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You searched for: Spectrum0=0,1/2,1/2,1

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61

New Number: 15.1 |  AESZ:  |  Superseeker: 800 38825120  |  Hash: c26e6797c51f4c09c1dfbc9e354ce168  

Degree: 15

\(\theta^4+2^{4} x\left(240\theta^4-96\theta^3-24\theta^2+24\theta+7\right)+2^{12} x^{2}\left(912\theta^4-192\theta^3+948\theta^2+120\theta-35\right)-2^{21} x^{3}\left(240\theta^4-1152\theta^3+832\theta^2+156\theta-5\right)-2^{29} x^{4}\left(2064\theta^4+5280\theta^3+4834\theta^2+3988\theta+1289\right)+2^{36} x^{5}\left(928\theta^4-10496\theta^3-26568\theta^2-20840\theta-6149\right)+2^{44} x^{6}\left(5472\theta^4+47424\theta^3+81628\theta^2+53832\theta+15073\right)-2^{54} x^{7}\left(736\theta^4+1808\theta^3-13652\theta^2-22662\theta-9257\right)+2^{62} x^{8}\left(228\theta^4-11376\theta^3-49855\theta^2-49982\theta-17627\right)+2^{72} x^{9}\left(111\theta^4+2454\theta^3+5183\theta^2+855\theta-620\right)-2^{80} x^{10}\left(319\theta^4+1592\theta^3-3479\theta^2-8814\theta-4317\right)+2^{89} x^{11}\left(63\theta^4-102\theta^3-2675\theta^2-3688\theta-1502\right)+2^{98} x^{12}\left(10\theta^4+408\theta^3+1273\theta^2+1278\theta+431\right)-2^{108} x^{13}\left(4\theta^4+68\theta^3+179\theta^2+175\theta+59\right)+2^{116} x^{14}(5\theta^2+22\theta+22)(\theta+1)^2-2^{125} x^{15}(\theta+1)^2(\theta+2)^2\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, -112, 25872, -5691136, 1522998544, ...
--> OEIS
Normalized instanton numbers (n0=1): 800, -121088, 38825120, -15641910336, 7303803435104, ... ; Common denominator:...

Discriminant

\(-(512z+1)(65536z^2-256z-1)(256z+1)^2(67108864z^3+1792z+1)^2(256z-1)^4\)

Local exponents

\(-\frac{ 1}{ 256}\)\(\frac{ 1}{ 512}-\frac{ 1}{ 512}\sqrt{ 5}\)\(-\frac{ 1}{ 512}\) ≈\(-0.000552\)\(0\) ≈\(0.000276-0.00519I\) ≈\(0.000276+0.00519I\)\(\frac{ 1}{ 256}\)\(\frac{ 1}{ 512}+\frac{ 1}{ 512}\sqrt{ 5}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(\frac{ 1}{ 2}\)\(1\)\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)\(1\)\(1\)
\(\frac{ 1}{ 2}\)\(1\)\(1\)\(3\)\(0\)\(3\)\(3\)\(1\)\(1\)\(2\)
\(1\)\(2\)\(2\)\(4\)\(0\)\(4\)\(4\)\(2\)\(2\)\(2\)

Note:

This is operator "15.1" from ...

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62

New Number: 13.5 |  AESZ:  |  Superseeker: 224 4999008  |  Hash: 6d924b9c12ee7379761d409ee75e42ab  

Degree: 13

\(\theta^4-2^{4} x\left(80\theta^4+160\theta^3+152\theta^2+72\theta+15\right)+2^{14} x^{2}\left(24\theta^4+240\theta^3+355\theta^2+230\theta+69\right)+2^{20} x^{3}\left(416\theta^4-2400\theta^3-6216\theta^2-4824\theta-1773\right)-2^{28} x^{4}\left(1840\theta^4-544\theta^3-15328\theta^2-15056\theta-6525\right)+2^{38} 3 x^{5}\left(236\theta^4+1040\theta^3-1629\theta^2-2248\theta-1208\right)+2^{47} 3 x^{6}\left(8\theta^4-1512\theta^3+192\theta^2+951\theta+786\right)-2^{53} 3 x^{7}\left(1568\theta^4-7952\theta^3-4278\theta^2-740\theta+1981\right)+2^{60} 3 x^{8}\left(6976\theta^4-6656\theta^3-9268\theta^2-7912\theta-55\right)-2^{70} x^{9}\left(6680\theta^4+8856\theta^3+8397\theta^2+3060\theta+1017\right)+2^{76} x^{10}\left(22672\theta^4+71840\theta^3+113068\theta^2+90072\theta+30483\right)-2^{84} x^{11}\left(12912\theta^4+62592\theta^3+128336\theta^2+126736\theta+49707\right)+2^{93} 7 x^{12}(2\theta+3)(164\theta^3+810\theta^2+1434\theta+891)-2^{102} 7^{2} x^{13}(\theta+2)^2(2\theta+3)(2\theta+5)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 240, 44304, 7503616, 1459723536, ...
--> OEIS
Normalized instanton numbers (n0=1): 224, -22712, 4999008, -855952448, 199163179936, ... ; Common denominator:...

Discriminant

\(-(65536z^2-256z+1)^2(117440512z^3-196608z^2+1)^2(256z-1)^3\)

Local exponents

≈\(-0.00161\)\(0\) ≈\(0.001642-0.00161I\) ≈\(0.001642+0.00161I\)\(\frac{ 1}{ 512}-\frac{ 1}{ 512}\sqrt{ 3}I\)\(\frac{ 1}{ 512}+\frac{ 1}{ 512}\sqrt{ 3}I\)\(\frac{ 1}{ 256}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 3}{ 2}\)
\(1\)\(0\)\(1\)\(1\)\(\frac{ 1}{ 2}\)\(\frac{ 1}{ 2}\)\(0\)\(2\)
\(3\)\(0\)\(3\)\(3\)\(\frac{ 1}{ 2}\)\(\frac{ 1}{ 2}\)\(0\)\(2\)
\(4\)\(0\)\(4\)\(4\)\(1\)\(1\)\(0\)\(\frac{ 5}{ 2}\)

Note:

This is operator "13.5" from ...

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63

New Number: 13.6 |  AESZ:  |  Superseeker: 2 421/9  |  Hash: 679aa37a05aafe03e8d68785d566fcfb  

Degree: 13

\(\theta^4-x\left(217\theta^4+178\theta^3+178\theta^2+89\theta+18\right)+x^{2}\left(6192+24334\theta+39795\theta^2+33324\theta^3+20643\theta^4\right)-2^{3} x^{3}\left(139307\theta^4+333558\theta^3+457560\theta^2+315505\theta+89244\right)+2^{4} x^{4}\left(2283535\theta^4+7259062\theta^3+11103058\theta^2+8192571\theta+2419362\right)-2^{6} 3 x^{5}\left(3630237\theta^4+14551206\theta^3+23954402\theta^2+17624013\theta+4953960\right)+2^{6} 3^{2} x^{6}\left(9379387\theta^4+48172928\theta^3+74157721\theta^2+31932048\theta-1833876\right)+2^{9} 3^{5} x^{7}\left(495945\theta^4+2307886\theta^3+6892788\theta^2+10676039\theta+5452406\right)-2^{12} 3^{4} x^{8}\left(5269994\theta^4+31826568\theta^3+83327461\theta^2+106595346\theta+49104855\right)+2^{15} 3^{7} x^{9}\left(129774\theta^4+976140\theta^3+2673571\theta^2+3442327\theta+1597000\right)+2^{18} 3^{10} x^{10}(\theta+1)(6759\theta^3+40481\theta^2+97855\theta+79397)-2^{21} 3^{9} x^{11}(\theta+1)(\theta+2)(29107\theta^2+160713\theta+251822)-2^{27} 3^{12} x^{12}(\theta+3)(\theta+2)(\theta+1)(17\theta+4)+2^{29} 3^{15} 5 x^{13}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 18, 378, 8280, 187434, ...
--> OEIS
Normalized instanton numbers (n0=1): 2, -3/2, 421/9, -519/2, 285, ... ; Common denominator:...

Discriminant

\((16z-1)(19440z^3-2187z^2+81z-1)(24z-1)^2(648z^2-48z+1)^2(8z+1)^3\)

Local exponents

\(-\frac{ 1}{ 8}\)\(0\) ≈\(0.032165-0.005771I\) ≈\(0.032165+0.005771I\)\(\frac{ 1}{ 27}-\frac{ 1}{ 108}\sqrt{ 2}I\)\(\frac{ 1}{ 27}+\frac{ 1}{ 108}\sqrt{ 2}I\)\(\frac{ 1}{ 24}\) ≈\(0.04817\)\(\frac{ 1}{ 16}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(\frac{ 1}{ 2}\)\(0\)\(1\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)\(1\)\(1\)\(2\)
\(\frac{ 3}{ 2}\)\(0\)\(1\)\(1\)\(3\)\(3\)\(\frac{ 1}{ 2}\)\(1\)\(1\)\(3\)
\(2\)\(0\)\(2\)\(2\)\(4\)\(4\)\(1\)\(2\)\(2\)\(4\)

Note:

This is operator "13.6" from ...

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64

New Number: 13.7 |  AESZ:  |  Superseeker: 10 7709/9  |  Hash: 47093f7f3b7ab4544ef6b418bdae778b  

Degree: 13

\(\theta^4+x\left(127\theta^4-2\theta^3+22\theta^2+23\theta+6\right)+x^{2}\left(4803\theta^4+1644\theta^3+3459\theta^2+430\theta-384\right)+2^{3} x^{3}\left(2507\theta^4+8118\theta^3-2448\theta^2-7127\theta-2940\right)-2^{4} x^{4}\left(94175\theta^4+88358\theta^3+133418\theta^2+111507\theta+38898\right)+2^{6} 3 x^{5}\left(22347\theta^4+197706\theta^3+783766\theta^2+893091\theta+359952\right)+2^{6} 3^{2} x^{6}\left(869067\theta^4+4718208\theta^3+11162457\theta^2+11758320\theta+4583500\right)-2^{9} 3^{3} x^{7}\left(245985\theta^4+1338174\theta^3+3414812\theta^2+4418167\theta+2103502\right)-2^{12} 3^{4} x^{8}\left(234234\theta^4+2167368\theta^3+7012373\theta^2+9416514\theta+4375751\right)+2^{15} 3^{5} x^{9}\left(81234\theta^4+643380\theta^3+1815861\theta^2+2193249\theta+947968\right)+2^{18} 3^{6} x^{10}(\theta+1)(15879\theta^3+214401\theta^2+816191\theta+896789)-2^{21} 3^{7} x^{11}(\theta+1)(\theta+2)(8037\theta^2+71103\theta+151546)+2^{27} 3^{9} x^{12}(\theta+3)(\theta+2)(\theta+1)(31\theta+152)-2^{29} 3^{9} 5 x^{13}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, -6, 90, -1368, 21546, ...
--> OEIS
Normalized instanton numbers (n0=1): 10, -149/2, 7709/9, -27333/2, 242829, ... ; Common denominator:...

Discriminant

\(-(16z+1)(2160z^3+27z^2-9z+1)(24z+1)^2(72z^2-48z-1)^2(8z-1)^3\)

Local exponents

≈\(-0.100198\)\(-\frac{ 1}{ 16}\)\(-\frac{ 1}{ 24}\)\(\frac{ 1}{ 3}-\frac{ 1}{ 4}\sqrt{ 2}\)\(0\) ≈\(0.043849-0.05194I\) ≈\(0.043849+0.05194I\)\(\frac{ 1}{ 8}\)\(\frac{ 1}{ 3}+\frac{ 1}{ 4}\sqrt{ 2}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(\frac{ 1}{ 2}\)\(1\)\(0\)\(1\)\(1\)\(\frac{ 1}{ 2}\)\(1\)\(2\)
\(1\)\(1\)\(\frac{ 1}{ 2}\)\(3\)\(0\)\(1\)\(1\)\(\frac{ 3}{ 2}\)\(3\)\(3\)
\(2\)\(2\)\(1\)\(4\)\(0\)\(2\)\(2\)\(2\)\(4\)\(4\)

Note:

This is operator "13.7" from ...

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65

New Number: 13.8 |  AESZ:  |  Superseeker: 8 -830/9  |  Hash: bcea3fff557004b4da26e9aa34caac6c  

Degree: 13

\(\theta^4-x\left(55\theta^4+142\theta^3+112\theta^2+41\theta+6\right)+x^{2}\left(456\theta^4+4668\theta^3+7455\theta^2+3958\theta+696\right)+x^{3}\left(35078\theta^4+127188\theta^3+175671\theta^2+133507\theta+41718\right)+x^{4}\left(82753\theta^4+664768\theta^3+2450839\theta^2+2316756\theta+736812\right)-3 x^{5}\left(885105\theta^4+1342938\theta^3-883331\theta^2-2706576\theta-1350228\right)-2 3^{2} x^{6}\left(345501\theta^4+3334206\theta^3+4969485\theta^2+2964744\theta+630748\right)+2^{2} 3^{3} x^{7}\left(459939\theta^4+270666\theta^3-1625381\theta^2-2377792\theta-962956\right)+2^{4} 3^{4} x^{8}\left(112581\theta^4+699447\theta^3+1277449\theta^2+1022649\theta+314494\right)-2^{4} 3^{5} x^{9}\left(34101\theta^4-33864\theta^3-473835\theta^2-744726\theta-350272\right)-2^{5} 3^{6} x^{10}(\theta+1)(20847\theta^3+146325\theta^2+303230\theta+217616)+2^{6} 3^{7} x^{11}(\theta+1)(\theta+2)(1791\theta^2-1173\theta-14800)+2^{9} 3^{9} x^{12}(\theta+3)(\theta+2)(\theta+1)(52\theta+257)-2^{10} 3^{9} 17 x^{13}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 6, 90, 1044, -5670, ...
--> OEIS
Normalized instanton numbers (n0=1): 8, -45/2, -830/9, -5301/2, 2790, ... ; Common denominator:...

Discriminant

\(-(2z+1)(3672z^3+1728z^2-72z+1)(6z-1)^2(12z+1)^2(3z+1)^2(z-1)^3\)

Local exponents

≈\(-0.510076\)\(-\frac{ 1}{ 2}\)\(-\frac{ 1}{ 3}\)\(-\frac{ 1}{ 12}\)\(0\) ≈\(0.019744-0.012003I\) ≈\(0.019744+0.012003I\)\(\frac{ 1}{ 6}\)\(1\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(\frac{ 1}{ 2}\)\(1\)\(0\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)\(2\)
\(1\)\(1\)\(\frac{ 1}{ 2}\)\(3\)\(0\)\(1\)\(1\)\(3\)\(\frac{ 3}{ 2}\)\(3\)
\(2\)\(2\)\(1\)\(4\)\(0\)\(2\)\(2\)\(4\)\(2\)\(4\)

Note:

This is operator "13.8" from ...

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66

New Number: 13.9 |  AESZ:  |  Superseeker: 8 2200/9  |  Hash: 31ff3b7bd4c8fed070ee43b6903d3752  

Degree: 13

\(\theta^4+2^{3} x\theta(4\theta^3-8\theta^2-5\theta-1)-2^{4} x^{2}\left(48\theta^4+120\theta^3+45\theta^2+74\theta+36\right)-2^{7} x^{3}\left(101\theta^4-342\theta^3-387\theta^2-410\theta-171\right)+2^{8} x^{4}\left(3121\theta^4+14104\theta^3+30889\theta^2+27720\theta+9351\right)+2^{11} 3^{2} x^{5}\left(655\theta^4+4062\theta^3+10081\theta^2+10272\theta+3856\right)-2^{12} 3^{2} x^{6}\left(2272\theta^4+2816\theta^3-9950\theta^2-18768\theta-8813\right)-2^{15} 3^{3} x^{7}\left(1546\theta^4+12172\theta^3+30708\theta^2+33880\theta+13843\right)+2^{16} 3^{4} x^{8}\left(1099\theta^4+1344\theta^3-11134\theta^2-23964\theta-13063\right)+2^{19} 3^{5} x^{9}\left(458\theta^4+4828\theta^3+15325\theta^2+19721\theta+8830\right)-2^{20} 3^{6} x^{10}(\theta+1)(368\theta^3+1752\theta^2+1297\theta-1035)-2^{23} 3^{7} x^{11}(\theta+1)(\theta+2)(39\theta^2+513\theta+1172)+2^{24} 3^{9} x^{12}(\theta+3)(\theta+2)(\theta+1)(17\theta+82)-2^{27} 3^{10} x^{13}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 0, 36, -192, -4284, ...
--> OEIS
Normalized instanton numbers (n0=1): 8, -75/2, 2200/9, -8117/2, 47936, ... ; Common denominator:...

Discriminant

\(-(8z+1)(5184z^3+432z^2-36z+1)(12z+1)^2(144z^2-24z-1)^2(4z-1)^3\)

Local exponents

≈\(-0.141868\)\(-\frac{ 1}{ 8}\)\(-\frac{ 1}{ 12}\)\(\frac{ 1}{ 12}-\frac{ 1}{ 12}\sqrt{ 2}\)\(0\) ≈\(0.029267-0.022431I\) ≈\(0.029267+0.022431I\)\(\frac{ 1}{ 12}+\frac{ 1}{ 12}\sqrt{ 2}\)\(\frac{ 1}{ 4}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(\frac{ 1}{ 2}\)\(1\)\(0\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)\(2\)
\(1\)\(1\)\(\frac{ 1}{ 2}\)\(3\)\(0\)\(1\)\(1\)\(3\)\(\frac{ 3}{ 2}\)\(3\)
\(2\)\(2\)\(1\)\(4\)\(0\)\(2\)\(2\)\(4\)\(2\)\(4\)

Note:

This is operator "13.9" from ...

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67

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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68

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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69

New Number: 14.2 |  AESZ:  |  Superseeker: 27/5 1619/5  |  Hash: c0f6d85270164c8c5a63d1bb2deaba83  

Degree: 14

\(5^{2} \theta^4+3^{2} 5 x\theta(6\theta^3-36\theta^2-23\theta-5)-x^{2}\left(43856\theta^4+189068\theta^3+226691\theta^2+135510\theta+33600\right)-3^{2} x^{3}\left(224236\theta^4+916896\theta^3+1403247\theta^2+1048995\theta+313920\right)-x^{4}\left(44621090\theta^4+199900036\theta^3+357072757\theta^2+304636250\theta+101358144\right)-3^{2} x^{5}\left(69593744\theta^4+347076728\theta^3+696076003\theta^2+653370139\theta+234075456\right)-3^{2} x^{6}\left(681084088\theta^4+3766244020\theta^3+8299124637\theta^2+8400442322\theta+3184811840\right)-3^{3} x^{7}\left(1616263276\theta^4+9835107968\theta^3+23484467027\theta^2+25311872719\theta+10046134656\right)-3^{3} x^{8}\left(8527956293\theta^4+56671723156\theta^3+145225420081\theta^2+165230257706\theta+68152357440\right)-2 3^{4} x^{9}\left(5575274615\theta^4+40185448970\theta^3+109721715457\theta^2+130944512374\theta+55834822464\right)-2^{3} 3^{3} x^{10}\left(12062719219\theta^4+93737716664\theta^3+271167874625\theta^2+337796659588\theta+148305175248\right)-2^{5} 3^{5} x^{11}(\theta+1)(691573543\theta^3+5071601663\theta^2+12510902832\theta+10260936720)-2^{7} 3^{6} x^{12}(\theta+1)(\theta+2)(80620421\theta^2+475174733\theta+711172676)-2^{14} 3^{6} 5 x^{13}(\theta+3)(\theta+2)(\theta+1)(107069\theta+369433)-2^{19} 3^{8} 5^{2} 29 x^{14}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 0, 84, 1944, 70476, ...
--> OEIS
Normalized instanton numbers (n0=1): 27/5, 158/5, 1619/5, 51193/10, 485082/5, ... ; Common denominator:...

Discriminant

\(-(9z+1)(6z+1)(348z^2+51z-1)(5z+1)^2(4z+1)^2(576z^3+357z^2+72z+5)^2\)

Local exponents

≈\(-0.298314\)\(-\frac{ 1}{ 4}\)\(-\frac{ 1}{ 5}\)\(-\frac{ 1}{ 6}\)\(-\frac{ 17}{ 232}-\frac{ 11}{ 696}\sqrt{ 33}\) ≈\(-0.160739-0.057112I\) ≈\(-0.160739+0.057112I\)\(-\frac{ 1}{ 9}\)\(0\)\(-\frac{ 17}{ 232}+\frac{ 11}{ 696}\sqrt{ 33}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(\frac{ 1}{ 2}\)\(\frac{ 1}{ 2}\)\(1\)\(1\)\(1\)\(1\)\(1\)\(0\)\(1\)\(2\)
\(3\)\(\frac{ 1}{ 2}\)\(\frac{ 1}{ 2}\)\(1\)\(1\)\(3\)\(3\)\(1\)\(0\)\(1\)\(3\)
\(4\)\(1\)\(1\)\(2\)\(2\)\(4\)\(4\)\(2\)\(0\)\(2\)\(4\)

Note:

This is operator "14.2" from ...

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70

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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71

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

Degree: 15

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

Maple   LaTex

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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72

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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73

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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74

New Number: 6.10 |  AESZ:  |  Superseeker: 23 16723  |  Hash: 23025d094839fb9d8e76076bd9a0bfa7  

Degree: 6

\(\theta^4-x\left(254\theta^4+508\theta^3+391\theta^2+137\theta+18\right)+x^{2}\left(4657\theta^4+18628\theta^3+27265\theta^2+17274\theta+3672\right)-2^{2} 3 x^{3}\left(2920\theta^4+17520\theta^3+36833\theta^2+31659\theta+8235\right)+2^{3} 3^{4} x^{4}\left(204\theta^4+1632\theta^3+4449\theta^2+4740\theta+1400\right)-2^{4} 3^{5} x^{5}(16\theta^2+80\theta+35)(2\theta+5)^2+2^{4} 3^{6} x^{6}(2\theta+11)(2\theta+7)(2\theta+5)(2\theta+1)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 18, 1242, 138420, 18954810, ...
--> OEIS
Normalized instanton numbers (n0=1): 23, 462, 16723, 923487, 61874817, ... ; Common denominator:...

Discriminant

\((3z-1)(3888z^3-1944z^2+243z-1)(4z-1)^2\)

Local exponents

\(0\) ≈\(0.004259\) ≈\(0.215449\)\(\frac{ 1}{ 4}\) ≈\(0.280292\)\(\frac{ 1}{ 3}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(0\)\(1\)\(1\)\(\frac{ 1}{ 2}\)\(1\)\(1\)\(\frac{ 5}{ 2}\)
\(0\)\(1\)\(1\)\(\frac{ 1}{ 2}\)\(1\)\(1\)\(\frac{ 7}{ 2}\)
\(0\)\(2\)\(2\)\(1\)\(2\)\(2\)\(\frac{ 11}{ 2}\)

Note:

This is operator "6.10" from ...

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75

New Number: 6.11 |  AESZ:  |  Superseeker: 27296 369676901920  |  Hash: 480dfd541eda896f1434450e820ef263  

Degree: 6

\(\theta^4+2^{4} x\left(4480\theta^4-6016\theta^3-3632\theta^2-624\theta-57\right)+2^{14} x^{2}\left(56512\theta^4-238208\theta^3+88016\theta^2+21584\theta+2943\right)-2^{24} 3^{2} x^{3}\left(93952\theta^4+21248\theta^3+15264\theta^2+2176\theta+155\right)-2^{34} 3^{3} x^{4}\left(41664\theta^4+57088\theta^3+4448\theta^2-21248\theta-7191\right)+2^{48} 3^{3} 13 x^{5}(\theta+1)(808\theta^3+2352\theta^2+2099\theta+582)-2^{58} 3^{5} 13^{2} x^{6}(\theta+1)(\theta+2)(2\theta+1)(2\theta+5)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 912, 2320656, 9507313920, 49468269165840, ...
--> OEIS
Normalized instanton numbers (n0=1): 27296, -70540912, 369676901920, -2547102730999216, 20534034788092596960, ... ; Common denominator:...

Discriminant

\(-(3072z+1)(9216z-1)(39936z+1)^2(1024z-1)^2\)

Local exponents

\(-\frac{ 1}{ 3072}\)\(-\frac{ 1}{ 39936}\)\(0\)\(\frac{ 1}{ 9216}\)\(\frac{ 1}{ 1024}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(1\)\(0\)\(1\)\(\frac{ 1}{ 2}\)\(1\)
\(1\)\(3\)\(0\)\(1\)\(\frac{ 1}{ 2}\)\(2\)
\(2\)\(4\)\(0\)\(2\)\(1\)\(\frac{ 5}{ 2}\)

Note:

This is operator "6.11" from ...

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76

New Number: 6.14 |  AESZ:  |  Superseeker: 8 9928/3  |  Hash: 44968de144621e2fa74ce3964a5435f7  

Degree: 6

\(\theta^4-2^{2} x(5\theta^2+5\theta+2)(13\theta^2+13\theta+3)+2^{5} x^{2}\left(533\theta^4+2132\theta^3+3137\theta^2+2010\theta+432\right)-2^{8} 3 x^{3}\left(652\theta^4+3912\theta^3+8229\theta^2+7083\theta+1845\right)+2^{12} 3^{2} x^{4}\left(204\theta^4+1632\theta^3+4449\theta^2+4740\theta+1400\right)-2^{15} 3^{3} x^{5}(16\theta^2+80\theta+35)(2\theta+5)^2+2^{17} 3^{4} x^{6}(2\theta+11)(2\theta+7)(2\theta+5)(2\theta+1)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 24, 1224, 96000, 9633960, ...
--> OEIS
Normalized instanton numbers (n0=1): 8, 471/2, 9928/3, 185385, 6071232, ... ; Common denominator:...

Discriminant

\((12z-1)(24z-1)(2304z^2-192z+1)(-1+16z)^2\)

Local exponents

\(0\)\(\frac{ 1}{ 24}-\frac{ 1}{ 48}\sqrt{ 3}\)\(\frac{ 1}{ 24}\)\(\frac{ 1}{ 16}\)\(\frac{ 1}{ 24}+\frac{ 1}{ 48}\sqrt{ 3}\)\(\frac{ 1}{ 12}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(0\)\(1\)\(1\)\(\frac{ 1}{ 2}\)\(1\)\(1\)\(\frac{ 5}{ 2}\)
\(0\)\(1\)\(1\)\(\frac{ 1}{ 2}\)\(1\)\(1\)\(\frac{ 7}{ 2}\)
\(0\)\(2\)\(2\)\(1\)\(2\)\(2\)\(\frac{ 11}{ 2}\)

Note:

This is operator "6.14" from ...

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77

New Number: 6.15 |  AESZ:  |  Superseeker: 64 76608  |  Hash: 0130ee676bad42a2e117bca3367f8cf0  

Degree: 6

\(\theta^4+2^{4} x\left(56\theta^4+16\theta^3+22\theta^2+14\theta+3\right)+2^{10} x^{2}\left(308\theta^4+272\theta^3+347\theta^2+174\theta+35\right)+2^{18} x^{3}\left(212\theta^4+384\theta^3+473\theta^2+282\theta+69\right)+2^{26} x^{4}\left(77\theta^4+232\theta^3+327\theta^2+226\theta+62\right)+2^{35} x^{5}(7\theta^2+17\theta+13)(\theta+1)^2+2^{42} x^{6}(\theta+1)^2(\theta+2)^2\)

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Coefficients of the holomorphic solution: 1, -48, 3088, -231168, 19207440, ...
--> OEIS
Normalized instanton numbers (n0=1): 64, -1732, 76608, -4429212, 296488640, ... ; Common denominator:...

Discriminant

\((64z+1)^2(128z+1)^2(256z+1)^2\)

Local exponents

\(-\frac{ 1}{ 64}\)\(-\frac{ 1}{ 128}\)\(-\frac{ 1}{ 256}\)\(0\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(1\)
\(\frac{ 1}{ 2}\)\(\frac{ 1}{ 2}\)\(1\)\(0\)\(1\)
\(\frac{ 1}{ 2}\)\(\frac{ 1}{ 2}\)\(3\)\(0\)\(2\)
\(1\)\(1\)\(4\)\(0\)\(2\)

Note:

This is operator "6.15" from ...

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78

New Number: 6.16 |  AESZ:  |  Superseeker: 2272 434311008  |  Hash: f30ffc268310c175e914066ee270f47b  

Degree: 6

\(\theta^4+2^{4} x\left(448\theta^4-544\theta^3-332\theta^2-60\theta-5\right)+2^{12} x^{2}\left(2576\theta^4-8416\theta^3+2808\theta^2+668\theta+35\right)-2^{20} x^{3}\left(9088\theta^4+5568\theta^3+5392\theta^2+3180\theta+667\right)-2^{28} 3^{2} x^{4}(2\theta+1)(744\theta^3+940\theta^2+798\theta+167)+2^{38} 3^{3} 5 x^{5}(16\theta^2+40\theta+33)(\theta+1)^2+2^{48} 3^{3} 5^{2} x^{6}(\theta+1)^2(\theta+2)^2\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 80, 30480, 9850112, 4649741584, ...
--> OEIS
Normalized instanton numbers (n0=1): 2272, -719992, 434311008, -343376572072, 316225589496736, ... ; Common denominator:...

Discriminant

\((768z-1)(256z-1)(256z+1)^2(3840z+1)^2\)

Local exponents

\(-\frac{ 1}{ 256}\)\(-\frac{ 1}{ 3840}\)\(0\)\(\frac{ 1}{ 768}\)\(\frac{ 1}{ 256}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(\frac{ 1}{ 2}\)\(1\)\(0\)\(1\)\(1\)\(1\)
\(\frac{ 1}{ 2}\)\(3\)\(0\)\(1\)\(1\)\(2\)
\(1\)\(4\)\(0\)\(2\)\(2\)\(2\)

Note:

This is operator "6.16" from ...

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79

New Number: 6.17 |  AESZ:  |  Superseeker: 2 224/9  |  Hash: bbcabbebf6c04783d4ec5d0a5664f174  

Degree: 6

\(\theta^4-x\left(14+73\theta+154\theta^2+162\theta^3+81\theta^4\right)+x^{2}\left(3256+11390\theta+15571\theta^2+9876\theta^3+2469\theta^4\right)-x^{3}\left(162708+457536\theta+476503\theta^2+215994\theta^3+35999\theta^4\right)+2 3 5 x^{4}\left(8837\theta^4+70696\theta^3+200535\theta^2+236572\theta+98316\right)-2^{2} 3^{2} 5^{2} 7 x^{5}(\theta+4)(\theta+1)(151\theta^2+755\theta+850)+2^{3} 3^{3} 5^{3} 7^{2} x^{6}(\theta+5)(\theta+4)(\theta+2)(\theta+1)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 14, 220, 3800, 70840, ...
--> OEIS
Normalized instanton numbers (n0=1): 2, -4, 224/9, -112, 4446/5, ... ; Common denominator:...

Discriminant

\((6z-1)(14z-1)(30z-1)(21z-1)(-1+5z)^2\)

Local exponents

\(0\)\(\frac{ 1}{ 30}\)\(\frac{ 1}{ 21}\)\(\frac{ 1}{ 14}\)\(\frac{ 1}{ 6}\)\(\frac{ 1}{ 5}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(0\)\(1\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)\(2\)
\(0\)\(1\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)\(4\)
\(0\)\(2\)\(2\)\(2\)\(2\)\(1\)\(5\)

Note:

This is operator "6.17" from ...

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80

New Number: 6.20 |  AESZ:  |  Superseeker: 0 -1/3  |  Hash: 5169c67af7361bf7e6467dabea9612bd  

Degree: 6

\(\theta^4+x\left(11\theta+26\theta^3+2+13\theta^4+24\theta^2\right)-x^{2}(141\theta^2+282\theta+296)(\theta+1)^2-2 x^{3}(\theta+2)(\theta+1)(407\theta^2+1221\theta+654)+2^{2} 7 x^{4}(\theta+3)(\theta+1)(389\theta^2+1556\theta+1460)-2^{3} 3 7^{2} x^{5}(\theta+4)(\theta+1)(29\theta^2+145\theta+166)+2^{5} 3 7^{3} x^{6}(\theta+5)(\theta+4)(\theta+2)(\theta+1)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, -2, 28, -224, 2464, ...
--> OEIS
Normalized instanton numbers (n0=1): 0, 1/2, -1/3, -1, -2, ... ; Common denominator:...

Discriminant

\((-1+2z)(4z-1)(21z^2-9z+1)(1+14z)^2\)

Local exponents

\(-\frac{ 1}{ 14}\)\(0\)\(\frac{ 3}{ 14}-\frac{ 1}{ 42}\sqrt{ 3}I\)\(\frac{ 3}{ 14}+\frac{ 1}{ 42}\sqrt{ 3}I\)\(\frac{ 1}{ 4}\)\(\frac{ 1}{ 2}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(\frac{ 1}{ 2}\)\(0\)\(1\)\(1\)\(1\)\(1\)\(2\)
\(\frac{ 1}{ 2}\)\(0\)\(1\)\(1\)\(1\)\(1\)\(4\)
\(1\)\(0\)\(2\)\(2\)\(2\)\(2\)\(5\)

Note:

This is operator "6.20" from ...

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81

New Number: 6.21 |  AESZ:  |  Superseeker: 1 11  |  Hash: 319d6b2f1541de5252840442cc6f8dcd  

Degree: 6

\(\theta^4+x\left(6+27\theta+47\theta^2+40\theta^3+20\theta^4\right)-x^{2}(143\theta^2+286\theta+120)(\theta+1)^2-2 3^{2} x^{3}(\theta+2)(\theta+1)(291\theta^2+873\theta+766)-2^{2} 3^{3} 5 x^{4}(\theta+3)(\theta+1)(41\theta^2+164\theta+196)+2^{3} 3^{3} 5^{2} x^{5}(\theta+4)(\theta+1)(29\theta^2+145\theta+150)+2^{5} 3^{5} 5^{3} x^{6}(\theta+5)(\theta+4)(\theta+2)(\theta+1)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, -6, 60, -480, 5040, ...
--> OEIS
Normalized instanton numbers (n0=1): 1, 13/4, 11, 50, 1674/5, ... ; Common denominator:...

Discriminant

\((6z-1)(15z-1)(9z+1)(12z+1)(10z+1)^2\)

Local exponents

\(-\frac{ 1}{ 9}\)\(-\frac{ 1}{ 10}\)\(-\frac{ 1}{ 12}\)\(0\)\(\frac{ 1}{ 15}\)\(\frac{ 1}{ 6}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(\frac{ 1}{ 2}\)\(1\)\(0\)\(1\)\(1\)\(2\)
\(1\)\(\frac{ 1}{ 2}\)\(1\)\(0\)\(1\)\(1\)\(4\)
\(2\)\(1\)\(2\)\(0\)\(2\)\(2\)\(5\)

Note:

This is operator "6.21" from ...

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82

New Number: 6.23 |  AESZ:  |  Superseeker: 24/29 284/29  |  Hash: 83e67651e4ea5ee123354c2989ff7460  

Degree: 6

\(29^{6} \theta^4-2 29^{5} x(2\theta^2+2\theta+1)(152\theta^2+152\theta+41)-2^{2} 29^{4} x^{2}\left(4104\theta^4+16416\theta^3+23786\theta^2+14740\theta+3267\right)+2^{2} 29^{3} x^{3}\left(517492\theta^4+3104952\theta^3+6923513\theta^2+6798255\theta+2465928\right)-2^{4} 3 29^{2} x^{4}\left(3104764\theta^4+24838112\theta^3+70273625\theta^2+82389604\theta+33870303\right)+2^{8} 3^{2} 19 23 29 x^{5}(\theta+4)(\theta+1)(5408\theta^2+27040\theta+30585)-2^{12} 3^{4} 19^{2} 23^{2} x^{6}(\theta+5)(\theta+4)(\theta+2)(\theta+1)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 82/29, 18498/841, 5789116/24389, 2183601010/707281, ...
--> OEIS
Normalized instanton numbers (n0=1): 24/29, 72/29, 284/29, 1616/29, 10632/29, ... ; Common denominator:...

Discriminant

\(-(92z+29)(1195632z^3-467248z^2+548332z-24389)(24z-29)^2\)

Local exponents

\(-\frac{ 29}{ 92}\)\(0\) ≈\(0.046074\) ≈\(0.172361-0.642668I\) ≈\(0.172361+0.642668I\)\(\frac{ 29}{ 24}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(0\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)\(2\)
\(1\)\(0\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)\(4\)
\(2\)\(0\)\(2\)\(2\)\(2\)\(1\)\(5\)

Note:

This is operator "6.23" from ...

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83

New Number: 6.26 |  AESZ:  |  Superseeker: 58/43 1024/43  |  Hash: 38ef7a13fad0ecbb53ba25dafe26b113  

Degree: 6

\(43^{2} \theta^4-43 x\left(830\theta^4+1750\theta^3+1434\theta^2+559\theta+86\right)-x^{2}\left(1342738\theta^3+368510+1383525\theta+354697\theta^4+2007703\theta^2\right)-x^{3}\left(2348230+6951423\theta+774028\theta^4+3928308\theta^3+7763518\theta^2\right)-3 5 x^{4}\left(44423\theta^4+264028\theta^3+597368\theta^2+599643\theta+221430\right)-2 3^{2} 5^{2} x^{5}(\theta+2)(\theta+1)(533\theta^2+1694\theta+1290)-3^{3} 5^{3} x^{6}(3\theta+5)(3\theta+4)(\theta+2)(\theta+1)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 2, 26, 344, 5650, ...
--> OEIS
Normalized instanton numbers (n0=1): 58/43, 211/43, 1024/43, 7544/43, 64880/43, ... ; Common denominator:...

Discriminant

\(-(5z+1)(27z-1)(15z+43)^2(z+1)^2\)

Local exponents

\(-\frac{ 43}{ 15}\)\(-1\)\(-\frac{ 1}{ 5}\)\(0\)\(\frac{ 1}{ 27}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(\frac{ 1}{ 2}\)\(1\)\(0\)\(1\)\(\frac{ 4}{ 3}\)
\(3\)\(\frac{ 1}{ 2}\)\(1\)\(0\)\(1\)\(\frac{ 5}{ 3}\)
\(4\)\(1\)\(2\)\(0\)\(2\)\(2\)

Note:

This is operator "6.26" from ...

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84

New Number: 6.27 |  AESZ:  |  Superseeker: 6/17 33/17  |  Hash: af5aea32756746d4fc4931e4da73756b  

Degree: 6

\(17^{6} \theta^4-17^{5} x\left(427\theta^4+854\theta^3+814\theta^2+387\theta+74\right)+17^{4} x^{2}\left(47239\theta^4+188956\theta^3+300763\theta^2+223614\theta+64536\right)-2 3 17^{3} x^{3}\left(237751\theta^4+1426506\theta^3+3169919\theta^2+3090480\theta+1104868\right)-2^{2} 3^{2} 17^{2} x^{4}\left(1549605\theta^4+12396840\theta^3+35038211\theta^2+40978124\theta+16802716\right)+2^{3} 3^{3} 7 17 139 x^{5}(\theta+4)(\theta+1)(3737\theta^2+18685\theta+21310)-2^{5} 3^{4} 7^{2} 139^{2} x^{6}(\theta+5)(\theta+4)(\theta+2)(\theta+1)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 74/17, 7788/289, 1036400/4913, 164905648/83521, ...
--> OEIS
Normalized instanton numbers (n0=1): 6/17, 25/34, 33/17, 157/17, 577/17, ... ; Common denominator:...

Discriminant

\(-(28z+17)(278z-17)(8757z^2-2805z+289)(6z-17)^2\)

Local exponents

\(-\frac{ 17}{ 28}\)\(0\)\(\frac{ 17}{ 278}\)\(\frac{ 935}{ 5838}-\frac{ 289}{ 5838}\sqrt{ 3}I\)\(\frac{ 935}{ 5838}+\frac{ 289}{ 5838}\sqrt{ 3}I\)\(\frac{ 17}{ 6}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(0\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)\(2\)
\(1\)\(0\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)\(4\)
\(2\)\(0\)\(2\)\(2\)\(2\)\(1\)\(5\)

Note:

This is operator "6.27" from ...

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85

New Number: 6.30 |  AESZ:  |  Superseeker: 4 436  |  Hash: bc45bbf252bff0ad05b31f8e076f64cb  

Degree: 6

\(\theta^4+2^{2} x(\theta^2+\theta+1)(18\theta^2+18\theta+5)+2^{4} x^{2}\left(39\theta^4+156\theta^3+337\theta^2+362\theta+135\right)-2^{6} x^{3}\left(1124\theta^4+6744\theta^3+14434\theta^2+12954\theta+4329\right)-2^{8} 3 7 x^{4}\left(445\theta^4+3560\theta^3+10034\theta^2+11656\theta+4779\right)-2^{10} 3^{2} 7^{2} x^{5}(\theta+4)(\theta+1)(62\theta^2+310\theta+345)-2^{12} 3^{4} 7^{3} x^{6}(\theta+5)(\theta+4)(\theta+2)(\theta+1)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, -20, 480, -11264, 285712, ...
--> OEIS
Normalized instanton numbers (n0=1): 4, 71/2, 436, 6728, 127212, ... ; Common denominator:...

Discriminant

\(-(-1+36z)(12z+1)^2(28z+1)^3\)

Local exponents

\(-\frac{ 1}{ 12}\)\(-\frac{ 1}{ 28}\)\(0\)\(\frac{ 1}{ 36}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(1\)
\(\frac{ 1}{ 2}\)\(0\)\(0\)\(1\)\(2\)
\(\frac{ 1}{ 2}\)\(-\frac{ 1}{ 4}\)\(0\)\(1\)\(4\)
\(1\)\(\frac{ 1}{ 4}\)\(0\)\(2\)\(5\)

Note:

This is operator "6.30" from ...

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86

New Number: 6.39 |  AESZ:  |  Superseeker: 8 3784/3  |  Hash: 6429f42cbe18bee944ac13edab1fbbcc  

Degree: 6

\(\theta^4+2^{2} x\left(49\theta^4+98\theta^3+86\theta^2+37\theta+6\right)+2^{5} x^{2}\left(593\theta^4+2372\theta^3+3521\theta^2+2298\theta+504\right)+2^{10} 3 x^{3}\left(332\theta^4+1992\theta^3+4194\theta^2+3618\theta+945\right)+2^{14} 3^{2} x^{4}\left(204\theta^4+1632\theta^3+4449\theta^2+4740\theta+1400\right)+2^{18} 3^{3} x^{5}(16\theta^2+80\theta+35)(2\theta+5)^2+2^{21} 3^{4} x^{6}(2\theta+11)(2\theta+7)(2\theta+5)(2\theta+1)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, -24, 648, -11520, -123480, ...
--> OEIS
Normalized instanton numbers (n0=1): 8, 39/2, 3784/3, 51036, 1659840, ... ; Common denominator:...

Discriminant

\((24z+1)(110592z^3+6912z^2+108z+1)(1+32z)^2\)

Local exponents

≈\(-0.045368\)\(-\frac{ 1}{ 24}\)\(-\frac{ 1}{ 32}\) ≈\(-0.008566-0.011222I\) ≈\(-0.008566+0.011222I\)\(0\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(1\)\(\frac{ 1}{ 2}\)\(1\)\(1\)\(0\)\(\frac{ 5}{ 2}\)
\(1\)\(1\)\(\frac{ 1}{ 2}\)\(1\)\(1\)\(0\)\(\frac{ 7}{ 2}\)
\(2\)\(2\)\(1\)\(2\)\(2\)\(0\)\(\frac{ 11}{ 2}\)

Note:

This is operator "6.39" from ...

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87

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

Degree: 6

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

Maple   LaTex

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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88

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

Degree: 6

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

Maple   LaTex

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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89

New Number: 6.5 |  AESZ:  |  Superseeker: -11 -3422/3  |  Hash: 6a4aeb5833b7673c962d5598842d3f2c  

Degree: 6

\(\theta^4-x\left(12+64\theta+125\theta^2+122\theta^3+61\theta^4\right)-2^{3} x^{2}\left(193\theta^4+772\theta^3+1033\theta^2+522\theta+72\right)+2^{9} 3 x^{3}\left(146\theta^4+876\theta^3+1838\theta^2+1572\theta+405\right)-2^{12} 3^{2} x^{4}\left(204\theta^4+1632\theta^3+4449\theta^2+4740\theta+1400\right)+2^{16} 3^{3} x^{5}(16\theta^2+80\theta+35)(2\theta+5)^2-2^{19} 3^{4} x^{6}(2\theta+11)(2\theta+7)(2\theta+5)(2\theta+1)\)

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Coefficients of the holomorphic solution: 1, 12, 324, 5760, 215460, ...
--> OEIS
Normalized instanton numbers (n0=1): -11, 68, -3422/3, 30735, -1014993, ... ; Common denominator:...

Discriminant

\(-(24z-1)(27648z^3-1728z^2+27z+1)(-1+32z)^2\)

Local exponents

≈\(-0.016119\)\(0\)\(\frac{ 1}{ 32}\) ≈\(0.03931-0.026431I\) ≈\(0.03931+0.026431I\)\(\frac{ 1}{ 24}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(0\)\(\frac{ 1}{ 2}\)\(1\)\(1\)\(1\)\(\frac{ 5}{ 2}\)
\(1\)\(0\)\(\frac{ 1}{ 2}\)\(1\)\(1\)\(1\)\(\frac{ 7}{ 2}\)
\(2\)\(0\)\(1\)\(2\)\(2\)\(2\)\(\frac{ 11}{ 2}\)

Note:

This is operator "6.5" from ...

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90

New Number: 6.6 |  AESZ:  |  Superseeker: 25 17452  |  Hash: e97e9b0e87960fe4cffbb22a5e935b4a  

Degree: 6

\(\theta^4-x\left(12+100\theta+305\theta^2+410\theta^3+205\theta^4\right)-2^{5} x^{2}\left(127\theta^4+508\theta^3+742\theta^2+468\theta+99\right)-2^{2} 3 x^{3}\left(2588\theta^4+15528\theta^3+32639\theta^2+28041\theta+7290\right)-2^{6} 3^{2} x^{4}\left(204\theta^4+1632\theta^3+4449\theta^2+4740\theta+1400\right)-2^{7} 3^{3} x^{5}(16\theta^2+80\theta+35)(2\theta+5)^2-2^{7} 3^{4} x^{6}(2\theta+11)(2\theta+7)(2\theta+5)(2\theta+1)\)

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Coefficients of the holomorphic solution: 1, 12, 972, 106200, 14027580, ...
--> OEIS
Normalized instanton numbers (n0=1): 25, 446, 17452, 958347, 65098152, ... ; Common denominator:...

Discriminant

\(-(3z+1)(3456z^3+1728z^2+216z-1)(4z+1)^2\)

Local exponents

\(-\frac{ 1}{ 3}\) ≈\(-0.252234-0.033647I\) ≈\(-0.252234+0.033647I\)\(-\frac{ 1}{ 4}\)\(0\)\(\frac{ 1}{ 12}2^(\frac{ 1}{ 3})+\frac{ 1}{ 24}2^(\frac{ 2}{ 3})-\frac{ 1}{ 6}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)\(0\)\(1\)\(\frac{ 5}{ 2}\)
\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)\(0\)\(1\)\(\frac{ 7}{ 2}\)
\(2\)\(2\)\(2\)\(1\)\(0\)\(2\)\(\frac{ 11}{ 2}\)

Note:

This is operator "6.6" from ...

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