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: 11.13 | AESZ: | Superseeker: 70/13 15323/39 | Hash: 89df09ff1ec0d5dfcae0791579c9095e
Degree: 11
\(13^{2} \theta^4-2 13 x\left(593\theta^4+850\theta^3+685\theta^2+260\theta+39\right)+2^{2} x^{2}\left(81227\theta^4+145178\theta^3+121774\theta^2+52312\theta+9477\right)-x^{3}\left(3180153\theta^4+8754414\theta^3+11733109\theta^2+7260552\theta+1687608\right)+2 x^{4}\left(9121117\theta^4+38823752\theta^3+61935546\theta^2+41745416\theta+10192764\right)-2^{2} x^{5}\left(14736265\theta^4+81359956\theta^3+152008790\theta^2+112521671\theta+29176827\right)+2^{2} 3^{2} x^{6}\left(1220244\theta^4+12211662\theta^3+31283769\theta^2+26817500\theta+7548762\right)+2^{2} 3^{2} x^{7}\left(4505067\theta^4+14797690\theta^3+6324743\theta^2-4986206\theta-2940402\right)-2^{3} 3^{3} x^{8}\left(855097\theta^4+3900198\theta^3+2679311\theta^2-619598\theta-662876\right)-2^{4} 3^{3} x^{9}\left(254021\theta^4+398518\theta^3+352691\theta^2+205022\theta+53940\right)+2^{5} 3^{3} 11 x^{10}\left(13283\theta^4+25990\theta^3+18039\theta^2+5062\theta+456\right)+2^{7} 3^{3} 11^{2} x^{11}(4\theta+3)(\theta+1)^2(4\theta+5)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 6, 126, 4092, 160110, ... --> OEIS Normalized instanton numbers (n0=1): 70/13, 420/13, 15323/39, 78225/13, 1564284/13, ... ; Common denominator:...
\((192z^2-69z+1)(2z^3+39z^2-5z+1)(13-112z-18z^2+132z^3)^2\)
| ≈\(-19.628663\) | ≈\(-0.912176\) | \(0\) | \(\frac{ 23}{ 128}-\frac{ 11}{ 384}\sqrt{ 33}\) | ≈\(0.064331-0.146063I\) | ≈\(0.064331+0.146063I\) | ≈\(0.115746\) | \(\frac{ 23}{ 128}+\frac{ 11}{ 384}\sqrt{ 33}\) | ≈\(0.932793\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 3}{ 4}\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(1\) | \(3\) | \(0\) | \(1\) | \(1\) | \(1\) | \(3\) | \(1\) | \(3\) | \(1\) |
| \(2\) | \(4\) | \(0\) | \(2\) | \(2\) | \(2\) | \(4\) | \(2\) | \(4\) | \(\frac{ 5}{ 4}\) |
5
New Number: 11.14 | AESZ: | Superseeker: 10 13958/9 | Hash: 0a4e6572e1bb29d996fd62dc404c2446
Degree: 11
\(3^{6} \theta^4-3^{6} x\left(111\theta^4+180\theta^3+140\theta^2+50\theta+7\right)+3^{3} x^{2}\left(31925\theta^4+11480\theta^3-42466\theta^2-34182\theta-7560\right)+3^{3} x^{3}\left(4877\theta^4+370644\theta^3+409430\theta^2+199476\theta+42297\right)-2 x^{4}\left(10348339\theta^4+26540048\theta^3+42009388\theta^2+29955528\theta+7880058\right)+2 x^{5}\left(9831565\theta^4+67438924\theta^3+143690304\theta^2+116711926\theta+33599143\right)+2 x^{6}\left(14540887\theta^4-5897448\theta^3-129216202\theta^2-158647410\theta-56400514\right)-2 x^{7}\left(20947985\theta^4+93882580\theta^3+71337738\theta^2-9343940\theta-17269525\right)+x^{8}\left(1325117\theta^4+114002144\theta^3+209338120\theta^2+141064960\theta+32960772\right)+3^{4} x^{9}\left(254941\theta^4+471612\theta^3+445052\theta^2+300870\theta+101457\right)-3^{8} x^{10}\left(1621\theta^4+5816\theta^3+8326\theta^2+5418\theta+1332\right)+3^{13} x^{11}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 7, 231, 11185, 654199, ... --> OEIS Normalized instanton numbers (n0=1): 10, 2591/27, 13958/9, 1037839/27, 3535478/3, ... ; Common denominator:...
\((z-1)(243z^4-520z^3+310z^2+96z-1)(27-189z-143z^2+81z^3)^2\)
| ≈\(-0.97581\) | \(0\) | ≈\(0.130861\) | \(1\) | ≈\(2.610381\) | \(#ND+#NDI\) | \(\infty\) |
|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(3\) | \(0\) | \(3\) | \(1\) | \(3\) | \(1\) | \(1\) |
| \(4\) | \(0\) | \(4\) | \(2\) | \(4\) | \(2\) | \(1\) |
6
New Number: 11.15 | AESZ: | Superseeker: 26 1205094 | Hash: 3569012dbdb9fd87263426cf2bb6fc1e
Degree: 11
\(\theta^4+x\left(1621\theta^4+668\theta^3+604\theta^2+270\theta+45\right)+3 x^{2}\left(254941\theta^4+548152\theta^3+559862\theta^2+194162\theta+28968\right)-3^{2} x^{3}\left(1325117\theta^4-108701676\theta^3-124717610\theta^2-59094684\theta-11443095\right)-2 3^{7} x^{4}\left(20947985\theta^4-10090640\theta^3-84622092\theta^2-45836384\theta-9522442\right)-2 3^{12} x^{5}\left(14540887\theta^4+64060996\theta^3-24278536\theta^2-23929102\theta-6530971\right)+2 3^{17} x^{6}\left(9831565\theta^4-28112664\theta^3+362922\theta^2+7678170\theta+2970162\right)+2 3^{22} x^{7}\left(10348339\theta^4+14853308\theta^3+24479278\theta^2+15836460\theta+3742209\right)+3^{30} x^{8}\left(4877\theta^4-351136\theta^3-673240\theta^2-473040\theta-113516\right)-3^{35} x^{9}\left(31925\theta^4+116220\theta^3+114644\theta^2+42510\theta+4601\right)-3^{43} x^{10}\left(111\theta^4+264\theta^3+266\theta^2+134\theta+28\right)-3^{48} x^{11}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -45, 3591, -147771, -62088201, ... --> OEIS Normalized instanton numbers (n0=1): 26, -15173, 1205094, -256830529, 38564264386, ... ; Common denominator:...
\(-(243z+1)(14348907z^4+5668704z^3-75330z^2-520z-1)(-1-429z+137781z^2+4782969z^3)^2\)
| ≈\(-0.031447\) | \(-\frac{ 1}{ 243}\) | ≈\(-0.001576\) | \(0\) | ≈\(0.004217\) | \(#ND+#NDI\) | \(\infty\) |
|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) |
| \(3\) | \(1\) | \(3\) | \(0\) | \(3\) | \(1\) | \(1\) |
| \(4\) | \(2\) | \(4\) | \(0\) | \(4\) | \(2\) | \(1\) |
7
New Number: 11.16 | AESZ: | Superseeker: 211/35 19279/35 | Hash: dc993c4f73af62a0915341e2b6d1f81f
Degree: 11
\(5^{2} 7^{2} \theta^4-5 7 x\left(2658\theta^4+4272\theta^3+3361\theta^2+1225\theta+175\right)-x^{2}\left(482475+2058700\theta+2927049\theta^2+1102432\theta^3-364211\theta^4\right)+x^{3}\left(1107645+7584675\theta+17848802\theta^2+16891206\theta^3+3547267\theta^4\right)-x^{4}\left(5628891+26546780\theta+46592338\theta^2+38194636\theta^3+16110878\theta^4\right)-3 x^{5}\left(2019469\theta^4+2698822\theta^3+453746\theta^2+985337\theta+832575\right)+3^{2} x^{6}\left(3186847\theta^4+10570488\theta^3+13101727\theta^2+7620366\theta+1780951\right)+3^{3} x^{7}\left(515831\theta^4+2708278\theta^3+5879206\theta^2+4986803\theta+1463799\right)-3^{4} x^{8}\left(94081\theta^4+60208\theta^3-440794\theta^2-635338\theta-240009\right)-3^{6} x^{9}\left(4919\theta^4+23958\theta^3+26539\theta^2+8334\theta-480\right)+2 3^{6} x^{10}\left(392\theta^4-674\theta^3-2747\theta^2-2410\theta-663\right)+2^{2} 3^{10} x^{11}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 5, 129, 4523, 191329, ... --> OEIS Normalized instanton numbers (n0=1): 211/35, 1643/35, 19279/35, 69901/7, 7789913/35, ... ; Common denominator:...
\((1-66z-379z^2+427z^3+439z^4+81z^5)(35-174z-81z^2+54z^3)^2\)
| ≈\(-1.31797\) | \(0\) | ≈\(0.186913\) | ≈\(2.631057\) | \(#ND+#NDI\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(3\) | \(0\) | \(3\) | \(3\) | \(1\) | \(1\) |
| \(4\) | \(0\) | \(4\) | \(4\) | \(2\) | \(1\) |
8
New Number: 11.17 | AESZ: | Superseeker: -263/2 -218434 | Hash: 8aa8ad0296efe97c979c0336a2ec2312
Degree: 11
\(2^{2} \theta^4+2 x\left(392\theta^4+2242\theta^3+1627\theta^2+506\theta+66\right)-3^{4} x^{2}\left(4919\theta^4-4282\theta^3-15821\theta^2-7454\theta-1314\right)-3^{6} x^{3}\left(94081\theta^4+316116\theta^3-56932\theta^2-50550\theta-11592\right)+3^{9} x^{4}\left(515831\theta^4-644954\theta^3+849358\theta^2+710099\theta+163755\right)+3^{12} x^{5}\left(3186847\theta^4+2176900\theta^3+511345\theta^2-380988\theta-121329\right)-3^{15} x^{6}\left(2019469\theta^4+5379054\theta^3+4474094\theta^2-96435\theta-378369\right)-3^{18} x^{7}\left(16110878\theta^4+26248876\theta^3+28673698\theta^2+16497500\theta+3590691\right)+3^{22} x^{8}\left(3547267\theta^4-2702138\theta^3-11541214\theta^2-8371621\theta-1972167\right)+3^{26} x^{9}\left(364211\theta^4+2559276\theta^3+2565513\theta^2+968742\theta+115819\right)-3^{30} 5 7 x^{10}\left(2658\theta^4+6360\theta^3+6493\theta^2+3313\theta+697\right)+3^{34} 5^{2} 7^{2} x^{11}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -33, 3321, -480255, 82588329, ... --> OEIS Normalized instanton numbers (n0=1): -263/2, -21293/8, -218434, -32618595/2, -1709392950, ... ; Common denominator:...
\((43046721z^5-35075106z^4-2486619z^3+34587z^2+439z+1)(2-243z-42282z^2+688905z^3)^2\)
| ≈\(-0.009367\) | \(0\) | ≈\(0.004692\) | ≈\(0.066051\) | \(#ND+#NDI\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(3\) | \(0\) | \(3\) | \(3\) | \(1\) | \(1\) |
| \(4\) | \(0\) | \(4\) | \(4\) | \(2\) | \(1\) |
9
New Number: 11.18 | AESZ: | Superseeker: -343/26 -27836/13 | Hash: 7fd9e473da9a826dea365ad9c234d2b1
Degree: 11
\(2^{2} 13^{2} \theta^4+2 13 x\left(2902\theta^4+6146\theta^3+4763\theta^2+1690\theta+234\right)-3 x^{2}\left(96469\theta^4+49486\theta^3-135373\theta^2-115726\theta-26754\right)+3 x^{3}\left(107658\theta^4-7866\theta^3+142429\theta^2+209352\theta+70434\right)+3^{2} x^{4}\left(27312\theta^4-323430\theta^3-1054064\theta^2-786941\theta-191951\right)-3^{4} x^{5}\left(1180\theta^4-103322\theta^3-143955\theta^2-85327\theta-20494\right)-3^{5} x^{6}\left(2379\theta^4+12696\theta^3+45266\theta^2+49297\theta+16562\right)-3^{6} x^{7}\left(929\theta^4+13156\theta^3-15355\theta^2-25877\theta-8920\right)+3^{7} x^{8}\left(1318\theta^4+2950\theta^3+2915\theta^2+772\theta-131\right)+3^{7} x^{9}\left(315\theta^4-3006\theta^3-5005\theta^2-2784\theta-504\right)-2^{2} 3^{8} x^{10}\left(42\theta^4+66\theta^3+25\theta^2-8\theta-5\right)+2^{4} 3^{10} x^{11}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -9, 333, -18639, 1264509, ... --> OEIS Normalized instanton numbers (n0=1): -343/26, 11207/104, -27836/13, 764852/13, -52338075/26, ... ; Common denominator:...
\((1+116z+75z^2+162z^3-108z^4+81z^5)(26-57z+9z^2+108z^3)^2\)
| ≈\(-0.92963\) | \(0\) | ≈\(0.423148-0.282683I\) | ≈\(0.423148+0.282683I\) | \(#ND+#NDI\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(3\) | \(0\) | \(3\) | \(3\) | \(1\) | \(1\) |
| \(4\) | \(0\) | \(4\) | \(4\) | \(2\) | \(1\) |
10
New Number: 11.19 | AESZ: | Superseeker: 21/4 -1045/6 | Hash: acf903f94ac2a08b9f2b26dff65a52ff
Degree: 11
\(2^{4} \theta^4-2^{2} 3 x\left(42\theta^4+102\theta^3+79\theta^2+28\theta+4\right)+3^{3} x^{2}\left(315\theta^4+4266\theta^3+5903\theta^2+3052\theta+596\right)+3^{6} x^{3}\left(1318\theta^4+2322\theta^3+1973\theta^2+1480\theta+380\right)-3^{8} x^{4}\left(929\theta^4-9440\theta^3-49249\theta^2-40585\theta-10625\right)-3^{10} x^{5}\left(2379\theta^4-3180\theta^3+21452\theta^2+12663\theta+2214\right)-3^{12} x^{6}\left(1180\theta^4+108042\theta^3+173091\theta^2+112103\theta+25380\right)+3^{13} x^{7}\left(27312\theta^4+432678\theta^3+80098\theta^2-241649\theta-108332\right)+3^{15} x^{8}\left(107658\theta^4+438498\theta^3+811975\theta^2+529736\theta+119035\right)-3^{18} x^{9}\left(96469\theta^4+336390\theta^3+294983\theta^2+82398\theta+582\right)+2 3^{20} 13 x^{10}\left(2902\theta^4+5462\theta^3+3737\theta^2+1006\theta+63\right)+2^{2} 3^{23} 13^{2} x^{11}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 3, -27, -1563, -40491, ... --> OEIS Normalized instanton numbers (n0=1): 21/4, -969/16, -1045/6, -35199/4, 536619/4, ... ; Common denominator:...
\((1-36z+1458z^2+18225z^3+761076z^4+177147z^5)(4+9z-1539z^2+18954z^3)^2\)
| ≈\(-4.272671\) | ≈\(-0.039841\) | ≈\(-0.024843\) | ≈\(-0.024843\) | \(0\) | ≈\(0.01303\) | ≈\(0.01303\) | ≈\(0.060519-0.040429I\) | ≈\(0.060519+0.040429I\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(1\) | \(3\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(3\) | \(3\) | \(1\) |
| \(2\) | \(4\) | \(2\) | \(2\) | \(0\) | \(2\) | \(2\) | \(4\) | \(4\) | \(1\) |
11
New Number: 11.1 | AESZ: | Superseeker: -4 550/3 | Hash: 9e36d74a520997fe52f0cbbfafae6aaf
Degree: 11
\(\theta^4+x\left(6+38\theta+96\theta^2+116\theta^3+91\theta^4\right)+x^{2}\left(1218+5950\theta+11076\theta^2+9388\theta^3+3649\theta^4\right)+x^{3}\left(32814+148542\theta+258070\theta^2+203832\theta^3+63585\theta^4\right)+2 x^{4}\left(244543\theta^4+938432\theta^3+1417427\theta^2+933049\theta+226317\right)+2^{2} x^{5}\left(374407\theta^4+1908784\theta^3+3407293\theta^2+2501538\theta+653454\right)+2^{2} 3 x^{6}\left(130530\theta^4+686256\theta^3+1382165\theta^2+1159645\theta+333030\right)+2^{3} x^{7}\left(276464\theta^4-92912\theta^3-3194335\theta^2-3755703\theta-1224450\right)+2^{4} x^{8}\left(341712\theta^4+1614816\theta^3+1576879\theta^2+219863\theta-145632\right)-2^{5} x^{9}\left(29968\theta^4+412128\theta^3+489227\theta^2+156573\theta-3258\right)+2^{8} 3 x^{10}\left(6368\theta^4+13600\theta^3+11014\theta^2+4187\theta+681\right)-2^{11} 3^{2} x^{11}(4\theta+3)(\theta+1)^2(4\theta+5)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -6, 54, 12, -26010, ... --> OEIS Normalized instanton numbers (n0=1): -4, -11, 550/3, -2965/2, -3316, ... ; Common denominator:...
\(-(4z+1)(3z+1)(96z^3-1576z^2-62z-1)(1+11z-6z^2+16z^3)^2\)
| \(-\frac{ 1}{ 3}\) | \(-\frac{ 1}{ 4}\) | ≈\(-0.085955\) | ≈\(-0.019642-0.015722I\) | ≈\(-0.019642+0.015722I\) | \(0\) | ≈\(0.230478-0.820976I\) | ≈\(0.230478+0.820976I\) | ≈\(16.455951\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 3}{ 4}\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(1\) | \(1\) | \(3\) | \(1\) | \(1\) | \(0\) | \(3\) | \(3\) | \(1\) | \(1\) |
| \(2\) | \(2\) | \(4\) | \(2\) | \(2\) | \(0\) | \(4\) | \(4\) | \(2\) | \(\frac{ 5}{ 4}\) |
12
New Number: 11.20 | AESZ: | Superseeker: 21/4 1285/2 | Hash: b07e191c8c5d8b6a2c25e842f85fcaf0
Degree: 11
\(2^{4} \theta^4-2^{2} x\left(278\theta^4+394\theta^3+309\theta^2+112\theta+16\right)-x^{2}\left(11952+57616\theta+96951\theta^2+56722\theta^3+4615\theta^4\right)+2 x^{3}\left(129366\theta^4+473682\theta^3+531879\theta^2+282576\theta+62656\right)-x^{4}\left(1430728+5365104\theta+7153953\theta^2+3814866\theta^3+1139565\theta^4\right)-2 3 x^{5}\left(286602\theta^4-694990\theta^3-3072025\theta^2-2917584\theta-895328\right)+2^{2} x^{6}\left(1338547\theta^4+4488552\theta^3+821964\theta^2-3171240\theta-1633306\right)+2^{4} x^{7}\left(17380\theta^4-1361536\theta^3-2049918\theta^2-1043692\theta-152703\right)-2^{6} x^{8}\left(106051\theta^4+123172\theta^3+23589\theta^2-28382\theta-10873\right)+2^{10} x^{9}\left(4885\theta^4+15033\theta^3+20559\theta^2+13908\theta+3737\right)-2^{12} x^{10}\left(335\theta^4+1270\theta^3+1875\theta^2+1240\theta+307\right)+2^{17} x^{11}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 4, 116, 3856, 163636, ... --> OEIS Normalized instanton numbers (n0=1): 21/4, 1965/32, 1285/2, 103095/8, 1157421/4, ... ; Common denominator:...
\((z-1)(16z^2-16z-1)(32z^2-71z+1)(4-27z-50z^2+16z^3)^2\)
| ≈\(-0.573963\) | \(\frac{ 1}{ 2}-\frac{ 1}{ 4}\sqrt{ 5}\) | \(0\) | \(\frac{ 71}{ 64}-\frac{ 17}{ 64}\sqrt{ 17}\) | ≈\(0.121762\) | \(1\) | \(\frac{ 1}{ 2}+\frac{ 1}{ 4}\sqrt{ 5}\) | \(\frac{ 71}{ 64}+\frac{ 17}{ 64}\sqrt{ 17}\) | ≈\(3.577201\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(3\) | \(1\) | \(0\) | \(1\) | \(3\) | \(1\) | \(1\) | \(1\) | \(3\) | \(1\) |
| \(4\) | \(2\) | \(0\) | \(2\) | \(4\) | \(2\) | \(2\) | \(2\) | \(4\) | \(1\) |
13
New Number: 11.21 | AESZ: | Superseeker: 240 31333936 | Hash: 9a8c2dbc999179b3ef13a33cce17dc01
Degree: 11
\(\theta^4+2^{4} x\left(335\theta^4+70\theta^3+75\theta^2+40\theta+7\right)+2^{11} x^{2}\left(4885\theta^4+4507\theta^3+4770\theta^2+1651\theta+240\right)+2^{16} x^{3}\left(106051\theta^4+301032\theta^3+290379\theta^2+130248\theta+23977\right)+2^{23} x^{4}\left(17380\theta^4+1431056\theta^3+2138970\theta^2+1097984\theta+219987\right)-2^{30} x^{5}\left(1338547\theta^4+865636\theta^3-4612410\theta^2-3296300\theta-790107\right)-2^{38} 3 x^{6}\left(286602\theta^4+1841398\theta^3+732557\theta^2+4912\theta-68177\right)+2^{46} x^{7}\left(1139565\theta^4+743394\theta^3+2546745\theta^2+2056464\theta+544276\right)+2^{56} x^{8}\left(129366\theta^4+43782\theta^3-112971\theta^2-122400\theta-32357\right)+2^{64} x^{9}\left(4615\theta^4-38262\theta^3-45525\theta^2-15420\theta-820\right)-2^{75} x^{10}\left(278\theta^4+718\theta^3+795\theta^2+436\theta+97\right)-2^{86} x^{11}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -112, 28304, -9202432, 3381592336, ... --> OEIS Normalized instanton numbers (n0=1): 240, -95082, 31333936, -15748488666, 8901200955216, ... ; Common denominator:...
\(-(512z+1)(8192z^2+1136z+1)(16384z^2-512z-1)(-1-1600z+442368z^2+33554432z^3)^2\)
| \(-\frac{ 71}{ 1024}-\frac{ 17}{ 1024}\sqrt{ 17}\) | ≈\(-0.01604\) | \(-\frac{ 1}{ 512}\) | \(\frac{ 1}{ 64}-\frac{ 1}{ 128}\sqrt{ 5}\) | \(-\frac{ 71}{ 1024}+\frac{ 17}{ 1024}\sqrt{ 17}\) | ≈\(-0.000546\) | \(0\) | ≈\(0.003403\) | \(\frac{ 1}{ 64}+\frac{ 1}{ 128}\sqrt{ 5}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) |
| \(1\) | \(3\) | \(1\) | \(1\) | \(1\) | \(3\) | \(0\) | \(3\) | \(1\) | \(1\) |
| \(2\) | \(4\) | \(2\) | \(2\) | \(2\) | \(4\) | \(0\) | \(4\) | \(2\) | \(1\) |
14
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:...
\(-(12z^2+6z+1)(7457z^5+6100z^4+1929z^3+257z^2+7z-1)(97+912z+2028z^2)^2\)
| \(-\frac{ 38}{ 169}-\frac{ 1}{ 1014}\sqrt{ 2805}\) | \(-\frac{ 1}{ 4}-\frac{ 1}{ 12}\sqrt{ 3}I\) | \(-\frac{ 1}{ 4}+\frac{ 1}{ 12}\sqrt{ 3}I\) | \(-\frac{ 38}{ 169}+\frac{ 1}{ 1014}\sqrt{ 2805}\) | \(0\) | \(#ND+#NDI\) | \(\infty\) |
|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(2\) |
| \(3\) | \(1\) | \(1\) | \(3\) | \(0\) | \(1\) | \(3\) |
| \(4\) | \(2\) | \(2\) | \(4\) | \(0\) | \(2\) | \(4\) |
15
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:...
\(-(3z+1)(11971z^6+16085z^5+8704z^4+2334z^3+289z^2+7z-1)(91+573z+770z^2)^2\)
| \(-\frac{ 573}{ 1540}-\frac{ 1}{ 1540}\sqrt{ 48049}\) | \(-\frac{ 1}{ 3}\) | \(-\frac{ 573}{ 1540}+\frac{ 1}{ 1540}\sqrt{ 48049}\) | \(0\) | \(#ND+#NDI\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(2\) |
| \(3\) | \(1\) | \(3\) | \(0\) | \(1\) | \(3\) |
| \(4\) | \(2\) | \(4\) | \(0\) | \(2\) | \(4\) |
16
New Number: 11.4 | AESZ: | Superseeker: 116/5 29628/5 | Hash: 4222cdacde3dbaf06ed32adadb70f0d6
Degree: 11
\(5^{2} \theta^4-2^{2} 5 x\left(197\theta^4+418\theta^3+319\theta^2+110\theta+15\right)+2^{4} x^{2}\left(181\theta^4+5068\theta^3+10291\theta^2+6750\theta+1585\right)-2^{6} x^{3}\left(1727\theta^4-4758\theta^3-11365\theta^2-4560\theta-345\right)+2^{9} x^{4}\left(2351\theta^4+4552\theta^3-11125\theta^2-12552\theta-3833\right)-2^{12} x^{5}\left(527\theta^4+1448\theta^3+16\theta^2-1811\theta-887\right)+2^{15} x^{6}\left(493\theta^4-1527\theta^3-789\theta^2-363\theta-116\right)-2^{17} x^{7}\left(780\theta^4-282\theta^3+865\theta^2+1459\theta+563\right)+2^{20} x^{8}\left(151\theta^4-104\theta^3-291\theta^2-239\theta-65\right)-2^{22} x^{9}\left(23\theta^4+24\theta^3+85\theta^2+132\theta+55\right)+2^{25} x^{10}(\theta+1)(7\theta^3+31\theta^2+35\theta+12)-2^{28} x^{11}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 12, 572, 42960, 3944556, ... --> OEIS Normalized instanton numbers (n0=1): 116/5, 1059/5, 29628/5, 2227181/10, 51562768/5, ... ; Common denominator:...
\(-(-1+156z+160z^2+256z^3)(4z-1)^2(256z^3-128z^2-16z-5)^2\)
| ≈\(-0.315684-0.716756I\) | ≈\(-0.315684+0.716756I\) | ≈\(-0.072055-0.158527I\) | ≈\(-0.072055+0.158527I\) | \(0\) | ≈\(0.006368\) | \(\frac{ 1}{ 4}\) | ≈\(0.64411\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) |
| \(1\) | \(1\) | \(3\) | \(3\) | \(0\) | \(1\) | \(\frac{ 1}{ 2}\) | \(3\) | \(1\) |
| \(2\) | \(2\) | \(4\) | \(4\) | \(0\) | \(2\) | \(1\) | \(4\) | \(1\) |
17
New Number: 11.5 | AESZ: | Superseeker: -32 608 | Hash: f5f2274632f5544ebf559c6c512159d1
Degree: 11
\(\theta^4-2^{4} x\theta(7\theta^3-10\theta^2-6\theta-1)+2^{8} x^{2}\left(23\theta^4+68\theta^3+151\theta^2+58\theta+7\right)-2^{13} x^{3}\left(151\theta^4+708\theta^3+927\theta^2+573\theta+138\right)+2^{17} x^{4}\left(780\theta^4+3402\theta^3+6391\theta^2+4237\theta+1031\right)-2^{22} x^{5}\left(493\theta^4+3499\theta^3+6750\theta^2+5338\theta+1478\right)+2^{26} x^{6}\left(527\theta^4+660\theta^3-1166\theta^2-393\theta+19\right)-2^{30} x^{7}\left(2351\theta^4+4852\theta^3-10675\theta^2-13950\theta-4607\right)+2^{34} x^{8}\left(1727\theta^4+11666\theta^3+13271\theta^2+3012\theta-665\right)-2^{39} x^{9}\left(181\theta^4-4344\theta^3-3827\theta^2-648\theta+239\right)+2^{44} 5 x^{10}\left(197\theta^4+370\theta^3+247\theta^2+62\theta+3\right)-2^{49} 5^{2} x^{11}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, -112, 13824, -136944, ... --> OEIS Normalized instanton numbers (n0=1): -32, -616, 608, -21270, -15181664, ... ; Common denominator:...
\(-(-1-80z-9984z^2+8192z^3)(32z-1)^2(40960z^3+1024z^2+64z-1)^2\)
| ≈\(-0.018565-0.040844I\) | ≈\(-0.018565+0.040844I\) | ≈\(-0.004021-0.009129I\) | ≈\(-0.004021+0.009129I\) | \(0\) | ≈\(0.012129\) | \(\frac{ 1}{ 32}\) | ≈\(1.226791\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) |
| \(3\) | \(3\) | \(1\) | \(1\) | \(0\) | \(3\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) |
| \(4\) | \(4\) | \(2\) | \(2\) | \(0\) | \(4\) | \(1\) | \(2\) | \(1\) |
18
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:...
\(-(-1+7z+219z^2+1115z^3+1934z^4+679z^5)(z+1)^2(100z^2-197z-102)^2\)
| \(-1\) | \(\frac{ 197}{ 200}-\frac{ 1}{ 200}\sqrt{ 79609}\) | \(0\) | \(\frac{ 197}{ 200}+\frac{ 1}{ 200}\sqrt{ 79609}\) | \(#ND+#NDI\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(\frac{ 1}{ 3}\) | \(1\) | \(0\) | \(1\) | \(1\) | \(2\) |
| \(\frac{ 2}{ 3}\) | \(3\) | \(0\) | \(3\) | \(1\) | \(3\) |
| \(1\) | \(4\) | \(0\) | \(4\) | \(2\) | \(4\) |
19
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:...
\((18z+1)(189z^2+18z+1)(27z+1)^2(9z-1)^2(81z^2+54z+1)^2\)
| \(-\frac{ 1}{ 3}-\frac{ 2}{ 9}\sqrt{ 2}\) | \(-\frac{ 1}{ 18}\) | \(-\frac{ 1}{ 21}-\frac{ 2}{ 63}\sqrt{ 3}I\) | \(-\frac{ 1}{ 21}+\frac{ 2}{ 63}\sqrt{ 3}I\) | \(-\frac{ 1}{ 27}\) | \(-\frac{ 1}{ 3}+\frac{ 2}{ 9}\sqrt{ 2}\) | \(0\) | \(\frac{ 1}{ 9}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(0\) | \(\frac{ 1}{ 2}\) | \(2\) |
| \(3\) | \(1\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(3\) | \(0\) | \(\frac{ 1}{ 2}\) | \(3\) |
| \(4\) | \(2\) | \(2\) | \(2\) | \(1\) | \(4\) | \(0\) | \(1\) | \(4\) |
20
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:...
\((10z+1)(6z-1)(1096z^3+228z^2+14z-1)(2z-1)^2(1284z^2+232z-17)^2\)
| \(-\frac{ 29}{ 321}-\frac{ 1}{ 642}\sqrt{ 8821}\) | ≈\(-0.124082-0.085658I\) | ≈\(-0.124082+0.085658I\) | \(-\frac{ 1}{ 10}\) | \(0\) | ≈\(0.040135\) | \(-\frac{ 29}{ 321}+\frac{ 1}{ 642}\sqrt{ 8821}\) | \(\frac{ 1}{ 6}\) | \(\frac{ 1}{ 2}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(0\) | \(2\) |
| \(3\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(3\) | \(1\) | \(1\) | \(3\) |
| \(4\) | \(2\) | \(2\) | \(2\) | \(0\) | \(2\) | \(4\) | \(2\) | \(1\) | \(4\) |
21
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:...
\(-(5z+1)(13z+1)(6z+1)(368z^2+56z-1)(4z+1)^2(8z^2-26z-3)^2\)
| \(-\frac{ 1}{ 4}\) | \(-\frac{ 1}{ 5}\) | \(-\frac{ 7}{ 92}-\frac{ 3}{ 46}\sqrt{ 2}\) | \(-\frac{ 1}{ 6}\) | \(\frac{ 13}{ 8}-\frac{ 1}{ 8}\sqrt{ 193}\) | \(-\frac{ 1}{ 13}\) | \(0\) | \(-\frac{ 7}{ 92}+\frac{ 3}{ 46}\sqrt{ 2}\) | \(\frac{ 13}{ 8}+\frac{ 1}{ 8}\sqrt{ 193}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(2\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(3\) | \(1\) | \(0\) | \(1\) | \(3\) | \(3\) |
| \(1\) | \(2\) | \(2\) | \(2\) | \(4\) | \(2\) | \(0\) | \(2\) | \(4\) | \(4\) |