Summary

You searched for: Spectrum0=0,1,-2,3

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1

New Number: 10.10 |  AESZ:  |  Superseeker: 28/3 83612/81  |  Hash: 8270c1ecc701d7cbd422a656c6118587  

Degree: 10

\(3^{2} \theta^4+2^{2} 3 x\left(220\theta^4+152\theta^3+207\theta^2+131\theta+31\right)+2^{4} x^{2}\left(20608\theta^4+32896\theta^3+50132\theta^2+37496\theta+11991\right)+2^{8} x^{3}\left(89936\theta^4+243168\theta^3+429080\theta^2+391080\theta+152645\right)+2^{12} x^{4}\left(242448\theta^4+966912\theta^3+2030168\theta^2+2199488\theta+1002377\right)+2^{20} x^{5}\left(26320\theta^4+142696\theta^3+359216\theta^2+454946\theta+237357\right)+2^{23} x^{6}\left(59600\theta^4+415872\theta^3+1247376\theta^2+1826640\theta+1079063\right)+2^{28} x^{7}\left(21712\theta^4+187424\theta^3+661000\theta^2+1107048\theta+733353\right)+2^{32} x^{8}\left(9744\theta^4+100992\theta^3+412312\theta^2+779936\theta+572857\right)+2^{39} x^{9}\left(304\theta^4+3696\theta^3+17208\theta^2+36300\theta+29211\right)+2^{44} x^{10}\left((2\theta+7)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, -124/3, 1220, -872528/27, 67351172/81, ...
--> OEIS
Normalized instanton numbers (n0=1): 28/3, -695/9, 83612/81, -4447894/243, 274874464/729, ... ; Common denominator:...

Discriminant

\((1+48z+256z^2)(32z+1)^2(16z+1)^2(32z+3)^2(64z+1)^2\)

Local exponents

\(-\frac{ 3}{ 32}-\frac{ 1}{ 32}\sqrt{ 5}\)\(-\frac{ 3}{ 32}\)\(-\frac{ 1}{ 16}\)\(-\frac{ 1}{ 32}\)\(-\frac{ 3}{ 32}+\frac{ 1}{ 32}\sqrt{ 5}\)\(-\frac{ 1}{ 64}\)\(0\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 7}{ 2}\)
\(1\)\(1\)\(0\)\(0\)\(1\)\(1\)\(0\)\(\frac{ 7}{ 2}\)
\(1\)\(-2\)\(1\)\(1\)\(1\)\(3\)\(0\)\(\frac{ 7}{ 2}\)
\(2\)\(3\)\(1\)\(1\)\(2\)\(4\)\(0\)\(\frac{ 7}{ 2}\)

Note:

This is operator "10.10" from ...

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2

New Number: 10.9 |  AESZ:  |  Superseeker: 4 116  |  Hash: dbcf215f85612454543d472ffd3bffa9  

Degree: 10

\(\theta^4-2^{2} x\left(38\theta^4+70\theta^3+93\theta^2+58\theta+14\right)+2^{4} x^{2}\left(609\theta^4+2214\theta^3+4255\theta^2+4118\theta+1630\right)-2^{8} x^{3}\left(1357\theta^4+7284\theta^3+18055\theta^2+22233\theta+11143\right)+2^{10} x^{4}\left(7450\theta^4+52316\theta^3+157665\theta^2+230387\theta+134924\right)-2^{14} x^{5}\left(6580\theta^4+56446\theta^3+198857\theta^2+332342\theta+219249\right)+2^{16} x^{6}\left(15153\theta^4+151710\theta^3+606095\theta^2+1128594\theta+818733\right)-2^{20} x^{7}\left(5621\theta^4+63496\theta^3+280382\theta^2+568755\theta+444393\right)+2^{22} x^{8}\left(5152\theta^4+63904\theta^3+304853\theta^2+659693\theta+544236\right)-2^{26} 3 x^{9}\left(220\theta^4+2928\theta^3+14781\theta^2+33462\theta+28605\right)+2^{28} 3^{2} x^{10}\left((2\theta+7)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 56, 2192, 74112, 2319376, ...
--> OEIS
Normalized instanton numbers (n0=1): 4, 31/2, 116, 2477/2, 16876, ... ; Common denominator:...

Discriminant

\((1-48z+256z^2)(4z-1)^2(24z-1)^2(8z-1)^2(16z-1)^2\)

Local exponents

\(0\)\(\frac{ 3}{ 32}-\frac{ 1}{ 32}\sqrt{ 5}\)\(\frac{ 1}{ 24}\)\(\frac{ 1}{ 16}\)\(\frac{ 1}{ 8}\)\(\frac{ 3}{ 32}+\frac{ 1}{ 32}\sqrt{ 5}\)\(\frac{ 1}{ 4}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 7}{ 2}\)
\(0\)\(1\)\(1\)\(0\)\(0\)\(1\)\(1\)\(\frac{ 7}{ 2}\)
\(0\)\(1\)\(-2\)\(1\)\(1\)\(1\)\(3\)\(\frac{ 7}{ 2}\)
\(0\)\(2\)\(3\)\(1\)\(1\)\(2\)\(4\)\(\frac{ 7}{ 2}\)

Note:

This is operator "10.9" from ...

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3

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

Degree: 13

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

Maple   LaTex

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

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

Maple   LaTex

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: 14.10 |  AESZ:  |  Superseeker: 2 38  |  Hash: 364dddcd3359111a8e01be8efc1de60c  

Degree: 14

\(\theta^4+2 x\left(72\theta^4+48\theta^3+59\theta^2+35\theta+8\right)+2^{2} x^{2}\left(2277\theta^4+3252\theta^3+4573\theta^2+3266\theta+992\right)+2^{4} x^{3}\left(20907\theta^4+47634\theta^3+77375\theta^2+65724\theta+24022\right)+2^{7} x^{4}\left(62171\theta^4+199492\theta^3+375946\theta^2+371450\theta+156488\right)+2^{9} x^{5}\left(253302\theta^4+1066440\theta^3+2327568\theta^2+2630202\theta+1250623\right)+2^{10} x^{6}\left(1459436\theta^4+7698000\theta^3+19344508\theta^2+24706800\theta+13098093\right)+2^{12} x^{7}\left(3024300\theta^4+19348248\theta^3+55554208\theta^2+79484188\theta+46581901\right)+2^{15} x^{8}\left(2268548\theta^4+17191376\theta^3+55960360\theta^2+89050336\theta+57303573\right)+2^{18} x^{9}\left(1227744\theta^4+10826688\theta^3+39662704\theta^2+69775740\theta+49021017\right)+2^{20} x^{10}\left(945104\theta^4+9566080\theta^3+39177592\theta^2+75788768\theta+57836847\right)+2^{22} x^{11}\left(502368\theta^4+5772864\theta^3+26266668\theta^2+55590540\theta+45853745\right)+2^{25} x^{12}\left(87264\theta^4+1128192\theta^3+5668024\theta^2+13052400\theta+11573495\right)+2^{30} 5 x^{13}\left(444\theta^4+6408\theta^3+35315\theta^2+87905\theta+83203\right)+2^{35} 5^{2} x^{14}\left((\theta+4)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, -16, 196, -2352, 29920, ...
--> OEIS
Normalized instanton numbers (n0=1): 2, -29/4, 38, -2077/8, 2034, ... ; Common denominator:...

Discriminant

\((4z+1)(2z+1)^2(64z^2+24z+1)^2(160z^2+32z+1)^2(8z+1)^3\)

Local exponents

\(-\frac{ 1}{ 2}\)\(-\frac{ 3}{ 16}-\frac{ 1}{ 16}\sqrt{ 5}\)\(-\frac{ 1}{ 4}\)\(-\frac{ 1}{ 10}-\frac{ 1}{ 40}\sqrt{ 6}\)\(-\frac{ 1}{ 8}\)\(-\frac{ 3}{ 16}+\frac{ 1}{ 16}\sqrt{ 5}\)\(-\frac{ 1}{ 10}+\frac{ 1}{ 40}\sqrt{ 6}\)\(0\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(4\)
\(1\)\(\frac{ 1}{ 2}\)\(1\)\(1\)\(0\)\(\frac{ 1}{ 2}\)\(1\)\(0\)\(4\)
\(-2\)\(\frac{ 1}{ 2}\)\(1\)\(3\)\(0\)\(\frac{ 1}{ 2}\)\(3\)\(0\)\(4\)
\(3\)\(1\)\(2\)\(4\)\(0\)\(1\)\(4\)\(0\)\(4\)

Note:

This is operator "14.10" from ...

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7

New Number: 14.11 |  AESZ:  |  Superseeker: 52/5 13436/5  |  Hash: c3784675984d5e6eac952e2484ce5404  

Degree: 14

\(5^{2} \theta^4-2^{2} 5 x\left(104\theta^4+256\theta^3+483\theta^2+355\theta+95\right)-2^{4} x^{2}\left(416\theta^4-4672\theta^3+2816\theta^2+12600\theta+7865\right)+2^{10} x^{3}\left(3248\theta^4+17808\theta^3+48534\theta^2+70980\theta+43885\right)-2^{12} x^{4}\left(1024\theta^4+36416\theta^3+105744\theta^2+110264\theta+16363\right)-2^{18} x^{5}\left(8760\theta^4+76704\theta^3+282893\theta^2+513127\theta+376109\right)-2^{21} 3 x^{6}\left(888\theta^4+896\theta^3-8544\theta^2-17976\theta-2111\right)+2^{28} x^{7}\left(2848\theta^4+34496\theta^3+165049\theta^2+366072\theta+314912\right)+2^{29} x^{8}\left(10216\theta^4+125440\theta^3+627568\theta^2+1479624\theta+1370831\right)-2^{34} x^{9}\left(5720\theta^4+84576\theta^3+485065\theta^2+1262925\theta+1248247\right)-2^{36} x^{10}\left(16640\theta^4+273472\theta^3+1728064\theta^2+4911896\theta+5256897\right)+2^{42} x^{11}\left(336\theta^4+1392\theta^3-16378\theta^2-112292\theta-182997\right)+2^{44} x^{12}\left(2720\theta^4+43584\theta^3+258352\theta^2+671784\theta+646989\right)+2^{50} 3 x^{13}\left(8\theta^4+256\theta^3+2199\theta^2+7393\theta+8717\right)-2^{56} 3^{2} x^{14}\left((\theta+4)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 76, 5228, 322224, 18933228, ...
--> OEIS
Normalized instanton numbers (n0=1): 52/5, 115, 13436/5, 89632, 18465296/5, ... ; Common denominator:...

Discriminant

\(-(-1+16z)(48z-1)^2(256z^2-32z-5)^2(256z^2+16z-1)^2(16z+1)^3\)

Local exponents

\(-\frac{ 1}{ 32}-\frac{ 1}{ 32}\sqrt{ 5}\)\(\frac{ 1}{ 16}-\frac{ 1}{ 16}\sqrt{ 6}\)\(-\frac{ 1}{ 16}\)\(0\)\(\frac{ 1}{ 48}\)\(-\frac{ 1}{ 32}+\frac{ 1}{ 32}\sqrt{ 5}\)\(\frac{ 1}{ 16}\)\(\frac{ 1}{ 16}+\frac{ 1}{ 16}\sqrt{ 6}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(4\)
\(\frac{ 1}{ 2}\)\(1\)\(0\)\(0\)\(1\)\(\frac{ 1}{ 2}\)\(1\)\(1\)\(4\)
\(\frac{ 1}{ 2}\)\(3\)\(0\)\(0\)\(-2\)\(\frac{ 1}{ 2}\)\(1\)\(3\)\(4\)
\(1\)\(4\)\(0\)\(0\)\(3\)\(1\)\(2\)\(4\)\(4\)

Note:

This is operator "14.11" from ...

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8

New Number: 14.9 |  AESZ:  |  Superseeker: 44/3 220588/81  |  Hash: 32527b63e2e6c7ca027dfb5cb9afac16  

Degree: 14

\(3^{2} \theta^4+2^{2} 3 x\left(8\theta^4-128\theta^3-105\theta^2-41\theta-7\right)-2^{4} x^{2}\left(2720\theta^4-64\theta^3-3536\theta^2-680\theta+429\right)+2^{10} x^{3}\left(336\theta^4+3984\theta^3-826\theta^2+468\theta+1051\right)+2^{12} x^{4}\left(16640\theta^4-7232\theta^3+43840\theta^2+45800\theta+15969\right)-2^{18} x^{5}\left(5720\theta^4+6944\theta^3+19273\theta^2+22267\theta+9043\right)-2^{21} x^{6}\left(10216\theta^4+38016\theta^3+103024\theta^2+135096\theta+80559\right)+2^{28} x^{7}\left(2848\theta^4+11072\theta^3+24505\theta^2+27600\theta+12752\right)+2^{29} 3 x^{8}\left(888\theta^4+13312\theta^3+65952\theta^2+133944\theta+103073\right)-2^{34} x^{9}\left(8760\theta^4+63456\theta^3+203405\theta^2+310785\theta+183393\right)+2^{36} x^{10}\left(1024\theta^4-20032\theta^3-232944\theta^2-750136\theta-801269\right)+2^{42} x^{11}\left(3248\theta^4+34160\theta^3+146646\theta^2+293996\theta+228285\right)+2^{44} x^{12}\left(416\theta^4+11328\theta^3+98816\theta^2+340680\theta+408025\right)-2^{50} 5 x^{13}\left(104\theta^4+1408\theta^3+7395\theta^2+17845\theta+16643\right)-2^{56} 5^{2} x^{14}\left((\theta+4)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 28/3, 260, 116240/27, 7153796/81, ...
--> OEIS
Normalized instanton numbers (n0=1): 44/3, -1421/9, 220588/81, -14752264/243, 1138508000/729, ... ; Common denominator:...

Discriminant

\(-(1+16z)(16z+3)^2(1280z^2-32z-1)^2(256z^2+16z-1)^2(16z-1)^3\)

Local exponents

\(-\frac{ 3}{ 16}\)\(-\frac{ 1}{ 32}-\frac{ 1}{ 32}\sqrt{ 5}\)\(-\frac{ 1}{ 16}\)\(\frac{ 1}{ 80}-\frac{ 1}{ 80}\sqrt{ 6}\)\(0\)\(-\frac{ 1}{ 32}+\frac{ 1}{ 32}\sqrt{ 5}\)\(\frac{ 1}{ 80}+\frac{ 1}{ 80}\sqrt{ 6}\)\(\frac{ 1}{ 16}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(4\)
\(1\)\(\frac{ 1}{ 2}\)\(1\)\(1\)\(0\)\(\frac{ 1}{ 2}\)\(1\)\(0\)\(4\)
\(-2\)\(\frac{ 1}{ 2}\)\(1\)\(3\)\(0\)\(\frac{ 1}{ 2}\)\(3\)\(0\)\(4\)
\(3\)\(1\)\(2\)\(4\)\(0\)\(1\)\(4\)\(0\)\(4\)

Note:

This is operator "14.9" from ...

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9

New Number: 6.33 |  AESZ:  |  Superseeker: 352 26115552  |  Hash: 0677bb20f37d2fa88bafbc665d5157c1  

Degree: 6

\(\theta^4-2^{4} x\left(96\theta^4+192\theta^3+404\theta^2+308\theta+85\right)+2^{12} x^{2}\left(112\theta^4+448\theta^3+416\theta^2-64\theta-159\right)+2^{20} x^{3}\left(192\theta^4+1152\theta^3+3448\theta^2+5160\theta+3101\right)-2^{28} x^{4}\left(272\theta^4+2176\theta^3+6880\theta^2+10112\theta+5757\right)-2^{38} 3 x^{5}\left(8\theta^4+80\theta^3+315\theta^2+575\theta+407\right)+2^{48} 3^{2} x^{6}\left((\theta+3)^4\right)\)

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Coefficients of the holomorphic solution: 1, 1360, 1516304, 1522167040, 1444349938960, ...
--> OEIS
Normalized instanton numbers (n0=1): 352, 60664, 26115552, 16623590600, 13165993300256, ... ; Common denominator:...

Discriminant

\((256z-1)^2(768z-1)^2(256z+1)^2\)

Local exponents

\(-\frac{ 1}{ 256}\)\(0\)\(\frac{ 1}{ 768}\)\(\frac{ 1}{ 256}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(3\)
\(0\)\(0\)\(1\)\(\frac{ 1}{ 2}\)\(3\)
\(1\)\(0\)\(-2\)\(\frac{ 1}{ 2}\)\(3\)
\(1\)\(0\)\(3\)\(1\)\(3\)

Note:

This is operator "6.33" from ...

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10

New Number: 6.34 |  AESZ:  |  Superseeker: 4/3 -124/81  |  Hash: 1153f8807d42d96ede28f7a8d06c144b  

Degree: 6

\(3^{2} \theta^4-2^{2} 3 x\left(8\theta^4+16\theta^3+27\theta^2+19\theta+5\right)-2^{4} x^{2}\left(272\theta^4+1088\theta^3+1984\theta^2+1792\theta+621\right)+2^{8} x^{3}\left(192\theta^4+1152\theta^3+3448\theta^2+5160\theta+3101\right)+2^{12} x^{4}\left(112\theta^4+896\theta^3+2432\theta^2+2560\theta+753\right)-2^{16} x^{5}\left(96\theta^4+960\theta^3+3860\theta^2+7300\theta+5389\right)+2^{24} x^{6}\left((\theta+3)^4\right)\)

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Coefficients of the holomorphic solution: 1, 20/3, 332/3, 13360/27, 966020/81, ...
--> OEIS
Normalized instanton numbers (n0=1): 4/3, -14/9, -124/81, -4498/243, 37024/729, ... ; Common denominator:...

Discriminant

\((16z-1)^2(16z-3)^2(16z+1)^2\)

Local exponents

\(-\frac{ 1}{ 16}\)\(0\)\(\frac{ 1}{ 16}\)\(\frac{ 3}{ 16}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(3\)
\(0\)\(0\)\(\frac{ 1}{ 2}\)\(1\)\(3\)
\(1\)\(0\)\(\frac{ 1}{ 2}\)\(-2\)\(3\)
\(1\)\(0\)\(1\)\(3\)\(3\)

Note:

This is operator "6.34" from ...

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