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You searched for: Spectrum0=4,4,4,4

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1

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

Degree: 14

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

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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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2

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

Degree: 14

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

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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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3

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

Degree: 14

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

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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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4

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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