12a
1008
(K12a
1008
)
A knot diagram
1
Linearized knot diagam
4 6 12 1 9 10 11 2 3 8 7 5
Solving Sequence
8,10
11 7
3,12
4 6 2 1 9 5
c
10
c
7
c
11
c
3
c
6
c
2
c
1
c
9
c
5
c
4
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.74164 × 10
99
u
97
− 2.39833 × 10
99
u
96
+ ··· + 5.41171 × 10
99
b − 4.92742 × 10
99
,
− 1.17514 × 10
100
u
97
− 1.21460 × 10
100
u
96
+ ··· + 1.62351 × 10
100
a − 3.33497 × 10
100
, u
98
+ u
97
+ ··· + 7u + 1i
* 1 irreducible components of dim
C
= 0, with total 98 representations.
1
The image of knot diagram is generated by the software “Draw programme” developed by An-
drew Bartholomew(http://www.layer8.co.uk/maths/draw/index.htm#Running-draw), where we modi-
fied some parts for our purpose(https://github.com/CATsTAILs/LinksPainter).
2
All coefficients of polynomials are rational numbers. But the coefficients are sometimes approximated
in decimal forms when there is not enough margin.
1
I. I
u
1
= h−1.74 × 10
99
u
97
− 2.40 × 10
99
u
96
+ · · · + 5.41 × 10
99
b − 4.93 ×
10
99
, −1.18 × 10
100
u
97
− 1.21 × 10
100
u
96
+ · · · + 1.62 × 10
100
a − 3.33 ×
10
100
, u
98
+ u
97
+ · · · + 7u + 1i
(i) Arc colorings
a
8
=
0
u
a
10
=
1
0
a
11
=
1
−u
2
a
7
=
−u
u
3
+ u
a
3
=
0.723826u
97
+ 0.748131u
96
+ ··· + 9.72154u + 2.05417
0.321828u
97
+ 0.443174u
96
+ ··· + 2.19227u + 0.910511
a
12
=
u
2
+ 1
−u
4
− 2u
2
a
4
=
0.277264u
97
+ 0.211124u
96
+ ··· + 0.311999u − 0.131270
0.341983u
97
+ 0.481916u
96
+ ··· + 2.95324u + 1.11161
a
6
=
−u
3
− 2u
u
3
+ u
a
2
=
0.584829u
97
+ 0.589965u
96
+ ··· + 8.85637u + 1.69336
0.177735u
97
+ 0.401736u
96
+ ··· + 2.77552u + 1.13266
a
1
=
0.114232u
97
+ 0.167614u
96
+ ··· − 6.85932u + 0.337484
0.558912u
97
+ 0.496393u
96
+ ··· + 2.96597u + 0.396995
a
9
=
0.372776u
97
+ 0.474477u
96
+ ··· − 13.0178u − 2.46360
0.0439798u
97
− 0.196807u
96
+ ··· + 8.61268u + 0.546451
a
5
=
−0.188677u
97
− 0.176374u
96
+ ··· − 10.6917u − 1.81247
−0.102684u
97
+ 0.00278592u
96
+ ··· + 5.61235u + 0.465124
(ii) Obstruction class = −1
(iii) Cusp Shapes = 3.08296u
97
+ 2.89378u
96
+ ··· − 32.7657u − 10.5076
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
12
u
98
− u
97
+ ··· − 7u + 1
c
2
u
98
− 7u
97
+ ··· − u + 1
c
3
u
98
+ u
97
+ ··· − 1473u + 2657
c
5
u
98
+ 7u
97
+ ··· + u + 1
c
6
u
98
− u
97
+ ··· + 1473u + 2657
c
7
, c
10
, c
11
u
98
+ u
97
+ ··· + 7u + 1
c
8
u
98
− u
97
+ ··· + 35u + 1
c
9
u
98
+ u
97
+ ··· − 35u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
7
c
10
, c
11
, c
12
y
98
+ 85y
97
+ ··· − 7y + 1
c
2
, c
5
y
98
− 7y
97
+ ··· − 7y + 1
c
3
, c
6
y
98
− 23y
97
+ ··· + 268190649y + 7059649
c
8
, c
9
y
98
+ 109y
97
+ ··· + 105y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.491853 + 0.893635I
a = −1.072020 + 0.324278I
b = 0.929642 − 1.042110I
3.33970 + 9.01230I 0
u = −0.491853 − 0.893635I
a = −1.072020 − 0.324278I
b = 0.929642 + 1.042110I
3.33970 − 9.01230I 0
u = −0.444484 + 0.841841I
a = 0.894161 − 0.134799I
b = −0.867284 + 0.915723I
−1.86918 + 5.22735I 0
u = −0.444484 − 0.841841I
a = 0.894161 + 0.134799I
b = −0.867284 − 0.915723I
−1.86918 − 5.22735I 0
u = 0.925739 + 0.132292I
a = 0.615421 + 0.470349I
b = −0.146037 − 0.355716I
6.47609 − 2.18771I 0
u = 0.925739 − 0.132292I
a = 0.615421 − 0.470349I
b = −0.146037 + 0.355716I
6.47609 + 2.18771I 0
u = 0.859784 + 0.362587I
a = −0.488034 − 1.051690I
b = −0.031553 + 0.814056I
6.05540 + 4.75636I 0
u = 0.859784 − 0.362587I
a = −0.488034 + 1.051690I
b = −0.031553 − 0.814056I
6.05540 − 4.75636I 0
u = 0.615615 + 0.643904I
a = −0.194810 − 0.998527I
b = −0.344505 + 0.869009I
5.01703 + 0.24238I 0
u = 0.615615 − 0.643904I
a = −0.194810 + 0.998527I
b = −0.344505 − 0.869009I
5.01703 − 0.24238I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.404108 + 1.039140I
a = 0.131418 − 0.338902I
b = −0.282590 + 0.595738I
−1.20967 + 4.26417I 0
u = 0.404108 − 1.039140I
a = 0.131418 + 0.338902I
b = −0.282590 − 0.595738I
−1.20967 − 4.26417I 0
u = −0.324321 + 1.086230I
a = 0.378494 − 0.891205I
b = −0.476957 + 1.108320I
6.66619 + 0.28302I 0
u = −0.324321 − 1.086230I
a = 0.378494 + 0.891205I
b = −0.476957 − 1.108320I
6.66619 − 0.28302I 0
u = −0.823277 + 0.259534I
a = 0.51125 + 2.25920I
b = −1.07954 − 1.22599I
5.3291 − 13.6594I 4.15756 + 8.91846I
u = −0.823277 − 0.259534I
a = 0.51125 − 2.25920I
b = −1.07954 + 1.22599I
5.3291 + 13.6594I 4.15756 − 8.91846I
u = 0.529507 + 1.014770I
a = −0.296000 + 0.544554I
b = 0.462969 − 0.589380I
3.75109 + 7.28743I 0
u = 0.529507 − 1.014770I
a = −0.296000 − 0.544554I
b = 0.462969 + 0.589380I
3.75109 − 7.28743I 0
u = −0.791041 + 0.262127I
a = −0.45282 − 2.07274I
b = 1.06829 + 1.10332I
− 9.63418I 0. + 8.34982I
u = −0.791041 − 0.262127I
a = −0.45282 + 2.07274I
b = 1.06829 − 1.10332I
9.63418I 0. − 8.34982I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.041265 + 0.825235I
a = 0.111753 + 0.211346I
b = 0.433665 − 0.812752I
−0.00404 + 1.44418I 1.13532 − 1.46067I
u = −0.041265 − 0.825235I
a = 0.111753 − 0.211346I
b = 0.433665 + 0.812752I
−0.00404 − 1.44418I 1.13532 + 1.46067I
u = 0.737032 + 0.343671I
a = 0.332554 + 1.052110I
b = 0.186303 − 0.768333I
1.23192 + 2.00806I 5.65102 − 9.68372I
u = 0.737032 − 0.343671I
a = 0.332554 − 1.052110I
b = 0.186303 + 0.768333I
1.23192 − 2.00806I 5.65102 + 9.68372I
u = −0.126983 + 1.213760I
a = 1.68278 − 0.99045I
b = −0.0803647 − 0.0485501I
1.53901 + 3.15170I 0
u = −0.126983 − 1.213760I
a = 1.68278 + 0.99045I
b = −0.0803647 + 0.0485501I
1.53901 − 3.15170I 0
u = −0.740426 + 0.239849I
a = 0.21070 + 1.84366I
b = −0.964592 − 0.936497I
1.86918 − 5.22735I 2.60772 + 4.54430I
u = −0.740426 − 0.239849I
a = 0.21070 − 1.84366I
b = −0.964592 + 0.936497I
1.86918 + 5.22735I 2.60772 − 4.54430I
u = −0.763529 + 0.134041I
a = 0.29520 − 2.22646I
b = 0.589019 + 1.029750I
9.55575 − 4.27219I 8.58109 + 5.06376I
u = −0.763529 − 0.134041I
a = 0.29520 + 2.22646I
b = 0.589019 − 1.029750I
9.55575 + 4.27219I 8.58109 − 5.06376I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.759398 + 0.065192I
a = 0.072398 − 0.348855I
b = −0.325726 + 0.222097I
1.79931 + 0.03648I 7.92424 + 1.99664I
u = 0.759398 − 0.065192I
a = 0.072398 + 0.348855I
b = −0.325726 − 0.222097I
1.79931 − 0.03648I 7.92424 − 1.99664I
u = 0.214822 + 1.254110I
a = 2.41307 + 0.74573I
b = −0.01191 − 2.30223I
0.711582 − 0.106264I 0
u = 0.214822 − 1.254110I
a = 2.41307 − 0.74573I
b = −0.01191 + 2.30223I
0.711582 + 0.106264I 0
u = 0.179533 + 1.301260I
a = −1.64385 − 0.90921I
b = −0.86058 + 1.67816I
−3.90106 + 2.22326I 0
u = 0.179533 − 1.301260I
a = −1.64385 + 0.90921I
b = −0.86058 − 1.67816I
−3.90106 − 2.22326I 0
u = −0.130364 + 1.321870I
a = 0.694450 + 0.523183I
b = 0.912458 − 0.693022I
−2.06229 + 2.57316I 0
u = −0.130364 − 1.321870I
a = 0.694450 − 0.523183I
b = 0.912458 + 0.693022I
−2.06229 − 2.57316I 0
u = −0.119121 + 0.650491I
a = 0.168707 − 0.156400I
b = 0.471898 − 0.684230I
1.43893I 0. − 1.86825I
u = −0.119121 − 0.650491I
a = 0.168707 + 0.156400I
b = 0.471898 + 0.684230I
− 1.43893I 0. + 1.86825I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.640284 + 0.152950I
a = −0.93888 − 2.47544I
b = 0.352365 + 0.452218I
4.45798 − 5.89647I 4.64634 + 10.02185I
u = −0.640284 − 0.152950I
a = −0.93888 + 2.47544I
b = 0.352365 − 0.452218I
4.45798 + 5.89647I 4.64634 − 10.02185I
u = 0.214030 + 1.327020I
a = 2.17660 + 0.61903I
b = −0.33650 − 3.26712I
−4.39226 + 3.08452I 0
u = 0.214030 − 1.327020I
a = 2.17660 − 0.61903I
b = −0.33650 + 3.26712I
−4.39226 − 3.08452I 0
u = −0.147885 + 1.336830I
a = −1.00637 + 1.26279I
b = −0.399194 − 0.082160I
−5.01703 + 0.24238I 0
u = −0.147885 − 1.336830I
a = −1.00637 − 1.26279I
b = −0.399194 + 0.082160I
−5.01703 − 0.24238I 0
u = 0.179239 + 1.335770I
a = −1.44799 − 0.58902I
b = 0.06224 + 2.67019I
−0.711582 + 0.106264I 0
u = 0.179239 − 1.335770I
a = −1.44799 + 0.58902I
b = 0.06224 − 2.67019I
−0.711582 − 0.106264I 0
u = 0.238733 + 1.326700I
a = −2.39362 − 1.04411I
b = 0.14054 + 3.39407I
6.16223I 0
u = 0.238733 − 1.326700I
a = −2.39362 + 1.04411I
b = 0.14054 − 3.39407I
− 6.16223I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.407050 + 1.295550I
a = −0.483654 − 0.252955I
b = −0.0279211 + 0.0800526I
2.06229 + 2.57316I 0
u = 0.407050 − 1.295550I
a = −0.483654 + 0.252955I
b = −0.0279211 − 0.0800526I
2.06229 − 2.57316I 0
u = 0.271941 + 1.332540I
a = 0.303666 + 0.763175I
b = 0.921025 − 0.196432I
−2.61445 + 3.62644I 0
u = 0.271941 − 1.332540I
a = 0.303666 − 0.763175I
b = 0.921025 + 0.196432I
−2.61445 − 3.62644I 0
u = −0.186956 + 1.347380I
a = −1.113010 − 0.157375I
b = −0.927277 + 0.209373I
−6.47609 − 2.18771I 0
u = −0.186956 − 1.347380I
a = −1.113010 + 0.157375I
b = −0.927277 − 0.209373I
−6.47609 + 2.18771I 0
u = −0.239809 + 0.584484I
a = −0.029496 − 0.515841I
b = 0.553533 − 0.581287I
0.00404 + 1.44418I −1.13532 − 1.46067I
u = −0.239809 − 0.584484I
a = −0.029496 + 0.515841I
b = 0.553533 + 0.581287I
0.00404 − 1.44418I −1.13532 + 1.46067I
u = −0.216219 + 1.356030I
a = 0.51352 − 1.71587I
b = 0.411531 + 0.436944I
−6.05540 − 4.75636I 0
u = −0.216219 − 1.356030I
a = 0.51352 + 1.71587I
b = 0.411531 − 0.436944I
−6.05540 + 4.75636I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.258735 + 1.352590I
a = −0.24119 + 1.74230I
b = −0.366526 − 0.691479I
−0.30461 − 9.18272I 0
u = −0.258735 − 1.352590I
a = −0.24119 − 1.74230I
b = −0.366526 + 0.691479I
−0.30461 + 9.18272I 0
u = −0.313473 + 1.342640I
a = −1.42543 + 1.24289I
b = −0.673201 − 0.929889I
4.90854 − 8.15583I 0
u = −0.313473 − 1.342640I
a = −1.42543 − 1.24289I
b = −0.673201 + 0.929889I
4.90854 + 8.15583I 0
u = −0.579443 + 0.206889I
a = −0.362023 + 0.973041I
b = −0.857221 − 0.465218I
1.20967 − 4.26417I 0.08812 + 10.07805I
u = −0.579443 − 0.206889I
a = −0.362023 − 0.973041I
b = −0.857221 + 0.465218I
1.20967 + 4.26417I 0.08812 − 10.07805I
u = 0.611541 + 0.059110I
a = −0.25353 + 5.90685I
b = 0.18864 − 3.13222I
4.39226 + 3.08452I −13.5720 + 13.4593I
u = 0.611541 − 0.059110I
a = −0.25353 − 5.90685I
b = 0.18864 + 3.13222I
4.39226 − 3.08452I −13.5720 − 13.4593I
u = −0.237120 + 1.365180I
a = 1.227450 − 0.550603I
b = 0.979542 + 0.307425I
−3.75109 − 7.28743I 0
u = −0.237120 − 1.365180I
a = 1.227450 + 0.550603I
b = 0.979542 − 0.307425I
−3.75109 + 7.28743I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.30129 + 1.39827I
a = 1.00627 − 1.19660I
b = 1.15721 + 0.94192I
−3.33970 − 9.01230I 0
u = −0.30129 − 1.39827I
a = 1.00627 + 1.19660I
b = 1.15721 − 0.94192I
−3.33970 + 9.01230I 0
u = −0.32103 + 1.41287I
a = −0.92973 + 1.37587I
b = −1.23582 − 1.14903I
−5.3291 − 13.6594I 0
u = −0.32103 − 1.41287I
a = −0.92973 − 1.37587I
b = −1.23582 + 1.14903I
−5.3291 + 13.6594I 0
u = 0.548150 + 0.055238I
a = −0.04072 − 5.03875I
b = 0.07612 + 2.55999I
0.300544I 0. + 22.0421I
u = 0.548150 − 0.055238I
a = −0.04072 + 5.03875I
b = 0.07612 − 2.55999I
− 0.300544I 0. − 22.0421I
u = −0.33662 + 1.41634I
a = 0.93777 − 1.49938I
b = 1.22307 + 1.29344I
− 17.8495I 0
u = −0.33662 − 1.41634I
a = 0.93777 + 1.49938I
b = 1.22307 − 1.29344I
17.8495I 0
u = −0.06444 + 1.45773I
a = −0.407673 + 0.574390I
b = −0.958355 + 0.252161I
−6.66619 + 0.28302I 0
u = −0.06444 − 1.45773I
a = −0.407673 − 0.574390I
b = −0.958355 − 0.252161I
−6.66619 − 0.28302I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.513990 + 0.166730I
a = 0.51823 + 2.41670I
b = −0.309151 − 0.143004I
−1.23192 − 2.00806I −5.65102 + 9.68372I
u = −0.513990 − 0.166730I
a = 0.51823 − 2.41670I
b = −0.309151 + 0.143004I
−1.23192 + 2.00806I −5.65102 − 9.68372I
u = 0.22495 + 1.45392I
a = 0.556886 + 0.623730I
b = 0.803523 − 0.893568I
−1.53901 + 3.15170I 0
u = 0.22495 − 1.45392I
a = 0.556886 − 0.623730I
b = 0.803523 + 0.893568I
−1.53901 − 3.15170I 0
u = 0.31225 + 1.43920I
a = −0.565517 − 0.656986I
b = −0.515398 + 0.774169I
−4.45798 + 5.89647I 0
u = 0.31225 − 1.43920I
a = −0.565517 + 0.656986I
b = −0.515398 − 0.774169I
−4.45798 − 5.89647I 0
u = −0.02139 + 1.49276I
a = 0.292535 − 0.309292I
b = 1.087210 − 0.444161I
−9.55575 + 4.27219I 0
u = −0.02139 − 1.49276I
a = 0.292535 + 0.309292I
b = 1.087210 + 0.444161I
−9.55575 − 4.27219I 0
u = 0.35530 + 1.45139I
a = 0.625663 + 0.645751I
b = 0.318307 − 0.814644I
0.30461 + 9.18272I 0
u = 0.35530 − 1.45139I
a = 0.625663 − 0.645751I
b = 0.318307 + 0.814644I
0.30461 − 9.18272I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.00920 + 1.51732I
a = −0.217252 + 0.129601I
b = −1.158630 + 0.580121I
−4.90854 + 8.15583I 0
u = 0.00920 − 1.51732I
a = −0.217252 − 0.129601I
b = −1.158630 − 0.580121I
−4.90854 − 8.15583I 0
u = 0.444457 + 0.136212I
a = −1.13792 + 4.29178I
b = 0.59925 − 1.81081I
3.90106 − 2.22326I 3.17343 + 9.01181I
u = 0.444457 − 0.136212I
a = −1.13792 − 4.29178I
b = 0.59925 + 1.81081I
3.90106 + 2.22326I 3.17343 − 9.01181I
u = −0.307396 + 0.134961I
a = 1.163900 + 0.512937I
b = 0.852872 + 0.021588I
−1.79931 + 0.03648I −7.92424 + 1.99664I
u = −0.307396 − 0.134961I
a = 1.163900 − 0.512937I
b = 0.852872 − 0.021588I
−1.79931 − 0.03648I −7.92424 − 1.99664I
u = −0.059630 + 0.321612I
a = 0.30671 − 2.44133I
b = −1.044390 + 0.280142I
2.61445 + 3.62644I −0.784461 − 0.771743I
u = −0.059630 − 0.321612I
a = 0.30671 + 2.44133I
b = −1.044390 − 0.280142I
2.61445 − 3.62644I −0.784461 + 0.771743I
14
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
12
u
98
− u
97
+ ··· − 7u + 1
c
2
u
98
− 7u
97
+ ··· − u + 1
c
3
u
98
+ u
97
+ ··· − 1473u + 2657
c
5
u
98
+ 7u
97
+ ··· + u + 1
c
6
u
98
− u
97
+ ··· + 1473u + 2657
c
7
, c
10
, c
11
u
98
+ u
97
+ ··· + 7u + 1
c
8
u
98
− u
97
+ ··· + 35u + 1
c
9
u
98
+ u
97
+ ··· − 35u + 1
15
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
7
c
10
, c
11
, c
12
y
98
+ 85y
97
+ ··· − 7y + 1
c
2
, c
5
y
98
− 7y
97
+ ··· − 7y + 1
c
3
, c
6
y
98
− 23y
97
+ ··· + 268190649y + 7059649
c
8
, c
9
y
98
+ 109y
97
+ ··· + 105y + 1
16
