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You searched for: Spectrum0=2,2,2,2

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1

New Number: 14.7 |  AESZ:  |  Superseeker: 48 3184  |  Hash: 9e304ff532f3cfafc29dfac77fdff067  

Degree: 14

\(\theta^4-2^{4} x\left(35\theta^4+50\theta^3+49\theta^2+24\theta+5\right)+2^{9} x^{2}\left(255\theta^4+722\theta^3+1027\theta^2+740\theta+227\right)-2^{14} x^{3}\left(1033\theta^4+4298\theta^3+7994\theta^2+7243\theta+2695\right)+2^{19} x^{4}\left(2699\theta^4+13730\theta^3+30984\theta^2+33699\theta+14443\right)-2^{24} x^{5}\left(5407\theta^4+26718\theta^3+63946\theta^2+80619\theta+38786\right)+2^{29} x^{6}\left(10081\theta^4+39658\theta^3+68604\theta^2+85851\theta+43438\right)-2^{34} x^{7}\left(17583\theta^4+63666\theta^3+51252\theta^2-1045\theta-18966\right)+2^{39} x^{8}\left(25019\theta^4+98594\theta^3+101972\theta^2-44371\theta-87630\right)-2^{44} x^{9}\left(29162\theta^4+103060\theta^3+189337\theta^2+75677\theta-39871\right)+2^{49} x^{10}\left(32428\theta^4+78424\theta^3+166293\theta^2+155877\theta+49943\right)-2^{54} x^{11}\left(33248\theta^4+85104\theta^3+119906\theta^2+105882\theta+49279\right)+2^{59} x^{12}\left(24144\theta^4+97280\theta^3+159468\theta^2+125460\theta+41819\right)-2^{67} 5 x^{13}\left(244\theta^4+1456\theta^3+3353\theta^2+3523\theta+1423\right)+2^{75} 5^{2} x^{14}\left((\theta+2)^4\right)\)

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Coefficients of the holomorphic solution: 1, 80, 5776, 422144, 32579856, ...
--> OEIS
Normalized instanton numbers (n0=1): 48, 46, 3184, 409910, -3351792, ... ; Common denominator:...

Discriminant

\((16z-1)(32z-1)(4096z^2-192z+1)(163840z^3+1024z^2+32z-1)^2(64z-1)^4\)

Local exponents

≈\(-0.009802-0.019I\) ≈\(-0.009802+0.019I\)\(0\)\(\frac{ 3}{ 128}-\frac{ 1}{ 128}\sqrt{ 5}\) ≈\(0.013353\)\(\frac{ 1}{ 64}\)\(\frac{ 1}{ 32}\)\(\frac{ 3}{ 128}+\frac{ 1}{ 128}\sqrt{ 5}\)\(\frac{ 1}{ 16}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(-\frac{ 1}{ 2}\)\(0\)\(0\)\(0\)\(2\)
\(1\)\(1\)\(0\)\(1\)\(1\)\(-\frac{ 1}{ 2}\)\(1\)\(1\)\(1\)\(2\)
\(3\)\(3\)\(0\)\(1\)\(3\)\(\frac{ 1}{ 2}\)\(1\)\(1\)\(1\)\(2\)
\(4\)\(4\)\(0\)\(2\)\(4\)\(\frac{ 1}{ 2}\)\(2\)\(2\)\(2\)\(2\)

Note:

This is operator "14.7" from ...

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2

New Number: 14.8 |  AESZ:  |  Superseeker: 92/5 -76/5  |  Hash: a787adbb87527c14af9a5f2508991317  

Degree: 14

\(5^{2} \theta^4-2^{2} 5 x\left(244\theta^4+496\theta^3+473\theta^2+225\theta+45\right)+2^{4} x^{2}\left(24144\theta^4+95872\theta^3+155244\theta^2+117660\theta+36835\right)-2^{9} x^{3}\left(33248\theta^4+180880\theta^3+407234\theta^2+416430\theta+168275\right)+2^{14} x^{4}\left(32428\theta^4+181000\theta^3+474021\theta^2+605903\theta+294817\right)-2^{19} x^{5}\left(29162\theta^4+130236\theta^3+270865\theta^2+378135\theta+208235\right)+2^{24} x^{6}\left(25019\theta^4+101558\theta^3+110864\theta^2+69739\theta+20552\right)-2^{29} x^{7}\left(17583\theta^4+76998\theta^3+91248\theta^2+4717\theta-39868\right)+2^{34} x^{8}\left(10081\theta^4+40990\theta^3+72600\theta^2+35261\theta-9816\right)-2^{39} x^{9}\left(5407\theta^4+16538\theta^3+33406\theta^2+27573\theta+6100\right)+2^{44} x^{10}\left(2699\theta^4+7862\theta^3+13380\theta^2+11845\theta+4325\right)-2^{49} x^{11}\left(1033\theta^4+3966\theta^3+6998\theta^2+6213\theta+2329\right)+2^{54} x^{12}\left(255\theta^4+1318\theta^3+2815\theta^2+2864\theta+1159\right)-2^{59} x^{13}\left(35\theta^4+230\theta^3+589\theta^2+692\theta+313\right)+2^{65} x^{14}\left((\theta+2)^4\right)\)

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Coefficients of the holomorphic solution: 1, 36, 1196, 41488, 1543916, ...
--> OEIS
Normalized instanton numbers (n0=1): 92/5, -342/5, -76/5, 75394/5, -2156752/5, ... ; Common denominator:...

Discriminant

\((64z-1)(32z-1)(256z^2-48z+1)(32768z^3-1024z^2-5-32z)^2(16z-1)^4\)

Local exponents

≈\(-0.020941-0.040594I\) ≈\(-0.020941+0.040594I\)\(0\)\(\frac{ 1}{ 64}\)\(\frac{ 3}{ 32}-\frac{ 1}{ 32}\sqrt{ 5}\)\(\frac{ 1}{ 32}\)\(\frac{ 1}{ 16}\) ≈\(0.073133\)\(\frac{ 3}{ 32}+\frac{ 1}{ 32}\sqrt{ 5}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(-\frac{ 1}{ 2}\)\(0\)\(0\)\(2\)
\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)\(-\frac{ 1}{ 2}\)\(1\)\(1\)\(2\)
\(3\)\(3\)\(0\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)\(3\)\(1\)\(2\)
\(4\)\(4\)\(0\)\(2\)\(2\)\(2\)\(\frac{ 1}{ 2}\)\(4\)\(2\)\(2\)

Note:

This is operator "14.8" from ...

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3

New Number: 15.2 |  AESZ:  |  Superseeker: 2 38  |  Hash: 76d5c5e186c39f14d8f32dfa0f13e22a  

Degree: 15

\(\theta^4+2 x\left(73\theta^4+40\theta^3+47\theta^2+27\theta+6\right)+2^{2} x^{2}\left(2349\theta^4+2724\theta^3+3516\theta^2+2273\theta+614\right)+2^{3} x^{3}\left(44091\theta^4+80304\theta^3+115043\theta^2+84574\theta+26356\right)+2^{5} x^{4}\left(269591\theta^4+678346\theta^3+1084179\theta^2+893856\theta+309842\right)+2^{8} x^{5}\left(568775\theta^4+1835004\theta^3+3266314\theta^2+2971734\theta+1120498\right)+2^{11} x^{6}\left(856369\theta^4+3369012\theta^3+6631886\theta^2+6564309\theta+2651780\right)+2^{11} x^{7}\left(7508036\theta^4+34719008\theta^3+74840604\theta^2+79593816\theta+34039943\right)+2^{13} x^{8}\left(12098492\theta^4+63919352\theta^3+149239952\theta^2+168641212\theta+75569097\right)+2^{16} x^{9}\left(7179524\theta^4+42349744\theta^3+105902696\theta^2+125838704\theta+58525593\right)+2^{19} x^{10}\left(3117952\theta^4+20136896\theta^3+53326176\theta^2+65967996\theta+31556287\right)+2^{21} x^{11}\left(1949840\theta^4+13550976\theta^3+37571920\theta^2+47915544\theta+23371681\right)+2^{23} x^{12}\left(851424\theta^4+6266688\theta^3+17985676\theta^2+23424156\theta+11560933\right)+2^{26} x^{13}\left(122784\theta^4+942720\theta^3+2770088\theta^2+3654240\theta+1815239\right)+2^{31} 5 x^{14}\left(524\theta^4+4136\theta^3+12323\theta^2+16373\theta+8173\right)+2^{36} 5^{2} x^{15}\left((\theta+2)^4\right)\)

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Coefficients of the holomorphic solution: 1, -12, 136, -1632, 21296, ...
--> OEIS
Normalized instanton numbers (n0=1): 2, -29/4, 38, -2077/8, 2034, ... ; Common denominator:...

Discriminant

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

Local exponents

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

Note:

This is operator "15.2" from ...

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4

New Number: 15.3 |  AESZ:  |  Superseeker: 44/3 220588/81  |  Hash: ae51313cd958206bb1b7a3c8ae23e509  

Degree: 15

\(3^{3} \theta^4+2^{2} 3^{2} x\left(12\theta^4-160\theta^3-153\theta^2-73\theta-15\right)-2^{4} 3 x^{2}\left(2688\theta^4+704\theta^3-6380\theta^2-6164\theta-2343\right)+2^{8} x^{3}\left(1312\theta^4+69632\theta^3+26456\theta^2+3928\theta-4305\right)+2^{12} x^{4}\left(51264\theta^4-16512\theta^3-16360\theta^2-16088\theta-1785\right)-2^{16} x^{5}\left(52000\theta^4+223680\theta^3+316652\theta^2+308700\theta+133179\right)-2^{21} x^{6}\left(42088\theta^4+36416\theta^3+31682\theta^2-15530\theta-24313\right)+2^{25} x^{7}\left(58136\theta^4+309440\theta^3+666728\theta^2+761160\theta+351769\right)+2^{29} x^{8}\left(30776\theta^4+26112\theta^3-81496\theta^2-231912\theta-165231\right)-2^{33} 3 x^{9}\left(16632\theta^4+120704\theta^3+332890\theta^2+441546\theta+227145\right)-2^{36} x^{10}\left(31968\theta^4+33600\theta^3-297916\theta^2-852260\theta-648637\right)+2^{40} x^{11}\left(40000\theta^4+381696\theta^3+1258584\theta^2+1813272\theta+964287\right)+2^{44} x^{12}\left(14240\theta^4+66688\theta^3+44952\theta^2-163928\theta-198345\right)-2^{48} x^{13}\left(5824\theta^4+76480\theta^3+307828\theta^2+490020\theta+272659\right)-2^{54} 5 x^{14}\left(164\theta^4+1536\theta^3+5043\theta^2+7113\theta+3693\right)-2^{60} 5^{2} x^{15}\left((\theta+2)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 20, 388, 7344, 141636, ...
--> OEIS
Normalized instanton numbers (n0=1): 44/3, -1421/9, 220588/81, -14752264/243, 1138508000/729, ... ; Common denominator:...

Discriminant

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

Local exponents

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

Note:

This is operator "15.3" from ...

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5

New Number: 15.4 |  AESZ:  |  Superseeker: 52/5 13436/5  |  Hash: 2306e85a3af0a97d616dedf03cc93f69  

Degree: 15

\(5^{2} \theta^4-2^{2} 5 x\left(524\theta^4+56\theta^3+83\theta^2+55\theta+15\right)+2^{4} x^{2}\left(122784\theta^4+39552\theta^3+60584\theta^2+42560\theta+9895\right)-2^{8} x^{3}\left(851424\theta^4+544704\theta^3+819724\theta^2+563860\theta+144605\right)+2^{13} x^{4}\left(1949840\theta^4+2047744\theta^3+3062224\theta^2+2155304\theta+617905\right)-2^{18} x^{5}\left(3117952\theta^4+4806720\theta^3+7335648\theta^2+5468420\theta+1717063\right)+2^{22} x^{6}\left(7179524\theta^4+15086448\theta^3+24112808\theta^2+19319920\theta+6533401\right)-2^{26} x^{7}\left(12098492\theta^4+32868584\theta^3+56087648\theta^2+48438116\theta+17467537\right)+2^{31} x^{8}\left(7508036\theta^4+25345280\theta^3+46719420\theta^2+43397656\theta+16591239\right)-2^{38} x^{9}\left(856369\theta^4+3481940\theta^3+6970670\theta^2+6938899\theta+2800514\right)+2^{42} x^{10}\left(568775\theta^4+2715196\theta^3+5906890\theta^2+6274274\theta+2662654\right)-2^{46} x^{11}\left(269591\theta^4+1478382\theta^3+3484287\theta^2+3929620\theta+1745534\right)+2^{51} x^{12}\left(44091\theta^4+272424\theta^3+691403\theta^2+822862\theta+380404\right)-2^{57} x^{13}\left(2349\theta^4+16068\theta^3+43548\theta^2+54271\theta+25924\right)+2^{63} x^{14}\left(73\theta^4+544\theta^3+1559\theta^2+2017\theta+988\right)-2^{69} x^{15}\left((\theta+2)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 12, 44, -3792, -207124, ...
--> OEIS
Normalized instanton numbers (n0=1): 52/5, 115, 13436/5, 89632, 18465296/5, ... ; Common denominator:...

Discriminant

\(-(-1+32z)(256z^2-48z+1)^2(512z^2-128z+5)^2(64z-1)^3(16z-1)^3\)

Local exponents

\(0\)\(\frac{ 1}{ 64}\)\(\frac{ 3}{ 32}-\frac{ 1}{ 32}\sqrt{ 5}\)\(\frac{ 1}{ 32}\)\(\frac{ 1}{ 8}-\frac{ 1}{ 32}\sqrt{ 6}\)\(\frac{ 1}{ 16}\)\(\frac{ 3}{ 32}+\frac{ 1}{ 32}\sqrt{ 5}\)\(\frac{ 1}{ 8}+\frac{ 1}{ 32}\sqrt{ 6}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(2\)
\(0\)\(2\)\(\frac{ 1}{ 2}\)\(1\)\(1\)\(0\)\(\frac{ 1}{ 2}\)\(1\)\(2\)
\(0\)\(3\)\(\frac{ 1}{ 2}\)\(1\)\(3\)\(0\)\(\frac{ 1}{ 2}\)\(3\)\(2\)
\(0\)\(5\)\(1\)\(2\)\(4\)\(0\)\(1\)\(4\)\(2\)

Note:

This is operator "15.4" from ...

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6

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   LaTex

Coefficients of the holomorphic solution: 1, -4, 147, 4496, 223111, ...
--> OEIS
Normalized instanton numbers (n0=1): 10, 77, 3394/3, 24029, 640402, ... ; Common denominator:...

Discriminant

\(-(-1+81z)(9z-1)^2(81z^2+14z+1)^2\)

Local exponents

\(-\frac{ 7}{ 81}-\frac{ 4}{ 81}\sqrt{ 2}I\)\(-\frac{ 7}{ 81}+\frac{ 4}{ 81}\sqrt{ 2}I\)\(0\)\(\frac{ 1}{ 81}\)\(\frac{ 1}{ 9}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(2\)
\(-\frac{ 1}{ 2}\)\(-\frac{ 1}{ 2}\)\(0\)\(1\)\(1\)\(2\)
\(1\)\(1\)\(0\)\(1\)\(3\)\(2\)
\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(0\)\(2\)\(4\)\(2\)

Note:

This is operator "7.20" from ...

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7

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   LaTex

Coefficients of the holomorphic solution: 1, 252, 40419, 2460816, -1025424441, ...
--> OEIS
Normalized instanton numbers (n0=1): 90, -4365, 413926, -38862153, 4502063682, ... ; Common denominator:...

Discriminant

\((1+27z)(243z+1)^2(59049z^2-378z+1)^2\)

Local exponents

\(-\frac{ 1}{ 27}\)\(-\frac{ 1}{ 243}\)\(0\)\(\frac{ 7}{ 2187}-\frac{ 4}{ 2187}\sqrt{ 2}I\)\(\frac{ 7}{ 2187}+\frac{ 4}{ 2187}\sqrt{ 2}I\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(2\)
\(1\)\(1\)\(0\)\(-\frac{ 1}{ 2}\)\(-\frac{ 1}{ 2}\)\(2\)
\(1\)\(3\)\(0\)\(1\)\(1\)\(2\)
\(2\)\(4\)\(0\)\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(2\)

Note:

This is operator "7.21" from ...

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