You searched for: Spectrum0=0,0,0,0
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331
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:...
\((1+116z+75z^2+162z^3-108z^4+81z^5)(26-57z+9z^2+108z^3)^2\)
| ≈\(-0.92963\) | \(0\) | ≈\(0.423148-0.282683I\) | ≈\(0.423148+0.282683I\) | \(#ND+#NDI\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(3\) | \(0\) | \(3\) | \(3\) | \(1\) | \(1\) |
| \(4\) | \(0\) | \(4\) | \(4\) | \(2\) | \(1\) |
332
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:...
\((1-36z+1458z^2+18225z^3+761076z^4+177147z^5)(4+9z-1539z^2+18954z^3)^2\)
| ≈\(-4.272671\) | ≈\(-0.039841\) | ≈\(-0.024843\) | ≈\(-0.024843\) | \(0\) | ≈\(0.01303\) | ≈\(0.01303\) | ≈\(0.060519-0.040429I\) | ≈\(0.060519+0.040429I\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(1\) | \(3\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(3\) | \(3\) | \(1\) |
| \(2\) | \(4\) | \(2\) | \(2\) | \(0\) | \(2\) | \(2\) | \(4\) | \(4\) | \(1\) |
333
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:...
\(-(4z+1)(3z+1)(96z^3-1576z^2-62z-1)(1+11z-6z^2+16z^3)^2\)
| \(-\frac{ 1}{ 3}\) | \(-\frac{ 1}{ 4}\) | ≈\(-0.085955\) | ≈\(-0.019642-0.015722I\) | ≈\(-0.019642+0.015722I\) | \(0\) | ≈\(0.230478-0.820976I\) | ≈\(0.230478+0.820976I\) | ≈\(16.455951\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 3}{ 4}\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(1\) | \(1\) | \(3\) | \(1\) | \(1\) | \(0\) | \(3\) | \(3\) | \(1\) | \(1\) |
| \(2\) | \(2\) | \(4\) | \(2\) | \(2\) | \(0\) | \(4\) | \(4\) | \(2\) | \(\frac{ 5}{ 4}\) |
334
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:...
\((z-1)(16z^2-16z-1)(32z^2-71z+1)(4-27z-50z^2+16z^3)^2\)
| ≈\(-0.573963\) | \(\frac{ 1}{ 2}-\frac{ 1}{ 4}\sqrt{ 5}\) | \(0\) | \(\frac{ 71}{ 64}-\frac{ 17}{ 64}\sqrt{ 17}\) | ≈\(0.121762\) | \(1\) | \(\frac{ 1}{ 2}+\frac{ 1}{ 4}\sqrt{ 5}\) | \(\frac{ 71}{ 64}+\frac{ 17}{ 64}\sqrt{ 17}\) | ≈\(3.577201\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(3\) | \(1\) | \(0\) | \(1\) | \(3\) | \(1\) | \(1\) | \(1\) | \(3\) | \(1\) |
| \(4\) | \(2\) | \(0\) | \(2\) | \(4\) | \(2\) | \(2\) | \(2\) | \(4\) | \(1\) |
335
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:...
\(-(512z+1)(8192z^2+1136z+1)(16384z^2-512z-1)(-1-1600z+442368z^2+33554432z^3)^2\)
| \(-\frac{ 71}{ 1024}-\frac{ 17}{ 1024}\sqrt{ 17}\) | ≈\(-0.01604\) | \(-\frac{ 1}{ 512}\) | \(\frac{ 1}{ 64}-\frac{ 1}{ 128}\sqrt{ 5}\) | \(-\frac{ 71}{ 1024}+\frac{ 17}{ 1024}\sqrt{ 17}\) | ≈\(-0.000546\) | \(0\) | ≈\(0.003403\) | \(\frac{ 1}{ 64}+\frac{ 1}{ 128}\sqrt{ 5}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) |
| \(1\) | \(3\) | \(1\) | \(1\) | \(1\) | \(3\) | \(0\) | \(3\) | \(1\) | \(1\) |
| \(2\) | \(4\) | \(2\) | \(2\) | \(2\) | \(4\) | \(0\) | \(4\) | \(2\) | \(1\) |
336
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:...
\(-(12z^2+6z+1)(7457z^5+6100z^4+1929z^3+257z^2+7z-1)(97+912z+2028z^2)^2\)
| \(-\frac{ 38}{ 169}-\frac{ 1}{ 1014}\sqrt{ 2805}\) | \(-\frac{ 1}{ 4}-\frac{ 1}{ 12}\sqrt{ 3}I\) | \(-\frac{ 1}{ 4}+\frac{ 1}{ 12}\sqrt{ 3}I\) | \(-\frac{ 38}{ 169}+\frac{ 1}{ 1014}\sqrt{ 2805}\) | \(0\) | \(#ND+#NDI\) | \(\infty\) |
|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(2\) |
| \(3\) | \(1\) | \(1\) | \(3\) | \(0\) | \(1\) | \(3\) |
| \(4\) | \(2\) | \(2\) | \(4\) | \(0\) | \(2\) | \(4\) |
337
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:...
\(-(3z+1)(11971z^6+16085z^5+8704z^4+2334z^3+289z^2+7z-1)(91+573z+770z^2)^2\)
| \(-\frac{ 573}{ 1540}-\frac{ 1}{ 1540}\sqrt{ 48049}\) | \(-\frac{ 1}{ 3}\) | \(-\frac{ 573}{ 1540}+\frac{ 1}{ 1540}\sqrt{ 48049}\) | \(0\) | \(#ND+#NDI\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(2\) |
| \(3\) | \(1\) | \(3\) | \(0\) | \(1\) | \(3\) |
| \(4\) | \(2\) | \(4\) | \(0\) | \(2\) | \(4\) |
338
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:...
\(-(-1+156z+160z^2+256z^3)(4z-1)^2(256z^3-128z^2-16z-5)^2\)
| ≈\(-0.315684-0.716756I\) | ≈\(-0.315684+0.716756I\) | ≈\(-0.072055-0.158527I\) | ≈\(-0.072055+0.158527I\) | \(0\) | ≈\(0.006368\) | \(\frac{ 1}{ 4}\) | ≈\(0.64411\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) |
| \(1\) | \(1\) | \(3\) | \(3\) | \(0\) | \(1\) | \(\frac{ 1}{ 2}\) | \(3\) | \(1\) |
| \(2\) | \(2\) | \(4\) | \(4\) | \(0\) | \(2\) | \(1\) | \(4\) | \(1\) |
339
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:...
\(-(-1-80z-9984z^2+8192z^3)(32z-1)^2(40960z^3+1024z^2+64z-1)^2\)
| ≈\(-0.018565-0.040844I\) | ≈\(-0.018565+0.040844I\) | ≈\(-0.004021-0.009129I\) | ≈\(-0.004021+0.009129I\) | \(0\) | ≈\(0.012129\) | \(\frac{ 1}{ 32}\) | ≈\(1.226791\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) |
| \(3\) | \(3\) | \(1\) | \(1\) | \(0\) | \(3\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) |
| \(4\) | \(4\) | \(2\) | \(2\) | \(0\) | \(4\) | \(1\) | \(2\) | \(1\) |
340
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:...
\(-(-1+7z+219z^2+1115z^3+1934z^4+679z^5)(z+1)^2(100z^2-197z-102)^2\)
| \(-1\) | \(\frac{ 197}{ 200}-\frac{ 1}{ 200}\sqrt{ 79609}\) | \(0\) | \(\frac{ 197}{ 200}+\frac{ 1}{ 200}\sqrt{ 79609}\) | \(#ND+#NDI\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(\frac{ 1}{ 3}\) | \(1\) | \(0\) | \(1\) | \(1\) | \(2\) |
| \(\frac{ 2}{ 3}\) | \(3\) | \(0\) | \(3\) | \(1\) | \(3\) |
| \(1\) | \(4\) | \(0\) | \(4\) | \(2\) | \(4\) |
341
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:...
\((18z+1)(189z^2+18z+1)(27z+1)^2(9z-1)^2(81z^2+54z+1)^2\)
| \(-\frac{ 1}{ 3}-\frac{ 2}{ 9}\sqrt{ 2}\) | \(-\frac{ 1}{ 18}\) | \(-\frac{ 1}{ 21}-\frac{ 2}{ 63}\sqrt{ 3}I\) | \(-\frac{ 1}{ 21}+\frac{ 2}{ 63}\sqrt{ 3}I\) | \(-\frac{ 1}{ 27}\) | \(-\frac{ 1}{ 3}+\frac{ 2}{ 9}\sqrt{ 2}\) | \(0\) | \(\frac{ 1}{ 9}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(0\) | \(\frac{ 1}{ 2}\) | \(2\) |
| \(3\) | \(1\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(3\) | \(0\) | \(\frac{ 1}{ 2}\) | \(3\) |
| \(4\) | \(2\) | \(2\) | \(2\) | \(1\) | \(4\) | \(0\) | \(1\) | \(4\) |
342
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:...
\((10z+1)(6z-1)(1096z^3+228z^2+14z-1)(2z-1)^2(1284z^2+232z-17)^2\)
| \(-\frac{ 29}{ 321}-\frac{ 1}{ 642}\sqrt{ 8821}\) | ≈\(-0.124082-0.085658I\) | ≈\(-0.124082+0.085658I\) | \(-\frac{ 1}{ 10}\) | \(0\) | ≈\(0.040135\) | \(-\frac{ 29}{ 321}+\frac{ 1}{ 642}\sqrt{ 8821}\) | \(\frac{ 1}{ 6}\) | \(\frac{ 1}{ 2}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(0\) | \(2\) |
| \(3\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(3\) | \(1\) | \(1\) | \(3\) |
| \(4\) | \(2\) | \(2\) | \(2\) | \(0\) | \(2\) | \(4\) | \(2\) | \(1\) | \(4\) |
343
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:...
\(-(5z+1)(13z+1)(6z+1)(368z^2+56z-1)(4z+1)^2(8z^2-26z-3)^2\)
| \(-\frac{ 1}{ 4}\) | \(-\frac{ 1}{ 5}\) | \(-\frac{ 7}{ 92}-\frac{ 3}{ 46}\sqrt{ 2}\) | \(-\frac{ 1}{ 6}\) | \(\frac{ 13}{ 8}-\frac{ 1}{ 8}\sqrt{ 193}\) | \(-\frac{ 1}{ 13}\) | \(0\) | \(-\frac{ 7}{ 92}+\frac{ 3}{ 46}\sqrt{ 2}\) | \(\frac{ 13}{ 8}+\frac{ 1}{ 8}\sqrt{ 193}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(2\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(3\) | \(1\) | \(0\) | \(1\) | \(3\) | \(3\) |
| \(1\) | \(2\) | \(2\) | \(2\) | \(4\) | \(2\) | \(0\) | \(2\) | \(4\) | \(4\) |
344
New Number: 12.10 | AESZ: | Superseeker: 224 4999008 | Hash: d0e84951fc25cf38a32ec7fba5893d59
Degree: 12
\(\theta^4+2^{4} x\left(160\theta^4+32\theta^3+56\theta^2+40\theta+9\right)+2^{13} x^{2}\left(328\theta^4+304\theta^3+442\theta^2+240\theta+57\right)+2^{22} x^{3}\left(416\theta^4+696\theta^3+939\theta^2+738\theta+225\right)+2^{28} 3 x^{4}\left(1120\theta^4+1856\theta^3+3196\theta^2+2832\theta+959\right)+2^{39} 3^{2} x^{5}\left(76\theta^4+128\theta^3+168\theta^2+168\theta+61\right)+2^{45} 3 x^{6}\left(1232\theta^4+2160\theta^3+2420\theta^2+1344\theta+273\right)+2^{54} 3 x^{7}\left(696\theta^4+1272\theta^3+1781\theta^2+554\theta-109\right)+2^{60} 3 x^{8}\left(2608\theta^4+4960\theta^3+8764\theta^2+4440\theta+423\right)+2^{68} 5 x^{9}\left(1216\theta^4+2592\theta^3+4596\theta^2+3456\theta+999\right)+2^{76} 5 x^{10}\left(736\theta^4+2048\theta^3+3128\theta^2+2536\theta+867\right)+2^{84} 5^{2} x^{11}\left(64\theta^4+256\theta^3+412\theta^2+312\theta+93\right)+2^{92} 5^{2} x^{12}\left((2\theta+3)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -144, 13584, -80128, -173794032, ... --> OEIS Normalized instanton numbers (n0=1): 224, -22712, 4999008, -855952448, 199163179936, ... ; Common denominator:...
\((256z+1)^2(65536z^2+256z+1)^2(83886080z^3+768z+1)^2\)
| \(-\frac{ 1}{ 256}\) | \(-\frac{ 1}{ 512}-\frac{ 1}{ 512}\sqrt{ 3}I\) | \(-\frac{ 1}{ 512}+\frac{ 1}{ 512}\sqrt{ 3}I\) | ≈\(-0.00114\) | \(0\) | ≈\(0.00057-0.003183I\) | ≈\(0.00057+0.003183I\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 3}{ 2}\) |
| \(\frac{ 1}{ 2}\) | \(\frac{ 1}{ 2}\) | \(\frac{ 1}{ 2}\) | \(1\) | \(0\) | \(1\) | \(1\) | \(\frac{ 3}{ 2}\) |
| \(\frac{ 1}{ 2}\) | \(\frac{ 1}{ 2}\) | \(\frac{ 1}{ 2}\) | \(3\) | \(0\) | \(3\) | \(3\) | \(\frac{ 3}{ 2}\) |
| \(1\) | \(1\) | \(1\) | \(4\) | \(0\) | \(4\) | \(4\) | \(\frac{ 3}{ 2}\) |
345
New Number: 12.4 | AESZ: | Superseeker: 4 -228/5 | Hash: c24070a1d4a449404cd7b46398fa6d6e
Degree: 12
\(5^{2} \theta^4-2^{2} 5^{2} x\left(16\theta^4+32\theta^3+31\theta^2+15\theta+3\right)+2^{4} 5 x^{2}\left(736\theta^4+2368\theta^3+3848\theta^2+2960\theta+915\right)-2^{10} 5 x^{3}\left(304\theta^4+1176\theta^3+2337\theta^2+2313\theta+891\right)+2^{12} 3 x^{4}\left(2608\theta^4+10688\theta^3+21652\theta^2+23580\theta+9945\right)-2^{16} 3 x^{5}\left(2784\theta^4+11616\theta^3+21812\theta^2+22396\theta+9191\right)+2^{21} 3 x^{6}\left(1232\theta^4+5232\theta^3+9332\theta^2+7968\theta+2649\right)-2^{25} 3^{2} x^{7}\left(304\theta^4+1312\theta^3+2472\theta^2+1992\theta+559\right)+2^{30} 3 x^{8}\left(280\theta^4+1216\theta^3+2491\theta^2+2337\theta+827\right)-2^{32} x^{9}\left(1664\theta^4+7200\theta^3+13692\theta^2+11988\theta+3951\right)+2^{38} x^{10}\left(164\theta^4+832\theta^3+1751\theta^2+1731\theta+663\right)-2^{40} x^{11}\left(160\theta^4+928\theta^3+2072\theta^2+2072\theta+777\right)+2^{44} x^{12}\left((2\theta+3)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 12, 108, 688, 3564, ... --> OEIS Normalized instanton numbers (n0=1): 4, -29/5, -228/5, 3724/5, -31856/5, ... ; Common denominator:...
\((16z-1)^2(256z^2-16z+1)^2(4096z^3-768z^2-5)^2\)
| ≈\(-0.013312-0.074322I\) | ≈\(-0.013312+0.074322I\) | \(0\) | \(\frac{ 1}{ 32}-\frac{ 1}{ 32}\sqrt{ 3}I\) | \(\frac{ 1}{ 32}+\frac{ 1}{ 32}\sqrt{ 3}I\) | \(\frac{ 1}{ 16}\) | ≈\(0.214124\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 3}{ 2}\) |
| \(1\) | \(1\) | \(0\) | \(\frac{ 1}{ 2}\) | \(\frac{ 1}{ 2}\) | \(\frac{ 1}{ 2}\) | \(1\) | \(\frac{ 3}{ 2}\) |
| \(3\) | \(3\) | \(0\) | \(\frac{ 1}{ 2}\) | \(\frac{ 1}{ 2}\) | \(\frac{ 1}{ 2}\) | \(3\) | \(\frac{ 3}{ 2}\) |
| \(4\) | \(4\) | \(0\) | \(1\) | \(1\) | \(1\) | \(4\) | \(\frac{ 3}{ 2}\) |
346
New Number: 12.12 | AESZ: | Superseeker: 48 3184 | Hash: 2b1c995b5f2826ce90fc016ad86fd66f
Degree: 12
\(\theta^4-2^{4} x\left(27\theta^4+42\theta^3+37\theta^2+16\theta+3\right)+2^{9} x^{2}\left(139\theta^4+430\theta^3+579\theta^2+376\theta+103\right)-2^{14} x^{3}\left(369\theta^4+1638\theta^3+2992\theta^2+2481\theta+819\right)+2^{19} x^{4}\left(667\theta^4+2870\theta^3+6158\theta^2+6571\theta+2559\right)-2^{24} x^{5}\left(1263\theta^4+3066\theta^3+2692\theta^2+4295\theta+2110\right)+2^{29} 3 x^{6}\left(787\theta^4+1842\theta^3-1598\theta^2-3339\theta-1652\right)-2^{34} x^{7}\left(3087\theta^4+9750\theta^3+2942\theta^2-13117\theta-9816\right)+2^{39} x^{8}\left(3227\theta^4+6254\theta^3+14286\theta^2+4793\theta-1948\right)-2^{44} x^{9}\left(3906\theta^4+1440\theta^3+5279\theta^2+7593\theta+3747\right)+2^{49} x^{10}\left(3896\theta^4+6208\theta^3+3391\theta^2+725\theta+525\right)-2^{54} 5 x^{11}\left(408\theta^4+1536\theta^3+2230\theta^2+1460\theta+361\right)+2^{59} 5^{2} x^{12}\left((2\theta+3)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 48, 2704, 179968, 14147856, ... --> OEIS Normalized instanton numbers (n0=1): 48, 46, 3184, 409910, -3351792, ... ; Common denominator:...
\((16z-1)(32z-1)(4096z^2-192z+1)(64z-1)^2(163840z^3+1024z^2+32z-1)^2\)
| ≈\(-0.009802-0.019I\) | ≈\(-0.009802+0.019I\) | \(0\) | \(\frac{ 3}{ 128}-\frac{ 1}{ 128}\sqrt{ 5}\) | ≈\(0.013353\) | \(\frac{ 1}{ 64}\) | \(\frac{ 1}{ 32}\) | \(\frac{ 3}{ 128}+\frac{ 1}{ 128}\sqrt{ 5}\) | \(\frac{ 1}{ 16}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 3}{ 2}\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(\frac{ 3}{ 2}\) |
| \(3\) | \(3\) | \(0\) | \(1\) | \(3\) | \(1\) | \(1\) | \(1\) | \(1\) | \(\frac{ 3}{ 2}\) |
| \(4\) | \(4\) | \(0\) | \(2\) | \(4\) | \(1\) | \(2\) | \(2\) | \(2\) | \(\frac{ 3}{ 2}\) |
347
New Number: 12.13 | AESZ: | Superseeker: 92/5 -76/5 | Hash: dba247c75acfa39c7b95fa5054ec0315
Degree: 12
\(5^{2} \theta^4-2^{2} 5 x\left(204\theta^4+456\theta^3+413\theta^2+185\theta+35\right)+2^{4} x^{2}\left(15584\theta^4+68672\theta^3+112204\theta^2+80560\theta+23355\right)-2^{8} x^{3}\left(31248\theta^4+175968\theta^3+412240\theta^2+410040\theta+153195\right)+2^{12} x^{4}\left(51632\theta^4+209728\theta^3+475320\theta^2+630640\theta+291767\right)-2^{17} x^{5}\left(49392\theta^4+140352\theta^3+11864\theta^2-35120\theta-12789\right)+2^{22} 3 x^{6}\left(12592\theta^4+46080\theta^3+11800\theta^2-52224\theta-39545\right)-2^{27} x^{7}\left(20208\theta^4+72192\theta^3+95128\theta^2+2176\theta-35669\right)+2^{32} x^{8}\left(10672\theta^4+18112\theta^3+35960\theta^2+24560\theta+3975\right)-2^{37} x^{9}\left(5904\theta^4+9216\theta^3+9640\theta^2+6720\theta+2709\right)+2^{42} x^{10}\left(2224\theta^4+6464\theta^3+8328\theta^2+5360\theta+1507\right)-2^{47} x^{11}\left(432\theta^4+1920\theta^3+3400\theta^2+2816\theta+915\right)+2^{53} x^{12}\left((2\theta+3)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 28, 876, 30512, 1161964, ... --> OEIS Normalized instanton numbers (n0=1): 92/5, -342/5, -76/5, 75394/5, -2156752/5, ... ; Common denominator:...
\((64z-1)(32z-1)(256z^2-48z+1)(16z-1)^2(32768z^3-1024z^2-32z-5)^2\)
| ≈\(-0.020941-0.040594I\) | ≈\(-0.020941+0.040594I\) | \(0\) | \(\frac{ 1}{ 64}\) | \(\frac{ 3}{ 32}-\frac{ 1}{ 32}\sqrt{ 5}\) | \(\frac{ 1}{ 32}\) | \(\frac{ 1}{ 16}\) | ≈\(0.073133\) | \(\frac{ 3}{ 32}+\frac{ 1}{ 32}\sqrt{ 5}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 3}{ 2}\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(\frac{ 3}{ 2}\) |
| \(3\) | \(3\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(3\) | \(1\) | \(\frac{ 3}{ 2}\) |
| \(4\) | \(4\) | \(0\) | \(2\) | \(2\) | \(2\) | \(1\) | \(4\) | \(2\) | \(\frac{ 3}{ 2}\) |
348
New Number: 12.14 | AESZ: | Superseeker: 7/2 237/2 | Hash: 614b95fc4275078df0800c7546870e7f
Degree: 12
\(2^{2} \theta^4+2 x\left(74\theta^4+22\theta^3+77\theta^2+66\theta+18\right)+3^{2} x^{2}\left(97\theta^4+1206\theta^3+2235\theta^2+1750\theta+642\right)+3^{4} x^{3}\left(126\theta^4+3910\theta^3+7341\theta^2+8588\theta+3750\right)+3^{6} x^{4}\left(832\theta^4+6078\theta^3+26372\theta^2+37719\theta+21825\right)+3^{8} x^{5}\left(442\theta^4+12544\theta^3+62654\theta^2+116087\theta+78828\right)-3^{10} x^{6}\left(1032\theta^4-5126\theta^3-73629\theta^2-192529\theta-165306\right)-2 3^{12} x^{7}\left(1432\theta^4+11737\theta^3+11907\theta^2-41634\theta-71496\right)-3^{14} x^{8}\left(1871\theta^4+35422\theta^3+145979\theta^2+220752\theta+99504\right)+2 3^{17} x^{9}\left(151\theta^4-2094\theta^3-20341\theta^2-54972\theta-48672\right)+2^{3} 3^{19} x^{10}(\theta+3)(86\theta^3+414\theta^2+181\theta-936)+2^{3} 3^{22} x^{11}(\theta+4)(\theta+3)(21\theta^2+137\theta+224)+2^{4} 3^{24} x^{12}(\theta+3)(\theta+5)(\theta+4)^2\)
Maple LaTexCoefficients of the holomorphic solution: 1, -9, -18, 747, -5751, ... --> OEIS Normalized instanton numbers (n0=1): 7/2, -193/8, 237/2, -6119/4, 16307, ... ; Common denominator:...
\((9z+1)(z+1)(324z^2-18z+1)(81z^2+9z+1)^2(486z^2-27z-2)^2\)
| \(-1\) | \(-\frac{ 1}{ 9}\) | \(-\frac{ 1}{ 18}-\frac{ 1}{ 18}\sqrt{ 3}I\) | \(-\frac{ 1}{ 18}+\frac{ 1}{ 18}\sqrt{ 3}I\) | \(\frac{ 1}{ 36}-\frac{ 1}{ 108}\sqrt{ 57}\) | \(0\) | \(\frac{ 1}{ 36}-\frac{ 1}{ 36}\sqrt{ 3}I\) | \(\frac{ 1}{ 36}+\frac{ 1}{ 36}\sqrt{ 3}I\) | \(\frac{ 1}{ 36}+\frac{ 1}{ 108}\sqrt{ 57}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(3\) |
| \(1\) | \(1\) | \(0\) | \(0\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(4\) |
| \(1\) | \(1\) | \(-1\) | \(-1\) | \(3\) | \(0\) | \(1\) | \(1\) | \(3\) | \(4\) |
| \(2\) | \(2\) | \(1\) | \(1\) | \(4\) | \(0\) | \(2\) | \(2\) | \(4\) | \(5\) |
349
New Number: 12.15 | AESZ: | Superseeker: 27/5 1619/5 | Hash: f7297f2850190f8613d1cbc3a7363a23
Degree: 12
\(5^{2} \theta^4-5 x\left(296\theta^4+574\theta^3+457\theta^2+170\theta+25\right)-x^{2}\left(4531\theta^4+24118\theta^3+37791\theta^2+23710\theta+5550\right)+2^{2} x^{3}\left(559\theta^4+9744\theta^3+19448\theta^2+14280\theta+4055\right)+x^{4}\left(1455\theta^4-636\theta^3+151398\theta^2+254100\theta+114136\right)+x^{5}\left(80304\theta^4+79818\theta^3-776517\theta^2-952026\theta-338569\right)-x^{6}\left(18597\theta^4-67050\theta^3-680097\theta^2-608202\theta-164470\right)-2 x^{7}\left(19086\theta^4+454818\theta^3+525507\theta^2-112266\theta-235189\right)-2^{2} x^{8}\left(52779\theta^4-252492\theta^3-39867\theta^2+316368\theta+192050\right)-2^{3} x^{9}\left(27325\theta^4+45630\theta^3-118827\theta^2-223839\theta-101599\right)+2^{2} 17 x^{10}\left(8047\theta^4+9182\theta^3-8905\theta^2-20876\theta-9476\right)+2^{5} 17^{2} x^{11}(\theta+1)(19\theta^3+129\theta^2+246\theta+145)-2^{4} 17^{3} x^{12}(\theta+2)(\theta+1)(2\theta+3)^2\)
Maple LaTexCoefficients of the holomorphic solution: 1, 5, 109, 3329, 122581, ... --> OEIS Normalized instanton numbers (n0=1): 27/5, 158/5, 1619/5, 51193/10, 485082/5, ... ; Common denominator:...
\(-(4z+1)(z+1)(68z^2+61z-1)(z-1)^2(34z^3-12z^2+3z-5)^2\)
| \(-1\) | \(-\frac{ 61}{ 136}-\frac{ 11}{ 136}\sqrt{ 33}\) | \(-\frac{ 1}{ 4}\) | ≈\(-0.126959-0.475615I\) | ≈\(-0.126959+0.475615I\) | \(0\) | \(-\frac{ 61}{ 136}+\frac{ 11}{ 136}\sqrt{ 33}\) | ≈\(0.606859\) | \(1\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(\frac{ 3}{ 2}\) |
| \(1\) | \(1\) | \(1\) | \(3\) | \(3\) | \(0\) | \(1\) | \(3\) | \(\frac{ 1}{ 2}\) | \(\frac{ 3}{ 2}\) |
| \(2\) | \(2\) | \(2\) | \(4\) | \(4\) | \(0\) | \(2\) | \(4\) | \(1\) | \(2\) |
350
New Number: 12.16 | AESZ: | Superseeker: 288 -8252768 | Hash: e5412f8624ff9afc10459abda2d297d0
Degree: 12
\(\theta^4-2^{4} x\left(160\theta^4+224\theta^3+200\theta^2+88\theta+17\right)+2^{12} x^{2}\left(992\theta^4+1184\theta^3+1664\theta^2+1368\theta+399\right)-2^{22} x^{3}\left(1172\theta^4+1104\theta^3+542\theta^2+912\theta+331\right)+2^{28} x^{4}\left(16624\theta^4+15104\theta^3+5408\theta^2-752\theta-1829\right)-2^{37} x^{5}\left(23072\theta^4+16784\theta^3+23748\theta^2+1100\theta-4281\right)+2^{47} x^{6}\left(12696\theta^4+8556\theta^3+18218\theta^2+6591\theta+144\right)-2^{52} x^{7}\left(167440\theta^4+175808\theta^3+289048\theta^2+160176\theta+37033\right)+2^{61} x^{8}\left(96496\theta^4+172672\theta^3+241896\theta^2+158752\theta+44823\right)-2^{70} x^{9}\left(36784\theta^4+100224\theta^3+148008\theta^2+108576\theta+32891\right)+2^{79} x^{10}\left(8720\theta^4+32704\theta^3+54968\theta^2+44784\theta+14529\right)-2^{91} x^{11}\left(144\theta^4+696\theta^3+1352\theta^2+1222\theta+427\right)+2^{99} x^{12}\left((2\theta+3)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 272, 85264, 30040320, 11678489872, ... --> OEIS Normalized instanton numbers (n0=1): 288, 59200, -8252768, -1223488576, 585571467872, ... ; Common denominator:...
\((512z-1)(65536z^2-768z+1)(134217728z^3-655360z^2+256z-1)^2(256z-1)^3\)
| \(0\) | ≈\(3.7e-05-0.001244I\) | ≈\(3.7e-05+0.001244I\) | \(\frac{ 3}{ 512}-\frac{ 1}{ 512}\sqrt{ 5}\) | \(\frac{ 1}{ 512}\) | \(\frac{ 1}{ 256}\) | ≈\(0.004808\) | \(\frac{ 3}{ 512}+\frac{ 1}{ 512}\sqrt{ 5}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 3}{ 2}\) |
| \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(\frac{ 3}{ 2}\) |
| \(0\) | \(3\) | \(3\) | \(1\) | \(1\) | \(0\) | \(3\) | \(1\) | \(\frac{ 3}{ 2}\) |
| \(0\) | \(4\) | \(4\) | \(2\) | \(2\) | \(0\) | \(4\) | \(2\) | \(\frac{ 3}{ 2}\) |
351
New Number: 12.17 | AESZ: | Superseeker: 4 52 | Hash: e65be092d4832d3740d2a3078755f447
Degree: 12
\(\theta^4+2^{2} x\left(24\theta^4+6\theta^3+11\theta^2+8\theta+2\right)+2^{4} x^{2}\left(209\theta^4+2\theta^3+23\theta^2-10\right)+2^{7} x^{3}\left(223\theta^4-1218\theta^3-2225\theta^2-2088\theta-776\right)-2^{10} x^{4}\left(1409\theta^4+9634\theta^3+19337\theta^2+18420\theta+6872\right)-2^{13} x^{5}\left(6527\theta^4+35858\theta^3+78357\theta^2+78428\theta+30414\right)-2^{17} x^{6}\left(6276\theta^4+37704\theta^3+91143\theta^2+97914\theta+40036\right)-2^{21} x^{7}\left(2923\theta^4+22130\theta^3+61939\theta^2+73401\theta+32138\right)-2^{24} x^{8}\left(602\theta^4+10928\theta^3+42765\theta^2+60182\theta+29287\right)+2^{26} x^{9}\left(2352\theta^4+7392\theta^3-7024\theta^2-31968\theta-21891\right)+2^{29} x^{10}\left(1584\theta^4+11904\theta^3+24696\theta^2+19776\theta+4915\right)-2^{35} x^{11}\left(16\theta^4-176\theta^3-784\theta^2-1036\theta-449\right)-2^{39} x^{12}\left((2\theta+3)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -8, 112, -1152, 19216, ... --> OEIS Normalized instanton numbers (n0=1): 4, 7/2, 52, 500, 2796, ... ; Common denominator:...
\(-(8z+1)(256z^2+16z-1)(1024z^3-160z^2-28z-1)^2(16z+1)^3\)
| \(-\frac{ 1}{ 8}\) | \(-\frac{ 1}{ 32}-\frac{ 1}{ 32}\sqrt{ 5}\) | \(-\frac{ 1}{ 16}\) | ≈\(-0.057187-0.018391I\) | ≈\(-0.057187+0.018391I\) | \(0\) | \(-\frac{ 1}{ 32}+\frac{ 1}{ 32}\sqrt{ 5}\) | ≈\(0.270624\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 3}{ 2}\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(\frac{ 3}{ 2}\) |
| \(1\) | \(1\) | \(0\) | \(3\) | \(3\) | \(0\) | \(1\) | \(3\) | \(\frac{ 3}{ 2}\) |
| \(2\) | \(2\) | \(0\) | \(4\) | \(4\) | \(0\) | \(2\) | \(4\) | \(\frac{ 3}{ 2}\) |
352
New Number: 12.7 | AESZ: | Superseeker: -24/7 117 | Hash: fedf397077a0af56af404f5156e1b5c0
Degree: 12
\(7^{2} \theta^4+2 3 7 x\left(111\theta^4+120\theta^3+102\theta^2+42\theta+7\right)+2^{2} 3 x^{2}\left(16827\theta^4+34008\theta^3+38464\theta^2+20846\theta+4494\right)+3^{3} x^{3}\left(178553\theta^4+439878\theta^3+528099\theta^2+313502\theta+74536\right)+2 3^{3} x^{4}\left(1355053\theta^4+3438698\theta^3+3854711\theta^2+2221354\theta+519896\right)+2^{2} 3^{4} x^{5}\left(2406561\theta^4+5708802\theta^3+5082043\theta^2+2161754\theta+336752\right)+2^{3} 3^{5} x^{6}\left(3133411\theta^4+6625998\theta^3+4266961\theta^2+238710\theta-485736\right)+2^{6} 3^{6} x^{7}\left(746186\theta^4+1366021\theta^3+743388\theta^2-203279\theta-212552\right)+2^{7} 3^{7} x^{8}\left(506499\theta^4+760668\theta^3+404459\theta^2-112958\theta-117216\right)+2^{11} 3^{8} x^{9}\left(27992\theta^4+34962\theta^3+7197\theta^2-14685\theta-7604\right)+2^{14} 3^{9} x^{10}\left(1381\theta^4+1244\theta^3-2460\theta^2-4030\theta-1571\right)-2^{18} 3^{10} x^{11}(22\theta^2+98\theta+105)(\theta+1)^2-2^{22} 3^{11} x^{12}(\theta+1)^2(\theta+2)^2\)
Maple LaTexCoefficients of the holomorphic solution: 1, -6, 54, -276, -8442, ... --> OEIS Normalized instanton numbers (n0=1): -24/7, -24/7, 117, -564, 948/7, ... ; Common denominator:...
\(-(6z+1)(10368z^5-864z^4-7371z^3-1440z^2-60z-1)(7+102z+648z^2+3456z^3)^2\)
| \(-\frac{ 1}{ 6}\) | ≈\(-0.097659\) | ≈\(-0.04492-0.136829I\) | ≈\(-0.04492+0.136829I\) | \(0\) | \(#ND+#NDI\) | \(\infty\) |
|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) |
| \(1\) | \(3\) | \(3\) | \(3\) | \(0\) | \(1\) | \(2\) |
| \(2\) | \(4\) | \(4\) | \(4\) | \(0\) | \(2\) | \(2\) |
353
New Number: 12.2 | AESZ: | Superseeker: 64 39744 | Hash: b92032007ecbbf3af5801c4b1e4cf97a
Degree: 12
\(\theta^4+2^{5} x\theta(4\theta^3-10\theta^2-6\theta-1)-2^{8} x^{2}\left(92\theta^4+248\theta^3+200\theta^2+228\theta+89\right)-2^{14} x^{3}\left(84\theta^4+336\theta^3+664\theta^2+132\theta-51\right)+2^{18} x^{4}\left(944\theta^4+1312\theta^3+8928\theta^2+7384\theta+2567\right)-2^{26} x^{5}\left(176\theta^4-1456\theta^3-3477\theta^2-3814\theta-1741\right)-2^{32} x^{6}\left(216\theta^4+1200\theta^3+576\theta^2+1314\theta+697\right)+2^{38} x^{7}\left(456\theta^4+624\theta^3-3085\theta^2-5590\theta-3089\right)-2^{43} x^{8}\left(176\theta^4-3616\theta^3-2404\theta^2-288\theta+1027\right)-2^{50} x^{9}\left(208\theta^4+1824\theta^3+2581\theta^2+1434\theta+73\right)+2^{57} x^{10}\left(122\theta^4-44\theta^3-718\theta^2-1005\theta-410\right)-2^{62} 5 x^{11}\left(4\theta^4-32\theta^3-145\theta^2-190\theta-82\right)-2^{66} 5^{2} x^{12}\left((2\theta+3)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, 1424, 13312, 4213008, ... --> OEIS Normalized instanton numbers (n0=1): 64, -692, 39744, -2001358, 95440576, ... ; Common denominator:...
\(-(-1+64z+4096z^2)(64z-1)^2(64z+1)^2(655360z^3-4096z^2+96z+1)^2\)
| \(-\frac{ 1}{ 128}-\frac{ 1}{ 128}\sqrt{ 5}\) | \(-\frac{ 1}{ 64}\) | ≈\(-0.006598\) | \(0\) | ≈\(0.006424-0.013784I\) | ≈\(0.006424+0.013784I\) | \(-\frac{ 1}{ 128}+\frac{ 1}{ 128}\sqrt{ 5}\) | \(\frac{ 1}{ 64}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 3}{ 2}\) |
| \(1\) | \(0\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(\frac{ 3}{ 2}\) |
| \(1\) | \(1\) | \(3\) | \(0\) | \(3\) | \(3\) | \(1\) | \(\frac{ 1}{ 2}\) | \(\frac{ 3}{ 2}\) |
| \(2\) | \(1\) | \(4\) | \(0\) | \(4\) | \(4\) | \(2\) | \(1\) | \(\frac{ 3}{ 2}\) |
354
New Number: 12.3 | AESZ: | Superseeker: -12/5 444/5 | Hash: 45726409a4c817f929c9e6e49b33a941
Degree: 12
\(5^{2} \theta^4+2^{2} 5 x\left(4\theta^4+56\theta^3+53\theta^2+25\theta+5\right)-2^{4} x^{2}\left(976\theta^4+6208\theta^3+9016\theta^2+6360\theta+1985\right)+2^{8} x^{3}\left(832\theta^4-2304\theta^3-11276\theta^2-12780\theta-5495\right)+2^{13} x^{4}\left(176\theta^4+4672\theta^3+16244\theta^2+19860\theta+9145\right)-2^{16} x^{5}\left(1824\theta^4+8448\theta^3+1052\theta^2-6884\theta-5771\right)+2^{21} x^{6}\left(432\theta^4+192\theta^3-3816\theta^2-9540\theta-5869\right)+2^{24} x^{7}\left(704\theta^4+10048\theta^3+21804\theta^2+22348\theta+7847\right)-2^{29} x^{8}\left(472\theta^4+2176\theta^3+7884\theta^2+11644\theta+5965\right)+2^{32} x^{9}\left(336\theta^4+672\theta^3+1144\theta^2+2904\theta+2145\right)+2^{36} x^{10}\left(368\theta^4+1216\theta^3+1304\theta^2-240\theta-697\right)-2^{44} x^{11}(2\theta+3)(4\theta^3+28\theta^2+51\theta+28)-2^{46} x^{12}\left((2\theta+3)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -4, 108, -912, 21484, ... --> OEIS Normalized instanton numbers (n0=1): -12/5, 103/5, 444/5, 1148/5, -6704, ... ; Common denominator:...
\(-(-1-16z+256z^2)(16z+1)^2(16z-1)^2(8192z^3+768z^2-32z+5)^2\)
| ≈\(-0.148005\) | \(-\frac{ 1}{ 16}\) | \(\frac{ 1}{ 32}-\frac{ 1}{ 32}\sqrt{ 5}\) | \(0\) | ≈\(0.027128-0.058206I\) | ≈\(0.027128+0.058206I\) | \(\frac{ 1}{ 16}\) | \(\frac{ 1}{ 32}+\frac{ 1}{ 32}\sqrt{ 5}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 3}{ 2}\) |
| \(1\) | \(0\) | \(1\) | \(0\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(\frac{ 3}{ 2}\) |
| \(3\) | \(1\) | \(1\) | \(0\) | \(3\) | \(3\) | \(\frac{ 1}{ 2}\) | \(1\) | \(\frac{ 3}{ 2}\) |
| \(4\) | \(1\) | \(2\) | \(0\) | \(4\) | \(4\) | \(1\) | \(2\) | \(\frac{ 3}{ 2}\) |
355
New Number: 12.5 | AESZ: | Superseeker: 4 2252/9 | Hash: bb257a283455fdd1fa17fef9649505e3
Degree: 12
\(\theta^4+2^{2} x\left(43\theta^4+22\theta^3+25\theta^2+14\theta+3\right)+2^{4} x^{2}\left(753\theta^4+924\theta^3+1107\theta^2+622\theta+141\right)+2^{7} x^{3}\left(3377\theta^4+7218\theta^3+9261\theta^2+5764\theta+1455\right)+2^{10} x^{4}\left(7570\theta^4+24718\theta^3+34375\theta^2+21933\theta+5310\right)+2^{12} 3^{2} x^{5}\left(901\theta^4+5118\theta^3+5777\theta^2-84\theta-1829\right)-2^{14} 3^{2} x^{6}\left(7783\theta^4+33872\theta^3+83851\theta^2+107556\theta+49489\right)-2^{17} 3^{3} x^{7}\left(4895\theta^4+28154\theta^3+69267\theta^2+83564\theta+36929\right)-2^{20} 3^{4} x^{8}\left(44\theta^4+528\theta^3+247\theta^2+240\theta+274\right)+2^{23} 3^{5} x^{9}\left(664\theta^4+4760\theta^3+13781\theta^2+17353\theta+7679\right)+2^{26} 3^{6} x^{10}(\theta+1)(109\theta^3+651\theta^2+1373\theta+933)-2^{29} 3^{7} x^{11}(\theta+1)(\theta+2)(27\theta^2+153\theta+199)-2^{33} 3^{9} x^{12}(\theta+1)(\theta+2)^2(\theta+3)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -12, 180, -2736, 42948, ... --> OEIS Normalized instanton numbers (n0=1): 4, -31, 2252/9, -11109/4, 33312, ... ; Common denominator:...
\(-(16z+1)(432z^2+36z+1)(24z+1)^2(288z^2+48z+1)^2(8z-1)^3\)
| \(-\frac{ 1}{ 12}-\frac{ 1}{ 24}\sqrt{ 2}\) | \(-\frac{ 1}{ 16}\) | \(-\frac{ 1}{ 24}-\frac{ 1}{ 72}\sqrt{ 3}I\) | \(-\frac{ 1}{ 24}\) | \(-\frac{ 1}{ 24}+\frac{ 1}{ 72}\sqrt{ 3}I\) | \(-\frac{ 1}{ 12}+\frac{ 1}{ 24}\sqrt{ 2}\) | \(0\) | \(\frac{ 1}{ 8}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(0\) | \(\frac{ 1}{ 2}\) | \(2\) |
| \(3\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(3\) | \(0\) | \(\frac{ 3}{ 2}\) | \(2\) |
| \(4\) | \(2\) | \(2\) | \(1\) | \(2\) | \(4\) | \(0\) | \(2\) | \(3\) |
356
New Number: 12.6 | AESZ: | Superseeker: 5 953/3 | Hash: 4ea78627bfc56ef9555d9b6b3c949e7a
Degree: 12
\(\theta^4-x\theta(5\theta^3+46\theta^2+29\theta+6)-2 3 x^{2}\left(258\theta^4+1038\theta^3+1387\theta^2+818\theta+192\right)-2^{2} 3^{3} x^{3}\left(381\theta^4+1664\theta^3+2804\theta^2+2126\theta+624\right)-2^{4} 3^{3} x^{4}\left(1231\theta^4+5927\theta^3+11019\theta^2+9266\theta+3000\right)-2^{4} 3^{4} x^{5}\left(2621\theta^4+16730\theta^3+39069\theta^2+35141\theta+11748\right)-2^{5} 3^{5} x^{6}\left(150\theta^4+11268\theta^3+45560\theta^2+50253\theta+18756\right)+2^{6} 3^{7} x^{7}\left(1024\theta^4+800\theta^3-8483\theta^2-13641\theta-6108\right)+2^{8} 3^{7} x^{8}\left(1724\theta^4+6608\theta^3+1047\theta^2-7027\theta-4488\right)+2^{11} 3^{8} x^{9}\left(74\theta^4+1416\theta^3+1889\theta^2+687\theta-81\right)-2^{13} 3^{10} x^{10}\left(26\theta^4-16\theta^3-125\theta^2-128\theta-39\right)-2^{14} 3^{11} x^{11}(\theta+1)(16\theta^3+40\theta^2+31\theta+6)-2^{16} 3^{11} x^{12}(\theta+2)(\theta+1)(2\theta+3)^2\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, 72, 1344, 48600, ... --> OEIS Normalized instanton numbers (n0=1): 5, 83/2, 953/3, 5319, 97812, ... ; Common denominator:...
\(-(4z+1)(12z+1)(3z+1)(1728z^3+864z^2+36z-1)(-1-6z-36z^2+432z^3)^2\)
| ≈\(-0.450956\) | \(-\frac{ 1}{ 3}\) | \(-\frac{ 1}{ 4}\) | \(-\frac{ 1}{ 12}\) | ≈\(-0.067934\) | ≈\(-0.061146-0.08671I\) | ≈\(-0.061146+0.08671I\) | \(0\) | ≈\(0.01889\) | ≈\(0.205625\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(\frac{ 3}{ 2}\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(3\) | \(3\) | \(0\) | \(1\) | \(3\) | \(\frac{ 3}{ 2}\) |
| \(2\) | \(2\) | \(2\) | \(2\) | \(2\) | \(4\) | \(4\) | \(0\) | \(2\) | \(4\) | \(2\) |
357
New Number: 12.8 | AESZ: | Superseeker: 288 12718752 | Hash: 3373bbe821cc39369e8ba8c46ec88532
Degree: 12
\(\theta^4+2^{4} 3 x\left(112\theta^4+32\theta^3+40\theta^2+24\theta+5\right)+2^{13} x^{2}\left(1408\theta^4+1312\theta^3+1596\theta^2+784\theta+165\right)+2^{22} 3 x^{3}\left(988\theta^4+2088\theta^3+2591\theta^2+1485\theta+372\right)+2^{28} x^{4}\left(24464\theta^4+111040\theta^3+165136\theta^2+111992\theta+31983\right)+2^{38} 3^{2} x^{5}\left(288\theta^4+6544\theta^3+13980\theta^2+11216\theta+3605\right)-2^{46} x^{6}\left(14528\theta^4-36480\theta^3-205340\theta^2-205716\theta-76023\right)-2^{55} 3 x^{7}\left(4848\theta^4+13680\theta^3-20224\theta^2-34444\theta-16035\right)-2^{64} 3^{2} x^{8}\left(384\theta^4+4704\theta^3+2868\theta^2-852\theta-1307\right)+2^{74} 3 x^{9}\left(388\theta^4-1800\theta^3-3283\theta^2-2097\theta-333\right)+2^{80} 3^{2} x^{10}\left(784\theta^4+1184\theta^3+240\theta^2-592\theta-297\right)+2^{93} 3^{3} x^{11}(4\theta^2+8\theta+5)(\theta+1)^2+2^{100} 3^{2} x^{12}(\theta+2)(\theta+1)(2\theta+3)^2\)
Maple LaTexCoefficients of the holomorphic solution: 1, -240, 68880, -22281984, 7875829008, ... --> OEIS Normalized instanton numbers (n0=1): 288, -71872, 12718752, -4499223616, 1510063178336, ... ; Common denominator:...
\((1+768z+65536z^2)(256z+1)^2(512z+1)^2(201326592z^3-1536z-1)^2\)
| \(-\frac{ 3}{ 512}-\frac{ 1}{ 512}\sqrt{ 5}\) | \(-\frac{ 1}{ 256}\) | ≈\(-0.002348\) | \(-\frac{ 1}{ 512}\) | \(-\frac{ 3}{ 512}+\frac{ 1}{ 512}\sqrt{ 5}\) | ≈\(-0.000695\) | \(0\) | ≈\(0.003043\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(0\) | \(1\) | \(\frac{ 3}{ 2}\) |
| \(1\) | \(\frac{ 1}{ 2}\) | \(3\) | \(\frac{ 1}{ 2}\) | \(1\) | \(3\) | \(0\) | \(3\) | \(\frac{ 3}{ 2}\) |
| \(2\) | \(1\) | \(4\) | \(1\) | \(2\) | \(4\) | \(0\) | \(4\) | \(2\) |
358
New Number: 12.9 | AESZ: | Superseeker: 800 38825120 | Hash: 7e2f8423069147eb36cfd1d714d1996a
Degree: 12
\(\theta^4+2^{4} x\left(288\theta^4-96\theta^3-24\theta^2+24\theta+7\right)+2^{13} x^{2}\left(864\theta^4-240\theta^3+438\theta^2+96\theta-7\right)+2^{20} x^{3}\left(3856\theta^4+1152\theta^3+1036\theta^2+192\theta-53\right)+2^{30} x^{4}\left(636\theta^4-1440\theta^3-2303\theta^2-1988\theta-672\right)-2^{38} x^{5}\left(320\theta^4+7928\theta^3+14109\theta^2+11270\theta+3517\right)-2^{48} x^{6}\left(134\theta^4+1830\theta^3+3688\theta^2+3585\theta+1195\right)-2^{56} x^{7}\left(187\theta^4+356\theta^3-2355\theta^2-2866\theta-1199\right)-2^{65} x^{8}\left(91\theta^4+202\theta^3-1069\theta^2-2020\theta-948\right)-2^{74} x^{9}\left(2\theta^4-120\theta^3-211\theta^2-198\theta-69\right)+2^{84} x^{10}\left(\theta^4+44\theta^3+122\theta^2+121\theta+41\right)+2^{92} x^{11}(\theta^2+2\theta+2)(\theta+1)^2+2^{101} x^{12}(\theta+1)^2(\theta+2)^2\)
Maple LaTexCoefficients of the holomorphic solution: 1, -112, 25872, -5691136, 1522998544, ... --> OEIS Normalized instanton numbers (n0=1): 800, -121088, 38825120, -15641910336, 7303803435104, ... ; Common denominator:...
\((256z-1)(512z+1)(65536z^2-256z-1)(256z+1)^2(67108864z^3+1792z+1)^2\)
| \(-\frac{ 1}{ 256}\) | \(\frac{ 1}{ 512}-\frac{ 1}{ 512}\sqrt{ 5}\) | \(-\frac{ 1}{ 512}\) | ≈\(-0.000552\) | \(0\) | ≈\(0.000276-0.00519I\) | ≈\(0.000276+0.00519I\) | \(\frac{ 1}{ 256}\) | \(\frac{ 1}{ 512}+\frac{ 1}{ 512}\sqrt{ 5}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(3\) | \(0\) | \(3\) | \(3\) | \(1\) | \(1\) | \(2\) |
| \(1\) | \(2\) | \(2\) | \(4\) | \(0\) | \(4\) | \(4\) | \(2\) | \(2\) | \(2\) |
359
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:...
\((8z-1)(10368z^3-1728z^2+72z-1)(12z-1)^2(288z^2-24z+1)^2(4z+1)^3\)
| \(-\frac{ 1}{ 4}\) | \(0\) | ≈\(0.027033-0.011216I\) | ≈\(0.027033+0.011216I\) | \(\frac{ 1}{ 24}-\frac{ 1}{ 24}I\) | \(\frac{ 1}{ 24}+\frac{ 1}{ 24}I\) | \(\frac{ 1}{ 12}\) | ≈\(0.112601\) | \(\frac{ 1}{ 8}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(\frac{ 1}{ 2}\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(2\) |
| \(\frac{ 3}{ 2}\) | \(0\) | \(1\) | \(1\) | \(3\) | \(3\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(3\) |
| \(2\) | \(0\) | \(2\) | \(2\) | \(4\) | \(4\) | \(1\) | \(2\) | \(2\) | \(4\) |
360
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:...
\((2z-1)(4131z^3-2187z^2+81z-1)(3z-1)^2(81z^2-6z+1)^2(z+1)^3\)
| \(-1\) | \(0\) | ≈\(0.019487-0.01067I\) | ≈\(0.019487+0.01067I\) | \(\frac{ 1}{ 27}-\frac{ 2}{ 27}\sqrt{ 2}I\) | \(\frac{ 1}{ 27}+\frac{ 2}{ 27}\sqrt{ 2}I\) | \(\frac{ 1}{ 3}\) | ≈\(0.490438\) | \(\frac{ 1}{ 2}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(\frac{ 1}{ 2}\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(2\) |
| \(\frac{ 3}{ 2}\) | \(0\) | \(1\) | \(1\) | \(3\) | \(3\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(3\) |
| \(2\) | \(0\) | \(2\) | \(2\) | \(4\) | \(4\) | \(1\) | \(2\) | \(2\) | \(4\) |