You searched for: Spectrum0=0,0,0,0
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421
New Number: 6.3 | AESZ: | Superseeker: 178/7 129516/7 | Hash: ec9e21dc2ccd3b4b4156ae1438454b96
Degree: 6
\(7^{2} \theta^4-2 7 x\left(1488\theta^4+1452\theta^3+1125\theta^2+399\theta+56\right)+2^{2} x^{2}\left(766392\theta^4+1184952\theta^3+1010797\theta^2+454076\theta+83776\right)-2^{4} x^{3}\left(12943616\theta^4+28354200\theta^3+30710572\theta^2+16054731\theta+3215254\right)+2^{6} x^{4}\left(105973188\theta^4+333359304\theta^3+436182381\theta^2+261265857\theta+57189166\right)-2^{11} 127 x^{5}(\theta+1)(390972\theta^3+1350660\theta^2+1486781\theta+460439)+2^{14} 23^{2} 127^{2} x^{6}(\theta+1)(\theta+2)(2\theta+1)(2\theta+5)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 16, 864, 80800, 9624160, ... --> OEIS Normalized instanton numbers (n0=1): 178/7, 3375/7, 129516/7, 6515900/7, 409239710/7, ... ; Common denominator:...
\((1-248z+8464z^2)(508z-7)^2(16z-1)^2\)
| \(0\) | \(\frac{ 31}{ 2116}-\frac{ 3}{ 529}\sqrt{ 3}\) | \(\frac{ 7}{ 508}\) | \(\frac{ 31}{ 2116}+\frac{ 3}{ 529}\sqrt{ 3}\) | \(\frac{ 1}{ 16}\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(0\) | \(1\) | \(1\) | \(1\) | \(\frac{ 1}{ 3}\) | \(1\) |
| \(0\) | \(1\) | \(3\) | \(1\) | \(\frac{ 2}{ 3}\) | \(2\) |
| \(0\) | \(2\) | \(4\) | \(2\) | \(1\) | \(\frac{ 5}{ 2}\) |
422
New Number: 6.4 | AESZ: | Superseeker: 370/19 140636/19 | Hash: 0f3ddf420018e2870561a3e9fd2551cc
Degree: 6
\(19^{2} \theta^4-19 x\left(4333\theta^4+6212\theta^3+4778\theta^2+1672\theta+228\right)+x^{2}\left(4307495\theta^4+7600484\theta^3+6216406\theta^2+2802424\theta+530556\right)-x^{3}\left(93729369\theta^4+213316800\theta^3+236037196\theta^2+125748612\theta+25260804\right)+2^{2} x^{4}\left(240813800\theta^4+778529200\theta^3+1041447759\theta^2+631802809\theta+138510993\right)-2^{2} 409 x^{5}(\theta+1)(2851324\theta^3+10035516\theta^2+11221241\theta+3481470)+2^{2} 3^{2} 19^{2} 409^{2} x^{6}(\theta+1)(\theta+2)(2\theta+1)(2\theta+5)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 12, 588, 46200, 4446540, ... --> OEIS Normalized instanton numbers (n0=1): 370/19, 276, 140636/19, 5568700/19, 277119292/19, ... ; Common denominator:...
\((9z-1)(5776z^3-1920z^2+176z-1)(-19+409z)^2\)
| \(0\) | ≈\(0.006077\) | \(\frac{ 19}{ 409}\) | \(\frac{ 1}{ 9}\) | ≈\(0.163166-0.043179I\) | ≈\(0.163166+0.043179I\) | \(\infty\) |
|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(0\) | \(1\) | \(3\) | \(1\) | \(1\) | \(1\) | \(2\) |
| \(0\) | \(2\) | \(4\) | \(2\) | \(2\) | \(2\) | \(\frac{ 5}{ 2}\) |
423
New Number: 6.5 | AESZ: | Superseeker: -11 -3422/3 | Hash: 6a4aeb5833b7673c962d5598842d3f2c
Degree: 6
\(\theta^4-x\left(12+64\theta+125\theta^2+122\theta^3+61\theta^4\right)-2^{3} x^{2}\left(193\theta^4+772\theta^3+1033\theta^2+522\theta+72\right)+2^{9} 3 x^{3}\left(146\theta^4+876\theta^3+1838\theta^2+1572\theta+405\right)-2^{12} 3^{2} x^{4}\left(204\theta^4+1632\theta^3+4449\theta^2+4740\theta+1400\right)+2^{16} 3^{3} x^{5}(16\theta^2+80\theta+35)(2\theta+5)^2-2^{19} 3^{4} x^{6}(2\theta+11)(2\theta+7)(2\theta+5)(2\theta+1)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 12, 324, 5760, 215460, ... --> OEIS Normalized instanton numbers (n0=1): -11, 68, -3422/3, 30735, -1014993, ... ; Common denominator:...
\(-(24z-1)(27648z^3-1728z^2+27z+1)(-1+32z)^2\)
| ≈\(-0.016119\) | \(0\) | \(\frac{ 1}{ 32}\) | ≈\(0.03931-0.026431I\) | ≈\(0.03931+0.026431I\) | \(\frac{ 1}{ 24}\) | \(\infty\) |
|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(1\) | \(0\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(1\) | \(\frac{ 5}{ 2}\) |
| \(1\) | \(0\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(1\) | \(\frac{ 7}{ 2}\) |
| \(2\) | \(0\) | \(1\) | \(2\) | \(2\) | \(2\) | \(\frac{ 11}{ 2}\) |
424
New Number: 6.6 | AESZ: | Superseeker: 25 17452 | Hash: e97e9b0e87960fe4cffbb22a5e935b4a
Degree: 6
\(\theta^4-x\left(12+100\theta+305\theta^2+410\theta^3+205\theta^4\right)-2^{5} x^{2}\left(127\theta^4+508\theta^3+742\theta^2+468\theta+99\right)-2^{2} 3 x^{3}\left(2588\theta^4+15528\theta^3+32639\theta^2+28041\theta+7290\right)-2^{6} 3^{2} x^{4}\left(204\theta^4+1632\theta^3+4449\theta^2+4740\theta+1400\right)-2^{7} 3^{3} x^{5}(16\theta^2+80\theta+35)(2\theta+5)^2-2^{7} 3^{4} x^{6}(2\theta+11)(2\theta+7)(2\theta+5)(2\theta+1)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 12, 972, 106200, 14027580, ... --> OEIS Normalized instanton numbers (n0=1): 25, 446, 17452, 958347, 65098152, ... ; Common denominator:...
\(-(3z+1)(3456z^3+1728z^2+216z-1)(4z+1)^2\)
| \(-\frac{ 1}{ 3}\) | ≈\(-0.252234-0.033647I\) | ≈\(-0.252234+0.033647I\) | \(-\frac{ 1}{ 4}\) | \(0\) | \(\frac{ 1}{ 12}2^(\frac{ 1}{ 3})+\frac{ 1}{ 24}2^(\frac{ 2}{ 3})-\frac{ 1}{ 6}\) | \(\infty\) |
|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(1\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(0\) | \(1\) | \(\frac{ 5}{ 2}\) |
| \(1\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(0\) | \(1\) | \(\frac{ 7}{ 2}\) |
| \(2\) | \(2\) | \(2\) | \(1\) | \(0\) | \(2\) | \(\frac{ 11}{ 2}\) |
425
New Number: 6.7 | AESZ: | Superseeker: -9 217/3 | Hash: 9492f991c909a6774f5546668ff53b6a
Degree: 6
\(\theta^4-3 x\left(42\theta^4+84\theta^3+77\theta^2+35\theta+6\right)+3^{3} x^{2}\left(291\theta^4+1164\theta^3+1747\theta^2+1166\theta+264\right)-2^{2} 3^{5} x^{3}\left(360\theta^4+2160\theta^3+4553\theta^2+3939\theta+1035\right)+2^{3} 3^{8} x^{4}\left(204\theta^4+1632\theta^3+4449\theta^2+4740\theta+1400\right)-2^{4} 3^{11} x^{5}(16\theta^2+80\theta+35)(2\theta+5)^2+2^{4} 3^{14} x^{6}(2\theta+11)(2\theta+7)(2\theta+5)(2\theta+1)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 18, 378, 8820, 266490, ... --> OEIS Normalized instanton numbers (n0=1): -9, 18, 217/3, -9, -146079, ... ; Common denominator:...
\((27z-1)(34992z^3-1944z^2+27z-1)(-1+36z)^2\)
| \(0\) | ≈\(0.002095-0.023494I\) | ≈\(0.002095+0.023494I\) | \(\frac{ 1}{ 36}\) | \(\frac{ 1}{ 27}\) | ≈\(0.051365\) | \(\infty\) |
|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(0\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(\frac{ 5}{ 2}\) |
| \(0\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(\frac{ 7}{ 2}\) |
| \(0\) | \(2\) | \(2\) | \(1\) | \(2\) | \(2\) | \(\frac{ 11}{ 2}\) |
426
New Number: 6.8 | AESZ: | Superseeker: 567/13 512341/13 | Hash: 00104510dfaa4ae75940f08df0a52bf5
Degree: 6
\(13^{2} \theta^4-13 x\left(5041\theta^4+7634\theta^3+5767\theta^2+1950\theta+260\right)+2^{3} x^{2}\left(744635\theta^4+1560842\theta^3+1510101\theta^2+768170\theta+156078\right)-2^{6} 3 x^{3}\left(1232985\theta^4+3409302\theta^3+4189688\theta^2+2419209\theta+518414\right)+2^{9} x^{4}\left(9225025\theta^4+33675338\theta^3+49289090\theta^2+31849807\theta+7296732\right)-2^{12} 3 17 x^{5}(\theta+1)(222704\theta^3+833160\theta^2+989659\theta+317310)+2^{15} 3^{2} 17^{2} 23^{2} x^{6}(\theta+1)(\theta+2)(2\theta+1)(2\theta+5)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 20, 1524, 196400, 31587220, ... --> OEIS Normalized instanton numbers (n0=1): 567/13, 11392/13, 512341/13, 34191454/13, 2850663840/13, ... ; Common denominator:...
\((1-293z+4232z^2)(408z-13)^2(16z-1)^2\)
| \(0\) | \(\frac{ 293}{ 8464}-\frac{ 41}{ 8464}\sqrt{ 41}\) | \(\frac{ 13}{ 408}\) | \(\frac{ 1}{ 16}\) | \(\frac{ 293}{ 8464}+\frac{ 41}{ 8464}\sqrt{ 41}\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(0\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) |
| \(0\) | \(1\) | \(3\) | \(\frac{ 1}{ 2}\) | \(1\) | \(2\) |
| \(0\) | \(2\) | \(4\) | \(1\) | \(2\) | \(\frac{ 5}{ 2}\) |
427
New Number: 6.9 | AESZ: | Superseeker: 31/81 29/9 | Hash: 98af5121f39c27098356e3ade277f975
Degree: 6
\(3^{8} \theta^4-3^{4} x\left(1234\theta^4+2168\theta^3+1975\theta^2+891\theta+162\right)-x^{2}\left(428004+1521180\theta+2033921\theta^2+1177556\theta^3+205589\theta^4\right)+x^{3}\left(2310517\theta^4+12882402\theta^3+26939429\theta^2+25052328\theta+8683524\right)-2^{2} 5^{2} x^{4}\left(51526\theta^4+332687\theta^3+804453\theta^2+849398\theta+325796\right)+2^{2} 5^{4} x^{5}(\theta+1)(1593\theta^3+8667\theta^2+15104\theta+8516)-2^{4} 5^{6} x^{6}(\theta+2)(\theta+1)(2\theta+3)^2\)
Maple LaTexCoefficients of the holomorphic solution: 1, 2, 14, 104, 1030, ... --> OEIS Normalized instanton numbers (n0=1): 31/81, 40/27, 29/9, 1532/81, 6551/81, ... ; Common denominator:...
\(-(16z-1)(25z^3-17z^2+2z+1)(-81+50z)^2\)
| ≈\(-0.17455\) | \(0\) | \(\frac{ 1}{ 16}\) | ≈\(0.427275-0.215865I\) | ≈\(0.427275+0.215865I\) | \(\frac{ 81}{ 50}\) | \(\infty\) |
|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(\frac{ 3}{ 2}\) |
| \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(3\) | \(\frac{ 3}{ 2}\) |
| \(2\) | \(0\) | \(2\) | \(2\) | \(2\) | \(4\) | \(2\) |
428
New Number: 7.10 | AESZ: | Superseeker: 1 11 | Hash: b1c277f62ba740f9f7e0371ba53e4194
Degree: 7
\(\theta^4-x\left(76\theta^4+80\theta^3+73\theta^2+33\theta+6\right)+x^{2}\left(2209\theta^4+4228\theta^3+4745\theta^2+2726\theta+648\right)-2 3^{2} x^{3}\left(1735\theta^4+4646\theta^3+6099\theta^2+4072\theta+1124\right)+2^{2} 3^{3} x^{4}\left(2085\theta^4+7388\theta^3+11695\theta^2+9140\theta+2844\right)-2^{3} 3^{3} x^{5}(\theta+1)(3707\theta^3+14055\theta^2+20242\theta+10704)+2^{6} 3^{5} x^{6}(\theta+1)(\theta+2)(86\theta^2+285\theta+262)-2^{7} 3^{8} x^{7}(\theta+1)(\theta+2)^2(\theta+3)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 6, 60, 816, 13104, ... --> OEIS Normalized instanton numbers (n0=1): 1, 13/4, 11, 50, 1674/5, ... ; Common denominator:...
\(-(3z-1)(18z-1)(27z-1)(12z-1)^2(-1+2z)^2\)
| \(0\) | \(\frac{ 1}{ 27}\) | \(\frac{ 1}{ 18}\) | \(\frac{ 1}{ 12}\) | \(\frac{ 1}{ 3}\) | \(\frac{ 1}{ 2}\) | \(\infty\) |
|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(2\) |
| \(0\) | \(1\) | \(1\) | \(3\) | \(1\) | \(\frac{ 1}{ 2}\) | \(2\) |
| \(0\) | \(2\) | \(2\) | \(4\) | \(2\) | \(1\) | \(3\) |
429
New Number: 7.11 | AESZ: | Superseeker: -8 -3784/3 | Hash: cb1bf6566f9c1a0dbfe98fb55f81944c
Degree: 7
\(\theta^4+2^{2} x\left(23\theta^4-34\theta^3-30\theta^2-13\theta-2\right)+2^{5} x^{2}\left(177\theta^4+108\theta^3+577\theta^2+518\theta+116\right)+2^{10} x^{3}\left(355\theta^4+960\theta^3+1178\theta^2+139\theta-44\right)+2^{15} x^{4}\left(451\theta^4+1228\theta^3+997\theta^2+489\theta+103\right)+2^{20} x^{5}\left(285\theta^4+720\theta^3+766\theta^2+410\theta+83\right)+2^{26} x^{6}(2\theta+1)(20\theta^3+50\theta^2+49\theta+17)+2^{31} x^{7}(2\theta+1)(\theta+1)^2(2\theta+3)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 8, -120, -4480, 55720, ... --> OEIS Normalized instanton numbers (n0=1): -8, 43/2, -3784/3, 51036, -1659840, ... ; Common denominator:...
\((8z+1)(32768z^3+3072z^2-12z+1)(32z+1)^3\)
| \(-\frac{ 1}{ 8}\) | ≈\(-0.100423\) | \(-\frac{ 1}{ 32}\) | \(0\) | ≈\(0.003336-0.01711I\) | ≈\(0.003336+0.01711I\) | \(\infty\) |
|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(1\) | \(1\) | \(2\) | \(0\) | \(1\) | \(1\) | \(1\) |
| \(1\) | \(1\) | \(3\) | \(0\) | \(1\) | \(1\) | \(1\) |
| \(2\) | \(2\) | \(5\) | \(0\) | \(2\) | \(2\) | \(\frac{ 3}{ 2}\) |
430
New Number: 7.12 | AESZ: | Superseeker: -21 -7941 | Hash: 0841b278bc566a089b643bbe2460fe8b
Degree: 7
\(\theta^4+3 x\left(99\theta^4+162\theta^3+139\theta^2+58\theta+10\right)+2 3^{4} x^{2}\left(135\theta^4+738\theta^3+945\theta^2+518\theta+116\right)-2^{2} 3^{7} x^{3}\left(117\theta^4-738\theta^3-2010\theta^2-1493\theta-406\right)-2^{3} 3^{10} x^{4}\left(333\theta^4+774\theta^3-898\theta^2-1269\theta-454\right)-2^{4} 3^{13} x^{5}\left(54\theta^4+1224\theta^3+1179\theta^2+347\theta-22\right)+2^{5} 3^{16} x^{6}\left(180\theta^4+72\theta^3-327\theta^2-359\theta-106\right)+2^{7} 3^{19} x^{7}(\theta+1)^2(6\theta+5)(6\theta+7)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -30, 1458, -89076, 6250050, ... --> OEIS Normalized instanton numbers (n0=1): -21, -399, -7941, -986355/4, -8179455, ... ; Common denominator:...
\((27z+1)(54z+1)(54z-1)^2(108z+1)^3\)
| \(-\frac{ 1}{ 27}\) | \(-\frac{ 1}{ 54}\) | \(-\frac{ 1}{ 108}\) | \(0\) | \(\frac{ 1}{ 54}\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 5}{ 6}\) |
| \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(0\) | \(1\) | \(1\) |
| \(1\) | \(1\) | \(\frac{ 3}{ 2}\) | \(0\) | \(3\) | \(1\) |
| \(2\) | \(2\) | \(2\) | \(0\) | \(4\) | \(\frac{ 7}{ 6}\) |
431
New Number: 7.13 | AESZ: | Superseeker: -32 -107936 | Hash: 80eaab6a34199e98f88d8472c115c4df
Degree: 7
\(\theta^4+2^{4} x\left(44\theta^4+72\theta^3+64\theta^2+28\theta+5\right)+2^{11} x^{2}\left(60\theta^4+328\theta^3+420\theta^2+228\theta+51\right)-2^{18} x^{3}\left(52\theta^4-328\theta^3-885\theta^2-663\theta-181\right)-2^{25} x^{4}\left(148\theta^4+344\theta^3-403\theta^2-559\theta-199\right)-2^{32} x^{5}\left(24\theta^4+544\theta^3+519\theta^2+147\theta-12\right)+2^{39} x^{6}\left(80\theta^4+32\theta^3-147\theta^2-159\theta-46\right)+2^{47} x^{7}(4\theta+3)(\theta+1)^2(4\theta+5)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -80, 10512, -1703168, 309951760, ... --> OEIS Normalized instanton numbers (n0=1): -32, -2840, -107936, -7514224, -575948640, ... ; Common denominator:...
\((64z+1)(128z+1)(128z-1)^2(256z+1)^3\)
| \(-\frac{ 1}{ 64}\) | \(-\frac{ 1}{ 128}\) | \(-\frac{ 1}{ 256}\) | \(0\) | \(\frac{ 1}{ 128}\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 3}{ 4}\) |
| \(1\) | \(1\) | \(\frac{ 1}{ 4}\) | \(0\) | \(1\) | \(1\) |
| \(1\) | \(1\) | \(\frac{ 7}{ 4}\) | \(0\) | \(3\) | \(1\) |
| \(2\) | \(2\) | \(2\) | \(0\) | \(4\) | \(\frac{ 5}{ 4}\) |
432
New Number: 7.14 | AESZ: | Superseeker: -48 -38929520 | Hash: d8c602210ad81a2daef74d36a78ea933
Degree: 7
\(\theta^4+2^{4} 3 x\left(99\theta^4+162\theta^3+151\theta^2+70\theta+13\right)+2^{9} 3^{4} x^{2}\left(135\theta^4+738\theta^3+945\theta^2+506\theta+113\right)-2^{14} 3^{7} x^{3}\left(117\theta^4-738\theta^3-1965\theta^2-1490\theta-409\right)-2^{19} 3^{10} x^{4}\left(333\theta^4+774\theta^3-919\theta^2-1242\theta-439\right)-2^{25} 3^{13} x^{5}\left(27\theta^4+612\theta^3+576\theta^2+154\theta-17\right)+2^{31} 3^{16} x^{6}\left(45\theta^4+18\theta^3-84\theta^2-89\theta-25\right)+2^{37} 3^{19} x^{7}(\theta+1)^2(3\theta+2)(3\theta+4)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -624, 633744, -768218880, 1020122073360, ... --> OEIS Normalized instanton numbers (n0=1): -48, -160806, -38929520, -13792511646, -7174458915600, ... ; Common denominator:...
\((432z+1)(864z+1)(864z-1)^2(1728z+1)^3\)
| \(-\frac{ 1}{ 432}\) | \(-\frac{ 1}{ 864}\) | \(-\frac{ 1}{ 1728}\) | \(0\) | \(\frac{ 1}{ 864}\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 2}{ 3}\) |
| \(1\) | \(1\) | \(0\) | \(0\) | \(1\) | \(1\) |
| \(1\) | \(1\) | \(2\) | \(0\) | \(3\) | \(1\) |
| \(2\) | \(2\) | \(2\) | \(0\) | \(4\) | \(\frac{ 4}{ 3}\) |
433
New Number: 7.15 | AESZ: | Superseeker: -2 -952 | Hash: d9a911258d890c112974a4ba19e93e6d
Degree: 7
\(\theta^4+2 x\left(138\theta^4+156\theta^3+137\theta^2+59\theta+10\right)+2^{2} x^{2}\left(4796\theta^4+15824\theta^3+16719\theta^2+7610\theta+1400\right)-2^{4} 5 x^{3}\left(5876\theta^4-28824\theta^3-58439\theta^2-39075\theta-9350\right)-2^{6} 5 x^{4}\left(184592\theta^4+414976\theta^3-60816\theta^2-180968\theta-60145\right)+2^{10} 3 x^{5}\left(240624\theta^4-905760\theta^3-1250920\theta^2-576920\theta-83925\right)+2^{18} 3^{2} x^{6}\left(13608\theta^4+48276\theta^3+66402\theta^2+41679\theta+9935\right)-2^{20} 3^{5} x^{7}(6\theta+5)^2(6\theta+7)^2\)
Maple LaTexCoefficients of the holomorphic solution: 1, -20, 900, -55280, 3962500, ... --> OEIS Normalized instanton numbers (n0=1): -2, -343/2, -952, -45148, -17303644/25, ... ; Common denominator:...
\(-(-1-16z+256z^2)(32z-1)^2(108z+1)^3\)
| \(\frac{ 1}{ 32}-\frac{ 1}{ 32}\sqrt{ 5}\) | \(-\frac{ 1}{ 108}\) | \(0\) | \(\frac{ 1}{ 32}\) | \(\frac{ 1}{ 32}+\frac{ 1}{ 32}\sqrt{ 5}\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 5}{ 6}\) |
| \(1\) | \(\frac{ 1}{ 2}\) | \(0\) | \(1\) | \(1\) | \(\frac{ 5}{ 6}\) |
| \(1\) | \(\frac{ 3}{ 2}\) | \(0\) | \(3\) | \(1\) | \(\frac{ 7}{ 6}\) |
| \(2\) | \(2\) | \(0\) | \(4\) | \(2\) | \(\frac{ 7}{ 6}\) |
434
New Number: 7.16 | AESZ: | Superseeker: 22/5 68 | Hash: 660211ce6175f36772066594bfc33cbb
Degree: 7
\(5^{2} \theta^4-2 5 x\theta(15+71\theta+112\theta^2+38\theta^3)-2^{2} x^{2}\left(4364\theta^4+15872\theta^3+24679\theta^2+19360\theta+6000\right)-2^{4} 3^{2} 5 x^{3}\left(92\theta^4+224\theta^3+103\theta^2-176\theta-165\right)+2^{6} 3^{2} x^{4}\left(1228\theta^4+10496\theta^3+30154\theta^2+35736\theta+14715\right)+2^{9} 3^{4} x^{5}(\theta+1)(38\theta^3+74\theta^2-304\theta-495)-2^{10} 3^{4} x^{6}(2\theta+13)(2\theta+3)(17\theta+39)(\theta+1)-2^{12} 3^{6} x^{7}(\theta+1)(2\theta+5)(2\theta+3)(\theta+3)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, 60, 480, 16524, ... --> OEIS Normalized instanton numbers (n0=1): 22/5, 8, 68, 3292/5, 38826/5, ... ; Common denominator:...
\(-(-1+36z)(12z+5)^2(12z+1)^2(4z-1)^2\)
| \(-\frac{ 5}{ 12}\) | \(-\frac{ 1}{ 12}\) | \(0\) | \(\frac{ 1}{ 36}\) | \(\frac{ 1}{ 4}\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(0\) | \(0\) | \(1\) | \(\frac{ 1}{ 2}\) | \(\frac{ 3}{ 2}\) |
| \(3\) | \(1\) | \(0\) | \(1\) | \(\frac{ 1}{ 2}\) | \(\frac{ 5}{ 2}\) |
| \(4\) | \(1\) | \(0\) | \(2\) | \(1\) | \(3\) |
435
New Number: 7.17 | AESZ: | Superseeker: 0 18 | Hash: c248fd7c807d0aae71ef687a9ee40c80
Degree: 7
\(\theta^4+3 x\left(87\theta^4+84\theta^3+86\theta^2+44\theta+9\right)+2 3^{3} x^{2}\left(539\theta^4+1076\theta^3+1366\theta^2+880\theta+233\right)+2 3^{5} x^{3}\left(3699\theta^4+11424\theta^3+17579\theta^2+13389\theta+4088\right)+3^{7} x^{4}\left(30367\theta^4+128696\theta^3+235722\theta^2+205070\theta+69226\right)+3^{9} x^{5}\left(74547\theta^4+405660\theta^3+871096\theta^2+848930\theta+310507\right)+2 3^{11} 5 x^{6}(2\theta+3)(5066\theta^3+26325\theta^2+44815\theta+23766)+2^{2} 3^{14} 5^{2} 7^{2} x^{7}(\theta+1)(2\theta+5)(2\theta+3)(\theta+3)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -27, 783, -23481, 717903, ... --> OEIS Normalized instanton numbers (n0=1): 0, -27/2, 18, -999/2, 1566, ... ; Common denominator:...
\((27z+1)(1323z^2+72z+1)(36z+1)^2(45z+1)^2\)
| \(-\frac{ 1}{ 27}\) | \(-\frac{ 1}{ 36}\) | \(-\frac{ 4}{ 147}-\frac{ 1}{ 441}\sqrt{ 3}I\) | \(-\frac{ 4}{ 147}+\frac{ 1}{ 441}\sqrt{ 3}I\) | \(-\frac{ 1}{ 45}\) | \(0\) | \(\infty\) |
|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(1\) | \(0\) | \(\frac{ 3}{ 2}\) |
| \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(3\) | \(0\) | \(\frac{ 5}{ 2}\) |
| \(2\) | \(1\) | \(2\) | \(2\) | \(4\) | \(0\) | \(3\) |
436
New Number: 7.18 | AESZ: | Superseeker: 352 26115552 | Hash: df2c3b4e6a3366531b24bb05809eb1a4
Degree: 7
\(\theta^4-2^{4} x\left(144\theta^4-192\theta^3-172\theta^2-76\theta-11\right)+2^{14} x^{2}\left(100\theta^4-320\theta^3-25\theta^2+155\theta+36\right)-2^{21} x^{3}\left(72\theta^4-1248\theta^3+628\theta^2-180\theta-97\right)-2^{30} x^{4}\left(212\theta^4+256\theta^3-14\theta^2+86\theta+15\right)+2^{36} 3 x^{5}\left(240\theta^4-320\theta^3-332\theta^2-380\theta-119\right)+2^{46} 3^{2} x^{6}\left(12\theta^4+64\theta^3+99\theta^2+67\theta+17\right)-2^{56} 3^{3} x^{7}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -176, 17168, -4715264, 653856016, ... --> OEIS Normalized instanton numbers (n0=1): 352, 60664, 26115552, 16623590600, 13165993300256, ... ; Common denominator:...
\(-(256z-1)^2(256z+1)^2(768z-1)^3\)
| \(-\frac{ 1}{ 256}\) | \(0\) | \(\frac{ 1}{ 768}\) | \(\frac{ 1}{ 256}\) | \(\infty\) |
|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(0\) | \(0\) | \(2\) | \(\frac{ 1}{ 2}\) | \(1\) |
| \(1\) | \(0\) | \(3\) | \(\frac{ 1}{ 2}\) | \(1\) |
| \(1\) | \(0\) | \(5\) | \(1\) | \(1\) |
437
New Number: 7.19 | AESZ: | Superseeker: 4/3 -124/81 | Hash: f7f0f5d883101c38ed22cb74c80c8f5c
Degree: 7
\(3^{3} \theta^4-2^{2} 3^{2} x\left(12\theta^4-16\theta^3-21\theta^2-13\theta-3\right)-2^{4} 3 x^{2}\left(240\theta^4+1280\theta^3+2068\theta^2+1636\theta+489\right)+2^{10} x^{3}\left(212\theta^4+592\theta^3+490\theta^2-34\theta-129\right)+2^{13} x^{4}\left(72\theta^4+1536\theta^3+4804\theta^2+5468\theta+2031\right)-2^{18} x^{5}\left(100\theta^4+720\theta^3+1535\theta^2+1155\theta+276\right)+2^{20} x^{6}\left(144\theta^4+768\theta^3+1268\theta^2+884\theta+229\right)-2^{28} x^{7}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -4, 68, -496, 9796, ... --> OEIS Normalized instanton numbers (n0=1): 4/3, -14/9, -124/81, -4498/243, 37024/729, ... ; Common denominator:...
\(-(16z-1)^2(16z+1)^2(16z-3)^3\)
| \(-\frac{ 1}{ 16}\) | \(0\) | \(\frac{ 1}{ 16}\) | \(\frac{ 3}{ 16}\) | \(\infty\) |
|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(0\) | \(0\) | \(\frac{ 1}{ 2}\) | \(2\) | \(1\) |
| \(1\) | \(0\) | \(\frac{ 1}{ 2}\) | \(3\) | \(1\) |
| \(1\) | \(0\) | \(1\) | \(5\) | \(1\) |
438
New Number: 7.1 | AESZ: | Superseeker: 10/7 508/7 | Hash: 08ab3cb496250adfa30bc3e24ac63c4f
Degree: 7
\(7^{2} \theta^4-2 7 x\theta(46\theta^3+52\theta^2+33\theta+7)-2^{2} x^{2}\left(7332\theta^4+28848\theta^3+42633\theta^2+26670\theta+6272\right)-2^{4} x^{3}\left(2860\theta^4+44760\theta^3+120483\theta^2+111279\theta+35098\right)+2^{9} x^{4}\left(2230\theta^4+5920\theta^3-741\theta^2-6509\theta-3049\right)+2^{14} x^{5}\left(174\theta^4+1320\theta^3+1971\theta^2+1095\theta+190\right)-2^{19} x^{6}\left(22\theta^4+24\theta^3-9\theta^2-21\theta-7\right)-2^{25} x^{7}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, 32, 288, 7776, ... --> OEIS Normalized instanton numbers (n0=1): 10/7, 100/7, 508/7, 808, 59910/7, ... ; Common denominator:...
\(-(16z+1)(32z-1)(32z-7)^2(4z+1)^3\)
| \(-\frac{ 1}{ 4}\) | \(-\frac{ 1}{ 16}\) | \(0\) | \(\frac{ 1}{ 32}\) | \(\frac{ 7}{ 32}\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(\frac{ 1}{ 2}\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) |
| \(\frac{ 3}{ 2}\) | \(1\) | \(0\) | \(1\) | \(3\) | \(1\) |
| \(2\) | \(2\) | \(0\) | \(2\) | \(4\) | \(1\) |
439
New Number: 7.20 | AESZ: | Superseeker: 10 3394/3 | Hash: 9d5791eaabb9d0e9cb4b5cd0b2158b12
Degree: 7
\(\theta^4-x\left(88\theta^3-4+71\theta^4+42\theta^2-2\theta\right)-x^{2}\left(10462\theta+13294\theta^2+875\theta^4+6848\theta^3+3132\right)+3^{2} x^{3}\left(373\theta^4-6360\theta^3-30716\theta^2-44868\theta-23180\right)+3^{4} x^{4}\left(1843\theta^4+8384\theta^3+3236\theta^2-14996\theta-15180\right)+3^{8} x^{5}\left(75\theta^4+1272\theta^3+3454\theta^2+3554\theta+1192\right)-3^{11} x^{6}\left(27\theta^4-414\theta^2-918\theta-584\right)-3^{16} x^{7}\left((\theta+2)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -4, 147, 4496, 223111, ... --> OEIS Normalized instanton numbers (n0=1): 10, 77, 3394/3, 24029, 640402, ... ; Common denominator:...
\(-(-1+81z)(9z-1)^2(81z^2+14z+1)^2\)
| \(-\frac{ 7}{ 81}-\frac{ 4}{ 81}\sqrt{ 2}I\) | \(-\frac{ 7}{ 81}+\frac{ 4}{ 81}\sqrt{ 2}I\) | \(0\) | \(\frac{ 1}{ 81}\) | \(\frac{ 1}{ 9}\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(2\) |
| \(-\frac{ 1}{ 2}\) | \(-\frac{ 1}{ 2}\) | \(0\) | \(1\) | \(1\) | \(2\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(3\) | \(2\) |
| \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(0\) | \(2\) | \(4\) | \(2\) |
440
New Number: 7.21 | AESZ: | Superseeker: 90 413926 | Hash: f2cdf32038c22a3da2f5752ad59eaa27
Degree: 7
\(\theta^4-3^{2} x\left(27\theta^4+216\theta^3+234\theta^2+126\theta+28\right)-3^{6} x^{2}\left(75\theta^4-672\theta^3-2378\theta^2-2602\theta-1076\right)+3^{9} x^{3}\left(1843\theta^4+6360\theta^3-2836\theta^2-13692\theta-9828\right)-3^{14} x^{4}\left(373\theta^4+9344\theta^3+16396\theta^2+10260\theta+540\right)-3^{19} x^{5}\left(875\theta^4+152\theta^3-6794\theta^2-11462\theta-5400\right)+3^{26} x^{6}\left(71\theta^4+480\theta^3+1218\theta^2+1386\theta+600\right)+3^{33} x^{7}\left((\theta+2)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 252, 40419, 2460816, -1025424441, ... --> OEIS Normalized instanton numbers (n0=1): 90, -4365, 413926, -38862153, 4502063682, ... ; Common denominator:...
\((1+27z)(243z+1)^2(59049z^2-378z+1)^2\)
| \(-\frac{ 1}{ 27}\) | \(-\frac{ 1}{ 243}\) | \(0\) | \(\frac{ 7}{ 2187}-\frac{ 4}{ 2187}\sqrt{ 2}I\) | \(\frac{ 7}{ 2187}+\frac{ 4}{ 2187}\sqrt{ 2}I\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(2\) |
| \(1\) | \(1\) | \(0\) | \(-\frac{ 1}{ 2}\) | \(-\frac{ 1}{ 2}\) | \(2\) |
| \(1\) | \(3\) | \(0\) | \(1\) | \(1\) | \(2\) |
| \(2\) | \(4\) | \(0\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(2\) |
441
New Number: 7.2 | AESZ: | Superseeker: -80 -249872 | Hash: 341389ebf4ab0242c5b70d9a8fd7a1d9
Degree: 7
\(\theta^4+2^{4} x\left(22\theta^4+64\theta^3+51\theta^2+19\theta+3\right)-2^{9} x^{2}\left(174\theta^4-624\theta^3-945\theta^2-417\theta-80\right)-2^{14} x^{3}\left(2230\theta^4+3000\theta^3-5121\theta^2-3813\theta-971\right)+2^{19} x^{4}\left(2860\theta^4-33320\theta^3+3363\theta^2+6847\theta+2402\right)+2^{27} x^{5}\left(7332\theta^4+480\theta^3+81\theta^2+1380\theta+719\right)+2^{36} 7 x^{6}(\theta+1)(46\theta^3+86\theta^2+67\theta+20)-2^{45} 7^{2} x^{7}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -48, 5072, -733440, 124117776, ... --> OEIS Normalized instanton numbers (n0=1): -80, -4202, -249872, -22251117, -2195810928, ... ; Common denominator:...
\(-(64z+1)(32z-1)(224z-1)^2(256z+1)^3\)
| \(-\frac{ 1}{ 64}\) | \(-\frac{ 1}{ 256}\) | \(0\) | \(\frac{ 1}{ 224}\) | \(\frac{ 1}{ 32}\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(\frac{ 1}{ 2}\) | \(0\) | \(1\) | \(1\) | \(1\) |
| \(1\) | \(\frac{ 3}{ 2}\) | \(0\) | \(3\) | \(1\) | \(1\) |
| \(2\) | \(2\) | \(0\) | \(4\) | \(2\) | \(1\) |
442
New Number: 7.3 | AESZ: | Superseeker: 3 64 | Hash: 8413250555ca536f1bdccfeed506ea4e
Degree: 7
\(\theta^4+x\theta(39\theta^3-30\theta^2-19\theta-4)+2 x^{2}\left(16\theta^4-1070\theta^3-1057\theta^2-676\theta-192\right)-2^{2} 3^{2} x^{3}(3\theta+2)(171\theta^3+566\theta^2+600\theta+316)-2^{5} 3^{3} x^{4}\left(384\theta^4+1542\theta^3+2635\theta^2+2173\theta+702\right)-2^{6} 3^{3} x^{5}(\theta+1)(1393\theta^3+5571\theta^2+8378\theta+4584)-2^{10} 3^{5} x^{6}(\theta+1)(\theta+2)(31\theta^2+105\theta+98)-2^{12} 3^{7} x^{7}(\theta+1)(\theta+2)^2(\theta+3)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, 24, 192, 3384, ... --> OEIS Normalized instanton numbers (n0=1): 3, -4, 64, -253, 4292, ... ; Common denominator:...
\(-(8z+1)(24z-1)(3z+1)(4z+1)(12z+1)(1+18z)^2\)
| \(-\frac{ 1}{ 3}\) | \(-\frac{ 1}{ 4}\) | \(-\frac{ 1}{ 8}\) | \(-\frac{ 1}{ 12}\) | \(-\frac{ 1}{ 18}\) | \(0\) | \(\frac{ 1}{ 24}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(2\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(3\) | \(0\) | \(1\) | \(2\) |
| \(2\) | \(2\) | \(2\) | \(2\) | \(4\) | \(0\) | \(2\) | \(3\) |
443
New Number: 7.4 | AESZ: | Superseeker: -988/3 -14008436/3 | Hash: 9bddfb88498c0a263be6ca541ae7e980
Degree: 7
\(3^{2} \theta^4+2^{2} 3 x\left(760\theta^4+2048\theta^3+1423\theta^2+399\theta+42\right)-2^{7} x^{2}\left(20440\theta^4+25216\theta^3-4415\theta^2-4845\theta-795\right)+2^{12} x^{3}\left(39928\theta^4+16512\theta^3+23719\theta^2+11637\theta+1830\right)+2^{17} x^{4}\left(2928\theta^4-41856\theta^3-42871\theta^2-16873\theta-2425\right)+2^{23} x^{5}\left(608\theta^4+3968\theta^3+10676\theta^2+6177\theta+1089\right)+2^{29} x^{6}\left(272\theta^4+1056\theta^3+861\theta^2+264\theta+27\right)+2^{35} x^{7}\left((2\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -56, 21096, -12540800, 9146271400, ... --> OEIS Normalized instanton numbers (n0=1): -988/3, 57289/3, -14008436/3, 1385404666, -1599785191904/3, ... ; Common denominator:...
\((1+1248z-10240z^2+131072z^3)(-3+352z+2048z^2)^2\)
| \(-\frac{ 11}{ 128}-\frac{ 1}{ 128}\sqrt{ 145}\) | ≈\(-0.000796\) | \(0\) | \(-\frac{ 11}{ 128}+\frac{ 1}{ 128}\sqrt{ 145}\) | ≈\(0.039461-0.089595I\) | ≈\(0.039461+0.089595I\) | \(\infty\) |
|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) |
| \(3\) | \(1\) | \(0\) | \(3\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) |
| \(4\) | \(2\) | \(0\) | \(4\) | \(2\) | \(2\) | \(\frac{ 1}{ 2}\) |
444
New Number: 7.5 | AESZ: | Superseeker: 8096 9215266592 | Hash: 90403d92f72b2839164c2bbd30933deb
Degree: 7
\(\theta^4+2^{4} x\left(1088\theta^4-2048\theta^3-1260\theta^2-236\theta-19\right)+2^{15} x^{2}\left(1216\theta^4-5504\theta^3+11272\theta^2+3654\theta+423\right)+2^{24} x^{3}\left(11712\theta^4+190848\theta^3+97220\theta^2+27432\theta+2835\right)+2^{35} x^{4}\left(159712\theta^4+253376\theta^3+235372\theta^2+78648\theta+9491\right)-2^{46} x^{5}\left(81760\theta^4+62656\theta^3-46316\theta^2-33048\theta-5403\right)+2^{57} 3 x^{6}\left(3040\theta^4-2112\theta^3-2036\theta^2-528\theta-41\right)+2^{69} 3^{2} x^{7}\left((2\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 304, -113904, -2048902400, -4778502402800, ... --> OEIS Normalized instanton numbers (n0=1): 8096, -9179600, 9215266592, -8060820053720, 27014124083677664, ... ; Common denominator:...
\((2147483648z^3+40894464z^2-5120z+1)(-1-11264z+6291456z^2)^2\)
| ≈\(-0.019169\) | \(\frac{ 11}{ 12288}-\frac{ 1}{ 12288}\sqrt{ 145}\) | \(0\) | ≈\(6.3e-05-0.000143I\) | ≈\(6.3e-05+0.000143I\) | \(\frac{ 11}{ 12288}+\frac{ 1}{ 12288}\sqrt{ 145}\) | \(\infty\) |
|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) |
| \(1\) | \(3\) | \(0\) | \(1\) | \(1\) | \(3\) | \(\frac{ 1}{ 2}\) |
| \(2\) | \(4\) | \(0\) | \(2\) | \(2\) | \(4\) | \(\frac{ 1}{ 2}\) |
445
New Number: 7.6 | AESZ: | Superseeker: 1/3 5/3 | Hash: 24ba77c97bc4b46c39a41c77cc1d1ef4
Degree: 7
\(3^{2} \theta^4-3 x\left(112\theta^4+140\theta^3+133\theta^2+63\theta+12\right)+x^{2}\left(4393\theta^4+9340\theta^3+10903\theta^2+6360\theta+1488\right)-2 x^{3}\left(11669\theta^4+27720\theta^3+27019\theta^2+8460\theta-912\right)+2^{2} x^{4}\left(6799\theta^4-10288\theta^3-82183\theta^2-119168\theta-52672\right)+2^{3} 7 x^{5}(\theta+1)(2611\theta^3+15537\theta^2+26998\theta+14360)-2^{6} 7^{2} x^{6}(\theta+1)(\theta+2)(83\theta^2+105\theta-66)-2^{10} 7^{3} x^{7}(\theta+1)(\theta+2)^2(\theta+3)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 4, 28, 232, 2188, ... --> OEIS Normalized instanton numbers (n0=1): 1/3, 5/6, 5/3, 19/3, 29, ... ; Common denominator:...
\(-(2z+1)(8z-1)(7z-1)(16z-1)(z+1)(-3+14z)^2\)
| \(-1\) | \(-\frac{ 1}{ 2}\) | \(0\) | \(\frac{ 1}{ 16}\) | \(\frac{ 1}{ 8}\) | \(\frac{ 1}{ 7}\) | \(\frac{ 3}{ 14}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(2\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(3\) | \(2\) |
| \(2\) | \(2\) | \(0\) | \(2\) | \(2\) | \(2\) | \(4\) | \(3\) |
446
New Number: 7.7 | AESZ: | Superseeker: 2/3 13/3 | Hash: c7abb9c42d46f14955f0f23351082bef
Degree: 7
\(3^{2} \theta^4-2 3 x\left(88\theta^4+110\theta^3+103\theta^2+48\theta+9\right)+2^{2} x^{2}\left(2923\theta^4+6610\theta^3+8041\theta^2+4908\theta+1206\right)-x^{3}\left(123365\theta^4+374814\theta^3+519741\theta^2+346176\theta+89676\right)+2 x^{4}\left(309657\theta^4+1102938\theta^3+1591157\theta^2+1032920\theta+249740\right)-2^{3} 11 x^{5}(\theta+1)(12897\theta^3+35469\theta^2+31181\theta+8042)-2^{3} 11^{2} x^{6}(\theta+1)(\theta+2)(355\theta^2+1047\theta+806)-2^{4} 11^{3} x^{7}(\theta+1)(\theta+2)^2(\theta+3)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 6, 56, 636, 8196, ... --> OEIS Normalized instanton numbers (n0=1): 2/3, 5/3, 13/3, 59/3, 119, ... ; Common denominator:...
\(-(11z-1)(4z^2+22z-1)(z^2+11z-1)(-3+22z)^2\)
| \(-\frac{ 11}{ 2}-\frac{ 5}{ 2}\sqrt{ 5}\) | \(-\frac{ 11}{ 4}-\frac{ 5}{ 4}\sqrt{ 5}\) | \(0\) | \(-\frac{ 11}{ 4}+\frac{ 5}{ 4}\sqrt{ 5}\) | \(-\frac{ 11}{ 2}+\frac{ 5}{ 2}\sqrt{ 5}\) | \(\frac{ 1}{ 11}\) | \(\frac{ 3}{ 22}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(2\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(3\) | \(2\) |
| \(2\) | \(2\) | \(0\) | \(2\) | \(2\) | \(2\) | \(4\) | \(3\) |
447
New Number: 7.8 | AESZ: | Superseeker: -1/3 -5/3 | Hash: d5b8cfd5049e5d8670dac5bb5499d46a
Degree: 7
\(3^{2} \theta^4-3 x\left(272\theta^4+340\theta^3+347\theta^2+177\theta+36\right)+x^{2}\left(31273\theta^4+76540\theta^3+103783\theta^2+71112\theta+19728\right)-2 x^{3}\left(328219\theta^4+1181160\theta^3+1977957\theta^2+1620036\theta+522288\right)+2^{2} x^{4}\left(2036999\theta^4+9602752\theta^3+19022113\theta^2+17726192\theta+6309408\right)-2^{3} 17 x^{5}(\theta+1)(439669\theta^3+2114103\theta^2+3708554\theta+2306280)+2^{6} 3^{3} 17^{2} x^{6}(\theta+1)(\theta+2)(481\theta^2+1875\theta+1962)-2^{10} 3^{4} 17^{3} x^{7}(\theta+1)(\theta+2)^2(\theta+3)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 12, 156, 2136, 30348, ... --> OEIS Normalized instanton numbers (n0=1): -1/3, 11/12, -5/3, 19/3, -29, ... ; Common denominator:...
\(-(17z-1)(9z-1)(8z-1)(18z-1)(16z-1)(-3+34z)^2\)
| \(0\) | \(\frac{ 1}{ 18}\) | \(\frac{ 1}{ 17}\) | \(\frac{ 1}{ 16}\) | \(\frac{ 3}{ 34}\) | \(\frac{ 1}{ 9}\) | \(\frac{ 1}{ 8}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(2\) |
| \(0\) | \(1\) | \(1\) | \(1\) | \(3\) | \(1\) | \(1\) | \(2\) |
| \(0\) | \(2\) | \(2\) | \(2\) | \(4\) | \(2\) | \(2\) | \(3\) |
448
New Number: 7.9 | AESZ: | Superseeker: -3 -245/3 | Hash: 5641c09b76662b0741e41b41b0c6f105
Degree: 7
\(\theta^4-3 x\left(96\theta^4+120\theta^3+127\theta^2+67\theta+14\right)+3^{2} x^{2}\left(3897\theta^4+9540\theta^3+13209\theta^2+9246\theta+2608\right)-2 3^{4} x^{3}\left(14445\theta^4+52002\theta^3+88179\theta^2+73278\theta+23920\right)+2^{2} 3^{6} x^{4}\left(31671\theta^4+149364\theta^3+298089\theta^2+280512\theta+100780\right)-2^{3} 3^{12} x^{5}(\theta+1)(507\theta^3+2439\theta^2+4306\theta+2704)+2^{6} 3^{14} x^{6}(\theta+1)(\theta+2)(90\theta^2+351\theta+370)-2^{7} 3^{19} x^{7}(\theta+1)(\theta+2)^2(\theta+3)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 42, 1872, 86712, 4126716, ... --> OEIS Normalized instanton numbers (n0=1): -3, 69/4, -245/3, 879, -11829, ... ; Common denominator:...
\(-(36z-1)^2(27z-1)^2(54z-1)^3\)
| \(0\) | \(\frac{ 1}{ 54}\) | \(\frac{ 1}{ 36}\) | \(\frac{ 1}{ 27}\) | \(\infty\) |
|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(0\) | \(0\) | \(1\) | \(\frac{ 1}{ 3}\) | \(2\) |
| \(0\) | \(-\frac{ 1}{ 3}\) | \(3\) | \(\frac{ 2}{ 3}\) | \(2\) |
| \(0\) | \(\frac{ 1}{ 3}\) | \(4\) | \(1\) | \(3\) |
449
New Number: 8.10 | AESZ: 123 | Superseeker: 12 1828/3 | Hash: f0d76ab2b6b8808f4faa4ab8ecadff2c
Degree: 8
\(\theta^4-2^{2} x(3\theta^2+3\theta+1)(10\theta^2+10\theta+3)+2^{4} x^{2}\left(209\theta^4+1052\theta^3+1471\theta^2+838\theta+183\right)+2^{7} 3^{2} x^{3}\left(30\theta^4-180\theta^3-551\theta^2-417\theta-111\right)-2^{10} 3^{2} x^{4}\left(227\theta^4+454\theta^3-550\theta^2-777\theta-261\right)+2^{12} 3^{4} x^{5}\left(30\theta^4+300\theta^3+169\theta^2-25\theta-35\right)+2^{14} 3^{4} x^{6}\left(209\theta^4-216\theta^3-431\theta^2-216\theta-27\right)-2^{17} 3^{6} x^{7}(3\theta^2+3\theta+1)(10\theta^2+10\theta+3)+2^{20} 3^{8} x^{8}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 12, 300, 10416, 431964, ... --> OEIS Normalized instanton numbers (n0=1): 12, -47/2, 1828/3, -10813/4, 127948, ... ; Common denominator:...
\((36z-1)(8z-1)(72z-1)(4z-1)(-1+288z^2)^2\)
| \(-\frac{ 1}{ 24}\sqrt{ 2}\) | \(0\) | \(\frac{ 1}{ 72}\) | \(\frac{ 1}{ 36}\) | \(\frac{ 1}{ 24}\sqrt{ 2}\) | \(\frac{ 1}{ 8}\) | \(\frac{ 1}{ 4}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(3\) | \(0\) | \(1\) | \(1\) | \(3\) | \(1\) | \(1\) | \(1\) |
| \(4\) | \(0\) | \(2\) | \(2\) | \(4\) | \(2\) | \(2\) | \(1\) |
450
New Number: 8.11 | AESZ: 162 | Superseeker: 9 242/3 | Hash: 542708b59b898c35f43e00120897ff8d
Degree: 8
\(\theta^4-3 x(3\theta^2+3\theta+1)(10\theta^2+10\theta+3)+3^{3} x^{2}\left(91\theta^4+472\theta^3+659\theta^2+374\theta+81\right)+3^{6} x^{3}\left(30\theta^4-180\theta^3-551\theta^2-417\theta-111\right)-3^{8} x^{4}\left(200\theta^4+400\theta^3-514\theta^2-714\theta-237\right)+3^{11} x^{5}\left(30\theta^4+300\theta^3+169\theta^2-25\theta-35\right)+3^{13} x^{6}\left(91\theta^4-108\theta^3-211\theta^2-108\theta-15\right)-3^{16} x^{7}(3\theta^2+3\theta+1)(10\theta^2+10\theta+3)+3^{20} x^{8}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 9, 135, 1953, 5751, ... --> OEIS Normalized instanton numbers (n0=1): 9, -153/4, 242/3, -4923, 34245, ... ; Common denominator:...
\((27z^2-9z+1)(2187z^2-81z+1)(-1+243z^2)^2\)
| \(-\frac{ 1}{ 27}\sqrt{ 3}\) | \(0\) | \(\frac{ 1}{ 54}-\frac{ 1}{ 162}\sqrt{ 3}I\) | \(\frac{ 1}{ 54}+\frac{ 1}{ 162}\sqrt{ 3}I\) | \(\frac{ 1}{ 27}\sqrt{ 3}\) | \(\frac{ 1}{ 6}-\frac{ 1}{ 18}\sqrt{ 3}I\) | \(\frac{ 1}{ 6}+\frac{ 1}{ 18}\sqrt{ 3}I\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(3\) | \(0\) | \(1\) | \(1\) | \(3\) | \(1\) | \(1\) | \(1\) |
| \(4\) | \(0\) | \(2\) | \(2\) | \(4\) | \(2\) | \(2\) | \(1\) |