1
New Number: 11.10 | AESZ: | Superseeker: 307/31 30366/31 | Hash: 4af67003a52ef978f182204bfaff3b67
Degree: 11
\(31^{2} \theta^4-31 x\theta(37\theta^3+3404\theta^2+2167\theta+465)-x^{2}\left(3584242\theta^4+13193680\theta^3+15543050\theta^2+9592175\theta+2490912\right)-3^{2} x^{3}\left(19107317\theta^4+73205086\theta^3+112285993\theta^2+86123611\theta+26445852\right)-3 x^{4}\left(1372729742\theta^4+6047894734\theta^3+11016338393\theta^2+9650491725\theta+3283335324\right)-x^{5}\left(61079790533\theta^4+312026249948\theta^3+649293087145\theta^2+630130831252\theta+231606447564\right)-2 3^{2} x^{6}\left(33534165907\theta^4+196973375042\theta^3+458528416805\theta^2+484791515686\theta+189712671726\right)-3^{2} 7 x^{7}\left(64606565117\theta^4+431259053450\theta^3+1107908854519\theta^2+1261805762830\theta+520567245048\right)-3^{4} 7^{2} x^{8}(\theta+1)(4683541363\theta^3+30431977551\theta^2+68128269606\theta+51768680224)-2^{2} 3^{3} 7^{3} x^{9}(\theta+1)(\theta+2)(1489780280\theta^2+7942046183\theta+10944040794)-2^{2} 3^{4} 7^{4} 53 x^{10}(\theta+3)(\theta+2)(\theta+1)(2336627\theta+7400894)-2^{5} 3^{3} 7^{5} 19 53^{2} 97 x^{11}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, 162, 5472, 282366, ... --> OEIS Normalized instanton numbers (n0=1): 307/31, 1814/31, 30366/31, 639686/31, 17126962/31, ... ; Common denominator:...
\(-(8z+1)(679z^2+74z-1)(57z^2+15z+1)(7z+1)^2(2226z^2+555z+31)^2\)
| \(-\frac{ 185}{ 1484}-\frac{ 1}{ 4452}\sqrt{ 32001}\) | \(-\frac{ 1}{ 7}\) | \(-\frac{ 5}{ 38}-\frac{ 1}{ 114}\sqrt{ 3}I\) | \(-\frac{ 5}{ 38}+\frac{ 1}{ 114}\sqrt{ 3}I\) | \(-\frac{ 1}{ 8}\) | \(-\frac{ 37}{ 679}-\frac{ 32}{ 679}\sqrt{ 2}\) | \(-\frac{ 185}{ 1484}+\frac{ 1}{ 4452}\sqrt{ 32001}\) | \(0\) | \(-\frac{ 37}{ 679}+\frac{ 32}{ 679}\sqrt{ 2}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(2\) |
| \(3\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(1\) | \(1\) | \(3\) | \(0\) | \(1\) | \(3\) |
| \(4\) | \(1\) | \(2\) | \(2\) | \(2\) | \(2\) | \(4\) | \(0\) | \(2\) | \(4\) |
2
New Number: 11.11 | AESZ: | Superseeker: 256/31 28062/31 | Hash: dbd551a4eb6b44b1575c949fe3158ad8
Degree: 11
\(31^{2} \theta^4-31 x\theta(790\theta^3+2930\theta^2+1868\theta+403)-x^{2}\left(2814085\theta^4+9964954\theta^3+13382605\theta^2+8541027\theta+2183392\right)-x^{3}\left(77649704\theta^4+350426364\theta^3+626329390\theta^2+517109481\theta+165295596\right)-x^{4}\left(1130950485\theta^4+6282081612\theta^3+13577302372\theta^2+13176194701\theta+4791500140\right)-2 x^{5}\left(5087102169\theta^4+33490353027\theta^3+83662730413\theta^2+91498335797\theta+36413643210\right)-x^{6}\left(59691820411\theta^4+451633384578\theta^3+1266886011283\theta^2+1521913712448\theta+648339514868\right)-2^{2} x^{7}\left(57682690343\theta^4+488627614012\theta^3+1504693262559\theta^2+1947925954210\theta+874695283544\right)-2^{2} x^{8}(\theta+1)(143617960931\theta^3+1184948771451\theta^2+3211500965214\theta+2815433689448)-2^{5} x^{9}(\theta+1)(\theta+2)(27089561480\theta^2+184897066731\theta+314481835312)-2^{6} 3 7 53 x^{10}(\theta+3)(\theta+2)(\theta+1)(9822371\theta+40000042)-2^{9} 3^{2} 7^{2} 53^{2} 359 x^{11}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, 142, 4632, 227538, ... --> OEIS Normalized instanton numbers (n0=1): 256/31, 1982/31, 28062/31, 591475/31, 15400630/31, ... ; Common denominator:...
\(-(8z+1)(359z^2+74z-1)(7z+1)^2(6z+1)^2(212z^2+225z+31)^2\)
| \(-\frac{ 225}{ 424}-\frac{ 1}{ 424}\sqrt{ 24337}\) | \(-\frac{ 37}{ 359}-\frac{ 24}{ 359}\sqrt{ 3}\) | \(-\frac{ 1}{ 6}\) | \(-\frac{ 225}{ 424}+\frac{ 1}{ 424}\sqrt{ 24337}\) | \(-\frac{ 1}{ 7}\) | \(-\frac{ 1}{ 8}\) | \(0\) | \(-\frac{ 37}{ 359}+\frac{ 24}{ 359}\sqrt{ 3}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(0\) | \(1\) | \(2\) |
| \(3\) | \(1\) | \(1\) | \(3\) | \(\frac{ 1}{ 2}\) | \(1\) | \(0\) | \(1\) | \(3\) |
| \(4\) | \(2\) | \(1\) | \(4\) | \(1\) | \(2\) | \(0\) | \(2\) | \(4\) |
3
New Number: 11.12 | AESZ: | Superseeker: 226/35 3959/7 | Hash: dea88e564bf3d9a3c445795800a932fd
Degree: 11
\(5^{2} 7^{2} \theta^4-5 7 x\theta(913\theta^3+2762\theta^2+1766\theta+385)-x^{2}\left(2524749\theta^4+9069852\theta^3+12659629\theta^2+8291990\theta+2156000\right)-2 3 x^{3}\left(8810271\theta^4+42507742\theta^3+80155619\theta^2+68498780\theta+22423100\right)-2^{3} x^{4}\left(72233462\theta^4+442878292\theta^3+1027312839\theta^2+1042690171\theta+390711800\right)-2^{4} 3 x^{5}\left(78678044\theta^4+588264556\theta^3+1609189009\theta^2+1863445805\theta+769363148\right)-2^{5} x^{6}\left(472939267\theta^4+4201829760\theta^3+13245452180\theta^2+17123706057\theta+7634545706\right)-2^{6} x^{7}\left(551391703\theta^4+5765755514\theta^3+20753496824\theta^2+29644168669\theta+14122329342\right)-2^{7} x^{8}(\theta+1)(299511992\theta^3+3514696980\theta^2+12474987717\theta+12944991068)+2^{8} 3 x^{9}(\theta+1)(\theta+2)(3500769\theta^2-93979701\theta-505363628)+2^{8} 3^{5} 17 x^{10}(\theta+3)(\theta+2)(\theta+1)(25977\theta+154654)-2^{9} 3^{3} 5^{2} 17^{2} 79 x^{11}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, 110, 3084, 130914, ... --> OEIS Normalized instanton numbers (n0=1): 226/35, 1599/35, 3959/7, 51101/5, 8052703/35, ... ; Common denominator:...
\(-(-1+53z+919z^2+4792z^3+7900z^4)(34z+7)^2(2z-5)^2(6z+1)^3\)
| \(-\frac{ 7}{ 34}\) | \(-\frac{ 1}{ 6}\) | \(0\) | \(\frac{ 5}{ 2}\) | \(#ND+#NDI\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(0\) | \(0\) | \(1\) | \(1\) | \(2\) |
| \(3\) | \(0\) | \(0\) | \(3\) | \(1\) | \(3\) |
| \(4\) | \(0\) | \(0\) | \(4\) | \(2\) | \(4\) |
4
New Number: 11.2 | AESZ: | Superseeker: 136/97 1768/97 | Hash: 940a6a9fb87fe9b9613bd73b990374c1
Degree: 11
\(97^{2} \theta^4+97 x\theta(1727\theta^3-2018\theta^2-1300\theta-291)-x^{2}\left(1652135\theta^4+13428812\theta^3+16174393\theta^2+10216234\theta+2709792\right)-3 x^{3}\left(27251145\theta^4+121375398\theta^3+189546499\theta^2+147705198\theta+46000116\right)-2 x^{4}\left(587751431\theta^4+2711697232\theta^3+5003189285\theta^2+4434707760\theta+1524637512\right)-x^{5}\left(9726250397\theta^4+50507429234\theta^3+106108023451\theta^2+103964102350\theta+38537290992\right)-2 3 x^{6}\left(8793822649\theta^4+52062405804\theta^3+122175610025\theta^2+130254629814\theta+51340027968\right)-2^{2} 3^{2} x^{7}\left(5429262053\theta^4+36477756530\theta^3+94431307279\theta^2+108363704338\theta+44982230808\right)-2^{4} 3^{2} x^{8}(\theta+1)(3432647479\theta^3+22487363787\theta^2+50808614711\theta+38959393614)-2^{4} 3^{3} x^{9}(\theta+1)(\theta+2)(1903493629\theta^2+10262864555\theta+14314039440)-2^{5} 3^{4} 13^{2} x^{10}(\theta+3)(\theta+2)(\theta+1)(1862987\theta+5992902)-2^{6} 3^{3} 13^{4} 7457 x^{11}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, 18, 168, 2430, ... --> OEIS Normalized instanton numbers (n0=1): 136/97, 292/97, 1768/97, 10128/97, 83387/97, ... ; Common denominator:...
\(-(12z^2+6z+1)(7457z^5+6100z^4+1929z^3+257z^2+7z-1)(97+912z+2028z^2)^2\)
| \(-\frac{ 38}{ 169}-\frac{ 1}{ 1014}\sqrt{ 2805}\) | \(-\frac{ 1}{ 4}-\frac{ 1}{ 12}\sqrt{ 3}I\) | \(-\frac{ 1}{ 4}+\frac{ 1}{ 12}\sqrt{ 3}I\) | \(-\frac{ 38}{ 169}+\frac{ 1}{ 1014}\sqrt{ 2805}\) | \(0\) | \(#ND+#NDI\) | \(\infty\) |
|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(2\) |
| \(3\) | \(1\) | \(1\) | \(3\) | \(0\) | \(1\) | \(3\) |
| \(4\) | \(2\) | \(2\) | \(4\) | \(0\) | \(2\) | \(4\) |
5
New Number: 11.3 | AESZ: | Superseeker: 118/91 268/13 | Hash: 082df0c6e37c18b98ea10260e3e1c195
Degree: 11
\(7^{2} 13^{2} \theta^4+7 13 x\theta(782\theta^3-1874\theta^2-1210\theta-273)-x^{2}\left(2515785\theta^4+11622522\theta^3+15227939\theta^2+9962953\theta+2649920\right)-x^{3}\left(59827597\theta^4+258678126\theta^3+432607868\theta^2+348819198\theta+110445426\right)-2 x^{4}\left(306021521\theta^4+1499440609\theta^3+2950997910\theta^2+2719866190\theta+957861945\right)-3 x^{5}\left(1254280114\theta^4+7075609686\theta^3+15834414271\theta^2+16174233521\theta+6159865002\right)-x^{6}\left(15265487382\theta^4+98210309094\theta^3+244753624741\theta^2+271941545379\theta+110147546634\right)-2 x^{7}\left(21051636001\theta^4+152243816141\theta^3+415982528557\theta^2+495914741301\theta+211134581226\right)-2 x^{8}(\theta+1)(39253400626\theta^3+275108963001\theta^2+654332416678\theta+521254338620)-x^{9}(\theta+1)(\theta+2)(94987355417\theta^2+545340710193\theta+799002779040)-2^{2} 5 7 11 x^{10}(\theta+3)(\theta+2)(\theta+1)(43765159\theta+149264765)-2^{2} 3 5^{2} 7^{2} 11^{2} 11971 x^{11}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, 20, 186, 2940, ... --> OEIS Normalized instanton numbers (n0=1): 118/91, 373/91, 268/13, 12732/91, 105020/91, ... ; Common denominator:...
\(-(3z+1)(11971z^6+16085z^5+8704z^4+2334z^3+289z^2+7z-1)(91+573z+770z^2)^2\)
| \(-\frac{ 573}{ 1540}-\frac{ 1}{ 1540}\sqrt{ 48049}\) | \(-\frac{ 1}{ 3}\) | \(-\frac{ 573}{ 1540}+\frac{ 1}{ 1540}\sqrt{ 48049}\) | \(0\) | \(#ND+#NDI\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(2\) |
| \(3\) | \(1\) | \(3\) | \(0\) | \(1\) | \(3\) |
| \(4\) | \(2\) | \(4\) | \(0\) | \(2\) | \(4\) |
6
New Number: 11.6 | AESZ: | Superseeker: 95/102 1421/102 | Hash: e79a3108441c74cdc23a53a603a6181e
Degree: 11
\(2^{2} 3^{2} 17^{2} \theta^4-2 3 17 x\theta(116\theta^3+1414\theta^2+911\theta+204)-x^{2}\left(2596259\theta^4+9892670\theta^3+14508941\theta^2+9947652\theta+2663424\right)-3 x^{3}\left(8561767\theta^4+41744696\theta^3+79668236\theta^2+68977704\theta+22655832\right)-2^{2} x^{4}\left(28089475\theta^4+171762758\theta^3+396877187\theta^2+402013525\theta+149622901\right)-2 x^{5}\left(127339346\theta^4+963856934\theta^3+2636877099\theta^2+3042828449\theta+1247694978\right)-x^{6}\left(283337071\theta^4+2758627602\theta^3+9101625228\theta^2+11995897911\theta+5385015134\right)-2 x^{7}\left(43252385\theta^4+777895672\theta^3+3537873325\theta^2+5604936458\theta+2806067360\right)+2^{2} 3 x^{8}(\theta+1)(7613560\theta^3+27844427\theta^2-51849552\theta-134696600)+x^{9}(\theta+1)(\theta+2)(60585089\theta^2+495871401\theta+595115780)-2^{3} 3 5^{2} x^{10}(\theta+3)(\theta+2)(\theta+1)(10279\theta-113205)-2^{4} 5^{4} 7 97 x^{11}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, 16, 114, 1680, ... --> OEIS Normalized instanton numbers (n0=1): 95/102, 58/17, 1421/102, 1451/17, 31474/51, ... ; Common denominator:...
\(-(-1+7z+219z^2+1115z^3+1934z^4+679z^5)(z+1)^2(100z^2-197z-102)^2\)
| \(-1\) | \(\frac{ 197}{ 200}-\frac{ 1}{ 200}\sqrt{ 79609}\) | \(0\) | \(\frac{ 197}{ 200}+\frac{ 1}{ 200}\sqrt{ 79609}\) | \(#ND+#NDI\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(\frac{ 1}{ 3}\) | \(1\) | \(0\) | \(1\) | \(1\) | \(2\) |
| \(\frac{ 2}{ 3}\) | \(3\) | \(0\) | \(3\) | \(1\) | \(3\) |
| \(1\) | \(4\) | \(0\) | \(4\) | \(2\) | \(4\) |
7
New Number: 11.7 | AESZ: | Superseeker: 9 2564/3 | Hash: 3933e1482d30ea8bca1e5e5f914286e2
Degree: 11
\(\theta^4+3 x\left(60\theta^4+12\theta^3+19\theta^2+13\theta+3\right)+3^{3} x^{2}\left(463\theta^4+304\theta^3+405\theta^2+184\theta+27\right)+3^{5} x^{3}\left(1710\theta^4+2268\theta^3+2450\theta^2+1080\theta+153\right)+3^{7} x^{4}\left(2870\theta^4+5344\theta^3+4044\theta^2-188\theta-981\right)+3^{9} x^{5}\left(560\theta^4-4552\theta^3-20650\theta^2-29130\theta-13389\right)-3^{11} x^{6}\left(5114\theta^4+37440\theta^3+101098\theta^2+119700\theta+51219\right)-3^{13} x^{7}\left(6620\theta^4+48712\theta^3+130868\theta^2+152172\theta+63981\right)-3^{16} x^{8}(\theta+1)(83\theta^3-2739\theta^2-16257\theta-20563)+3^{17} x^{9}(\theta+1)(\theta+2)(4676\theta^2+42864\theta+94887)+3^{20} x^{10}(\theta+3)(\theta+2)(\theta+1)(505\theta+2522)+2 3^{23} 7 x^{11}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -9, 135, -2115, 38799, ... --> OEIS Normalized instanton numbers (n0=1): 9, -72, 2564/3, -12924, 228024, ... ; Common denominator:...
\((18z+1)(189z^2+18z+1)(27z+1)^2(9z-1)^2(81z^2+54z+1)^2\)
| \(-\frac{ 1}{ 3}-\frac{ 2}{ 9}\sqrt{ 2}\) | \(-\frac{ 1}{ 18}\) | \(-\frac{ 1}{ 21}-\frac{ 2}{ 63}\sqrt{ 3}I\) | \(-\frac{ 1}{ 21}+\frac{ 2}{ 63}\sqrt{ 3}I\) | \(-\frac{ 1}{ 27}\) | \(-\frac{ 1}{ 3}+\frac{ 2}{ 9}\sqrt{ 2}\) | \(0\) | \(\frac{ 1}{ 9}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(0\) | \(\frac{ 1}{ 2}\) | \(2\) |
| \(3\) | \(1\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(3\) | \(0\) | \(\frac{ 1}{ 2}\) | \(3\) |
| \(4\) | \(2\) | \(2\) | \(2\) | \(1\) | \(4\) | \(0\) | \(1\) | \(4\) |
8
New Number: 11.8 | AESZ: | Superseeker: 6/17 688/17 | Hash: a0a3e346d09b91b8ad96e54854c136ad
Degree: 11
\(17^{2} \theta^4-2 3 17 x\theta^2(117\theta^2+2\theta+1)+2^{2} x^{2}\left(8475\theta^4-64176\theta^3-97010\theta^2-63580\theta-16184\right)+2^{2} x^{3}\left(717094\theta^4+1400796\theta^3+1493367\theta^2+893571\theta+254082\right)-2^{4} x^{4}\left(464294\theta^4-1133264\theta^3-1648391\theta^2-1200310\theta-375336\right)-2^{4} x^{5}\left(18282700\theta^4+46995928\theta^3+83098711\theta^2+73517673\theta+25685438\right)-2^{6} 3 x^{6}\left(2709886\theta^4+7353008\theta^3+18175093\theta^2+18787708\theta+5966228\right)+2^{6} x^{7}\left(154368940\theta^4+947965400\theta^3+2363187035\theta^2+2646307981\theta+1071488886\right)+2^{8} x^{8}(\theta+1)(119648213\theta^3+399067803\theta^2+77665606\theta-498465144)-2^{8} 3 x^{9}(\theta+1)(\theta+2)(120410834\theta^2+865960638\theta+1188072247)-2^{10} 3^{2} 107 x^{10}(\theta+3)(\theta+2)(\theta+1)(218683\theta-39394)+2^{11} 3^{3} 5 107^{2} 137 x^{11}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, 14, 72, 1554, ... --> OEIS Normalized instanton numbers (n0=1): 6/17, 83/17, 688/17, 7350/17, 5150, ... ; Common denominator:...
\((10z+1)(6z-1)(1096z^3+228z^2+14z-1)(2z-1)^2(1284z^2+232z-17)^2\)
| \(-\frac{ 29}{ 321}-\frac{ 1}{ 642}\sqrt{ 8821}\) | ≈\(-0.124082-0.085658I\) | ≈\(-0.124082+0.085658I\) | \(-\frac{ 1}{ 10}\) | \(0\) | ≈\(0.040135\) | \(-\frac{ 29}{ 321}+\frac{ 1}{ 642}\sqrt{ 8821}\) | \(\frac{ 1}{ 6}\) | \(\frac{ 1}{ 2}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(0\) | \(2\) |
| \(3\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(3\) | \(1\) | \(1\) | \(3\) |
| \(4\) | \(2\) | \(2\) | \(2\) | \(0\) | \(2\) | \(4\) | \(2\) | \(1\) | \(4\) |
9
New Number: 11.9 | AESZ: | Superseeker: 17/3 4127/9 | Hash: fa7c260e6f07cef5d727e6af380a6373
Degree: 11
\(3^{2} \theta^4-3 x\theta(20\theta^3+196\theta^2+125\theta+27)-x^{2}\left(19127\theta^4+69044\theta^3+89705\theta^2+54504\theta+13248\right)-2 x^{3}\left(285799\theta^4+1251420\theta^3+2142633\theta^2+1678248\theta+511560\right)-2^{2} x^{4}\left(2058125\theta^4+11190220\theta^3+23374875\theta^2+21658060\theta+7556504\right)-2^{3} x^{5}\left(8570685\theta^4+57030456\theta^3+140934413\theta^2+149627146\theta+57858760\right)-2^{6} x^{6}\left(5382486\theta^4+43183593\theta^3+124360784\theta^2+148979343\theta+62839586\right)-2^{7} x^{7}\left(7897671\theta^4+75745098\theta^3+252663545\theta^2+339244430\theta+154810568\right)-2^{10} x^{8}(\theta+1)(1454893\theta^3+15409953\theta^2+50286726\theta+48898444)-2^{11} x^{9}(\theta+1)(\theta+2)(227963\theta^2+3375435\theta+10342960)+2^{14} x^{10}(\theta+3)(\theta+2)(\theta+1)(48476\theta+271867)-2^{15} 3 5 13 23 x^{11}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, 92, 2328, 91212, ... --> OEIS Normalized instanton numbers (n0=1): 17/3, 257/6, 4127/9, 23827/3, 496999/3, ... ; Common denominator:...
\(-(5z+1)(13z+1)(6z+1)(368z^2+56z-1)(4z+1)^2(8z^2-26z-3)^2\)
| \(-\frac{ 1}{ 4}\) | \(-\frac{ 1}{ 5}\) | \(-\frac{ 7}{ 92}-\frac{ 3}{ 46}\sqrt{ 2}\) | \(-\frac{ 1}{ 6}\) | \(\frac{ 13}{ 8}-\frac{ 1}{ 8}\sqrt{ 193}\) | \(-\frac{ 1}{ 13}\) | \(0\) | \(-\frac{ 7}{ 92}+\frac{ 3}{ 46}\sqrt{ 2}\) | \(\frac{ 13}{ 8}+\frac{ 1}{ 8}\sqrt{ 193}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(2\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(3\) | \(1\) | \(0\) | \(1\) | \(3\) | \(3\) |
| \(1\) | \(2\) | \(2\) | \(2\) | \(4\) | \(2\) | \(0\) | \(2\) | \(4\) | \(4\) |
10
New Number: 13.10 | AESZ: | Superseeker: 4 -628/9 | Hash: 2a9fda379889eb2fd218bd01f2520f7a
Degree: 13
\(\theta^4-2^{2} x\left(35\theta^4+38\theta^3+35\theta^2+16\theta+3\right)+2^{4} x^{2}\left(546\theta^4+1068\theta^3+1287\theta^2+790\theta+201\right)-2^{6} x^{3}\left(4928\theta^4+12888\theta^3+17829\theta^2+12673\theta+3693\right)+2^{8} x^{4}\left(28123\theta^4+88408\theta^3+131977\theta^2+98226\theta+29511\right)-2^{10} 3^{2} x^{5}\left(11315\theta^4+41094\theta^3+65088\theta^2+47691\theta+13532\right)+2^{13} 3^{2} x^{6}\left(11674\theta^4+48674\theta^3+79399\theta^2+52683\theta+11716\right)-2^{15} 3^{3} x^{7}\left(2063\theta^4+11102\theta^3+11184\theta^2-9217\theta-10762\right)-2^{17} 3^{4} x^{8}\left(3277\theta^4+16284\theta^3+42329\theta^2+57018\theta+27266\right)+2^{20} 3^{5} x^{9}\left(1124\theta^4+7114\theta^3+18121\theta^2+22265\theta+10018\right)+2^{24} 3^{6} x^{10}(\theta+1)(\theta^3-105\theta^2-277\theta-267)-2^{25} 3^{7} x^{11}(\theta+1)(\theta+2)(93\theta^2+441\theta+607)+2^{27} 3^{10} x^{12}(\theta+3)(\theta+2)(\theta+1)(\theta+6)+2^{30} 3^{10} x^{13}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 12, 180, 2928, 47556, ... --> OEIS Normalized instanton numbers (n0=1): 4, 5, -628/9, -2823/4, 672, ... ; Common denominator:...
\((8z-1)(10368z^3-1728z^2+72z-1)(12z-1)^2(288z^2-24z+1)^2(4z+1)^3\)
| \(-\frac{ 1}{ 4}\) | \(0\) | ≈\(0.027033-0.011216I\) | ≈\(0.027033+0.011216I\) | \(\frac{ 1}{ 24}-\frac{ 1}{ 24}I\) | \(\frac{ 1}{ 24}+\frac{ 1}{ 24}I\) | \(\frac{ 1}{ 12}\) | ≈\(0.112601\) | \(\frac{ 1}{ 8}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(\frac{ 1}{ 2}\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(2\) |
| \(\frac{ 3}{ 2}\) | \(0\) | \(1\) | \(1\) | \(3\) | \(3\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(3\) |
| \(2\) | \(0\) | \(2\) | \(2\) | \(4\) | \(4\) | \(1\) | \(2\) | \(2\) | \(4\) |
11
New Number: 13.11 | AESZ: | Superseeker: 7 -2044/9 | Hash: d6e183df7853fe5068c8b8cdeb3f63cb
Degree: 13
\(\theta^4-x\left(98\theta^4+164\theta^3+137\theta^2+55\theta+9\right)+x^{2}\left(3822\theta^4+11400\theta^3+14901\theta^2+8746\theta+2007\right)-x^{3}\left(64148\theta^4+196344\theta^3+271665\theta^2+199855\theta+60354\right)+x^{4}\left(802771\theta^4+2242504\theta^3+2203855\theta^2+1316868\theta+390636\right)-2 3 x^{5}\left(1040145\theta^4+2982426\theta^3+3578912\theta^2+1897395\theta+345411\right)+2 3^{2} x^{6}\left(1927994\theta^4+4917832\theta^3+7329041\theta^2+5154630\theta+1338003\right)-2 3^{5} x^{7}\left(219316\theta^4+761432\theta^3+1064075\theta^2+703129\theta+181966\right)+3^{4} x^{8}\left(754759\theta^4+7471824\theta^3+13904030\theta^2+8830464\theta+1544112\right)+3^{7} x^{9}\left(174966\theta^4+736236\theta^3+1307237\theta^2+1340471\theta+568265\right)-3^{10} x^{10}(\theta+1)(8018\theta^3+62342\theta^2+139257\theta+108861)-3^{9} x^{11}(\theta+1)(\theta+2)(28988\theta^2+81396\theta+36331)+3^{12} x^{12}(\theta+3)(\theta+2)(\theta+1)(1061\theta+5386)+2 3^{15} 17 x^{13}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 9, 135, 2115, 18063, ... --> OEIS Normalized instanton numbers (n0=1): 7, -31/4, -2044/9, -1380, -8520, ... ; Common denominator:...
\((2z-1)(4131z^3-2187z^2+81z-1)(3z-1)^2(81z^2-6z+1)^2(z+1)^3\)
| \(-1\) | \(0\) | ≈\(0.019487-0.01067I\) | ≈\(0.019487+0.01067I\) | \(\frac{ 1}{ 27}-\frac{ 2}{ 27}\sqrt{ 2}I\) | \(\frac{ 1}{ 27}+\frac{ 2}{ 27}\sqrt{ 2}I\) | \(\frac{ 1}{ 3}\) | ≈\(0.490438\) | \(\frac{ 1}{ 2}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(\frac{ 1}{ 2}\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(2\) |
| \(\frac{ 3}{ 2}\) | \(0\) | \(1\) | \(1\) | \(3\) | \(3\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(3\) |
| \(2\) | \(0\) | \(2\) | \(2\) | \(4\) | \(4\) | \(1\) | \(2\) | \(2\) | \(4\) |
12
New Number: 13.6 | AESZ: | Superseeker: 2 421/9 | Hash: 679aa37a05aafe03e8d68785d566fcfb
Degree: 13
\(\theta^4-x\left(217\theta^4+178\theta^3+178\theta^2+89\theta+18\right)+x^{2}\left(6192+24334\theta+39795\theta^2+33324\theta^3+20643\theta^4\right)-2^{3} x^{3}\left(139307\theta^4+333558\theta^3+457560\theta^2+315505\theta+89244\right)+2^{4} x^{4}\left(2283535\theta^4+7259062\theta^3+11103058\theta^2+8192571\theta+2419362\right)-2^{6} 3 x^{5}\left(3630237\theta^4+14551206\theta^3+23954402\theta^2+17624013\theta+4953960\right)+2^{6} 3^{2} x^{6}\left(9379387\theta^4+48172928\theta^3+74157721\theta^2+31932048\theta-1833876\right)+2^{9} 3^{5} x^{7}\left(495945\theta^4+2307886\theta^3+6892788\theta^2+10676039\theta+5452406\right)-2^{12} 3^{4} x^{8}\left(5269994\theta^4+31826568\theta^3+83327461\theta^2+106595346\theta+49104855\right)+2^{15} 3^{7} x^{9}\left(129774\theta^4+976140\theta^3+2673571\theta^2+3442327\theta+1597000\right)+2^{18} 3^{10} x^{10}(\theta+1)(6759\theta^3+40481\theta^2+97855\theta+79397)-2^{21} 3^{9} x^{11}(\theta+1)(\theta+2)(29107\theta^2+160713\theta+251822)-2^{27} 3^{12} x^{12}(\theta+3)(\theta+2)(\theta+1)(17\theta+4)+2^{29} 3^{15} 5 x^{13}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 18, 378, 8280, 187434, ... --> OEIS Normalized instanton numbers (n0=1): 2, -3/2, 421/9, -519/2, 285, ... ; Common denominator:...
\((16z-1)(19440z^3-2187z^2+81z-1)(24z-1)^2(648z^2-48z+1)^2(8z+1)^3\)
| \(-\frac{ 1}{ 8}\) | \(0\) | ≈\(0.032165-0.005771I\) | ≈\(0.032165+0.005771I\) | \(\frac{ 1}{ 27}-\frac{ 1}{ 108}\sqrt{ 2}I\) | \(\frac{ 1}{ 27}+\frac{ 1}{ 108}\sqrt{ 2}I\) | \(\frac{ 1}{ 24}\) | ≈\(0.04817\) | \(\frac{ 1}{ 16}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(\frac{ 1}{ 2}\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(2\) |
| \(\frac{ 3}{ 2}\) | \(0\) | \(1\) | \(1\) | \(3\) | \(3\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(3\) |
| \(2\) | \(0\) | \(2\) | \(2\) | \(4\) | \(4\) | \(1\) | \(2\) | \(2\) | \(4\) |
13
New Number: 13.7 | AESZ: | Superseeker: 10 7709/9 | Hash: 47093f7f3b7ab4544ef6b418bdae778b
Degree: 13
\(\theta^4+x\left(127\theta^4-2\theta^3+22\theta^2+23\theta+6\right)+x^{2}\left(4803\theta^4+1644\theta^3+3459\theta^2+430\theta-384\right)+2^{3} x^{3}\left(2507\theta^4+8118\theta^3-2448\theta^2-7127\theta-2940\right)-2^{4} x^{4}\left(94175\theta^4+88358\theta^3+133418\theta^2+111507\theta+38898\right)+2^{6} 3 x^{5}\left(22347\theta^4+197706\theta^3+783766\theta^2+893091\theta+359952\right)+2^{6} 3^{2} x^{6}\left(869067\theta^4+4718208\theta^3+11162457\theta^2+11758320\theta+4583500\right)-2^{9} 3^{3} x^{7}\left(245985\theta^4+1338174\theta^3+3414812\theta^2+4418167\theta+2103502\right)-2^{12} 3^{4} x^{8}\left(234234\theta^4+2167368\theta^3+7012373\theta^2+9416514\theta+4375751\right)+2^{15} 3^{5} x^{9}\left(81234\theta^4+643380\theta^3+1815861\theta^2+2193249\theta+947968\right)+2^{18} 3^{6} x^{10}(\theta+1)(15879\theta^3+214401\theta^2+816191\theta+896789)-2^{21} 3^{7} x^{11}(\theta+1)(\theta+2)(8037\theta^2+71103\theta+151546)+2^{27} 3^{9} x^{12}(\theta+3)(\theta+2)(\theta+1)(31\theta+152)-2^{29} 3^{9} 5 x^{13}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -6, 90, -1368, 21546, ... --> OEIS Normalized instanton numbers (n0=1): 10, -149/2, 7709/9, -27333/2, 242829, ... ; Common denominator:...
\(-(16z+1)(2160z^3+27z^2-9z+1)(24z+1)^2(72z^2-48z-1)^2(8z-1)^3\)
| ≈\(-0.100198\) | \(-\frac{ 1}{ 16}\) | \(-\frac{ 1}{ 24}\) | \(\frac{ 1}{ 3}-\frac{ 1}{ 4}\sqrt{ 2}\) | \(0\) | ≈\(0.043849-0.05194I\) | ≈\(0.043849+0.05194I\) | \(\frac{ 1}{ 8}\) | \(\frac{ 1}{ 3}+\frac{ 1}{ 4}\sqrt{ 2}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(0\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(2\) |
| \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(3\) | \(0\) | \(1\) | \(1\) | \(\frac{ 3}{ 2}\) | \(3\) | \(3\) |
| \(2\) | \(2\) | \(1\) | \(4\) | \(0\) | \(2\) | \(2\) | \(2\) | \(4\) | \(4\) |
14
New Number: 13.8 | AESZ: | Superseeker: 8 -830/9 | Hash: bcea3fff557004b4da26e9aa34caac6c
Degree: 13
\(\theta^4-x\left(55\theta^4+142\theta^3+112\theta^2+41\theta+6\right)+x^{2}\left(456\theta^4+4668\theta^3+7455\theta^2+3958\theta+696\right)+x^{3}\left(35078\theta^4+127188\theta^3+175671\theta^2+133507\theta+41718\right)+x^{4}\left(82753\theta^4+664768\theta^3+2450839\theta^2+2316756\theta+736812\right)-3 x^{5}\left(885105\theta^4+1342938\theta^3-883331\theta^2-2706576\theta-1350228\right)-2 3^{2} x^{6}\left(345501\theta^4+3334206\theta^3+4969485\theta^2+2964744\theta+630748\right)+2^{2} 3^{3} x^{7}\left(459939\theta^4+270666\theta^3-1625381\theta^2-2377792\theta-962956\right)+2^{4} 3^{4} x^{8}\left(112581\theta^4+699447\theta^3+1277449\theta^2+1022649\theta+314494\right)-2^{4} 3^{5} x^{9}\left(34101\theta^4-33864\theta^3-473835\theta^2-744726\theta-350272\right)-2^{5} 3^{6} x^{10}(\theta+1)(20847\theta^3+146325\theta^2+303230\theta+217616)+2^{6} 3^{7} x^{11}(\theta+1)(\theta+2)(1791\theta^2-1173\theta-14800)+2^{9} 3^{9} x^{12}(\theta+3)(\theta+2)(\theta+1)(52\theta+257)-2^{10} 3^{9} 17 x^{13}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 6, 90, 1044, -5670, ... --> OEIS Normalized instanton numbers (n0=1): 8, -45/2, -830/9, -5301/2, 2790, ... ; Common denominator:...
\(-(2z+1)(3672z^3+1728z^2-72z+1)(6z-1)^2(12z+1)^2(3z+1)^2(z-1)^3\)
| ≈\(-0.510076\) | \(-\frac{ 1}{ 2}\) | \(-\frac{ 1}{ 3}\) | \(-\frac{ 1}{ 12}\) | \(0\) | ≈\(0.019744-0.012003I\) | ≈\(0.019744+0.012003I\) | \(\frac{ 1}{ 6}\) | \(1\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(2\) |
| \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(3\) | \(0\) | \(1\) | \(1\) | \(3\) | \(\frac{ 3}{ 2}\) | \(3\) |
| \(2\) | \(2\) | \(1\) | \(4\) | \(0\) | \(2\) | \(2\) | \(4\) | \(2\) | \(4\) |
15
New Number: 13.9 | AESZ: | Superseeker: 8 2200/9 | Hash: 31ff3b7bd4c8fed070ee43b6903d3752
Degree: 13
\(\theta^4+2^{3} x\theta(4\theta^3-8\theta^2-5\theta-1)-2^{4} x^{2}\left(48\theta^4+120\theta^3+45\theta^2+74\theta+36\right)-2^{7} x^{3}\left(101\theta^4-342\theta^3-387\theta^2-410\theta-171\right)+2^{8} x^{4}\left(3121\theta^4+14104\theta^3+30889\theta^2+27720\theta+9351\right)+2^{11} 3^{2} x^{5}\left(655\theta^4+4062\theta^3+10081\theta^2+10272\theta+3856\right)-2^{12} 3^{2} x^{6}\left(2272\theta^4+2816\theta^3-9950\theta^2-18768\theta-8813\right)-2^{15} 3^{3} x^{7}\left(1546\theta^4+12172\theta^3+30708\theta^2+33880\theta+13843\right)+2^{16} 3^{4} x^{8}\left(1099\theta^4+1344\theta^3-11134\theta^2-23964\theta-13063\right)+2^{19} 3^{5} x^{9}\left(458\theta^4+4828\theta^3+15325\theta^2+19721\theta+8830\right)-2^{20} 3^{6} x^{10}(\theta+1)(368\theta^3+1752\theta^2+1297\theta-1035)-2^{23} 3^{7} x^{11}(\theta+1)(\theta+2)(39\theta^2+513\theta+1172)+2^{24} 3^{9} x^{12}(\theta+3)(\theta+2)(\theta+1)(17\theta+82)-2^{27} 3^{10} x^{13}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, 36, -192, -4284, ... --> OEIS Normalized instanton numbers (n0=1): 8, -75/2, 2200/9, -8117/2, 47936, ... ; Common denominator:...
\(-(8z+1)(5184z^3+432z^2-36z+1)(12z+1)^2(144z^2-24z-1)^2(4z-1)^3\)
| ≈\(-0.141868\) | \(-\frac{ 1}{ 8}\) | \(-\frac{ 1}{ 12}\) | \(\frac{ 1}{ 12}-\frac{ 1}{ 12}\sqrt{ 2}\) | \(0\) | ≈\(0.029267-0.022431I\) | ≈\(0.029267+0.022431I\) | \(\frac{ 1}{ 12}+\frac{ 1}{ 12}\sqrt{ 2}\) | \(\frac{ 1}{ 4}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(2\) |
| \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(3\) | \(0\) | \(1\) | \(1\) | \(3\) | \(\frac{ 3}{ 2}\) | \(3\) |
| \(2\) | \(2\) | \(1\) | \(4\) | \(0\) | \(2\) | \(2\) | \(4\) | \(2\) | \(4\) |
16
New Number: 14.2 | AESZ: | Superseeker: 27/5 1619/5 | Hash: c0f6d85270164c8c5a63d1bb2deaba83
Degree: 14
\(5^{2} \theta^4+3^{2} 5 x\theta(6\theta^3-36\theta^2-23\theta-5)-x^{2}\left(43856\theta^4+189068\theta^3+226691\theta^2+135510\theta+33600\right)-3^{2} x^{3}\left(224236\theta^4+916896\theta^3+1403247\theta^2+1048995\theta+313920\right)-x^{4}\left(44621090\theta^4+199900036\theta^3+357072757\theta^2+304636250\theta+101358144\right)-3^{2} x^{5}\left(69593744\theta^4+347076728\theta^3+696076003\theta^2+653370139\theta+234075456\right)-3^{2} x^{6}\left(681084088\theta^4+3766244020\theta^3+8299124637\theta^2+8400442322\theta+3184811840\right)-3^{3} x^{7}\left(1616263276\theta^4+9835107968\theta^3+23484467027\theta^2+25311872719\theta+10046134656\right)-3^{3} x^{8}\left(8527956293\theta^4+56671723156\theta^3+145225420081\theta^2+165230257706\theta+68152357440\right)-2 3^{4} x^{9}\left(5575274615\theta^4+40185448970\theta^3+109721715457\theta^2+130944512374\theta+55834822464\right)-2^{3} 3^{3} x^{10}\left(12062719219\theta^4+93737716664\theta^3+271167874625\theta^2+337796659588\theta+148305175248\right)-2^{5} 3^{5} x^{11}(\theta+1)(691573543\theta^3+5071601663\theta^2+12510902832\theta+10260936720)-2^{7} 3^{6} x^{12}(\theta+1)(\theta+2)(80620421\theta^2+475174733\theta+711172676)-2^{14} 3^{6} 5 x^{13}(\theta+3)(\theta+2)(\theta+1)(107069\theta+369433)-2^{19} 3^{8} 5^{2} 29 x^{14}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, 84, 1944, 70476, ... --> OEIS Normalized instanton numbers (n0=1): 27/5, 158/5, 1619/5, 51193/10, 485082/5, ... ; Common denominator:...
\(-(9z+1)(6z+1)(348z^2+51z-1)(5z+1)^2(4z+1)^2(576z^3+357z^2+72z+5)^2\)
| ≈\(-0.298314\) | \(-\frac{ 1}{ 4}\) | \(-\frac{ 1}{ 5}\) | \(-\frac{ 1}{ 6}\) | \(-\frac{ 17}{ 232}-\frac{ 11}{ 696}\sqrt{ 33}\) | ≈\(-0.160739-0.057112I\) | ≈\(-0.160739+0.057112I\) | \(-\frac{ 1}{ 9}\) | \(0\) | \(-\frac{ 17}{ 232}+\frac{ 11}{ 696}\sqrt{ 33}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(\frac{ 1}{ 2}\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(2\) |
| \(3\) | \(\frac{ 1}{ 2}\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(3\) | \(3\) | \(1\) | \(0\) | \(1\) | \(3\) |
| \(4\) | \(1\) | \(1\) | \(2\) | \(2\) | \(4\) | \(4\) | \(2\) | \(0\) | \(2\) | \(4\) |
17
New Number: 14.3 | AESZ: | Superseeker: 21/4 1285/2 | Hash: fed06deb794f226dc9bf5119acb5fcf2
Degree: 14
\(2^{4} \theta^4-2^{2} x\theta(32+149\theta+234\theta^2+54\theta^3)-x^{2}\left(39143\theta^4+143570\theta^3+193959\theta^2+113504\theta+25600\right)-2 x^{3}\left(488914\theta^4+2366790\theta^3+4293033\theta^2+3346032\theta+1000416\right)-x^{4}\left(10882749\theta^4+71055186\theta^3+164405289\theta^2+154949112\theta+53930896\right)-2 x^{5}\left(27668482\theta^4+276475198\theta^3+837116993\theta^2+935359976\theta+366972272\right)+2^{2} x^{6}\left(417907\theta^4-460236984\theta^3-2273346630\theta^2-3128567370\theta-1388917916\right)+2^{4} x^{7}\left(101741100\theta^4+252571782\theta^3-1076988014\theta^2-2508674129\theta-1362925766\right)+2^{6} x^{8}\left(136151221\theta^4+982924270\theta^3+1322951772\theta^2+257785345\theta-274176968\right)+2^{8} x^{9}\left(54403942\theta^4+889245288\theta^3+2318053632\theta^2+2306501340\theta+802166039\right)-2^{10} 3 x^{10}\left(16110621\theta^4-52456644\theta^3-344061634\theta^2-516147274\theta-239510540\right)-2^{12} x^{11}(\theta+1)(75181760\theta^3+257537898\theta^2+246848548\theta+22104519)-2^{14} 3 x^{12}(\theta+1)(\theta+2)(14369939\theta^2+55966221\theta+56991175)-2^{17} 3^{3} 5 x^{13}(\theta+3)(\theta+2)(\theta+1)(45377\theta+116950)-2^{20} 3^{5} 5^{2} 59 x^{14}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, 100, 2592, 112308, ... --> OEIS Normalized instanton numbers (n0=1): 21/4, 1965/32, 1285/2, 103095/8, 1157421/4, ... ; Common denominator:...
\(-(3z+1)(64z^2+24z+1)(236z^2+63z-1)(360z^3+74z^2-21z-4)^2(4z+1)^3\)
| \(-\frac{ 1}{ 3}\) | \(-\frac{ 3}{ 16}-\frac{ 1}{ 16}\sqrt{ 5}\) | \(-\frac{ 63}{ 472}-\frac{ 17}{ 472}\sqrt{ 17}\) | ≈\(-0.268785\) | \(-\frac{ 1}{ 4}\) | ≈\(-0.174147\) | \(-\frac{ 3}{ 16}+\frac{ 1}{ 16}\sqrt{ 5}\) | \(0\) | \(-\frac{ 63}{ 472}+\frac{ 17}{ 472}\sqrt{ 17}\) | ≈\(0.237376\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(2\) |
| \(1\) | \(1\) | \(1\) | \(3\) | \(0\) | \(3\) | \(1\) | \(0\) | \(1\) | \(3\) | \(3\) |
| \(2\) | \(2\) | \(2\) | \(4\) | \(0\) | \(4\) | \(2\) | \(0\) | \(2\) | \(4\) | \(4\) |
18
New Number: 14.4 | AESZ: | Superseeker: 10 13958/9 | Hash: 0091fcfec3692ae6ced2f585ef96177c
Degree: 14
\(3^{6} \theta^4-3^{6} x\theta(15+70\theta+110\theta^2+13\theta^3)-3^{3} x^{2}\left(120409\theta^4+434560\theta^3+542371\theta^2+323352\theta+78624\right)-3^{3} x^{3}\left(5396953\theta^4+22626666\theta^3+37042425\theta^2+28217556\theta+8482968\right)-2 x^{4}\left(1704421489\theta^4+8538160718\theta^3+16779519205\theta^2+14919147216\theta+5077251288\right)-2^{2} 3 x^{5}\left(4201278867\theta^4+24797778110\theta^3+56302322281\theta^2+56325956066\theta+20967103728\right)-2^{3} x^{6}\left(63154319213\theta^4+432278933514\theta^3+1110085421927\theta^2+1224810967950\theta+489654799596\right)-2^{5} 3 x^{7}\left(36597277323\theta^4+286904817870\theta^3+822690934223\theta^2+989019393562\theta+419959932336\right)-2^{6} x^{8}\left(263122045911\theta^4+2344932626130\theta^3+7455815983415\theta^2+9696396501490\theta+4343347545434\right)-2^{7} 5 x^{9}\left(83257168289\theta^4+843955668354\theta^3+2974370084181\theta^2+4174636770342\theta+1965917099796\right)-2^{9} 5 x^{10}\left(38447331387\theta^4+453440983815\theta^3+1797507529325\theta^2+2740147614260\theta+1358896159983\right)-2^{8} 5^{2} 23 x^{11}(\theta+1)(421574469\theta^3+6597293181\theta^2+28022760832\theta+32033938840)+2^{9} 5^{2} 7 23^{2} x^{12}(\theta+2)(\theta+1)(2012137\theta^2+10160979\theta-151326)+2^{10} 5^{3} 7^{2} 23^{3} x^{13}(1525\theta+10484)(\theta+3)(\theta+2)(\theta+1)-2^{11} 3 5^{3} 7^{3} 23^{4} x^{14}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, 182, 7020, 401730, ... --> OEIS Normalized instanton numbers (n0=1): 10, 2591/27, 13958/9, 1037839/27, 3535478/3, ... ; Common denominator:...
\(-(6z+1)(42320z^4+16560z^3+2032z^2+68z-1)(920z^3-1180z^2-378z-27)^2(7z+1)^3\)
| \(-\frac{ 1}{ 6}\) | ≈\(-0.157194\) | ≈\(-0.157194\) | ≈\(-0.151128\) | \(-\frac{ 1}{ 7}\) | ≈\(-0.124614\) | ≈\(-0.087777\) | \(0\) | ≈\(0.010861\) | ≈\(1.55835\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(2\) |
| \(1\) | \(1\) | \(1\) | \(3\) | \(0\) | \(3\) | \(1\) | \(0\) | \(1\) | \(3\) | \(3\) |
| \(2\) | \(2\) | \(2\) | \(4\) | \(0\) | \(4\) | \(2\) | \(0\) | \(2\) | \(4\) | \(4\) |
19
New Number: 14.5 | AESZ: | Superseeker: 211/35 19279/35 | Hash: f3806aa0de676048470ecaa401cb173e
Degree: 14
\(5^{2} 7^{2} \theta^4-5 7 x\theta(208\theta^3+2522\theta^2+1611\theta+350)-x^{2}\left(2895864\theta^4+10743882\theta^3+13787199\theta^2+8373750\theta+2038400\right)-x^{3}\left(100271073\theta^4+431892504\theta^3+723680933\theta^2+561181425\theta+170041830\right)-x^{4}\left(1779494918\theta^4+9127622236\theta^3+18290497093\theta^2+16539531755\theta+5684071466\right)-x^{5}\left(19827182682\theta^4+119162684736\theta^3+274771737213\theta^2+279000299901\theta+104851723790\right)-x^{6}\left(149204258817\theta^4+1032818408748\theta^3+2681116117542\theta^2+2993600486151\theta+1206564891326\right)-x^{7}\left(778822250193\theta^4+6126161719824\theta^3+17659178255613\theta^2+21402250647384\theta+9142529120612\right)-x^{8}\left(2812797944541\theta^4+24913922595768\theta^3+79078287326181\theta^2+103186060627602\theta+46367068712696\right)-2 x^{9}\left(3396806566178\theta^4+33765210209691\theta^3+117624369015258\theta^2+164571138801333\theta+77449742958250\right)-x^{10}\left(10000008656989\theta^4+112554410392382\theta^3+432872666762301\theta^2+650564904626120\theta+320443815723404\right)-2^{2} 3 x^{11}(\theta+1)(551266200382\theta^3+6974826522501\theta^2+26399880418886\theta+28678364691672)+2^{2} 5 x^{12}(\theta+1)(\theta+2)(92480406417\theta^2+96008519961\theta-1687668183707)+2^{3} 5^{2} 163 x^{13}(\theta+3)(\theta+2)(\theta+1)(106246927\theta+649964324)-2^{2} 3^{3} 5^{3} 163^{2} 2687 x^{14}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, 104, 2838, 118344, ... --> OEIS Normalized instanton numbers (n0=1): 211/35, 1643/35, 19279/35, 69901/7, 7789913/35, ... ; Common denominator:...
\(-(-1+41z+1449z^2+13908z^3+53591z^4+72549z^5)(326z^3-804z^2-351z-35)^2(5z+1)^3\)
| ≈\(-0.216454\) | \(-\frac{ 1}{ 5}\) | ≈\(-0.173649\) | \(0\) | ≈\(2.85636\) | \(#ND+#NDI\) | \(\infty\) |
|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(0\) | \(1\) | \(0\) | \(1\) | \(1\) | \(2\) |
| \(3\) | \(0\) | \(3\) | \(0\) | \(3\) | \(1\) | \(3\) |
| \(4\) | \(0\) | \(4\) | \(0\) | \(4\) | \(2\) | \(4\) |
20
New Number: 14.6 | AESZ: | Superseeker: 343/26 27836/13 | Hash: b419826ae9a841fd2485cf17a33e3c82
Degree: 14
\(2^{2} 13^{2} \theta^4+2 13 x\theta(374\theta^3-3806\theta^2-2423\theta-520)-3 x^{2}\left(1378165\theta^4+5692942\theta^3+6262109\theta^2+3632408\theta+908544\right)-3 x^{3}\left(109634670\theta^4+414665370\theta^3+585954355\theta^2+424721388\theta+125838648\right)-3^{2} x^{4}\left(1430057388\theta^4+5835126030\theta^3+9693559559\theta^2+7980072398\theta+2602285652\right)-3^{4} x^{5}\left(3973724102\theta^4+18016019762\theta^3+33809871817\theta^2+30548046888\theta+10682005352\right)-3^{5} x^{6}\left(23181342780\theta^4+117157350210\theta^3+242997310916\theta^2+236792965009\theta+87556639706\right)-3^{6} x^{7}\left(98661453307\theta^4+553704139946\theta^3+1252095727942\theta^2+1301834765069\theta+504487460698\right)-3^{7} x^{8}\left(312059119661\theta^4+1933538622170\theta^3+4722871403800\theta^2+5200539067181\theta+2098928967026\right)-3^{7} x^{9}\left(2207453009832\theta^4+15008943280014\theta^3+39332490555167\theta^2+45616623444051\theta+19085482478826\right)-3^{8} x^{10}\left(3839323955127\theta^4+28479004361040\theta^3+79653137355055\theta^2+96880903986262\theta+41867518152496\right)-3^{10} x^{11}(\theta+1)(1597618239529\theta^3+11261457267015\theta^2+26962321719782\theta+21625438724040)-3^{12} x^{12}(\theta+1)(\theta+2)(452183900223\theta^2+2573271558279\theta+3747021993116)-2^{4} 3^{16} 109 x^{13}(\theta+3)(\theta+2)(\theta+1)(4973417\theta+16619273)-2^{6} 3^{16} 109^{2} 8167 x^{14}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, 252, 11106, 735660, ... --> OEIS Normalized instanton numbers (n0=1): 343/26, 1358/13, 27836/13, 764852/13, 52338075/26, ... ; Common denominator:...
\(-(661527z^5+290250z^4+47223z^3+3291z^2+71z-1)(23544z^3+7353z^2+759z+26)^2(9z+1)^3\)
| ≈\(-0.126194\) | \(-\frac{ 1}{ 9}\) | ≈\(-0.093057-0.009552I\) | ≈\(-0.093057+0.009552I\) | \(0\) | \(#ND+#NDI\) | \(\infty\) |
|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(0\) | \(1\) | \(1\) | \(0\) | \(1\) | \(2\) |
| \(3\) | \(0\) | \(3\) | \(3\) | \(0\) | \(1\) | \(3\) |
| \(4\) | \(0\) | \(4\) | \(4\) | \(0\) | \(2\) | \(4\) |
21
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:...
\(-(3z+1)(13z^2+5z+1)(153z^3+75z^2+14z-1)(13+11z)^2\)
| \(-\frac{ 13}{ 11}\) | \(-\frac{ 1}{ 3}\) | ≈\(-0.272124-0.216493I\) | ≈\(-0.272124+0.216493I\) | \(-\frac{ 5}{ 26}-\frac{ 3}{ 26}\sqrt{ 3}I\) | \(-\frac{ 5}{ 26}+\frac{ 3}{ 26}\sqrt{ 3}I\) | \(0\) | ≈\(0.054052\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(2\) |
| \(3\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(3\) |
| \(4\) | \(2\) | \(2\) | \(2\) | \(2\) | \(2\) | \(0\) | \(2\) | \(4\) |
22
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:...
\(-(6z+1)(152z^3+84z^2+14z-1)(2z+1)^2(82z+29)^2\)
| \(-\frac{ 1}{ 2}\) | \(-\frac{ 29}{ 82}\) | ≈\(-0.302804-0.180271I\) | ≈\(-0.302804+0.180271I\) | \(-\frac{ 1}{ 6}\) | \(0\) | ≈\(0.052976\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(2\) |
| \(\frac{ 1}{ 2}\) | \(3\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(3\) |
| \(1\) | \(4\) | \(2\) | \(2\) | \(2\) | \(0\) | \(2\) | \(4\) |
23
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:...
\(-(23z-1)(5z+1)(2z+1)(z+1)(13z+4)^2(4z+1)^2\)
| \(-1\) | \(-\frac{ 1}{ 2}\) | \(-\frac{ 4}{ 13}\) | \(-\frac{ 1}{ 4}\) | \(-\frac{ 1}{ 5}\) | \(0\) | \(\frac{ 1}{ 23}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(\frac{ 1}{ 3}\) | \(1\) | \(0\) | \(1\) | \(2\) |
| \(1\) | \(1\) | \(3\) | \(\frac{ 2}{ 3}\) | \(1\) | \(0\) | \(1\) | \(3\) |
| \(2\) | \(2\) | \(4\) | \(1\) | \(2\) | \(0\) | \(2\) | \(4\) |
24
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:...
\((3z-1)(2z-1)(10z-1)(6z+1)(25z^2-5z-1)(-23+90z)^2\)
| \(-\frac{ 1}{ 6}\) | \(\frac{ 1}{ 10}-\frac{ 1}{ 10}\sqrt{ 5}\) | \(0\) | \(\frac{ 1}{ 10}\) | \(\frac{ 23}{ 90}\) | \(\frac{ 1}{ 10}+\frac{ 1}{ 10}\sqrt{ 5}\) | \(\frac{ 1}{ 3}\) | \(\frac{ 1}{ 2}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(2\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(3\) | \(1\) | \(1\) | \(1\) | \(3\) |
| \(2\) | \(2\) | \(0\) | \(2\) | \(4\) | \(2\) | \(2\) | \(2\) | \(4\) |
25
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:...
\(-(7z+1)(25z-1)(2z+1)^2(101z+43)^2(3z+1)^2\)
| \(-\frac{ 1}{ 2}\) | \(-\frac{ 43}{ 101}\) | \(-\frac{ 1}{ 3}\) | \(-\frac{ 1}{ 7}\) | \(0\) | \(\frac{ 1}{ 25}\) | \(\infty\) |
|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(\frac{ 1}{ 3}\) | \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(0\) | \(1\) | \(2\) |
| \(\frac{ 2}{ 3}\) | \(3\) | \(\frac{ 1}{ 2}\) | \(1\) | \(0\) | \(1\) | \(3\) |
| \(1\) | \(4\) | \(1\) | \(2\) | \(0\) | \(2\) | \(4\) |
26
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:...
\((4z+1)(6z+1)(43z^2+13z+1)(2z+1)^2(12z-1)^2\)
| \(-\frac{ 1}{ 2}\) | \(-\frac{ 1}{ 4}\) | \(-\frac{ 1}{ 6}\) | \(-\frac{ 13}{ 86}-\frac{ 1}{ 86}\sqrt{ 3}I\) | \(-\frac{ 13}{ 86}+\frac{ 1}{ 86}\sqrt{ 3}I\) | \(0\) | \(\frac{ 1}{ 12}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(\frac{ 1}{ 2}\) | \(2\) |
| \(3\) | \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(\frac{ 1}{ 2}\) | \(3\) |
| \(4\) | \(2\) | \(2\) | \(2\) | \(2\) | \(0\) | \(1\) | \(4\) |
27
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:...
\(-(12z-1)(6z+1)(7z^2-z+1)(4z+1)^2(74z+17)^2\)
| \(-\frac{ 1}{ 4}\) | \(-\frac{ 17}{ 74}\) | \(-\frac{ 1}{ 6}\) | \(0\) | \(\frac{ 1}{ 14}-\frac{ 3}{ 14}\sqrt{ 3}I\) | \(\frac{ 1}{ 14}+\frac{ 3}{ 14}\sqrt{ 3}I\) | \(\frac{ 1}{ 12}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(2\) |
| \(\frac{ 1}{ 2}\) | \(3\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(3\) |
| \(1\) | \(4\) | \(2\) | \(0\) | \(2\) | \(2\) | \(2\) | \(4\) |
28
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:...
\(-(7z+1)(6z+1)(639z^2+87z-1)(2z+3)^2(8z+1)^2\)
| \(-\frac{ 3}{ 2}\) | \(-\frac{ 1}{ 6}\) | \(-\frac{ 29}{ 426}-\frac{ 5}{ 142}\sqrt{ 5}\) | \(-\frac{ 1}{ 7}\) | \(-\frac{ 1}{ 8}\) | \(0\) | \(-\frac{ 29}{ 426}+\frac{ 5}{ 142}\sqrt{ 5}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(0\) | \(1\) | \(2\) |
| \(3\) | \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(3\) |
| \(4\) | \(2\) | \(2\) | \(2\) | \(1\) | \(0\) | \(2\) | \(4\) |
29
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:...
\(-(-1+96z+896z^2)(9z+1)^2(96z+13)^2(8z+1)^2\)
| \(-\frac{ 13}{ 96}\) | \(-\frac{ 1}{ 8}\) | \(-\frac{ 3}{ 56}-\frac{ 5}{ 112}\sqrt{ 2}\) | \(-\frac{ 1}{ 9}\) | \(0\) | \(-\frac{ 3}{ 56}+\frac{ 5}{ 112}\sqrt{ 2}\) | \(\infty\) |
|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(0\) | \(1\) | \(0\) | \(0\) | \(1\) | \(2\) |
| \(3\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(3\) |
| \(4\) | \(1\) | \(2\) | \(1\) | \(0\) | \(2\) | \(4\) |
30
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:...
\(-(-1+56z)(20z-1)^2(8z-1)^2(8z+1)^3\)
| \(-\frac{ 1}{ 8}\) | \(0\) | \(\frac{ 1}{ 56}\) | \(\frac{ 1}{ 20}\) | \(\frac{ 1}{ 8}\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(0\) | \(0\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(2\) |
| \(-\frac{ 1}{ 4}\) | \(0\) | \(1\) | \(3\) | \(\frac{ 1}{ 2}\) | \(3\) |
| \(\frac{ 1}{ 4}\) | \(0\) | \(2\) | \(4\) | \(1\) | \(4\) |