### Summary

You searched for: inst=8

1

New Number: 2.55 |  AESZ: 42  |  Superseeker: 8 1000  |  Hash: c389d3bc0e31801bc4b7b3e186702bc9

Degree: 2

$\theta^4-2^{3} x(2\theta+1)^2(3\theta^2+3\theta+1)+2^{6} x^{2}(2\theta+1)(\theta+1)^2(2\theta+3)$

Maple   LaTex

Coefficients of the holomorphic solution: 1, 8, 240, 10880, 597520, ...
--> OEIS
Normalized instanton numbers (n0=1): 8, 63, 1000, 44369/2, 606168, ... ; Common denominator:...

#### Discriminant

$1-96z+256z^2$

#### Local exponents

$0$$\frac{ 3}{ 16}-\frac{ 1}{ 8}\sqrt{ 2}$$\frac{ 3}{ 16}+\frac{ 1}{ 8}\sqrt{ 2}$$\infty$
$0$$0$$0$$\frac{ 1}{ 2}$
$0$$1$$1$$1$
$0$$1$$1$$1$
$0$$2$$2$$\frac{ 3}{ 2}$

#### Note:

Hadamard product $I \ast \epsilon$

2

New Number: 2.65 |  AESZ: 183  |  Superseeker: -4 -556/9  |  Hash: 04a3788c3f9ed53281ae824deb33d833

Degree: 2

$\theta^4+2^{2} x(2\theta+1)^2(7\theta^2+7\theta+3)+2^{4} 3 x^{2}(2\theta+1)(4\theta+3)(4\theta+5)(2\theta+3)$

Maple   LaTex

Coefficients of the holomorphic solution: 1, -12, 324, -11280, 447300, ...
--> OEIS
Normalized instanton numbers (n0=1): -4, 8, -556/9, 624, -8928, ... ; Common denominator:...

#### Discriminant

$(48z+1)(64z+1)$

#### Local exponents

$-\frac{ 1}{ 48}$$-\frac{ 1}{ 64}$$0$$\infty$
$0$$0$$0$$\frac{ 1}{ 2}$
$1$$1$$0$$\frac{ 3}{ 4}$
$1$$1$$0$$\frac{ 5}{ 4}$
$2$$2$$0$$\frac{ 3}{ 2}$

#### Note:

This is operator "2.65" from ...

3

New Number: 10.5 |  AESZ:  |  Superseeker: 8 -830/9  |  Hash: 26cb7b62aea8fead9548cb08c510d8cc

Degree: 10

$\theta^4-x\left(5+36\theta+102\theta^2+132\theta^3+42\theta^4\right)+x^{2}\left(321+2500\theta+5078\theta^2+2676\theta^3-126\theta^4\right)+x^{3}\left(58511+193314\theta+255284\theta^2+165228\theta^3+36750\theta^4\right)+3 x^{4}\left(149076\theta^4+788140\theta^3+1818454\theta^2+1636604\theta+537147\right)+x^{5}\left(18978161+48287282\theta+41352784\theta^2+10485348\theta^3-282726\theta^4\right)+x^{6}\left(75240839+129474252\theta+18361102\theta^2-64936644\theta^3-20164434\theta^4\right)-x^{7}\left(192652267+790586058\theta+1080753300\theta^2+555817116\theta^3+53729334\theta^4\right)-x^{8}\left(1469856277+3396870740\theta+2385867946\theta^2+267688500\theta^3-184083363\theta^4\right)+2 5 13 x^{9}(2\theta+3)(3678542\theta^3+13483935\theta^2+14333215\theta+4727112)+2^{2} 3 5^{2} 13^{2} 73^{2} x^{10}(\theta+1)(2\theta+5)(2\theta+3)(\theta+3)$

Maple   LaTex

Coefficients of the holomorphic solution: 1, 5, 79, 791, -9329, ...
--> OEIS
Normalized instanton numbers (n0=1): 8, -45/2, -830/9, -5301/2, 2790, ... ; Common denominator:...

#### Discriminant

$(3z+1)(5329z^3+1587z^2-69z+1)(13z+1)^2(4z+1)^2(5z-1)^2$

#### Local exponents

≈$-0.337782$$-\frac{ 1}{ 3}$$-\frac{ 1}{ 4}$$-\frac{ 1}{ 13}$$0$ ≈$0.019989-0.01249I$ ≈$0.019989+0.01249I$$\frac{ 1}{ 5}$$\infty$
$0$$0$$0$$0$$0$$0$$0$$0$$1$
$1$$1$$\frac{ 1}{ 2}$$1$$0$$1$$1$$1$$\frac{ 3}{ 2}$
$1$$1$$\frac{ 1}{ 2}$$3$$0$$1$$1$$3$$\frac{ 5}{ 2}$
$2$$2$$1$$4$$0$$2$$2$$4$$3$

#### Note:

This is operator "10.5" from ...

4

New Number: 10.6 |  AESZ:  |  Superseeker: 8 2200/9  |  Hash: b5aa0abf76ddfbd280ec220a43822aa4

Degree: 10

$\theta^4+2^{2} x\left(21\theta^4-6\theta^3+3\theta+1\right)+2^{4} x^{2}\left(126\theta^4-96\theta^3-16\theta^2-56\theta-33\right)+2^{6} x^{3}\left(84\theta^4-336\theta^3-226\theta^2-366\theta-163\right)+2^{11} 3 x^{4}\left(39\theta^4+500\theta^3+1230\theta^2+1160\theta+407\right)+2^{12} x^{5}\left(7029\theta^4+50118\theta^3+125086\theta^2+129149\theta+48902\right)+2^{14} x^{6}\left(38550\theta^4+294456\theta^3+806428\theta^2+911232\theta+368273\right)+2^{16} x^{7}\left(77544\theta^4+708720\theta^3+2233434\theta^2+2804346\theta+1214177\right)+2^{20} x^{8}\left(9171\theta^4+117228\theta^3+467444\theta^2+684316\theta+324572\right)-2^{23} x^{9}(2\theta+3)(2114\theta^3+16713\theta^2+37111\theta+22497)+2^{26} 3 5^{2} x^{10}(\theta+1)(2\theta+5)(2\theta+3)(\theta+3)$

Maple   LaTex

Coefficients of the holomorphic solution: 1, -4, 52, -688, 2500, ...
--> OEIS
Normalized instanton numbers (n0=1): 8, -75/2, 2200/9, -8117/2, 47936, ... ; Common denominator:...

#### Discriminant

$(12z+1)(6400z^3+192z^2-24z+1)(16z+1)^2(32z^2-32z-1)^2$

#### Local exponents

≈$-0.090507$$-\frac{ 1}{ 12}$$-\frac{ 1}{ 16}$$\frac{ 1}{ 2}-\frac{ 3}{ 8}\sqrt{ 2}$$0$ ≈$0.030254-0.02848I$ ≈$0.030254+0.02848I$$\frac{ 1}{ 2}+\frac{ 3}{ 8}\sqrt{ 2}$$\infty$
$0$$0$$0$$0$$0$$0$$0$$0$$1$
$1$$1$$\frac{ 1}{ 2}$$1$$0$$1$$1$$1$$\frac{ 3}{ 2}$
$1$$1$$\frac{ 1}{ 2}$$3$$0$$1$$1$$3$$\frac{ 5}{ 2}$
$2$$2$$1$$4$$0$$2$$2$$4$$3$

#### Note:

This is operator "10.6" from ...

5

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 ...

6

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 ...

7

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 ...

8

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 ...

9

New Number: 7.16 |  AESZ:  |  Superseeker: 22/5 68  |  Hash: 660211ce6175f36772066594bfc33cbb

Degree: 7

$5^{2} \theta^4-2 5 x\theta(15+71\theta+112\theta^2+38\theta^3)-2^{2} x^{2}\left(4364\theta^4+15872\theta^3+24679\theta^2+19360\theta+6000\right)-2^{4} 3^{2} 5 x^{3}\left(92\theta^4+224\theta^3+103\theta^2-176\theta-165\right)+2^{6} 3^{2} x^{4}\left(1228\theta^4+10496\theta^3+30154\theta^2+35736\theta+14715\right)+2^{9} 3^{4} x^{5}(\theta+1)(38\theta^3+74\theta^2-304\theta-495)-2^{10} 3^{4} x^{6}(2\theta+13)(2\theta+3)(17\theta+39)(\theta+1)-2^{12} 3^{6} x^{7}(\theta+1)(2\theta+5)(2\theta+3)(\theta+3)$

Maple   LaTex

Coefficients of the holomorphic solution: 1, 0, 60, 480, 16524, ...
--> OEIS
Normalized instanton numbers (n0=1): 22/5, 8, 68, 3292/5, 38826/5, ... ; Common denominator:...

#### Discriminant

$-(-1+36z)(12z+5)^2(12z+1)^2(4z-1)^2$

#### Local exponents

$-\frac{ 5}{ 12}$$-\frac{ 1}{ 12}$$0$$\frac{ 1}{ 36}$$\frac{ 1}{ 4}$$\infty$
$0$$0$$0$$0$$0$$1$
$1$$0$$0$$1$$\frac{ 1}{ 2}$$\frac{ 3}{ 2}$
$3$$1$$0$$1$$\frac{ 1}{ 2}$$\frac{ 5}{ 2}$
$4$$1$$0$$2$$1$$3$

#### Note:

This is operator "7.16" from ...

10

New Number: 8.1 |  AESZ: 102  |  Superseeker: 8 1053  |  Hash: e928905653beb9d844e6a942f50d94ac

Degree: 8

$\theta^4-x(7\theta^2+7\theta+2)(11\theta^2+11\theta+3)-x^{2}\left(1049\theta^4+4100\theta^3+5689\theta^2+3178\theta+640\right)+2^{3} x^{3}\left(77\theta^4-462\theta^3-1420\theta^2-1053\theta-252\right)+2^{4} x^{4}\left(1041\theta^4+2082\theta^3-1406\theta^2-2447\theta-746\right)+2^{6} x^{5}\left(77\theta^4+770\theta^3+428\theta^2-93\theta-80\right)-2^{6} x^{6}\left(1049\theta^4+96\theta^3-317\theta^2+96\theta+100\right)-2^{9} x^{7}(7\theta^2+7\theta+2)(11\theta^2+11\theta+3)+2^{12} x^{8}\left((\theta+1)^4\right)$

Maple   LaTex

Coefficients of the holomorphic solution: 1, 6, 190, 8232, 432846, ...
--> OEIS
Normalized instanton numbers (n0=1): 8, 153/2, 1053, 49101/2, 670214, ... ; Common denominator:...

#### Discriminant

$(64z^2+88z-1)(z^2-11z-1)(-1+8z^2)^2$

#### Local exponents

$-\frac{ 11}{ 16}-\frac{ 5}{ 16}\sqrt{ 5}$$-\frac{ 1}{ 4}\sqrt{ 2}$$\frac{ 11}{ 2}-\frac{ 5}{ 2}\sqrt{ 5}$$0$$-\frac{ 11}{ 16}+\frac{ 5}{ 16}\sqrt{ 5}$$\frac{ 1}{ 4}\sqrt{ 2}$$\frac{ 11}{ 2}+\frac{ 5}{ 2}\sqrt{ 5}$$\infty$
$0$$0$$0$$0$$0$$0$$0$$1$
$1$$1$$1$$0$$1$$1$$1$$1$
$1$$3$$1$$0$$1$$3$$1$$1$
$2$$4$$2$$0$$2$$4$$2$$1$

#### Note:

Hadamard product $a \ast b$. The operator has a second MUM-point at infinity with the same instanton numbers. In fact, there is a symmetry in the operator. It can be reduced to an operator with a single MUM point of degree 4, defined over $Q(\sqrt{2})$.

11

New Number: 8.3 |  AESZ: 105  |  Superseeker: 8 -104  |  Hash: 7b27135451cf2016217211c633b7ab83

Degree: 8

$\theta^4-2^{2} x(3\theta^2+3\theta+1)(7\theta^2+7\theta+2)+2^{5} 3 x^{2}\left(15\theta^4+28\theta^3+39\theta^2+22\theta+4\right)-2^{10} x^{3}\left(21\theta^4-126\theta^3-386\theta^2-291\theta-76\right)+2^{14} x^{4}\left(37\theta^4+74\theta^3+50\theta^2+13\theta+6\right)+2^{18} x^{5}\left(21\theta^4+210\theta^3+118\theta^2-19\theta-24\right)+2^{21} 3 x^{6}\left(15\theta^4+32\theta^3+45\theta^2+32\theta+8\right)+2^{26} x^{7}(3\theta^2+3\theta+1)(7\theta^2+7\theta+2)+2^{32} x^{8}\left((\theta+1)^4\right)$

Maple   LaTex

Coefficients of the holomorphic solution: 1, 8, 200, 6272, 233896, ...
--> OEIS
Normalized instanton numbers (n0=1): 8, 71/2, -104, 4202, 50112, ... ; Common denominator:...

#### Discriminant

$(8z+1)(64z-1)(4z+1)(32z-1)(1+256z^2)^2$

#### Local exponents

$-\frac{ 1}{ 4}$$-\frac{ 1}{ 8}$$0-\frac{ 1}{ 16}I$$0$$0+\frac{ 1}{ 16}I$$\frac{ 1}{ 64}$$\frac{ 1}{ 32}$$\infty$
$0$$0$$0$$0$$0$$0$$0$$1$
$1$$1$$1$$0$$1$$1$$1$$1$
$1$$1$$3$$0$$3$$1$$1$$1$
$2$$2$$4$$0$$4$$2$$2$$1$

#### Note:

Hadamard product $a \ast d$. This operator has a second MUM-point at infinity with the same instanton numbers.
It can be reduced to an operator of degree 4 with a single MUM-point defined over
$Q(\sqrt{-1})$.

12

New Number: 8.79 |  AESZ:  |  Superseeker: 22/5 68  |  Hash: 064e5b590dd8b6a4daa1e905fbe693c2

Degree: 8

$5^{2} \theta^4-2 5 x\left(338\theta^4+412\theta^3+371\theta^2+165\theta+30\right)+2^{2} x^{2}\left(46396\theta^4+103408\theta^3+125291\theta^2+76370\theta+19080\right)-2^{4} 3 x^{3}\left(115508\theta^4+357896\theta^3+524149\theta^2+375205\theta+106530\right)+2^{6} 3^{2} x^{4}\left(173456\theta^4+669024\theta^3+1118292\theta^2+883484\theta+269049\right)-2^{11} 3^{3} x^{5}\left(20272\theta^4+91616\theta^3+168594\theta^2+142006\theta+45053\right)+2^{14} 3^{4} x^{6}\left(5792\theta^4+29504\theta^3+58300\theta^2+51220\theta+16641\right)-2^{21} 3^{5} x^{7}(\theta+1)^2(58\theta^2+208\theta+201)+2^{26} 3^{6} x^{8}(\theta+1)^2(\theta+2)^2$

Maple   LaTex

Coefficients of the holomorphic solution: 1, 12, 204, 4368, 112140, ...
--> OEIS
Normalized instanton numbers (n0=1): 22/5, 8, 68, 3292/5, 38826/5, ... ; Common denominator:...

#### Discriminant

$(-1+48z)(16z-1)^2(48z-5)^2(12z-1)^3$

#### Local exponents

$0$$\frac{ 1}{ 48}$$\frac{ 1}{ 16}$$\frac{ 1}{ 12}$$\frac{ 5}{ 48}$$\infty$
$0$$0$$0$$0$$0$$1$
$0$$1$$\frac{ 1}{ 2}$$\frac{ 1}{ 2}$$1$$1$
$0$$1$$\frac{ 1}{ 2}$$\frac{ 3}{ 2}$$3$$2$
$0$$2$$1$$2$$4$$2$

#### Note:

This is operator "8.79" from ...