You searched for: Spectrum0=0,0,0,0
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511
New Number: 8.67 | AESZ: | Superseeker: -49/5 -5776/5 | Hash: 807c6166f3d1991fadc5a93fdf4671e8
Degree: 8
\(5^{2} \theta^4+5 x\left(477\theta^4+978\theta^3+769\theta^2+280\theta+40\right)-2^{2} x^{2}\left(46\theta^4-2582\theta^3-5689\theta^2-4120\theta-1040\right)+2^{2} x^{3}\left(772\theta^4-4872\theta^3-11765\theta^2-7335\theta-1480\right)+2^{4} 3 x^{4}\left(140\theta^4+500\theta^3-672\theta^2-1313\theta-512\right)-2^{6} x^{5}\left(31\theta^4+154\theta^3-596\theta^2-729\theta-227\right)+2^{7} x^{6}\left(32\theta^4-264\theta^3-500\theta^2-303\theta-58\right)+2^{8} x^{7}\left(12\theta^4+72\theta^3+121\theta^2+85\theta+22\right)-2^{12} x^{8}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -8, 244, -11312, 635716, ... --> OEIS Normalized instanton numbers (n0=1): -49/5, 1441/20, -5776/5, 26480, -748058, ... ; Common denominator:...
\(-(z+1)(64z^3-48z^2-96z-1)(5-4z+8z^2)^2\)
| \(-1\) | ≈\(-0.899067\) | ≈\(-0.010472\) | \(0\) | \(\frac{ 1}{ 4}-\frac{ 3}{ 4}I\) | \(\frac{ 1}{ 4}+\frac{ 3}{ 4}I\) | ≈\(1.659539\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(0\) | \(3\) | \(3\) | \(1\) | \(1\) |
| \(2\) | \(2\) | \(2\) | \(0\) | \(4\) | \(4\) | \(2\) | \(1\) |
512
New Number: 8.68 | AESZ: | Superseeker: 6/17 33/17 | Hash: 0c0662f5b46ac6cb0bd298a63cf364c7
Degree: 8
\(17^{2} \theta^4+17 x\theta(165\theta^3-114\theta^2-74\theta-17)-x^{2}\left(20619\theta^4+122880\theta^3+175353\theta^2+126480\theta+36992\right)-2 x^{3}\left(201857\theta^4+853944\theta^3+1437673\theta^2+1174122\theta+375972\right)-2^{2} x^{4}\left(571275\theta^4+2711616\theta^3+5301571\theta^2+4856674\theta+1694372\right)-2^{3} 3 x^{5}(\theta+1)(295815\theta^3+1523993\theta^2+2924668\theta+1983212)-2^{5} x^{6}(\theta+1)(\theta+2)(558823\theta^2+2951265\theta+4136951)-2^{7} 3 37 x^{7}(\theta+3)(\theta+2)(\theta+1)(2797\theta+9878)-2^{9} 3^{2} 7 37^{2} x^{8}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, 8, 24, 288, ... --> OEIS Normalized instanton numbers (n0=1): 6/17, 25/34, 33/17, 157/17, 577/17, ... ; Common denominator:...
\(-(12z-1)(6z+1)(7z^2-z+1)(4z+1)^2(74z+17)^2\)
| \(-\frac{ 1}{ 4}\) | \(-\frac{ 17}{ 74}\) | \(-\frac{ 1}{ 6}\) | \(0\) | \(\frac{ 1}{ 14}-\frac{ 3}{ 14}\sqrt{ 3}I\) | \(\frac{ 1}{ 14}+\frac{ 3}{ 14}\sqrt{ 3}I\) | \(\frac{ 1}{ 12}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(2\) |
| \(\frac{ 1}{ 2}\) | \(3\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(3\) |
| \(1\) | \(4\) | \(2\) | \(0\) | \(2\) | \(2\) | \(2\) | \(4\) |
513
New Number: 8.69 | AESZ: | Superseeker: 4 52 | Hash: e303d10e77a367612be2fb706f37b895
Degree: 8
\(\theta^4-2^{2} x\left(20\theta^4+34\theta^3+29\theta^2+12\theta+2\right)+2^{4} x^{2}\left(125\theta^4+362\theta^3+471\theta^2+284\theta+66\right)-2^{7} x^{3}\left(191\theta^4+606\theta^3+855\theta^2+588\theta+154\right)+2^{10} x^{4}\left(192\theta^4+552\theta^3+562\theta^2+268\theta+49\right)-2^{13} x^{5}\left(134\theta^4+380\theta^3+373\theta^2+124\theta+3\right)+2^{16} x^{6}\left(61\theta^4+150\theta^3+173\theta^2+93\theta+19\right)-2^{19} x^{7}\left(19\theta^4+50\theta^3+56\theta^2+31\theta+7\right)+2^{23} x^{8}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 8, 128, 2816, 74896, ... --> OEIS Normalized instanton numbers (n0=1): 4, 15/2, 52, 1563/2, 7276, ... ; Common denominator:...
\((16z-1)(8z-1)(64z^2-48z+1)(1-4z+32z^2)^2\)
| \(0\) | \(\frac{ 3}{ 8}-\frac{ 1}{ 4}\sqrt{ 2}\) | \(\frac{ 1}{ 16}-\frac{ 1}{ 16}\sqrt{ 7}I\) | \(\frac{ 1}{ 16}\) | \(\frac{ 1}{ 16}+\frac{ 1}{ 16}\sqrt{ 7}I\) | \(\frac{ 1}{ 8}\) | \(\frac{ 3}{ 8}+\frac{ 1}{ 4}\sqrt{ 2}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(0\) | \(1\) | \(3\) | \(1\) | \(3\) | \(1\) | \(1\) | \(1\) |
| \(0\) | \(2\) | \(4\) | \(2\) | \(4\) | \(2\) | \(2\) | \(1\) |
514
New Number: 8.6 | AESZ: 113 | Superseeker: 11 1200 | Hash: 3754b3cce7930e99efa8acb802e524bb
Degree: 8
\(\theta^4-x(10\theta^2+10\theta+3)(11\theta^2+11\theta+3)+x^{2}\left(1025\theta^4+3992\theta^3+5533\theta^2+3082\theta+615\right)-3^{2} x^{3}\left(110\theta^4-660\theta^3-2027\theta^2-1509\theta-369\right)+3^{2} x^{4}\left(2032\theta^4+4064\theta^3-2726\theta^2-4758\theta-1431\right)+3^{4} x^{5}\left(110\theta^4+1100\theta^3+613\theta^2-125\theta-117\right)+3^{4} x^{6}\left(1025\theta^4+108\theta^3-293\theta^2+108\theta+99\right)+3^{6} x^{7}(10\theta^2+10\theta+3)(11\theta^2+11\theta+3)+3^{8} x^{8}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 9, 285, 13671, 799389, ... --> OEIS Normalized instanton numbers (n0=1): 11, 66, 1200, 28201, 802124, ... ; Common denominator:...
\((81z^2+99z-1)(z^2+11z-1)(1+9z^2)^2\)
| \(-\frac{ 11}{ 2}-\frac{ 5}{ 2}\sqrt{ 5}\) | \(-\frac{ 11}{ 18}-\frac{ 5}{ 18}\sqrt{ 5}\) | \(0-\frac{ 1}{ 3}I\) | \(0\) | \(0+\frac{ 1}{ 3}I\) | \(-\frac{ 11}{ 18}+\frac{ 5}{ 18}\sqrt{ 5}\) | \(-\frac{ 11}{ 2}+\frac{ 5}{ 2}\sqrt{ 5}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(1\) | \(1\) | \(3\) | \(0\) | \(3\) | \(1\) | \(1\) | \(1\) |
| \(2\) | \(2\) | \(4\) | \(0\) | \(4\) | \(2\) | \(2\) | \(1\) |
515
New Number: 8.70 | AESZ: | Superseeker: 32 8608 | Hash: 664bcad4360eb63fde0fdd3018aed2f2
Degree: 8
\(\theta^4-2^{4} x\left(19\theta^4+26\theta^3+20\theta^2+7\theta+1\right)+2^{9} x^{2}\left(61\theta^4+94\theta^3+89\theta^2+47\theta+10\right)-2^{14} x^{3}\left(134\theta^4+156\theta^3+37\theta^2+18\theta+6\right)+2^{19} x^{4}\left(192\theta^4+216\theta^3+58\theta^2-32\theta-17\right)-2^{24} x^{5}\left(191\theta^4+158\theta^3+183\theta^2+68\theta+6\right)+2^{29} x^{6}\left(125\theta^4+138\theta^3+135\theta^2+72\theta+16\right)-2^{35} x^{7}\left(20\theta^4+46\theta^3+47\theta^2+24\theta+5\right)+2^{41} x^{8}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 16, 848, 72448, 7745296, ... --> OEIS Normalized instanton numbers (n0=1): 32, 504, 8608, 475061, 28268384, ... ; Common denominator:...
\((16z-1)(32z-1)(1024z^2-192z+1)(1-32z+2048z^2)^2\)
| \(0\) | \(\frac{ 3}{ 32}-\frac{ 1}{ 16}\sqrt{ 2}\) | \(\frac{ 1}{ 128}-\frac{ 1}{ 128}\sqrt{ 7}I\) | \(\frac{ 1}{ 128}+\frac{ 1}{ 128}\sqrt{ 7}I\) | \(\frac{ 1}{ 32}\) | \(\frac{ 1}{ 16}\) | \(\frac{ 3}{ 32}+\frac{ 1}{ 16}\sqrt{ 2}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(0\) | \(1\) | \(3\) | \(3\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(0\) | \(2\) | \(4\) | \(4\) | \(2\) | \(2\) | \(2\) | \(1\) |
516
New Number: 8.71 | AESZ: | Superseeker: -15 14044/3 | Hash: de469dbb89801caa07ec523e3b0e4772
Degree: 8
\(\theta^4+3 x\left(111\theta^4+186\theta^3+169\theta^2+76\theta+14\right)+2 3^{2} x^{2}\left(2529\theta^4+6930\theta^3+9483\theta^2+6096\theta+1508\right)+2^{2} 3^{4} x^{3}\left(11367\theta^4+32886\theta^3+47658\theta^2+36099\theta+10084\right)+2^{3} 3^{6} x^{4}\left(37017\theta^4+100278\theta^3+103626\theta^2+56025\theta+11582\right)+2^{4} 3^{9} x^{5}\left(29160\theta^4+80676\theta^3+84897\theta^2+27261\theta-568\right)+2^{5} 3^{12} x^{6}\left(16200\theta^4+40824\theta^3+53991\theta^2+31131\theta+6578\right)+2^{7} 3^{17} x^{7}\left(360\theta^4+936\theta^3+1056\theta^2+585\theta+131\right)+2^{9} 3^{20} x^{8}(\theta+1)^2(6\theta+5)(6\theta+7)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -42, 2682, -200436, 16310250, ... --> OEIS Normalized instanton numbers (n0=1): -15, 39, 14044/3, 213069/2, 462576, ... ; Common denominator:...
\((27z+1)(54z+1)(108z+1)^2(1944z^2+18z+1)^2\)
| \(-\frac{ 1}{ 27}\) | \(-\frac{ 1}{ 54}\) | \(-\frac{ 1}{ 108}\) | \(-\frac{ 1}{ 216}-\frac{ 1}{ 216}\sqrt{ 23}I\) | \(-\frac{ 1}{ 216}+\frac{ 1}{ 216}\sqrt{ 23}I\) | \(0\) | \(\infty\) |
|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 5}{ 6}\) |
| \(1\) | \(1\) | \(\frac{ 1}{ 6}\) | \(1\) | \(1\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(\frac{ 5}{ 6}\) | \(3\) | \(3\) | \(0\) | \(1\) |
| \(2\) | \(2\) | \(1\) | \(4\) | \(4\) | \(0\) | \(\frac{ 7}{ 6}\) |
517
New Number: 8.72 | AESZ: | Superseeker: 32/3 14279/9 | Hash: d1b06e21c273cae807016268cd540d98
Degree: 8
\(3^{2} \theta^4-2 3 x\theta(85\theta^3+176\theta^2+112\theta+24)-2^{2} x^{2}\left(6581\theta^4+25808\theta^3+38672\theta^2+26184\theta+6912\right)-x^{3}\left(433513\theta^4+2497158\theta^3+5333997\theta^2+4967532\theta+1724868\right)-2 x^{4}\left(1751393\theta^4+13178758\theta^3+35803021\theta^2+40983788\theta+16698948\right)-2^{2} x^{5}(\theta+1)(3719315\theta^3+30248511\theta^2+79801768\theta+66666732)-2^{3} 3^{3} x^{6}(\theta+1)(\theta+2)(144041\theta^2+1060683\theta+1963346)-2^{7} 3^{4} x^{7}(\theta+3)(\theta+2)(\theta+1)(2449\theta+10862)-2^{9} 3^{3} 7 71 x^{8}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, 192, 7524, 438912, ... --> OEIS Normalized instanton numbers (n0=1): 32/3, 284/3, 14279/9, 118940/3, 1226784, ... ; Common denominator:...
\(-(7z+1)(6z+1)(639z^2+87z-1)(2z+3)^2(8z+1)^2\)
| \(-\frac{ 3}{ 2}\) | \(-\frac{ 1}{ 6}\) | \(-\frac{ 29}{ 426}-\frac{ 5}{ 142}\sqrt{ 5}\) | \(-\frac{ 1}{ 7}\) | \(-\frac{ 1}{ 8}\) | \(0\) | \(-\frac{ 29}{ 426}+\frac{ 5}{ 142}\sqrt{ 5}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(0\) | \(1\) | \(2\) |
| \(3\) | \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(3\) |
| \(4\) | \(2\) | \(2\) | \(2\) | \(1\) | \(0\) | \(2\) | \(4\) |
518
New Number: 8.73 | AESZ: | Superseeker: 161/13 26946/13 | Hash: 13db5d8c98a3d4f31589970217896191
Degree: 8
\(13^{2} \theta^4-13 x\theta(614\theta^3+1804\theta^2+1149\theta+247)-x^{2}\left(775399\theta^4+2692636\theta^3+3693483\theta^2+2450110\theta+648960\right)-2^{2} x^{3}\left(5408420\theta^4+24616488\theta^3+45163287\theta^2+38795913\theta+12838410\right)-2^{5} x^{4}\left(9763642\theta^4+55386224\theta^3+123097843\theta^2+124066416\theta+46600563\right)-2^{9} 3 x^{5}(\theta+1)(1717504\theta^3+9940776\theta^2+20063523\theta+13933966)-2^{13} 3^{2} x^{6}(\theta+1)(\theta+2)(178975\theta^2+874119\theta+1112486)-2^{19} 3^{4} x^{7}(\theta+3)(\theta+2)(\theta+1)(857\theta+2533)-2^{23} 3^{6} 7 x^{8}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, 240, 10440, 679104, ... --> OEIS Normalized instanton numbers (n0=1): 161/13, 1406/13, 26946/13, 742982/13, 25168759/13, ... ; Common denominator:...
\(-(-1+96z+896z^2)(9z+1)^2(96z+13)^2(8z+1)^2\)
| \(-\frac{ 13}{ 96}\) | \(-\frac{ 1}{ 8}\) | \(-\frac{ 3}{ 56}-\frac{ 5}{ 112}\sqrt{ 2}\) | \(-\frac{ 1}{ 9}\) | \(0\) | \(-\frac{ 3}{ 56}+\frac{ 5}{ 112}\sqrt{ 2}\) | \(\infty\) |
|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(0\) | \(1\) | \(0\) | \(0\) | \(1\) | \(2\) |
| \(3\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(3\) |
| \(4\) | \(1\) | \(2\) | \(1\) | \(0\) | \(2\) | \(4\) |
519
New Number: 8.74 | AESZ: | Superseeker: 4 436 | Hash: a0fbd8561e58a032d489a1dabee1e026
Degree: 8
\(\theta^4-2^{2} x\theta(22\theta^3+14\theta^2+9\theta+2)+2^{4} x^{2}\left(109\theta^4-74\theta^3-293\theta^2-258\theta-80\right)+2^{8} x^{3}\left(39\theta^4+414\theta^3+674\theta^2+504\theta+144\right)-2^{10} x^{4}\left(405\theta^4+1170\theta^3+1321\theta^2+424\theta-104\right)-2^{14} x^{5}(\theta+1)(12\theta^3+558\theta^2+1495\theta+1255)+2^{16} x^{6}(\theta+1)(\theta+2)(467\theta^2+1593\theta+1540)-2^{20} 5 x^{7}(\theta+3)(\theta+2)(\theta+1)(\theta-40)-2^{22} 5^{2} 7 x^{8}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, 80, 1536, 56592, ... --> OEIS Normalized instanton numbers (n0=1): 4, 71/2, 436, 6728, 127212, ... ; Common denominator:...
\(-(-1+56z)(20z-1)^2(8z-1)^2(8z+1)^3\)
| \(-\frac{ 1}{ 8}\) | \(0\) | \(\frac{ 1}{ 56}\) | \(\frac{ 1}{ 20}\) | \(\frac{ 1}{ 8}\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(0\) | \(0\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(2\) |
| \(-\frac{ 1}{ 4}\) | \(0\) | \(1\) | \(3\) | \(\frac{ 1}{ 2}\) | \(3\) |
| \(\frac{ 1}{ 4}\) | \(0\) | \(2\) | \(4\) | \(1\) | \(4\) |
520
New Number: 8.75 | AESZ: | Superseeker: -100/3 66364 | Hash: 76a0af78cc3434c7a78f3edc406baa61
Degree: 8
\(3^{2} \theta^4+2^{2} 3 x\left(592\theta^4+992\theta^3+913\theta^2+417\theta+78\right)+2^{7} x^{2}\left(17984\theta^4+49280\theta^3+67508\theta^2+43356\theta+10623\right)+2^{15} x^{3}\left(13472\theta^4+38976\theta^3+56498\theta^2+42534\theta+11589\right)+2^{21} x^{4}\left(29248\theta^4+79232\theta^3+81724\theta^2+43620\theta+8603\right)+2^{30} x^{5}\left(5760\theta^4+15936\theta^3+16712\theta^2+5206\theta-123\right)+2^{37} x^{6}\left(3200\theta^4+8064\theta^3+10616\theta^2+6036\theta+1263\right)+2^{47} x^{7}\left(160\theta^4+416\theta^3+466\theta^2+255\theta+56\right)+2^{55} x^{8}(4\theta+3)(\theta+1)^2(4\theta+5)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -104, 16488, -3037568, 605558440, ... --> OEIS Normalized instanton numbers (n0=1): -100/3, 538/3, 66364, 9836374/3, 67135456/3, ... ; Common denominator:...
\((64z+1)(128z+1)(256z+1)^2(32768z^2+128z+3)^2\)
| \(-\frac{ 1}{ 64}\) | \(-\frac{ 1}{ 128}\) | \(-\frac{ 1}{ 256}\) | \(-\frac{ 1}{ 512}-\frac{ 1}{ 512}\sqrt{ 23}I\) | \(-\frac{ 1}{ 512}+\frac{ 1}{ 512}\sqrt{ 23}I\) | \(0\) | \(\infty\) |
|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 3}{ 4}\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(3\) | \(3\) | \(0\) | \(1\) |
| \(2\) | \(2\) | \(1\) | \(4\) | \(4\) | \(0\) | \(\frac{ 5}{ 4}\) |
521
New Number: 8.76 | AESZ: | Superseeker: -204 66054580/3 | Hash: a1b606169a188129e64002b152d24330
Degree: 8
\(\theta^4+2^{2} 3 x\left(444\theta^4+744\theta^3+697\theta^2+325\theta+62\right)+2^{7} 3^{2} x^{2}\left(10116\theta^4+27720\theta^3+38031\theta^2+24393\theta+5891\right)+2^{12} 3^{4} x^{3}\left(45468\theta^4+131544\theta^3+190749\theta^2+142371\theta+37390\right)+2^{17} 3^{6} x^{4}\left(148068\theta^4+401112\theta^3+412641\theta^2+216243\theta+39599\right)+2^{23} 3^{9} x^{5}\left(58320\theta^4+161352\theta^3+168390\theta^2+50175\theta-1409\right)+2^{29} 3^{12} x^{6}\left(16200\theta^4+40824\theta^3+53397\theta^2+29754\theta+6131\right)+2^{35} 3^{17} x^{7}\left(360\theta^4+936\theta^3+1038\theta^2+558\theta+119\right)+2^{43} 3^{20} x^{8}(\theta+1)^2(3\theta+2)(3\theta+4)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -744, 843624, -1099121280, 1536242069160, ... --> OEIS Normalized instanton numbers (n0=1): -204, 6654, 66054580/3, 6573546582, 118182295200, ... ; Common denominator:...
\((432z+1)(864z+1)(1728z+1)^2(497664z^2+288z+1)^2\)
| \(-\frac{ 1}{ 432}\) | \(-\frac{ 1}{ 864}\) | \(-\frac{ 1}{ 1728}\) | \(-\frac{ 1}{ 3456}-\frac{ 1}{ 3456}\sqrt{ 23}I\) | \(-\frac{ 1}{ 3456}+\frac{ 1}{ 3456}\sqrt{ 23}I\) | \(0\) | \(\infty\) |
|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 2}{ 3}\) |
| \(1\) | \(1\) | \(-\frac{ 1}{ 6}\) | \(1\) | \(1\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(3\) | \(3\) | \(0\) | \(1\) |
| \(2\) | \(2\) | \(\frac{ 7}{ 6}\) | \(4\) | \(4\) | \(0\) | \(\frac{ 4}{ 3}\) |
522
New Number: 8.77 | AESZ: | Superseeker: 91/5 25991/5 | Hash: fa37d863a8d0cc4b7a34e7d9b5e3a1a5
Degree: 8
\(5^{2} \theta^4-5 x\left(693\theta^4+1242\theta^3+931\theta^2+310\theta+40\right)-2^{4} x^{2}\left(659\theta^4+9977\theta^3+17174\theta^2+10200\theta+2160\right)-2^{5} x^{3}\left(7235\theta^4-19374\theta^3-34715\theta^2-7290\theta+1560\right)-2^{8} x^{4}\left(14861\theta^4+40168\theta^3-70511\theta^2-88342\theta-26424\right)-2^{10} x^{5}\left(6973\theta^4+29386\theta^3+99859\theta^2+58446\theta+9864\right)-2^{14} x^{6}\left(6951\theta^4-25713\theta^3-34544\theta^2-14472\theta-1680\right)-2^{15} 11 x^{7}\left(2029\theta^4+5030\theta^3+5139\theta^2+2570\theta+520\right)+2^{18} 3 11^{2} x^{8}(\theta+1)^2(3\theta+2)(3\theta+4)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 8, 408, 28160, 2360440, ... --> OEIS Normalized instanton numbers (n0=1): 91/5, 1158/5, 25991/5, 192163, 42855113/5, ... ; Common denominator:...
\((z-1)(8z+1)(864z^2+136z-1)(5-24z+352z^2)^2\)
| \(-\frac{ 17}{ 216}-\frac{ 7}{ 216}\sqrt{ 7}\) | \(-\frac{ 1}{ 8}\) | \(0\) | \(-\frac{ 17}{ 216}+\frac{ 7}{ 216}\sqrt{ 7}\) | \(\frac{ 3}{ 88}-\frac{ 1}{ 88}\sqrt{ 101}I\) | \(\frac{ 3}{ 88}+\frac{ 1}{ 88}\sqrt{ 101}I\) | \(1\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 2}{ 3}\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(3\) | \(3\) | \(1\) | \(1\) |
| \(2\) | \(2\) | \(0\) | \(2\) | \(4\) | \(4\) | \(2\) | \(\frac{ 4}{ 3}\) |
523
New Number: 8.78 | AESZ: | Superseeker: 52 48732 | Hash: 2fb524ad6efb19e0117ae7acbd9f67b9
Degree: 8
\(\theta^4-2^{2} x\left(184\theta^4+224\theta^3+175\theta^2+63\theta+9\right)+2^{4} 3 x^{2}\left(3472\theta^4+9664\theta^3+9864\theta^2+4264\theta+705\right)-2^{8} 3^{2} x^{3}\left(1936\theta^4+27936\theta^3+43336\theta^2+21528\theta+3933\right)-2^{16} 3^{3} x^{4}\left(1384\theta^4+524\theta^3-4555\theta^2-3404\theta-753\right)+2^{19} 3^{4} x^{5}\left(3440\theta^4+13712\theta^3-58\theta^2-3774\theta-1161\right)+2^{22} 3^{5} x^{6}\left(11312\theta^4-9888\theta^3-10808\theta^2-1608\theta+459\right)-2^{26} 3^{7} x^{7}(2\theta+1)(1336\theta^3+2772\theta^2+2234\theta+663)-2^{32} 3^{9} x^{8}(2\theta+1)(4\theta+3)(4\theta+5)(2\theta+3)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 36, 3780, 555120, 95199300, ... --> OEIS Normalized instanton numbers (n0=1): 52, -399, 48732, -992750, 98106208, ... ; Common denominator:...
\(-(256z-1)(110592z^3+6912z^2-288z+1)(-1+96z+13824z^2)^2\)
| ≈\(-0.091906\) | \(-\frac{ 1}{ 288}-\frac{ 1}{ 288}\sqrt{ 7}\) | \(0\) | ≈\(0.00385\) | \(\frac{ 1}{ 256}\) | \(-\frac{ 1}{ 288}+\frac{ 1}{ 288}\sqrt{ 7}\) | ≈\(0.025556\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(\frac{ 3}{ 4}\) |
| \(1\) | \(3\) | \(0\) | \(1\) | \(1\) | \(3\) | \(1\) | \(\frac{ 5}{ 4}\) |
| \(2\) | \(4\) | \(0\) | \(2\) | \(2\) | \(4\) | \(2\) | \(\frac{ 3}{ 2}\) |
524
New Number: 8.79 | AESZ: | Superseeker: 22/5 68 | Hash: 064e5b590dd8b6a4daa1e905fbe693c2
Degree: 8
\(5^{2} \theta^4-2 5 x\left(338\theta^4+412\theta^3+371\theta^2+165\theta+30\right)+2^{2} x^{2}\left(46396\theta^4+103408\theta^3+125291\theta^2+76370\theta+19080\right)-2^{4} 3 x^{3}\left(115508\theta^4+357896\theta^3+524149\theta^2+375205\theta+106530\right)+2^{6} 3^{2} x^{4}\left(173456\theta^4+669024\theta^3+1118292\theta^2+883484\theta+269049\right)-2^{11} 3^{3} x^{5}\left(20272\theta^4+91616\theta^3+168594\theta^2+142006\theta+45053\right)+2^{14} 3^{4} x^{6}\left(5792\theta^4+29504\theta^3+58300\theta^2+51220\theta+16641\right)-2^{21} 3^{5} x^{7}(\theta+1)^2(58\theta^2+208\theta+201)+2^{26} 3^{6} x^{8}(\theta+1)^2(\theta+2)^2\)
Maple LaTexCoefficients of the holomorphic solution: 1, 12, 204, 4368, 112140, ... --> OEIS Normalized instanton numbers (n0=1): 22/5, 8, 68, 3292/5, 38826/5, ... ; Common denominator:...
\((-1+48z)(16z-1)^2(48z-5)^2(12z-1)^3\)
| \(0\) | \(\frac{ 1}{ 48}\) | \(\frac{ 1}{ 16}\) | \(\frac{ 1}{ 12}\) | \(\frac{ 5}{ 48}\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(0\) | \(1\) | \(\frac{ 1}{ 2}\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) |
| \(0\) | \(1\) | \(\frac{ 1}{ 2}\) | \(\frac{ 3}{ 2}\) | \(3\) | \(2\) |
| \(0\) | \(2\) | \(1\) | \(2\) | \(4\) | \(2\) |
525
New Number: 8.7 | AESZ: 106 | Superseeker: 12 356 | Hash: fe1c90929d18b81637eaaa93366409ed
Degree: 8
\(\theta^4-2^{2} x(3\theta^2+3\theta+1)(11\theta^2+11\theta+3)+2^{4} x^{2}\left(241\theta^4+940\theta^3+1303\theta^2+726\theta+145\right)-2^{7} x^{3}\left(33\theta^4-198\theta^3-607\theta^2-456\theta-117\right)+2^{10} x^{4}\left(239\theta^4+478\theta^3-322\theta^2-561\theta-169\right)+2^{12} x^{5}\left(33\theta^4+330\theta^3+185\theta^2-32\theta-37\right)+2^{14} x^{6}\left(241\theta^4+24\theta^3-71\theta^2+24\theta+23\right)+2^{17} x^{7}(3\theta^2+3\theta+1)(11\theta^2+11\theta+3)+2^{20} x^{8}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 12, 380, 16464, 845676, ... --> OEIS Normalized instanton numbers (n0=1): 12, 20, 356, 34561/4, 161840, ... ; Common denominator:...
\((64z^2+88z-1)(16z^2+44z-1)(1+32z^2)^2\)
| \(-\frac{ 11}{ 8}-\frac{ 5}{ 8}\sqrt{ 5}\) | \(-\frac{ 11}{ 16}-\frac{ 5}{ 16}\sqrt{ 5}\) | \(0-\frac{ 1}{ 8}\sqrt{ 2}I\) | \(0\) | \(0+\frac{ 1}{ 8}\sqrt{ 2}I\) | \(-\frac{ 11}{ 16}+\frac{ 5}{ 16}\sqrt{ 5}\) | \(-\frac{ 11}{ 8}+\frac{ 5}{ 8}\sqrt{ 5}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(1\) | \(1\) | \(3\) | \(0\) | \(3\) | \(1\) | \(1\) | \(1\) |
| \(2\) | \(2\) | \(4\) | \(0\) | \(4\) | \(2\) | \(2\) | \(1\) |
526
New Number: 8.80 | AESZ: | Superseeker: -28/3 2764/3 | Hash: 01b1872abfd55652952ae535920a40fe
Degree: 8
\(3^{2} \theta^4+2^{2} 3 x\left(148\theta^4+248\theta^3+223\theta^2+99\theta+18\right)+2^{7} x^{2}\left(1124\theta^4+3080\theta^3+4211\theta^2+2709\theta+675\right)+2^{12} x^{3}\left(1684\theta^4+4872\theta^3+7059\theta^2+5373\theta+1530\right)+2^{17} x^{4}\left(1828\theta^4+4952\theta^3+5125\theta^2+2799\theta+599\right)+2^{23} x^{5}\left(720\theta^4+1992\theta^3+2102\theta^2+691\theta-13\right)+2^{29} x^{6}\left(200\theta^4+504\theta^3+669\theta^2+390\theta+83\right)+2^{35} x^{7}\left(40\theta^4+104\theta^3+118\theta^2+66\theta+15\right)+2^{43} x^{8}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -24, 872, -37248, 1740456, ... --> OEIS Normalized instanton numbers (n0=1): -28/3, 49/3, 2764/3, 13414, 44384, ... ; Common denominator:...
\((16z+1)(32z+1)(64z+1)^2(2048z^2+32z+3)^2\)
| \(-\frac{ 1}{ 16}\) | \(-\frac{ 1}{ 32}\) | \(-\frac{ 1}{ 64}\) | \(-\frac{ 1}{ 128}-\frac{ 1}{ 128}\sqrt{ 23}I\) | \(-\frac{ 1}{ 128}+\frac{ 1}{ 128}\sqrt{ 23}I\) | \(0\) | \(\infty\) |
|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(3\) | \(3\) | \(0\) | \(1\) |
| \(2\) | \(2\) | \(1\) | \(4\) | \(4\) | \(0\) | \(1\) |
527
New Number: 8.81 | AESZ: | Superseeker: -64 54464 | Hash: 3cc4cfea037192a297dc29928555ed1d
Degree: 8
\(\theta^4+2^{4} x\left(40\theta^4+56\theta^3+46\theta^2+18\theta+3\right)+2^{10} x^{2}\left(200\theta^4+296\theta^3+357\theta^2+236\theta+58\right)+2^{16} x^{3}\left(720\theta^4+888\theta^3+446\theta^2+417\theta+126\right)+2^{22} x^{4}\left(1828\theta^4+2360\theta^3+1237\theta^2-93\theta-199\right)+2^{29} x^{5}\left(1684\theta^4+1864\theta^3+2547\theta^2+865\theta+28\right)+2^{36} x^{6}\left(1124\theta^4+1416\theta^3+1715\theta^2+969\theta+221\right)+2^{43} 3 x^{7}\left(148\theta^4+344\theta^3+367\theta^2+195\theta+42\right)+2^{53} 3^{2} x^{8}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -48, 4112, -470784, 65066256, ... --> OEIS Normalized instanton numbers (n0=1): -64, 2380, 54464, -1677212, -279711424, ... ; Common denominator:...
\((128z+1)(256z+1)(64z+1)^2(24576z^2+64z+1)^2\)
| \(-\frac{ 1}{ 64}\) | \(-\frac{ 1}{ 128}\) | \(-\frac{ 1}{ 256}\) | \(-\frac{ 1}{ 768}-\frac{ 1}{ 768}\sqrt{ 23}I\) | \(-\frac{ 1}{ 768}+\frac{ 1}{ 768}\sqrt{ 23}I\) | \(0\) | \(\infty\) |
|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) |
| \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(3\) | \(3\) | \(0\) | \(1\) |
| \(1\) | \(2\) | \(2\) | \(4\) | \(4\) | \(0\) | \(1\) |
528
New Number: 8.82 | AESZ: | Superseeker: 0 -1/3 | Hash: 8bab1ddc8b31cb2c21f01402f27895ce
Degree: 8
\(\theta^4-x\theta(3\theta^3-6\theta^2-4\theta-1)-x^{2}\left(211\theta^4+856\theta^3+1433\theta^2+1184\theta+384\right)+2 x^{3}\left(761\theta^4+3288\theta^3+6477\theta^2+6654\theta+2700\right)+2^{2} x^{4}(\theta+1)(2013\theta^3+17379\theta^2+40726\theta+28548)-2^{3} x^{5}(\theta+1)(15719\theta^3+126105\theta^2+325408\theta+269508)+2^{5} 3^{2} x^{6}(\theta+1)(\theta+2)(1817\theta^2+11967\theta+19631)-2^{7} 3^{4} x^{7}(\theta+3)(\theta+2)(\theta+1)(89\theta+350)+2^{9} 3^{3} 43 x^{8}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, 24, -72, 1296, ... --> OEIS Normalized instanton numbers (n0=1): 0, 1/2, -1/3, -1, -2, ... ; Common denominator:...
\((6z-1)(4z-1)(43z^2-13z+1)(12z+1)^2(-1+2z)^2\)
| \(-\frac{ 1}{ 12}\) | \(0\) | \(\frac{ 13}{ 86}-\frac{ 1}{ 86}\sqrt{ 3}I\) | \(\frac{ 13}{ 86}+\frac{ 1}{ 86}\sqrt{ 3}I\) | \(\frac{ 1}{ 6}\) | \(\frac{ 1}{ 4}\) | \(\frac{ 1}{ 2}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(\frac{ 1}{ 2}\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(2\) |
| \(\frac{ 1}{ 2}\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(3\) | \(3\) |
| \(1\) | \(0\) | \(2\) | \(2\) | \(2\) | \(2\) | \(4\) | \(4\) |
529
New Number: 8.83 | AESZ: | Superseeker: 208 642704 | Hash: 7314ca8e48f991223dc4e1c8b4893b95
Degree: 8
\(\theta^4-2^{4} x\left(116\theta^4+160\theta^3+119\theta^2+39\theta+5\right)+2^{9} x^{2}\left(2096\theta^4+5600\theta^3+5694\theta^2+2366\theta+355\right)-2^{15} x^{3}\left(4232\theta^4+22416\theta^3+28566\theta^2+11646\theta+1745\right)-2^{21} x^{4}\left(20616\theta^4+8496\theta^3-69074\theta^2-48074\theta-9335\right)+2^{27} x^{5}\left(49408\theta^4+114208\theta^3-29684\theta^2-42372\theta-9585\right)+2^{34} x^{6}\left(46496\theta^4-21984\theta^3-28956\theta^2-5580\theta+375\right)-2^{41} 5 x^{7}(2\theta+1)^2(344\theta^2+416\theta+163)-2^{48} 5^{2} x^{8}(2\theta+1)^2(2\theta+3)^2\)
Maple LaTexCoefficients of the holomorphic solution: 1, 80, 23760, 9900800, 4805155600, ... --> OEIS Normalized instanton numbers (n0=1): 208, 3154, 642704, -4424361, 3864242160, ... ; Common denominator:...
\(-(16384z^2-768z+1)(4096z^2+704z-1)(128z+1)^2(320z-1)^2\)
| \(-\frac{ 11}{ 128}-\frac{ 5}{ 128}\sqrt{ 5}\) | \(-\frac{ 1}{ 128}\) | \(0\) | \(\frac{ 3}{ 128}-\frac{ 1}{ 64}\sqrt{ 2}\) | \(-\frac{ 11}{ 128}+\frac{ 5}{ 128}\sqrt{ 5}\) | \(\frac{ 1}{ 320}\) | \(\frac{ 3}{ 128}+\frac{ 1}{ 64}\sqrt{ 2}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) |
| \(1\) | \(3\) | \(0\) | \(1\) | \(1\) | \(3\) | \(1\) | \(\frac{ 3}{ 2}\) |
| \(2\) | \(4\) | \(0\) | \(2\) | \(2\) | \(4\) | \(2\) | \(\frac{ 3}{ 2}\) |
530
New Number: 8.84 | AESZ: | Superseeker: 1/5 224/5 | Hash: 258fab6f0a4f132fe597fc6f30e54eea
Degree: 8
\(5^{2} \theta^4+5 x\theta^2(-1-2\theta+107\theta^2)+2^{2} x^{2}\left(2174\theta^4+5942\theta^3+8569\theta^2+5200\theta+1200\right)+2^{2} 3^{2} x^{3}\left(308\theta^4-4248\theta^3-17051\theta^2-16785\theta-5280\right)-2^{4} 3^{2} x^{4}\left(7060\theta^4+39500\theta^3+69820\theta^2+52851\theta+14688\right)-2^{6} 3^{4} x^{5}\left(881\theta^4+3974\theta^3+8648\theta^2+7983\theta+2581\right)+2^{7} 3^{4} x^{6}\left(1192\theta^4+2376\theta^3-1132\theta^2-4185\theta-1926\right)+2^{8} 3^{6} x^{7}\left(68\theta^4+568\theta^3+1095\theta^2+811\theta+210\right)-2^{12} 3^{8} x^{8}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, -12, 144, 324, ... --> OEIS Normalized instanton numbers (n0=1): 1/5, -6, 224/5, -448/5, -4334/5, ... ; Common denominator:...
\(-(9z-1)(576z^3+368z^2+16z+1)(-5-36z+72z^2)^2\)
| ≈\(-0.597246\) | \(\frac{ 1}{ 4}-\frac{ 1}{ 12}\sqrt{ 19}\) | ≈\(-0.020821-0.049733I\) | ≈\(-0.020821+0.049733I\) | \(0\) | \(\frac{ 1}{ 9}\) | \(\frac{ 1}{ 4}+\frac{ 1}{ 12}\sqrt{ 19}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) |
| \(1\) | \(3\) | \(1\) | \(1\) | \(0\) | \(1\) | \(3\) | \(1\) |
| \(2\) | \(4\) | \(2\) | \(2\) | \(0\) | \(2\) | \(4\) | \(1\) |
531
New Number: 8.85 | AESZ: | Superseeker: 196 1986884/3 | Hash: d959f61fe3ba327116d3bae5ae5a0ade
Degree: 8
\(\theta^4+2^{2} x\left(68\theta^4-296\theta^3-201\theta^2-53\theta-6\right)-2^{7} x^{2}\left(1192\theta^4+2392\theta^3-1108\theta^2-439\theta-57\right)-2^{12} 3^{2} x^{3}\left(881\theta^4-450\theta^3+2012\theta^2+915\theta+153\right)+2^{16} 3^{2} x^{4}\left(7060\theta^4-11260\theta^3-6320\theta^2-3471\theta-783\right)+2^{20} 3^{4} x^{5}\left(308\theta^4+5480\theta^3-2459\theta^2-3341\theta-990\right)-2^{26} 3^{4} x^{6}\left(2174\theta^4+2754\theta^3+3787\theta^2+2808\theta+801\right)+2^{30} 3^{6} 5 x^{7}(107\theta^2+216\theta+108)(\theta+1)^2-2^{36} 3^{8} 5^{2} x^{8}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 24, 2472, 412800, 83283624, ... --> OEIS Normalized instanton numbers (n0=1): 196, -5988, 1986884/3, -62128884, 8854857504, ... ; Common denominator:...
\(-(64z+1)(331776z^3-9216z^2+368z-1)(-1-288z+23040z^2)^2\)
| \(-\frac{ 1}{ 64}\) | \(\frac{ 1}{ 160}-\frac{ 1}{ 480}\sqrt{ 19}\) | \(0\) | ≈\(0.002907\) | ≈\(0.012435-0.029703I\) | ≈\(0.012435+0.029703I\) | \(\frac{ 1}{ 160}+\frac{ 1}{ 480}\sqrt{ 19}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(1\) | \(3\) | \(0\) | \(1\) | \(1\) | \(1\) | \(3\) | \(1\) |
| \(2\) | \(4\) | \(0\) | \(2\) | \(2\) | \(2\) | \(4\) | \(1\) |
532
New Number: 8.86 | AESZ: | Superseeker: 226/35 3959/7 | Hash: 815127e123ce989d9ab793a009bb2e6a
Degree: 8
\(5^{2} 7^{2} \theta^4-5 7 x\left(3223\theta^4+4862\theta^3+3866\theta^2+1435\theta+210\right)-x^{2}\left(6440-193270\theta-1217171\theta^2-2477628\theta^3-1818051\theta^4\right)-2^{4} 3 x^{3}\left(248985\theta^4+335357\theta^3+239138\theta^2+105280\theta+22400\right)+2^{6} x^{4}\left(618707\theta^4+1107118\theta^3+1179459\theta^2+710680\theta+177284\right)-2^{11} 3 x^{5}\left(12903\theta^4+34738\theta^3+48739\theta^2+33712\theta+8972\right)+2^{15} x^{6}\left(3323\theta^4+12570\theta^3+20137\theta^2+14550\theta+3916\right)-2^{20} x^{7}(\theta+1)(99+295\theta+286\theta^2+88\theta^3)+2^{25} x^{8}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 6, 146, 5280, 229986, ... --> OEIS Normalized instanton numbers (n0=1): 226/35, 1599/35, 3959/7, 51101/5, 8052703/35, ... ; Common denominator:...
\((1-77z+251z^2-352z^3+512z^4)(32z-5)^2(8z-7)^2\)
| \(0\) | \(\frac{ 5}{ 32}\) | \(\frac{ 7}{ 8}\) | \(#ND+#NDI\) | \(\infty\) |
|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(0\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(0\) | \(3\) | \(3\) | \(1\) | \(1\) |
| \(0\) | \(4\) | \(4\) | \(2\) | \(1\) |
533
New Number: 8.8 | AESZ: 161 | Superseeker: 9 -1229/3 | Hash: 641d1de9a6564241575c5db52faef694
Degree: 8
\(\theta^4-3 x(3\theta^2+3\theta+1)(11\theta^2+11\theta+3)+3^{2} x^{2}\left(366\theta^4+1428\theta^3+1980\theta^2+1104\theta+221\right)-3^{4} x^{3}\left(33\theta^4-198\theta^3-607\theta^2-456\theta-117\right)+3^{5} x^{4}\left(726\theta^4+1452\theta^3-978\theta^2-1704\theta-515\right)+3^{7} x^{5}\left(33\theta^4+330\theta^3+185\theta^2-32\theta-37\right)+3^{8} x^{6}\left(366\theta^4+36\theta^3-108\theta^2+36\theta+35\right)+3^{10} x^{7}(3\theta^2+3\theta+1)(11\theta^2+11\theta+3)+3^{12} x^{8}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 9, 171, 3087, 11259, ... --> OEIS Normalized instanton numbers (n0=1): 9, -81/4, -1229/3, -4644, -26685, ... ; Common denominator:...
\((729z^4+2673z^3+3240z^2-99z+1)(1+27z^2)^2\)
| ≈\(-1.848362\) | ≈\(-1.848362\) | \(0-\frac{ 1}{ 9}\sqrt{ 3}I\) | \(0\) | \(0+\frac{ 1}{ 9}\sqrt{ 3}I\) | ≈\(0.015028\) | ≈\(0.015028\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(1\) | \(1\) | \(3\) | \(0\) | \(3\) | \(1\) | \(1\) | \(1\) |
| \(2\) | \(2\) | \(4\) | \(0\) | \(4\) | \(2\) | \(2\) | \(1\) |
534
New Number: 8.9 | AESZ: 174 | Superseeker: 16 -13 | Hash: 3f987b46d9ebf201eeead1a885b78e66
Degree: 8
\(\theta^4-x(11\theta^2+11\theta+3)(17\theta^2+17\theta+6)+x^{2}\left(8711\theta^4+33980\theta^3+47095\theta^2+26230\theta+5232\right)-2^{3} 3^{2} x^{3}\left(187\theta^4-1122\theta^3-3436\theta^2-2595\theta-684\right)+2^{4} 3^{2} x^{4}\left(8639\theta^4+17278\theta^3-11650\theta^2-20289\theta-6102\right)+2^{6} 3^{4} x^{5}\left(187\theta^4+1870\theta^3+1052\theta^2-163\theta-216\right)+2^{6} 3^{4} x^{6}\left(8711\theta^4+864\theta^3-2579\theta^2+864\theta+828\right)+2^{9} 3^{6} x^{7}(11\theta^2+11\theta+3)(17\theta^2+17\theta+6)+2^{12} 3^{8} x^{8}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 18, 798, 45864, 2994894, ... --> OEIS Normalized instanton numbers (n0=1): 16, 7/2, -13, 11663/2, -26414, ... ; Common denominator:...
\((81z^2+99z-1)(64z^2+88z-1)(1+72z^2)^2\)
| \(-\frac{ 11}{ 16}-\frac{ 5}{ 16}\sqrt{ 5}\) | \(-\frac{ 11}{ 18}-\frac{ 5}{ 18}\sqrt{ 5}\) | \(0-\frac{ 1}{ 12}\sqrt{ 2}I\) | \(0\) | \(0+\frac{ 1}{ 12}\sqrt{ 2}I\) | \(-\frac{ 11}{ 18}+\frac{ 5}{ 18}\sqrt{ 5}\) | \(-\frac{ 11}{ 16}+\frac{ 5}{ 16}\sqrt{ 5}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(1\) | \(1\) | \(3\) | \(0\) | \(3\) | \(1\) | \(1\) | \(1\) |
| \(2\) | \(2\) | \(4\) | \(0\) | \(4\) | \(2\) | \(2\) | \(1\) |
535
New Number: 9.10 | AESZ: | Superseeker: 307/31 30366/31 | Hash: 7a61ae3114ae9cdc48f662244260cd65
Degree: 9
\(31^{2} \theta^4-31 x\left(2424\theta^4+5574\theta^3+4337\theta^2+1550\theta+217\right)-x^{2}\left(184202+713186\theta+1382715\theta^2+1756478\theta^3+914057\theta^4\right)-x^{3}\left(2273850+8903076\theta+13251149\theta^2+8635710\theta^3+3075537\theta^4\right)-x^{4}\left(11927218+37908836\theta+46269935\theta^2+23766918\theta^3+2064696\theta^4\right)-x^{5}\left(30324779+80902562\theta+70842936\theta^2+13913564\theta^3-3177385\theta^4\right)+2 x^{6}\left(2606232\theta^4+10916676\theta^3-6409705\theta^2-26416695\theta-14341608\right)+2^{2} 7 x^{7}\left(74376\theta^4+1138248\theta^3+2184799\theta^2+1451482\theta+280295\right)-2^{4} 5 7^{2} x^{8}(\theta+1)(592\theta^3-1128\theta^2-5448\theta-4091)-2^{6} 5^{2} 7^{3} x^{9}(\theta+2)(\theta+1)(2\theta+3)^2\)
Maple LaTexCoefficients of the holomorphic solution: 1, 7, 211, 9217, 485611, ... --> OEIS Normalized instanton numbers (n0=1): 307/31, 1814/31, 30366/31, 639686/31, 17126962/31, ... ; Common denominator:...
\(-(z+1)(z^2+z+1)(112z^2+88z-1)(-31-121z+140z^2)^2\)
| \(-1\) | \(-\frac{ 11}{ 28}-\frac{ 2}{ 7}\sqrt{ 2}\) | \(-\frac{ 1}{ 2}-\frac{ 1}{ 2}\sqrt{ 3}I\) | \(-\frac{ 1}{ 2}+\frac{ 1}{ 2}\sqrt{ 3}I\) | \(\frac{ 121}{ 280}-\frac{ 1}{ 280}\sqrt{ 32001}\) | \(0\) | \(-\frac{ 11}{ 28}+\frac{ 2}{ 7}\sqrt{ 2}\) | \(\frac{ 121}{ 280}+\frac{ 1}{ 280}\sqrt{ 32001}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(\frac{ 3}{ 2}\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(3\) | \(0\) | \(1\) | \(3\) | \(\frac{ 3}{ 2}\) |
| \(2\) | \(2\) | \(2\) | \(2\) | \(4\) | \(0\) | \(2\) | \(4\) | \(2\) |
536
New Number: 9.1 | AESZ: | Superseeker: -4/7 955/63 | Hash: d32eab6005ac34ecc01a9db7675daa24
Degree: 9
\(7^{2} \theta^4-7 x\theta(-7-32\theta-50\theta^2+29\theta^3)+3 x^{2}\theta(532+1165\theta+512\theta^2+1235\theta^3)-2 3^{2} x^{3}\left(5373\theta^4+29040\theta^3+61493\theta^2+51786\theta+15876\right)+2^{2} 3^{3} x^{4}\left(10813\theta^4+68120\theta^3+160529\theta^2+154570\theta+53396\right)-2^{3} 3^{4} x^{5}\left(13929\theta^4+84348\theta^3+181015\theta^2+171080\theta+59172\right)+2^{5} 3^{5} x^{6}\left(6160\theta^4+35964\theta^3+69935\theta^2+58677\theta+18110\right)-2^{8} 3^{6} x^{7}\left(944\theta^4+5308\theta^3+10916\theta^2+9657\theta+3109\right)+2^{11} 3^{7} x^{8}(96\theta^2+300\theta+265)(\theta+1)^2-2^{15} 3^{9} x^{9}(\theta+1)^2(\theta+2)^2\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, 0, 72, -432, ... --> OEIS Normalized instanton numbers (n0=1): -4/7, -4/7, 955/63, -262/7, -1002/7, ... ; Common denominator:...
\(-(6z-1)(27z^2-9z+1)(192z^2+16z+1)(7-18z+144z^2)^2\)
| \(-\frac{ 1}{ 24}-\frac{ 1}{ 24}\sqrt{ 2}I\) | \(-\frac{ 1}{ 24}+\frac{ 1}{ 24}\sqrt{ 2}I\) | \(0\) | \(\frac{ 1}{ 16}-\frac{ 1}{ 48}\sqrt{ 103}I\) | \(\frac{ 1}{ 16}+\frac{ 1}{ 48}\sqrt{ 103}I\) | \(\frac{ 1}{ 6}-\frac{ 1}{ 18}\sqrt{ 3}I\) | \(\frac{ 1}{ 6}\) | \(\frac{ 1}{ 6}+\frac{ 1}{ 18}\sqrt{ 3}I\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(1\) | \(1\) | \(0\) | \(3\) | \(3\) | \(1\) | \(1\) | \(1\) | \(2\) |
| \(2\) | \(2\) | \(0\) | \(4\) | \(4\) | \(2\) | \(2\) | \(2\) | \(2\) |
537
New Number: 9.2 | AESZ: | Superseeker: 9/7 49/3 | Hash: 356d4564e48d7a04e815fa223b6ccc46
Degree: 9
\(7^{2} \theta^4+7 x\theta(165\theta^3-102\theta^2-65\theta-14)-2^{3} x^{2}\left(920\theta^4+11726\theta^3+15277\theta^2+9478\theta+2352\right)-2^{4} 3^{2} x^{3}\left(4035\theta^4+19554\theta^3+29157\theta^2+20706\theta+5761\right)-2^{8} 3^{2} x^{4}\left(4156\theta^4+17951\theta^3+28198\theta^2+21045\theta+6096\right)-2^{11} 3^{3} x^{5}\left(1538\theta^4+6560\theta^3+10755\theta^2+8234\theta+2420\right)-2^{13} 3^{4} x^{6}\left(695\theta^4+3051\theta^3+5285\theta^2+4191\theta+1259\right)-2^{14} 3^{5} x^{7}\left(385\theta^4+1802\theta^3+3319\theta^2+2754\theta+855\right)-2^{18} 3^{6} x^{8}(\theta+1)^2(15\theta^2+48\theta+43)-2^{20} 3^{7} x^{9}(\theta+1)^2(\theta+2)^2\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, 24, 144, 3240, ... --> OEIS Normalized instanton numbers (n0=1): 9/7, 47/7, 49/3, 1370/7, 10063/7, ... ; Common denominator:...
\(-(8z+1)(24z-1)(3z+1)(4z+1)(12z+1)(7+72z+288z^2)^2\)
| \(-\frac{ 1}{ 3}\) | \(-\frac{ 1}{ 4}\) | \(-\frac{ 1}{ 8}-\frac{ 1}{ 24}\sqrt{ 5}I\) | \(-\frac{ 1}{ 8}\) | \(-\frac{ 1}{ 8}+\frac{ 1}{ 24}\sqrt{ 5}I\) | \(-\frac{ 1}{ 12}\) | \(0\) | \(\frac{ 1}{ 24}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) |
| \(1\) | \(1\) | \(3\) | \(1\) | \(3\) | \(1\) | \(0\) | \(1\) | \(2\) |
| \(2\) | \(2\) | \(4\) | \(2\) | \(4\) | \(2\) | \(0\) | \(2\) | \(2\) |
538
New Number: 9.3 | AESZ: | Superseeker: 10 3394/3 | Hash: 40e3715abcc5c4cb07e700ca79f80abf
Degree: 9
\(\theta^4-x\left(57\theta^4+116\theta^3+84\theta^2+26\theta+3\right)-2 x^{2}\left(894\theta^4+3208\theta^3+4571\theta^2+2771\theta+651\right)-2 x^{3}\left(7322\theta^4+56368\theta^3+124783\theta^2+101099\theta+29757\right)+2 3^{2} x^{4}\left(6967\theta^4-27080\theta^3-139991\theta^2-138507\theta-45297\right)+2 3^{4} x^{5}\left(17617\theta^4+49068\theta^3-31255\theta^2-79893\theta-34578\right)+2 3^{8} x^{6}\left(1082\theta^4+8360\theta^3+7967\theta^2+1439\theta-773\right)-2 3^{11} x^{7}\left(198\theta^4-864\theta^3-1545\theta^2-909\theta-155\right)-3^{15} x^{8}\left(69\theta^4+144\theta^3+126\theta^2+54\theta+10\right)-3^{20} x^{9}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 3, 135, 5349, 258039, ... --> OEIS Normalized instanton numbers (n0=1): 10, 77, 3394/3, 24029, 640402, ... ; Common denominator:...
\(-(-1+81z)(-1+9z)^2(81z^2+14z+1)^3\)
| \(-\frac{ 7}{ 81}-\frac{ 4}{ 81}\sqrt{ 2}I\) | \(-\frac{ 7}{ 81}+\frac{ 4}{ 81}\sqrt{ 2}I\) | \(0\) | \(\frac{ 1}{ 81}\) | \(\frac{ 1}{ 9}\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(\frac{ 1}{ 2}\) | \(\frac{ 1}{ 2}\) | \(0\) | \(1\) | \(1\) | \(1\) |
| \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(0\) | \(1\) | \(3\) | \(1\) |
| \(2\) | \(2\) | \(0\) | \(2\) | \(4\) | \(1\) |
539
New Number: 9.4 | AESZ: | Superseeker: -90 -413926 | Hash: e2329b2f9cd1e3f65d29644e6ce39d24
Degree: 9
\(\theta^4+3^{2} x\left(69\theta^4+132\theta^3+108\theta^2+42\theta+7\right)+2 3^{5} x^{2}\left(198\theta^4+1656\theta^3+2235\theta^2+1203\theta+271\right)-2 3^{9} x^{3}\left(1082\theta^4-4032\theta^3-10621\theta^2-6257\theta-1523\right)-2 3^{12} x^{4}\left(17617\theta^4+21400\theta^3-72757\theta^2-59353\theta-17391\right)-2 3^{17} x^{5}\left(6967\theta^4+54948\theta^3-16949\theta^2-32367\theta-12734\right)+2 3^{22} x^{6}\left(7322\theta^4-27080\theta^3-389\theta^2+8651\theta+4395\right)+2 3^{29} x^{7}\left(894\theta^4+368\theta^3+311\theta^2+323\theta+137\right)+3^{36} x^{8}\left(57\theta^4+112\theta^3+78\theta^2+22\theta+2\right)-3^{43} x^{9}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -63, 4455, 34551, -114913161, ... --> OEIS Normalized instanton numbers (n0=1): -90, -8685/2, -413926, -38862153, -4502063682, ... ; Common denominator:...
\(-(-1+27z)(-1+243z)^2(59049z^2+378z+1)^3\)
| \(-\frac{ 7}{ 2187}-\frac{ 4}{ 2187}\sqrt{ 2}I\) | \(-\frac{ 7}{ 2187}+\frac{ 4}{ 2187}\sqrt{ 2}I\) | \(0\) | \(\frac{ 1}{ 243}\) | \(\frac{ 1}{ 27}\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(\frac{ 1}{ 2}\) | \(\frac{ 1}{ 2}\) | \(0\) | \(1\) | \(1\) | \(1\) |
| \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(0\) | \(3\) | \(1\) | \(1\) |
| \(2\) | \(2\) | \(0\) | \(4\) | \(2\) | \(1\) |
540
New Number: 9.5 | AESZ: | Superseeker: 17/3 4127/9 | Hash: 98a7e046a956f1c9ec13973072ab8283
Degree: 9
\(3^{2} \theta^4-3 x\left(152\theta^4+316\theta^3+245\theta^2+87\theta+12\right)-x^{2}\left(5808+25608\theta+43193\theta^2+31076\theta^3+8807\theta^4\right)-2 x^{3}\left(10633\theta^4+106320\theta^3+235087\theta^2+185292\theta+52896\right)+2^{2} x^{4}\left(65651\theta^4+19144\theta^3-434467\theta^2-508704\theta-175376\right)+2^{3} x^{5}\left(151497\theta^4+645060\theta^3+272053\theta^2-269230\theta-183720\right)-2^{8} x^{6}\left(3386\theta^4-52470\theta^3-83275\theta^2-46299\theta-7926\right)-2^{10} x^{7}\left(11425\theta^4+14072\theta^3-3794\theta^2-13632\theta-5575\right)-2^{15} x^{8}(590\theta^2+1126\theta+597)(\theta+1)^2-2^{20} 3^{2} x^{9}(\theta+1)^2(\theta+2)^2\)
Maple LaTexCoefficients of the holomorphic solution: 1, 4, 108, 3496, 137548, ... --> OEIS Normalized instanton numbers (n0=1): 17/3, 257/6, 4127/9, 23827/3, 496999/3, ... ; Common denominator:...
\(-(9z+1)(2z+1)(z+1)(128z^2+64z-1)(-3-2z+64z^2)^2\)
| \(-1\) | \(-\frac{ 1}{ 4}-\frac{ 3}{ 16}\sqrt{ 2}\) | \(-\frac{ 1}{ 2}\) | \(\frac{ 1}{ 64}-\frac{ 1}{ 64}\sqrt{ 193}\) | \(-\frac{ 1}{ 9}\) | \(0\) | \(-\frac{ 1}{ 4}+\frac{ 3}{ 16}\sqrt{ 2}\) | \(\frac{ 1}{ 64}+\frac{ 1}{ 64}\sqrt{ 193}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(3\) | \(1\) | \(0\) | \(1\) | \(3\) | \(2\) |
| \(2\) | \(2\) | \(2\) | \(4\) | \(2\) | \(0\) | \(2\) | \(4\) | \(2\) |