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You searched for: degz=13

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1

New Number: 13.10 |  AESZ:  |  Superseeker: 4 -628/9  |  Hash: 2a9fda379889eb2fd218bd01f2520f7a  

Degree: 13

\(\theta^4-2^{2} x\left(35\theta^4+38\theta^3+35\theta^2+16\theta+3\right)+2^{4} x^{2}\left(546\theta^4+1068\theta^3+1287\theta^2+790\theta+201\right)-2^{6} x^{3}\left(4928\theta^4+12888\theta^3+17829\theta^2+12673\theta+3693\right)+2^{8} x^{4}\left(28123\theta^4+88408\theta^3+131977\theta^2+98226\theta+29511\right)-2^{10} 3^{2} x^{5}\left(11315\theta^4+41094\theta^3+65088\theta^2+47691\theta+13532\right)+2^{13} 3^{2} x^{6}\left(11674\theta^4+48674\theta^3+79399\theta^2+52683\theta+11716\right)-2^{15} 3^{3} x^{7}\left(2063\theta^4+11102\theta^3+11184\theta^2-9217\theta-10762\right)-2^{17} 3^{4} x^{8}\left(3277\theta^4+16284\theta^3+42329\theta^2+57018\theta+27266\right)+2^{20} 3^{5} x^{9}\left(1124\theta^4+7114\theta^3+18121\theta^2+22265\theta+10018\right)+2^{24} 3^{6} x^{10}(\theta+1)(\theta^3-105\theta^2-277\theta-267)-2^{25} 3^{7} x^{11}(\theta+1)(\theta+2)(93\theta^2+441\theta+607)+2^{27} 3^{10} x^{12}(\theta+3)(\theta+2)(\theta+1)(\theta+6)+2^{30} 3^{10} x^{13}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)

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Coefficients of the holomorphic solution: 1, 12, 180, 2928, 47556, ...
--> OEIS
Normalized instanton numbers (n0=1): 4, 5, -628/9, -2823/4, 672, ... ; Common denominator:...

Discriminant

\((8z-1)(10368z^3-1728z^2+72z-1)(12z-1)^2(288z^2-24z+1)^2(4z+1)^3\)

Local exponents

\(-\frac{ 1}{ 4}\)\(0\) ≈\(0.027033-0.011216I\) ≈\(0.027033+0.011216I\)\(\frac{ 1}{ 24}-\frac{ 1}{ 24}I\)\(\frac{ 1}{ 24}+\frac{ 1}{ 24}I\)\(\frac{ 1}{ 12}\) ≈\(0.112601\)\(\frac{ 1}{ 8}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(\frac{ 1}{ 2}\)\(0\)\(1\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)\(1\)\(1\)\(2\)
\(\frac{ 3}{ 2}\)\(0\)\(1\)\(1\)\(3\)\(3\)\(\frac{ 1}{ 2}\)\(1\)\(1\)\(3\)
\(2\)\(0\)\(2\)\(2\)\(4\)\(4\)\(1\)\(2\)\(2\)\(4\)

Note:

This is operator "13.10" from ...

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2

New Number: 13.11 |  AESZ:  |  Superseeker: 7 -2044/9  |  Hash: d6e183df7853fe5068c8b8cdeb3f63cb  

Degree: 13

\(\theta^4-x\left(98\theta^4+164\theta^3+137\theta^2+55\theta+9\right)+x^{2}\left(3822\theta^4+11400\theta^3+14901\theta^2+8746\theta+2007\right)-x^{3}\left(64148\theta^4+196344\theta^3+271665\theta^2+199855\theta+60354\right)+x^{4}\left(802771\theta^4+2242504\theta^3+2203855\theta^2+1316868\theta+390636\right)-2 3 x^{5}\left(1040145\theta^4+2982426\theta^3+3578912\theta^2+1897395\theta+345411\right)+2 3^{2} x^{6}\left(1927994\theta^4+4917832\theta^3+7329041\theta^2+5154630\theta+1338003\right)-2 3^{5} x^{7}\left(219316\theta^4+761432\theta^3+1064075\theta^2+703129\theta+181966\right)+3^{4} x^{8}\left(754759\theta^4+7471824\theta^3+13904030\theta^2+8830464\theta+1544112\right)+3^{7} x^{9}\left(174966\theta^4+736236\theta^3+1307237\theta^2+1340471\theta+568265\right)-3^{10} x^{10}(\theta+1)(8018\theta^3+62342\theta^2+139257\theta+108861)-3^{9} x^{11}(\theta+1)(\theta+2)(28988\theta^2+81396\theta+36331)+3^{12} x^{12}(\theta+3)(\theta+2)(\theta+1)(1061\theta+5386)+2 3^{15} 17 x^{13}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)

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Coefficients of the holomorphic solution: 1, 9, 135, 2115, 18063, ...
--> OEIS
Normalized instanton numbers (n0=1): 7, -31/4, -2044/9, -1380, -8520, ... ; Common denominator:...

Discriminant

\((2z-1)(4131z^3-2187z^2+81z-1)(3z-1)^2(81z^2-6z+1)^2(z+1)^3\)

Local exponents

\(-1\)\(0\) ≈\(0.019487-0.01067I\) ≈\(0.019487+0.01067I\)\(\frac{ 1}{ 27}-\frac{ 2}{ 27}\sqrt{ 2}I\)\(\frac{ 1}{ 27}+\frac{ 2}{ 27}\sqrt{ 2}I\)\(\frac{ 1}{ 3}\) ≈\(0.490438\)\(\frac{ 1}{ 2}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(\frac{ 1}{ 2}\)\(0\)\(1\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)\(1\)\(1\)\(2\)
\(\frac{ 3}{ 2}\)\(0\)\(1\)\(1\)\(3\)\(3\)\(\frac{ 1}{ 2}\)\(1\)\(1\)\(3\)
\(2\)\(0\)\(2\)\(2\)\(4\)\(4\)\(1\)\(2\)\(2\)\(4\)

Note:

This is operator "13.11" from ...

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3

New Number: 13.12 |  AESZ:  |  Superseeker: 76/3 746444/81  |  Hash: fec1670f7378fb309308803574ce2a00  

Degree: 13

\(3^{2} \theta^4+2^{2} 3 x\left(4\theta^4-208\theta^3-189\theta^2-85\theta-17\right)-2^{4} x^{2}\left(5120\theta^4-7168\theta^3-21704\theta^2-15788\theta-5307\right)+2^{9} x^{3}\left(6080\theta^4+28992\theta^3-21720\theta^2-27270\theta-13529\right)+2^{12} x^{4}\left(40096\theta^4-258688\theta^3-41760\theta^2+16820\theta+38071\right)-2^{17} x^{5}\left(123088\theta^4-63104\theta^3+45236\theta^2+55562\theta+46257\right)+2^{21} x^{6}\left(219712\theta^4+380352\theta^3+753688\theta^2+810222\theta+409897\right)-2^{24} x^{7}\left(107008\theta^4+264320\theta^3+651536\theta^2+1298596\theta+1113327\right)-2^{28} x^{8}\left(704944\theta^4+3925888\theta^3+9920672\theta^2+12076292\theta+5776605\right)+2^{34} x^{9}\left(220796\theta^4+1480752\theta^3+4427225\theta^2+6675624\theta+4170854\right)-2^{36} 3 x^{10}\left(9216\theta^4-66432\theta^3-131864\theta^2+696808\theta+1370197\right)-2^{40} 3 x^{11}\left(168448\theta^4+1796608\theta^3+7226400\theta^2+13138336\theta+9227347\right)+2^{47} 3^{2} x^{12}\left(3584\theta^4+43776\theta^3+208688\theta^2+457392\theta+385875\right)-2^{52} 3^{2} x^{13}(4\theta+15)^2(4\theta+13)^2\)

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Coefficients of the holomorphic solution: 1, 68/3, 1036/3, 44464/27, -8491132/81, ...
--> OEIS
Normalized instanton numbers (n0=1): 76/3, -3641/9, 746444/81, -69221068/243, 7315935712/729, ... ; Common denominator:...

Discriminant

\(-(-1+16z)(16z-3)^2(16z+1)^2(3072z^2-48z-1)^2(1024z^2-48z+1)^2\)

Local exponents

\(-\frac{ 1}{ 16}\)\(\frac{ 1}{ 128}-\frac{ 1}{ 384}\sqrt{ 57}\)\(0\)\(\frac{ 3}{ 128}-\frac{ 1}{ 128}\sqrt{ 7}I\)\(\frac{ 3}{ 128}+\frac{ 1}{ 128}\sqrt{ 7}I\)\(\frac{ 1}{ 128}+\frac{ 1}{ 384}\sqrt{ 57}\)\(\frac{ 1}{ 16}\)\(\frac{ 3}{ 16}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 13}{ 4}\)
\(\frac{ 1}{ 2}\)\(1\)\(0\)\(\frac{ 1}{ 2}\)\(\frac{ 1}{ 2}\)\(1\)\(1\)\(1\)\(\frac{ 13}{ 4}\)
\(\frac{ 1}{ 2}\)\(3\)\(0\)\(\frac{ 1}{ 2}\)\(\frac{ 1}{ 2}\)\(3\)\(1\)\(-2\)\(\frac{ 15}{ 4}\)
\(1\)\(4\)\(0\)\(1\)\(1\)\(4\)\(2\)\(3\)\(\frac{ 15}{ 4}\)

Note:

This is operator "13.12" from ...

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4

New Number: 13.13 |  AESZ:  |  Superseeker: 32 74144  |  Hash: e20067c633b6371dc19f760a1140f0e4  

Degree: 13

\(\theta^4-2^{3} x\left(74\theta^4+52\theta^3+70\theta^2+44\theta+11\right)+2^{6} x^{2}\left(1948\theta^4+2320\theta^3+3750\theta^2+3244\theta+1117\right)-2^{11} x^{3}\left(5498\theta^4+9708\theta^3+17699\theta^2+12099\theta+2024\right)+2^{12} x^{4}\left(90192\theta^4+243456\theta^3+317216\theta^2-2080\theta-132883\right)+2^{16} x^{5}\left(35024\theta^4+171680\theta^3+1168736\theta^2+2029296\theta+1162051\right)-2^{20} x^{6}\left(249200\theta^4+1529280\theta^3+3887240\theta^2+5111280\theta+2830091\right)+2^{24} x^{7}\left(6224\theta^4+297952\theta^3+1078344\theta^2+1331848\theta+442349\right)+2^{29} x^{8}\left(78896\theta^4+725696\theta^3+2501496\theta^2+3908720\theta+2314163\right)+2^{34} x^{9}\left(9584\theta^4+62208\theta^3+120960\theta^2+36216\theta-71103\right)+2^{38} x^{10}\left(2864\theta^4+44992\theta^3+291624\theta^2+843472\theta+893907\right)-2^{42} x^{11}\left(8176\theta^4+131296\theta^3+780536\theta^2+2035976\theta+1968867\right)-2^{47} 3 x^{12}\left(752\theta^4+11328\theta^3+62952\theta^2+153648\theta+139383\right)-2^{52} 3^{2} x^{13}\left((2\theta+7)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 88, 6576, 475776, 37804816, ...
--> OEIS
Normalized instanton numbers (n0=1): 32, 1048, 74144, 7046865, 788076384, ... ; Common denominator:...

Discriminant

\(-(16z-1)(262144z^4-8192z^3+2304z^2-256z+1)(48z-1)^2(16z+1)^2(512z^2+128z-1)^2\)

Local exponents

\(-\frac{ 1}{ 8}-\frac{ 3}{ 32}\sqrt{ 2}\)\(-\frac{ 1}{ 16}\) ≈\(-0.024399\) ≈\(-0.024399\)\(0\) ≈\(0.004052\)\(-\frac{ 1}{ 8}+\frac{ 3}{ 32}\sqrt{ 2}\)\(\frac{ 1}{ 48}\)\(\frac{ 1}{ 16}\) ≈\(0.075996\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 7}{ 2}\)
\(1\)\(\frac{ 1}{ 2}\)\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)\(1\)\(1\)\(\frac{ 7}{ 2}\)
\(3\)\(\frac{ 1}{ 2}\)\(1\)\(1\)\(0\)\(1\)\(3\)\(-2\)\(1\)\(1\)\(\frac{ 7}{ 2}\)
\(4\)\(1\)\(2\)\(2\)\(0\)\(2\)\(4\)\(3\)\(2\)\(2\)\(\frac{ 7}{ 2}\)

Note:

This is operator "13.13" from ...

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5

New Number: 13.14 |  AESZ:  |  Superseeker: 20/3 36340/81  |  Hash: 4b391bfc7d7d7a60edd430907aff9fae  

Degree: 13

\(3^{2} \theta^4+2^{2} 3 x\left(47\theta^4-50\theta^3-45\theta^2-20\theta-4\right)+2^{4} x^{2}\left(511\theta^4-1052\theta^3+179\theta^2+302\theta+132\right)-2^{7} x^{3}\left(179\theta^4-306\theta^3+1857\theta^2+2226\theta+931\right)-2^{8} x^{4}\left(2396\theta^4+17992\theta^3+43050\theta^2+42004\theta+13733\right)-2^{10} x^{5}\left(19724\theta^4+94712\theta^3+170136\theta^2+115772\theta+521\right)-2^{12} x^{6}\left(1556\theta^4-52704\theta^3-398172\theta^2-916440\theta-712527\right)+2^{15} x^{7}\left(62300\theta^4+489880\theta^3+1536500\theta^2+2159040\theta+1096749\right)-2^{18} x^{8}\left(8756\theta^4+79664\theta^3+485090\theta^2+1462308\theta+1567885\right)-2^{20} x^{9}\left(45096\theta^4+509616\theta^3+2195020\theta^2+4371756\theta+3428277\right)+2^{22} x^{10}\left(43984\theta^4+538112\theta^3+2558944\theta^2+5583456\theta+4682427\right)-2^{25} x^{11}\left(7792\theta^4+99808\theta^3+490272\theta^2+1087312\theta+914209\right)+2^{28} x^{12}\left(592\theta^4+7872\theta^3+39704\theta^2+89808\theta+76717\right)-2^{31} x^{13}\left((2\theta+7)^4\right)\)

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Coefficients of the holomorphic solution: 1, 16/3, 52/3, 3200/27, 129668/81, ...
--> OEIS
Normalized instanton numbers (n0=1): 20/3, -410/9, 36340/81, -5386783/972, 57719264/729, ... ; Common denominator:...

Discriminant

\(-(8z-1)(1024z^4-2048z^3+144z^2-4z+1)(8z-3)^2(8z+1)^2(32z^2-32z-1)^2\)

Local exponents

\(-\frac{ 1}{ 8}\)\(\frac{ 1}{ 2}-\frac{ 3}{ 8}\sqrt{ 2}\) ≈\(-0.015388\) ≈\(-0.015388\)\(0\) ≈\(0.102801\)\(\frac{ 1}{ 8}\)\(\frac{ 3}{ 8}\)\(\frac{ 1}{ 2}+\frac{ 3}{ 8}\sqrt{ 2}\) ≈\(1.927975\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 7}{ 2}\)
\(\frac{ 1}{ 2}\)\(1\)\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)\(1\)\(1\)\(\frac{ 7}{ 2}\)
\(\frac{ 1}{ 2}\)\(3\)\(1\)\(1\)\(0\)\(1\)\(1\)\(-2\)\(3\)\(1\)\(\frac{ 7}{ 2}\)
\(1\)\(4\)\(2\)\(2\)\(0\)\(2\)\(2\)\(3\)\(4\)\(2\)\(\frac{ 7}{ 2}\)

Note:

This is operator "13.14" from ...

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6

New Number: 13.15 |  AESZ:  |  Superseeker: 6 626/3  |  Hash: 3e24fdfe8119ac950ce846460f109e44  

Degree: 13

\(\theta^4-2 x\left(16\theta^4+50\theta^3+39\theta^2+14\theta+2\right)-2^{2} x^{2}\left(219\theta^4+390\theta^3+335\theta^2+214\theta+62\right)-2^{4} x^{3}\left(115\theta^4+1068\theta^3+2660\theta^2+2022\theta+582\right)+2^{6} x^{4}\left(122\theta^4-788\theta^3+151\theta^2-913\theta-696\right)-2^{8} 3 x^{5}\left(303\theta^4-1488\theta^3-2955\theta^2-2550\theta-827\right)-2^{10} 3 x^{6}\left(37\theta^4+714\theta^3-5760\theta^2-8319\theta-3550\right)-2^{13} 3 x^{7}\left(101\theta^4+82\theta^3+102\theta^2-1679\theta-1322\right)+2^{15} 3 x^{8}\left(48\theta^4+948\theta^3-461\theta^2-1447\theta-628\right)-2^{17} x^{9}\left(89\theta^4-4392\theta^3-6123\theta^2-450\theta+1902\right)-2^{20} x^{10}\left(121\theta^4-532\theta^3-3072\theta^2-3697\theta-1348\right)+2^{23} 5 x^{11}(\theta+1)(21\theta^3+63\theta^2+206\theta+218)+2^{25} 5^{2} x^{12}(\theta+2)(\theta+1)(2\theta^2-12\theta-27)+2^{27} 5^{3} x^{13}(\theta+1)(\theta+2)^2(\theta+3)\)

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Coefficients of the holomorphic solution: 1, 4, 76, 1936, 57820, ...
--> OEIS
Normalized instanton numbers (n0=1): 6, 41/4, 626/3, 12349/8, 33062, ... ; Common denominator:...

Discriminant

\((4z-1)(4z+1)(16z^2+4z+1)(640z^3+96z^2+48z-1)(1+6z-48z^2+320z^3)^2\)

Local exponents

\(-\frac{ 1}{ 4}\)\(-\frac{ 1}{ 8}-\frac{ 1}{ 8}\sqrt{ 3}I\)\(-\frac{ 1}{ 8}+\frac{ 1}{ 8}\sqrt{ 3}I\) ≈\(-0.084967-0.266773I\) ≈\(-0.084967+0.266773I\) ≈\(-0.082432\)\(0\) ≈\(0.019933\) ≈\(0.116216-0.156217I\) ≈\(0.116216+0.156217I\)\(\frac{ 1}{ 4}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(1\)\(1\)\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)\(1\)\(2\)
\(1\)\(1\)\(1\)\(1\)\(1\)\(3\)\(0\)\(1\)\(3\)\(3\)\(1\)\(2\)
\(2\)\(2\)\(2\)\(2\)\(2\)\(4\)\(0\)\(2\)\(4\)\(4\)\(2\)\(3\)

Note:

This is operator "13.15" from ...

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7

New Number: 13.16 |  AESZ:  |  Superseeker: 5 581/3  |  Hash: 2ab5512d2cfda3cde6ee0ea98a12d6fb  

Degree: 13

\(\theta^4-x\left(106\theta^4+140\theta^3+125\theta^2+55\theta+10\right)+x^{2}\left(2472+4265\theta^4+12596\theta^3+15925\theta^2+9718\theta\right)-2^{3} x^{3}\left(9346\theta^4+58443\theta^3+105118\theta^2+80373\theta+24412\right)+2^{4} 3 x^{4}\left(1747\theta^4+173306\theta^3+488163\theta^2+460544\theta+161900\right)+2^{6} 3 x^{5}\left(108841\theta^4-198029\theta^3-1835967\theta^2-2248271\theta-919518\right)-2^{8} 3 x^{6}\left(510411\theta^4+1710438\theta^3-2652339\theta^2-5816622\theta-2956384\right)+2^{12} 3 x^{7}\left(213944\theta^4+2327365\theta^3+1622852\theta^2-837189\theta-1027734\right)+2^{10} 3 x^{8}\left(4640003\theta^4-76516006\theta^3-140342311\theta^2-92680566\theta-16297224\right)-2^{13} x^{9}\left(56543147\theta^4-21416544\theta^3-251991507\theta^2-314165376\theta-118113840\right)+2^{16} x^{10}\left(70691941\theta^4+213840362\theta^3+253613996\theta^2+121602823\theta+15102754\right)-2^{19} 73 x^{11}(\theta+1)(680053\theta^3+2794143\theta^2+4238129\theta+2311527)+2^{22} 73^{2} x^{12}(\theta+2)(\theta+1)(3707\theta^2+13713\theta+13693)-2^{25} 3^{2} 73^{3} x^{13}(\theta+1)(\theta+2)^2(\theta+3)\)

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Coefficients of the holomorphic solution: 1, 10, 118, 1864, 38566, ...
--> OEIS
Normalized instanton numbers (n0=1): 5, -53/4, 581/3, -1231, 19810, ... ; Common denominator:...

Discriminant

\(-(9z-1)(8z-1)(4672z^3-840z^2+57z-1)(64z^2-8z+1)(1-12z-192z^2+2336z^3)^2\)

Local exponents

≈\(-0.071938\)\(0\) ≈\(0.026164\)\(\frac{ 1}{ 16}-\frac{ 1}{ 16}\sqrt{ 3}I\)\(\frac{ 1}{ 16}+\frac{ 1}{ 16}\sqrt{ 3}I\) ≈\(0.076815-0.047751I\) ≈\(0.076815+0.047751I\) ≈\(0.077065-0.003429I\) ≈\(0.077065+0.003429I\)\(\frac{ 1}{ 9}\)\(\frac{ 1}{ 8}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(0\)\(1\)\(1\)\(1\)\(1\)\(1\)\(1\)\(1\)\(1\)\(1\)\(2\)
\(3\)\(0\)\(1\)\(1\)\(1\)\(1\)\(1\)\(3\)\(3\)\(1\)\(1\)\(2\)
\(4\)\(0\)\(2\)\(2\)\(2\)\(2\)\(2\)\(4\)\(4\)\(2\)\(2\)\(3\)

Note:

This is operator "13.16" from ...

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8

New Number: 13.2 |  AESZ:  |  Superseeker: 288 -8252768  |  Hash: ad47c122958add1c452a9858793ef177  

Degree: 13

\(\theta^4-2^{4} x\left(192\theta^4+352\theta^3+392\theta^2+216\theta+49\right)+2^{12} x^{2}\left(1312\theta^4+2912\theta^3+5328\theta^2+4968\theta+1777\right)-2^{21} x^{3}\left(3336\theta^4+7360\theta^3+12252\theta^2+14040\theta+6269\right)+2^{28} x^{4}\left(26000\theta^4+61440\theta^3+92496\theta^2+79216\theta+30659\right)-2^{38} x^{5}\left(19848\theta^4+49192\theta^3+87106\theta^2+61486\theta+15137\right)+2^{46} x^{6}\left(48464\theta^4+126184\theta^3+248968\theta^2+204418\theta+60711\right)-2^{52} x^{7}\left(370576\theta^4+1125248\theta^3+2210040\theta^2+2071840\theta+776313\right)+2^{64} x^{8}\left(32992\theta^4+127280\theta^3+257876\theta^2+261776\theta+109291\right)-2^{71} x^{9}\left(66640\theta^4+329440\theta^3+743448\theta^2+827560\theta+373765\right)+2^{81} x^{10}\left(11376\theta^4+70016\theta^3+181088\theta^2+224296\theta+110253\right)-2^{88} x^{11}\left(9872\theta^4+73152\theta^3+216216\theta^2+297488\theta+159121\right)+2^{99} x^{12}\left(304\theta^4+2640\theta^3+8824\theta^2+13396\theta+7763\right)-2^{108} x^{13}\left((2\theta+5)^4\right)\)

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Coefficients of the holomorphic solution: 1, 784, 486672, 279216384, 154637278480, ...
--> OEIS
Normalized instanton numbers (n0=1): 288, 59200, -8252768, -1223488576, 585571467872, ... ; Common denominator:...

Discriminant

\(-(1-768z+65536z^2)(512z-1)^2(134217728z^3-655360z^2+256z-1)^2(256z-1)^3\)

Local exponents

\(0\) ≈\(3.7e-05-0.001244I\) ≈\(3.7e-05+0.001244I\)\(\frac{ 3}{ 512}-\frac{ 1}{ 512}\sqrt{ 5}\)\(\frac{ 1}{ 512}\)\(\frac{ 1}{ 256}\) ≈\(0.004808\)\(\frac{ 3}{ 512}+\frac{ 1}{ 512}\sqrt{ 5}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 5}{ 2}\)
\(0\)\(1\)\(1\)\(1\)\(0\)\(0\)\(1\)\(1\)\(\frac{ 5}{ 2}\)
\(0\)\(3\)\(3\)\(1\)\(-1\)\(0\)\(3\)\(1\)\(\frac{ 5}{ 2}\)
\(0\)\(4\)\(4\)\(2\)\(1\)\(0\)\(4\)\(2\)\(\frac{ 5}{ 2}\)

Note:

This is operator "13.2" from ...

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9

New Number: 13.3 |  AESZ:  |  Superseeker: 4 52  |  Hash: 9127ce057848ca38f220a7bb67e245a2  

Degree: 13

\(\theta^4-2^{2} x\left(38\theta^4+50\theta^3+53\theta^2+28\theta+6\right)+2^{4} x^{2}\left(617\theta^4+1598\theta^3+2361\theta^2+1812\theta+586\right)-2^{8} x^{3}\left(1422\theta^4+5468\theta^3+10321\theta^2+9918\theta+3961\right)+2^{11} x^{4}\left(4165\theta^4+21060\theta^3+48228\theta^2+54855\theta+25440\right)-2^{14} x^{5}\left(8248\theta^4+50660\theta^3+135119\theta^2+175776\theta+91644\right)+2^{16} x^{6}\left(23161\theta^4+161282\theta^3+479205\theta^2+690060\theta+393943\right)-2^{20} x^{7}\left(12116\theta^4+89614\theta^3+279997\theta^2+425868\theta+256804\right)+2^{23} x^{8}\left(9924\theta^4+74644\theta^3+231233\theta^2+346097\theta+206261\right)-2^{27} x^{9}\left(3250\theta^4+24820\theta^3+75837\theta^2+107033\theta+58293\right)+2^{28} x^{10}\left(6672\theta^4+52000\theta^3+164304\theta^2+235440\theta+126113\right)-2^{32} x^{11}\left(1312\theta^4+10208\theta^3+32688\theta^2+49072\theta+28407\right)+2^{36} x^{12}\left(192\theta^4+1568\theta^3+4952\theta^2+7144\theta+3959\right)-2^{40} x^{13}\left((2\theta+5)^4\right)\)

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Coefficients of the holomorphic solution: 1, 24, 464, 8832, 178960, ...
--> OEIS
Normalized instanton numbers (n0=1): 4, 7/2, 52, 500, 2796, ... ; Common denominator:...

Discriminant

\(-(1-48z+256z^2)(8z-1)^2(512z^3-32z^2+20z-1)^2(16z-1)^3\)

Local exponents

\(0\) ≈\(0.005863-0.196043I\) ≈\(0.005863+0.196043I\)\(\frac{ 3}{ 32}-\frac{ 1}{ 32}\sqrt{ 5}\) ≈\(0.050774\)\(\frac{ 1}{ 16}\)\(\frac{ 1}{ 8}\)\(\frac{ 3}{ 32}+\frac{ 1}{ 32}\sqrt{ 5}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 5}{ 2}\)
\(0\)\(1\)\(1\)\(1\)\(1\)\(0\)\(0\)\(1\)\(\frac{ 5}{ 2}\)
\(0\)\(3\)\(3\)\(1\)\(3\)\(0\)\(-1\)\(1\)\(\frac{ 5}{ 2}\)
\(0\)\(4\)\(4\)\(2\)\(4\)\(0\)\(1\)\(2\)\(\frac{ 5}{ 2}\)

Note:

This is operator "13.3" from ...

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10

New Number: 13.4 |  AESZ:  |  Superseeker: 128 341632  |  Hash: e2189010cb583bd9f4eab25b75b409cf  

Degree: 13

\(\theta^4-2^{5} x\left(4\theta^4+34\theta^3+28\theta^2+11\theta+2\right)-2^{8} x^{2}\left(380\theta^4-872\theta^3-2096\theta^2-1252\theta-351\right)+2^{14} x^{3}\left(1572\theta^4+2760\theta^3-6140\theta^2-4788\theta-1727\right)+2^{18} x^{4}\left(112\theta^4-71968\theta^3+30800\theta^2+34304\theta+16775\right)-2^{25} x^{5}\left(25792\theta^4-66000\theta^3+21380\theta^2+29896\theta+17669\right)+2^{30} x^{6}\left(147184\theta^4-74240\theta^3+128248\theta^2+131808\theta+68259\right)-2^{36} x^{7}\left(204848\theta^4+52096\theta^3+180984\theta^2+135280\theta+61687\right)+2^{42} x^{8}\left(149520\theta^4+15104\theta^3-78056\theta^2-161888\theta-66647\right)-2^{49} x^{9}\left(15408\theta^4-100672\theta^3-280440\theta^2-315312\theta-124965\right)-2^{56} x^{10}\left(10256\theta^4+80960\theta^3+191000\theta^2+198384\theta+76409\right)+2^{63} x^{11}\left(4880\theta^4+28864\theta^3+65080\theta^2+65776\theta+24913\right)-2^{73} x^{12}\left(112\theta^4+648\theta^3+1448\theta^2+1450\theta+545\right)+2^{79} x^{13}\left((2\theta+3)^4\right)\)

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Coefficients of the holomorphic solution: 1, 64, 4496, 339968, 27330832, ...
--> OEIS
Normalized instanton numbers (n0=1): 128, -4796, 341632, -31623118, 3395329408, ... ; Common denominator:...

Discriminant

\((128z-1)(4096z^2+64z-1)(1048576z^3-28672z^2+160z+1)^2(64z-1)^4\)

Local exponents

\(-\frac{ 1}{ 128}-\frac{ 1}{ 128}\sqrt{ 5}\) ≈\(-0.003609\)\(0\)\(\frac{ 1}{ 128}\)\(-\frac{ 1}{ 128}+\frac{ 1}{ 128}\sqrt{ 5}\) ≈\(0.015476-0.004977I\) ≈\(0.015476+0.004977I\)\(\frac{ 1}{ 64}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 3}{ 2}\)
\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)\(1\)\(0\)\(\frac{ 3}{ 2}\)
\(1\)\(3\)\(0\)\(1\)\(1\)\(3\)\(3\)\(0\)\(\frac{ 3}{ 2}\)
\(2\)\(4\)\(0\)\(2\)\(2\)\(4\)\(4\)\(0\)\(\frac{ 3}{ 2}\)

Note:

This is operator "13.4" from ...

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11

New Number: 13.5 |  AESZ:  |  Superseeker: 224 4999008  |  Hash: 6d924b9c12ee7379761d409ee75e42ab  

Degree: 13

\(\theta^4-2^{4} x\left(80\theta^4+160\theta^3+152\theta^2+72\theta+15\right)+2^{14} x^{2}\left(24\theta^4+240\theta^3+355\theta^2+230\theta+69\right)+2^{20} x^{3}\left(416\theta^4-2400\theta^3-6216\theta^2-4824\theta-1773\right)-2^{28} x^{4}\left(1840\theta^4-544\theta^3-15328\theta^2-15056\theta-6525\right)+2^{38} 3 x^{5}\left(236\theta^4+1040\theta^3-1629\theta^2-2248\theta-1208\right)+2^{47} 3 x^{6}\left(8\theta^4-1512\theta^3+192\theta^2+951\theta+786\right)-2^{53} 3 x^{7}\left(1568\theta^4-7952\theta^3-4278\theta^2-740\theta+1981\right)+2^{60} 3 x^{8}\left(6976\theta^4-6656\theta^3-9268\theta^2-7912\theta-55\right)-2^{70} x^{9}\left(6680\theta^4+8856\theta^3+8397\theta^2+3060\theta+1017\right)+2^{76} x^{10}\left(22672\theta^4+71840\theta^3+113068\theta^2+90072\theta+30483\right)-2^{84} x^{11}\left(12912\theta^4+62592\theta^3+128336\theta^2+126736\theta+49707\right)+2^{93} 7 x^{12}(2\theta+3)(164\theta^3+810\theta^2+1434\theta+891)-2^{102} 7^{2} x^{13}(\theta+2)^2(2\theta+3)(2\theta+5)\)

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Coefficients of the holomorphic solution: 1, 240, 44304, 7503616, 1459723536, ...
--> OEIS
Normalized instanton numbers (n0=1): 224, -22712, 4999008, -855952448, 199163179936, ... ; Common denominator:...

Discriminant

\(-(65536z^2-256z+1)^2(117440512z^3-196608z^2+1)^2(256z-1)^3\)

Local exponents

≈\(-0.00161\)\(0\) ≈\(0.001642-0.00161I\) ≈\(0.001642+0.00161I\)\(\frac{ 1}{ 512}-\frac{ 1}{ 512}\sqrt{ 3}I\)\(\frac{ 1}{ 512}+\frac{ 1}{ 512}\sqrt{ 3}I\)\(\frac{ 1}{ 256}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 3}{ 2}\)
\(1\)\(0\)\(1\)\(1\)\(\frac{ 1}{ 2}\)\(\frac{ 1}{ 2}\)\(0\)\(2\)
\(3\)\(0\)\(3\)\(3\)\(\frac{ 1}{ 2}\)\(\frac{ 1}{ 2}\)\(0\)\(2\)
\(4\)\(0\)\(4\)\(4\)\(1\)\(1\)\(0\)\(\frac{ 5}{ 2}\)

Note:

This is operator "13.5" from ...

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12

New Number: 13.6 |  AESZ:  |  Superseeker: 2 421/9  |  Hash: 679aa37a05aafe03e8d68785d566fcfb  

Degree: 13

\(\theta^4-x\left(217\theta^4+178\theta^3+178\theta^2+89\theta+18\right)+x^{2}\left(6192+24334\theta+39795\theta^2+33324\theta^3+20643\theta^4\right)-2^{3} x^{3}\left(139307\theta^4+333558\theta^3+457560\theta^2+315505\theta+89244\right)+2^{4} x^{4}\left(2283535\theta^4+7259062\theta^3+11103058\theta^2+8192571\theta+2419362\right)-2^{6} 3 x^{5}\left(3630237\theta^4+14551206\theta^3+23954402\theta^2+17624013\theta+4953960\right)+2^{6} 3^{2} x^{6}\left(9379387\theta^4+48172928\theta^3+74157721\theta^2+31932048\theta-1833876\right)+2^{9} 3^{5} x^{7}\left(495945\theta^4+2307886\theta^3+6892788\theta^2+10676039\theta+5452406\right)-2^{12} 3^{4} x^{8}\left(5269994\theta^4+31826568\theta^3+83327461\theta^2+106595346\theta+49104855\right)+2^{15} 3^{7} x^{9}\left(129774\theta^4+976140\theta^3+2673571\theta^2+3442327\theta+1597000\right)+2^{18} 3^{10} x^{10}(\theta+1)(6759\theta^3+40481\theta^2+97855\theta+79397)-2^{21} 3^{9} x^{11}(\theta+1)(\theta+2)(29107\theta^2+160713\theta+251822)-2^{27} 3^{12} x^{12}(\theta+3)(\theta+2)(\theta+1)(17\theta+4)+2^{29} 3^{15} 5 x^{13}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)

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Coefficients of the holomorphic solution: 1, 18, 378, 8280, 187434, ...
--> OEIS
Normalized instanton numbers (n0=1): 2, -3/2, 421/9, -519/2, 285, ... ; Common denominator:...

Discriminant

\((16z-1)(19440z^3-2187z^2+81z-1)(24z-1)^2(648z^2-48z+1)^2(8z+1)^3\)

Local exponents

\(-\frac{ 1}{ 8}\)\(0\) ≈\(0.032165-0.005771I\) ≈\(0.032165+0.005771I\)\(\frac{ 1}{ 27}-\frac{ 1}{ 108}\sqrt{ 2}I\)\(\frac{ 1}{ 27}+\frac{ 1}{ 108}\sqrt{ 2}I\)\(\frac{ 1}{ 24}\) ≈\(0.04817\)\(\frac{ 1}{ 16}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(\frac{ 1}{ 2}\)\(0\)\(1\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)\(1\)\(1\)\(2\)
\(\frac{ 3}{ 2}\)\(0\)\(1\)\(1\)\(3\)\(3\)\(\frac{ 1}{ 2}\)\(1\)\(1\)\(3\)
\(2\)\(0\)\(2\)\(2\)\(4\)\(4\)\(1\)\(2\)\(2\)\(4\)

Note:

This is operator "13.6" from ...

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13

New Number: 13.7 |  AESZ:  |  Superseeker: 10 7709/9  |  Hash: 47093f7f3b7ab4544ef6b418bdae778b  

Degree: 13

\(\theta^4+x\left(127\theta^4-2\theta^3+22\theta^2+23\theta+6\right)+x^{2}\left(4803\theta^4+1644\theta^3+3459\theta^2+430\theta-384\right)+2^{3} x^{3}\left(2507\theta^4+8118\theta^3-2448\theta^2-7127\theta-2940\right)-2^{4} x^{4}\left(94175\theta^4+88358\theta^3+133418\theta^2+111507\theta+38898\right)+2^{6} 3 x^{5}\left(22347\theta^4+197706\theta^3+783766\theta^2+893091\theta+359952\right)+2^{6} 3^{2} x^{6}\left(869067\theta^4+4718208\theta^3+11162457\theta^2+11758320\theta+4583500\right)-2^{9} 3^{3} x^{7}\left(245985\theta^4+1338174\theta^3+3414812\theta^2+4418167\theta+2103502\right)-2^{12} 3^{4} x^{8}\left(234234\theta^4+2167368\theta^3+7012373\theta^2+9416514\theta+4375751\right)+2^{15} 3^{5} x^{9}\left(81234\theta^4+643380\theta^3+1815861\theta^2+2193249\theta+947968\right)+2^{18} 3^{6} x^{10}(\theta+1)(15879\theta^3+214401\theta^2+816191\theta+896789)-2^{21} 3^{7} x^{11}(\theta+1)(\theta+2)(8037\theta^2+71103\theta+151546)+2^{27} 3^{9} x^{12}(\theta+3)(\theta+2)(\theta+1)(31\theta+152)-2^{29} 3^{9} 5 x^{13}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, -6, 90, -1368, 21546, ...
--> OEIS
Normalized instanton numbers (n0=1): 10, -149/2, 7709/9, -27333/2, 242829, ... ; Common denominator:...

Discriminant

\(-(16z+1)(2160z^3+27z^2-9z+1)(24z+1)^2(72z^2-48z-1)^2(8z-1)^3\)

Local exponents

≈\(-0.100198\)\(-\frac{ 1}{ 16}\)\(-\frac{ 1}{ 24}\)\(\frac{ 1}{ 3}-\frac{ 1}{ 4}\sqrt{ 2}\)\(0\) ≈\(0.043849-0.05194I\) ≈\(0.043849+0.05194I\)\(\frac{ 1}{ 8}\)\(\frac{ 1}{ 3}+\frac{ 1}{ 4}\sqrt{ 2}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(\frac{ 1}{ 2}\)\(1\)\(0\)\(1\)\(1\)\(\frac{ 1}{ 2}\)\(1\)\(2\)
\(1\)\(1\)\(\frac{ 1}{ 2}\)\(3\)\(0\)\(1\)\(1\)\(\frac{ 3}{ 2}\)\(3\)\(3\)
\(2\)\(2\)\(1\)\(4\)\(0\)\(2\)\(2\)\(2\)\(4\)\(4\)

Note:

This is operator "13.7" from ...

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14

New Number: 13.8 |  AESZ:  |  Superseeker: 8 -830/9  |  Hash: bcea3fff557004b4da26e9aa34caac6c  

Degree: 13

\(\theta^4-x\left(55\theta^4+142\theta^3+112\theta^2+41\theta+6\right)+x^{2}\left(456\theta^4+4668\theta^3+7455\theta^2+3958\theta+696\right)+x^{3}\left(35078\theta^4+127188\theta^3+175671\theta^2+133507\theta+41718\right)+x^{4}\left(82753\theta^4+664768\theta^3+2450839\theta^2+2316756\theta+736812\right)-3 x^{5}\left(885105\theta^4+1342938\theta^3-883331\theta^2-2706576\theta-1350228\right)-2 3^{2} x^{6}\left(345501\theta^4+3334206\theta^3+4969485\theta^2+2964744\theta+630748\right)+2^{2} 3^{3} x^{7}\left(459939\theta^4+270666\theta^3-1625381\theta^2-2377792\theta-962956\right)+2^{4} 3^{4} x^{8}\left(112581\theta^4+699447\theta^3+1277449\theta^2+1022649\theta+314494\right)-2^{4} 3^{5} x^{9}\left(34101\theta^4-33864\theta^3-473835\theta^2-744726\theta-350272\right)-2^{5} 3^{6} x^{10}(\theta+1)(20847\theta^3+146325\theta^2+303230\theta+217616)+2^{6} 3^{7} x^{11}(\theta+1)(\theta+2)(1791\theta^2-1173\theta-14800)+2^{9} 3^{9} x^{12}(\theta+3)(\theta+2)(\theta+1)(52\theta+257)-2^{10} 3^{9} 17 x^{13}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 6, 90, 1044, -5670, ...
--> OEIS
Normalized instanton numbers (n0=1): 8, -45/2, -830/9, -5301/2, 2790, ... ; Common denominator:...

Discriminant

\(-(2z+1)(3672z^3+1728z^2-72z+1)(6z-1)^2(12z+1)^2(3z+1)^2(z-1)^3\)

Local exponents

≈\(-0.510076\)\(-\frac{ 1}{ 2}\)\(-\frac{ 1}{ 3}\)\(-\frac{ 1}{ 12}\)\(0\) ≈\(0.019744-0.012003I\) ≈\(0.019744+0.012003I\)\(\frac{ 1}{ 6}\)\(1\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(\frac{ 1}{ 2}\)\(1\)\(0\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)\(2\)
\(1\)\(1\)\(\frac{ 1}{ 2}\)\(3\)\(0\)\(1\)\(1\)\(3\)\(\frac{ 3}{ 2}\)\(3\)
\(2\)\(2\)\(1\)\(4\)\(0\)\(2\)\(2\)\(4\)\(2\)\(4\)

Note:

This is operator "13.8" from ...

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15

New Number: 13.9 |  AESZ:  |  Superseeker: 8 2200/9  |  Hash: 31ff3b7bd4c8fed070ee43b6903d3752  

Degree: 13

\(\theta^4+2^{3} x\theta(4\theta^3-8\theta^2-5\theta-1)-2^{4} x^{2}\left(48\theta^4+120\theta^3+45\theta^2+74\theta+36\right)-2^{7} x^{3}\left(101\theta^4-342\theta^3-387\theta^2-410\theta-171\right)+2^{8} x^{4}\left(3121\theta^4+14104\theta^3+30889\theta^2+27720\theta+9351\right)+2^{11} 3^{2} x^{5}\left(655\theta^4+4062\theta^3+10081\theta^2+10272\theta+3856\right)-2^{12} 3^{2} x^{6}\left(2272\theta^4+2816\theta^3-9950\theta^2-18768\theta-8813\right)-2^{15} 3^{3} x^{7}\left(1546\theta^4+12172\theta^3+30708\theta^2+33880\theta+13843\right)+2^{16} 3^{4} x^{8}\left(1099\theta^4+1344\theta^3-11134\theta^2-23964\theta-13063\right)+2^{19} 3^{5} x^{9}\left(458\theta^4+4828\theta^3+15325\theta^2+19721\theta+8830\right)-2^{20} 3^{6} x^{10}(\theta+1)(368\theta^3+1752\theta^2+1297\theta-1035)-2^{23} 3^{7} x^{11}(\theta+1)(\theta+2)(39\theta^2+513\theta+1172)+2^{24} 3^{9} x^{12}(\theta+3)(\theta+2)(\theta+1)(17\theta+82)-2^{27} 3^{10} x^{13}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 0, 36, -192, -4284, ...
--> OEIS
Normalized instanton numbers (n0=1): 8, -75/2, 2200/9, -8117/2, 47936, ... ; Common denominator:...

Discriminant

\(-(8z+1)(5184z^3+432z^2-36z+1)(12z+1)^2(144z^2-24z-1)^2(4z-1)^3\)

Local exponents

≈\(-0.141868\)\(-\frac{ 1}{ 8}\)\(-\frac{ 1}{ 12}\)\(\frac{ 1}{ 12}-\frac{ 1}{ 12}\sqrt{ 2}\)\(0\) ≈\(0.029267-0.022431I\) ≈\(0.029267+0.022431I\)\(\frac{ 1}{ 12}+\frac{ 1}{ 12}\sqrt{ 2}\)\(\frac{ 1}{ 4}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(\frac{ 1}{ 2}\)\(1\)\(0\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)\(2\)
\(1\)\(1\)\(\frac{ 1}{ 2}\)\(3\)\(0\)\(1\)\(1\)\(3\)\(\frac{ 3}{ 2}\)\(3\)
\(2\)\(2\)\(1\)\(4\)\(0\)\(2\)\(2\)\(4\)\(2\)\(4\)

Note:

This is operator "13.9" from ...

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16

New Number: 13.17 |  AESZ:  |  Superseeker: 51/7 4071/7  |  Hash: 1eb2bb810b4c7f191a26886aee350e18  

Degree: 13

\(5^{2} 7^{2} \theta^4-3 5^{2} 7 x\left(169\theta^4+342\theta^3+269\theta^2+98\theta+14\right)-2 5 x^{2}\left(29068\theta^4+101254\theta^3+142979\theta^2+94430\theta+24780\right)-5 x^{3}\left(72227\theta^4+286050\theta^3+501033\theta^2+425670\theta+139608\right)+2 x^{4}\left(286748\theta^4-779402\theta^3-3422963\theta^2-2684470\theta-681300\right)-x^{5}\left(7490076+19892278\theta+15897011\theta^2-984006\theta^3-2224575\theta^4\right)+2 x^{6}\left(1109623\theta^4+1537878\theta^3-5243929\theta^2-10596978\theta-5189688\right)-2^{2} x^{7}\left(237446\theta^4-1827746\theta^3+1743127\theta^2+3795959\theta+1620252\right)-2^{3} 3^{2} x^{8}\left(58344\theta^4-162618\theta^3-74839\theta^2+120781\theta+86822\right)-2^{2} 3^{2} x^{9}\left(77741\theta^4-159874\theta^3-463443\theta^2-327512\theta-56132\right)+2^{3} 3^{3} x^{10}\left(721\theta^4+12222\theta^3+39317\theta^2+44772\theta+17268\right)-2^{5} 3^{3} x^{11}(\theta+1)(657\theta^3+1363\theta^2+689\theta-222)-2^{5} 3^{3} 13 x^{12}(\theta+2)(\theta+1)(115\theta^2+339\theta+270)-2^{6} 3^{3} 13^{2} x^{13}(\theta+1)(\theta+2)^2(\theta+3)\)

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Coefficients of the holomorphic solution: 1, 6, 156, 5796, 259296, ...
--> OEIS
Normalized instanton numbers (n0=1): 51/7, 1552/35, 4071/7, 378248/35, 1721920/7, ... ; Common denominator:...

Discriminant

\(\)

No data for singularities

Note:

This is operator "13.17" from ...

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