8
\(\theta^4-x(10\theta^2+10\theta+3)(7\theta^2+7\theta+2)-x^{2}\left(71\theta^4+1148\theta^3+1591\theta^2+886\theta+192\right)-2^{3} 3^{2} x^{3}\left(70\theta^4-420\theta^3-1289\theta^2-963\theta-240\right)-2^{4} 3^{2} x^{4}\left(143\theta^4+286\theta^3-1138\theta^2-1281\theta-414\right)+2^{6} 3^{4} x^{5}\left(70\theta^4+700\theta^3+391\theta^2-75\theta-76\right)-2^{6} 3^{4} x^{6}\left(71\theta^4-864\theta^3-1427\theta^2-864\theta-180\right)+2^{9} 3^{6} x^{7}(10\theta^2+10\theta+3)(7\theta^2+7\theta+2)+2^{12} 3^{8} x^{8}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 6, 150, 5208, 221094, ... --> OEIS Normalized instanton numbers (n0=1): 7, 93/2, 1271/3, 18507/2, 190710, ... ; Common denominator:...
\((9z+1)(8z-1)(72z-1)(z+1)(1+72z^2)^2\)
| \(-1\) | \(-\frac{ 1}{ 9}\) | \(0-\frac{ 1}{ 12}\sqrt{ 2}I\) | \(0\) | \(0+\frac{ 1}{ 12}\sqrt{ 2}I\) | \(\frac{ 1}{ 72}\) | \(\frac{ 1}{ 8}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(1\) | \(1\) | \(3\) | \(0\) | \(3\) | \(1\) | \(1\) | \(1\) |
| \(2\) | \(2\) | \(4\) | \(0\) | \(4\) | \(2\) | \(2\) | \(1\) |
393
New Number: 8.30 | AESZ: 314 | Superseeker: 229/4 297111/4 | Hash: 893692ba7eb3effcbc0c3b48d405456a
Degree: 8
\(2^{4} \theta^4-2^{2} x\left(1282\theta^4+2618\theta^3+1909\theta^2+600\theta+72\right)-3^{2} x^{2}\left(9503\theta^4+26810\theta^3+31755\theta^2+15944\theta+2936\right)+3^{4} x^{3}\left(15627\theta^4-18288\theta^3-91412\theta^2-53256\theta-9688\right)+2 3^{6} x^{4}\left(15106\theta^4+20300\theta^3-20421\theta^2-23443\theta-5907\right)-2^{2} 3^{8} x^{5}\left(2072\theta^4-18256\theta^3-2563\theta^2+4626\theta+1495\right)-2^{2} 3^{10} x^{6}\left(6204\theta^4+360\theta^3-281\theta^2+1017\theta+434\right)-2^{5} 3^{12} x^{7}(2\theta+1)(100\theta^3+162\theta^2+95\theta+21)+2^{8} 3^{14} x^{8}(2\theta+1)(\theta+1)^2(2\theta+3)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 18, 1926, 310860, 61060230, ... --> OEIS Normalized instanton numbers (n0=1): 229/4, 1293, 297111/4, 6150238, 2540085295/4, ... ; Common denominator:...
\((z-1)(11664z^3+3888z^2+324z-1)(-4-9z+648z^2)^2\)
| ≈\(-0.168156-0.022431I\) | ≈\(-0.168156+0.022431I\) | \(\frac{ 1}{ 144}-\frac{ 1}{ 144}\sqrt{ 129}\) | \(0\) | \(\frac{ 1}{ 18}2^(\frac{ 1}{ 3})+\frac{ 1}{ 36}2^(\frac{ 2}{ 3})-\frac{ 1}{ 9}\) | \(\frac{ 1}{ 144}+\frac{ 1}{ 144}\sqrt{ 129}\) | \(1\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(1\) | \(1\) | \(3\) | \(0\) | \(1\) | \(3\) | \(1\) | \(1\) |
| \(2\) | \(2\) | \(4\) | \(0\) | \(2\) | \(4\) | \(2\) | \(\frac{ 3}{ 2}\) |
394
New Number: 8.31 | AESZ: 315 | Superseeker: 38 26135 | Hash: 44be55b95bb1c725c5aaa2c9a6635e89
Degree: 8
\(5^{2} \theta^4-5^{2} x\left(239\theta^4+496\theta^3+368\theta^2+120\theta+15\right)-2 3 5 x^{2}\left(1727\theta^4+3206\theta^3+2341\theta^2+1090\theta+245\right)-3^{2} 5 x^{3}\left(1519\theta^4+7338\theta^3+14271\theta^2+8340\theta+1690\right)+3^{3} x^{4}\left(10358\theta^4-16622\theta^3-49763\theta^2-37900\theta-10210\right)+3^{4} 5 x^{5}\left(922\theta^4+3526\theta^3-1357\theta^2-3028\theta-1031\right)-3^{5} x^{6}\left(1219\theta^4-6030\theta^3-6441\theta^2-1740\theta+160\right)-2^{2} 3^{6} x^{7}\left(162\theta^4+234\theta^3+65\theta^2-52\theta-25\right)-2^{4} 3^{8} x^{8}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 15, 1179, 140505, 20362059, ... --> OEIS Normalized instanton numbers (n0=1): 38, 3068/5, 26135, 7871998/5, 117518569, ... ; Common denominator:...
\(-(z+1)(81z^3+351z^2+246z-1)(-5-15z+36z^2)^2\)
| ≈\(-3.452681\) | \(-1\) | ≈\(-0.884694\) | \(\frac{ 5}{ 24}-\frac{ 1}{ 24}\sqrt{ 105}\) | \(0\) | ≈\(0.004042\) | \(\frac{ 5}{ 24}+\frac{ 1}{ 24}\sqrt{ 105}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(3\) | \(0\) | \(1\) | \(3\) | \(1\) |
| \(2\) | \(2\) | \(2\) | \(4\) | \(0\) | \(2\) | \(4\) | \(1\) |
395
New Number: 8.32 | AESZ: 317 | Superseeker: 69/4 14365/12 | Hash: cda8cce31025f51636125bea67a820d1
Degree: 8
\(2^{4} \theta^4-2^{2} 3 x\left(162\theta^4+414\theta^3+335\theta^2+128\theta+20\right)+3^{3} x^{2}\left(1219\theta^4+10906\theta^3+18963\theta^2+11824\theta+2708\right)+3^{5} 5 x^{3}\left(922\theta^4+162\theta^3-6403\theta^2-6576\theta-1964\right)-3^{7} x^{4}\left(10358\theta^4+58054\theta^3+62251\theta^2+29672\theta+4907\right)-3^{9} 5 x^{5}\left(1519\theta^4-1262\theta^3+1371\theta^2+4264\theta+1802\right)+2 3^{11} 5 x^{6}\left(1727\theta^4+3702\theta^3+3085\theta^2+882\theta+17\right)-3^{13} 5^{2} x^{7}\left(239\theta^4+460\theta^3+314\theta^2+84\theta+6\right)-3^{16} 5^{2} x^{8}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 15, 459, 19545, 1019259, ... --> OEIS Normalized instanton numbers (n0=1): 69/4, -30, 14365/12, 3015/2, 1376205/4, ... ; Common denominator:...
\(-(27z-1)(243z^3+2214z^2-117z+1)(-4-45z+405z^2)^2\)
| ≈\(-9.163702\) | \(\frac{ 1}{ 18}-\frac{ 1}{ 90}\sqrt{ 105}\) | \(0\) | ≈\(0.010727\) | \(\frac{ 1}{ 27}\) | ≈\(0.041864\) | \(\frac{ 1}{ 18}+\frac{ 1}{ 90}\sqrt{ 105}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(1\) | \(3\) | \(0\) | \(1\) | \(1\) | \(1\) | \(3\) | \(1\) |
| \(2\) | \(4\) | \(0\) | \(2\) | \(2\) | \(2\) | \(4\) | \(1\) |
396
New Number: 8.33 | AESZ: 322 | Superseeker: 4/3 95/3 | Hash: a19da26bf1a7748e3b7e6151e803da30
Degree: 8
\(3^{2} \theta^4+3 x\left(5\theta^4-122\theta^3-100\theta^2-39\theta-6\right)-x^{2}\left(5052+23736\theta+41729\theta^2+32600\theta^3+8603\theta^4\right)-2^{2} x^{3}\left(33304\theta^4+108297\theta^3+122347\theta^2+61470\theta+11712\right)-2^{2} x^{4}\left(180401\theta^4+547606\theta^3+638125\theta^2+339248\theta+69036\right)-2^{4} x^{5}\left(94934\theta^4+298745\theta^3+355667\theta^2+189660\theta+38224\right)-2^{4} x^{6}\left(73291\theta^4+204216\theta^3+190453\theta^2+68916\theta+6964\right)-2^{7} 3 x^{7}\left(811\theta^4+1886\theta^3+1804\theta^2+861\theta+174\right)-2^{10} 3^{2} x^{8}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 2, 46, 632, 16846, ... --> OEIS Normalized instanton numbers (n0=1): 4/3, 18, 95/3, 14575/12, 18158/3, ... ; Common denominator:...
\(-(-1+13z+827z^2+1928z^3+64z^4)(3+22z+12z^2)^2\)
| \(-\frac{ 11}{ 12}-\frac{ 1}{ 12}\sqrt{ 85}\) | \(-\frac{ 11}{ 12}+\frac{ 1}{ 12}\sqrt{ 85}\) | \(0\) | \(#ND+#NDI\) | \(\infty\) |
|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) |
| \(3\) | \(3\) | \(0\) | \(1\) | \(1\) |
| \(4\) | \(4\) | \(0\) | \(2\) | \(1\) |
397
New Number: 8.34 | AESZ: 323 | Superseeker: 100/3 73111/3 | Hash: 77c03b04c3a10350b5b0ccd2d204b18f
Degree: 8
\(3^{2} \theta^4-3 x\left(811\theta^4+1358\theta^3+1012\theta^2+333\theta+42\right)-x^{2}\left(2424+7494\theta-17551\theta^2-88948\theta^3-73291\theta^4\right)-2^{3} x^{3}\left(94934\theta^4+80991\theta^3+29036\theta^2+5175\theta+420\right)+2^{4} x^{4}\left(180401\theta^4+173998\theta^3+77713\theta^2+15788\theta+708\right)-2^{7} x^{5}\left(33304\theta^4+24919\theta^3-2720\theta^2-8451\theta-2404\right)+2^{8} x^{6}\left(8603\theta^4+1812\theta^3-4453\theta^2-3666\theta-952\right)+2^{11} 3 x^{7}\left(5\theta^4+142\theta^3+296\theta^2+225\theta+60\right)-2^{14} 3^{2} x^{8}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 14, 1054, 120776, 16816846, ... --> OEIS Normalized instanton numbers (n0=1): 100/3, 1880/3, 73111/3, 4310384/3, 314245046/3, ... ; Common denominator:...
\(-(-1+241z-827z^2+104z^3+64z^4)(3-44z+48z^2)^2\)
| \(0\) | \(\frac{ 11}{ 24}-\frac{ 1}{ 24}\sqrt{ 85}\) | \(\frac{ 11}{ 24}+\frac{ 1}{ 24}\sqrt{ 85}\) | \(#ND+#NDI\) | \(\infty\) |
|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(0\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(0\) | \(3\) | \(3\) | \(1\) | \(1\) |
| \(0\) | \(4\) | \(4\) | \(2\) | \(1\) |
398
New Number: 8.35 | AESZ: 326 | Superseeker: 11/13 385/39 | Hash: 946b91838924db64fe0ebdf0d473e621
Degree: 8
\(13^{2} \theta^4-13 x\theta(56\theta^3+178\theta^2+115\theta+26)-x^{2}\left(28466\theta^4+109442\theta^3+165603\theta^2+117338\theta+32448\right)-x^{3}\left(233114\theta^4+1257906\theta^3+2622815\theta^2+2467842\theta+872352\right)-x^{4}\left(989585\theta^4+6852298\theta^3+17737939\theta^2+19969754\theta+8108448\right)-x^{5}(\theta+1)(2458967\theta^3+18007287\theta^2+44047582\theta+35386584)-3^{2} x^{6}(\theta+1)(\theta+2)(393163\theta^2+2539029\theta+4164444)-3^{3} 11 x^{7}(\theta+3)(\theta+2)(\theta+1)(8683\theta+34604)-3^{3} 11^{2} 13 17 x^{8}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, 12, 96, 1116, ... --> OEIS Normalized instanton numbers (n0=1): 11/13, 30/13, 385/39, 672/13, 4437/13, ... ; Common denominator:...
\(-(3z+1)(13z^2+5z+1)(153z^3+75z^2+14z-1)(13+11z)^2\)
| \(-\frac{ 13}{ 11}\) | \(-\frac{ 1}{ 3}\) | ≈\(-0.272124-0.216493I\) | ≈\(-0.272124+0.216493I\) | \(-\frac{ 5}{ 26}-\frac{ 3}{ 26}\sqrt{ 3}I\) | \(-\frac{ 5}{ 26}+\frac{ 3}{ 26}\sqrt{ 3}I\) | \(0\) | ≈\(0.054052\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(2\) |
| \(3\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(3\) |
| \(4\) | \(2\) | \(2\) | \(2\) | \(2\) | \(2\) | \(0\) | \(2\) | \(4\) |
399
New Number: 8.36 | AESZ: 327 | Superseeker: 24/29 284/29 | Hash: 586c1906112cbba9b2d54c57ce2add99
Degree: 8
\(29^{2} \theta^4+2 29 x\theta(24\theta^3-198\theta^2-128\theta-29)-2^{2} x^{2}\left(44284\theta^4+172954\theta^3+248589\theta^2+172057\theta+47096\right)-2^{2} x^{3}\left(525708\theta^4+2414772\theta^3+4447643\theta^2+3839049\theta+1275594\right)-2^{3} x^{4}\left(1415624\theta^4+7911004\theta^3+17395449\theta^2+17396359\theta+6496262\right)-2^{4} x^{5}(\theta+1)(2152040\theta^3+12186636\theta^2+24179373\theta+16560506)-2^{5} x^{6}(\theta+1)(\theta+2)(1912256\theta^2+9108540\theta+11349571)-2^{8} 41 x^{7}(\theta+3)(\theta+2)(\theta+1)(5671\theta+16301)-2^{8} 3 19 41^{2} x^{8}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, 14, 96, 1266, ... --> OEIS Normalized instanton numbers (n0=1): 24/29, 72/29, 284/29, 1616/29, 10632/29, ... ; Common denominator:...
\(-(6z+1)(152z^3+84z^2+14z-1)(2z+1)^2(82z+29)^2\)
| \(-\frac{ 1}{ 2}\) | \(-\frac{ 29}{ 82}\) | ≈\(-0.302804-0.180271I\) | ≈\(-0.302804+0.180271I\) | \(-\frac{ 1}{ 6}\) | \(0\) | ≈\(0.052976\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(2\) |
| \(\frac{ 1}{ 2}\) | \(3\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(3\) |
| \(1\) | \(4\) | \(2\) | \(2\) | \(2\) | \(0\) | \(2\) | \(4\) |
400
New Number: 8.37 | AESZ: 345 | Superseeker: -12/11 357/11 | Hash: 60f282ab4e1936cd96eb5ba12983db2d
Degree: 8
\(11^{2} \theta^4+3 11 x\left(113\theta^4+184\theta^3+158\theta^2+66\theta+11\right)+2 x^{2}\left(28397\theta^4+95138\theta^3+128420\theta^2+77715\theta+17622\right)-3 x^{3}\left(3165\theta^4+180822\theta^3+560611\theta^2+539022\theta+167508\right)-3 x^{4}\left(233330\theta^4+1052614\theta^3+1424797\theta^2+774518\theta+145896\right)-3^{2} x^{5}\left(12866\theta^4-98902\theta^3-52127\theta^2+102028\theta+63723\right)+3^{2} x^{6}\left(183763\theta^4+473778\theta^3+427847\theta^2+147060\theta+11268\right)-2^{3} 3^{3} x^{7}\left(5006\theta^4+13414\theta^3+14935\theta^2+8228\theta+1869\right)+2^{6} 3^{7} x^{8}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -3, 9, 141, -3879, ... --> OEIS Normalized instanton numbers (n0=1): -12/11, -28/11, 357/11, -1172/11, -5250/11, ... ; Common denominator:...
\((3z-1)(81z^3-457z^2-30z-1)(-11-21z+24z^2)^2\)
| \(\frac{ 7}{ 16}-\frac{ 1}{ 48}\sqrt{ 1497}\) | ≈\(-0.032637-0.033136I\) | ≈\(-0.032637+0.033136I\) | \(0\) | \(\frac{ 1}{ 3}\) | \(\frac{ 7}{ 16}+\frac{ 1}{ 48}\sqrt{ 1497}\) | ≈\(5.707249\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(3\) | \(1\) | \(1\) | \(0\) | \(1\) | \(3\) | \(1\) | \(1\) |
| \(4\) | \(2\) | \(2\) | \(0\) | \(2\) | \(4\) | \(2\) | \(1\) |
401
New Number: 8.38 | AESZ: 346 | Superseeker: 713/8 571555/2 | Hash: 65579ed94e039ed095e1b5b7db3674ff
Degree: 8
\(2^{6} \theta^4-2^{3} x\left(5006\theta^4+6610\theta^3+4729\theta^2+1424\theta+168\right)+3^{3} x^{2}\left(183763\theta^4+261274\theta^3+109091\theta^2+22352\theta+2040\right)-3^{7} x^{3}\left(12866\theta^4+150366\theta^3+321775\theta^2+141888\theta+21336\right)-3^{10} x^{4}\left(233330\theta^4-119294\theta^3-333065\theta^2-149446\theta-23109\right)-3^{14} x^{5}\left(3165\theta^4-168162\theta^3+37135\theta^2+52394\theta+11440\right)+2 3^{17} x^{6}\left(28397\theta^4+18450\theta^3+13388\theta^2+7299\theta+1586\right)+3^{22} 11 x^{7}\left(113\theta^4+268\theta^3+284\theta^2+150\theta+32\right)+3^{25} 11^{2} x^{8}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 21, 2889, 636357, 171536121, ... --> OEIS Normalized instanton numbers (n0=1): 713/8, 3274, 571555/2, 66913005/2, 20047292157/4, ... ; Common denominator:...
\((27z-1)(6561z^3+2430z^2+457z-1)(-8+567z+24057z^2)^2\)
| ≈\(-0.186267-0.189115I\) | ≈\(-0.186267+0.189115I\) | \(-\frac{ 7}{ 594}-\frac{ 1}{ 1782}\sqrt{ 1497}\) | \(0\) | ≈\(0.002163\) | \(-\frac{ 7}{ 594}+\frac{ 1}{ 1782}\sqrt{ 1497}\) | \(\frac{ 1}{ 27}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(1\) | \(1\) | \(3\) | \(0\) | \(1\) | \(3\) | \(1\) | \(1\) |
| \(2\) | \(2\) | \(4\) | \(0\) | \(2\) | \(4\) | \(2\) | \(1\) |
402
New Number: 8.39 | AESZ: | Superseeker: -12/5 136/3 | Hash: c1330764e09752f7bb8e86b15541c588
Degree: 8
\(5^{2} \theta^4+2 3 5 x\left(51\theta^4+84\theta^3+72\theta^2+30\theta+5\right)+2^{2} 3 x^{2}\left(3297\theta^4+10236\theta^3+13562\theta^2+8110\theta+1830\right)+2^{2} 3^{3} x^{3}\left(3866\theta^4+14088\theta^3+21137\theta^2+14355\theta+3600\right)+2^{3} 3^{3} x^{4}\left(11680\theta^4+38792\theta^3+45641\theta^2+24205\theta+4854\right)+2^{4} 3^{5} x^{5}\left(2624\theta^4+8240\theta^3+8275\theta^2+2971\theta+216\right)+2^{5} 3^{5} x^{6}\left(3248\theta^4+8832\theta^3+9739\theta^2+4803\theta+882\right)+2^{7} 3^{7} x^{7}\left(144\theta^4+384\theta^3+428\theta^2+233\theta+51\right)+2^{9} 3^{7} x^{8}(4\theta+3)(\theta+1)^2(4\theta+5)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -6, 54, -348, -3690, ... --> OEIS Normalized instanton numbers (n0=1): -12/5, -21/5, 136/3, -1743/10, -1056/5, ... ; Common denominator:...
\((1+54z+1152z^2+6048z^3+3456z^4)(5+18z+72z^2)^2\)
| ≈\(-1.540068\) | ≈\(-0.152177\) | \(-\frac{ 1}{ 8}-\frac{ 1}{ 24}\sqrt{ 31}I\) | \(-\frac{ 1}{ 8}+\frac{ 1}{ 24}\sqrt{ 31}I\) | ≈\(-0.028878\) | ≈\(-0.028878\) | \(0\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 3}{ 4}\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(3\) | \(3\) | \(1\) | \(1\) | \(0\) | \(1\) |
| \(2\) | \(2\) | \(4\) | \(4\) | \(2\) | \(2\) | \(0\) | \(\frac{ 5}{ 4}\) |
403
New Number: 8.3 | AESZ: 105 | Superseeker: 8 -104 | Hash: 7b27135451cf2016217211c633b7ab83
Degree: 8
\(\theta^4-2^{2} x(3\theta^2+3\theta+1)(7\theta^2+7\theta+2)+2^{5} 3 x^{2}\left(15\theta^4+28\theta^3+39\theta^2+22\theta+4\right)-2^{10} x^{3}\left(21\theta^4-126\theta^3-386\theta^2-291\theta-76\right)+2^{14} x^{4}\left(37\theta^4+74\theta^3+50\theta^2+13\theta+6\right)+2^{18} x^{5}\left(21\theta^4+210\theta^3+118\theta^2-19\theta-24\right)+2^{21} 3 x^{6}\left(15\theta^4+32\theta^3+45\theta^2+32\theta+8\right)+2^{26} x^{7}(3\theta^2+3\theta+1)(7\theta^2+7\theta+2)+2^{32} x^{8}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 8, 200, 6272, 233896, ... --> OEIS Normalized instanton numbers (n0=1): 8, 71/2, -104, 4202, 50112, ... ; Common denominator:...
\((8z+1)(64z-1)(4z+1)(32z-1)(1+256z^2)^2\)
| \(-\frac{ 1}{ 4}\) | \(-\frac{ 1}{ 8}\) | \(0-\frac{ 1}{ 16}I\) | \(0\) | \(0+\frac{ 1}{ 16}I\) | \(\frac{ 1}{ 64}\) | \(\frac{ 1}{ 32}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(1\) | \(1\) | \(3\) | \(0\) | \(3\) | \(1\) | \(1\) | \(1\) |
| \(2\) | \(2\) | \(4\) | \(0\) | \(4\) | \(2\) | \(2\) | \(1\) |
404
New Number: 8.40 | AESZ: | Superseeker: 5/4 35/2 | Hash: d3cb0fbbc65d6c5dace733d3d1ca181b
Degree: 8
\(2^{4} \theta^4-2^{2} x\theta(2\theta^3+82\theta^2+53\theta+12)-x^{2}\left(4895\theta^4+18410\theta^3+26199\theta^2+18308\theta+5120\right)-x^{3}\left(60679\theta^4+272424\theta^3+497452\theta^2+430092\theta+143808\right)-x^{4}\left(344527\theta^4+1870838\theta^3+4034628\theta^2+3987101\theta+1478544\right)-x^{5}(\theta+1)(1076509\theta^3+5847783\theta^2+11226106\theta+7492832)-2 x^{6}(\theta+1)(\theta+2)(944887\theta^2+4249317\theta+5045304)-2^{8} 13 x^{7}(\theta+3)(\theta+2)(\theta+1)(518\theta+1381)-2^{5} 5 13^{2} 23 x^{8}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, 20, 168, 2652, ... --> OEIS Normalized instanton numbers (n0=1): 5/4, 57/16, 35/2, 459/4, 3615/4, ... ; Common denominator:...
\(-(23z-1)(5z+1)(2z+1)(z+1)(13z+4)^2(4z+1)^2\)
| \(-1\) | \(-\frac{ 1}{ 2}\) | \(-\frac{ 4}{ 13}\) | \(-\frac{ 1}{ 4}\) | \(-\frac{ 1}{ 5}\) | \(0\) | \(\frac{ 1}{ 23}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(\frac{ 1}{ 3}\) | \(1\) | \(0\) | \(1\) | \(2\) |
| \(1\) | \(1\) | \(3\) | \(\frac{ 2}{ 3}\) | \(1\) | \(0\) | \(1\) | \(3\) |
| \(2\) | \(2\) | \(4\) | \(1\) | \(2\) | \(0\) | \(2\) | \(4\) |
405
New Number: 8.41 | AESZ: | Superseeker: 16 7568/3 | Hash: 051d7068f49d14c45c3c3369d63d56b5
Degree: 8
\(3^{2} \theta^4-2^{2} 3^{2} x\left(23\theta^4+58\theta^3+44\theta^2+15\theta+2\right)-2^{5} 3 x^{2}\left(254\theta^4+662\theta^3+623\theta^2+309\theta+66\right)-2^{8} 3 x^{3}\left(569\theta^4+1092\theta^3+602\theta^2+285\theta+78\right)-2^{11} x^{4}\left(2266\theta^4+4076\theta^3+2167\theta^2+537\theta+18\right)-2^{16} x^{5}\left(519\theta^4+798\theta^3+821\theta^2+391\theta+62\right)-2^{19} x^{6}\left(305\theta^4+558\theta^3+625\theta^2+360\theta+82\right)-2^{24} x^{7}\left(26\theta^4+70\theta^3+83\theta^2+48\theta+11\right)-2^{29} x^{8}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 8, 328, 18944, 1324456, ... --> OEIS Normalized instanton numbers (n0=1): 16, 751/6, 7568/3, 229516/3, 8099456/3, ... ; Common denominator:...
\(-(4z+1)(2048z^3+768z^2+112z-1)(3+24z+256z^2)^2\)
| \(-\frac{ 1}{ 4}\) | ≈\(-0.191715-0.145483I\) | ≈\(-0.191715+0.145483I\) | \(-\frac{ 3}{ 64}-\frac{ 1}{ 64}\sqrt{ 39}I\) | \(-\frac{ 3}{ 64}+\frac{ 1}{ 64}\sqrt{ 39}I\) | \(0\) | ≈\(0.00843\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(3\) | \(3\) | \(0\) | \(1\) | \(1\) |
| \(2\) | \(2\) | \(2\) | \(4\) | \(4\) | \(0\) | \(2\) | \(1\) |
406
New Number: 8.42 | AESZ: | Superseeker: -4 140 | Hash: 7bc3855c04953ca11620400320722844
Degree: 8
\(\theta^4+2^{2} x\left(26\theta^4+34\theta^3+29\theta^2+12\theta+2\right)+2^{4} x^{2}\left(305\theta^4+662\theta^3+781\theta^2+436\theta+94\right)+2^{8} x^{3}\left(519\theta^4+1278\theta^3+1541\theta^2+933\theta+213\right)+2^{10} x^{4}\left(2266\theta^4+4988\theta^3+3535\theta^2+633\theta-162\right)+2^{14} 3 x^{5}\left(569\theta^4+1184\theta^3+740\theta^2-81\theta-128\right)+2^{18} 3 x^{6}\left(254\theta^4+354\theta^3+161\theta^2-33\theta-28\right)+2^{22} 3^{2} x^{7}\left(23\theta^4+34\theta^3+8\theta^2-9\theta-4\right)-2^{27} 3^{2} x^{8}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -8, 112, -1664, 23056, ... --> OEIS Normalized instanton numbers (n0=1): -4, 1/2, 140, 1025/2, -9196, ... ; Common denominator:...
\(-(32z+1)(1024z^3-896z^2-48z-1)(1+12z+192z^2)^2\)
| \(-\frac{ 1}{ 32}-\frac{ 1}{ 96}\sqrt{ 39}I\) | \(-\frac{ 1}{ 32}\) | \(-\frac{ 1}{ 32}+\frac{ 1}{ 96}\sqrt{ 39}I\) | ≈\(-0.025859-0.019623I\) | ≈\(-0.025859+0.019623I\) | \(0\) | ≈\(0.926719\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) |
| \(3\) | \(1\) | \(3\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) |
| \(4\) | \(2\) | \(4\) | \(2\) | \(2\) | \(0\) | \(2\) | \(1\) |
407
New Number: 8.43 | AESZ: | Superseeker: 66/7 8716/7 | Hash: 923554dba37f79c41bf0f67b875c36f7
Degree: 8
\(7^{2} \theta^4-2 7 x\left(452\theta^4+640\theta^3+509\theta^2+189\theta+28\right)+2^{2} x^{2}\left(47156\theta^4+78224\theta^3+63963\theta^2+31010\theta+7000\right)-2^{5} x^{3}\left(77224\theta^4+150936\theta^3+155876\theta^2+86751\theta+19838\right)+2^{8} x^{4}\left(65988\theta^4+160584\theta^3+193653\theta^2+117501\theta+28198\right)-2^{12} x^{5}\left(15712\theta^4+46888\theta^3+63382\theta^2+41163\theta+10338\right)+2^{16} x^{6}\left(2088\theta^4+7272\theta^3+10589\theta^2+7140\theta+1828\right)-2^{22} x^{7}\left(36\theta^4+138\theta^3+206\theta^2+137\theta+34\right)+2^{26} x^{8}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 8, 224, 10016, 547936, ... --> OEIS Normalized instanton numbers (n0=1): 66/7, 573/7, 8716/7, 197852/7, 5617614/7, ... ; Common denominator:...
\((1-96z+256z^2)(4z-1)^2(128z^2-88z+7)^2\)
| \(0\) | \(\frac{ 3}{ 16}-\frac{ 1}{ 8}\sqrt{ 2}\) | \(\frac{ 11}{ 32}-\frac{ 1}{ 32}\sqrt{ 65}\) | \(\frac{ 1}{ 4}\) | \(\frac{ 3}{ 16}+\frac{ 1}{ 8}\sqrt{ 2}\) | \(\frac{ 11}{ 32}+\frac{ 1}{ 32}\sqrt{ 65}\) | \(\infty\) |
|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(0\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(1\) |
| \(0\) | \(1\) | \(3\) | \(\frac{ 1}{ 2}\) | \(1\) | \(3\) | \(1\) |
| \(0\) | \(2\) | \(4\) | \(1\) | \(2\) | \(4\) | \(1\) |
408
New Number: 8.44 | AESZ: | Superseeker: -64 -131904 | Hash: 2d570a3dc1cbc5b6596272f33b48fc98
Degree: 8
\(\theta^4-2^{5} x\left(36\theta^4+6\theta^3+8\theta^2+5\theta+1\right)+2^{8} x^{2}\left(2088\theta^4+1080\theta^3+1301\theta^2+574\theta+93\right)-2^{13} x^{3}\left(15712\theta^4+15960\theta^3+16990\theta^2+7785\theta+1381\right)+2^{18} x^{4}\left(65988\theta^4+103368\theta^3+107829\theta^2+52005\theta+9754\right)-2^{24} x^{5}\left(77224\theta^4+157960\theta^3+166412\theta^2+81089\theta+15251\right)+2^{30} x^{6}\left(47156\theta^4+110400\theta^3+112227\theta^2+50868\theta+8885\right)-2^{38} 7 x^{7}\left(452\theta^4+1168\theta^3+1301\theta^2+717\theta+160\right)+2^{46} 7^{2} x^{8}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 32, 2096, 172544, 15870736, ... --> OEIS Normalized instanton numbers (n0=1): -64, -2084, -131904, -10745878, -1015115456, ... ; Common denominator:...
\((1-192z+1024z^2)(128z-1)^2(14336z^2-352z+1)^2\)
| \(0\) | \(\frac{ 11}{ 896}-\frac{ 1}{ 896}\sqrt{ 65}\) | \(\frac{ 3}{ 32}-\frac{ 1}{ 16}\sqrt{ 2}\) | \(\frac{ 1}{ 128}\) | \(\frac{ 11}{ 896}+\frac{ 1}{ 896}\sqrt{ 65}\) | \(\frac{ 3}{ 32}+\frac{ 1}{ 16}\sqrt{ 2}\) | \(\infty\) |
|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(0\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(1\) |
| \(0\) | \(3\) | \(1\) | \(\frac{ 1}{ 2}\) | \(3\) | \(1\) | \(1\) |
| \(0\) | \(4\) | \(2\) | \(1\) | \(4\) | \(2\) | \(1\) |
409
New Number: 8.45 | AESZ: | Superseeker: -12/5 -20 | Hash: 52e4f6959f297529016ddef66a399c12
Degree: 8
\(5^{2} \theta^4+2^{2} 5 x\left(19\theta^4+86\theta^3+73\theta^2+30\theta+5\right)+2^{4} x^{2}\left(709\theta^4+4252\theta^3+7339\theta^2+4830\theta+1165\right)-2^{8} x^{3}\left(420\theta^4+114\theta^3-3294\theta^2-3960\theta-1325\right)-2^{10} x^{4}\left(949\theta^4+6782\theta^3+11350\theta^2+7719\theta+1889\right)+2^{12} x^{5}\left(1315\theta^4+4282\theta^3+7199\theta^2+5744\theta+1691\right)+2^{14} x^{6}\left(613\theta^4+1560\theta^3+973\theta^2-216\theta-249\right)+2^{18} x^{7}\left(11\theta^4-2\theta^3-40\theta^2-39\theta-11\right)-2^{20} x^{8}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -4, -4, 464, -4244, ... --> OEIS Normalized instanton numbers (n0=1): -12/5, -83/5, -20, 3941/20, -13872/5, ... ; Common denominator:...
\(-(8z+1)(128z^3-624z^2-20z-1)(-5+32z+32z^2)^2\)
| \(-\frac{ 1}{ 2}-\frac{ 1}{ 8}\sqrt{ 26}\) | \(-\frac{ 1}{ 8}\) | ≈\(-0.016083-0.036516I\) | ≈\(-0.016083+0.036516I\) | \(0\) | \(-\frac{ 1}{ 2}+\frac{ 1}{ 8}\sqrt{ 26}\) | ≈\(4.907166\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) |
| \(3\) | \(1\) | \(1\) | \(1\) | \(0\) | \(3\) | \(1\) | \(1\) |
| \(4\) | \(2\) | \(2\) | \(2\) | \(0\) | \(4\) | \(2\) | \(1\) |
410
New Number: 8.46 | AESZ: | Superseeker: 192 616896 | Hash: e38642e59fc2f9e3117437fcdbfe450e
Degree: 8
\(\theta^4-2^{5} x\left(11\theta^4+46\theta^3+32\theta^2+9\theta+1\right)-2^{8} x^{2}\left(613\theta^4+892\theta^3-29\theta^2-66\theta-7\right)-2^{13} x^{3}\left(1315\theta^4+978\theta^3+2243\theta^2+1068\theta+179\right)+2^{18} x^{4}\left(949\theta^4-2986\theta^3-3302\theta^2-1569\theta-313\right)+2^{23} x^{5}\left(420\theta^4+1566\theta^3-1116\theta^2-1290\theta-353\right)-2^{26} x^{6}\left(709\theta^4-1416\theta^3-1163\theta^2-72\theta+131\right)-2^{31} 5 x^{7}\left(19\theta^4-10\theta^3-71\theta^2-66\theta-19\right)-2^{36} 5^{2} x^{8}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 32, 6224, 1859072, 679223056, ... --> OEIS Normalized instanton numbers (n0=1): 192, 3108, 616896, 73692781, 15330708544, ... ; Common denominator:...
\(-(16z+1)(16384z^3+2560z^2+624z-1)(-1-128z+2560z^2)^2\)
| ≈\(-0.078921-0.179189I\) | ≈\(-0.078921+0.179189I\) | \(-\frac{ 1}{ 16}\) | \(\frac{ 1}{ 40}-\frac{ 1}{ 160}\sqrt{ 26}\) | \(0\) | ≈\(0.001592\) | \(\frac{ 1}{ 40}+\frac{ 1}{ 160}\sqrt{ 26}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(3\) | \(0\) | \(1\) | \(3\) | \(1\) |
| \(2\) | \(2\) | \(2\) | \(4\) | \(0\) | \(2\) | \(4\) | \(1\) |
411
New Number: 8.47 | AESZ: | Superseeker: 31/3 43174/9 | Hash: b79bf25fcecf028aa40c1a6a8233efe7
Degree: 8
\(3^{4} \theta^4-3^{3} x\left(367\theta^4+398\theta^3+295\theta^2+96\theta+12\right)-2^{4} 3^{3} x^{2}\left(200\theta^4+2081\theta^3+3614\theta^2+2009\theta+392\right)+2^{6} 3 x^{3}\left(72449\theta^4+102684\theta^3-48579\theta^2-77922\theta-22536\right)+2^{10} x^{4}\left(109873\theta^4+619970\theta^3+56260\theta^2-219027\theta-78216\right)-2^{14} 7 x^{5}\left(40669\theta^4-18266\theta^3-36570\theta^2-16190\theta-1955\right)-2^{17} 7 x^{6}\left(80805\theta^4+76590\theta^3+51265\theta^2+23076\theta+4780\right)-2^{24} 7^{2} x^{7}\left(437\theta^4+1117\theta^3+1236\theta^2+664\theta+140\right)-2^{29} 3 7^{2} x^{8}(\theta+1)^2(3\theta+2)(3\theta+4)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 4, 228, 12640, 901540, ... --> OEIS Normalized instanton numbers (n0=1): 31/3, 1964/9, 43174/9, 1469755/9, 19813517/3, ... ; Common denominator:...
\(-(27z+1)(2048z^3+768z^2+112z-1)(-9+168z+3584z^2)^2\)
| ≈\(-0.191715-0.145483I\) | ≈\(-0.191715+0.145483I\) | \(-\frac{ 3}{ 128}-\frac{ 3}{ 896}\sqrt{ 273}\) | \(-\frac{ 1}{ 27}\) | \(0\) | ≈\(0.00843\) | \(-\frac{ 3}{ 128}+\frac{ 3}{ 896}\sqrt{ 273}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 2}{ 3}\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) |
| \(1\) | \(1\) | \(3\) | \(1\) | \(0\) | \(1\) | \(3\) | \(1\) |
| \(2\) | \(2\) | \(4\) | \(2\) | \(0\) | \(2\) | \(4\) | \(\frac{ 4}{ 3}\) |
412
New Number: 8.48 | AESZ: | Superseeker: 359/13 393749/13 | Hash: de7301c14448dbf584c01cc3722d0e58
Degree: 8
\(13^{2} \theta^4-13 x\left(5249\theta^4+4930\theta^3+3687\theta^2+1222\theta+156\right)+2^{4} 3 x^{2}\left(175601\theta^4+188064\theta^3+90243\theta^2+19422\theta+1547\right)-2^{7} x^{3}\left(3336915\theta^4+3777024\theta^3+2377229\theta^2+746148\theta+94185\right)+2^{10} x^{4}\left(8591694\theta^4+11872968\theta^3+7381951\theta^2+2132674\theta+236280\right)-2^{12} x^{5}\left(15421829\theta^4+18326342\theta^3+7032841\theta^2+833608\theta-2718\right)+2^{16} 3^{2} x^{6}\left(334895\theta^4+615600\theta^3+867965\theta^2+590850\theta+138536\right)-2^{19} 3^{4} 7 x^{7}(\theta+1)(2\theta+1)(646\theta^2+1715\theta+1044)+2^{22} 3^{6} 7^{2} x^{8}(2\theta+1)(\theta+1)^2(2\theta+3)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 12, 852, 94800, 12860820, ... --> OEIS Normalized instanton numbers (n0=1): 359/13, 9162/13, 393749/13, 23364200/13, 1734245216/13, ... ; Common denominator:...
\((1-261z+6896z^2-6656z^3+36864z^4)(13-928z+4032z^2)^2\)
| \(0\) | \(\frac{ 29}{ 252}-\frac{ 1}{ 504}\sqrt{ 2545}\) | \(\frac{ 29}{ 252}+\frac{ 1}{ 504}\sqrt{ 2545}\) | \(#ND+#NDI\) | \(\infty\) |
|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(0\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(0\) | \(3\) | \(3\) | \(1\) | \(1\) |
| \(0\) | \(4\) | \(4\) | \(2\) | \(\frac{ 3}{ 2}\) |
413
New Number: 8.49 | AESZ: | Superseeker: 56/3 17704/3 | Hash: 4fa01cbee2fc74e3a62e00386e6fa1c0
Degree: 8
\(3^{2} \theta^4-2^{2} 3 x\left(29\theta^4+178\theta^3+134\theta^2+45\theta+6\right)-2^{5} x^{2}\left(2233\theta^4+2536\theta^3+607\theta^2+132\theta+12\right)-2^{10} x^{3}\left(1274\theta^4+7425\theta^3+20002\theta^2+12717\theta+2670\right)+2^{13} x^{4}\left(2539\theta^4-36538\theta^3-52775\theta^2-31122\theta-6192\right)+2^{20} x^{5}\left(1617\theta^4+9771\theta^3+4484\theta^2-674\theta-556\right)+2^{25} x^{6}\left(1135\theta^4+4272\theta^3+3439\theta^2+858\theta+16\right)-2^{31} 3 x^{7}(2\theta+1)(110\theta^3+225\theta^2+184\theta+57)+2^{37} 3^{2} x^{8}(2\theta+1)(\theta+1)^2(2\theta+3)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 8, 264, 16640, 1130920, ... --> OEIS Normalized instanton numbers (n0=1): 56/3, -83/6, 17704/3, -25024/3, 13408832/3, ... ; Common denominator:...
\((4z-1)(131072z^3+2048z^2+88z-1)(48z+1)^2(64z-3)^2\)
| \(-\frac{ 1}{ 48}\) | ≈\(-0.01214-0.027095I\) | ≈\(-0.01214+0.027095I\) | \(0\) | ≈\(0.008655\) | \(\frac{ 3}{ 64}\) | \(\frac{ 1}{ 4}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(3\) | \(1\) | \(1\) | \(0\) | \(1\) | \(3\) | \(1\) | \(1\) |
| \(4\) | \(2\) | \(2\) | \(0\) | \(2\) | \(4\) | \(2\) | \(\frac{ 3}{ 2}\) |
414
New Number: 8.4 | AESZ: 160 | Superseeker: 6 -325 | Hash: 8ce8667fe6e49ce6625fafe044b1641b
Degree: 8
\(\theta^4-3 x(3\theta^2+3\theta+1)(7\theta^2+7\theta+2)+3^{2} x^{2}\left(171\theta^4+396\theta^3+555\theta^2+318\theta+64\right)-2^{3} 3^{4} x^{3}\left(21\theta^4-126\theta^3-386\theta^2-291\theta-76\right)+2^{4} 3^{5} x^{4}\left(147\theta^4+294\theta^3+102\theta^2-45\theta-14\right)+2^{6} 3^{7} x^{5}\left(21\theta^4+210\theta^3+118\theta^2-19\theta-24\right)+2^{6} 3^{8} x^{6}\left(171\theta^4+288\theta^3+393\theta^2+288\theta+76\right)+2^{9} 3^{10} x^{7}(3\theta^2+3\theta+1)(7\theta^2+7\theta+2)+2^{12} 3^{12} x^{8}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 6, 90, 1176, 3114, ... --> OEIS Normalized instanton numbers (n0=1): 6, 6, -325, -1977/2, -5421, ... ; Common denominator:...
\((27z^2+9z+1)(1728z^2-72z+1)(1+216z^2)^2\)
| \(-\frac{ 1}{ 6}-\frac{ 1}{ 18}\sqrt{ 3}I\) | \(-\frac{ 1}{ 6}+\frac{ 1}{ 18}\sqrt{ 3}I\) | \(0-\frac{ 1}{ 36}\sqrt{ 6}I\) | \(0\) | \(0+\frac{ 1}{ 36}\sqrt{ 6}I\) | \(\frac{ 1}{ 48}-\frac{ 1}{ 144}\sqrt{ 3}I\) | \(\frac{ 1}{ 48}+\frac{ 1}{ 144}\sqrt{ 3}I\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(1\) | \(1\) | \(3\) | \(0\) | \(3\) | \(1\) | \(1\) | \(1\) |
| \(2\) | \(2\) | \(4\) | \(0\) | \(4\) | \(2\) | \(2\) | \(1\) |
415
New Number: 8.50 | AESZ: | Superseeker: 2/23 27/23 | Hash: 68499833fa99ef8841a3d64e042d4a6e
Degree: 8
\(23^{2} \theta^4-2 23 x\theta^2(136\theta^2+2\theta+1)-2^{2} x^{2}\left(7589\theta^4+54926\theta^3+89975\theta^2+69828\theta+21160\right)+x^{3}\left(573259\theta^4+2342274\theta^3+3791849\theta^2+3070914\theta+1010160\right)-2 5 x^{4}\left(122351\theta^4+62266\theta^3-795547\theta^2-1404486\theta-669744\right)-2^{3} 3 5^{2} x^{5}(\theta+1)(16105\theta^3+133047\theta^2+320040\theta+245740)+2^{4} 3^{2} 5^{3} x^{6}(\theta+1)(\theta+2)(3107\theta^2+16911\theta+22834)-2^{4} 3^{4} 5^{4} x^{7}(\theta+3)(\theta+2)(\theta+1)(133\theta+404)+2^{5} 3^{6} 5^{5} x^{8}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, 10, 0, 270, ... --> OEIS Normalized instanton numbers (n0=1): 2/23, 18/23, 27/23, 136/23, 395/23, ... ; Common denominator:...
\((3z-1)(2z-1)(10z-1)(6z+1)(25z^2-5z-1)(-23+90z)^2\)
| \(-\frac{ 1}{ 6}\) | \(\frac{ 1}{ 10}-\frac{ 1}{ 10}\sqrt{ 5}\) | \(0\) | \(\frac{ 1}{ 10}\) | \(\frac{ 23}{ 90}\) | \(\frac{ 1}{ 10}+\frac{ 1}{ 10}\sqrt{ 5}\) | \(\frac{ 1}{ 3}\) | \(\frac{ 1}{ 2}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(2\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(3\) | \(1\) | \(1\) | \(1\) | \(3\) |
| \(2\) | \(2\) | \(0\) | \(2\) | \(4\) | \(2\) | \(2\) | \(2\) | \(4\) |
416
New Number: 8.51 | AESZ: | Superseeker: 58/43 1024/43 | Hash: 85b9064701880ae8e0518e47cff1b030
Degree: 8
\(43^{2} \theta^4-43 x\theta(142\theta^3+890\theta^2+574\theta+129)-x^{2}\left(647269\theta^4+2441818\theta^3+3538503\theta^2+2423953\theta+650848\right)-x^{3}\left(7200000\theta^4+34423908\theta^3+65337898\theta^2+57379329\theta+19251960\right)-x^{4}\left(37610765\theta^4+220029964\theta^3+499781264\theta^2+511393545\theta+194039928\right)-2 x^{5}(\theta+1)(54978121\theta^3+324737370\theta^2+665066226\theta+466789876)-x^{6}(\theta+1)(\theta+2)(185181547\theta^2+915931425\theta+1176131796)-2^{2} 3 101 x^{7}(\theta+3)(\theta+2)(\theta+1)(138979\theta+413408)-2^{2} 3^{2} 5^{2} 7 101^{2} x^{8}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, 22, 204, 3474, ... --> OEIS Normalized instanton numbers (n0=1): 58/43, 211/43, 1024/43, 7544/43, 64880/43, ... ; Common denominator:...
\(-(7z+1)(25z-1)(2z+1)^2(101z+43)^2(3z+1)^2\)
| \(-\frac{ 1}{ 2}\) | \(-\frac{ 43}{ 101}\) | \(-\frac{ 1}{ 3}\) | \(-\frac{ 1}{ 7}\) | \(0\) | \(\frac{ 1}{ 25}\) | \(\infty\) |
|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(\frac{ 1}{ 3}\) | \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(0\) | \(1\) | \(2\) |
| \(\frac{ 2}{ 3}\) | \(3\) | \(\frac{ 1}{ 2}\) | \(1\) | \(0\) | \(1\) | \(3\) |
| \(1\) | \(4\) | \(1\) | \(2\) | \(0\) | \(2\) | \(4\) |
417
New Number: 8.52 | AESZ: | Superseeker: 416 9734432 | Hash: 87729f275f24cb2daf88133571476576
Degree: 8
\(\theta^4+2^{4} x\left(176\theta^4-32\theta^3+4\theta^2+20\theta+5\right)+2^{12} x^{2}\left(640\theta^4+256\theta^3+680\theta^2+224\theta+27\right)+2^{22} x^{3}\left(220\theta^4+648\theta^3+596\theta^2+348\theta+85\right)+2^{30} x^{4}\left(116\theta^4+1024\theta^3+1608\theta^2+1072\theta+281\right)-2^{38} x^{5}\left(32\theta^4-448\theta^3-1588\theta^2-1404\theta-437\right)-2^{46} x^{6}\left(80\theta^4+288\theta^3-88\theta^2-384\theta-179\right)-2^{57} x^{7}\left(2\theta^4+28\theta^3+56\theta^2+42\theta+11\right)+2^{66} x^{8}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -80, 6928, -597248, 95243536, ... --> OEIS Normalized instanton numbers (n0=1): 416, -52752, 9734432, -2404009688, 687625871328, ... ; Common denominator:...
\((1+256z+65536z^2)(256z+1)^2(131072z^2-1024z-1)^2\)
| \(-\frac{ 1}{ 256}\) | \(-\frac{ 1}{ 512}-\frac{ 1}{ 512}\sqrt{ 3}I\) | \(-\frac{ 1}{ 512}+\frac{ 1}{ 512}\sqrt{ 3}I\) | \(\frac{ 1}{ 256}-\frac{ 1}{ 512}\sqrt{ 6}\) | \(0\) | \(\frac{ 1}{ 256}+\frac{ 1}{ 512}\sqrt{ 6}\) | \(\infty\) |
|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) |
| \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(3\) | \(0\) | \(3\) | \(1\) |
| \(1\) | \(2\) | \(2\) | \(4\) | \(0\) | \(4\) | \(1\) |
418
New Number: 8.53 | AESZ: | Superseeker: -64 -64320 | Hash: 0714a480e1c587ebada71771f7e3b555
Degree: 8
\(\theta^4-2^{5} x\left(2\theta^4-20\theta^3-16\theta^2-6\theta-1\right)-2^{8} x^{2}\left(80\theta^4+32\theta^3-472\theta^2-336\theta-91\right)-2^{14} x^{3}\left(32\theta^4+576\theta^3-52\theta^2-300\theta-141\right)+2^{20} x^{4}\left(116\theta^4-560\theta^3-768\theta^2-464\theta-91\right)+2^{26} x^{5}\left(220\theta^4+232\theta^3-28\theta^2-220\theta-95\right)+2^{30} x^{6}\left(640\theta^4+2304\theta^3+3752\theta^2+2928\theta+867\right)+2^{36} x^{7}\left(176\theta^4+736\theta^3+1156\theta^2+788\theta+197\right)+2^{46} x^{8}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -32, 1168, -43520, 1777936, ... --> OEIS Normalized instanton numbers (n0=1): -64, -1604, -64320, -3255802, -191614656, ... ; Common denominator:...
\((1+64z+4096z^2)(64z+1)^2(2048z^2+128z-1)^2\)
| \(-\frac{ 1}{ 32}-\frac{ 1}{ 64}\sqrt{ 6}\) | \(-\frac{ 1}{ 64}\) | \(-\frac{ 1}{ 128}-\frac{ 1}{ 128}\sqrt{ 3}I\) | \(-\frac{ 1}{ 128}+\frac{ 1}{ 128}\sqrt{ 3}I\) | \(0\) | \(-\frac{ 1}{ 32}+\frac{ 1}{ 64}\sqrt{ 6}\) | \(\infty\) |
|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) |
| \(3\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(0\) | \(3\) | \(1\) |
| \(4\) | \(1\) | \(2\) | \(2\) | \(0\) | \(4\) | \(1\) |
419
New Number: 8.54 | AESZ: | Superseeker: 0 1/3 | Hash: bb80872017d0578a4ae56172666b807c
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:...
\((4z+1)(6z+1)(43z^2+13z+1)(2z+1)^2(12z-1)^2\)
| \(-\frac{ 1}{ 2}\) | \(-\frac{ 1}{ 4}\) | \(-\frac{ 1}{ 6}\) | \(-\frac{ 13}{ 86}-\frac{ 1}{ 86}\sqrt{ 3}I\) | \(-\frac{ 13}{ 86}+\frac{ 1}{ 86}\sqrt{ 3}I\) | \(0\) | \(\frac{ 1}{ 12}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(\frac{ 1}{ 2}\) | \(2\) |
| \(3\) | \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(\frac{ 1}{ 2}\) | \(3\) |
| \(4\) | \(2\) | \(2\) | \(2\) | \(2\) | \(0\) | \(1\) | \(4\) |
420
New Number: 8.55 | AESZ: | Superseeker: 1 68/9 | Hash: 39ed8ce7572bc79a333f77c892033bcf
Degree: 8
\(\theta^4-x\left(33\theta^4+98\theta^3+105\theta^2+56\theta+12\right)+2^{3} x^{2}\left(34\theta^4+276\theta^3+609\theta^2+582\theta+216\right)+2^{4} 3 x^{3}\left(11\theta^4-170\theta^3-941\theta^2-1520\theta-846\right)-2^{7} 3^{2} x^{4}(2\theta^2+6\theta+5)(4\theta^2+12\theta-31)+2^{8} 3 x^{5}\left(11\theta^4+302\theta^3+1183\theta^2+1652\theta+726\right)+2^{11} x^{6}\left(34\theta^4+132\theta^3-39\theta^2-708\theta-747\right)-2^{12} x^{7}\left(33\theta^4+298\theta^3+1005\theta^2+1492\theta+816\right)+2^{16} x^{8}\left((\theta+3)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 12, 120, 1216, 13080, ... --> OEIS Normalized instanton numbers (n0=1): 1, -2, 68/9, -30, 150, ... ; Common denominator:...
\((z-1)(16z-1)(16z^2-16z+1)(4z-1)^2(4z+1)^2\)
| \(-\frac{ 1}{ 4}\) | \(0\) | \(\frac{ 1}{ 16}\) | \(\frac{ 1}{ 2}-\frac{ 1}{ 4}\sqrt{ 3}\) | \(\frac{ 1}{ 4}\) | \(\frac{ 1}{ 2}+\frac{ 1}{ 4}\sqrt{ 3}\) | \(1\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(3\) |
| \(1\) | \(0\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(3\) |
| \(3\) | \(0\) | \(1\) | \(1\) | \(-1\) | \(1\) | \(1\) | \(3\) |
| \(4\) | \(0\) | \(2\) | \(2\) | \(1\) | \(2\) | \(2\) | \(3\) |