Summary

You searched for: inst=-82705/4

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1

New Number: 32.1 |  AESZ:  |  Superseeker: 13 1275  |  Hash: 5c2e3e1d3e85022a77a9136d2272db2f  

Degree: 32

\(\theta^4+x\left(52\theta^4-36\theta-142\theta^3-5-107\theta^2\right)-x^{2}\left(620\theta+8686\theta^3+170+2477\theta^2+1603\theta^4\right)-2 x^{3}\left(57842\theta^4+88182\theta^3+89923\theta^2+53586\theta+14064\right)-x^{4}\left(2697348\theta^3+3016956\theta+1218741\theta^4+4034478\theta^2+1011862\right)+x^{5}\left(4154284\theta^4-36611635\theta^2-9502094\theta^3-20359939-44530432\theta\right)-x^{6}\left(337605744\theta-48775967\theta^4+194246629\theta^2-5346306\theta^3+193227408\right)-2^{2} x^{7}\left(20258471\theta^4-183191522\theta^3-458704813\theta^2-332600094\theta-41903870\right)-2^{3} x^{8}\left(66325647\theta^4-411353730\theta^3-1541171000\theta^2-2130504013\theta-1105449340\right)+2^{5} 3 x^{9}\left(1066771\theta^4-131777420\theta^3+79983198\theta^2+543150745\theta+463708954\right)-2^{4} x^{10}\left(143783659\theta^4+4053640514\theta^3+9858746999\theta^2+7077509476\theta-502326500\right)+2^{7} x^{11}\left(138368083\theta^4+183238033\theta^3-3310018192\theta^2-6653286340\theta-3889203872\right)+2^{7} x^{12}\left(496481718\theta^4+4322462304\theta^3+199787519\theta^2-15317512629\theta-16640068710\right)-2^{8} x^{13}\left(289743462\theta^4-4401242298\theta^3-13355918183\theta^2-7397020754\theta+6375065509\right)-2^{10} x^{14}\left(396133743\theta^4-1333996518\theta^3-15885985865\theta^2-33541445647\theta-23107708481\right)-2^{11} x^{15}\left(453981938\theta^4+4435638750\theta^3+3949663684\theta^2-11263025013\theta-17739853167\right)-2^{12} x^{16}\left(227785391\theta^4+9832817848\theta^3+42310236910\theta^2+74461395968\theta+49621401789\right)+2^{15} x^{17}\left(198897592\theta^4+11771212\theta^3-3867168178\theta^2-11297299537\theta-10235944704\right)+2^{16} x^{18}\left(383086368\theta^4+3420815388\theta^3+11952116012\theta^2+20508953472\theta+14439167835\right)+2^{17} x^{19}\left(190788296\theta^4+2425061392\theta^3+10401497028\theta^2+20606177314\theta+16211593657\right)-2^{19} x^{20}\left(54126314\theta^4+419989028\theta^3+1520710075\theta^2+2841733138\theta+2156782988\right)-2^{21} 3 x^{21}\left(13401434\theta^4+146502422\theta^3+639965165\theta^2+1327396637\theta+1086335005\right)-2^{22} x^{22}\left(10981880\theta^4+141779260\theta^3+691712182\theta^2+1569642590\theta+1393845167\right)+2^{23} x^{23}\left(6721988\theta^4+71373164\theta^3+305959012\theta^2+607082692\theta+457859591\right)+2^{24} x^{24}\left(5172254\theta^4+63781560\theta^3+312564510\theta^2+712915992\theta+628949703\right)+2^{27} x^{25}\left(151244\theta^4+2505628\theta^3+15500094\theta^2+43116865\theta+45072668\right)-2^{28} x^{26}\left(133829\theta^4+1536890\theta^3+6680129\theta^2+12566244\theta+8313095\right)-2^{29} x^{27}\left(54212\theta^4+746052\theta^3+3929140\theta^2+9277842\theta+8249757\right)-2^{31} x^{28}\left(1640\theta^4+35404\theta^3+249484\theta^2+728729\theta+767131\right)+2^{32} x^{29}\left(1266\theta^4+15354\theta^3+69999\theta^2+141732\theta+107131\right)+2^{34} x^{30}\left(187\theta^4+2670\theta^3+14509\theta^2+35511\theta+32982\right)+2^{35} x^{31}\left(22\theta^4+338\theta^3+1960\theta^2+5079\theta+4958\right)+2^{36} x^{32}\left((\theta+4)^4\right)\)

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Coefficients of the holomorphic solution: 1, 5, 85, 2033, 56701, ...
--> OEIS
Normalized instanton numbers (n0=1): 13, -305/4, 1275, -82705/4, 456346, ... ; Common denominator:...

Discriminant

\((2z+1)(z+1)(8z^2+16z+1)(8z^3+28z^2+46z-1)(8z^3+8z^2+z-1)(z-1)^2(8z^2+1)^2(1024z^8+2560z^7-1792z^6-3520z^5-1616z^4+920z^3+36z^2-41z-1)^2\)

Local exponents

\(-1\)\(-\frac{ 1}{ 2}\)\(0\)\(s_18\)\(s_15\)\(s_14\)\(s_17\)\(s_16\)\(s_11\)\(s_10\)\(s_13\)\(s_12\)\(s_1\)\(s_3\)\(s_2\)\(s_5\)\(s_4\)\(s_7\)\(s_6\)\(s_9\)\(s_8\)\(1\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(4\)
\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)\(1\)\(1\)\(1\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)\(1\)\(\frac{ 1}{ 2}\)\(1\)\(1\)\(1\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)\(4\)
\(1\)\(1\)\(0\)\(3\)\(3\)\(3\)\(3\)\(3\)\(3\)\(1\)\(3\)\(3\)\(\frac{ 1}{ 2}\)\(1\)\(\frac{ 1}{ 2}\)\(1\)\(1\)\(1\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)\(4\)
\(2\)\(2\)\(0\)\(4\)\(4\)\(4\)\(4\)\(4\)\(4\)\(2\)\(4\)\(4\)\(1\)\(2\)\(1\)\(2\)\(2\)\(2\)\(2\)\(2\)\(2\)\(1\)\(4\)

Note:

This is operator "32.1" from ...

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