### Summary

You searched for: degz=7

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1

New Number: 7.10 |  AESZ:  |  Superseeker: 1 11  |  Hash: b1c277f62ba740f9f7e0371ba53e4194

Degree: 7

$\theta^4-x\left(76\theta^4+80\theta^3+73\theta^2+33\theta+6\right)+x^{2}\left(2209\theta^4+4228\theta^3+4745\theta^2+2726\theta+648\right)-2 3^{2} x^{3}\left(1735\theta^4+4646\theta^3+6099\theta^2+4072\theta+1124\right)+2^{2} 3^{3} x^{4}\left(2085\theta^4+7388\theta^3+11695\theta^2+9140\theta+2844\right)-2^{3} 3^{3} x^{5}(\theta+1)(3707\theta^3+14055\theta^2+20242\theta+10704)+2^{6} 3^{5} x^{6}(\theta+1)(\theta+2)(86\theta^2+285\theta+262)-2^{7} 3^{8} x^{7}(\theta+1)(\theta+2)^2(\theta+3)$

Maple   LaTex

Coefficients of the holomorphic solution: 1, 6, 60, 816, 13104, ...
--> OEIS
Normalized instanton numbers (n0=1): 1, 13/4, 11, 50, 1674/5, ... ; Common denominator:...

#### Discriminant

$-(3z-1)(18z-1)(27z-1)(12z-1)^2(-1+2z)^2$

#### Local exponents

$0$$\frac{ 1}{ 27}$$\frac{ 1}{ 18}$$\frac{ 1}{ 12}$$\frac{ 1}{ 3}$$\frac{ 1}{ 2}$$\infty$
$0$$0$$0$$0$$0$$0$$1$
$0$$1$$1$$1$$1$$\frac{ 1}{ 2}$$2$
$0$$1$$1$$3$$1$$\frac{ 1}{ 2}$$2$
$0$$2$$2$$4$$2$$1$$3$

#### Note:

This is operator "7.10" from ...

2

New Number: 7.11 |  AESZ:  |  Superseeker: -8 -3784/3  |  Hash: cb1bf6566f9c1a0dbfe98fb55f81944c

Degree: 7

$\theta^4+2^{2} x\left(23\theta^4-34\theta^3-30\theta^2-13\theta-2\right)+2^{5} x^{2}\left(177\theta^4+108\theta^3+577\theta^2+518\theta+116\right)+2^{10} x^{3}\left(355\theta^4+960\theta^3+1178\theta^2+139\theta-44\right)+2^{15} x^{4}\left(451\theta^4+1228\theta^3+997\theta^2+489\theta+103\right)+2^{20} x^{5}\left(285\theta^4+720\theta^3+766\theta^2+410\theta+83\right)+2^{26} x^{6}(2\theta+1)(20\theta^3+50\theta^2+49\theta+17)+2^{31} x^{7}(2\theta+1)(\theta+1)^2(2\theta+3)$

Maple   LaTex

Coefficients of the holomorphic solution: 1, 8, -120, -4480, 55720, ...
--> OEIS
Normalized instanton numbers (n0=1): -8, 43/2, -3784/3, 51036, -1659840, ... ; Common denominator:...

#### Discriminant

$(8z+1)(32768z^3+3072z^2-12z+1)(32z+1)^3$

#### Local exponents

$-\frac{ 1}{ 8}$ ≈$-0.100423$$-\frac{ 1}{ 32}$$0$ ≈$0.003336-0.01711I$ ≈$0.003336+0.01711I$$\infty$
$0$$0$$0$$0$$0$$0$$\frac{ 1}{ 2}$
$1$$1$$2$$0$$1$$1$$1$
$1$$1$$3$$0$$1$$1$$1$
$2$$2$$5$$0$$2$$2$$\frac{ 3}{ 2}$

#### Note:

This is operator "7.11" from ...

3

New Number: 7.12 |  AESZ:  |  Superseeker: -21 -7941  |  Hash: 0841b278bc566a089b643bbe2460fe8b

Degree: 7

$\theta^4+3 x\left(99\theta^4+162\theta^3+139\theta^2+58\theta+10\right)+2 3^{4} x^{2}\left(135\theta^4+738\theta^3+945\theta^2+518\theta+116\right)-2^{2} 3^{7} x^{3}\left(117\theta^4-738\theta^3-2010\theta^2-1493\theta-406\right)-2^{3} 3^{10} x^{4}\left(333\theta^4+774\theta^3-898\theta^2-1269\theta-454\right)-2^{4} 3^{13} x^{5}\left(54\theta^4+1224\theta^3+1179\theta^2+347\theta-22\right)+2^{5} 3^{16} x^{6}\left(180\theta^4+72\theta^3-327\theta^2-359\theta-106\right)+2^{7} 3^{19} x^{7}(\theta+1)^2(6\theta+5)(6\theta+7)$

Maple   LaTex

Coefficients of the holomorphic solution: 1, -30, 1458, -89076, 6250050, ...
--> OEIS
Normalized instanton numbers (n0=1): -21, -399, -7941, -986355/4, -8179455, ... ; Common denominator:...

#### Discriminant

$(27z+1)(54z+1)(54z-1)^2(108z+1)^3$

#### Local exponents

$-\frac{ 1}{ 27}$$-\frac{ 1}{ 54}$$-\frac{ 1}{ 108}$$0$$\frac{ 1}{ 54}$$\infty$
$0$$0$$0$$0$$0$$\frac{ 5}{ 6}$
$1$$1$$\frac{ 1}{ 2}$$0$$1$$1$
$1$$1$$\frac{ 3}{ 2}$$0$$3$$1$
$2$$2$$2$$0$$4$$\frac{ 7}{ 6}$

#### Note:

This is operator "7.12" from ...

4

New Number: 7.13 |  AESZ:  |  Superseeker: -32 -107936  |  Hash: 80eaab6a34199e98f88d8472c115c4df

Degree: 7

$\theta^4+2^{4} x\left(44\theta^4+72\theta^3+64\theta^2+28\theta+5\right)+2^{11} x^{2}\left(60\theta^4+328\theta^3+420\theta^2+228\theta+51\right)-2^{18} x^{3}\left(52\theta^4-328\theta^3-885\theta^2-663\theta-181\right)-2^{25} x^{4}\left(148\theta^4+344\theta^3-403\theta^2-559\theta-199\right)-2^{32} x^{5}\left(24\theta^4+544\theta^3+519\theta^2+147\theta-12\right)+2^{39} x^{6}\left(80\theta^4+32\theta^3-147\theta^2-159\theta-46\right)+2^{47} x^{7}(4\theta+3)(\theta+1)^2(4\theta+5)$

Maple   LaTex

Coefficients of the holomorphic solution: 1, -80, 10512, -1703168, 309951760, ...
--> OEIS
Normalized instanton numbers (n0=1): -32, -2840, -107936, -7514224, -575948640, ... ; Common denominator:...

#### Discriminant

$(64z+1)(128z+1)(128z-1)^2(256z+1)^3$

#### Local exponents

$-\frac{ 1}{ 64}$$-\frac{ 1}{ 128}$$-\frac{ 1}{ 256}$$0$$\frac{ 1}{ 128}$$\infty$
$0$$0$$0$$0$$0$$\frac{ 3}{ 4}$
$1$$1$$\frac{ 1}{ 4}$$0$$1$$1$
$1$$1$$\frac{ 7}{ 4}$$0$$3$$1$
$2$$2$$2$$0$$4$$\frac{ 5}{ 4}$

#### Note:

This is operator "7.13" from ...

5

New Number: 7.14 |  AESZ:  |  Superseeker: -48 -38929520  |  Hash: d8c602210ad81a2daef74d36a78ea933

Degree: 7

$\theta^4+2^{4} 3 x\left(99\theta^4+162\theta^3+151\theta^2+70\theta+13\right)+2^{9} 3^{4} x^{2}\left(135\theta^4+738\theta^3+945\theta^2+506\theta+113\right)-2^{14} 3^{7} x^{3}\left(117\theta^4-738\theta^3-1965\theta^2-1490\theta-409\right)-2^{19} 3^{10} x^{4}\left(333\theta^4+774\theta^3-919\theta^2-1242\theta-439\right)-2^{25} 3^{13} x^{5}\left(27\theta^4+612\theta^3+576\theta^2+154\theta-17\right)+2^{31} 3^{16} x^{6}\left(45\theta^4+18\theta^3-84\theta^2-89\theta-25\right)+2^{37} 3^{19} x^{7}(\theta+1)^2(3\theta+2)(3\theta+4)$

Maple   LaTex

Coefficients of the holomorphic solution: 1, -624, 633744, -768218880, 1020122073360, ...
--> OEIS
Normalized instanton numbers (n0=1): -48, -160806, -38929520, -13792511646, -7174458915600, ... ; Common denominator:...

#### Discriminant

$(432z+1)(864z+1)(864z-1)^2(1728z+1)^3$

#### Local exponents

$-\frac{ 1}{ 432}$$-\frac{ 1}{ 864}$$-\frac{ 1}{ 1728}$$0$$\frac{ 1}{ 864}$$\infty$
$0$$0$$0$$0$$0$$\frac{ 2}{ 3}$
$1$$1$$0$$0$$1$$1$
$1$$1$$2$$0$$3$$1$
$2$$2$$2$$0$$4$$\frac{ 4}{ 3}$

#### Note:

This is operator "7.14" from ...

6

New Number: 7.15 |  AESZ:  |  Superseeker: -2 -952  |  Hash: d9a911258d890c112974a4ba19e93e6d

Degree: 7

$\theta^4+2 x\left(138\theta^4+156\theta^3+137\theta^2+59\theta+10\right)+2^{2} x^{2}\left(4796\theta^4+15824\theta^3+16719\theta^2+7610\theta+1400\right)-2^{4} 5 x^{3}\left(5876\theta^4-28824\theta^3-58439\theta^2-39075\theta-9350\right)-2^{6} 5 x^{4}\left(184592\theta^4+414976\theta^3-60816\theta^2-180968\theta-60145\right)+2^{10} 3 x^{5}\left(240624\theta^4-905760\theta^3-1250920\theta^2-576920\theta-83925\right)+2^{18} 3^{2} x^{6}\left(13608\theta^4+48276\theta^3+66402\theta^2+41679\theta+9935\right)-2^{20} 3^{5} x^{7}(6\theta+5)^2(6\theta+7)^2$

Maple   LaTex

Coefficients of the holomorphic solution: 1, -20, 900, -55280, 3962500, ...
--> OEIS
Normalized instanton numbers (n0=1): -2, -343/2, -952, -45148, -17303644/25, ... ; Common denominator:...

#### Discriminant

$-(-1-16z+256z^2)(32z-1)^2(108z+1)^3$

#### Local exponents

$\frac{ 1}{ 32}-\frac{ 1}{ 32}\sqrt{ 5}$$-\frac{ 1}{ 108}$$0$$\frac{ 1}{ 32}$$\frac{ 1}{ 32}+\frac{ 1}{ 32}\sqrt{ 5}$$\infty$
$0$$0$$0$$0$$0$$\frac{ 5}{ 6}$
$1$$\frac{ 1}{ 2}$$0$$1$$1$$\frac{ 5}{ 6}$
$1$$\frac{ 3}{ 2}$$0$$3$$1$$\frac{ 7}{ 6}$
$2$$2$$0$$4$$2$$\frac{ 7}{ 6}$

#### Note:

This is operator "7.15" from ...

7

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 ...

8

New Number: 7.17 |  AESZ:  |  Superseeker: 0 18  |  Hash: c248fd7c807d0aae71ef687a9ee40c80

Degree: 7

$\theta^4+3 x\left(87\theta^4+84\theta^3+86\theta^2+44\theta+9\right)+2 3^{3} x^{2}\left(539\theta^4+1076\theta^3+1366\theta^2+880\theta+233\right)+2 3^{5} x^{3}\left(3699\theta^4+11424\theta^3+17579\theta^2+13389\theta+4088\right)+3^{7} x^{4}\left(30367\theta^4+128696\theta^3+235722\theta^2+205070\theta+69226\right)+3^{9} x^{5}\left(74547\theta^4+405660\theta^3+871096\theta^2+848930\theta+310507\right)+2 3^{11} 5 x^{6}(2\theta+3)(5066\theta^3+26325\theta^2+44815\theta+23766)+2^{2} 3^{14} 5^{2} 7^{2} x^{7}(\theta+1)(2\theta+5)(2\theta+3)(\theta+3)$

Maple   LaTex

Coefficients of the holomorphic solution: 1, -27, 783, -23481, 717903, ...
--> OEIS
Normalized instanton numbers (n0=1): 0, -27/2, 18, -999/2, 1566, ... ; Common denominator:...

#### Discriminant

$(27z+1)(1323z^2+72z+1)(36z+1)^2(45z+1)^2$

#### Local exponents

$-\frac{ 1}{ 27}$$-\frac{ 1}{ 36}$$-\frac{ 4}{ 147}-\frac{ 1}{ 441}\sqrt{ 3}I$$-\frac{ 4}{ 147}+\frac{ 1}{ 441}\sqrt{ 3}I$$-\frac{ 1}{ 45}$$0$$\infty$
$0$$0$$0$$0$$0$$0$$1$
$1$$\frac{ 1}{ 2}$$1$$1$$1$$0$$\frac{ 3}{ 2}$
$1$$\frac{ 1}{ 2}$$1$$1$$3$$0$$\frac{ 5}{ 2}$
$2$$1$$2$$2$$4$$0$$3$

#### Note:

This is operator "7.17" from ...

9

New Number: 7.18 |  AESZ:  |  Superseeker: 352 26115552  |  Hash: df2c3b4e6a3366531b24bb05809eb1a4

Degree: 7

$\theta^4-2^{4} x\left(144\theta^4-192\theta^3-172\theta^2-76\theta-11\right)+2^{14} x^{2}\left(100\theta^4-320\theta^3-25\theta^2+155\theta+36\right)-2^{21} x^{3}\left(72\theta^4-1248\theta^3+628\theta^2-180\theta-97\right)-2^{30} x^{4}\left(212\theta^4+256\theta^3-14\theta^2+86\theta+15\right)+2^{36} 3 x^{5}\left(240\theta^4-320\theta^3-332\theta^2-380\theta-119\right)+2^{46} 3^{2} x^{6}\left(12\theta^4+64\theta^3+99\theta^2+67\theta+17\right)-2^{56} 3^{3} x^{7}\left((\theta+1)^4\right)$

Maple   LaTex

Coefficients of the holomorphic solution: 1, -176, 17168, -4715264, 653856016, ...
--> OEIS
Normalized instanton numbers (n0=1): 352, 60664, 26115552, 16623590600, 13165993300256, ... ; Common denominator:...

#### Discriminant

$-(256z-1)^2(256z+1)^2(768z-1)^3$

#### Local exponents

$-\frac{ 1}{ 256}$$0$$\frac{ 1}{ 768}$$\frac{ 1}{ 256}$$\infty$
$0$$0$$0$$0$$1$
$0$$0$$2$$\frac{ 1}{ 2}$$1$
$1$$0$$3$$\frac{ 1}{ 2}$$1$
$1$$0$$5$$1$$1$

#### Note:

This is operator "7.18" from ...

10

New Number: 7.19 |  AESZ:  |  Superseeker: 4/3 -124/81  |  Hash: f7f0f5d883101c38ed22cb74c80c8f5c

Degree: 7

$3^{3} \theta^4-2^{2} 3^{2} x\left(12\theta^4-16\theta^3-21\theta^2-13\theta-3\right)-2^{4} 3 x^{2}\left(240\theta^4+1280\theta^3+2068\theta^2+1636\theta+489\right)+2^{10} x^{3}\left(212\theta^4+592\theta^3+490\theta^2-34\theta-129\right)+2^{13} x^{4}\left(72\theta^4+1536\theta^3+4804\theta^2+5468\theta+2031\right)-2^{18} x^{5}\left(100\theta^4+720\theta^3+1535\theta^2+1155\theta+276\right)+2^{20} x^{6}\left(144\theta^4+768\theta^3+1268\theta^2+884\theta+229\right)-2^{28} x^{7}\left((\theta+1)^4\right)$

Maple   LaTex

Coefficients of the holomorphic solution: 1, -4, 68, -496, 9796, ...
--> OEIS
Normalized instanton numbers (n0=1): 4/3, -14/9, -124/81, -4498/243, 37024/729, ... ; Common denominator:...

#### Discriminant

$-(16z-1)^2(16z+1)^2(16z-3)^3$

#### Local exponents

$-\frac{ 1}{ 16}$$0$$\frac{ 1}{ 16}$$\frac{ 3}{ 16}$$\infty$
$0$$0$$0$$0$$1$
$0$$0$$\frac{ 1}{ 2}$$2$$1$
$1$$0$$\frac{ 1}{ 2}$$3$$1$
$1$$0$$1$$5$$1$

#### Note:

This is operator "7.19" from ...

11

New Number: 7.1 |  AESZ:  |  Superseeker: 10/7 508/7  |  Hash: 08ab3cb496250adfa30bc3e24ac63c4f

Degree: 7

$7^{2} \theta^4-2 7 x\theta(46\theta^3+52\theta^2+33\theta+7)-2^{2} x^{2}\left(7332\theta^4+28848\theta^3+42633\theta^2+26670\theta+6272\right)-2^{4} x^{3}\left(2860\theta^4+44760\theta^3+120483\theta^2+111279\theta+35098\right)+2^{9} x^{4}\left(2230\theta^4+5920\theta^3-741\theta^2-6509\theta-3049\right)+2^{14} x^{5}\left(174\theta^4+1320\theta^3+1971\theta^2+1095\theta+190\right)-2^{19} x^{6}\left(22\theta^4+24\theta^3-9\theta^2-21\theta-7\right)-2^{25} x^{7}\left((\theta+1)^4\right)$

Maple   LaTex

Coefficients of the holomorphic solution: 1, 0, 32, 288, 7776, ...
--> OEIS
Normalized instanton numbers (n0=1): 10/7, 100/7, 508/7, 808, 59910/7, ... ; Common denominator:...

#### Discriminant

$-(16z+1)(32z-1)(32z-7)^2(4z+1)^3$

#### Local exponents

$-\frac{ 1}{ 4}$$-\frac{ 1}{ 16}$$0$$\frac{ 1}{ 32}$$\frac{ 7}{ 32}$$\infty$
$0$$0$$0$$0$$0$$1$
$\frac{ 1}{ 2}$$1$$0$$1$$1$$1$
$\frac{ 3}{ 2}$$1$$0$$1$$3$$1$
$2$$2$$0$$2$$4$$1$

#### Note:

This is operator "7.1" from ...

12

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 ...

13

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 ...

14

New Number: 7.2 |  AESZ:  |  Superseeker: -80 -249872  |  Hash: 341389ebf4ab0242c5b70d9a8fd7a1d9

Degree: 7

$\theta^4+2^{4} x\left(22\theta^4+64\theta^3+51\theta^2+19\theta+3\right)-2^{9} x^{2}\left(174\theta^4-624\theta^3-945\theta^2-417\theta-80\right)-2^{14} x^{3}\left(2230\theta^4+3000\theta^3-5121\theta^2-3813\theta-971\right)+2^{19} x^{4}\left(2860\theta^4-33320\theta^3+3363\theta^2+6847\theta+2402\right)+2^{27} x^{5}\left(7332\theta^4+480\theta^3+81\theta^2+1380\theta+719\right)+2^{36} 7 x^{6}(\theta+1)(46\theta^3+86\theta^2+67\theta+20)-2^{45} 7^{2} x^{7}\left((\theta+1)^4\right)$

Maple   LaTex

Coefficients of the holomorphic solution: 1, -48, 5072, -733440, 124117776, ...
--> OEIS
Normalized instanton numbers (n0=1): -80, -4202, -249872, -22251117, -2195810928, ... ; Common denominator:...

#### Discriminant

$-(64z+1)(32z-1)(224z-1)^2(256z+1)^3$

#### Local exponents

$-\frac{ 1}{ 64}$$-\frac{ 1}{ 256}$$0$$\frac{ 1}{ 224}$$\frac{ 1}{ 32}$$\infty$
$0$$0$$0$$0$$0$$1$
$1$$\frac{ 1}{ 2}$$0$$1$$1$$1$
$1$$\frac{ 3}{ 2}$$0$$3$$1$$1$
$2$$2$$0$$4$$2$$1$

#### Note:

This is operator "7.2" from ...

15

New Number: 7.3 |  AESZ:  |  Superseeker: 3 64  |  Hash: 8413250555ca536f1bdccfeed506ea4e

Degree: 7

$\theta^4+x\theta(39\theta^3-30\theta^2-19\theta-4)+2 x^{2}\left(16\theta^4-1070\theta^3-1057\theta^2-676\theta-192\right)-2^{2} 3^{2} x^{3}(3\theta+2)(171\theta^3+566\theta^2+600\theta+316)-2^{5} 3^{3} x^{4}\left(384\theta^4+1542\theta^3+2635\theta^2+2173\theta+702\right)-2^{6} 3^{3} x^{5}(\theta+1)(1393\theta^3+5571\theta^2+8378\theta+4584)-2^{10} 3^{5} x^{6}(\theta+1)(\theta+2)(31\theta^2+105\theta+98)-2^{12} 3^{7} x^{7}(\theta+1)(\theta+2)^2(\theta+3)$

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Coefficients of the holomorphic solution: 1, 0, 24, 192, 3384, ...
--> OEIS
Normalized instanton numbers (n0=1): 3, -4, 64, -253, 4292, ... ; Common denominator:...

#### Discriminant

$-(8z+1)(24z-1)(3z+1)(4z+1)(12z+1)(1+18z)^2$

#### Local exponents

$-\frac{ 1}{ 3}$$-\frac{ 1}{ 4}$$-\frac{ 1}{ 8}$$-\frac{ 1}{ 12}$$-\frac{ 1}{ 18}$$0$$\frac{ 1}{ 24}$$\infty$
$0$$0$$0$$0$$0$$0$$0$$1$
$1$$1$$1$$1$$1$$0$$1$$2$
$1$$1$$1$$1$$3$$0$$1$$2$
$2$$2$$2$$2$$4$$0$$2$$3$

#### Note:

This is operator "7.3" from ...

16

New Number: 7.4 |  AESZ:  |  Superseeker: -988/3 -14008436/3  |  Hash: 9bddfb88498c0a263be6ca541ae7e980

Degree: 7

$3^{2} \theta^4+2^{2} 3 x\left(760\theta^4+2048\theta^3+1423\theta^2+399\theta+42\right)-2^{7} x^{2}\left(20440\theta^4+25216\theta^3-4415\theta^2-4845\theta-795\right)+2^{12} x^{3}\left(39928\theta^4+16512\theta^3+23719\theta^2+11637\theta+1830\right)+2^{17} x^{4}\left(2928\theta^4-41856\theta^3-42871\theta^2-16873\theta-2425\right)+2^{23} x^{5}\left(608\theta^4+3968\theta^3+10676\theta^2+6177\theta+1089\right)+2^{29} x^{6}\left(272\theta^4+1056\theta^3+861\theta^2+264\theta+27\right)+2^{35} x^{7}\left((2\theta+1)^4\right)$

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Coefficients of the holomorphic solution: 1, -56, 21096, -12540800, 9146271400, ...
--> OEIS
Normalized instanton numbers (n0=1): -988/3, 57289/3, -14008436/3, 1385404666, -1599785191904/3, ... ; Common denominator:...

#### Discriminant

$(1+1248z-10240z^2+131072z^3)(-3+352z+2048z^2)^2$

#### Local exponents

$-\frac{ 11}{ 128}-\frac{ 1}{ 128}\sqrt{ 145}$ ≈$-0.000796$$0$$-\frac{ 11}{ 128}+\frac{ 1}{ 128}\sqrt{ 145}$ ≈$0.039461-0.089595I$ ≈$0.039461+0.089595I$$\infty$
$0$$0$$0$$0$$0$$0$$\frac{ 1}{ 2}$
$1$$1$$0$$1$$1$$1$$\frac{ 1}{ 2}$
$3$$1$$0$$3$$1$$1$$\frac{ 1}{ 2}$
$4$$2$$0$$4$$2$$2$$\frac{ 1}{ 2}$

#### Note:

This is operator "7.4" from ...

17

New Number: 7.5 |  AESZ:  |  Superseeker: 8096 9215266592  |  Hash: 90403d92f72b2839164c2bbd30933deb

Degree: 7

$\theta^4+2^{4} x\left(1088\theta^4-2048\theta^3-1260\theta^2-236\theta-19\right)+2^{15} x^{2}\left(1216\theta^4-5504\theta^3+11272\theta^2+3654\theta+423\right)+2^{24} x^{3}\left(11712\theta^4+190848\theta^3+97220\theta^2+27432\theta+2835\right)+2^{35} x^{4}\left(159712\theta^4+253376\theta^3+235372\theta^2+78648\theta+9491\right)-2^{46} x^{5}\left(81760\theta^4+62656\theta^3-46316\theta^2-33048\theta-5403\right)+2^{57} 3 x^{6}\left(3040\theta^4-2112\theta^3-2036\theta^2-528\theta-41\right)+2^{69} 3^{2} x^{7}\left((2\theta+1)^4\right)$

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Coefficients of the holomorphic solution: 1, 304, -113904, -2048902400, -4778502402800, ...
--> OEIS
Normalized instanton numbers (n0=1): 8096, -9179600, 9215266592, -8060820053720, 27014124083677664, ... ; Common denominator:...

#### Discriminant

$(2147483648z^3+40894464z^2-5120z+1)(-1-11264z+6291456z^2)^2$

#### Local exponents

≈$-0.019169$$\frac{ 11}{ 12288}-\frac{ 1}{ 12288}\sqrt{ 145}$$0$ ≈$6.3e-05-0.000143I$ ≈$6.3e-05+0.000143I$$\frac{ 11}{ 12288}+\frac{ 1}{ 12288}\sqrt{ 145}$$\infty$
$0$$0$$0$$0$$0$$0$$\frac{ 1}{ 2}$
$1$$1$$0$$1$$1$$1$$\frac{ 1}{ 2}$
$1$$3$$0$$1$$1$$3$$\frac{ 1}{ 2}$
$2$$4$$0$$2$$2$$4$$\frac{ 1}{ 2}$

#### Note:

This is operator "7.5" from ...

18

New Number: 7.6 |  AESZ:  |  Superseeker: 1/3 5/3  |  Hash: 24ba77c97bc4b46c39a41c77cc1d1ef4

Degree: 7

$3^{2} \theta^4-3 x\left(112\theta^4+140\theta^3+133\theta^2+63\theta+12\right)+x^{2}\left(4393\theta^4+9340\theta^3+10903\theta^2+6360\theta+1488\right)-2 x^{3}\left(11669\theta^4+27720\theta^3+27019\theta^2+8460\theta-912\right)+2^{2} x^{4}\left(6799\theta^4-10288\theta^3-82183\theta^2-119168\theta-52672\right)+2^{3} 7 x^{5}(\theta+1)(2611\theta^3+15537\theta^2+26998\theta+14360)-2^{6} 7^{2} x^{6}(\theta+1)(\theta+2)(83\theta^2+105\theta-66)-2^{10} 7^{3} x^{7}(\theta+1)(\theta+2)^2(\theta+3)$

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Coefficients of the holomorphic solution: 1, 4, 28, 232, 2188, ...
--> OEIS
Normalized instanton numbers (n0=1): 1/3, 5/6, 5/3, 19/3, 29, ... ; Common denominator:...

#### Discriminant

$-(2z+1)(8z-1)(7z-1)(16z-1)(z+1)(-3+14z)^2$

#### Local exponents

$-1$$-\frac{ 1}{ 2}$$0$$\frac{ 1}{ 16}$$\frac{ 1}{ 8}$$\frac{ 1}{ 7}$$\frac{ 3}{ 14}$$\infty$
$0$$0$$0$$0$$0$$0$$0$$1$
$1$$1$$0$$1$$1$$1$$1$$2$
$1$$1$$0$$1$$1$$1$$3$$2$
$2$$2$$0$$2$$2$$2$$4$$3$

#### Note:

This is operator "7.6" from ...

19

New Number: 7.7 |  AESZ:  |  Superseeker: 2/3 13/3  |  Hash: c7abb9c42d46f14955f0f23351082bef

Degree: 7

$3^{2} \theta^4-2 3 x\left(88\theta^4+110\theta^3+103\theta^2+48\theta+9\right)+2^{2} x^{2}\left(2923\theta^4+6610\theta^3+8041\theta^2+4908\theta+1206\right)-x^{3}\left(123365\theta^4+374814\theta^3+519741\theta^2+346176\theta+89676\right)+2 x^{4}\left(309657\theta^4+1102938\theta^3+1591157\theta^2+1032920\theta+249740\right)-2^{3} 11 x^{5}(\theta+1)(12897\theta^3+35469\theta^2+31181\theta+8042)-2^{3} 11^{2} x^{6}(\theta+1)(\theta+2)(355\theta^2+1047\theta+806)-2^{4} 11^{3} x^{7}(\theta+1)(\theta+2)^2(\theta+3)$

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Coefficients of the holomorphic solution: 1, 6, 56, 636, 8196, ...
--> OEIS
Normalized instanton numbers (n0=1): 2/3, 5/3, 13/3, 59/3, 119, ... ; Common denominator:...

#### Discriminant

$-(11z-1)(4z^2+22z-1)(z^2+11z-1)(-3+22z)^2$

#### Local exponents

$-\frac{ 11}{ 2}-\frac{ 5}{ 2}\sqrt{ 5}$$-\frac{ 11}{ 4}-\frac{ 5}{ 4}\sqrt{ 5}$$0$$-\frac{ 11}{ 4}+\frac{ 5}{ 4}\sqrt{ 5}$$-\frac{ 11}{ 2}+\frac{ 5}{ 2}\sqrt{ 5}$$\frac{ 1}{ 11}$$\frac{ 3}{ 22}$$\infty$
$0$$0$$0$$0$$0$$0$$0$$1$
$1$$1$$0$$1$$1$$1$$1$$2$
$1$$1$$0$$1$$1$$1$$3$$2$
$2$$2$$0$$2$$2$$2$$4$$3$

#### Note:

This is operator "7.7" from ...

20

New Number: 7.8 |  AESZ:  |  Superseeker: -1/3 -5/3  |  Hash: d5b8cfd5049e5d8670dac5bb5499d46a

Degree: 7

$3^{2} \theta^4-3 x\left(272\theta^4+340\theta^3+347\theta^2+177\theta+36\right)+x^{2}\left(31273\theta^4+76540\theta^3+103783\theta^2+71112\theta+19728\right)-2 x^{3}\left(328219\theta^4+1181160\theta^3+1977957\theta^2+1620036\theta+522288\right)+2^{2} x^{4}\left(2036999\theta^4+9602752\theta^3+19022113\theta^2+17726192\theta+6309408\right)-2^{3} 17 x^{5}(\theta+1)(439669\theta^3+2114103\theta^2+3708554\theta+2306280)+2^{6} 3^{3} 17^{2} x^{6}(\theta+1)(\theta+2)(481\theta^2+1875\theta+1962)-2^{10} 3^{4} 17^{3} x^{7}(\theta+1)(\theta+2)^2(\theta+3)$

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Coefficients of the holomorphic solution: 1, 12, 156, 2136, 30348, ...
--> OEIS
Normalized instanton numbers (n0=1): -1/3, 11/12, -5/3, 19/3, -29, ... ; Common denominator:...

#### Discriminant

$-(17z-1)(9z-1)(8z-1)(18z-1)(16z-1)(-3+34z)^2$

#### Local exponents

$0$$\frac{ 1}{ 18}$$\frac{ 1}{ 17}$$\frac{ 1}{ 16}$$\frac{ 3}{ 34}$$\frac{ 1}{ 9}$$\frac{ 1}{ 8}$$\infty$
$0$$0$$0$$0$$0$$0$$0$$1$
$0$$1$$1$$1$$1$$1$$1$$2$
$0$$1$$1$$1$$3$$1$$1$$2$
$0$$2$$2$$2$$4$$2$$2$$3$

#### Note:

This is operator "7.8" from ...

21

New Number: 7.9 |  AESZ:  |  Superseeker: -3 -245/3  |  Hash: 5641c09b76662b0741e41b41b0c6f105

Degree: 7

$\theta^4-3 x\left(96\theta^4+120\theta^3+127\theta^2+67\theta+14\right)+3^{2} x^{2}\left(3897\theta^4+9540\theta^3+13209\theta^2+9246\theta+2608\right)-2 3^{4} x^{3}\left(14445\theta^4+52002\theta^3+88179\theta^2+73278\theta+23920\right)+2^{2} 3^{6} x^{4}\left(31671\theta^4+149364\theta^3+298089\theta^2+280512\theta+100780\right)-2^{3} 3^{12} x^{5}(\theta+1)(507\theta^3+2439\theta^2+4306\theta+2704)+2^{6} 3^{14} x^{6}(\theta+1)(\theta+2)(90\theta^2+351\theta+370)-2^{7} 3^{19} x^{7}(\theta+1)(\theta+2)^2(\theta+3)$

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Coefficients of the holomorphic solution: 1, 42, 1872, 86712, 4126716, ...
--> OEIS
Normalized instanton numbers (n0=1): -3, 69/4, -245/3, 879, -11829, ... ; Common denominator:...

#### Discriminant

$-(36z-1)^2(27z-1)^2(54z-1)^3$

#### Local exponents

$0$$\frac{ 1}{ 54}$$\frac{ 1}{ 36}$$\frac{ 1}{ 27}$$\infty$
$0$$0$$0$$0$$1$
$0$$0$$1$$\frac{ 1}{ 3}$$2$
$0$$-\frac{ 1}{ 3}$$3$$\frac{ 2}{ 3}$$2$
$0$$\frac{ 1}{ 3}$$4$$1$$3$

#### Note:

This is operator "7.9" from ...