5 1: Difference between revisions

Revision as of 05:11, 3 March 2013

4_1

5_2

(KnotPlot image)

See the full Rolfsen Knot Table.

Visit $n$ &id= $k$ 5 1's page at the Knot Server (KnotPlot driven, includes 3D interactive images!)

Visit 5 1 at Knotilus!

[edit 5 1 Quick Notes]

An interlaced pentagram, this is known variously as the "Cinquefoil Knot", after certain herbs and shrubs of the rose family which have 5-lobed leaves and 5-petaled flowers (see e.g. [4]), as the "Pentafoil Knot" (visit Bert Jagers' pentafoil page), as the "Double Overhand Knot", as 5_1, or finally as the torus knot T(5,2).

[edit 5 1 Further Notes and Views]

A kolam of a 2x3 dot array	The VISA Interlink Logo [1]	Version of the US bicentennial emblem
A pentagonal table by Bob Mackay [2]	The Utah State Parks logo	As impossible object ("Penrose" pentagram)
Folded ribbon which is single-sided (more complex version of Möbius Strip).	Non-pentagonal shape.	Pentagram of circles.
Alternate pentagram of intersecting circles.	3D-looking rendition.	Partial view of US bicentennial logo on a shirt seen in Lisboa [3]
Non-prime knot with two 5_1 configurations on a closed loop.	Knotted epitrochoid	Sum of two 5_1s, Vienna, orthodox church

This sentence was last edited by Dror. Sometime later, Scott added this sentence.

Knot presentations

Planar diagram presentation	X₁₆₂₇ X₃₈₄₉ X_5,10,6,1 X₇₂₈₃ X_9,4,10,5
Gauss code	-1, 4, -2, 5, -3, 1, -4, 2, -5, 3
Dowker-Thistlethwaite code	6 8 10 2 4
Conway Notation	[5]

Minimum Braid Representative

A Morse Link Presentation

An Arc Presentation

Length is 5, width is 2,

Braid index is 2

[{7, 2}, {1, 3}, {2, 4}, {3, 5}, {4, 6}, {5, 7}, {6, 1}]

[edit Notes on presentations of 5 1]

Knot 5_1.

A graph, knot 5_1.

Computer Talk

The above data is available with the Mathematica package KnotTheory`. Your input (in red) is realistic; all else should have the same content as in a real mathematica session, but with different formatting.

(The path below may be different on your system, and possibly also the KnotTheory` date)

In[1]:= AppendTo[$Path, "C:/drorbn/projects/KAtlas/"]; << KnotTheory`

Loading KnotTheory` version of May 31, 2006, 14:15:20.091.

Read more at http://katlas.org/wiki/KnotTheory.

In[3]:= K = Knot["5 1"];

In[4]:= PD[K]

KnotTheory::loading: Loading precomputed data in PD4Knots`.

Out[4]= X₁₆₂₇ X₃₈₄₉ X_5,10,6,1 X₇₂₈₃ X_9,4,10,5

In[5]:= GaussCode[K]

Out[5]= -1, 4, -2, 5, -3, 1, -4, 2, -5, 3

In[6]:= DTCode[K]

Out[6]= 6 8 10 2 4

(The path below may be different on your system)

In[7]:= AppendTo[$Path, "C:/bin/LinKnot/"];

In[8]:= ConwayNotation[K]

Out[8]= [5]

In[9]:= br = BR[K]

KnotTheory::credits: The minimum braids representing the knots with up to 10 crossings were provided by Thomas Gittings. See arXiv:math.GT/0401051.

Out[9]= ${\textrm {BR}}(2,\{-1,-1,-1,-1,-1\})$

In[10]:= {First[br], Crossings[br], BraidIndex[K]}

KnotTheory::credits: The braid index data known to KnotTheory` is taken from Charles Livingston's http://www.indiana.edu/~knotinfo/.

KnotTheory::loading: Loading precomputed data in IndianaData`.

Out[10]= { 2, 5, 2 }

In[11]:= Show[BraidPlot[br]]

Out[11]= -Graphics-

In[12]:= Show[DrawMorseLink[K]]

KnotTheory::credits: "MorseLink was added to KnotTheory` by Siddarth Sankaran at the University of Toronto in the summer of 2005."

KnotTheory::credits: "DrawMorseLink was written by Siddarth Sankaran at the University of Toronto in the summer of 2005."

Out[12]= -Graphics-

In[13]:= ap = ArcPresentation[K]

Out[13]= ArcPresentation[{7, 2}, {1, 3}, {2, 4}, {3, 5}, {4, 6}, {5, 7}, {6, 1}]

In[14]:= Draw[ap]

Out[14]= -Graphics-

Three dimensional invariants

Symmetry type	Reversible
Unknotting number	2
3-genus	2
Bridge index	2
Super bridge index	3
Nakanishi index	1
Maximal Thurston-Bennequin number	[-10][3]
Hyperbolic Volume	Not hyperbolic
A-Polynomial	See Data:5 1/A-polynomial

[edit Notes for 5 1's three dimensional invariants]

Four dimensional invariants

Smooth 4 genus	$2$
Topological 4 genus	$2$
Concordance genus	${\textrm {ConcordanceGenus}}({\textrm {Knot}}(5,1))$
Rasmussen s-Invariant	-4

[edit Notes for 5 1's four dimensional invariants]

Polynomial invariants

Alexander polynomial	$t^{2}+t^{-2}-t-t^{-1}+1$
Conway polynomial	$z^{4}+3z^{2}+1$
2nd Alexander ideal (db, data sources)	$\{1\}$
Determinant and Signature	{ 5, -4 }
Jones polynomial	$-q^{-7}+q^{-6}-q^{-5}+q^{-4}+q^{-2}$
HOMFLY-PT polynomial (db, data sources)	$a^{6}\left(-z^{2}\right)-2a^{6}+a^{4}z^{4}+4a^{4}z^{2}+3a^{4}$
Kauffman polynomial (db, data sources)	$a^{9}z+a^{8}z^{2}+a^{7}z^{3}-a^{7}z+a^{6}z^{4}-3a^{6}z^{2}+2a^{6}+a^{5}z^{3}-2a^{5}z+a^{4}z^{4}-4a^{4}z^{2}+3a^{4}$
The A2 invariant	$-q^{22}-q^{20}-q^{18}+q^{14}+q^{12}+2q^{10}+q^{8}+q^{6}$
The G2 invariant	$q^{120}-q^{100}-q^{98}-q^{92}-q^{90}-q^{88}-q^{82}-q^{80}-q^{78}-q^{72}+q^{58}+q^{56}+q^{52}+2q^{50}+q^{48}+q^{46}+q^{44}+q^{42}+2q^{40}+q^{38}+q^{34}+q^{32}+q^{30}$

Further Quantum Invariants

Further quantum knot invariants for 5_1.

A1 Invariants.

Weight	Invariant
1	$-q^{15}+q^{7}+q^{5}+q^{3}$
2	$q^{40}-q^{32}-q^{30}-q^{28}+q^{14}+q^{12}+q^{10}+q^{8}+q^{6}$
3	$-q^{75}+q^{67}+q^{65}+q^{63}-q^{49}-q^{47}-q^{45}-q^{43}-q^{41}+q^{21}+q^{19}+q^{17}+q^{15}+q^{13}+q^{11}+q^{9}$
4	$q^{120}-q^{112}-q^{110}-q^{108}+q^{94}+q^{92}+q^{90}+q^{88}+q^{86}-q^{66}-q^{64}-q^{62}-q^{60}-q^{58}-q^{56}-q^{54}+q^{28}+q^{26}+q^{24}+q^{22}+q^{20}+q^{18}+q^{16}+q^{14}+q^{12}$
5	$-q^{175}+q^{167}+q^{165}+q^{163}-q^{149}-q^{147}-q^{145}-q^{143}-q^{141}+q^{121}+q^{119}+q^{117}+q^{115}+q^{113}+q^{111}+q^{109}-q^{83}-q^{81}-q^{79}-q^{77}-q^{75}-q^{73}-q^{71}-q^{69}-q^{67}+q^{35}+q^{33}+q^{31}+q^{29}+q^{27}+q^{25}+q^{23}+q^{21}+q^{19}+q^{17}+q^{15}$
6	$q^{240}-q^{232}-q^{230}-q^{228}+q^{214}+q^{212}+q^{210}+q^{208}+q^{206}-q^{186}-q^{184}-q^{182}-q^{180}-q^{178}-q^{176}-q^{174}+q^{148}+q^{146}+q^{144}+q^{142}+q^{140}+q^{138}+q^{136}+q^{134}+q^{132}-q^{100}-q^{98}-q^{96}-q^{94}-q^{92}-q^{90}-q^{88}-q^{86}-q^{84}-q^{82}-q^{80}+q^{42}+q^{40}+q^{38}+q^{36}+q^{34}+q^{32}+q^{30}+q^{28}+q^{26}+q^{24}+q^{22}+q^{20}+q^{18}$
8	$q^{400}-q^{392}-q^{390}-q^{388}+q^{374}+q^{372}+q^{370}+q^{368}+q^{366}-q^{346}-q^{344}-q^{342}-q^{340}-q^{338}-q^{336}-q^{334}+q^{308}+q^{306}+q^{304}+q^{302}+q^{300}+q^{298}+q^{296}+q^{294}+q^{292}-q^{260}-q^{258}-q^{256}-q^{254}-q^{252}-q^{250}-q^{248}-q^{246}-q^{244}-q^{242}-q^{240}+q^{202}+q^{200}+q^{198}+q^{196}+q^{194}+q^{192}+q^{190}+q^{188}+q^{186}+q^{184}+q^{182}+q^{180}+q^{178}-q^{134}-q^{132}-q^{130}-q^{128}-q^{126}-q^{124}-q^{122}-q^{120}-q^{118}-q^{116}-q^{114}-q^{112}-q^{110}-q^{108}-q^{106}+q^{56}+q^{54}+q^{52}+q^{50}+q^{48}+q^{46}+q^{44}+q^{42}+q^{40}+q^{38}+q^{36}+q^{34}+q^{32}+q^{30}+q^{28}+q^{26}+q^{24}$

A2 Invariants.

Weight	Invariant
1,0	$-q^{22}-q^{20}-q^{18}+q^{14}+q^{12}+2q^{10}+q^{8}+q^{6}$
1,1	$q^{60}-2q^{36}-2q^{34}-4q^{32}-4q^{30}-3q^{28}+2q^{24}+4q^{22}+5q^{20}+4q^{18}+4q^{16}+2q^{14}+q^{12}$
2,0	$q^{54}+q^{52}+2q^{50}+q^{48}-2q^{44}-3q^{42}-3q^{40}-3q^{38}-2q^{36}-q^{34}+q^{28}+q^{26}+2q^{24}+2q^{22}+3q^{20}+2q^{18}+2q^{16}+q^{14}+q^{12}$
3,0	$-q^{96}-q^{94}-2q^{92}-2q^{90}-q^{88}+q^{86}+3q^{84}+4q^{82}+5q^{80}+4q^{78}+4q^{76}+2q^{74}+q^{72}-q^{70}-2q^{68}-3q^{66}-4q^{64}-5q^{62}-5q^{60}-5q^{58}-4q^{56}-3q^{54}-2q^{52}-q^{50}+q^{42}+q^{40}+2q^{38}+2q^{36}+3q^{34}+3q^{32}+4q^{30}+3q^{28}+3q^{26}+2q^{24}+2q^{22}+q^{20}+q^{18}$

A3 Invariants.

Weight	Invariant
0,1,0	$q^{50}-q^{36}-2q^{34}-3q^{32}-3q^{30}-2q^{28}-q^{26}+2q^{24}+3q^{22}+4q^{20}+3q^{18}+3q^{16}+q^{14}+q^{12}$
1,0,0	$-q^{29}-q^{27}-2q^{25}-q^{23}+q^{19}+2q^{17}+2q^{15}+2q^{13}+q^{11}+q^{9}$
1,0,1	$q^{80}+q^{58}+q^{56}+3q^{54}+3q^{52}+2q^{50}-q^{48}-5q^{46}-9q^{44}-12q^{42}-12q^{40}-9q^{38}-3q^{36}+2q^{34}+7q^{32}+10q^{30}+11q^{28}+10q^{26}+7q^{24}+5q^{22}+2q^{20}+q^{18}$

A4 Invariants.

Weight	Invariant
0,1,0,0	$q^{64}+q^{62}+q^{60}+q^{58}+q^{56}-q^{50}-2q^{48}-4q^{46}-5q^{44}-6q^{42}-6q^{40}-4q^{38}-q^{36}+2q^{34}+4q^{32}+7q^{30}+6q^{28}+6q^{26}+4q^{24}+3q^{22}+q^{20}+q^{18}$
1,0,0,0	$-q^{36}-q^{34}-2q^{32}-2q^{30}-q^{28}+q^{24}+2q^{22}+3q^{20}+2q^{18}+2q^{16}+q^{14}+q^{12}$

B2 Invariants.

Weight	Invariant
0,1	$-q^{50}-q^{36}-q^{32}-q^{30}+q^{26}+q^{22}+2q^{20}+q^{18}+q^{16}+q^{14}+q^{12}$
1,0	$q^{80}-q^{58}-q^{56}-q^{54}-q^{52}-2q^{50}-q^{48}-q^{46}-q^{44}+q^{38}+q^{36}+2q^{34}+q^{32}+2q^{30}+q^{28}+2q^{26}+q^{24}+q^{22}+q^{18}$

B3 Invariants.

Weight	Invariant
1,0,0	$q^{120}-q^{86}-q^{82}-q^{80}-2q^{78}-q^{76}-2q^{74}-q^{72}-2q^{70}-q^{68}-q^{66}-q^{64}+q^{58}+q^{56}+2q^{54}+q^{52}+3q^{50}+q^{48}+3q^{46}+q^{44}+2q^{42}+q^{40}+2q^{38}+q^{34}+q^{30}$

B4 Invariants.

Weight	Invariant
1,0,0,0	$q^{160}-q^{114}-q^{110}-2q^{106}-q^{104}-2q^{102}-q^{100}-2q^{98}-q^{96}-2q^{94}-q^{92}-2q^{90}-q^{88}-q^{86}+q^{78}+2q^{74}+q^{72}+3q^{70}+q^{68}+3q^{66}+q^{64}+3q^{62}+q^{60}+3q^{58}+q^{56}+2q^{54}+2q^{50}+q^{46}+q^{42}$

C3 Invariants.

Weight	Invariant
1,0,0	$-q^{70}-q^{50}-q^{48}-q^{46}-q^{44}-q^{42}-q^{40}+q^{34}+q^{32}+2q^{30}+2q^{28}+2q^{26}+q^{24}+2q^{22}+q^{20}+q^{18}$

C4 Invariants.

Weight	Invariant
1,0,0,0	$-q^{90}-q^{64}-q^{62}-2q^{60}-q^{58}-q^{56}-q^{54}-q^{52}-q^{50}-q^{48}+q^{44}+2q^{42}+2q^{40}+2q^{38}+2q^{36}+2q^{34}+2q^{32}+2q^{30}+2q^{28}+q^{26}+q^{24}$

D4 Invariants.

Weight	Invariant
0,1,0,0	$q^{120}-q^{100}-q^{98}-3q^{96}-3q^{94}-q^{92}-q^{90}+2q^{88}+6q^{86}+9q^{84}+11q^{82}+14q^{80}+11q^{78}+9q^{76}+3q^{74}-4q^{72}-12q^{70}-18q^{68}-24q^{66}-27q^{64}-27q^{62}-24q^{60}-17q^{58}-11q^{56}+7q^{52}+14q^{50}+19q^{48}+22q^{46}+19q^{44}+19q^{42}+14q^{40}+10q^{38}+6q^{36}+4q^{34}+q^{32}+q^{30}$
1,0,0,0	$q^{70}-q^{50}-q^{48}-3q^{46}-3q^{44}-3q^{42}-3q^{40}-2q^{38}+q^{34}+3q^{32}+4q^{30}+4q^{28}+4q^{26}+3q^{24}+2q^{22}+q^{20}+q^{18}$

G2 Invariants.

Weight

Invariant

0,1

q^{240}-q^{198}-q^{192}+q^{178}+q^{176}+q^{172}+2q^{170}+q^{168}+q^{166}+q^{164}+q^{162}+2q^{160}+q^{158}+q^{154}+q^{152}-q^{148}-q^{146}-q^{144}-q^{142}-2q^{140}-3q^{138}-2q^{136}-2q^{134}-3q^{132}-4q^{130}-4q^{128}-3q^{126}-3q^{124}-4q^{122}-4q^{120}-3q^{118}-2q^{116}-2q^{114}-3q^{112}-2q^{110}+q^{102}+q^{100}+2q^{98}+3q^{96}+2q^{94}+2q^{92}+4q^{90}+3q^{88}+3q^{86}+4q^{84}+3q^{82}+3q^{80}+4q^{78}+2q^{76}+2q^{74}+3q^{72}+2q^{70}+q^{68}+2q^{66}+q^{64}+q^{62}+q^{60}+q^{54}

1,0

q^{120}-q^{100}-q^{98}-q^{92}-q^{90}-q^{88}-q^{82}-q^{80}-q^{78}-q^{72}+q^{58}+q^{56}+q^{52}+2q^{50}+q^{48}+q^{46}+q^{44}+q^{42}+2q^{40}+q^{38}+q^{34}+q^{32}+q^{30}

.

Computer Talk

The above data is available with the Mathematica package KnotTheory`, as shown in the (simulated) Mathematica session below. Your input (in red) is realistic; all else should have the same content as in a real mathematica session, but with different formatting. This Mathematica session is also available (albeit only for the knot 5_2) as the notebook PolynomialInvariantsSession.nb.

(The path below may be different on your system, and possibly also the KnotTheory` date)

In[1]:= AppendTo[$Path, "C:/drorbn/projects/KAtlas/"]; << KnotTheory`

Loading KnotTheory` version of August 31, 2006, 11:25:27.5625.

In[3]:= K = Knot["5 1"];

In[4]:= Alexander[K][t]

KnotTheory::loading: Loading precomputed data in PD4Knots`.

Out[4]= $t^{2}+t^{-2}-t-t^{-1}+1$

In[5]:= Conway[K][z]

Out[5]= $z^{4}+3z^{2}+1$

In[6]:= Alexander[K, 2][t]

KnotTheory::credits: The program Alexander[K, r] to compute Alexander ideals was written by Jana Archibald at the University of Toronto in the summer of 2005.

Out[6]= $\{1\}$

In[7]:= {KnotDet[K], KnotSignature[K]}

Out[7]= { 5, -4 }

In[8]:= Jones[K][q]

KnotTheory::loading: Loading precomputed data in Jones4Knots`.

Out[8]= $-q^{-7}+q^{-6}-q^{-5}+q^{-4}+q^{-2}$

In[9]:= HOMFLYPT[K][a, z]

KnotTheory::credits: The HOMFLYPT program was written by Scott Morrison.

Out[9]= $a^{6}\left(-z^{2}\right)-2a^{6}+a^{4}z^{4}+4a^{4}z^{2}+3a^{4}$

In[10]:= Kauffman[K][a, z]

KnotTheory::loading: Loading precomputed data in Kauffman4Knots`.

Out[10]= $a^{9}z+a^{8}z^{2}+a^{7}z^{3}-a^{7}z+a^{6}z^{4}-3a^{6}z^{2}+2a^{6}+a^{5}z^{3}-2a^{5}z+a^{4}z^{4}-4a^{4}z^{2}+3a^{4}$

"Similar" Knots (within the Atlas)

Same Alexander/Conway Polynomial: {[[0_1]], [[K11n34]], [[K11n42]], }

Same Jones Polynomial (up to mirroring, $q\leftrightarrow q^{-1}$ ): {}

Computer Talk

The above data is available with the Mathematica package KnotTheory`. Your input (in red) is realistic; all else should have the same content as in a real mathematica session, but with different formatting.

(The path below may be different on your system, and possibly also the KnotTheory` date)

In[1]:= AppendTo[$Path, "C:/drorbn/projects/KAtlas/"]; << KnotTheory`

Loading KnotTheory` version of May 31, 2006, 14:15:20.091.

In[3]:= K = Knot["5 1"];

In[4]:= {A = Alexander[K][t], J = Jones[K][q]}

KnotTheory::loading: Loading precomputed data in PD4Knots`.

KnotTheory::loading: Loading precomputed data in Jones4Knots`.

Out[4]= { $t^{2}+t^{-2}-t-t^{-1}+1$ , $-q^{-7}+q^{-6}-q^{-5}+q^{-4}+q^{-2}$ }

In[5]:= DeleteCases[Select[AllKnots[], (A === Alexander[#][t]) &], K]

KnotTheory::loading: Loading precomputed data in DTCode4KnotsTo11`.

KnotTheory::credits: The GaussCode to PD conversion was written by Siddarth Sankaran at the University of Toronto in the summer of 2005.

Out[5]= {[[0_1]], [[K11n34]], [[K11n42]], }

In[6]:= DeleteCases[ Select[ AllKnots[], (J === Jones[#][q] || (J /. q -> 1/q) === Jones[#][q]) & ], K ]

KnotTheory::loading: Loading precomputed data in Jones4Knots11`.

Out[6]= {}

Vassiliev invariants

V₂ and V₃:

(3, -5)

V_2,1 through V_6,9:

V_2,1

V_3,1

V_4,1

V_4,2

V_4,3

V_5,1

V_5,2

V_5,3

V_5,4

V_6,1

V_6,2

V_6,3

V_6,4

V_6,5

V_6,6

V_6,7

V_6,8

V_6,9

12

-40

72

174

26

-480

-{\frac {2512}{3}}

-{\frac {448}{3}}

-104

288

800

2088

312

{\frac {41151}{10}}

{\frac {2494}{15}}

{\frac {7634}{5}}

{\frac {43}{2}}

{\frac {1951}{10}}

V_2,1 through V_6,9 were provided by Petr Dunin-Barkowski <barkovs@itep.ru>, Andrey Smirnov <asmirnov@itep.ru>, and Alexei Sleptsov <sleptsov@itep.ru> and uploaded on October 2010 by User:Drorbn. Note that they are normalized differently than V₂ and V₃.

Khovanov Homology

The coefficients of the monomials

t^{r}q^{j}

are shown, along with their alternating sums

\chi

(fixed

j

, alternation over

r

). The squares with yellow highlighting are those on the "critical diagonals", where

j-2r=s+1

or

j-2r=s-1

, where

s=

-4 is the signature of 5 1. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

\		r
	\
j		\

-5

-4

-3

-2

-1

0

χ

-3

1

-5

1

-7

1

-9

0

-11

1

0

-13

0

-15

1

-1

Integral Khovanov Homology

(db, data source)

$\dim {\mathcal {G}}_{2r+i}\operatorname {KH} _{\mathbb {Z} }^{r}$	$i=-5$	$i=-3$
$r=-5$	${\mathbb {Z} }$
$r=-4$	${\mathbb {Z} }_{2}$	${\mathbb {Z} }$
$r=-3$	${\mathbb {Z} }$
$r=-2$	${\mathbb {Z} }_{2}$	${\mathbb {Z} }$
$r=-1$
$r=0$	${\mathbb {Z} }$	${\mathbb {Z} }$

The Coloured Jones Polynomials

The Coloured Jones Polynomials (in the

n+1

-dimensional representation of

sl(2)

)

$n$	$J_{n}$
2	${\textrm {Apart}}\left[{\frac {{\textrm {Hold}}\left[{\textrm {REngine}}\left({\textrm {MorseLink}}({\textrm {MorseLink::Error:badinput}}),\left({\begin{array}{ccccccccc}q&0&0&0&0&0&0&0&0\\0&0&0&q^{2}&0&0&0&0&0\\0&0&0&0&0&0&q^{3}&0&0\\0&q^{2}&0&q-q^{3}&0&0&0&0&0\\0&0&0&0&q^{2}&0&-(q-1)\left(q^{5/4}+{\sqrt[{4}]{q}}\right)^{2}&0&0\\0&0&0&0&0&0&0&q^{2}&0\\0&0&q^{3}&0&q^{5/2}-q^{7/2}&0&(q-1)^{2}q(q+1)&0&0\\0&0&0&0&0&q^{2}&0&q-q^{3}&0\\0&0&0&0&0&0&0&0&q\end{array}}\right),\left({\begin{array}{ccccccccc}{\frac {1}{q}}&0&0&0&0&0&0&0&0\\0&{\frac {q^{2}-1}{q^{3}}}&0&{\frac {1}{q^{2}}}&0&0&0&0&0\\0&0&{\frac {(q-1)^{2}(q+1)}{q^{4}}}&0&{\frac {q-1}{q^{5/2}}}&0&{\frac {1}{q^{3}}}&0&0\\0&{\frac {1}{q^{2}}}&0&0&0&0&0&0&0\\0&0&{\frac {(q-1)(q+1)^{2}}{q^{9/2}}}&0&{\frac {1}{q^{2}}}&0&0&0&0\\0&0&0&0&0&{\frac {q^{2}-1}{q^{3}}}&0&{\frac {1}{q^{2}}}&0\\0&0&{\frac {1}{q^{3}}}&0&0&0&0&0&0\\0&0&0&0&0&{\frac {1}{q^{2}}}&0&0&0\\0&0&0&0&0&0&0&0&{\frac {1}{q}}\end{array}}\right),\left({\begin{array}{ccc}0&0&{\frac {1}{\sqrt {q}}}\\0&1&0\\{\sqrt {q}}&0&0\end{array}}\right),\left({\begin{array}{ccc}0&0&{\frac {1}{\sqrt {q}}}\\0&1&0\\{\sqrt {q}}&0&0\end{array}}\right),\left({\begin{array}{ccc}0&0&{\frac {1}{\sqrt {q}}}\\0&1&0\\{\sqrt {q}}&0&0\end{array}}\right),\left({\begin{array}{ccc}0&0&{\frac {1}{\sqrt {q}}}\\0&1&0\\{\sqrt {q}}&0&0\end{array}}\right)\right)\right]}{q+{\frac {1}{q}}+1}}\right]$
3	${\textrm {Apart}}\left[{\frac {{\textrm {Hold}}\left[{\textrm {REngine}}\left({\textrm {MorseLink}}({\textrm {MorseLink::Error:badinput}}),\left({\begin{array}{cccccccccccccccc}q^{3/2}&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0\\0&0&0&0&q^{3}&0&0&0&0&0&0&0&0&0&0&0\\0&0&0&0&0&0&0&0&q^{9/2}&0&0&0&0&0&0&0\\0&0&0&0&0&0&0&0&0&0&0&0&q^{6}&0&0&0\\0&q^{3}&0&0&q^{3/2}-q^{9/2}&0&0&0&0&0&0&0&0&0&0&0\\0&0&0&0&0&q^{7/2}&0&0&-q^{3/2}(q+1)\left(q^{3}-1\right)&0&0&0&0&0&0&0\\0&0&0&0&0&0&0&0&0&q^{4}&0&0&-(q-1)q^{3/2}\left(q^{2}+q+1\right)^{2}&0&0&0\\0&0&0&0&0&0&0&0&0&0&0&0&0&q^{9/2}&0&0\\0&0&q^{9/2}&0&0&q^{7/2}-q^{11/2}&0&0&q^{13/2}-q^{9/2}-q^{7/2}+q^{3/2}&0&0&0&0&0&0&0\\0&0&0&0&0&0&q^{4}&0&0&-(q-1)q^{5/2}(q+1)^{2}&0&0&(q+1)\left(q^{3}-1\right)^{2}&0&0&0\\0&0&0&0&0&0&0&0&0&0&q^{7/2}&0&0&-q^{3/2}(q+1)\left(q^{3}-1\right)&0&0\\0&0&0&0&0&0&0&0&0&0&0&0&0&0&q^{3}&0\\0&0&0&q^{6}&0&0&q^{11/2}-q^{13/2}&0&0&(q-1)^{2}q^{4}(q+1)&0&0&-(q-1)^{3}q^{3/2}(q+1)\left(q^{2}+q+1\right)&0&0&0\\0&0&0&0&0&0&0&q^{9/2}&0&0&q^{7/2}-q^{11/2}&0&0&q^{13/2}-q^{9/2}-q^{7/2}+q^{3/2}&0&0\\0&0&0&0&0&0&0&0&0&0&0&q^{3}&0&0&q^{3/2}-q^{9/2}&0\\0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&q^{3/2}\end{array}}\right),\left({\begin{array}{cccccccccccccccc}{\frac {1}{q^{3/2}}}&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0\\0&{\frac {q^{3}-1}{q^{9/2}}}&0&0&{\frac {1}{q^{3}}}&0&0&0&0&0&0&0&0&0&0&0\\0&0&{\frac {q^{5}-q^{3}-q^{2}+1}{q^{13/2}}}&0&0&{\frac {q^{2}-1}{q^{9/2}}}&0&0&{\frac {1}{q^{9/2}}}&0&0&0&0&0&0&0\\0&0&0&{\frac {(q-1)^{3}(q+1)\left(q^{2}+q+1\right)}{q^{15/2}}}&0&0&{\frac {(q-1)^{2}(q+1)}{q^{5}}}&0&0&{\frac {q-1}{q^{9/2}}}&0&0&{\frac {1}{q^{6}}}&0&0&0\\0&{\frac {1}{q^{3}}}&0&0&0&0&0&0&0&0&0&0&0&0&0&0\\0&0&{\frac {(q+1)\left(q^{3}-1\right)}{q^{13/2}}}&0&0&{\frac {1}{q^{7/2}}}&0&0&0&0&0&0&0&0&0&0\\0&0&0&{\frac {(q+1)\left(q^{3}-1\right)^{2}}{q^{9}}}&0&0&{\frac {(q-1)(q+1)^{2}}{q^{11/2}}}&0&0&{\frac {1}{q^{4}}}&0&0&0&0&0&0\\0&0&0&0&0&0&0&{\frac {q^{5}-q^{3}-q^{2}+1}{q^{13/2}}}&0&0&{\frac {q^{2}-1}{q^{9/2}}}&0&0&{\frac {1}{q^{9/2}}}&0&0\\0&0&{\frac {1}{q^{9/2}}}&0&0&0&0&0&0&0&0&0&0&0&0&0\\0&0&0&{\frac {(q-1)\left(q^{2}+q+1\right)^{2}}{q^{17/2}}}&0&0&{\frac {1}{q^{4}}}&0&0&0&0&0&0&0&0&0\\0&0&0&0&0&0&0&{\frac {(q+1)\left(q^{3}-1\right)}{q^{13/2}}}&0&0&{\frac {1}{q^{7/2}}}&0&0&0&0&0\\0&0&0&0&0&0&0&0&0&0&0&{\frac {q^{3}-1}{q^{9/2}}}&0&0&{\frac {1}{q^{3}}}&0\\0&0&0&{\frac {1}{q^{6}}}&0&0&0&0&0&0&0&0&0&0&0&0\\0&0&0&0&0&0&0&{\frac {1}{q^{9/2}}}&0&0&0&0&0&0&0&0\\0&0&0&0&0&0&0&0&0&0&0&{\frac {1}{q^{3}}}&0&0&0&0\\0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&{\frac {1}{q^{3/2}}}\end{array}}\right),\left({\begin{array}{cccc}0&0&0&{\frac {1}{q^{3/4}}}\\0&0&{\frac {1}{\sqrt[{4}]{q}}}&0\\0&{\sqrt[{4}]{q}}&0&0\\q^{3/4}&0&0&0\end{array}}\right),\left({\begin{array}{cccc}0&0&0&{\frac {1}{q^{3/4}}}\\0&0&{\frac {1}{\sqrt[{4}]{q}}}&0\\0&{\sqrt[{4}]{q}}&0&0\\q^{3/4}&0&0&0\end{array}}\right),\left({\begin{array}{cccc}0&0&0&{\frac {1}{q^{3/4}}}\\0&0&{\frac {1}{\sqrt[{4}]{q}}}&0\\0&{\sqrt[{4}]{q}}&0&0\\q^{3/4}&0&0&0\end{array}}\right),\left({\begin{array}{cccc}0&0&0&{\frac {1}{q^{3/4}}}\\0&0&{\frac {1}{\sqrt[{4}]{q}}}&0\\0&{\sqrt[{4}]{q}}&0&0\\q^{3/4}&0&0&0\end{array}}\right)\right)\right]}{q^{3/2}+{\sqrt {q}}+{\frac {1}{\sqrt {q}}}+{\frac {1}{q^{3/2}}}}}\right]$
4	Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. TeX parse error: MathJax internal buffer size exceeded; is there a recursive macro call?"): {\displaystyle {\textrm {Apart}}\left[{\frac {{\textrm {Hold}}\left[{\textrm {REngine}}\left({\textrm {MorseLink}}({\textrm {MorseLink::Error:badinput}}),\left({\begin{array}{ccccccccccccccccccccccccc}q^{2}&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0\\0&0&0&0&0&q^{4}&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0\\0&0&0&0&0&0&0&0&0&0&q^{6}&0&0&0&0&0&0&0&0&0&0&0&0&0&0\\0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&q^{8}&0&0&0&0&0&0&0&0&0\\0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&q^{10}&0&0&0&0\\0&q^{4}&0&0&0&q^{2}-q^{6}&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0\\0&0&0&0&0&0&q^{5}&0&0&0&-q^{15/2}-q^{13/2}+q^{7/2}+q^{5/2}&0&0&0&0&0&0&0&0&0&0&0&0&0&0\\0&0&0&0&0&0&0&0&0&0&0&q^{6}&0&0&0&-q^{3}\left(q^{2}+q+1\right)\left(q^{4}-1\right)&0&0&0&0&0&0&0&0&0\\0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&q^{7}&0&0&0&-(q-1)q^{7/2}\left(q^{3}+q^{2}+q+1\right)^{2}&0&0&0&0\\0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&q^{8}&0&0&0\\0&0&q^{6}&0&0&0&q^{9/2}-q^{15/2}&0&0&0&q^{9}-q^{6}-q^{5}+q^{2}&0&0&0&0&0&0&0&0&0&0&0&0&0&0\\0&0&0&0&0&0&0&q^{6}&0&0&0&-q^{4}(q+1)\left(q^{3}-1\right)&0&0&0&q\left(q^{3}-1\right)^{2}\left(q^{3}+q^{2}+q+1\right)&0&0&0&0&0&0&0&0&0\\0&0&0&0&0&0&0&0&0&0&0&0&q^{6}&0&0&0&-(q-1)q^{7/2}\left(q^{2}+q+1\right)^{2}&0&0&0&(q+1)\left(q^{5}+q^{3}-q^{2}-1\right)^{2}&0&0&0&0\\0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&q^{6}&0&0&0&-q^{3}\left(q^{2}+q+1\right)\left(q^{4}-1\right)&0&0&0\\0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&q^{6}&0&0\\0&0&0&q^{8}&0&0&0&q^{7}-q^{9}&0&0&0&q^{10}-q^{8}-q^{7}+q^{5}&0&0&0&-(q-1)^{3}q^{2}(q+1)^{2}\left(q^{2}+1\right)\left(q^{2}+q+1\right)&0&0&0&0&0&0&0&0&0\\0&0&0&0&0&0&0&0&q^{7}&0&0&0&-(q-1)q^{11/2}(q+1)^{2}&0&0&0&q^{3}(q+1)\left(q^{3}-1\right)^{2}&0&0&0&-{\frac {\left(q^{2}-1\right)^{3}\left(q^{2}+1\right)^{2}\left(q^{2}+q+1\right)}{\sqrt {q}}}&0&0&0&0\\0&0&0&0&0&0&0&0&0&0&0&0&0&q^{6}&0&0&0&-q^{4}(q+1)\left(q^{3}-1\right)&0&0&0&q\left(q^{3}-1\right)^{2}\left(q^{3}+q^{2}+q+1\right)&0&0&0\\0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&q^{5}&0&0&0&-q^{15/2}-q^{13/2}+q^{7/2}+q^{5/2}&0&0\\0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&q^{4}&0\\0&0&0&0&q^{10}&0&0&0&q^{19/2}-q^{21/2}&0&0&0&(q-1)^{2}q^{8}(q+1)&0&0&0&-(q-1)^{3}q^{11/2}(q+1)\left(q^{2}+q+1\right)&0&0&0&(q-1)^{4}q^{2}(q+1)^{2}\left(q^{2}+1\right)\left(q^{2}+q+1\right)&0&0&0&0\\0&0&0&0&0&0&0&0&0&q^{8}&0&0&0&q^{7}-q^{9}&0&0&0&q^{10}-q^{8}-q^{7}+q^{5}&0&0&0&-(q-1)^{3}q^{2}(q+1)^{2}\left(q^{2}+1\right)\left(q^{2}+q+1\right)&0&0&0\\0&0&0&0&0&0&0&0&0&0&0&0&0&0&q^{6}&0&0&0&q^{9/2}-q^{15/2}&0&0&0&q^{9}-q^{6}-q^{5}+q^{2}&0&0\\0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&q^{4}&0&0&0&q^{2}-q^{6}&0\\0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&q^{2}\end{array}}\right),\left({\begin{array}{ccccccccccccccccccccccccc}{\frac {1}{q^{2}}}&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0\\0&{\frac {q^{4}-1}{q^{6}}}&0&0&0&{\frac {1}{q^{4}}}&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0\\0&0&{\frac {q^{7}-q^{4}-q^{3}+1}{q^{9}}}&0&0&0&{\frac {q^{3}-1}{q^{13/2}}}&0&0&0&{\frac {1}{q^{6}}}&0&0&0&0&0&0&0&0&0&0&0&0&0&0\\0&0&0&{\frac {(q-1)^{3}(q+1)^{2}\left(q^{2}+1\right)\left(q^{2}+q+1\right)}{q^{11}}}&0&0&0&{\frac {q^{5}-q^{3}-q^{2}+1}{q^{8}}}&0&0&0&{\frac {q^{2}-1}{q^{7}}}&0&0&0&{\frac {1}{q^{8}}}&0&0&0&0&0&0&0&0&0\\0&0&0&0&{\frac {(q-1)^{4}(q+1)^{2}\left(q^{2}+1\right)\left(q^{2}+q+1\right)}{q^{12}}}&0&0&0&{\frac {(q-1)^{3}(q+1)\left(q^{2}+q+1\right)}{q^{17/2}}}&0&0&0&{\frac {(q-1)^{2}(q+1)}{q^{7}}}&0&0&0&{\frac {q-1}{q^{15/2}}}&0&0&0&{\frac {1}{q^{10}}}&0&0&0&0\\0&{\frac {1}{q^{4}}}&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0\\0&0&{\frac {q^{5}+q^{4}-q-1}{q^{17/2}}}&0&0&0&{\frac {1}{q^{5}}}&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0\\0&0&0&{\frac {\left(q^{3}-1\right)^{2}\left(q^{3}+q^{2}+q+1\right)}{q^{12}}}&0&0&0&{\frac {(q+1)\left(q^{3}-1\right)}{q^{8}}}&0&0&0&{\frac {1}{q^{6}}}&0&0&0&0&0&0&0&0&0&0&0&0&0\\0&0&0&0&{\frac {\left(q^{2}-1\right)^{3}\left(q^{2}+1\right)^{2}\left(q^{2}+q+1\right)}{q^{29/2}}}&0&0&0&{\frac {(q+1)\left(q^{3}-1\right)^{2}}{q^{10}}}&0&0&0&{\frac {(q-1)(q+1)^{2}}{q^{15/2}}}&0&0&0&{\frac {1}{q^{7}}}&0&0&0&0&0&0&0&0\\0&0&0&0&0&0&0&0&0&{\frac {(q-1)^{3}(q+1)^{2}\left(q^{2}+1\right)\left(q^{2}+q+1\right)}{q^{11}}}&0&0&0&{\frac {q^{5}-q^{3}-q^{2}+1}{q^{8}}}&0&0&0&{\frac {q^{2}-1}{q^{7}}}&0&0&0&{\frac {1}{q^{8}}}&0&0&0\\0&0&{\frac {1}{q^{6}}}&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0\\0&0&0&{\frac {\left(q^{2}+q+1\right)\left(q^{4}-1\right)}{q^{11}}}&0&0&0&{\frac {1}{q^{6}}}&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0\\0&0&0&0&{\frac {(q+1)\left(q^{5}+q^{3}-q^{2}-1\right)^{2}}{q^{15}}}&0&0&0&{\frac {(q-1)\left(q^{2}+q+1\right)^{2}}{q^{19/2}}}&0&0&0&{\frac {1}{q^{6}}}&0&0&0&0&0&0&0&0&0&0&0&0\\0&0&0&0&0&0&0&0&0&{\frac {\left(q^{3}-1\right)^{2}\left(q^{3}+q^{2}+q+1\right)}{q^{12}}}&0&0&0&{\frac {(q+1)\left(q^{3}-1\right)}{q^{8}}}&0&0&0&{\frac {1}{q^{6}}}&0&0&0&0&0&0&0\\0&0&0&0&0&0&0&0&0&0&0&0&0&0&{\frac {q^{7}-q^{4}-q^{3}+1}{q^{9}}}&0&0&0&{\frac {q^{3}-1}{q^{13/2}}}&0&0&0&{\frac {1}{q^{6}}}&0&0\\0&0&0&{\frac {1}{q^{8}}}&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0\\0&0&0&0&{\frac {(q-1)\left(q^{3}+q^{2}+q+1\right)^{2}}{q^{27/2}}}&0&0&0&{\frac {1}{q^{7}}}&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0\\0&0&0&0&0&0&0&0&0&{\frac {\left(q^{2}+q+1\right)\left(q^{4}-1\right)}{q^{11}}}&0&0&0&{\frac {1}{q^{6}}}&0&0&0&0&0&0&0&0&0&0&0\\0&0&0&0&0&0&0&0&0&0&0&0&0&0&{\frac {q^{5}+q^{4}-q-1}{q^{17/2}}}&0&0&0&{\frac {1}{q^{5}}}&0&0&0&0&0&0\\0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&{\frac {q^{4}-1}{q^{6}}}&0&0&0&{\frac {1}{q^{4}}}&0\\0&0&0&0&{\frac {1}{q^{10}}}&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0\\0&0&0&0&0&0&0&0&0&{\frac {1}{q^{8}}}&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0\\0&0&0&0&0&0&0&0&0&0&0&0&0&0&{\frac {1}{q^{6}}}&0&0&0&0&0&0&0&0&0&0\\0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&{\frac {1}{q^{4}}}&0&0&0&0&0\\0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&{\frac {1}{q^{2}}}\end{array}}\right),\left({\begin{array}{ccccc}0&0&0&0&{\frac {1}{q}}\\0&0&0&{\frac {1}{\sqrt {q}}}&0\\0&0&1&0&0\\0&{\sqrt {q}}&0&0&0\\q&0&0&0&0\end{array}}\right),\left({\begin{array}{ccccc}0&0&0&0&{\frac {1}{q}}\\0&0&0&{\frac {1}{\sqrt {q}}}&0\\0&0&1&0&0\\0&{\sqrt {q}}&0&0&0\\q&0&0&0&0\end{array}}\right),\left({\begin{array}{ccccc}0&0&0&0&{\frac {1}{q}}\\0&0&0&{\frac {1}{\sqrt {q}}}&0\\0&0&1&0&0\\0&{\sqrt {q}}&0&0&0\\q&0&0&0&0\end{array}}\right),\left({\begin{array}{ccccc}0&0&0&0&{\frac {1}{q}}\\0&0&0&{\frac {1}{\sqrt {q}}}&0\\0&0&1&0&0\\0&{\sqrt {q}}&0&0&0\\q&0&0&0&0\end{array}}\right)\right)\right]}{q^{2}+q+1+{\frac {1}{q}}+{\frac {1}{q^{2}}}}}\right]}
5	Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. TeX parse error: MathJax internal buffer size exceeded; is there a recursive macro call?"): {\displaystyle {\textrm {Apart}}\left[{\frac {{\textrm {Hold}}\left[{\textrm {REngine}}\left({\textrm {MorseLink}}({\textrm 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6	Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. TeX parse error: MathJax internal buffer size exceeded; is there a recursive macro call?"): {\displaystyle {\textrm {Apart}}\left[{\frac {{\textrm {Hold}}\left[{\textrm {REngine}}\left({\textrm {MorseLink}}({\textrm 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7	Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. TeX parse error: MathJax internal buffer size exceeded; is there a recursive macro call?"): {\displaystyle {\textrm {Apart}}\left[{\frac {{\textrm {Hold}}\left[{\textrm {REngine}}\left({\textrm {MorseLink}}({\textrm 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{(q-1)^{2}\left(q^{2}+1\right)\left(q^{4}+q^{3}+q^{2}+q+1\right)\left(q^{5}+q^{4}+q^{3}+q^{2}+q+1\right)\left(q^{6}+q^{5}+q^{4}+q^{3}+q^{2}+q+1\right)}{q^{30}}}&0&0&0&0&0&0&{\frac {(q-1)(q+1)^{2}\left(q^{2}+1\right)\left(q^{4}+q^{2}+1\right)}{q^{43/2}}}&0&0&0&0&0&0&{\frac {1}{q^{15}}}&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0\\0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&{\frac {\left(q^{2}+1\right)\left(q^{3}-1\right)^{2}\left(q^{3}+1\right)\left(q^{6}+q^{5}+q^{4}+q^{3}+q^{2}+q+1\right)}{q^{51/2}}}&0&0&0&0&0&0&{\frac {\left(q^{2}+q+1\right)^{2}\left(q^{4}-q^{3}+q-1\right)}{q^{37/2}}}&0&0&0&0&0&0&{\frac {1}{q^{27/2}}}&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0\\0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&{\frac {\left(q^{3}-1\right)^{2}\left(q^{3}+1\right)\left(q^{6}+q^{5}+q^{4}+q^{3}+q^{2}+q+1\right)}{q^{21}}}&0&0&0&0&0&0&{\frac {q^{7}+q^{6}-q-1}{q^{31/2}}}&0&0&0&0&0&0&{\frac {1}{q^{12}}}&0&0&0&0&0&0&0&0&0&0\\0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&{\frac {q^{13}-q^{7}-q^{6}+1}{q^{33/2}}}&0&0&0&0&0&0&{\frac {q^{6}-1}{q^{25/2}}}&0&0&0&0&0&0&{\frac {1}{q^{21/2}}}&0&0\\0&0&0&0&0&0&{\frac {1}{q^{49/2}}}&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0\\0&0&0&0&0&0&0&{\frac {\left(q^{7}-1\right)^{2}}{(q-1)q^{69/2}}}&0&0&0&0&0&0&{\frac {1}{q^{22}}}&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0\\0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&{\frac {\left(q^{5}+q^{4}+q^{3}+q^{2}+q+1\right)\left(q^{7}-1\right)}{q^{61/2}}}&0&0&0&0&0&0&{\frac {1}{q^{39/2}}}&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0\\0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&0&{\frac {\left(q^{4}+q^{3}+q^{2}+q+1\right)\left(q^{7}-1\right)}{q^{53/2}}}&0&0&0&0&0&0&{\frac 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{1}{\sqrt[{4}]{q}}}&0&0&0\\0&0&0&{\sqrt[{4}]{q}}&0&0&0&0\\0&0&q^{3/4}&0&0&0&0&0\\0&q^{5/4}&0&0&0&0&0&0\\q^{7/4}&0&0&0&0&0&0&0\end{array}}\right),\left({\begin{array}{cccccccc}0&0&0&0&0&0&0&{\frac {1}{q^{7/4}}}\\0&0&0&0&0&0&{\frac {1}{q^{5/4}}}&0\\0&0&0&0&0&{\frac {1}{q^{3/4}}}&0&0\\0&0&0&0&{\frac {1}{\sqrt[{4}]{q}}}&0&0&0\\0&0&0&{\sqrt[{4}]{q}}&0&0&0&0\\0&0&q^{3/4}&0&0&0&0&0\\0&q^{5/4}&0&0&0&0&0&0\\q^{7/4}&0&0&0&0&0&0&0\end{array}}\right)\right)\right]}{q^{7/2}+q^{5/2}+q^{3/2}+{\sqrt {q}}+{\frac {1}{\sqrt {q}}}+{\frac {1}{q^{3/2}}}+{\frac {1}{q^{5/2}}}+{\frac {1}{q^{7/2}}}}}\right]}

Computer Talk

Much of the above data can be recomputed by Mathematica using the package KnotTheory`. See A Sample KnotTheory` Session, or any of the Computer Talk sections above.

Modifying This Page

Read me first: Modifying Knot Pages

See/edit the Rolfsen Knot Page master template (intermediate).

See/edit the Rolfsen_Splice_Base (expert).

Back to the top.

4_1

5_2

5 1: Difference between revisions

Revision as of 05:11, 3 March 2013

Contents

Knot presentations

Three dimensional invariants

Four dimensional invariants

Polynomial invariants

"Similar" Knots (within the Atlas)

Vassiliev invariants

Khovanov Homology

The Coloured Jones Polynomials

Computer Talk

Modifying This Page

Navigation menu

Page actions

Page actions

Personal tools

Navigation

Search

Tools

@@ Line 1: / Line 1: @@
 <!--                       WARNING! WARNING! WARNING!
-<!-- This page was generated from the splice base [[Rolfsen_Splice_Base]]. Please do not edit!
+<!-- This page was generated from the splice template [[Rolfsen_Splice_Base]]. Please do not edit!
 <!-- You probably want to edit the template referred to immediately below. (See [[Category:Knot Page Template]].)
 <!-- This page itself was created by running [[Media:KnotPageSpliceRobot.nb]] on [[Rolfsen_Splice_Base]]. -->
@@ Line 6: / Line 6: @@
 <!--  -->
 {{Rolfsen Knot Page|
-n = 5 |
+n = <math>n</math> |
-k = 1 |
+k = <math>k</math> |
+same_alexander  = <nowiki>[[0_1]], [[K11n34]], [[K11n42]], </nowiki> |
-KnotilusURL = http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/-1,4,-2,5,-3,1,-4,2,-5,3/goTop.html |
+same_jones      =  |
-braid_table     = <table cellspacing=0 cellpadding=0 border=0>
+coloured_jones_2 = <math>\textrm{Apart}\left[\frac{\textrm{Hold}\left[\textrm{REngine}\left(\textrm{MorseLink}(\textrm{MorseLink::Error: bad input}),\left(
-<tr><td>[[Image:BraidPart3.gif]][[Image:BraidPart3.gif]][[Image:BraidPart3.gif]][[Image:BraidPart3.gif]][[Image:BraidPart3.gif]]</td></tr>
+\begin{array}{ccccccccc}
-<tr><td>[[Image:BraidPart4.gif]][[Image:BraidPart4.gif]][[Image:BraidPart4.gif]][[Image:BraidPart4.gif]][[Image:BraidPart4.gif]]</td></tr>
+ q & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
-</table> |
+& 0 & 0 & q^2 & 0 & 0 & 0 & 0 & 0 \\
-braid_crossings = 5 |
+& 0 & 0 & 0 & 0 & 0 & q^3 & 0 & 0 \\
-braid_width     = 2 |
+& q^2 & 0 & q-q^3 & 0 & 0 & 0 & 0 & 0 \\
-braid_index     = 2 |
+& 0 & 0 & 0 & q^2 & 0 & -(q-1) \left(q^{5/4}+\sqrt[4]{q}\right)^2 & 0 & 0 \\
-same_alexander  = [[10_132]],  |
+& 0 & 0 & 0 & 0 & 0 & 0 & q^2 & 0 \\
-same_jones      = [[10_132]],  |
+& 0 & q^3 & 0 & q^{5/2}-q^{7/2} & 0 & (q-1)^2 q (q+1) & 0 & 0 \\
-khovanov_table  = <table border=1>
+& 0 & 0 & 0 & 0 & q^2 & 0 & q-q^3 & 0 \\
-<tr align=center>
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & q
-<td width=20.%><table cellpadding=0 cellspacing=0>
+\end{array}
-  <tr><td>\</td><td>&nbsp;</td><td>r</td></tr>
+\right),\left(
-<tr><td>&nbsp;</td><td>&nbsp;\&nbsp;</td><td>&nbsp;</td></tr>
+\begin{array}{ccccccccc}
-<tr><td>j</td><td>&nbsp;</td><td>\</td></tr>
+ \frac{1}{q} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
-</table></td>
+& \frac{q^2-1}{q^3} & 0 & \frac{1}{q^2} & 0 & 0 & 0 & 0 & 0 \\
-  <td width=10.%>-5</td    ><td width=10.%>-4</td    ><td width=10.%>-3</td    ><td width=10.%>-2</td    ><td width=10.%>-1</td    ><td width=10.%>0</td    ><td width=20.%>&chi;</td></tr>
+& 0 & \frac{(q-1)^2 (q+1)}{q^4} & 0 & \frac{q-1}{q^{5/2}} & 0 & \frac{1}{q^3} & 0 & 0 \\
-<tr align=center><td>-3</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>1</td><td>1</td></tr>
+& \frac{1}{q^2} & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
-<tr align=center><td>-5</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>&nbsp;</td><td bgcolor=yellow>1</td><td>1</td></tr>
+& 0 & \frac{(q-1) (q+1)^2}{q^{9/2}} & 0 & \frac{1}{q^2} & 0 & 0 & 0 & 0 \\
-<tr align=center><td>-7</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>1</td><td bgcolor=yellow>&nbsp;</td><td>&nbsp;</td><td>1</td></tr>
+& 0 & 0 & 0 & 0 & \frac{q^2-1}{q^3} & 0 & \frac{1}{q^2} & 0 \\
-<tr align=center><td>-9</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>&nbsp;</td><td bgcolor=yellow>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>0</td></tr>
+& 0 & \frac{1}{q^3} & 0 & 0 & 0 & 0 & 0 & 0 \\
-<tr align=center><td>-11</td><td>&nbsp;</td><td bgcolor=yellow>1</td><td bgcolor=yellow>1</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>0</td></tr>
+& 0 & 0 & 0 & 0 & \frac{1}{q^2} & 0 & 0 & 0 \\
-<tr align=center><td>-13</td><td bgcolor=yellow>&nbsp;</td><td bgcolor=yellow>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>0</td></tr>
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & \frac{1}{q}
-<tr align=center><td>-15</td><td bgcolor=yellow>1</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>-1</td></tr>
+\end{array}
-</table> |
+\right),\left(
-coloured_jones_2 = <math> q^{-4} + q^{-7} - q^{-9} + q^{-10} - q^{-12} + q^{-13} -2 q^{-15} + q^{-16} - q^{-18} + q^{-19} </math> |
+\begin{array}{ccc}
-coloured_jones_3 = <math> q^{-6} + q^{-10} - q^{-13} + q^{-14} - q^{-17} + q^{-18} - q^{-21} - q^{-25} + q^{-27} - q^{-29} + q^{-31} + q^{-35} - q^{-36} </math> |
+& 0 & \frac{1}{\sqrt{q}} \\
-coloured_jones_4 = <math> q^{-8} + q^{-13} - q^{-17} + q^{-18} - q^{-22} + q^{-23} - q^{-27} + q^{-28} - q^{-29} - q^{-32} + q^{-33} - q^{-34} + q^{-36} - q^{-37} + q^{-38} - q^{-39} + q^{-41} - q^{-42} + q^{-43} - q^{-44} + q^{-45} + q^{-46} - q^{-47} + q^{-48} - q^{-49} + q^{-51} - q^{-52} + q^{-53} - q^{-54} - q^{-57} + q^{-58} </math> |
+& 1 & 0 \\
-coloured_jones_5 = <math> q^{-10} + q^{-16} - q^{-21} + q^{-22} - q^{-27} + q^{-28} - q^{-33} + q^{-34} - q^{-36} - q^{-39} + q^{-40} - q^{-42} + q^{-46} - q^{-48} + q^{-52} - q^{-54} + q^{-57} + q^{-58} - q^{-60} + q^{-63} - q^{-66} + q^{-69} - q^{-72} - q^{-73} + q^{-75} - q^{-79} + q^{-81} + q^{-84} - q^{-85} </math> |
+ \sqrt{q} & 0 & 0
-coloured_jones_6 = <math> q^{-12} + q^{-19} - q^{-25} + q^{-26} - q^{-32} + q^{-33} - q^{-39} + q^{-40} - q^{-43} - q^{-46} + q^{-47} - q^{-50} - q^{-53} +2 q^{-54} - q^{-57} - q^{-60} +2 q^{-61} - q^{-64} - q^{-67} +2 q^{-68} + q^{-69} - q^{-71} - q^{-74} +2 q^{-75} + q^{-76} -2 q^{-78} - q^{-81} +2 q^{-82} + q^{-83} -2 q^{-85} - q^{-88} +2 q^{-89} -2 q^{-92} - q^{-95} +2 q^{-96} + q^{-97} -2 q^{-99} - q^{-102} +2 q^{-103} + q^{-104} - q^{-106} - q^{-109} +2 q^{-110} - q^{-113} - q^{-116} + q^{-117} </math> |
+\end{array}
-coloured_jones_7 = <math> q^{-14} + q^{-22} - q^{-29} + q^{-30} - q^{-37} + q^{-38} - q^{-45} + q^{-46} - q^{-50} - q^{-53} + q^{-54} - q^{-58} - q^{-61} + q^{-62} + q^{-63} - q^{-66} - q^{-69} + q^{-70} + q^{-71} - q^{-74} - q^{-77} + q^{-78} + q^{-79} + q^{-81} - q^{-82} - q^{-85} + q^{-86} + q^{-87} + q^{-89} - q^{-90} - q^{-92} - q^{-93} + q^{-94} + q^{-95} + q^{-97} - q^{-98} - q^{-100} - q^{-101} + q^{-102} + q^{-103} + q^{-105} - q^{-106} - q^{-107} - q^{-108} - q^{-109} + q^{-110} + q^{-111} + q^{-113} - q^{-114} - q^{-115} - q^{-117} + q^{-118} + q^{-119} + q^{-121} - q^{-122} - q^{-123} - q^{-125} + q^{-126} + q^{-127} + q^{-128} + q^{-129} - q^{-130} - q^{-131} - q^{-133} + q^{-134} + q^{-136} + q^{-137} - q^{-138} - q^{-139} - q^{-141} + q^{-142} + q^{-145} - q^{-146} - q^{-147} + q^{-150} + q^{-153} - q^{-154} </math> |
+\right),\left(
-computer_talk =
+\begin{array}{ccc}
-         <table>
+& 0 & \frac{1}{\sqrt{q}} \\
-         <tr valign=top>
+& 1 & 0 \\
-         <td><pre style="color: blue; border: 0px; padding: 0em">In[1]:=&nbsp;&nbsp;&nbsp;&nbsp;</pre></td>
+ \sqrt{q} & 0 & 0
-         <td align=left><pre style="color: red; border: 0px; padding: 0em">&lt;&lt; KnotTheory`</pre></td>
+\end{array}
-         </tr>
+\right),\left(
-         <tr valign=top><td colspan=2><nowiki>Loading KnotTheory` (version of August 29, 2005, 15:33:11)...</nowiki></td></tr>
+\begin{array}{ccc}
-         </table>
+& 0 & \frac{1}{\sqrt{q}} \\
-         <table><tr align=left>
+& 1 & 0 \\
-<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[2]:=</code></td>
+ \sqrt{q} & 0 & 0
-<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>PD[Knot[5, 1]]</nowiki></code></td></tr>
+\end{array}
-<tr align=left>
+\right),\left(
-<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[2]:=</code></td>
+\begin{array}{ccc}
-<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>PD[X[1, 6, 2, 7], X[3, 8, 4, 9], X[5, 10, 6, 1], X[7, 2, 8, 3],
+& 0 & \frac{1}{\sqrt{q}} \\
+& 1 & 0 \\
-  X[9, 4, 10, 5]]</nowiki></code></td></tr>
+ \sqrt{q} & 0 & 0
-</table>
+\end{array}
-         <table><tr align=left>
+\right)\right)\right]}{q+\frac{1}{q}+1}\right]</math> |
-<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[3]:=</code></td>
+coloured_jones_3 = <math>\textrm{Apart}\left[\frac{\textrm{Hold}\left[\textrm{REngine}\left(\textrm{MorseLink}(\textrm{MorseLink::Error: bad input}),\left(
-<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>GaussCode[Knot[5, 1]]</nowiki></code></td></tr>
+\begin{array}{cccccccccccccccc}
-<tr align=left>
+ q^{3/2} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
-<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[3]:=</code></td>
+& 0 & 0 & 0 & q^3 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
-<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>GaussCode[-1, 4, -2, 5, -3, 1, -4, 2, -5, 3]</nowiki></code></td></tr>
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^{9/2} & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
-</table>
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^6 & 0 & 0 & 0 \\
-         <table><tr align=left>
+& q^3 & 0 & 0 & q^{3/2}-q^{9/2} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
-<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[4]:=</code></td>
+& 0 & 0 & 0 & 0 & q^{7/2} & 0 & 0 & -q^{3/2} (q+1) \left(q^3-1\right) & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
-<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>DTCode[Knot[5, 1]]</nowiki></code></td></tr>
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^4 & 0 & 0 & -(q-1) q^{3/2} \left(q^2+q+1\right)^2 & 0 & 0 & 0 \\
-<tr align=left>
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^{9/2} & 0 & 0 \\
-<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[4]:=</code></td>
+& 0 & q^{9/2} & 0 & 0 & q^{7/2}-q^{11/2} & 0 & 0 & q^{13/2}-q^{9/2}-q^{7/2}+q^{3/2} & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
-<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>DTCode[6, 8, 10, 2, 4]</nowiki></code></td></tr>
+& 0 & 0 & 0 & 0 & 0 & q^4 & 0 & 0 & -(q-1) q^{5/2} (q+1)^2 & 0 & 0 & (q+1) \left(q^3-1\right)^2 & 0 & 0 & 0 \\
-</table>
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^{7/2} & 0 & 0 & -q^{3/2} (q+1) \left(q^3-1\right) & 0 & 0 \\
-         <table><tr align=left>
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^3 & 0 \\
-<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[5]:=</code></td>
+& 0 & 0 & q^6 & 0 & 0 & q^{11/2}-q^{13/2} & 0 & 0 & (q-1)^2 q^4 (q+1) & 0 & 0 & -(q-1)^3 q^{3/2} (q+1) \left(q^2+q+1\right) & 0 & 0 & 0 \\
-<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>br = BR[Knot[5, 1]]</nowiki></code></td></tr>
+& 0 & 0 & 0 & 0 & 0 & 0 & q^{9/2} & 0 & 0 & q^{7/2}-q^{11/2} & 0 & 0 & q^{13/2}-q^{9/2}-q^{7/2}+q^{3/2} & 0 & 0 \\
-<tr align=left>
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^3 & 0 & 0 & q^{3/2}-q^{9/2} & 0 \\
-<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[5]:=</code></td>
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^{3/2}
-<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>BR[2, {-1, -1, -1, -1, -1}]</nowiki></code></td></tr>
+\end{array}
-</table>
+\right),\left(
-         <table><tr align=left>
+\begin{array}{cccccccccccccccc}
-<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[6]:=</code></td>
+ \frac{1}{q^{3/2}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
-<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>{First[br], Crossings[br]}</nowiki></code></td></tr>
+& \frac{q^3-1}{q^{9/2}} & 0 & 0 & \frac{1}{q^3} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
-<tr align=left>
+& 0 & \frac{q^5-q^3-q^2+1}{q^{13/2}} & 0 & 0 & \frac{q^2-1}{q^{9/2}} & 0 & 0 & \frac{1}{q^{9/2}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
-<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[6]:=</code></td>
+& 0 & 0 & \frac{(q-1)^3 (q+1) \left(q^2+q+1\right)}{q^{15/2}} & 0 & 0 & \frac{(q-1)^2 (q+1)}{q^5} & 0 & 0 & \frac{q-1}{q^{9/2}} & 0 & 0 & \frac{1}{q^6} & 0 & 0 & 0 \\
-<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>{2, 5}</nowiki></code></td></tr>
+& \frac{1}{q^3} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
-</table>
+& 0 & \frac{(q+1) \left(q^3-1\right)}{q^{13/2}} & 0 & 0 & \frac{1}{q^{7/2}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
-         <table><tr align=left>
+& 0 & 0 & \frac{(q+1) \left(q^3-1\right)^2}{q^9} & 0 & 0 & \frac{(q-1) (q+1)^2}{q^{11/2}} & 0 & 0 & \frac{1}{q^4} & 0 & 0 & 0 & 0 & 0 & 0 \\
-<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[7]:=</code></td>
+& 0 & 0 & 0 & 0 & 0 & 0 & \frac{q^5-q^3-q^2+1}{q^{13/2}} & 0 & 0 & \frac{q^2-1}{q^{9/2}} & 0 & 0 & \frac{1}{q^{9/2}} & 0 & 0 \\
-<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>BraidIndex[Knot[5, 1]]</nowiki></code></td></tr>
+& 0 & \frac{1}{q^{9/2}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
-<tr align=left>
+& 0 & 0 & \frac{(q-1) \left(q^2+q+1\right)^2}{q^{17/2}} & 0 & 0 & \frac{1}{q^4} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
-<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[7]:=</code></td>
+& 0 & 0 & 0 & 0 & 0 & 0 & \frac{(q+1) \left(q^3-1\right)}{q^{13/2}} & 0 & 0 & \frac{1}{q^{7/2}} & 0 & 0 & 0 & 0 & 0 \\
-<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>2</nowiki></code></td></tr>
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \frac{q^3-1}{q^{9/2}} & 0 & 0 & \frac{1}{q^3} & 0 \\
-</table>
+& 0 & 0 & \frac{1}{q^6} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
-         <table><tr align=left>
+& 0 & 0 & 0 & 0 & 0 & 0 & \frac{1}{q^{9/2}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
-<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[8]:=</code></td>
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \frac{1}{q^3} & 0 & 0 & 0 & 0 \\
-<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>Show[DrawMorseLink[Knot[5, 1]]]</nowiki></code></td></tr>
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \frac{1}{q^{3/2}}
-<tr align=left><td></td><td>[[Image:5_1_ML.gif]]</td></tr><tr align=left>
+\end{array}
-<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[8]:=</code></td>
+\right),\left(
-<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>-Graphics-</nowiki></code></td></tr>
+\begin{array}{cccc}
-</table>
+& 0 & 0 & \frac{1}{q^{3/4}} \\
-         <table><tr align=left>
+& 0 & \frac{1}{\sqrt[4]{q}} & 0 \\
-<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[9]:=</code></td>
+& \sqrt[4]{q} & 0 & 0 \\
-<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki> (#[Knot[5, 1]]&) /@ {
+ q^{3/4} & 0 & 0 & 0
-                 SymmetryType, UnknottingNumber, ThreeGenus,
+\end{array}
-                 BridgeIndex, SuperBridgeIndex, NakanishiIndex
+\right),\left(
-                }</nowiki></code></td></tr>
+\begin{array}{cccc}
-<tr align=left>
+& 0 & 0 & \frac{1}{q^{3/4}} \\
-<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[9]:=</code></td>
+& 0 & \frac{1}{\sqrt[4]{q}} & 0 \\
-<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>{Reversible, 2, 2, 2, 3, 1}</nowiki></code></td></tr>
+& \sqrt[4]{q} & 0 & 0 \\
-</table>
+ q^{3/4} & 0 & 0 & 0
-         <table><tr align=left>
+\end{array}
-<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[10]:=</code></td>
+\right),\left(
-<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>alex = Alexander[Knot[5, 1]][t]</nowiki></code></td></tr>
+\begin{array}{cccc}
-<tr align=left>
+& 0 & 0 & \frac{1}{q^{3/4}} \\
-<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[10]:=</code></td>
+& 0 & \frac{1}{\sqrt[4]{q}} & 0 \\
-<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>     -2   1        2
-+ t   - - - t + t
+& \sqrt[4]{q} & 0 & 0 \\
+ q^{3/4} & 0 & 0 & 0
-          t</nowiki></code></td></tr>
+\end{array}
-</table>
+\right),\left(
-         <table><tr align=left>
+\begin{array}{cccc}
-<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[11]:=</code></td>
+& 0 & 0 & \frac{1}{q^{3/4}} \\
-<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>Conway[Knot[5, 1]][z]</nowiki></code></td></tr>
+& 0 & \frac{1}{\sqrt[4]{q}} & 0 \\
-<tr align=left>
+& \sqrt[4]{q} & 0 & 0 \\
-<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[11]:=</code></td>
+ q^{3/4} & 0 & 0 & 0
-<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>       2    4
+\end{array}
-+ 3 z  + z</nowiki></code></td></tr>
+\right)\right)\right]}{q^{3/2}+\sqrt{q}+\frac{1}{\sqrt{q}}+\frac{1}{q^{3/2}}}\right]</math> |
-</table>
+coloured_jones_4 = <math>\textrm{Apart}\left[\frac{\textrm{Hold}\left[\textrm{REngine}\left(\textrm{MorseLink}(\textrm{MorseLink::Error: bad input}),\left(
-         <table><tr align=left>
+\begin{array}{ccccccccccccccccccccccccc}
-<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[12]:=</code></td>
+ q^2 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
-<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>Select[AllKnots[], (alex === Alexander[#][t])&]</nowiki></code></td></tr>
+& 0 & 0 & 0 & 0 & q^4 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
-<tr align=left>
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^6 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
-<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[12]:=</code></td>
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^8 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
-<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>{Knot[5, 1], Knot[10, 132]}</nowiki></code></td></tr>
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^{10} & 0 & 0 & 0 & 0 \\
-</table>
+& q^4 & 0 & 0 & 0 & q^2-q^6 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
-         <table><tr align=left>
+& 0 & 0 & 0 & 0 & 0 & q^5 & 0 & 0 & 0 & -q^{15/2}-q^{13/2}+q^{7/2}+q^{5/2} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
-<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[13]:=</code></td>
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^6 & 0 & 0 & 0 & -q^3 \left(q^2+q+1\right) \left(q^4-1\right) & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
-<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>{KnotDet[Knot[5, 1]], KnotSignature[Knot[5, 1]]}</nowiki></code></td></tr>
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^7 & 0 & 0 & 0 & -(q-1) q^{7/2} \left(q^3+q^2+q+1\right)^2 & 0 & 0 & 0 & 0 \\
-<tr align=left>
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^8 & 0 & 0 & 0 \\
-<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[13]:=</code></td>
+& 0 & q^6 & 0 & 0 & 0 & q^{9/2}-q^{15/2} & 0 & 0 & 0 & q^9-q^6-q^5+q^2 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
-<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>{5, -4}</nowiki></code></td></tr>
+& 0 & 0 & 0 & 0 & 0 & 0 & q^6 & 0 & 0 & 0 & -q^4 (q+1) \left(q^3-1\right) & 0 & 0 & 0 & q \left(q^3-1\right)^2 \left(q^3+q^2+q+1\right) & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
-</table>
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^6 & 0 & 0 & 0 & -(q-1) q^{7/2} \left(q^2+q+1\right)^2 & 0 & 0 & 0 & (q+1) \left(q^5+q^3-q^2-1\right)^2 & 0 & 0 & 0 & 0 \\
-         <table><tr align=left>
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^6 & 0 & 0 & 0 & -q^3 \left(q^2+q+1\right) \left(q^4-1\right) & 0 & 0 & 0 \\
-<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[14]:=</code></td>
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^6 & 0 & 0 \\
-<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>Jones[Knot[5, 1]][q]</nowiki></code></td></tr>
+& 0 & 0 & q^8 & 0 & 0 & 0 & q^7-q^9 & 0 & 0 & 0 & q^{10}-q^8-q^7+q^5 & 0 & 0 & 0 & -(q-1)^3 q^2 (q+1)^2 \left(q^2+1\right) \left(q^2+q+1\right) & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
-<tr align=left>
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^7 & 0 & 0 & 0 & -(q-1) q^{11/2} (q+1)^2 & 0 & 0 & 0 & q^3 (q+1) \left(q^3-1\right)^2 & 0 & 0 & 0 & -\frac{\left(q^2-1\right)^3 \left(q^2+1\right)^2 \left(q^2+q+1\right)}{\sqrt{q}} & 0 & 0 & 0 & 0 \\
-<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[14]:=</code></td>
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^6 & 0 & 0 & 0 & -q^4 (q+1) \left(q^3-1\right) & 0 & 0 & 0 & q \left(q^3-1\right)^2 \left(q^3+q^2+q+1\right) & 0 & 0 & 0 \\
-<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>  -7    -6    -5    -4    -2
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^5 & 0 & 0 & 0 & -q^{15/2}-q^{13/2}+q^{7/2}+q^{5/2} & 0 & 0 \\
--q   + q   - q   + q   + q</nowiki></code></td></tr>
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^4 & 0 \\
-</table>
+& 0 & 0 & 0 & q^{10} & 0 & 0 & 0 & q^{19/2}-q^{21/2} & 0 & 0 & 0 & (q-1)^2 q^8 (q+1) & 0 & 0 & 0 & -(q-1)^3 q^{11/2} (q+1) \left(q^2+q+1\right) & 0 & 0 & 0 & (q-1)^4 q^2 (q+1)^2 \left(q^2+1\right) \left(q^2+q+1\right) & 0 & 0 & 0 & 0 \\
-         <table><tr align=left>
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^8 & 0 & 0 & 0 & q^7-q^9 & 0 & 0 & 0 & q^{10}-q^8-q^7+q^5 & 0 & 0 & 0 & -(q-1)^3 q^2 (q+1)^2 \left(q^2+1\right) \left(q^2+q+1\right) & 0 & 0 & 0 \\
-<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[15]:=</code></td>
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^6 & 0 & 0 & 0 & q^{9/2}-q^{15/2} & 0 & 0 & 0 & q^9-q^6-q^5+q^2 & 0 & 0 \\
-<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>Select[AllKnots[], (J === Jones[#][q] || (J /. q-> 1/q) === Jones[#][q])&]</nowiki></code></td></tr>
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^4 & 0 & 0 & 0 & q^2-q^6 & 0 \\
-<tr align=left>
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^2
-<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[15]:=</code></td>
+\end{array}
-<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>{Knot[5, 1], Knot[10, 132]}</nowiki></code></td></tr>
+\right),\left(
-</table>
+\begin{array}{ccccccccccccccccccccccccc}
-         <table><tr align=left>
+ \frac{1}{q^2} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
-<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[16]:=</code></td>
+& \frac{q^4-1}{q^6} & 0 & 0 & 0 & \frac{1}{q^4} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
-<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>A2Invariant[Knot[5, 1]][q]</nowiki></code></td></tr>
+& 0 & \frac{q^7-q^4-q^3+1}{q^9} & 0 & 0 & 0 & \frac{q^3-1}{q^{13/2}} & 0 & 0 & 0 & \frac{1}{q^6} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
-<tr align=left>
+& 0 & 0 & \frac{(q-1)^3 (q+1)^2 \left(q^2+1\right) \left(q^2+q+1\right)}{q^{11}} & 0 & 0 & 0 & \frac{q^5-q^3-q^2+1}{q^8} & 0 & 0 & 0 & \frac{q^2-1}{q^7} & 0 & 0 & 0 & \frac{1}{q^8} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
-<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[16]:=</code></td>
+& 0 & 0 & 0 & \frac{(q-1)^4 (q+1)^2 \left(q^2+1\right) \left(q^2+q+1\right)}{q^{12}} & 0 & 0 & 0 & \frac{(q-1)^3 (q+1) \left(q^2+q+1\right)}{q^{17/2}} & 0 & 0 & 0 & \frac{(q-1)^2 (q+1)}{q^7} & 0 & 0 & 0 & \frac{q-1}{q^{15/2}} & 0 & 0 & 0 & \frac{1}{q^{10}} & 0 & 0 & 0 & 0 \\
-<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>  -22    -20    -18    -14    -12    2     -8    -6
--q    - q    - q    + q    + q    + --- + q   + q
+& \frac{1}{q^4} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & \frac{q^5+q^4-q-1}{q^{17/2}} & 0 & 0 & 0 & \frac{1}{q^5} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & \frac{\left(q^3-1\right)^2 \left(q^3+q^2+q+1\right)}{q^{12}} & 0 & 0 & 0 & \frac{(q+1) \left(q^3-1\right)}{q^8} & 0 & 0 & 0 & \frac{1}{q^6} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
-                                    q</nowiki></code></td></tr>
+& 0 & 0 & 0 & \frac{\left(q^2-1\right)^3 \left(q^2+1\right)^2 \left(q^2+q+1\right)}{q^{29/2}} & 0 & 0 & 0 & \frac{(q+1) \left(q^3-1\right)^2}{q^{10}} & 0 & 0 & 0 & \frac{(q-1) (q+1)^2}{q^{15/2}} & 0 & 0 & 0 & \frac{1}{q^7} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
-</table>
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \frac{(q-1)^3 (q+1)^2 \left(q^2+1\right) \left(q^2+q+1\right)}{q^{11}} & 0 & 0 & 0 & \frac{q^5-q^3-q^2+1}{q^8} & 0 & 0 & 0 & \frac{q^2-1}{q^7} & 0 & 0 & 0 & \frac{1}{q^8} & 0 & 0 & 0 \\
-         <table><tr align=left>
+& 0 & \frac{1}{q^6} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
-<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[17]:=</code></td>
+& 0 & 0 & \frac{\left(q^2+q+1\right) \left(q^4-1\right)}{q^{11}} & 0 & 0 & 0 & \frac{1}{q^6} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
-<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>HOMFLYPT[Knot[5, 1]][a, z]</nowiki></code></td></tr>
+& 0 & 0 & 0 & \frac{(q+1) \left(q^5+q^3-q^2-1\right)^2}{q^{15}} & 0 & 0 & 0 & \frac{(q-1) \left(q^2+q+1\right)^2}{q^{19/2}} & 0 & 0 & 0 & \frac{1}{q^6} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
-<tr align=left>
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \frac{\left(q^3-1\right)^2 \left(q^3+q^2+q+1\right)}{q^{12}} & 0 & 0 & 0 & \frac{(q+1) \left(q^3-1\right)}{q^8} & 0 & 0 & 0 & \frac{1}{q^6} & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
-<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[17]:=</code></td>
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \frac{q^7-q^4-q^3+1}{q^9} & 0 & 0 & 0 & \frac{q^3-1}{q^{13/2}} & 0 & 0 & 0 & \frac{1}{q^6} & 0 & 0 \\
-<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>   4      6      4  2    6  2    4  4
+& 0 & 0 & \frac{1}{q^8} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
-a  - 2 a  + 4 a  z  - a  z  + a  z</nowiki></code></td></tr>
+& 0 & 0 & 0 & \frac{(q-1) \left(q^3+q^2+q+1\right)^2}{q^{27/2}} & 0 & 0 & 0 & \frac{1}{q^7} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
-</table>
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \frac{\left(q^2+q+1\right) \left(q^4-1\right)}{q^{11}} & 0 & 0 & 0 & \frac{1}{q^6} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
-         <table><tr align=left>
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \frac{q^5+q^4-q-1}{q^{17/2}} & 0 & 0 & 0 & \frac{1}{q^5} & 0 & 0 & 0 & 0 & 0 & 0 \\
-<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[18]:=</code></td>
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \frac{q^4-1}{q^6} & 0 & 0 & 0 & \frac{1}{q^4} & 0 \\
-<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>Kauffman[Knot[5, 1]][a, z]</nowiki></code></td></tr>
+& 0 & 0 & 0 & \frac{1}{q^{10}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
-<tr align=left>
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \frac{1}{q^8} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
-<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[18]:=</code></td>
-<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>   4      6      5      7      9        4  2      6  2    8  2
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \frac{1}{q^6} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
-a  + 2 a  - 2 a  z - a  z + a  z - 4 a  z  - 3 a  z  + a  z  +
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \frac{1}{q^4} & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \frac{1}{q^2}
+\end{array}
-3    7  3    4  4    6  4
+\right),\left(
-  a  z  + a  z  + a  z  + a  z</nowiki></code></td></tr>
+\begin{array}{ccccc}
-</table>
+& 0 & 0 & 0 & \frac{1}{q} \\
-         <table><tr align=left>
+& 0 & 0 & \frac{1}{\sqrt{q}} & 0 \\
-<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[19]:=</code></td>
+& 0 & 1 & 0 & 0 \\
-<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>{Vassiliev[2][Knot[5, 1]], Vassiliev[3][Knot[5, 1]]}</nowiki></code></td></tr>
+& \sqrt{q} & 0 & 0 & 0 \\
-<tr align=left>
+ q & 0 & 0 & 0 & 0
-<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[19]:=</code></td>
+\end{array}
-<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>{3, -5}</nowiki></code></td></tr>
+\right),\left(
-</table>
+\begin{array}{ccccc}
-         <table><tr align=left>
+& 0 & 0 & 0 & \frac{1}{q} \\
-<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[20]:=</code></td>
+& 0 & 0 & \frac{1}{\sqrt{q}} & 0 \\
-<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>Kh[Knot[5, 1]][q, t]</nowiki></code></td></tr>
+& 0 & 1 & 0 & 0 \\
-<tr align=left>
+& \sqrt{q} & 0 & 0 & 0 \\
-<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[20]:=</code></td>
+ q & 0 & 0 & 0 & 0
-<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki> -5    -3     1        1        1        1
+\end{array}
-q   + q   + ------ + ------ + ------ + -----
+\right),\left(
-5    11  4    11  3    7  2
+\begin{array}{ccccc}
-            q   t    q   t    q   t    q  t</nowiki></code></td></tr>
+& 0 & 0 & 0 & \frac{1}{q} \\
-</table>
+& 0 & 0 & \frac{1}{\sqrt{q}} & 0 \\
-         <table><tr align=left>
+& 0 & 1 & 0 & 0 \\
-<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[21]:=</code></td>
+& \sqrt{q} & 0 & 0 & 0 \\
-<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>ColouredJones[Knot[5, 1], 2][q]</nowiki></code></td></tr>
+ q & 0 & 0 & 0 & 0
-<tr align=left>
+\end{array}
-<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[21]:=</code></td>
+\right),\left(
-<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki> -19    -18    -16    2     -13    -12    -10    -9    -7    -4
+\begin{array}{ccccc}
-q    - q    + q    - --- + q    - q    + q    - q   + q   + q
+& 0 & 0 & 0 & \frac{1}{q} \\
+& 0 & 0 & \frac{1}{\sqrt{q}} & 0 \\
-                     q</nowiki></code></td></tr>
+& 0 & 1 & 0 & 0 \\
-</table>  }}
+& \sqrt{q} & 0 & 0 & 0 \\
+ q & 0 & 0 & 0 & 0
+\end{array}
+\right)\right)\right]}{q^2+q+1+\frac{1}{q}+\frac{1}{q^2}}\right]</math> |
+coloured_jones_5 = <math>\textrm{Apart}\left[\frac{\textrm{Hold}\left[\textrm{REngine}\left(\textrm{MorseLink}(\textrm{MorseLink::Error: bad input}),\left(
+\begin{array}{cccccccccccccccccccccccccccccccccccc}
+ q^{5/2} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & q^5 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^{15/2} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^{10} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^{25/2} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^{15} & 0 & 0 & 0 & 0 & 0 \\
+& q^5 & 0 & 0 & 0 & 0 & q^{5/2}-q^{15/2} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & q^{13/2} & 0 & 0 & 0 & 0 & -q^{7/2} (q+1) \left(q^5-1\right) & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^8 & 0 & 0 & 0 & 0 & -q^{9/2} \left(q^2+q+1\right) \left(q^5-1\right) & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^{19/2} & 0 & 0 & 0 & 0 & -q^{11/2} \left(q^3+q^2+q+1\right) \left(q^5-1\right) & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^{11} & 0 & 0 & 0 & 0 & -(q-1) q^{13/2} \left(q^4+q^3+q^2+q+1\right)^2 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^{25/2} & 0 & 0 & 0 & 0 \\
+& 0 & q^{15/2} & 0 & 0 & 0 & 0 & q^{11/2}-q^{19/2} & 0 & 0 & 0 & 0 & q^{23/2}-q^{15/2}-q^{13/2}+q^{5/2} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^8 & 0 & 0 & 0 & 0 & -q^{21/2}-q^{19/2}+q^{13/2}+q^{11/2} & 0 & 0 & 0 & 0 & (q-1)^2 q^2 \left(q^2+q+1\right) \left(q^3+q^2+q+1\right) \left(q^4+q^3+q^2+q+1\right) & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^{17/2} & 0 & 0 & 0 & 0 & -q^{11/2} \left(q^2+q+1\right) \left(q^4-1\right) & 0 & 0 & 0 & 0 & (q-1)^2 q^{3/2} (q+1) \left(q^2+1\right)^2 \left(q^2+q+1\right) \left(q^4+q^3+q^2+q+1\right) & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^9 & 0 & 0 & 0 & 0 & -(q-1) q^{11/2} \left(q^3+q^2+q+1\right)^2 & 0 & 0 & 0 & 0 & q (q+1) \left(q^2+1\right)^2 \left(q^5-1\right)^2 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^{19/2} & 0 & 0 & 0 & 0 & -q^{11/2} \left(q^3+q^2+q+1\right) \left(q^5-1\right) & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^{10} & 0 & 0 & 0 \\
+& 0 & 0 & q^{10} & 0 & 0 & 0 & 0 & q^{17/2}-q^{23/2} & 0 & 0 & 0 & 0 & q^{13}-q^{10}-q^9+q^6 & 0 & 0 & 0 & 0 & -q^{5/2} \left(q^3-1\right) \left(q^4-1\right) \left(q^5-1\right) & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^{19/2} & 0 & 0 & 0 & 0 & -q^{15/2} (q+1) \left(q^3-1\right) & 0 & 0 & 0 & 0 & q^{9/2} \left(q^3-1\right)^2 \left(q^3+q^2+q+1\right) & 0 & 0 & 0 & 0 & -(q-1)^3 \left(q^2+q+1\right) \left(q^{13/4}+q^{9/4}+q^{5/4}+\sqrt[4]{q}\right)^2 \left(q^4+q^3+q^2+q+1\right) & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^9 & 0 & 0 & 0 & 0 & -(q-1) q^{13/2} \left(q^2+q+1\right)^2 & 0 & 0 & 0 & 0 & q^3 (q+1) \left(q^5+q^3-q^2-1\right)^2 & 0 & 0 & 0 & 0 & -\frac{(q-1)^3 (q+1) \left(q^2+1\right)^2 \left(q^2+q+1\right) \left(q^4+q^3+q^2+q+1\right)^2}{q^{3/2}} & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^{17/2} & 0 & 0 & 0 & 0 & -q^{11/2} \left(q^2+q+1\right) \left(q^4-1\right) & 0 & 0 & 0 & 0 & (q-1)^2 q^{3/2} (q+1) \left(q^2+1\right)^2 \left(q^2+q+1\right) \left(q^4+q^3+q^2+q+1\right) & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^8 & 0 & 0 & 0 & 0 & -q^{9/2} \left(q^2+q+1\right) \left(q^5-1\right) & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^{15/2} & 0 & 0 \\
+& 0 & 0 & 0 & q^{25/2} & 0 & 0 & 0 & 0 & q^{23/2}-q^{27/2} & 0 & 0 & 0 & 0 & q^{29/2}-q^{25/2}-q^{23/2}+q^{19/2} & 0 & 0 & 0 & 0 & -(q-1)^3 q^{13/2} (q+1)^2 \left(q^2+1\right) \left(q^2+q+1\right) & 0 & 0 & 0 & 0 & (q-1)^4 q^{5/2} (q+1)^2 \left(q^2+1\right) \left(q^2+q+1\right) \left(q^4+q^3+q^2+q+1\right) & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^{11} & 0 & 0 & 0 & 0 & -(q-1) q^{19/2} (q+1)^2 & 0 & 0 & 0 & 0 & q^7 (q+1) \left(q^3-1\right)^2 & 0 & 0 & 0 & 0 & -q^{7/2} \left(q^2-1\right)^3 \left(q^2+1\right)^2 \left(q^2+q+1\right) & 0 & 0 & 0 & 0 & \frac{(q-1)^4 (q+1)^2 \left(q^2+1\right) \left(q^2+q+1\right) \left(q^4+q^3+q^2+q+1\right)^2}{q} & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^{19/2} & 0 & 0 & 0 & 0 & -q^{15/2} (q+1) \left(q^3-1\right) & 0 & 0 & 0 & 0 & q^{9/2} \left(q^3-1\right)^2 \left(q^3+q^2+q+1\right) & 0 & 0 & 0 & 0 & -(q-1)^3 \left(q^2+q+1\right) \left(q^{13/4}+q^{9/4}+q^{5/4}+\sqrt[4]{q}\right)^2 \left(q^4+q^3+q^2+q+1\right) & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^8 & 0 & 0 & 0 & 0 & -q^{21/2}-q^{19/2}+q^{13/2}+q^{11/2} & 0 & 0 & 0 & 0 & (q-1)^2 q^2 \left(q^2+q+1\right) \left(q^3+q^2+q+1\right) \left(q^4+q^3+q^2+q+1\right) & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^{13/2} & 0 & 0 & 0 & 0 & -q^{7/2} (q+1) \left(q^5-1\right) & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^5 & 0 \\
+& 0 & 0 & 0 & 0 & q^{15} & 0 & 0 & 0 & 0 & q^{29/2}-q^{31/2} & 0 & 0 & 0 & 0 & (q-1)^2 q^{13} (q+1) & 0 & 0 & 0 & 0 & -(q-1)^3 q^{21/2} (q+1) \left(q^2+q+1\right) & 0 & 0 & 0 & 0 & (q-1)^4 q^7 (q+1)^2 \left(q^2+1\right) \left(q^2+q+1\right) & 0 & 0 & 0 & 0 & -(q-1)^5 q^{5/2} (q+1)^2 \left(q^2+1\right) \left(q^2+q+1\right) \left(q^4+q^3+q^2+q+1\right) & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^{25/2} & 0 & 0 & 0 & 0 & q^{23/2}-q^{27/2} & 0 & 0 & 0 & 0 & q^{29/2}-q^{25/2}-q^{23/2}+q^{19/2} & 0 & 0 & 0 & 0 & -(q-1)^3 q^{13/2} (q+1)^2 \left(q^2+1\right) \left(q^2+q+1\right) & 0 & 0 & 0 & 0 & (q-1)^4 q^{5/2} (q+1)^2 \left(q^2+1\right) \left(q^2+q+1\right) \left(q^4+q^3+q^2+q+1\right) & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^{10} & 0 & 0 & 0 & 0 & q^{17/2}-q^{23/2} & 0 & 0 & 0 & 0 & q^{13}-q^{10}-q^9+q^6 & 0 & 0 & 0 & 0 & -q^{5/2} \left(q^3-1\right) \left(q^4-1\right) \left(q^5-1\right) & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^{15/2} & 0 & 0 & 0 & 0 & q^{11/2}-q^{19/2} & 0 & 0 & 0 & 0 & q^{23/2}-q^{15/2}-q^{13/2}+q^{5/2} & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^5 & 0 & 0 & 0 & 0 & q^{5/2}-q^{15/2} & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^{5/2}
+\end{array}
+\right),\left(
+\begin{array}{cccccccccccccccccccccccccccccccccccc}
+ \frac{1}{q^{5/2}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& \frac{q^5-1}{q^{15/2}} & 0 & 0 & 0 & 0 & \frac{1}{q^5} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & \frac{q^9-q^5-q^4+1}{q^{23/2}} & 0 & 0 & 0 & 0 & \frac{q^4-1}{q^{17/2}} & 0 & 0 & 0 & 0 & \frac{1}{q^{15/2}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & \frac{\left(1-q^3\right) \left(1-q^4\right) \left(q^5-1\right)}{q^{29/2}} & 0 & 0 & 0 & 0 & \frac{q^7-q^4-q^3+1}{q^{11}} & 0 & 0 & 0 & 0 & \frac{q^3-1}{q^{19/2}} & 0 & 0 & 0 & 0 & \frac{1}{q^{10}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & \frac{(q-1)^4 (q+1)^2 \left(q^2+1\right) \left(q^2+q+1\right) \left(q^4+q^3+q^2+q+1\right)}{q^{33/2}} & 0 & 0 & 0 & 0 & \frac{(q-1)^3 (q+1)^2 \left(q^2+1\right) \left(q^2+q+1\right)}{q^{25/2}} & 0 & 0 & 0 & 0 & \frac{q^5-q^3-q^2+1}{q^{21/2}} & 0 & 0 & 0 & 0 & \frac{q^2-1}{q^{21/2}} & 0 & 0 & 0 & 0 & \frac{1}{q^{25/2}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & \frac{(q-1)^5 (q+1)^2 \left(q^2+1\right) \left(q^2+q+1\right) \left(q^4+q^3+q^2+q+1\right)}{q^{35/2}} & 0 & 0 & 0 & 0 & \frac{(q-1)^4 (q+1)^2 \left(q^2+1\right) \left(q^2+q+1\right)}{q^{13}} & 0 & 0 & 0 & 0 & \frac{(q-1)^3 (q+1) \left(q^2+q+1\right)}{q^{21/2}} & 0 & 0 & 0 & 0 & \frac{(q-1)^2 (q+1)}{q^{10}} & 0 & 0 & 0 & 0 & \frac{q-1}{q^{23/2}} & 0 & 0 & 0 & 0 & \frac{1}{q^{15}} & 0 & 0 & 0 & 0 & 0 \\
+& \frac{1}{q^5} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & \frac{(q+1) \left(q^5-1\right)}{q^{21/2}} & 0 & 0 & 0 & 0 & \frac{1}{q^{13/2}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & \frac{(q-1)^2 \left(q^2+q+1\right) \left(q^3+q^2+q+1\right) \left(q^4+q^3+q^2+q+1\right)}{q^{15}} & 0 & 0 & 0 & 0 & \frac{q^5+q^4-q-1}{q^{21/2}} & 0 & 0 & 0 & 0 & \frac{1}{q^8} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & \frac{(q-1)^3 \left(q^2+q+1\right) \left(q^3+q^2+q+1\right)^2 \left(q^4+q^3+q^2+q+1\right)}{q^{37/2}} & 0 & 0 & 0 & 0 & \frac{\left(q^3-1\right)^2 \left(q^3+q^2+q+1\right)}{q^{27/2}} & 0 & 0 & 0 & 0 & \frac{(q+1) \left(q^3-1\right)}{q^{21/2}} & 0 & 0 & 0 & 0 & \frac{1}{q^{19/2}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & \frac{(q-1)^4 (q+1)^2 \left(q^2+1\right) \left(q^2+q+1\right) \left(q^4+q^3+q^2+q+1\right)^2}{q^{21}} & 0 & 0 & 0 & 0 & \frac{\left(q^2-1\right)^3 \left(q^2+1\right)^2 \left(q^2+q+1\right)}{q^{31/2}} & 0 & 0 & 0 & 0 & \frac{(q+1) \left(q^3-1\right)^2}{q^{12}} & 0 & 0 & 0 & 0 & \frac{(q-1) (q+1)^2}{q^{21/2}} & 0 & 0 & 0 & 0 & \frac{1}{q^{11}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \frac{(q-1)^4 (q+1)^2 \left(q^2+1\right) \left(q^2+q+1\right) \left(q^4+q^3+q^2+q+1\right)}{q^{33/2}} & 0 & 0 & 0 & 0 & \frac{(q-1)^3 (q+1)^2 \left(q^2+1\right) \left(q^2+q+1\right)}{q^{25/2}} & 0 & 0 & 0 & 0 & \frac{q^5-q^3-q^2+1}{q^{21/2}} & 0 & 0 & 0 & 0 & \frac{q^2-1}{q^{21/2}} & 0 & 0 & 0 & 0 & \frac{1}{q^{25/2}} & 0 & 0 & 0 & 0 \\
+& 0 & \frac{1}{q^{15/2}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & \frac{\left(q^2+q+1\right) \left(q^5-1\right)}{q^{27/2}} & 0 & 0 & 0 & 0 & \frac{1}{q^8} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & \frac{(q-1)^2 (q+1) \left(q^2+1\right)^2 \left(q^2+q+1\right) \left(q^4+q^3+q^2+q+1\right)}{q^{37/2}} & 0 & 0 & 0 & 0 & \frac{\left(q^2+q+1\right) \left(q^4-1\right)}{q^{25/2}} & 0 & 0 & 0 & 0 & \frac{1}{q^{17/2}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & \frac{(q-1)^3 (q+1) \left(q^2+1\right)^2 \left(q^2+q+1\right) \left(q^4+q^3+q^2+q+1\right)^2}{q^{45/2}} & 0 & 0 & 0 & 0 & \frac{(q+1) \left(q^5+q^3-q^2-1\right)^2}{q^{16}} & 0 & 0 & 0 & 0 & \frac{(q-1) \left(q^2+q+1\right)^2}{q^{23/2}} & 0 & 0 & 0 & 0 & \frac{1}{q^9} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \frac{(q-1)^3 \left(q^2+q+1\right) \left(q^3+q^2+q+1\right)^2 \left(q^4+q^3+q^2+q+1\right)}{q^{37/2}} & 0 & 0 & 0 & 0 & \frac{\left(q^3-1\right)^2 \left(q^3+q^2+q+1\right)}{q^{27/2}} & 0 & 0 & 0 & 0 & \frac{(q+1) \left(q^3-1\right)}{q^{21/2}} & 0 & 0 & 0 & 0 & \frac{1}{q^{19/2}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \frac{\left(1-q^3\right) \left(1-q^4\right) \left(q^5-1\right)}{q^{29/2}} & 0 & 0 & 0 & 0 & \frac{q^7-q^4-q^3+1}{q^{11}} & 0 & 0 & 0 & 0 & \frac{q^3-1}{q^{19/2}} & 0 & 0 & 0 & 0 & \frac{1}{q^{10}} & 0 & 0 & 0 \\
+& 0 & 0 & \frac{1}{q^{10}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & \frac{\left(q^3+q^2+q+1\right) \left(q^5-1\right)}{q^{33/2}} & 0 & 0 & 0 & 0 & \frac{1}{q^{19/2}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & \frac{(q+1) \left(q^2+1\right)^2 \left(q^5-1\right)^2}{q^{22}} & 0 & 0 & 0 & 0 & \frac{(q-1) \left(q^3+q^2+q+1\right)^2}{q^{29/2}} & 0 & 0 & 0 & 0 & \frac{1}{q^9} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \frac{(q-1)^2 (q+1) \left(q^2+1\right)^2 \left(q^2+q+1\right) \left(q^4+q^3+q^2+q+1\right)}{q^{37/2}} & 0 & 0 & 0 & 0 & \frac{\left(q^2+q+1\right) \left(q^4-1\right)}{q^{25/2}} & 0 & 0 & 0 & 0 & \frac{1}{q^{17/2}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \frac{(q-1)^2 \left(q^2+q+1\right) \left(q^3+q^2+q+1\right) \left(q^4+q^3+q^2+q+1\right)}{q^{15}} & 0 & 0 & 0 & 0 & \frac{q^5+q^4-q-1}{q^{21/2}} & 0 & 0 & 0 & 0 & \frac{1}{q^8} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \frac{q^9-q^5-q^4+1}{q^{23/2}} & 0 & 0 & 0 & 0 & \frac{q^4-1}{q^{17/2}} & 0 & 0 & 0 & 0 & \frac{1}{q^{15/2}} & 0 & 0 \\
+& 0 & 0 & 0 & \frac{1}{q^{25/2}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & \frac{(q-1) \left(q^4+q^3+q^2+q+1\right)^2}{q^{39/2}} & 0 & 0 & 0 & 0 & \frac{1}{q^{11}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \frac{\left(q^3+q^2+q+1\right) \left(q^5-1\right)}{q^{33/2}} & 0 & 0 & 0 & 0 & \frac{1}{q^{19/2}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \frac{\left(q^2+q+1\right) \left(q^5-1\right)}{q^{27/2}} & 0 & 0 & 0 & 0 & \frac{1}{q^8} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \frac{(q+1) \left(q^5-1\right)}{q^{21/2}} & 0 & 0 & 0 & 0 & \frac{1}{q^{13/2}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \frac{q^5-1}{q^{15/2}} & 0 & 0 & 0 & 0 & \frac{1}{q^5} & 0 \\
+& 0 & 0 & 0 & 0 & \frac{1}{q^{15}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \frac{1}{q^{25/2}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \frac{1}{q^{10}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \frac{1}{q^{15/2}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \frac{1}{q^5} & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \frac{1}{q^{5/2}}
+\end{array}
+\right),\left(
+\begin{array}{cccccc}
+& 0 & 0 & 0 & 0 & \frac{1}{q^{5/4}} \\
+& 0 & 0 & 0 & \frac{1}{q^{3/4}} & 0 \\
+& 0 & 0 & \frac{1}{\sqrt[4]{q}} & 0 & 0 \\
+& 0 & \sqrt[4]{q} & 0 & 0 & 0 \\
+& q^{3/4} & 0 & 0 & 0 & 0 \\
+ q^{5/4} & 0 & 0 & 0 & 0 & 0
+\end{array}
+\right),\left(
+\begin{array}{cccccc}
+& 0 & 0 & 0 & 0 & \frac{1}{q^{5/4}} \\
+& 0 & 0 & 0 & \frac{1}{q^{3/4}} & 0 \\
+& 0 & 0 & \frac{1}{\sqrt[4]{q}} & 0 & 0 \\
+& 0 & \sqrt[4]{q} & 0 & 0 & 0 \\
+& q^{3/4} & 0 & 0 & 0 & 0 \\
+ q^{5/4} & 0 & 0 & 0 & 0 & 0
+\end{array}
+\right),\left(
+\begin{array}{cccccc}
+& 0 & 0 & 0 & 0 & \frac{1}{q^{5/4}} \\
+& 0 & 0 & 0 & \frac{1}{q^{3/4}} & 0 \\
+& 0 & 0 & \frac{1}{\sqrt[4]{q}} & 0 & 0 \\
+& 0 & \sqrt[4]{q} & 0 & 0 & 0 \\
+& q^{3/4} & 0 & 0 & 0 & 0 \\
+ q^{5/4} & 0 & 0 & 0 & 0 & 0
+\end{array}
+\right),\left(
+\begin{array}{cccccc}
+& 0 & 0 & 0 & 0 & \frac{1}{q^{5/4}} \\
+& 0 & 0 & 0 & \frac{1}{q^{3/4}} & 0 \\
+& 0 & 0 & \frac{1}{\sqrt[4]{q}} & 0 & 0 \\
+& 0 & \sqrt[4]{q} & 0 & 0 & 0 \\
+& q^{3/4} & 0 & 0 & 0 & 0 \\
+ q^{5/4} & 0 & 0 & 0 & 0 & 0
+\end{array}
+\right)\right)\right]}{q^{5/2}+q^{3/2}+\sqrt{q}+\frac{1}{\sqrt{q}}+\frac{1}{q^{3/2}}+\frac{1}{q^{5/2}}}\right]</math> |
+coloured_jones_6 = <math>\textrm{Apart}\left[\frac{\textrm{Hold}\left[\textrm{REngine}\left(\textrm{MorseLink}(\textrm{MorseLink::Error: bad input}),\left(
+\begin{array}{ccccccccccccccccccccccccccccccccccccccccccccccccc}
+ q^3 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & q^6 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^9 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^{12} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^{15} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^{18} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^{21} & 0 & 0 & 0 & 0 & 0 & 0 \\
+& q^6 & 0 & 0 & 0 & 0 & 0 & q^3-q^9 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^8 & 0 & 0 & 0 & 0 & 0 & -q^{23/2}-q^{21/2}+q^{11/2}+q^{9/2} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^{10} & 0 & 0 & 0 & 0 & 0 & -q^6 \left(q^2+q+1\right)^2 \left(q^4-q^3+q-1\right) & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^{12} & 0 & 0 & 0 & 0 & 0 & -q^{15/2} \left(q^3+q^2+q+1\right) \left(q^6-1\right) & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^{14} & 0 & 0 & 0 & 0 & 0 & -q^9 \left(q^4+q^3+q^2+q+1\right) \left(q^6-1\right) & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^{16} & 0 & 0 & 0 & 0 & 0 & -(q-1) q^{21/2} \left(q^5+q^4+q^3+q^2+q+1\right)^2 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^{18} & 0 & 0 & 0 & 0 & 0 \\
+& 0 & q^9 & 0 & 0 & 0 & 0 & 0 & q^{13/2}-q^{23/2} & 0 & 0 & 0 & 0 & 0 & q^{14}-q^9-q^8+q^3 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^{10} & 0 & 0 & 0 & 0 & 0 & -q^7 (q+1) \left(q^5-1\right) & 0 & 0 & 0 & 0 & 0 & q^3 \left(q^3-1\right)^2 \left(q^3+1\right) \left(q^4+q^3+q^2+q+1\right) & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^{11} & 0 & 0 & 0 & 0 & 0 & -q^{15/2} \left(q^2+q+1\right) \left(q^5-1\right) & 0 & 0 & 0 & 0 & 0 & q^3 \left(q^2+1\right) \left(q^3-1\right)^2 \left(q^3+1\right) \left(q^4+q^3+q^2+q+1\right) & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^{12} & 0 & 0 & 0 & 0 & 0 & -q^8 \left(q^3+q^2+q+1\right) \left(q^5-1\right) & 0 & 0 & 0 & 0 & 0 & q^3 \left(q^2+1\right) \left(q^5-1\right)^2 \left(q^5+q^4+q^3+q^2+q+1\right) & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^{13} & 0 & 0 & 0 & 0 & 0 & -(q-1) q^{17/2} \left(q^4+q^3+q^2+q+1\right)^2 & 0 & 0 & 0 & 0 & 0 & q^3 (q+1) \left(q^9+q^7+q^5-q^4-q^2-1\right)^2 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^{14} & 0 & 0 & 0 & 0 & 0 & -q^9 \left(q^4+q^3+q^2+q+1\right) \left(q^6-1\right) & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^{15} & 0 & 0 & 0 & 0 \\
+& 0 & 0 & q^{12} & 0 & 0 & 0 & 0 & 0 & q^{10}-q^{14} & 0 & 0 & 0 & 0 & 0 & q^{16}-q^{12}-q^{11}+q^7 & 0 & 0 & 0 & 0 & 0 & -q^3 \left(q^4-1\right) \left(q^5-1\right) \left(q^6-1\right) & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^{12} & 0 & 0 & 0 & 0 & 0 & -q^{29/2}-q^{27/2}+q^{21/2}+q^{19/2} & 0 & 0 & 0 & 0 & 0 & (q-1)^2 q^6 \left(q^2+q+1\right) \left(q^3+q^2+q+1\right) \left(q^4+q^3+q^2+q+1\right) & 0 & 0 & 0 & 0 & 0 & -q^{3/2} \left(q^2-1\right)^3 \left(q^2+1\right)^2 \left(q^4+q^2+1\right) \left(q^4+q^3+q^2+q+1\right) & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^{12} & 0 & 0 & 0 & 0 & 0 & -q^9 \left(q^2+q+1\right) \left(q^4-1\right) & 0 & 0 & 0 & 0 & 0 & (q-1)^2 q^5 (q+1) \left(q^2+1\right)^2 \left(q^2+q+1\right) \left(q^4+q^3+q^2+q+1\right) & 0 & 0 & 0 & 0 & 0 & -(q-1)^3 (q+1)^2 \left(q^2+1\right)^2 \left(q^4+q^2+1\right) \left(q^4+q^3+q^2+q+1\right)^2 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^{12} & 0 & 0 & 0 & 0 & 0 & -(q-1) q^{17/2} \left(q^3+q^2+q+1\right)^2 & 0 & 0 & 0 & 0 & 0 & q^4 (q+1) \left(q^2+1\right)^2 \left(q^5-1\right)^2 & 0 & 0 & 0 & 0 & 0 & -\frac{\left(q^2-1\right)^3 \left(q^2+q+1\right) \left(q^8+2 q^6+q^5+2 q^4+q^3+2 q^2+1\right)^2}{q^{3/2}} & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^{12} & 0 & 0 & 0 & 0 & 0 & -q^8 \left(q^3+q^2+q+1\right) \left(q^5-1\right) & 0 & 0 & 0 & 0 & 0 & q^3 \left(q^2+1\right) \left(q^5-1\right)^2 \left(q^5+q^4+q^3+q^2+q+1\right) & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^{12} & 0 & 0 & 0 & 0 & 0 & -q^{15/2} \left(q^3+q^2+q+1\right) \left(q^6-1\right) & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^{12} & 0 & 0 & 0 \\
+& 0 & 0 & 0 & q^{15} & 0 & 0 & 0 & 0 & 0 & q^{27/2}-q^{33/2} & 0 & 0 & 0 & 0 & 0 & q^{18}-q^{15}-q^{14}+q^{11} & 0 & 0 & 0 & 0 & 0 & -q^{15/2} \left(q^3-1\right) \left(q^4-1\right) \left(q^5-1\right) & 0 & 0 & 0 & 0 & 0 & q^3 \left(q^3-1\right) \left(q^4-1\right) \left(q^5-1\right) \left(q^6-1\right) & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^{14} & 0 & 0 & 0 & 0 & 0 & -q^{12} (q+1) \left(q^3-1\right) & 0 & 0 & 0 & 0 & 0 & q^9 \left(q^3-1\right)^2 \left(q^3+q^2+q+1\right) & 0 & 0 & 0 & 0 & 0 & -(q-1)^3 q^5 \left(q^2+q+1\right) \left(q^3+q^2+q+1\right)^2 \left(q^4+q^3+q^2+q+1\right) & 0 & 0 & 0 & 0 & 0 & (q-1)^4 (q+1)^2 \left(q^2+1\right) \left(q^2-q+1\right) \left(q^2+q+1\right)^2 \left(q^4+q^3+q^2+q+1\right)^2 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^{13} & 0 & 0 & 0 & 0 & 0 & -(q-1) q^{21/2} \left(q^2+q+1\right)^2 & 0 & 0 & 0 & 0 & 0 & q^7 (q+1) \left(q^5+q^3-q^2-1\right)^2 & 0 & 0 & 0 & 0 & 0 & -(q-1)^3 q^{5/2} (q+1) \left(q^2+1\right)^2 \left(q^2+q+1\right) \left(q^4+q^3+q^2+q+1\right)^2 & 0 & 0 & 0 & 0 & 0 & \frac{(q-1)^4 \left(q^2+1\right) \left(q^2+q+1\right)^3 \left(q^3+1\right)^2 \left(q^4+q^3+q^2+q+1\right)^2}{q^3} & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^{12} & 0 & 0 & 0 & 0 & 0 & -q^9 \left(q^2+q+1\right) \left(q^4-1\right) & 0 & 0 & 0 & 0 & 0 & (q-1)^2 q^5 (q+1) \left(q^2+1\right)^2 \left(q^2+q+1\right) \left(q^4+q^3+q^2+q+1\right) & 0 & 0 & 0 & 0 & 0 & -(q-1)^3 (q+1)^2 \left(q^2+1\right)^2 \left(q^4+q^2+1\right) \left(q^4+q^3+q^2+q+1\right)^2 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^{11} & 0 & 0 & 0 & 0 & 0 & -q^{15/2} \left(q^2+q+1\right) \left(q^5-1\right) & 0 & 0 & 0 & 0 & 0 & q^3 \left(q^2+1\right) \left(q^3-1\right)^2 \left(q^3+1\right) \left(q^4+q^3+q^2+q+1\right) & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^{10} & 0 & 0 & 0 & 0 & 0 & -q^6 \left(q^2+q+1\right)^2 \left(q^4-q^3+q-1\right) & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^9 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & q^{18} & 0 & 0 & 0 & 0 & 0 & q^{17}-q^{19} & 0 & 0 & 0 & 0 & 0 & q^{20}-q^{18}-q^{17}+q^{15} & 0 & 0 & 0 & 0 & 0 & -(q-1)^3 q^{12} (q+1)^2 \left(q^2+1\right) \left(q^2+q+1\right) & 0 & 0 & 0 & 0 & 0 & (q-1)^4 q^8 (q+1)^2 \left(q^2+1\right) \left(q^2+q+1\right) \left(q^4+q^3+q^2+q+1\right) & 0 & 0 & 0 & 0 & 0 & -(q-1)^5 q^3 (q+1)^3 \left(q^2+1\right) \left(q^2-q+1\right) \left(q^2+q+1\right)^2 \left(q^4+q^3+q^2+q+1\right) & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^{16} & 0 & 0 & 0 & 0 & 0 & -(q-1) q^{29/2} (q+1)^2 & 0 & 0 & 0 & 0 & 0 & q^{12} (q+1) \left(q^3-1\right)^2 & 0 & 0 & 0 & 0 & 0 & -q^{17/2} \left(q^2-1\right)^3 \left(q^2+1\right)^2 \left(q^2+q+1\right) & 0 & 0 & 0 & 0 & 0 & (q-1)^4 q^4 (q+1)^2 \left(q^2+1\right) \left(q^2+q+1\right) \left(q^4+q^3+q^2+q+1\right)^2 & 0 & 0 & 0 & 0 & 0 & -\frac{(q-1)^5 (q+1)^4 \left(q^2+1\right) \left(q^2-q+1\right)^2 \left(q^2+q+1\right)^3 \left(q^4+q^3+q^2+q+1\right)}{q^{3/2}} & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^{14} & 0 & 0 & 0 & 0 & 0 & -q^{12} (q+1) \left(q^3-1\right) & 0 & 0 & 0 & 0 & 0 & q^9 \left(q^3-1\right)^2 \left(q^3+q^2+q+1\right) & 0 & 0 & 0 & 0 & 0 & -(q-1)^3 q^5 \left(q^2+q+1\right) \left(q^3+q^2+q+1\right)^2 \left(q^4+q^3+q^2+q+1\right) & 0 & 0 & 0 & 0 & 0 & (q-1)^4 (q+1)^2 \left(q^2+1\right) \left(q^2-q+1\right) \left(q^2+q+1\right)^2 \left(q^4+q^3+q^2+q+1\right)^2 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^{12} & 0 & 0 & 0 & 0 & 0 & -q^{29/2}-q^{27/2}+q^{21/2}+q^{19/2} & 0 & 0 & 0 & 0 & 0 & (q-1)^2 q^6 \left(q^2+q+1\right) \left(q^3+q^2+q+1\right) \left(q^4+q^3+q^2+q+1\right) & 0 & 0 & 0 & 0 & 0 & -q^{3/2} \left(q^2-1\right)^3 \left(q^2+1\right)^2 \left(q^4+q^2+1\right) \left(q^4+q^3+q^2+q+1\right) & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^{10} & 0 & 0 & 0 & 0 & 0 & -q^7 (q+1) \left(q^5-1\right) & 0 & 0 & 0 & 0 & 0 & q^3 \left(q^3-1\right)^2 \left(q^3+1\right) \left(q^4+q^3+q^2+q+1\right) & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^8 & 0 & 0 & 0 & 0 & 0 & -q^{23/2}-q^{21/2}+q^{11/2}+q^{9/2} & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^6 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & q^{21} & 0 & 0 & 0 & 0 & 0 & q^{41/2}-q^{43/2} & 0 & 0 & 0 & 0 & 0 & (q-1)^2 q^{19} (q+1) & 0 & 0 & 0 & 0 & 0 & -(q-1)^3 q^{33/2} (q+1) \left(q^2+q+1\right) & 0 & 0 & 0 & 0 & 0 & (q-1)^4 q^{13} (q+1)^2 \left(q^2+1\right) \left(q^2+q+1\right) & 0 & 0 & 0 & 0 & 0 & -(q-1)^5 q^{17/2} (q+1)^2 \left(q^2+1\right) \left(q^2+q+1\right) \left(q^4+q^3+q^2+q+1\right) & 0 & 0 & 0 & 0 & 0 & (q-1)^6 q^3 (q+1)^3 \left(q^2+1\right) \left(q^2-q+1\right) \left(q^2+q+1\right)^2 \left(q^4+q^3+q^2+q+1\right) & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^{18} & 0 & 0 & 0 & 0 & 0 & q^{17}-q^{19} & 0 & 0 & 0 & 0 & 0 & q^{20}-q^{18}-q^{17}+q^{15} & 0 & 0 & 0 & 0 & 0 & -(q-1)^3 q^{12} (q+1)^2 \left(q^2+1\right) \left(q^2+q+1\right) & 0 & 0 & 0 & 0 & 0 & (q-1)^4 q^8 (q+1)^2 \left(q^2+1\right) \left(q^2+q+1\right) \left(q^4+q^3+q^2+q+1\right) & 0 & 0 & 0 & 0 & 0 & -(q-1)^5 q^3 (q+1)^3 \left(q^2+1\right) \left(q^2-q+1\right) \left(q^2+q+1\right)^2 \left(q^4+q^3+q^2+q+1\right) & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^{15} & 0 & 0 & 0 & 0 & 0 & q^{27/2}-q^{33/2} & 0 & 0 & 0 & 0 & 0 & q^{18}-q^{15}-q^{14}+q^{11} & 0 & 0 & 0 & 0 & 0 & -q^{15/2} \left(q^3-1\right) \left(q^4-1\right) \left(q^5-1\right) & 0 & 0 & 0 & 0 & 0 & q^3 \left(q^3-1\right) \left(q^4-1\right) \left(q^5-1\right) \left(q^6-1\right) & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^{12} & 0 & 0 & 0 & 0 & 0 & q^{10}-q^{14} & 0 & 0 & 0 & 0 & 0 & q^{16}-q^{12}-q^{11}+q^7 & 0 & 0 & 0 & 0 & 0 & -q^3 \left(q^4-1\right) \left(q^5-1\right) \left(q^6-1\right) & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^9 & 0 & 0 & 0 & 0 & 0 & q^{13/2}-q^{23/2} & 0 & 0 & 0 & 0 & 0 & q^{14}-q^9-q^8+q^3 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^6 & 0 & 0 & 0 & 0 & 0 & q^3-q^9 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^3
+\end{array}
+\right),\left(
+\begin{array}{ccccccccccccccccccccccccccccccccccccccccccccccccc}
+ \frac{1}{q^3} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& \frac{q^6-1}{q^9} & 0 & 0 & 0 & 0 & 0 & \frac{1}{q^6} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & \frac{q^{11}-q^6-q^5+1}{q^{14}} & 0 & 0 & 0 & 0 & 0 & \frac{q^5-1}{q^{21/2}} & 0 & 0 & 0 & 0 & 0 & \frac{1}{q^9} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & \frac{\left(q^2-\frac{1}{q^2}\right) \left(q^5-1\right) \left(q^6-1\right)}{q^{16}} & 0 & 0 & 0 & 0 & 0 & \frac{q^9-q^5-q^4+1}{q^{14}} & 0 & 0 & 0 & 0 & 0 & \frac{q^4-1}{q^{12}} & 0 & 0 & 0 & 0 & 0 & \frac{1}{q^{12}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & \frac{\left(1-q^3\right) \left(1-q^4\right) \left(q^5-1\right) \left(q^6-1\right)}{q^{21}} & 0 & 0 & 0 & 0 & 0 & \frac{\left(1-q^3\right) \left(1-q^4\right) \left(q^5-1\right)}{q^{33/2}} & 0 & 0 & 0 & 0 & 0 & \frac{q^7-q^4-q^3+1}{q^{14}} & 0 & 0 & 0 & 0 & 0 & \frac{q^3-1}{q^{27/2}} & 0 & 0 & 0 & 0 & 0 & \frac{1}{q^{15}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & \frac{(q-1)^5 (q+1)^3 \left(q^2+1\right) \left(q^2-q+1\right) \left(q^2+q+1\right)^2 \left(q^4+q^3+q^2+q+1\right)}{q^{23}} & 0 & 0 & 0 & 0 & 0 & \frac{(q-1)^4 (q+1)^2 \left(q^2+1\right) \left(q^2+q+1\right) \left(q^4+q^3+q^2+q+1\right)}{q^{18}} & 0 & 0 & 0 & 0 & 0 & \frac{(q-1)^3 (q+1)^2 \left(q^2+1\right) \left(q^2+q+1\right)}{q^{15}} & 0 & 0 & 0 & 0 & 0 & \frac{q^5-q^3-q^2+1}{q^{14}} & 0 & 0 & 0 & 0 & 0 & \frac{q^2-1}{q^{15}} & 0 & 0 & 0 & 0 & 0 & \frac{1}{q^{18}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & \frac{(q-1)^6 (q+1)^3 \left(q^2+1\right) \left(q^2-q+1\right) \left(q^2+q+1\right)^2 \left(q^4+q^3+q^2+q+1\right)}{q^{24}} & 0 & 0 & 0 & 0 & 0 & \frac{(q-1)^5 (q+1)^2 \left(q^2+1\right) \left(q^2+q+1\right) \left(q^4+q^3+q^2+q+1\right)}{q^{37/2}} & 0 & 0 & 0 & 0 & 0 & \frac{(q-1)^4 (q+1)^2 \left(q^2+1\right) \left(q^2+q+1\right)}{q^{15}} & 0 & 0 & 0 & 0 & 0 & \frac{(q-1)^3 (q+1) \left(q^2+q+1\right)}{q^{27/2}} & 0 & 0 & 0 & 0 & 0 & \frac{(q-1)^2 (q+1)}{q^{14}} & 0 & 0 & 0 & 0 & 0 & \frac{q-1}{q^{33/2}} & 0 & 0 & 0 & 0 & 0 & \frac{1}{q^{21}} & 0 & 0 & 0 & 0 & 0 & 0 \\
+& \frac{1}{q^6} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & \frac{q^7+q^6-q-1}{q^{25/2}} & 0 & 0 & 0 & 0 & 0 & \frac{1}{q^8} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & \frac{\left(q^3-1\right)^2 \left(q^3+1\right) \left(q^4+q^3+q^2+q+1\right)}{q^{18}} & 0 & 0 & 0 & 0 & 0 & \frac{(q+1) \left(q^5-1\right)}{q^{13}} & 0 & 0 & 0 & 0 & 0 & \frac{1}{q^{10}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & \frac{\left(q^2-1\right)^3 \left(q^2+1\right)^2 \left(q^4+q^2+1\right) \left(q^4+q^3+q^2+q+1\right)}{q^{45/2}} & 0 & 0 & 0 & 0 & 0 & \frac{(q-1)^2 \left(q^2+q+1\right) \left(q^3+q^2+q+1\right) \left(q^4+q^3+q^2+q+1\right)}{q^{17}} & 0 & 0 & 0 & 0 & 0 & \frac{q^5+q^4-q-1}{q^{27/2}} & 0 & 0 & 0 & 0 & 0 & \frac{1}{q^{12}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & \frac{(q-1)^4 (q+1)^2 \left(q^2+1\right) \left(q^2-q+1\right) \left(q^2+q+1\right)^2 \left(q^4+q^3+q^2+q+1\right)^2}{q^{26}} & 0 & 0 & 0 & 0 & 0 & \frac{(q-1)^3 \left(q^2+q+1\right) \left(q^3+q^2+q+1\right)^2 \left(q^4+q^3+q^2+q+1\right)}{q^{20}} & 0 & 0 & 0 & 0 & 0 & \frac{\left(q^3-1\right)^2 \left(q^3+q^2+q+1\right)}{q^{16}} & 0 & 0 & 0 & 0 & 0 & \frac{(q+1) \left(q^3-1\right)}{q^{14}} & 0 & 0 & 0 & 0 & 0 & \frac{1}{q^{14}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & \frac{(q-1)^5 (q+1)^4 \left(q^2+1\right) \left(q^2-q+1\right)^2 \left(q^2+q+1\right)^3 \left(q^4+q^3+q^2+q+1\right)}{q^{57/2}} & 0 & 0 & 0 & 0 & 0 & \frac{(q-1)^4 (q+1)^2 \left(q^2+1\right) \left(q^2+q+1\right) \left(q^4+q^3+q^2+q+1\right)^2}{q^{22}} & 0 & 0 & 0 & 0 & 0 & \frac{\left(q^2-1\right)^3 \left(q^2+1\right)^2 \left(q^2+q+1\right)}{q^{35/2}} & 0 & 0 & 0 & 0 & 0 & \frac{(q+1) \left(q^3-1\right)^2}{q^{15}} & 0 & 0 & 0 & 0 & 0 & \frac{(q-1) (q+1)^2}{q^{29/2}} & 0 & 0 & 0 & 0 & 0 & \frac{1}{q^{16}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \frac{(q-1)^5 (q+1)^3 \left(q^2+1\right) \left(q^2-q+1\right) \left(q^2+q+1\right)^2 \left(q^4+q^3+q^2+q+1\right)}{q^{23}} & 0 & 0 & 0 & 0 & 0 & \frac{(q-1)^4 (q+1)^2 \left(q^2+1\right) \left(q^2+q+1\right) \left(q^4+q^3+q^2+q+1\right)}{q^{18}} & 0 & 0 & 0 & 0 & 0 & \frac{(q-1)^3 (q+1)^2 \left(q^2+1\right) \left(q^2+q+1\right)}{q^{15}} & 0 & 0 & 0 & 0 & 0 & \frac{q^5-q^3-q^2+1}{q^{14}} & 0 & 0 & 0 & 0 & 0 & \frac{q^2-1}{q^{15}} & 0 & 0 & 0 & 0 & 0 & \frac{1}{q^{18}} & 0 & 0 & 0 & 0 & 0 \\
+& 0 & \frac{1}{q^9} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & \frac{\left(q^2+q+1\right)^2 \left(q^4-q^3+q-1\right)}{q^{16}} & 0 & 0 & 0 & 0 & 0 & \frac{1}{q^{10}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & \frac{\left(q^2+1\right) \left(q^3-1\right)^2 \left(q^3+1\right) \left(q^4+q^3+q^2+q+1\right)}{q^{22}} & 0 & 0 & 0 & 0 & 0 & \frac{\left(q^2+q+1\right) \left(q^5-1\right)}{q^{31/2}} & 0 & 0 & 0 & 0 & 0 & \frac{1}{q^{11}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & \frac{(q-1)^3 (q+1)^2 \left(q^2+1\right)^2 \left(q^4+q^2+1\right) \left(q^4+q^3+q^2+q+1\right)^2}{q^{27}} & 0 & 0 & 0 & 0 & 0 & \frac{(q-1)^2 (q+1) \left(q^2+1\right)^2 \left(q^2+q+1\right) \left(q^4+q^3+q^2+q+1\right)}{q^{20}} & 0 & 0 & 0 & 0 & 0 & \frac{\left(q^2+q+1\right) \left(q^4-1\right)}{q^{15}} & 0 & 0 & 0 & 0 & 0 & \frac{1}{q^{12}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & \frac{(q-1)^4 \left(q^2+1\right) \left(q^2+q+1\right)^3 \left(q^3+1\right)^2 \left(q^4+q^3+q^2+q+1\right)^2}{q^{31}} & 0 & 0 & 0 & 0 & 0 & \frac{(q-1)^3 (q+1) \left(q^2+1\right)^2 \left(q^2+q+1\right) \left(q^4+q^3+q^2+q+1\right)^2}{q^{47/2}} & 0 & 0 & 0 & 0 & 0 & \frac{(q+1) \left(q^5+q^3-q^2-1\right)^2}{q^{18}} & 0 & 0 & 0 & 0 & 0 & \frac{(q-1) \left(q^2+q+1\right)^2}{q^{29/2}} & 0 & 0 & 0 & 0 & 0 & \frac{1}{q^{13}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \frac{(q-1)^4 (q+1)^2 \left(q^2+1\right) \left(q^2-q+1\right) \left(q^2+q+1\right)^2 \left(q^4+q^3+q^2+q+1\right)^2}{q^{26}} & 0 & 0 & 0 & 0 & 0 & \frac{(q-1)^3 \left(q^2+q+1\right) \left(q^3+q^2+q+1\right)^2 \left(q^4+q^3+q^2+q+1\right)}{q^{20}} & 0 & 0 & 0 & 0 & 0 & \frac{\left(q^3-1\right)^2 \left(q^3+q^2+q+1\right)}{q^{16}} & 0 & 0 & 0 & 0 & 0 & \frac{(q+1) \left(q^3-1\right)}{q^{14}} & 0 & 0 & 0 & 0 & 0 & \frac{1}{q^{14}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \frac{\left(1-q^3\right) \left(1-q^4\right) \left(q^5-1\right) \left(q^6-1\right)}{q^{21}} & 0 & 0 & 0 & 0 & 0 & \frac{\left(1-q^3\right) \left(1-q^4\right) \left(q^5-1\right)}{q^{33/2}} & 0 & 0 & 0 & 0 & 0 & \frac{q^7-q^4-q^3+1}{q^{14}} & 0 & 0 & 0 & 0 & 0 & \frac{q^3-1}{q^{27/2}} & 0 & 0 & 0 & 0 & 0 & \frac{1}{q^{15}} & 0 & 0 & 0 & 0 \\
+& 0 & 0 & \frac{1}{q^{12}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & \frac{(q-1) (q+1)^2 \left(q^2+1\right) \left(q^4+q^2+1\right)}{q^{39/2}} & 0 & 0 & 0 & 0 & 0 & \frac{1}{q^{12}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & \frac{\left(q^2+1\right) \left(q^5-1\right)^2 \left(q^5+q^4+q^3+q^2+q+1\right)}{q^{26}} & 0 & 0 & 0 & 0 & 0 & \frac{\left(q^3+q^2+q+1\right) \left(q^5-1\right)}{q^{18}} & 0 & 0 & 0 & 0 & 0 & \frac{1}{q^{12}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & \frac{\left(q^2-1\right)^3 \left(q^2+q+1\right) \left(q^8+2 q^6+q^5+2 q^4+q^3+2 q^2+1\right)^2}{q^{63/2}} & 0 & 0 & 0 & 0 & 0 & \frac{(q+1) \left(q^2+1\right)^2 \left(q^5-1\right)^2}{q^{23}} & 0 & 0 & 0 & 0 & 0 & \frac{(q-1) \left(q^3+q^2+q+1\right)^2}{q^{33/2}} & 0 & 0 & 0 & 0 & 0 & \frac{1}{q^{12}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \frac{(q-1)^3 (q+1)^2 \left(q^2+1\right)^2 \left(q^4+q^2+1\right) \left(q^4+q^3+q^2+q+1\right)^2}{q^{27}} & 0 & 0 & 0 & 0 & 0 & \frac{(q-1)^2 (q+1) \left(q^2+1\right)^2 \left(q^2+q+1\right) \left(q^4+q^3+q^2+q+1\right)}{q^{20}} & 0 & 0 & 0 & 0 & 0 & \frac{\left(q^2+q+1\right) \left(q^4-1\right)}{q^{15}} & 0 & 0 & 0 & 0 & 0 & \frac{1}{q^{12}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \frac{\left(q^2-1\right)^3 \left(q^2+1\right)^2 \left(q^4+q^2+1\right) \left(q^4+q^3+q^2+q+1\right)}{q^{45/2}} & 0 & 0 & 0 & 0 & 0 & \frac{(q-1)^2 \left(q^2+q+1\right) \left(q^3+q^2+q+1\right) \left(q^4+q^3+q^2+q+1\right)}{q^{17}} & 0 & 0 & 0 & 0 & 0 & \frac{q^5+q^4-q-1}{q^{27/2}} & 0 & 0 & 0 & 0 & 0 & \frac{1}{q^{12}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \frac{\left(q^2-\frac{1}{q^2}\right) \left(q^5-1\right) \left(q^6-1\right)}{q^{16}} & 0 & 0 & 0 & 0 & 0 & \frac{q^9-q^5-q^4+1}{q^{14}} & 0 & 0 & 0 & 0 & 0 & \frac{q^4-1}{q^{12}} & 0 & 0 & 0 & 0 & 0 & \frac{1}{q^{12}} & 0 & 0 & 0 \\
+& 0 & 0 & 0 & \frac{1}{q^{15}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & \frac{\left(q^4+q^3+q^2+q+1\right) \left(q^6-1\right)}{q^{23}} & 0 & 0 & 0 & 0 & 0 & \frac{1}{q^{14}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & \frac{(q+1) \left(q^9+q^7+q^5-q^4-q^2-1\right)^2}{q^{30}} & 0 & 0 & 0 & 0 & 0 & \frac{(q-1) \left(q^4+q^3+q^2+q+1\right)^2}{q^{41/2}} & 0 & 0 & 0 & 0 & 0 & \frac{1}{q^{13}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \frac{\left(q^2+1\right) \left(q^5-1\right)^2 \left(q^5+q^4+q^3+q^2+q+1\right)}{q^{26}} & 0 & 0 & 0 & 0 & 0 & \frac{\left(q^3+q^2+q+1\right) \left(q^5-1\right)}{q^{18}} & 0 & 0 & 0 & 0 & 0 & \frac{1}{q^{12}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \frac{\left(q^2+1\right) \left(q^3-1\right)^2 \left(q^3+1\right) \left(q^4+q^3+q^2+q+1\right)}{q^{22}} & 0 & 0 & 0 & 0 & 0 & \frac{\left(q^2+q+1\right) \left(q^5-1\right)}{q^{31/2}} & 0 & 0 & 0 & 0 & 0 & \frac{1}{q^{11}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \frac{\left(q^3-1\right)^2 \left(q^3+1\right) \left(q^4+q^3+q^2+q+1\right)}{q^{18}} & 0 & 0 & 0 & 0 & 0 & \frac{(q+1) \left(q^5-1\right)}{q^{13}} & 0 & 0 & 0 & 0 & 0 & \frac{1}{q^{10}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \frac{q^{11}-q^6-q^5+1}{q^{14}} & 0 & 0 & 0 & 0 & 0 & \frac{q^5-1}{q^{21/2}} & 0 & 0 & 0 & 0 & 0 & \frac{1}{q^9} & 0 & 0 \\
+& 0 & 0 & 0 & 0 & \frac{1}{q^{18}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & \frac{(q-1) \left(q^5+q^4+q^3+q^2+q+1\right)^2}{q^{53/2}} & 0 & 0 & 0 & 0 & 0 & \frac{1}{q^{16}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \frac{\left(q^4+q^3+q^2+q+1\right) \left(q^6-1\right)}{q^{23}} & 0 & 0 & 0 & 0 & 0 & \frac{1}{q^{14}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \frac{(q-1) (q+1)^2 \left(q^2+1\right) \left(q^4+q^2+1\right)}{q^{39/2}} & 0 & 0 & 0 & 0 & 0 & \frac{1}{q^{12}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \frac{\left(q^2+q+1\right)^2 \left(q^4-q^3+q-1\right)}{q^{16}} & 0 & 0 & 0 & 0 & 0 & \frac{1}{q^{10}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \frac{q^7+q^6-q-1}{q^{25/2}} & 0 & 0 & 0 & 0 & 0 & \frac{1}{q^8} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \frac{q^6-1}{q^9} & 0 & 0 & 0 & 0 & 0 & \frac{1}{q^6} & 0 \\
+& 0 & 0 & 0 & 0 & 0 & \frac{1}{q^{21}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \frac{1}{q^{18}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \frac{1}{q^{15}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \frac{1}{q^{12}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \frac{1}{q^9} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \frac{1}{q^6} & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \frac{1}{q^3}
+\end{array}
+\right),\left(
+\begin{array}{ccccccc}
+& 0 & 0 & 0 & 0 & 0 & \frac{1}{q^{3/2}} \\
+& 0 & 0 & 0 & 0 & \frac{1}{q} & 0 \\
+& 0 & 0 & 0 & \frac{1}{\sqrt{q}} & 0 & 0 \\
+& 0 & 0 & 1 & 0 & 0 & 0 \\
+& 0 & \sqrt{q} & 0 & 0 & 0 & 0 \\
+& q & 0 & 0 & 0 & 0 & 0 \\
+ q^{3/2} & 0 & 0 & 0 & 0 & 0 & 0
+\end{array}
+\right),\left(
+\begin{array}{ccccccc}
+& 0 & 0 & 0 & 0 & 0 & \frac{1}{q^{3/2}} \\
+& 0 & 0 & 0 & 0 & \frac{1}{q} & 0 \\
+& 0 & 0 & 0 & \frac{1}{\sqrt{q}} & 0 & 0 \\
+& 0 & 0 & 1 & 0 & 0 & 0 \\
+& 0 & \sqrt{q} & 0 & 0 & 0 & 0 \\
+& q & 0 & 0 & 0 & 0 & 0 \\
+ q^{3/2} & 0 & 0 & 0 & 0 & 0 & 0
+\end{array}
+\right),\left(
+\begin{array}{ccccccc}
+& 0 & 0 & 0 & 0 & 0 & \frac{1}{q^{3/2}} \\
+& 0 & 0 & 0 & 0 & \frac{1}{q} & 0 \\
+& 0 & 0 & 0 & \frac{1}{\sqrt{q}} & 0 & 0 \\
+& 0 & 0 & 1 & 0 & 0 & 0 \\
+& 0 & \sqrt{q} & 0 & 0 & 0 & 0 \\
+& q & 0 & 0 & 0 & 0 & 0 \\
+ q^{3/2} & 0 & 0 & 0 & 0 & 0 & 0
+\end{array}
+\right),\left(
+\begin{array}{ccccccc}
+& 0 & 0 & 0 & 0 & 0 & \frac{1}{q^{3/2}} \\
+& 0 & 0 & 0 & 0 & \frac{1}{q} & 0 \\
+& 0 & 0 & 0 & \frac{1}{\sqrt{q}} & 0 & 0 \\
+& 0 & 0 & 1 & 0 & 0 & 0 \\
+& 0 & \sqrt{q} & 0 & 0 & 0 & 0 \\
+& q & 0 & 0 & 0 & 0 & 0 \\
+ q^{3/2} & 0 & 0 & 0 & 0 & 0 & 0
+\end{array}
+\right)\right)\right]}{q^3+q^2+q+1+\frac{1}{q}+\frac{1}{q^2}+\frac{1}{q^3}}\right]</math> |
+coloured_jones_7 = <math>\textrm{Apart}\left[\frac{\textrm{Hold}\left[\textrm{REngine}\left(\textrm{MorseLink}(\textrm{MorseLink::Error: bad input}),\left(
+\begin{array}{cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc}
+ q^{7/2} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^7 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^{21/2} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^{14} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^{35/2} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^{21} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^{49/2} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^{28} & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& q^7 & 0 & 0 & 0 & 0 & 0 & 0 & q^{7/2}-q^{21/2} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^{19/2} & 0 & 0 & 0 & 0 & 0 & 0 & -q^{11/2} (q+1) \left(q^7-1\right) & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^{12} & 0 & 0 & 0 & 0 & 0 & 0 & -q^{15/2} \left(q^2+q+1\right) \left(q^7-1\right) & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^{29/2} & 0 & 0 & 0 & 0 & 0 & 0 & -q^{19/2} \left(q^3+q^2+q+1\right) \left(q^7-1\right) & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^{17} & 0 & 0 & 0 & 0 & 0 & 0 & -q^{23/2} \left(q^4+q^3+q^2+q+1\right) \left(q^7-1\right) & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^{39/2} & 0 & 0 & 0 & 0 & 0 & 0 & -q^{27/2} \left(q^5+q^4+q^3+q^2+q+1\right) \left(q^7-1\right) & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^{22} & 0 & 0 & 0 & 0 & 0 & 0 & -\frac{q^{31/2} \left(q^7-1\right)^2}{q-1} & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^{49/2} & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & q^{21/2} & 0 & 0 & 0 & 0 & 0 & 0 & q^{15/2}-q^{27/2} & 0 & 0 & 0 & 0 & 0 & 0 & q^{33/2}-q^{21/2}-q^{19/2}+q^{7/2} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^{12} & 0 & 0 & 0 & 0 & 0 & 0 & -q^{31/2}-q^{29/2}+q^{19/2}+q^{17/2} & 0 & 0 & 0 & 0 & 0 & 0 & q^4 \left(q^3-1\right)^2 \left(q^3+1\right) \left(q^6+q^5+q^4+q^3+q^2+q+1\right) & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^{27/2} & 0 & 0 & 0 & 0 & 0 & 0 & -q^{19/2} \left(q^2+q+1\right)^2 \left(q^4-q^3+q-1\right) & 0 & 0 & 0 & 0 & 0 & 0 & q^{9/2} \left(q^2+1\right) \left(q^3-1\right)^2 \left(q^3+1\right) \left(q^6+q^5+q^4+q^3+q^2+q+1\right) & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^{15} & 0 & 0 & 0 & 0 & 0 & 0 & -q^{21/2} \left(q^3+q^2+q+1\right) \left(q^6-1\right) & 0 & 0 & 0 & 0 & 0 & 0 & (q-1)^2 q^5 \left(q^2+1\right) \left(q^4+q^3+q^2+q+1\right) \left(q^5+q^4+q^3+q^2+q+1\right) \left(q^6+q^5+q^4+q^3+q^2+q+1\right) & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^{33/2} & 0 & 0 & 0 & 0 & 0 & 0 & -q^{23/2} \left(q^4+q^3+q^2+q+1\right) \left(q^6-1\right) & 0 & 0 & 0 & 0 & 0 & 0 & (q-1)^2 q^{11/2} (q+1) \left(q^4+q^2+1\right)^2 \left(q^4+q^3+q^2+q+1\right) \left(q^6+q^5+q^4+q^3+q^2+q+1\right) & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^{18} & 0 & 0 & 0 & 0 & 0 & 0 & -(q-1) q^{25/2} \left(q^5+q^4+q^3+q^2+q+1\right)^2 & 0 & 0 & 0 & 0 & 0 & 0 & q^6 (q+1) \left(q^4+q^2+1\right)^2 \left(q^7-1\right)^2 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^{39/2} & 0 & 0 & 0 & 0 & 0 & 0 & -q^{27/2} \left(q^5+q^4+q^3+q^2+q+1\right) \left(q^7-1\right) & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^{21} & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & q^{14} & 0 & 0 & 0 & 0 & 0 & 0 & q^{23/2}-q^{33/2} & 0 & 0 & 0 & 0 & 0 & 0 & q^{19}-q^{14}-q^{13}+q^8 & 0 & 0 & 0 & 0 & 0 & 0 & -q^{43/2}+q^{33/2}+q^{31/2}+q^{29/2}-q^{21/2}-q^{19/2}-q^{17/2}+q^{7/2} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^{29/2} & 0 & 0 & 0 & 0 & 0 & 0 & -q^{23/2} (q+1) \left(q^5-1\right) & 0 & 0 & 0 & 0 & 0 & 0 & q^{15/2} \left(q^3-1\right)^2 \left(q^3+1\right) \left(q^4+q^3+q^2+q+1\right) & 0 & 0 & 0 & 0 & 0 & 0 & -q^{5/2} \left(q^3+q^2+q+1\right) \left(q^5-1\right) \left(q^6-1\right) \left(q^7-1\right) & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^{15} & 0 & 0 & 0 & 0 & 0 & 0 & -q^{23/2} \left(q^2+q+1\right) \left(q^5-1\right) & 0 & 0 & 0 & 0 & 0 & 0 & q^7 \left(q^2+1\right) \left(q^3-1\right)^2 \left(q^3+1\right) \left(q^4+q^3+q^2+q+1\right) & 0 & 0 & 0 & 0 & 0 & 0 & -(q-1)^3 q^{3/2} \left(q^2+1\right) \left(q^4+q^3+q^2+q+1\right)^2 \left(q^5+q^4+q^3+q^2+q+1\right) \left(q^6+q^5+q^4+q^3+q^2+q+1\right) & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^{31/2} & 0 & 0 & 0 & 0 & 0 & 0 & -q^{23/2} \left(q^3+q^2+q+1\right) \left(q^5-1\right) & 0 & 0 & 0 & 0 & 0 & 0 & q^{13/2} \left(q^2+1\right) \left(q^5-1\right)^2 \left(q^5+q^4+q^3+q^2+q+1\right) & 0 & 0 & 0 & 0 & 0 & 0 & -(q-1)^3 \sqrt{q} \left(q^2+1\right) \left(q^2+q+1\right) \left(q^3+1\right)^2 \left(q^4+q^3+q^2+q+1\right)^2 \left(q^6+q^5+q^4+q^3+q^2+q+1\right) & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^{16} & 0 & 0 & 0 & 0 & 0 & 0 & -(q-1) q^{23/2} \left(q^4+q^3+q^2+q+1\right)^2 & 0 & 0 & 0 & 0 & 0 & 0 & q^6 (q+1) \left(q^9+q^7+q^5-q^4-q^2-1\right)^2 & 0 & 0 & 0 & 0 & 0 & 0 & -\frac{(q-1)^3 (q+1) \left(q^2-q+1\right)^2 \left(q^2+q+1\right) \left(q^4+q^3+q^2+q+1\right)^2 \left(q^6+q^5+q^4+q^3+q^2+q+1\right)^2}{\sqrt{q}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^{33/2} & 0 & 0 & 0 & 0 & 0 & 0 & -q^{23/2} \left(q^4+q^3+q^2+q+1\right) \left(q^6-1\right) & 0 & 0 & 0 & 0 & 0 & 0 & (q-1)^2 q^{11/2} (q+1) \left(q^4+q^2+1\right)^2 \left(q^4+q^3+q^2+q+1\right) \left(q^6+q^5+q^4+q^3+q^2+q+1\right) & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^{17} & 0 & 0 & 0 & 0 & 0 & 0 & -q^{23/2} \left(q^4+q^3+q^2+q+1\right) \left(q^7-1\right) & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^{35/2} & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & q^{35/2} & 0 & 0 & 0 & 0 & 0 & 0 & q^{31/2}-q^{39/2} & 0 & 0 & 0 & 0 & 0 & 0 & q^{43/2}-q^{35/2}-q^{33/2}+q^{25/2} & 0 & 0 & 0 & 0 & 0 & 0 & -q^{17/2} \left(q^4-1\right) \left(q^5-1\right) \left(q^6-1\right) & 0 & 0 & 0 & 0 & 0 & 0 & q^{7/2} \left(q^4-1\right) \left(q^5-1\right) \left(q^6-1\right) \left(q^7-1\right) & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^{17} & 0 & 0 & 0 & 0 & 0 & 0 & -q^{39/2}-q^{37/2}+q^{31/2}+q^{29/2} & 0 & 0 & 0 & 0 & 0 & 0 & (q-1)^2 q^{11} \left(q^2+q+1\right) \left(q^3+q^2+q+1\right) \left(q^4+q^3+q^2+q+1\right) & 0 & 0 & 0 & 0 & 0 & 0 & -q^{13/2} \left(q^2-1\right)^3 \left(q^2+1\right)^2 \left(q^4+q^2+1\right) \left(q^4+q^3+q^2+q+1\right) & 0 & 0 & 0 & 0 & 0 & 0 & q \left(q^3+q^2+q+1\right) \left(q^5-1\right)^2 \left(q^6-1\right) \left(q^7-1\right) & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^{33/2} & 0 & 0 & 0 & 0 & 0 & 0 & -q^{27/2} \left(q^2+q+1\right) \left(q^4-1\right) & 0 & 0 & 0 & 0 & 0 & 0 & (q-1)^2 q^{19/2} (q+1) \left(q^2+1\right)^2 \left(q^2+q+1\right) \left(q^4+q^3+q^2+q+1\right) & 0 & 0 & 0 & 0 & 0 & 0 & -(q-1)^3 q^{9/2} (q+1)^2 \left(q^2+1\right)^2 \left(q^4+q^2+1\right) \left(q^4+q^3+q^2+q+1\right)^2 & 0 & 0 & 0 & 0 & 0 & 0 & \frac{(q-1)^4 \left(q^2+1\right) \left(q^4+q^3+q^2+q+1\right)^2 \left(q^5+q^4+q^3+q^2+q+1\right)^2 \left(q^6+q^5+q^4+q^3+q^2+q+1\right)}{q^{3/2}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^{16} & 0 & 0 & 0 & 0 & 0 & 0 & -(q-1) q^{25/2} \left(q^3+q^2+q+1\right)^2 & 0 & 0 & 0 & 0 & 0 & 0 & q^8 (q+1) \left(q^2+1\right)^2 \left(q^5-1\right)^2 & 0 & 0 & 0 & 0 & 0 & 0 & -q^{5/2} \left(q^2-1\right)^3 \left(q^2+q+1\right) \left(q^8+2 q^6+q^5+2 q^4+q^3+2 q^2+1\right)^2 & 0 & 0 & 0 & 0 & 0 & 0 & \frac{(q-1)^4 \left(q^2+1\right) \left(q^2+q+1\right) \left(q^3+1\right)^2 \left(q^4+q^3+q^2+q+1\right)^2 \left(q^6+q^5+q^4+q^3+q^2+q+1\right)^2}{q^4} & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^{31/2} & 0 & 0 & 0 & 0 & 0 & 0 & -q^{23/2} \left(q^3+q^2+q+1\right) \left(q^5-1\right) & 0 & 0 & 0 & 0 & 0 & 0 & q^{13/2} \left(q^2+1\right) \left(q^5-1\right)^2 \left(q^5+q^4+q^3+q^2+q+1\right) & 0 & 0 & 0 & 0 & 0 & 0 & -(q-1)^3 \sqrt{q} \left(q^2+1\right) \left(q^2+q+1\right) \left(q^3+1\right)^2 \left(q^4+q^3+q^2+q+1\right)^2 \left(q^6+q^5+q^4+q^3+q^2+q+1\right) & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^{15} & 0 & 0 & 0 & 0 & 0 & 0 & -q^{21/2} \left(q^3+q^2+q+1\right) \left(q^6-1\right) & 0 & 0 & 0 & 0 & 0 & 0 & (q-1)^2 q^5 \left(q^2+1\right) \left(q^4+q^3+q^2+q+1\right) \left(q^5+q^4+q^3+q^2+q+1\right) \left(q^6+q^5+q^4+q^3+q^2+q+1\right) & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^{29/2} & 0 & 0 & 0 & 0 & 0 & 0 & -q^{19/2} \left(q^3+q^2+q+1\right) \left(q^7-1\right) & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^{14} & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & q^{21} & 0 & 0 & 0 & 0 & 0 & 0 & q^{39/2}-q^{45/2} & 0 & 0 & 0 & 0 & 0 & 0 & q^{24}-q^{21}-q^{20}+q^{17} & 0 & 0 & 0 & 0 & 0 & 0 & -q^{27/2} \left(q^3-1\right) \left(q^4-1\right) \left(q^5-1\right) & 0 & 0 & 0 & 0 & 0 & 0 & q^9 \left(q^3-1\right) \left(q^4-1\right) \left(q^5-1\right) \left(q^6-1\right) & 0 & 0 & 0 & 0 & 0 & 0 & -q^{7/2} \left(q^3-1\right) \left(q^4-1\right) \left(q^5-1\right) \left(q^6-1\right) \left(q^7-1\right) & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^{39/2} & 0 & 0 & 0 & 0 & 0 & 0 & -q^{35/2} (q+1) \left(q^3-1\right) & 0 & 0 & 0 & 0 & 0 & 0 & q^{29/2} \left(q^3-1\right)^2 \left(q^3+q^2+q+1\right) & 0 & 0 & 0 & 0 & 0 & 0 & -(q-1)^3 q^{21/2} \left(q^2+q+1\right) \left(q^3+q^2+q+1\right)^2 \left(q^4+q^3+q^2+q+1\right) & 0 & 0 & 0 & 0 & 0 & 0 & (q-1)^4 q^{11/2} (q+1)^2 \left(q^2+1\right) \left(q^2-q+1\right) \left(q^2+q+1\right)^2 \left(q^4+q^3+q^2+q+1\right)^2 & 0 & 0 & 0 & 0 & 0 & 0 & -\frac{q^3 \left(q^{3/2}-\frac{1}{q^{3/2}}\right) \left(q^2-\frac{1}{q^2}\right) \left(q^5-1\right) \left(q^6-1\right)^2 \left(q^7-1\right)}{q-1} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^{18} & 0 & 0 & 0 & 0 & 0 & 0 & -(q-1) q^{31/2} \left(q^2+q+1\right)^2 & 0 & 0 & 0 & 0 & 0 & 0 & q^{12} (q+1) \left(q^5+q^3-q^2-1\right)^2 & 0 & 0 & 0 & 0 & 0 & 0 & -(q-1)^3 q^{15/2} (q+1) \left(q^2+1\right)^2 \left(q^2+q+1\right) \left(q^4+q^3+q^2+q+1\right)^2 & 0 & 0 & 0 & 0 & 0 & 0 & (q-1)^4 q^2 \left(q^2+1\right) \left(q^2+q+1\right)^3 \left(q^3+1\right)^2 \left(q^4+q^3+q^2+q+1\right)^2 & 0 & 0 & 0 & 0 & 0 & 0 & -\frac{(q-1)^5 \left(q^2+1\right) \left(q^2+q+1\right)^3 \left(q^3+1\right)^2 \left(q^4+q^3+q^2+q+1\right) \left(q^6+q^5+q^4+q^3+q^2+q+1\right)^2}{q^{9/2}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^{33/2} & 0 & 0 & 0 & 0 & 0 & 0 & -q^{27/2} \left(q^2+q+1\right) \left(q^4-1\right) & 0 & 0 & 0 & 0 & 0 & 0 & (q-1)^2 q^{19/2} (q+1) \left(q^2+1\right)^2 \left(q^2+q+1\right) \left(q^4+q^3+q^2+q+1\right) & 0 & 0 & 0 & 0 & 0 & 0 & -(q-1)^3 q^{9/2} (q+1)^2 \left(q^2+1\right)^2 \left(q^4+q^2+1\right) \left(q^4+q^3+q^2+q+1\right)^2 & 0 & 0 & 0 & 0 & 0 & 0 & \frac{(q-1)^4 \left(q^2+1\right) \left(q^4+q^3+q^2+q+1\right)^2 \left(q^5+q^4+q^3+q^2+q+1\right)^2 \left(q^6+q^5+q^4+q^3+q^2+q+1\right)}{q^{3/2}} & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^{15} & 0 & 0 & 0 & 0 & 0 & 0 & -q^{23/2} \left(q^2+q+1\right) \left(q^5-1\right) & 0 & 0 & 0 & 0 & 0 & 0 & q^7 \left(q^2+1\right) \left(q^3-1\right)^2 \left(q^3+1\right) \left(q^4+q^3+q^2+q+1\right) & 0 & 0 & 0 & 0 & 0 & 0 & -(q-1)^3 q^{3/2} \left(q^2+1\right) \left(q^4+q^3+q^2+q+1\right)^2 \left(q^5+q^4+q^3+q^2+q+1\right) \left(q^6+q^5+q^4+q^3+q^2+q+1\right) & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^{27/2} & 0 & 0 & 0 & 0 & 0 & 0 & -q^{19/2} \left(q^2+q+1\right)^2 \left(q^4-q^3+q-1\right) & 0 & 0 & 0 & 0 & 0 & 0 & q^{9/2} \left(q^2+1\right) \left(q^3-1\right)^2 \left(q^3+1\right) \left(q^6+q^5+q^4+q^3+q^2+q+1\right) & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^{12} & 0 & 0 & 0 & 0 & 0 & 0 & -q^{15/2} \left(q^2+q+1\right) \left(q^7-1\right) & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^{21/2} & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & q^{49/2} & 0 & 0 & 0 & 0 & 0 & 0 & -q^{47/2} \left(q^2-1\right) & 0 & 0 & 0 & 0 & 0 & 0 & q^{53/2}-q^{49/2}-q^{47/2}+q^{43/2} & 0 & 0 & 0 & 0 & 0 & 0 & -(q-1)^3 q^{37/2} (q+1)^2 \left(q^2+1\right) \left(q^2+q+1\right) & 0 & 0 & 0 & 0 & 0 & 0 & (q-1)^4 q^{29/2} (q+1)^2 \left(q^2+1\right) \left(q^2+q+1\right) \left(q^4+q^3+q^2+q+1\right) & 0 & 0 & 0 & 0 & 0 & 0 & -(q-1)^5 q^{19/2} (q+1)^3 \left(q^2+1\right) \left(q^2-q+1\right) \left(q^2+q+1\right)^2 \left(q^4+q^3+q^2+q+1\right) & 0 & 0 & 0 & 0 & 0 & 0 & (q-1)^3 q^{7/2} (q+1)^2 \left(q^2+1\right) \left(q^2+q+1\right) \left(q^5-1\right) \left(q^6-1\right) \left(q^7-1\right) & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^{22} & 0 & 0 & 0 & 0 & 0 & 0 & -(q-1) q^{41/2} (q+1)^2 & 0 & 0 & 0 & 0 & 0 & 0 & q^{18} (q+1) \left(q^3-1\right)^2 & 0 & 0 & 0 & 0 & 0 & 0 & -q^{29/2} \left(q^2-1\right)^3 \left(q^2+1\right)^2 \left(q^2+q+1\right) & 0 & 0 & 0 & 0 & 0 & 0 & (q-1)^4 q^{10} (q+1)^2 \left(q^2+1\right) \left(q^2+q+1\right) \left(q^4+q^3+q^2+q+1\right)^2 & 0 & 0 & 0 & 0 & 0 & 0 & -(q-1)^5 q^{9/2} (q+1)^4 \left(q^2+1\right) \left(q^2-q+1\right)^2 \left(q^2+q+1\right)^3 \left(q^4+q^3+q^2+q+1\right) & 0 & 0 & 0 & 0 & 0 & 0 & \frac{(q-1)^6 (q+1)^3 \left(q^2+1\right) \left(q^2-q+1\right) \left(q^2+q+1\right)^2 \left(q^4+q^3+q^2+q+1\right) \left(q^6+q^5+q^4+q^3+q^2+q+1\right)^2}{q^2} & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^{39/2} & 0 & 0 & 0 & 0 & 0 & 0 & -q^{35/2} (q+1) \left(q^3-1\right) & 0 & 0 & 0 & 0 & 0 & 0 & q^{29/2} \left(q^3-1\right)^2 \left(q^3+q^2+q+1\right) & 0 & 0 & 0 & 0 & 0 & 0 & -(q-1)^3 q^{21/2} \left(q^2+q+1\right) \left(q^3+q^2+q+1\right)^2 \left(q^4+q^3+q^2+q+1\right) & 0 & 0 & 0 & 0 & 0 & 0 & (q-1)^4 q^{11/2} (q+1)^2 \left(q^2+1\right) \left(q^2-q+1\right) \left(q^2+q+1\right)^2 \left(q^4+q^3+q^2+q+1\right)^2 & 0 & 0 & 0 & 0 & 0 & 0 & -\frac{q^3 \left(q^{3/2}-\frac{1}{q^{3/2}}\right) \left(q^2-\frac{1}{q^2}\right) \left(q^5-1\right) \left(q^6-1\right)^2 \left(q^7-1\right)}{q-1} & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^{17} & 0 & 0 & 0 & 0 & 0 & 0 & -q^{39/2}-q^{37/2}+q^{31/2}+q^{29/2} & 0 & 0 & 0 & 0 & 0 & 0 & (q-1)^2 q^{11} \left(q^2+q+1\right) \left(q^3+q^2+q+1\right) \left(q^4+q^3+q^2+q+1\right) & 0 & 0 & 0 & 0 & 0 & 0 & -q^{13/2} \left(q^2-1\right)^3 \left(q^2+1\right)^2 \left(q^4+q^2+1\right) \left(q^4+q^3+q^2+q+1\right) & 0 & 0 & 0 & 0 & 0 & 0 & q \left(q^3+q^2+q+1\right) \left(q^5-1\right)^2 \left(q^6-1\right) \left(q^7-1\right) & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^{29/2} & 0 & 0 & 0 & 0 & 0 & 0 & -q^{23/2} (q+1) \left(q^5-1\right) & 0 & 0 & 0 & 0 & 0 & 0 & q^{15/2} \left(q^3-1\right)^2 \left(q^3+1\right) \left(q^4+q^3+q^2+q+1\right) & 0 & 0 & 0 & 0 & 0 & 0 & -q^{5/2} \left(q^3+q^2+q+1\right) \left(q^5-1\right) \left(q^6-1\right) \left(q^7-1\right) & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^{12} & 0 & 0 & 0 & 0 & 0 & 0 & -q^{31/2}-q^{29/2}+q^{19/2}+q^{17/2} & 0 & 0 & 0 & 0 & 0 & 0 & q^4 \left(q^3-1\right)^2 \left(q^3+1\right) \left(q^6+q^5+q^4+q^3+q^2+q+1\right) & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^{19/2} & 0 & 0 & 0 & 0 & 0 & 0 & -q^{11/2} (q+1) \left(q^7-1\right) & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^7 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & q^{28} & 0 & 0 & 0 & 0 & 0 & 0 & -(q-1) q^{55/2} & 0 & 0 & 0 & 0 & 0 & 0 & (q-1)^2 q^{26} (q+1) & 0 & 0 & 0 & 0 & 0 & 0 & -(q-1)^3 q^{47/2} (q+1) \left(q^2+q+1\right) & 0 & 0 & 0 & 0 & 0 & 0 & (q-1)^4 q^{20} (q+1)^2 \left(q^2+1\right) \left(q^2+q+1\right) & 0 & 0 & 0 & 0 & 0 & 0 & -(q-1)^5 q^{31/2} (q+1)^2 \left(q^2+1\right) \left(q^2+q+1\right) \left(q^4+q^3+q^2+q+1\right) & 0 & 0 & 0 & 0 & 0 & 0 & (q-1)^6 q^{10} (q+1)^3 \left(q^2+1\right) \left(q^2-q+1\right) \left(q^2+q+1\right)^2 \left(q^4+q^3+q^2+q+1\right) & 0 & 0 & 0 & 0 & 0 & 0 & -(q-1)^7 q^{7/2} (q+1)^3 \left(q^2+1\right) \left(q^2-q+1\right) \left(q^2+q+1\right)^2 \left(q^4+q^3+q^2+q+1\right) \left(q^6+q^5+q^4+q^3+q^2+q+1\right) & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^{49/2} & 0 & 0 & 0 & 0 & 0 & 0 & -q^{47/2} \left(q^2-1\right) & 0 & 0 & 0 & 0 & 0 & 0 & q^{53/2}-q^{49/2}-q^{47/2}+q^{43/2} & 0 & 0 & 0 & 0 & 0 & 0 & -(q-1)^3 q^{37/2} (q+1)^2 \left(q^2+1\right) \left(q^2+q+1\right) & 0 & 0 & 0 & 0 & 0 & 0 & (q-1)^4 q^{29/2} (q+1)^2 \left(q^2+1\right) \left(q^2+q+1\right) \left(q^4+q^3+q^2+q+1\right) & 0 & 0 & 0 & 0 & 0 & 0 & -(q-1)^5 q^{19/2} (q+1)^3 \left(q^2+1\right) \left(q^2-q+1\right) \left(q^2+q+1\right)^2 \left(q^4+q^3+q^2+q+1\right) & 0 & 0 & 0 & 0 & 0 & 0 & (q-1)^3 q^{7/2} (q+1)^2 \left(q^2+1\right) \left(q^2+q+1\right) \left(q^5-1\right) \left(q^6-1\right) \left(q^7-1\right) & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^{21} & 0 & 0 & 0 & 0 & 0 & 0 & q^{39/2}-q^{45/2} & 0 & 0 & 0 & 0 & 0 & 0 & q^{24}-q^{21}-q^{20}+q^{17} & 0 & 0 & 0 & 0 & 0 & 0 & -q^{27/2} \left(q^3-1\right) \left(q^4-1\right) \left(q^5-1\right) & 0 & 0 & 0 & 0 & 0 & 0 & q^9 \left(q^3-1\right) \left(q^4-1\right) \left(q^5-1\right) \left(q^6-1\right) & 0 & 0 & 0 & 0 & 0 & 0 & -q^{7/2} \left(q^3-1\right) \left(q^4-1\right) \left(q^5-1\right) \left(q^6-1\right) \left(q^7-1\right) & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^{35/2} & 0 & 0 & 0 & 0 & 0 & 0 & q^{31/2}-q^{39/2} & 0 & 0 & 0 & 0 & 0 & 0 & q^{43/2}-q^{35/2}-q^{33/2}+q^{25/2} & 0 & 0 & 0 & 0 & 0 & 0 & -q^{17/2} \left(q^4-1\right) \left(q^5-1\right) \left(q^6-1\right) & 0 & 0 & 0 & 0 & 0 & 0 & q^{7/2} \left(q^4-1\right) \left(q^5-1\right) \left(q^6-1\right) \left(q^7-1\right) & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^{14} & 0 & 0 & 0 & 0 & 0 & 0 & q^{23/2}-q^{33/2} & 0 & 0 & 0 & 0 & 0 & 0 & q^{19}-q^{14}-q^{13}+q^8 & 0 & 0 & 0 & 0 & 0 & 0 & -q^{43/2}+q^{33/2}+q^{31/2}+q^{29/2}-q^{21/2}-q^{19/2}-q^{17/2}+q^{7/2} & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^{21/2} & 0 & 0 & 0 & 0 & 0 & 0 & q^{15/2}-q^{27/2} & 0 & 0 & 0 & 0 & 0 & 0 & q^{33/2}-q^{21/2}-q^{19/2}+q^{7/2} & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^7 & 0 & 0 & 0 & 0 & 0 & 0 & q^{7/2}-q^{21/2} & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & q^{7/2}
+\end{array}
+\right),\left(
+\begin{array}{cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc}
+ \frac{1}{q^{7/2}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& \frac{q^7-1}{q^{21/2}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{1}{q^7} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & \frac{q^{13}-q^7-q^6+1}{q^{33/2}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{q^6-1}{q^{25/2}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{1}{q^{21/2}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & \frac{\left(q^5-1\right) \left(q^6-1\right) \left(q^7-1\right)}{q^{43/2}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{q^{11}-q^6-q^5+1}{q^{17}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{q^5-1}{q^{29/2}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{1}{q^{14}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & \frac{\left(q^2-\frac{1}{q^2}\right) \left(q^5-1\right) \left(q^6-1\right) \left(q^7-1\right)}{q^{47/2}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{\left(q^2-\frac{1}{q^2}\right) \left(q^5-1\right) \left(q^6-1\right)}{q^{37/2}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{q^9-q^5-q^4+1}{q^{35/2}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{q^4-1}{q^{33/2}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{1}{q^{35/2}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & \frac{\left(1-q^3\right) \left(1-q^4\right) \left(q^5-1\right) \left(q^6-1\right) \left(q^7-1\right)}{q^{57/2}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{\left(1-q^3\right) \left(1-q^4\right) \left(q^5-1\right) \left(q^6-1\right)}{q^{23}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{\left(1-q^3\right) \left(1-q^4\right) \left(q^5-1\right)}{q^{39/2}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{q^7-q^4-q^3+1}{q^{18}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{q^3-1}{q^{37/2}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{1}{q^{21}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & \frac{\left(q^2-1\right) \left(1-q^3\right) \left(1-q^4\right) \left(q^5-1\right) \left(q^6-1\right) \left(q^7-1\right)}{q^{61/2}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{(q-1)^5 (q+1)^3 \left(q^2+1\right) \left(q^2-q+1\right) \left(q^2+q+1\right)^2 \left(q^4+q^3+q^2+q+1\right)}{q^{49/2}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{(q-1)^4 (q+1)^2 \left(q^2+1\right) \left(q^2+q+1\right) \left(q^4+q^3+q^2+q+1\right)}{q^{41/2}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{(q-1)^3 (q+1)^2 \left(q^2+1\right) \left(q^2+q+1\right)}{q^{37/2}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{q^5-q^3-q^2+1}{q^{37/2}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{q^2-1}{q^{41/2}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{1}{q^{49/2}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & \frac{(q-1)^7 (q+1)^3 \left(q^2+1\right) \left(q^2-q+1\right) \left(q^2+q+1\right)^2 \left(q^4+q^3+q^2+q+1\right) \left(q^6+q^5+q^4+q^3+q^2+q+1\right)}{q^{63/2}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{(q-1)^6 (q+1)^3 \left(q^2+1\right) \left(q^2-q+1\right) \left(q^2+q+1\right)^2 \left(q^4+q^3+q^2+q+1\right)}{q^{25}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{(q-1)^5 (q+1)^2 \left(q^2+1\right) \left(q^2+q+1\right) \left(q^4+q^3+q^2+q+1\right)}{q^{41/2}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{(q-1)^4 (q+1)^2 \left(q^2+1\right) \left(q^2+q+1\right)}{q^{18}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{(q-1)^3 (q+1) \left(q^2+q+1\right)}{q^{35/2}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{(q-1)^2 (q+1)}{q^{19}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{q-1}{q^{45/2}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{1}{q^{28}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& \frac{1}{q^7} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & \frac{(q+1) \left(q^7-1\right)}{q^{29/2}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{1}{q^{19/2}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & \frac{\left(q^3-1\right)^2 \left(q^3+1\right) \left(q^6+q^5+q^4+q^3+q^2+q+1\right)}{q^{21}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{q^7+q^6-q-1}{q^{31/2}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{1}{q^{12}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & \frac{\left(q^2-\frac{1}{q^2}\right) \left(q^5-1\right) \left(q^6-1\right) \left(q^7-1\right)}{(q-1) q^{49/2}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{\left(q^3-1\right)^2 \left(q^3+1\right) \left(q^4+q^3+q^2+q+1\right)}{q^{41/2}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{(q+1) \left(q^5-1\right)}{q^{33/2}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{1}{q^{29/2}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & \frac{\left(q^2-\frac{1}{q^2}\right) \left(q^5-1\right)^2 \left(q^6-1\right) \left(q^7-1\right)}{(q-1) q^{29}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{\left(q^2-1\right)^3 \left(q^2+1\right)^2 \left(q^4+q^2+1\right) \left(q^4+q^3+q^2+q+1\right)}{q^{49/2}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{(q-1)^2 \left(q^2+q+1\right) \left(q^3+q^2+q+1\right) \left(q^4+q^3+q^2+q+1\right)}{q^{20}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{q^5+q^4-q-1}{q^{35/2}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{1}{q^{17}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & \frac{\left(q^{3/2}-\frac{1}{q^{3/2}}\right) \left(q^2-\frac{1}{q^2}\right) \left(q^5-1\right) \left(q^6-1\right)^2 \left(q^7-1\right)}{(q-1) q^{31}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{(q-1)^4 (q+1)^2 \left(q^2+1\right) \left(q^2-q+1\right) \left(q^2+q+1\right)^2 \left(q^4+q^3+q^2+q+1\right)^2}{q^{55/2}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{(q-1)^3 \left(q^2+q+1\right) \left(q^3+q^2+q+1\right)^2 \left(q^4+q^3+q^2+q+1\right)}{q^{45/2}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{\left(q^3-1\right)^2 \left(q^3+q^2+q+1\right)}{q^{39/2}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{(q+1) \left(q^3-1\right)}{q^{37/2}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{1}{q^{39/2}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & \frac{(q-1)^6 (q+1)^3 \left(q^2+1\right) \left(q^2-q+1\right) \left(q^2+q+1\right)^2 \left(q^4+q^3+q^2+q+1\right) \left(q^6+q^5+q^4+q^3+q^2+q+1\right)^2}{q^{37}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{(q-1)^5 (q+1)^4 \left(q^2+1\right) \left(q^2-q+1\right)^2 \left(q^2+q+1\right)^3 \left(q^4+q^3+q^2+q+1\right)}{q^{59/2}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{(q-1)^4 (q+1)^2 \left(q^2+1\right) \left(q^2+q+1\right) \left(q^4+q^3+q^2+q+1\right)^2}{q^{24}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{\left(q^2-1\right)^3 \left(q^2+1\right)^2 \left(q^2+q+1\right)}{q^{41/2}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{(q+1) \left(q^3-1\right)^2}{q^{19}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{(q-1) (q+1)^2}{q^{39/2}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{1}{q^{22}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \frac{\left(q^2-1\right) \left(1-q^3\right) \left(1-q^4\right) \left(q^5-1\right) \left(q^6-1\right) \left(q^7-1\right)}{q^{61/2}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{(q-1)^5 (q+1)^3 \left(q^2+1\right) \left(q^2-q+1\right) \left(q^2+q+1\right)^2 \left(q^4+q^3+q^2+q+1\right)}{q^{49/2}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{(q-1)^4 (q+1)^2 \left(q^2+1\right) \left(q^2+q+1\right) \left(q^4+q^3+q^2+q+1\right)}{q^{41/2}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{(q-1)^3 (q+1)^2 \left(q^2+1\right) \left(q^2+q+1\right)}{q^{37/2}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{q^5-q^3-q^2+1}{q^{37/2}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{q^2-1}{q^{41/2}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{1}{q^{49/2}} & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & \frac{1}{q^{21/2}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & \frac{\left(q^2+q+1\right) \left(q^7-1\right)}{q^{37/2}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{1}{q^{12}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & \frac{\left(q^2+1\right) \left(q^3-1\right)^2 \left(q^3+1\right) \left(q^6+q^5+q^4+q^3+q^2+q+1\right)}{q^{51/2}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{\left(q^2+q+1\right)^2 \left(q^4-q^3+q-1\right)}{q^{37/2}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{1}{q^{27/2}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & \frac{(q-1)^3 \left(q^2+1\right) \left(q^4+q^3+q^2+q+1\right)^2 \left(q^5+q^4+q^3+q^2+q+1\right) \left(q^6+q^5+q^4+q^3+q^2+q+1\right)}{q^{63/2}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{\left(q^2+1\right) \left(q^3-1\right)^2 \left(q^3+1\right) \left(q^4+q^3+q^2+q+1\right)}{q^{24}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{\left(q^2+q+1\right) \left(q^5-1\right)}{q^{37/2}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{1}{q^{15}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & \frac{(q-1)^4 \left(q^2+1\right) \left(q^4+q^3+q^2+q+1\right)^2 \left(q^5+q^4+q^3+q^2+q+1\right)^2 \left(q^6+q^5+q^4+q^3+q^2+q+1\right)}{q^{73/2}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{(q-1)^3 (q+1)^2 \left(q^2+1\right)^2 \left(q^4+q^2+1\right) \left(q^4+q^3+q^2+q+1\right)^2}{q^{57/2}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{(q-1)^2 (q+1) \left(q^2+1\right)^2 \left(q^2+q+1\right) \left(q^4+q^3+q^2+q+1\right)}{q^{45/2}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{\left(q^2+q+1\right) \left(q^4-1\right)}{q^{37/2}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{1}{q^{33/2}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & \frac{(q-1)^5 \left(q^2+1\right) \left(q^2+q+1\right)^3 \left(q^3+1\right)^2 \left(q^4+q^3+q^2+q+1\right) \left(q^6+q^5+q^4+q^3+q^2+q+1\right)^2}{q^{81/2}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{(q-1)^4 \left(q^2+1\right) \left(q^2+q+1\right)^3 \left(q^3+1\right)^2 \left(q^4+q^3+q^2+q+1\right)^2}{q^{32}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{(q-1)^3 (q+1) \left(q^2+1\right)^2 \left(q^2+q+1\right) \left(q^4+q^3+q^2+q+1\right)^2}{q^{51/2}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{(q+1) \left(q^5+q^3-q^2-1\right)^2}{q^{21}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{(q-1) \left(q^2+q+1\right)^2}{q^{37/2}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{1}{q^{18}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \frac{\left(q^{3/2}-\frac{1}{q^{3/2}}\right) \left(q^2-\frac{1}{q^2}\right) \left(q^5-1\right) \left(q^6-1\right)^2 \left(q^7-1\right)}{(q-1) q^{31}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{(q-1)^4 (q+1)^2 \left(q^2+1\right) \left(q^2-q+1\right) \left(q^2+q+1\right)^2 \left(q^4+q^3+q^2+q+1\right)^2}{q^{55/2}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{(q-1)^3 \left(q^2+q+1\right) \left(q^3+q^2+q+1\right)^2 \left(q^4+q^3+q^2+q+1\right)}{q^{45/2}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{\left(q^3-1\right)^2 \left(q^3+q^2+q+1\right)}{q^{39/2}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{(q+1) \left(q^3-1\right)}{q^{37/2}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{1}{q^{39/2}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \frac{\left(1-q^3\right) \left(1-q^4\right) \left(q^5-1\right) \left(q^6-1\right) \left(q^7-1\right)}{q^{57/2}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{\left(1-q^3\right) \left(1-q^4\right) \left(q^5-1\right) \left(q^6-1\right)}{q^{23}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{\left(1-q^3\right) \left(1-q^4\right) \left(q^5-1\right)}{q^{39/2}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{q^7-q^4-q^3+1}{q^{18}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{q^3-1}{q^{37/2}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{1}{q^{21}} & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & \frac{1}{q^{14}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & \frac{\left(q^3+q^2+q+1\right) \left(q^7-1\right)}{q^{45/2}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{1}{q^{29/2}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & \frac{(q-1)^2 \left(q^2+1\right) \left(q^4+q^3+q^2+q+1\right) \left(q^5+q^4+q^3+q^2+q+1\right) \left(q^6+q^5+q^4+q^3+q^2+q+1\right)}{q^{30}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{(q-1) (q+1)^2 \left(q^2+1\right) \left(q^4+q^2+1\right)}{q^{43/2}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{1}{q^{15}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & \frac{(q-1)^3 \left(q^2+1\right) \left(q^2+q+1\right) \left(q^3+1\right)^2 \left(q^4+q^3+q^2+q+1\right)^2 \left(q^6+q^5+q^4+q^3+q^2+q+1\right)}{q^{73/2}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{\left(q^2+1\right) \left(q^5-1\right)^2 \left(q^5+q^4+q^3+q^2+q+1\right)}{q^{55/2}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{\left(q^3+q^2+q+1\right) \left(q^5-1\right)}{q^{41/2}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{1}{q^{31/2}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & \frac{(q-1)^4 \left(q^2+1\right) \left(q^2+q+1\right) \left(q^3+1\right)^2 \left(q^4+q^3+q^2+q+1\right)^2 \left(q^6+q^5+q^4+q^3+q^2+q+1\right)^2}{q^{42}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{\left(q^2-1\right)^3 \left(q^2+q+1\right) \left(q^8+2 q^6+q^5+2 q^4+q^3+2 q^2+1\right)^2}{q^{65/2}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{(q+1) \left(q^2+1\right)^2 \left(q^5-1\right)^2}{q^{25}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{(q-1) \left(q^3+q^2+q+1\right)^2}{q^{39/2}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{1}{q^{16}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \frac{(q-1)^4 \left(q^2+1\right) \left(q^4+q^3+q^2+q+1\right)^2 \left(q^5+q^4+q^3+q^2+q+1\right)^2 \left(q^6+q^5+q^4+q^3+q^2+q+1\right)}{q^{73/2}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{(q-1)^3 (q+1)^2 \left(q^2+1\right)^2 \left(q^4+q^2+1\right) \left(q^4+q^3+q^2+q+1\right)^2}{q^{57/2}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{(q-1)^2 (q+1) \left(q^2+1\right)^2 \left(q^2+q+1\right) \left(q^4+q^3+q^2+q+1\right)}{q^{45/2}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{\left(q^2+q+1\right) \left(q^4-1\right)}{q^{37/2}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{1}{q^{33/2}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \frac{\left(q^2-\frac{1}{q^2}\right) \left(q^5-1\right)^2 \left(q^6-1\right) \left(q^7-1\right)}{(q-1) q^{29}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{\left(q^2-1\right)^3 \left(q^2+1\right)^2 \left(q^4+q^2+1\right) \left(q^4+q^3+q^2+q+1\right)}{q^{49/2}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{(q-1)^2 \left(q^2+q+1\right) \left(q^3+q^2+q+1\right) \left(q^4+q^3+q^2+q+1\right)}{q^{20}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{q^5+q^4-q-1}{q^{35/2}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{1}{q^{17}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \frac{\left(q^2-\frac{1}{q^2}\right) \left(q^5-1\right) \left(q^6-1\right) \left(q^7-1\right)}{q^{47/2}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{\left(q^2-\frac{1}{q^2}\right) \left(q^5-1\right) \left(q^6-1\right)}{q^{37/2}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{q^9-q^5-q^4+1}{q^{35/2}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{q^4-1}{q^{33/2}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{1}{q^{35/2}} & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & \frac{1}{q^{35/2}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & \frac{\left(q^4+q^3+q^2+q+1\right) \left(q^7-1\right)}{q^{53/2}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{1}{q^{17}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & \frac{(q-1)^2 (q+1) \left(q^4+q^2+1\right)^2 \left(q^4+q^3+q^2+q+1\right) \left(q^6+q^5+q^4+q^3+q^2+q+1\right)}{q^{69/2}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{\left(q^4+q^3+q^2+q+1\right) \left(q^6-1\right)}{q^{49/2}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{1}{q^{33/2}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & \frac{(q-1)^3 (q+1) \left(q^2-q+1\right)^2 \left(q^2+q+1\right) \left(q^4+q^3+q^2+q+1\right)^2 \left(q^6+q^5+q^4+q^3+q^2+q+1\right)^2}{q^{83/2}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{(q+1) \left(q^9+q^7+q^5-q^4-q^2-1\right)^2}{q^{31}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{(q-1) \left(q^4+q^3+q^2+q+1\right)^2}{q^{45/2}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{1}{q^{16}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \frac{(q-1)^3 \left(q^2+1\right) \left(q^2+q+1\right) \left(q^3+1\right)^2 \left(q^4+q^3+q^2+q+1\right)^2 \left(q^6+q^5+q^4+q^3+q^2+q+1\right)}{q^{73/2}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{\left(q^2+1\right) \left(q^5-1\right)^2 \left(q^5+q^4+q^3+q^2+q+1\right)}{q^{55/2}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{\left(q^3+q^2+q+1\right) \left(q^5-1\right)}{q^{41/2}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{1}{q^{31/2}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \frac{(q-1)^3 \left(q^2+1\right) \left(q^4+q^3+q^2+q+1\right)^2 \left(q^5+q^4+q^3+q^2+q+1\right) \left(q^6+q^5+q^4+q^3+q^2+q+1\right)}{q^{63/2}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{\left(q^2+1\right) \left(q^3-1\right)^2 \left(q^3+1\right) \left(q^4+q^3+q^2+q+1\right)}{q^{24}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{\left(q^2+q+1\right) \left(q^5-1\right)}{q^{37/2}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{1}{q^{15}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \frac{\left(q^2-\frac{1}{q^2}\right) \left(q^5-1\right) \left(q^6-1\right) \left(q^7-1\right)}{(q-1) q^{49/2}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{\left(q^3-1\right)^2 \left(q^3+1\right) \left(q^4+q^3+q^2+q+1\right)}{q^{41/2}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{(q+1) \left(q^5-1\right)}{q^{33/2}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{1}{q^{29/2}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \frac{\left(q^5-1\right) \left(q^6-1\right) \left(q^7-1\right)}{q^{43/2}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{q^{11}-q^6-q^5+1}{q^{17}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{q^5-1}{q^{29/2}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{1}{q^{14}} & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & \frac{1}{q^{21}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & \frac{\left(q^5+q^4+q^3+q^2+q+1\right) \left(q^7-1\right)}{q^{61/2}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{1}{q^{39/2}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & \frac{(q+1) \left(q^4+q^2+1\right)^2 \left(q^7-1\right)^2}{q^{39}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{(q-1) \left(q^5+q^4+q^3+q^2+q+1\right)^2}{q^{55/2}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{1}{q^{18}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \frac{(q-1)^2 (q+1) \left(q^4+q^2+1\right)^2 \left(q^4+q^3+q^2+q+1\right) \left(q^6+q^5+q^4+q^3+q^2+q+1\right)}{q^{69/2}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{\left(q^4+q^3+q^2+q+1\right) \left(q^6-1\right)}{q^{49/2}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{1}{q^{33/2}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \frac{(q-1)^2 \left(q^2+1\right) \left(q^4+q^3+q^2+q+1\right) \left(q^5+q^4+q^3+q^2+q+1\right) \left(q^6+q^5+q^4+q^3+q^2+q+1\right)}{q^{30}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{(q-1) (q+1)^2 \left(q^2+1\right) \left(q^4+q^2+1\right)}{q^{43/2}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{1}{q^{15}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \frac{\left(q^2+1\right) \left(q^3-1\right)^2 \left(q^3+1\right) \left(q^6+q^5+q^4+q^3+q^2+q+1\right)}{q^{51/2}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{\left(q^2+q+1\right)^2 \left(q^4-q^3+q-1\right)}{q^{37/2}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{1}{q^{27/2}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \frac{\left(q^3-1\right)^2 \left(q^3+1\right) \left(q^6+q^5+q^4+q^3+q^2+q+1\right)}{q^{21}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{q^7+q^6-q-1}{q^{31/2}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{1}{q^{12}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \frac{q^{13}-q^7-q^6+1}{q^{33/2}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{q^6-1}{q^{25/2}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{1}{q^{21/2}} & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & \frac{1}{q^{49/2}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & \frac{\left(q^7-1\right)^2}{(q-1) q^{69/2}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{1}{q^{22}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \frac{\left(q^5+q^4+q^3+q^2+q+1\right) \left(q^7-1\right)}{q^{61/2}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{1}{q^{39/2}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \frac{\left(q^4+q^3+q^2+q+1\right) \left(q^7-1\right)}{q^{53/2}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{1}{q^{17}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \frac{\left(q^3+q^2+q+1\right) \left(q^7-1\right)}{q^{45/2}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{1}{q^{29/2}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \frac{\left(q^2+q+1\right) \left(q^7-1\right)}{q^{37/2}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{1}{q^{12}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \frac{(q+1) \left(q^7-1\right)}{q^{29/2}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{1}{q^{19/2}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \frac{q^7-1}{q^{21/2}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{1}{q^7} & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & \frac{1}{q^{28}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \frac{1}{q^{49/2}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \frac{1}{q^{21}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \frac{1}{q^{35/2}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \frac{1}{q^{14}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \frac{1}{q^{21/2}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \frac{1}{q^7} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \frac{1}{q^{7/2}}
+\end{array}
+\right),\left(
+\begin{array}{cccccccc}
+& 0 & 0 & 0 & 0 & 0 & 0 & \frac{1}{q^{7/4}} \\
+& 0 & 0 & 0 & 0 & 0 & \frac{1}{q^{5/4}} & 0 \\
+& 0 & 0 & 0 & 0 & \frac{1}{q^{3/4}} & 0 & 0 \\
+& 0 & 0 & 0 & \frac{1}{\sqrt[4]{q}} & 0 & 0 & 0 \\
+& 0 & 0 & \sqrt[4]{q} & 0 & 0 & 0 & 0 \\
+& 0 & q^{3/4} & 0 & 0 & 0 & 0 & 0 \\
+& q^{5/4} & 0 & 0 & 0 & 0 & 0 & 0 \\
+ q^{7/4} & 0 & 0 & 0 & 0 & 0 & 0 & 0
+\end{array}
+\right),\left(
+\begin{array}{cccccccc}
+& 0 & 0 & 0 & 0 & 0 & 0 & \frac{1}{q^{7/4}} \\
+& 0 & 0 & 0 & 0 & 0 & \frac{1}{q^{5/4}} & 0 \\
+& 0 & 0 & 0 & 0 & \frac{1}{q^{3/4}} & 0 & 0 \\
+& 0 & 0 & 0 & \frac{1}{\sqrt[4]{q}} & 0 & 0 & 0 \\
+& 0 & 0 & \sqrt[4]{q} & 0 & 0 & 0 & 0 \\
+& 0 & q^{3/4} & 0 & 0 & 0 & 0 & 0 \\
+& q^{5/4} & 0 & 0 & 0 & 0 & 0 & 0 \\
+ q^{7/4} & 0 & 0 & 0 & 0 & 0 & 0 & 0
+\end{array}
+\right),\left(
+\begin{array}{cccccccc}
+& 0 & 0 & 0 & 0 & 0 & 0 & \frac{1}{q^{7/4}} \\
+& 0 & 0 & 0 & 0 & 0 & \frac{1}{q^{5/4}} & 0 \\
+& 0 & 0 & 0 & 0 & \frac{1}{q^{3/4}} & 0 & 0 \\
+& 0 & 0 & 0 & \frac{1}{\sqrt[4]{q}} & 0 & 0 & 0 \\
+& 0 & 0 & \sqrt[4]{q} & 0 & 0 & 0 & 0 \\
+& 0 & q^{3/4} & 0 & 0 & 0 & 0 & 0 \\
+& q^{5/4} & 0 & 0 & 0 & 0 & 0 & 0 \\
+ q^{7/4} & 0 & 0 & 0 & 0 & 0 & 0 & 0
+\end{array}
+\right),\left(
+\begin{array}{cccccccc}
+& 0 & 0 & 0 & 0 & 0 & 0 & \frac{1}{q^{7/4}} \\
+& 0 & 0 & 0 & 0 & 0 & \frac{1}{q^{5/4}} & 0 \\
+& 0 & 0 & 0 & 0 & \frac{1}{q^{3/4}} & 0 & 0 \\
+& 0 & 0 & 0 & \frac{1}{\sqrt[4]{q}} & 0 & 0 & 0 \\
+& 0 & 0 & \sqrt[4]{q} & 0 & 0 & 0 & 0 \\
+& 0 & q^{3/4} & 0 & 0 & 0 & 0 & 0 \\
+& q^{5/4} & 0 & 0 & 0 & 0 & 0 & 0 \\
+ q^{7/4} & 0 & 0 & 0 & 0 & 0 & 0 & 0
+\end{array}
+\right)\right)\right]}{q^{7/2}+q^{5/2}+q^{3/2}+\sqrt{q}+\frac{1}{\sqrt{q}}+\frac{1}{q^{3/2}}+\frac{1}{q^{5/2}}+\frac{1}{q^{7/2}}}\right]</math>
+}}