5 1

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4 1.gif

4_1

5 2.gif

5_2

5 1.gif
(KnotPlot image)

See the full Rolfsen Knot Table.

Visit Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle n} &id=Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 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).

When taken off the post the strangle knot (hitch) of practical knot tying deforms to 5_1

[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 X5,10,6,1 X7283 X9,4,10,5
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
BraidPart3.gifBraidPart3.gifBraidPart3.gifBraidPart3.gifBraidPart3.gif
BraidPart4.gifBraidPart4.gifBraidPart4.gifBraidPart4.gifBraidPart4.gif

Length is 5, width is 2,

Braid index is 2

5 1 ML.gif 5 1 AP.gif
[{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 X5,10,6,1 X7283 X9,4,10,5
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]= Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \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]]
BraidPart3.gifBraidPart3.gifBraidPart3.gifBraidPart3.gifBraidPart3.gif
BraidPart4.gifBraidPart4.gifBraidPart4.gifBraidPart4.gifBraidPart4.gif
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."
5 1 ML.gif
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]
5 1 AP.gif
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 Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 2}
Topological 4 genus Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 2}
Concordance genus Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \textrm{ConcordanceGenus}(\textrm{Knot}(5,1))}
Rasmussen s-Invariant -4

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

Polynomial invariants

Alexander polynomial Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle t^2+ t^{-2} -t- t^{-1} +1}
Conway polynomial Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle z^4+3 z^2+1}
2nd Alexander ideal (db, data sources) Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \{1\}}
Determinant and Signature { 5, -4 }
Jones polynomial Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle - q^{-7} + q^{-6} - q^{-5} + q^{-4} + q^{-2} }
HOMFLY-PT polynomial (db, data sources) Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle a^6 \left(-z^2\right)-2 a^6+a^4 z^4+4 a^4 z^2+3 a^4}
Kauffman polynomial (db, data sources) Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle a^9 z+a^8 z^2+a^7 z^3-a^7 z+a^6 z^4-3 a^6 z^2+2 a^6+a^5 z^3-2 a^5 z+a^4 z^4-4 a^4 z^2+3 a^4}
The A2 invariant Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle -q^{22}-q^{20}-q^{18}+q^{14}+q^{12}+2 q^{10}+q^8+q^6}
The G2 invariant Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 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}+2 q^{50}+q^{48}+q^{46}+q^{44}+q^{42}+2 q^{40}+q^{38}+q^{34}+q^{32}+q^{30}}
Further Quantum Invariants
Further quantum knot invariants for 5_1.

A1 Invariants.

Weight Invariant
1 Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle -q^{15}+q^7+q^5+q^3}
2 Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle q^{40}-q^{32}-q^{30}-q^{28}+q^{14}+q^{12}+q^{10}+q^8+q^6}
3 Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle -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 Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 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 Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle -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 Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 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 Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 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 Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle -q^{22}-q^{20}-q^{18}+q^{14}+q^{12}+2 q^{10}+q^8+q^6}
1,1 Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle q^{60}-2 q^{36}-2 q^{34}-4 q^{32}-4 q^{30}-3 q^{28}+2 q^{24}+4 q^{22}+5 q^{20}+4 q^{18}+4 q^{16}+2 q^{14}+q^{12}}
2,0 Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle q^{54}+q^{52}+2 q^{50}+q^{48}-2 q^{44}-3 q^{42}-3 q^{40}-3 q^{38}-2 q^{36}-q^{34}+q^{28}+q^{26}+2 q^{24}+2 q^{22}+3 q^{20}+2 q^{18}+2 q^{16}+q^{14}+q^{12}}
3,0 Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle -q^{96}-q^{94}-2 q^{92}-2 q^{90}-q^{88}+q^{86}+3 q^{84}+4 q^{82}+5 q^{80}+4 q^{78}+4 q^{76}+2 q^{74}+q^{72}-q^{70}-2 q^{68}-3 q^{66}-4 q^{64}-5 q^{62}-5 q^{60}-5 q^{58}-4 q^{56}-3 q^{54}-2 q^{52}-q^{50}+q^{42}+q^{40}+2 q^{38}+2 q^{36}+3 q^{34}+3 q^{32}+4 q^{30}+3 q^{28}+3 q^{26}+2 q^{24}+2 q^{22}+q^{20}+q^{18}}

A3 Invariants.

Weight Invariant
0,1,0 Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle q^{50}-q^{36}-2 q^{34}-3 q^{32}-3 q^{30}-2 q^{28}-q^{26}+2 q^{24}+3 q^{22}+4 q^{20}+3 q^{18}+3 q^{16}+q^{14}+q^{12}}
1,0,0 Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle -q^{29}-q^{27}-2 q^{25}-q^{23}+q^{19}+2 q^{17}+2 q^{15}+2 q^{13}+q^{11}+q^9}
1,0,1 Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle q^{80}+q^{58}+q^{56}+3 q^{54}+3 q^{52}+2 q^{50}-q^{48}-5 q^{46}-9 q^{44}-12 q^{42}-12 q^{40}-9 q^{38}-3 q^{36}+2 q^{34}+7 q^{32}+10 q^{30}+11 q^{28}+10 q^{26}+7 q^{24}+5 q^{22}+2 q^{20}+q^{18}}

A4 Invariants.

Weight Invariant
0,1,0,0 Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle q^{64}+q^{62}+q^{60}+q^{58}+q^{56}-q^{50}-2 q^{48}-4 q^{46}-5 q^{44}-6 q^{42}-6 q^{40}-4 q^{38}-q^{36}+2 q^{34}+4 q^{32}+7 q^{30}+6 q^{28}+6 q^{26}+4 q^{24}+3 q^{22}+q^{20}+q^{18}}
1,0,0,0 Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle -q^{36}-q^{34}-2 q^{32}-2 q^{30}-q^{28}+q^{24}+2 q^{22}+3 q^{20}+2 q^{18}+2 q^{16}+q^{14}+q^{12}}

B2 Invariants.

Weight Invariant
0,1 Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle -q^{50}-q^{36}-q^{32}-q^{30}+q^{26}+q^{22}+2 q^{20}+q^{18}+q^{16}+q^{14}+q^{12}}
1,0

B3 Invariants.

Weight Invariant
1,0,0 Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle q^{120}-q^{86}-q^{82}-q^{80}-2 q^{78}-q^{76}-2 q^{74}-q^{72}-2 q^{70}-q^{68}-q^{66}-q^{64}+q^{58}+q^{56}+2 q^{54}+q^{52}+3 q^{50}+q^{48}+3 q^{46}+q^{44}+2 q^{42}+q^{40}+2 q^{38}+q^{34}+q^{30}}

B4 Invariants.

Weight Invariant
1,0,0,0 Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle q^{160}-q^{114}-q^{110}-2 q^{106}-q^{104}-2 q^{102}-q^{100}-2 q^{98}-q^{96}-2 q^{94}-q^{92}-2 q^{90}-q^{88}-q^{86}+q^{78}+2 q^{74}+q^{72}+3 q^{70}+q^{68}+3 q^{66}+q^{64}+3 q^{62}+q^{60}+3 q^{58}+q^{56}+2 q^{54}+2 q^{50}+q^{46}+q^{42}}

C3 Invariants.

Weight Invariant
1,0,0 Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle -q^{70}-q^{50}-q^{48}-q^{46}-q^{44}-q^{42}-q^{40}+q^{34}+q^{32}+2 q^{30}+2 q^{28}+2 q^{26}+q^{24}+2 q^{22}+q^{20}+q^{18}}

C4 Invariants.

Weight Invariant
1,0,0,0 Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle -q^{90}-q^{64}-q^{62}-2 q^{60}-q^{58}-q^{56}-q^{54}-q^{52}-q^{50}-q^{48}+q^{44}+2 q^{42}+2 q^{40}+2 q^{38}+2 q^{36}+2 q^{34}+2 q^{32}+2 q^{30}+2 q^{28}+q^{26}+q^{24}}

D4 Invariants.

Weight Invariant
0,1,0,0 Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle q^{120}-q^{100}-q^{98}-3 q^{96}-3 q^{94}-q^{92}-q^{90}+2 q^{88}+6 q^{86}+9 q^{84}+11 q^{82}+14 q^{80}+11 q^{78}+9 q^{76}+3 q^{74}-4 q^{72}-12 q^{70}-18 q^{68}-24 q^{66}-27 q^{64}-27 q^{62}-24 q^{60}-17 q^{58}-11 q^{56}+7 q^{52}+14 q^{50}+19 q^{48}+22 q^{46}+19 q^{44}+19 q^{42}+14 q^{40}+10 q^{38}+6 q^{36}+4 q^{34}+q^{32}+q^{30}}
1,0,0,0 Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle q^{70}-q^{50}-q^{48}-3 q^{46}-3 q^{44}-3 q^{42}-3 q^{40}-2 q^{38}+q^{34}+3 q^{32}+4 q^{30}+4 q^{28}+4 q^{26}+3 q^{24}+2 q^{22}+q^{20}+q^{18}}

G2 Invariants.

Weight Invariant
0,1 Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle q^{240}-q^{198}-q^{192}+q^{178}+q^{176}+q^{172}+2 q^{170}+q^{168}+q^{166}+q^{164}+q^{162}+2 q^{160}+q^{158}+q^{154}+q^{152}-q^{148}-q^{146}-q^{144}-q^{142}-2 q^{140}-3 q^{138}-2 q^{136}-2 q^{134}-3 q^{132}-4 q^{130}-4 q^{128}-3 q^{126}-3 q^{124}-4 q^{122}-4 q^{120}-3 q^{118}-2 q^{116}-2 q^{114}-3 q^{112}-2 q^{110}+q^{102}+q^{100}+2 q^{98}+3 q^{96}+2 q^{94}+2 q^{92}+4 q^{90}+3 q^{88}+3 q^{86}+4 q^{84}+3 q^{82}+3 q^{80}+4 q^{78}+2 q^{76}+2 q^{74}+3 q^{72}+2 q^{70}+q^{68}+2 q^{66}+q^{64}+q^{62}+q^{60}+q^{54}}
1,0 Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 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}+2 q^{50}+q^{48}+q^{46}+q^{44}+q^{42}+2 q^{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.

Read more at http://katlas.math.toronto.edu/wiki/KnotTheory.

In[3]:= K = Knot["5 1"];
In[4]:= Alexander[K][t]
KnotTheory::loading: Loading precomputed data in PD4Knots`.
Out[4]= Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle t^2+ t^{-2} -t- t^{-1} +1}
In[5]:= Conway[K][z]
Out[5]= Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle z^4+3 z^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]= Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \{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]= Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle - 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]= Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle a^6 \left(-z^2\right)-2 a^6+a^4 z^4+4 a^4 z^2+3 a^4}
In[10]:= Kauffman[K][a, z]
KnotTheory::loading: Loading precomputed data in Kauffman4Knots`.
Out[10]= Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle a^9 z+a^8 z^2+a^7 z^3-a^7 z+a^6 z^4-3 a^6 z^2+2 a^6+a^5 z^3-2 a^5 z+a^4 z^4-4 a^4 z^2+3 a^4}

"Similar" Knots (within the Atlas)

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

Same Jones Polynomial (up to mirroring, Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 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.

Read more at http://katlas.math.toronto.edu/wiki/KnotTheory.

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]= { , }
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)
V2,1 through V6,9:
V2,1 V3,1 V4,1 V4,2 V4,3 V5,1 V5,2 V5,3 V5,4 V6,1 V6,2 V6,3 V6,4 V6,5 V6,6 V6,7 V6,8 V6,9
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 72} Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle -\frac{2512}{3}} Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle -104} Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 288} Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 800} Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 2088} Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 312} Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{41151}{10}} Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{2494}{15}} Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{7634}{5}} Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{43}{2}} Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1951}{10}}

V2,1 through V6,9 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 Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle t^rq^j} are shown, along with their alternating sums Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \chi} (fixed Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle j} , alternation over Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle r} ). The squares with yellow highlighting are those on the "critical diagonals", where Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle j-2r=s+1} or Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle j-2r=s-1} , where Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle s=} -4 is the signature of 5 1. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.   
\ r
  \  
j \
 -5-4-3-2-10χ
-3     11
-5     11
-7   1  1
-9      0
-11 11   0
-13      0
-151     -1
Integral Khovanov Homology

(db, data source)

  
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \dim{\mathcal G}_{2r+i}\operatorname{KH}^r_{\mathbb Z}} Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle i=-5} Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle i=-3}
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle r=-5} Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle {\mathbb Z}}
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle r=-4} Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle {\mathbb Z}_2} Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle {\mathbb Z}}
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle r=-3} Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle {\mathbb Z}}
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle r=-2} Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle {\mathbb Z}_2} Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle {\mathbb Z}}
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle r=-1}
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle r=0} Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle {\mathbb Z}}

The Coloured Jones Polynomials

The Coloured Jones Polynomials (in the Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle n+1} -dimensional representation of Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle sl(2)} )

 Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle n}   Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle J_n}
2 Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \textrm{Apart}\left[\frac{\textrm{Hold}\left[\textrm{REngine}\left(\textrm{MorseLink}(\textrm{MorseLink::Error: bad input}),\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 Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \textrm{Apart}\left[\frac{\textrm{Hold}\left[\textrm{REngine}\left(\textrm{MorseLink}(\textrm{MorseLink::Error: bad input}),\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 (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \textrm{Apart}\left[\frac{\textrm{Hold}\left[\textrm{REngine}\left(\textrm{MorseLink}(\textrm{MorseLink::Error: bad input}),\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 (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \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 & 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 & 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 & 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 & 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 & 0 & q^{15} & 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 & 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 & 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 & 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 & 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 & 0 & q^{25/2} & 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 & 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 & 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 & 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 & 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 & 0 & q^{10} & 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 & 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 & 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 & 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 & 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 & 0 & q^{15/2} & 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 & 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 & 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 & 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 & 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 & 0 & q^5 & 0 \\ 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 & 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 & 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 & 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 & 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 & 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 \\ 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 & 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 & 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 & 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 & 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 \\ 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 & \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 & \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 & \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 & \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 & 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 & \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 & \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 & \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 & \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 & 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 & 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 & \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^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 & \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 & 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 & 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 & 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 & \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 & \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 & 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 & 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 & 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 & 0 & \frac{q^5-1}{q^{15/2}} & 0 & 0 & 0 & 0 & \frac{1}{q^5} & 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 & \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 & 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 & \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 & 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 & 0 & \frac{1}{q^{5/2}} \end{array} \right),\left( \begin{array}{cccccc} 0 & 0 & 0 & 0 & 0 & \frac{1}{q^{5/4}} \\ 0 & 0 & 0 & 0 & \frac{1}{q^{3/4}} & 0 \\ 0 & 0 & 0 & \frac{1}{\sqrt[4]{q}} & 0 & 0 \\ 0 & 0 & \sqrt[4]{q} & 0 & 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 & 0 & \frac{1}{q^{5/4}} \\ 0 & 0 & 0 & 0 & \frac{1}{q^{3/4}} & 0 \\ 0 & 0 & 0 & \frac{1}{\sqrt[4]{q}} & 0 & 0 \\ 0 & 0 & \sqrt[4]{q} & 0 & 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 & 0 & \frac{1}{q^{5/4}} \\ 0 & 0 & 0 & 0 & \frac{1}{q^{3/4}} & 0 \\ 0 & 0 & 0 & \frac{1}{\sqrt[4]{q}} & 0 & 0 \\ 0 & 0 & \sqrt[4]{q} & 0 & 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 & 0 & \frac{1}{q^{5/4}} \\ 0 & 0 & 0 & 0 & \frac{1}{q^{3/4}} & 0 \\ 0 & 0 & 0 & \frac{1}{\sqrt[4]{q}} & 0 & 0 \\ 0 & 0 & \sqrt[4]{q} & 0 & 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]}
6 Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \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 & 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 & 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 & 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 & 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 & 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 & 0 & q^{21} & 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 & 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 & 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 & 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 & 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 & 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 & 0 & q^{18} & 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 & 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 & 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 & 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 & 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 & 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 & 0 & q^{15} & 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 & 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 & 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 & 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 & 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 & 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 & 0 & q^{12} & 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 & 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 & 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 & 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 & 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 & 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 & 0 & q^9 & 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 & 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 & 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 & 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 & 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 & 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 & 0 & q^6 & 0 \\ 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 & 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 & 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 & 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 & 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 & 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 & 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 \\ 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 & 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 & 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 & 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 & 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 & 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 \\ 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 & \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 & \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 & \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 & \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 & \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 & 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 & \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 & \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 & \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 & \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 & \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 & 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 & 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 & \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{(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 & \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 & \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 & 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 & 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 & 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 & \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^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 & \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 & 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 & 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 & 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 & 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 & \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 & \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 & 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 & 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 & 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 & 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 & 0 & \frac{q^6-1}{q^9} & 0 & 0 & 0 & 0 & 0 & \frac{1}{q^6} & 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 & \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 & \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 & \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 & \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 & 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 & 0 & \frac{1}{q^3} \end{array} \right),\left( \begin{array}{ccccccc} 0 & 0 & 0 & 0 & 0 & 0 & \frac{1}{q^{3/2}} \\ 0 & 0 & 0 & 0 & 0 & \frac{1}{q} & 0 \\ 0 & 0 & 0 & 0 & \frac{1}{\sqrt{q}} & 0 & 0 \\ 0 & 0 & 0 & 1 & 0 & 0 & 0 \\ 0 & 0 & \sqrt{q} & 0 & 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 & 0 & \frac{1}{q^{3/2}} \\ 0 & 0 & 0 & 0 & 0 & \frac{1}{q} & 0 \\ 0 & 0 & 0 & 0 & \frac{1}{\sqrt{q}} & 0 & 0 \\ 0 & 0 & 0 & 1 & 0 & 0 & 0 \\ 0 & 0 & \sqrt{q} & 0 & 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 & 0 & \frac{1}{q^{3/2}} \\ 0 & 0 & 0 & 0 & 0 & \frac{1}{q} & 0 \\ 0 & 0 & 0 & 0 & \frac{1}{\sqrt{q}} & 0 & 0 \\ 0 & 0 & 0 & 1 & 0 & 0 & 0 \\ 0 & 0 & \sqrt{q} & 0 & 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 & 0 & \frac{1}{q^{3/2}} \\ 0 & 0 & 0 & 0 & 0 & \frac{1}{q} & 0 \\ 0 & 0 & 0 & 0 & \frac{1}{\sqrt{q}} & 0 & 0 \\ 0 & 0 & 0 & 1 & 0 & 0 & 0 \\ 0 & 0 & \sqrt{q} & 0 & 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]}
7 Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \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 & 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 & 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 & 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 & 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 & 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 & 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 & 0 & q^{28} & 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 & 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 & 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 & 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 & 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 & 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 & 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 & 0 & q^{49/2} & 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 & 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 & 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 & 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 & 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 & 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 & 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 & 0 & q^{21} & 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 & 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 & 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 & 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 & 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 & 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 & 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 & 0 & q^{35/2} & 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 & 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 & 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 & 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 & 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 & 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 & 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 & 0 & q^{14} & 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 & 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 & 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 & 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 & 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 & 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 & 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 & 0 & q^{21/2} & 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 & 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 & 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 & 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 & 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 & 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 & 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 & 0 & q^7 & 0 \\ 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 & 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 & 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 & 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 & 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 & 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 & 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 & 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 \\ 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 & 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 & 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 & 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 & 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 & 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 & 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 \\ 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 & \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 & \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 & \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 & \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 & \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 & \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 & 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 & \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 & \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 & \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 & \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 & \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 & \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 & 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 & 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 & \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 & \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 & \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 & \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 & \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 & 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 & 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 & 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 & \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 & \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 & \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 & \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 & 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 & 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 & 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 & 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 & \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 & \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 & \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 & 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 & 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 & 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{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 & 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 & 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 & 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 & 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 & \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 & 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 & 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 & 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 & 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 & 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 & 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 & 0 & \frac{1}{q^{7/2}} \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),\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),\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),\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.

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