Summary

You searched for: Spectrum0=1,3/2,3/2,2

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1

New Number: 12.15 |  AESZ:  |  Superseeker: 27/5 1619/5  |  Hash: f7297f2850190f8613d1cbc3a7363a23  

Degree: 12

\(5^{2} \theta^4-5 x\left(296\theta^4+574\theta^3+457\theta^2+170\theta+25\right)-x^{2}\left(4531\theta^4+24118\theta^3+37791\theta^2+23710\theta+5550\right)+2^{2} x^{3}\left(559\theta^4+9744\theta^3+19448\theta^2+14280\theta+4055\right)+x^{4}\left(1455\theta^4-636\theta^3+151398\theta^2+254100\theta+114136\right)+x^{5}\left(80304\theta^4+79818\theta^3-776517\theta^2-952026\theta-338569\right)-x^{6}\left(18597\theta^4-67050\theta^3-680097\theta^2-608202\theta-164470\right)-2 x^{7}\left(19086\theta^4+454818\theta^3+525507\theta^2-112266\theta-235189\right)-2^{2} x^{8}\left(52779\theta^4-252492\theta^3-39867\theta^2+316368\theta+192050\right)-2^{3} x^{9}\left(27325\theta^4+45630\theta^3-118827\theta^2-223839\theta-101599\right)+2^{2} 17 x^{10}\left(8047\theta^4+9182\theta^3-8905\theta^2-20876\theta-9476\right)+2^{5} 17^{2} x^{11}(\theta+1)(19\theta^3+129\theta^2+246\theta+145)-2^{4} 17^{3} x^{12}(\theta+2)(\theta+1)(2\theta+3)^2\)

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Coefficients of the holomorphic solution: 1, 5, 109, 3329, 122581, ...
--> OEIS
Normalized instanton numbers (n0=1): 27/5, 158/5, 1619/5, 51193/10, 485082/5, ... ; Common denominator:...

Discriminant

\(-(4z+1)(z+1)(68z^2+61z-1)(z-1)^2(34z^3-12z^2+3z-5)^2\)

Local exponents

\(-1\)\(-\frac{ 61}{ 136}-\frac{ 11}{ 136}\sqrt{ 33}\)\(-\frac{ 1}{ 4}\) ≈\(-0.126959-0.475615I\) ≈\(-0.126959+0.475615I\)\(0\)\(-\frac{ 61}{ 136}+\frac{ 11}{ 136}\sqrt{ 33}\) ≈\(0.606859\)\(1\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(1\)\(1\)\(1\)\(0\)\(1\)\(1\)\(\frac{ 1}{ 2}\)\(\frac{ 3}{ 2}\)
\(1\)\(1\)\(1\)\(3\)\(3\)\(0\)\(1\)\(3\)\(\frac{ 1}{ 2}\)\(\frac{ 3}{ 2}\)
\(2\)\(2\)\(2\)\(4\)\(4\)\(0\)\(2\)\(4\)\(1\)\(2\)

Note:

This is operator "12.15" from ...

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2

New Number: 12.6 |  AESZ:  |  Superseeker: 5 953/3  |  Hash: 4ea78627bfc56ef9555d9b6b3c949e7a  

Degree: 12

\(\theta^4-x\theta(5\theta^3+46\theta^2+29\theta+6)-2 3 x^{2}\left(258\theta^4+1038\theta^3+1387\theta^2+818\theta+192\right)-2^{2} 3^{3} x^{3}\left(381\theta^4+1664\theta^3+2804\theta^2+2126\theta+624\right)-2^{4} 3^{3} x^{4}\left(1231\theta^4+5927\theta^3+11019\theta^2+9266\theta+3000\right)-2^{4} 3^{4} x^{5}\left(2621\theta^4+16730\theta^3+39069\theta^2+35141\theta+11748\right)-2^{5} 3^{5} x^{6}\left(150\theta^4+11268\theta^3+45560\theta^2+50253\theta+18756\right)+2^{6} 3^{7} x^{7}\left(1024\theta^4+800\theta^3-8483\theta^2-13641\theta-6108\right)+2^{8} 3^{7} x^{8}\left(1724\theta^4+6608\theta^3+1047\theta^2-7027\theta-4488\right)+2^{11} 3^{8} x^{9}\left(74\theta^4+1416\theta^3+1889\theta^2+687\theta-81\right)-2^{13} 3^{10} x^{10}\left(26\theta^4-16\theta^3-125\theta^2-128\theta-39\right)-2^{14} 3^{11} x^{11}(\theta+1)(16\theta^3+40\theta^2+31\theta+6)-2^{16} 3^{11} x^{12}(\theta+2)(\theta+1)(2\theta+3)^2\)

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Coefficients of the holomorphic solution: 1, 0, 72, 1344, 48600, ...
--> OEIS
Normalized instanton numbers (n0=1): 5, 83/2, 953/3, 5319, 97812, ... ; Common denominator:...

Discriminant

\(-(4z+1)(12z+1)(3z+1)(1728z^3+864z^2+36z-1)(-1-6z-36z^2+432z^3)^2\)

Local exponents

≈\(-0.450956\)\(-\frac{ 1}{ 3}\)\(-\frac{ 1}{ 4}\)\(-\frac{ 1}{ 12}\) ≈\(-0.067934\) ≈\(-0.061146-0.08671I\) ≈\(-0.061146+0.08671I\)\(0\) ≈\(0.01889\) ≈\(0.205625\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(1\)\(1\)\(1\)\(1\)\(1\)\(0\)\(1\)\(1\)\(\frac{ 3}{ 2}\)
\(1\)\(1\)\(1\)\(1\)\(1\)\(3\)\(3\)\(0\)\(1\)\(3\)\(\frac{ 3}{ 2}\)
\(2\)\(2\)\(2\)\(2\)\(2\)\(4\)\(4\)\(0\)\(2\)\(4\)\(2\)

Note:

This is operator "12.6" from ...

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3

New Number: 12.8 |  AESZ:  |  Superseeker: 288 12718752  |  Hash: 3373bbe821cc39369e8ba8c46ec88532  

Degree: 12

\(\theta^4+2^{4} 3 x\left(112\theta^4+32\theta^3+40\theta^2+24\theta+5\right)+2^{13} x^{2}\left(1408\theta^4+1312\theta^3+1596\theta^2+784\theta+165\right)+2^{22} 3 x^{3}\left(988\theta^4+2088\theta^3+2591\theta^2+1485\theta+372\right)+2^{28} x^{4}\left(24464\theta^4+111040\theta^3+165136\theta^2+111992\theta+31983\right)+2^{38} 3^{2} x^{5}\left(288\theta^4+6544\theta^3+13980\theta^2+11216\theta+3605\right)-2^{46} x^{6}\left(14528\theta^4-36480\theta^3-205340\theta^2-205716\theta-76023\right)-2^{55} 3 x^{7}\left(4848\theta^4+13680\theta^3-20224\theta^2-34444\theta-16035\right)-2^{64} 3^{2} x^{8}\left(384\theta^4+4704\theta^3+2868\theta^2-852\theta-1307\right)+2^{74} 3 x^{9}\left(388\theta^4-1800\theta^3-3283\theta^2-2097\theta-333\right)+2^{80} 3^{2} x^{10}\left(784\theta^4+1184\theta^3+240\theta^2-592\theta-297\right)+2^{93} 3^{3} x^{11}(4\theta^2+8\theta+5)(\theta+1)^2+2^{100} 3^{2} x^{12}(\theta+2)(\theta+1)(2\theta+3)^2\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, -240, 68880, -22281984, 7875829008, ...
--> OEIS
Normalized instanton numbers (n0=1): 288, -71872, 12718752, -4499223616, 1510063178336, ... ; Common denominator:...

Discriminant

\((1+768z+65536z^2)(256z+1)^2(512z+1)^2(201326592z^3-1536z-1)^2\)

Local exponents

\(-\frac{ 3}{ 512}-\frac{ 1}{ 512}\sqrt{ 5}\)\(-\frac{ 1}{ 256}\) ≈\(-0.002348\)\(-\frac{ 1}{ 512}\)\(-\frac{ 3}{ 512}+\frac{ 1}{ 512}\sqrt{ 5}\) ≈\(-0.000695\)\(0\) ≈\(0.003043\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(\frac{ 1}{ 2}\)\(1\)\(\frac{ 1}{ 2}\)\(1\)\(1\)\(0\)\(1\)\(\frac{ 3}{ 2}\)
\(1\)\(\frac{ 1}{ 2}\)\(3\)\(\frac{ 1}{ 2}\)\(1\)\(3\)\(0\)\(3\)\(\frac{ 3}{ 2}\)
\(2\)\(1\)\(4\)\(1\)\(2\)\(4\)\(0\)\(4\)\(2\)

Note:

This is operator "12.8" from ...

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4

New Number: 6.9 |  AESZ:  |  Superseeker: 31/81 29/9  |  Hash: 98af5121f39c27098356e3ade277f975  

Degree: 6

\(3^{8} \theta^4-3^{4} x\left(1234\theta^4+2168\theta^3+1975\theta^2+891\theta+162\right)-x^{2}\left(428004+1521180\theta+2033921\theta^2+1177556\theta^3+205589\theta^4\right)+x^{3}\left(2310517\theta^4+12882402\theta^3+26939429\theta^2+25052328\theta+8683524\right)-2^{2} 5^{2} x^{4}\left(51526\theta^4+332687\theta^3+804453\theta^2+849398\theta+325796\right)+2^{2} 5^{4} x^{5}(\theta+1)(1593\theta^3+8667\theta^2+15104\theta+8516)-2^{4} 5^{6} x^{6}(\theta+2)(\theta+1)(2\theta+3)^2\)

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Coefficients 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:...

Discriminant

\(-(16z-1)(25z^3-17z^2+2z+1)(-81+50z)^2\)

Local exponents

≈\(-0.17455\)\(0\)\(\frac{ 1}{ 16}\) ≈\(0.427275-0.215865I\) ≈\(0.427275+0.215865I\)\(\frac{ 81}{ 50}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(0\)\(1\)\(1\)\(1\)\(1\)\(\frac{ 3}{ 2}\)
\(1\)\(0\)\(1\)\(1\)\(1\)\(3\)\(\frac{ 3}{ 2}\)
\(2\)\(0\)\(2\)\(2\)\(2\)\(4\)\(2\)

Note:

This is operator "6.9" from ...

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5

New Number: 9.10 |  AESZ:  |  Superseeker: 307/31 30366/31  |  Hash: 7a61ae3114ae9cdc48f662244260cd65  

Degree: 9

\(31^{2} \theta^4-31 x\left(2424\theta^4+5574\theta^3+4337\theta^2+1550\theta+217\right)-x^{2}\left(184202+713186\theta+1382715\theta^2+1756478\theta^3+914057\theta^4\right)-x^{3}\left(2273850+8903076\theta+13251149\theta^2+8635710\theta^3+3075537\theta^4\right)-x^{4}\left(11927218+37908836\theta+46269935\theta^2+23766918\theta^3+2064696\theta^4\right)-x^{5}\left(30324779+80902562\theta+70842936\theta^2+13913564\theta^3-3177385\theta^4\right)+2 x^{6}\left(2606232\theta^4+10916676\theta^3-6409705\theta^2-26416695\theta-14341608\right)+2^{2} 7 x^{7}\left(74376\theta^4+1138248\theta^3+2184799\theta^2+1451482\theta+280295\right)-2^{4} 5 7^{2} x^{8}(\theta+1)(592\theta^3-1128\theta^2-5448\theta-4091)-2^{6} 5^{2} 7^{3} x^{9}(\theta+2)(\theta+1)(2\theta+3)^2\)

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Coefficients 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:...

Discriminant

\(-(z+1)(z^2+z+1)(112z^2+88z-1)(-31-121z+140z^2)^2\)

Local exponents

\(-1\)\(-\frac{ 11}{ 28}-\frac{ 2}{ 7}\sqrt{ 2}\)\(-\frac{ 1}{ 2}-\frac{ 1}{ 2}\sqrt{ 3}I\)\(-\frac{ 1}{ 2}+\frac{ 1}{ 2}\sqrt{ 3}I\)\(\frac{ 121}{ 280}-\frac{ 1}{ 280}\sqrt{ 32001}\)\(0\)\(-\frac{ 11}{ 28}+\frac{ 2}{ 7}\sqrt{ 2}\)\(\frac{ 121}{ 280}+\frac{ 1}{ 280}\sqrt{ 32001}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(1\)\(1\)\(1\)\(0\)\(1\)\(1\)\(\frac{ 3}{ 2}\)
\(1\)\(1\)\(1\)\(1\)\(3\)\(0\)\(1\)\(3\)\(\frac{ 3}{ 2}\)
\(2\)\(2\)\(2\)\(2\)\(4\)\(0\)\(2\)\(4\)\(2\)

Note:

This is operator "9.10" from ...

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6

New Number: 9.7 |  AESZ:  |  Superseeker: 9 2564/3  |  Hash: 9bb7a7f3a3d5f66018396173696c194c  

Degree: 9

\(\theta^4+3 x\left(93\theta^4+42\theta^3+49\theta^2+28\theta+6\right)+2^{2} 3^{3} x^{2}\left(307\theta^4+328\theta^3+401\theta^2+230\theta+53\right)+2^{2} 3^{5} x^{3}\left(2268\theta^4+4128\theta^3+5443\theta^2+3525\theta+932\right)+2^{4} 3^{7} x^{4}\left(2588\theta^4+6880\theta^3+10145\theta^2+7398\theta+2167\right)+2^{6} 3^{9} x^{5}\left(1897\theta^4+6694\theta^3+11167\theta^2+9015\theta+2853\right)+2^{8} 3^{11} x^{6}\left(895\theta^4+3912\theta^3+7309\theta^2+6408\theta+2150\right)+2^{8} 3^{13} x^{7}\left(1048\theta^4+5360\theta^3+10939\theta^2+10155\theta+3534\right)+2^{10} 3^{15} x^{8}(\theta+1)(172\theta^3+804\theta^2+1295\theta+699)+2^{12} 3^{18} x^{9}(\theta+2)(\theta+1)(2\theta+3)^2\)

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Coefficients of the holomorphic solution: 1, -18, 378, -8676, 213354, ...
--> OEIS
Normalized instanton numbers (n0=1): 9, -72, 2564/3, -12924, 228024, ... ; Common denominator:...

Discriminant

\((27z+1)(432z^2+36z+1)(36z+1)^2(648z^2+72z+1)^2\)

Local exponents

\(-\frac{ 1}{ 18}-\frac{ 1}{ 36}\sqrt{ 2}\)\(-\frac{ 1}{ 24}-\frac{ 1}{ 72}\sqrt{ 3}I\)\(-\frac{ 1}{ 24}+\frac{ 1}{ 72}\sqrt{ 3}I\)\(-\frac{ 1}{ 27}\)\(-\frac{ 1}{ 36}\)\(-\frac{ 1}{ 18}+\frac{ 1}{ 36}\sqrt{ 2}\)\(0\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)\(1\)\(0\)\(\frac{ 3}{ 2}\)
\(3\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)\(3\)\(0\)\(\frac{ 3}{ 2}\)
\(4\)\(2\)\(2\)\(2\)\(1\)\(4\)\(0\)\(2\)

Note:

This is operator "9.7" from ...

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