11a
30
(K11a
30
)
A knot diagram
1
Linearized knot diagam
5 1 8 2 9 3 11 6 4 7 10
Solving Sequence
5,9 2,6
1 3 4 10 8 11 7
c
5
c
1
c
2
c
4
c
9
c
8
c
11
c
7
c
3
, c
6
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h7.58522 × 10
150
u
73
+ 3.69824 × 10
151
u
72
+ ··· + 2.11703 × 10
151
b − 1.30679 × 10
151
,
1.34088 × 10
151
u
73
+ 4.14720 × 10
151
u
72
+ ··· + 2.11703 × 10
151
a − 7.19346 × 10
151
, u
74
+ 5u
73
+ ··· + 3u + 1i
* 1 irreducible components of dim
C
= 0, with total 74 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
= h7.59 × 10
150
u
73
+ 3.70 × 10
151
u
72
+ · · · + 2.12 × 10
151
b − 1.31 ×
10
151
, 1.34 × 10
151
u
73
+ 4.15 × 10
151
u
72
+ · · · + 2.12 × 10
151
a − 7.19 ×
10
151
, u
74
+ 5u
73
+ · · · + 3u + 1i
(i) Arc colorings
a
5
=
1
0
a
9
=
0
u
a
2
=
−0.633380u
73
− 1.95897u
72
+ ··· − 1.62167u + 3.39790
−0.358296u
73
− 1.74690u
72
+ ··· − 2.41832u + 0.617277
a
6
=
1
u
2
a
1
=
−0.275084u
73
− 0.212070u
72
+ ··· + 0.796648u + 2.78063
−0.358296u
73
− 1.74690u
72
+ ··· − 2.41832u + 0.617277
a
3
=
−1.99536u
73
− 8.76954u
72
+ ··· − 4.79281u + 2.43887
−0.179627u
73
− 0.746401u
72
+ ··· − 1.87519u + 0.121634
a
4
=
−2.11453u
73
− 9.34193u
72
+ ··· − 5.30085u + 1.98157
−0.294975u
73
− 1.37123u
72
+ ··· − 2.33439u − 0.359107
a
10
=
−10.0014u
73
− 53.9101u
72
+ ··· − 19.0788u − 3.70357
0.992329u
73
+ 5.03105u
72
+ ··· + 5.38895u + 0.998316
a
8
=
u
u
3
+ u
a
11
=
7.15691u
73
+ 29.9861u
72
+ ··· − 18.6635u − 6.17364
−1.14246u
73
− 5.02812u
72
+ ··· − 5.85728u + 0.414142
a
7
=
−2.25610u
73
− 2.17362u
72
+ ··· + 32.2123u + 10.8684
0.846917u
73
+ 3.12950u
72
+ ··· + 2.74742u − 0.602325
a
7
=
−2.25610u
73
− 2.17362u
72
+ ··· + 32.2123u + 10.8684
0.846917u
73
+ 3.12950u
72
+ ··· + 2.74742u − 0.602325
(ii) Obstruction class = −1
(iii) Cusp Shapes = 1.48586u
73
+ 14.4117u
72
+ ··· + 21.1776u − 3.60826
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
74
+ u
73
+ ··· + u + 1
c
2
u
74
+ 29u
73
+ ··· + 57u + 1
c
3
u
74
− u
73
+ ··· − 11u + 1
c
5
, c
8
u
74
− 5u
73
+ ··· − 3u + 1
c
6
u
74
− 5u
73
+ ··· − 355u + 199
c
7
, c
10
u
74
− 5u
73
+ ··· − 3u + 1
c
9
u
74
− 15u
73
+ ··· + 10283u + 547
c
11
u
74
− 31u
73
+ ··· + 5u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
74
+ 29y
73
+ ··· + 57y + 1
c
2
y
74
+ 33y
73
+ ··· − 859y + 1
c
3
y
74
+ 5y
73
+ ··· + 33y + 1
c
5
, c
8
y
74
+ 53y
73
+ ··· + 5y + 1
c
6
y
74
− 63y
73
+ ··· + 1039717y + 39601
c
7
, c
10
y
74
− 31y
73
+ ··· + 5y + 1
c
9
y
74
+ 105y
73
+ ··· − 37429635y + 299209
c
11
y
74
+ 25y
73
+ ··· + 5y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.625887 + 0.806388I
a = 0.250075 − 1.091350I
b = −0.155697 − 0.809103I
−1.13641 − 1.44571I 0
u = 0.625887 − 0.806388I
a = 0.250075 + 1.091350I
b = −0.155697 + 0.809103I
−1.13641 + 1.44571I 0
u = −0.948725 + 0.166866I
a = −0.188753 + 0.646780I
b = −0.755320 + 0.469376I
0.70694 + 6.29193I 0
u = −0.948725 − 0.166866I
a = −0.188753 − 0.646780I
b = −0.755320 − 0.469376I
0.70694 − 6.29193I 0
u = −0.018872 + 1.052340I
a = 0.07987 + 7.64537I
b = 0.488379 − 0.853979I
1.62217 + 0.05885I 0
u = −0.018872 − 1.052340I
a = 0.07987 − 7.64537I
b = 0.488379 + 0.853979I
1.62217 − 0.05885I 0
u = −0.212838 + 1.055230I
a = −1.05204 + 1.70067I
b = 0.448860 + 1.081110I
1.70570 + 3.66146I 0
u = −0.212838 − 1.055230I
a = −1.05204 − 1.70067I
b = 0.448860 − 1.081110I
1.70570 − 3.66146I 0
u = −0.046860 + 0.912129I
a = 1.70545 + 5.91576I
b = 0.473139 + 0.843516I
1.60692 + 3.97998I 10.4876 − 34.2104I
u = −0.046860 − 0.912129I
a = 1.70545 − 5.91576I
b = 0.473139 − 0.843516I
1.60692 − 3.97998I 10.4876 + 34.2104I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.837681 + 0.298700I
a = 0.88363 + 1.74577I
b = −0.196875 + 1.092950I
−5.52578 − 1.17971I −8.59982 + 0.I
u = 0.837681 − 0.298700I
a = 0.88363 − 1.74577I
b = −0.196875 − 1.092950I
−5.52578 + 1.17971I −8.59982 + 0.I
u = −1.134810 + 0.070313I
a = 0.13504 − 1.56031I
b = −0.625155 − 1.073360I
−1.05098 + 11.53100I 0
u = −1.134810 − 0.070313I
a = 0.13504 + 1.56031I
b = −0.625155 + 1.073360I
−1.05098 − 11.53100I 0
u = −0.187862 + 1.125480I
a = −1.08777 + 1.12032I
b = 0.613032 + 1.148640I
1.81406 + 3.75257I 0
u = −0.187862 − 1.125480I
a = −1.08777 − 1.12032I
b = 0.613032 − 1.148640I
1.81406 − 3.75257I 0
u = 0.100705 + 1.152450I
a = 0.772241 + 0.259406I
b = −0.044485 − 0.183329I
1.47076 − 2.21494I 0
u = 0.100705 − 1.152450I
a = 0.772241 − 0.259406I
b = −0.044485 + 0.183329I
1.47076 + 2.21494I 0
u = 0.818597 + 0.196251I
a = 0.063573 − 0.472652I
b = −0.564206 − 0.338491I
−1.47671 − 1.08782I −3.50377 + 1.91086I
u = 0.818597 − 0.196251I
a = 0.063573 + 0.472652I
b = −0.564206 + 0.338491I
−1.47671 + 1.08782I −3.50377 − 1.91086I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.173450 + 0.131654I
a = 0.26621 + 1.50343I
b = −0.558020 + 1.039770I
−3.26838 − 5.57628I 0
u = 1.173450 − 0.131654I
a = 0.26621 − 1.50343I
b = −0.558020 − 1.039770I
−3.26838 + 5.57628I 0
u = 0.430301 + 1.100860I
a = −0.329551 − 1.227650I
b = 0.002331 − 1.262770I
−3.04551 − 3.42311I 0
u = 0.430301 − 1.100860I
a = −0.329551 + 1.227650I
b = 0.002331 + 1.262770I
−3.04551 + 3.42311I 0
u = 0.040169 + 1.186910I
a = −0.363209 + 0.248191I
b = 0.812545 − 0.520379I
3.70932 − 1.58303I 0
u = 0.040169 − 1.186910I
a = −0.363209 − 0.248191I
b = 0.812545 + 0.520379I
3.70932 + 1.58303I 0
u = 0.120286 + 1.184310I
a = −0.825738 − 0.446465I
b = 0.905631 − 0.988625I
4.76292 − 2.16296I 0
u = 0.120286 − 1.184310I
a = −0.825738 + 0.446465I
b = 0.905631 + 0.988625I
4.76292 + 2.16296I 0
u = 0.186745 + 1.177800I
a = −0.819850 − 0.925557I
b = 0.76722 − 1.25365I
3.27619 − 7.91420I 0
u = 0.186745 − 1.177800I
a = −0.819850 + 0.925557I
b = 0.76722 + 1.25365I
3.27619 + 7.91420I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.392213 + 1.130490I
a = −0.437347 + 1.232360I
b = 0.076509 + 1.358080I
−1.83044 + 8.58305I 0
u = −0.392213 − 1.130490I
a = −0.437347 − 1.232360I
b = 0.076509 − 1.358080I
−1.83044 − 8.58305I 0
u = −0.757116 + 0.241853I
a = 1.02976 − 1.87392I
b = −0.088093 − 1.145910I
−4.54644 − 4.33882I −6.72843 + 3.56231I
u = −0.757116 − 0.241853I
a = 1.02976 + 1.87392I
b = −0.088093 + 1.145910I
−4.54644 + 4.33882I −6.72843 − 3.56231I
u = −0.067110 + 1.217550I
a = −0.391607 + 0.135020I
b = 1.109800 + 0.659392I
5.77201 + 4.94079I 0
u = −0.067110 − 1.217550I
a = −0.391607 − 0.135020I
b = 1.109800 − 0.659392I
5.77201 − 4.94079I 0
u = −0.024144 + 1.223960I
a = −0.163591 + 0.005366I
b = 1.121610 + 0.263459I
6.19874 − 1.17606I 0
u = −0.024144 − 1.223960I
a = −0.163591 − 0.005366I
b = 1.121610 − 0.263459I
6.19874 + 1.17606I 0
u = −1.284930 + 0.186322I
a = 0.105342 + 1.106140I
b = −0.611725 + 0.837729I
3.80887 − 2.41257I 0
u = −1.284930 − 0.186322I
a = 0.105342 − 1.106140I
b = −0.611725 − 0.837729I
3.80887 + 2.41257I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.189587 + 0.598875I
a = 2.16432 + 1.10393I
b = 0.395146 + 0.549899I
1.52579 − 1.41180I 0.43215 + 2.14680I
u = 0.189587 − 0.598875I
a = 2.16432 − 1.10393I
b = 0.395146 − 0.549899I
1.52579 + 1.41180I 0.43215 − 2.14680I
u = 0.42111 + 1.36965I
a = 0.139491 + 0.258840I
b = −0.888102 − 0.494344I
3.37758 − 5.71754I 0
u = 0.42111 − 1.36965I
a = 0.139491 − 0.258840I
b = −0.888102 + 0.494344I
3.37758 + 5.71754I 0
u = −0.43876 + 1.36676I
a = 0.050379 − 0.285013I
b = −0.971458 + 0.512667I
5.45791 + 11.23760I 0
u = −0.43876 − 1.36676I
a = 0.050379 + 0.285013I
b = −0.971458 − 0.512667I
5.45791 − 11.23760I 0
u = −0.192289 + 0.521498I
a = 1.68589 + 0.46680I
b = 0.331910 + 0.162106I
1.59490 − 1.49760I 1.53502 + 0.67981I
u = −0.192289 − 0.521498I
a = 1.68589 − 0.46680I
b = 0.331910 − 0.162106I
1.59490 + 1.49760I 1.53502 − 0.67981I
u = −0.43660 + 1.41313I
a = 0.0966887 − 0.0595436I
b = −0.838266 + 0.662306I
9.17547 + 3.15433I 0
u = −0.43660 − 1.41313I
a = 0.0966887 + 0.0595436I
b = −0.838266 − 0.662306I
9.17547 − 3.15433I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.52442 + 1.38928I
a = 1.12438 − 1.24979I
b = −0.706951 − 1.138360I
3.5208 + 17.3478I 0
u = −0.52442 − 1.38928I
a = 1.12438 + 1.24979I
b = −0.706951 + 1.138360I
3.5208 − 17.3478I 0
u = 0.52458 + 1.40532I
a = 1.11916 + 1.19302I
b = −0.673568 + 1.112400I
1.50429 − 11.48100I 0
u = 0.52458 − 1.40532I
a = 1.11916 − 1.19302I
b = −0.673568 − 1.112400I
1.50429 + 11.48100I 0
u = −0.56997 + 1.40561I
a = 0.99031 − 1.17785I
b = −0.710205 − 1.019160I
8.07842 + 8.92677I 0
u = −0.56997 − 1.40561I
a = 0.99031 + 1.17785I
b = −0.710205 + 1.019160I
8.07842 − 8.92677I 0
u = −0.172386 + 0.392750I
a = 2.17729 + 1.53861I
b = 0.611740 + 0.677389I
1.44361 + 4.12461I −1.60848 − 8.74026I
u = −0.172386 − 0.392750I
a = 2.17729 − 1.53861I
b = 0.611740 − 0.677389I
1.44361 − 4.12461I −1.60848 + 8.74026I
u = −0.82422 + 1.34124I
a = 0.791277 − 1.047410I
b = −0.585176 − 0.803100I
3.48567 − 0.24626I 0
u = −0.82422 − 1.34124I
a = 0.791277 + 1.047410I
b = −0.585176 + 0.803100I
3.48567 + 0.24626I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.395918 + 0.044210I
a = 1.82559 − 1.94480I
b = 0.427892 − 1.048720I
−1.13505 − 1.41023I −4.53209 + 0.05631I
u = −0.395918 − 0.044210I
a = 1.82559 + 1.94480I
b = 0.427892 + 1.048720I
−1.13505 + 1.41023I −4.53209 − 0.05631I
u = 0.26620 + 1.58230I
a = 0.535870 − 0.189293I
b = −0.510315 − 0.716522I
1.85423 − 1.80714I 0
u = 0.26620 − 1.58230I
a = 0.535870 + 0.189293I
b = −0.510315 + 0.716522I
1.85423 + 1.80714I 0
u = 0.388854 + 0.067367I
a = 1.98534 − 2.01885I
b = 0.549545 − 1.067760I
−0.22924 − 5.70067I −3.12131 + 5.75856I
u = 0.388854 − 0.067367I
a = 1.98534 + 2.01885I
b = 0.549545 + 1.067760I
−0.22924 + 5.70067I −3.12131 − 5.75856I
u = −0.222996 + 0.282133I
a = 1.85857 − 1.61104I
b = 0.372530 − 0.824350I
−0.30697 − 1.55903I −1.96359 + 5.08447I
u = −0.222996 − 0.282133I
a = 1.85857 + 1.61104I
b = 0.372530 + 0.824350I
−0.30697 + 1.55903I −1.96359 − 5.08447I
u = 0.60524 + 1.54626I
a = 0.948097 + 0.971022I
b = −0.570967 + 0.950116I
1.08144 − 6.25961I 0
u = 0.60524 − 1.54626I
a = 0.948097 − 0.971022I
b = −0.570967 − 0.950116I
1.08144 + 6.25961I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.241373 + 0.216455I
a = 2.17068 − 1.78758I
b = 0.636273 − 0.871096I
0.979140 − 0.794104I −4.88709 − 0.51596I
u = 0.241373 − 0.216455I
a = 2.17068 + 1.78758I
b = 0.636273 + 0.871096I
0.979140 + 0.794104I −4.88709 + 0.51596I
u = −0.61772 + 1.58812I
a = 0.204945 + 0.462300I
b = −0.589516 + 0.882245I
3.23570 − 4.91684I 0
u = −0.61772 − 1.58812I
a = 0.204945 − 0.462300I
b = −0.589516 − 0.882245I
3.23570 + 4.91684I 0
12
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
4
u
74
+ u
73
+ ··· + u + 1
c
2
u
74
+ 29u
73
+ ··· + 57u + 1
c
3
u
74
− u
73
+ ··· − 11u + 1
c
5
, c
8
u
74
− 5u
73
+ ··· − 3u + 1
c
6
u
74
− 5u
73
+ ··· − 355u + 199
c
7
, c
10
u
74
− 5u
73
+ ··· − 3u + 1
c
9
u
74
− 15u
73
+ ··· + 10283u + 547
c
11
u
74
− 31u
73
+ ··· + 5u + 1
13
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
74
+ 29y
73
+ ··· + 57y + 1
c
2
y
74
+ 33y
73
+ ··· − 859y + 1
c
3
y
74
+ 5y
73
+ ··· + 33y + 1
c
5
, c
8
y
74
+ 53y
73
+ ··· + 5y + 1
c
6
y
74
− 63y
73
+ ··· + 1039717y + 39601
c
7
, c
10
y
74
− 31y
73
+ ··· + 5y + 1
c
9
y
74
+ 105y
73
+ ··· − 37429635y + 299209
c
11
y
74
+ 25y
73
+ ··· + 5y + 1
14
