11a
71
(K11a
71
)
A knot diagram
1
Linearized knot diagam
5 1 9 10 2 3 4 11 7 8 6
Solving Sequence
2,6
5 1 3 7
8,11
9 10 4
c
5
c
1
c
2
c
6
c
11
c
8
c
10
c
4
c
3
, c
7
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h7.83384 × 10
25
u
79
− 2.56733 × 10
25
u
78
+ ··· + 1.29163 × 10
26
b − 2.49920 × 10
25
,
2.29485 × 10
26
u
79
+ 3.32810 × 10
26
u
78
+ ··· + 6.45815 × 10
25
a + 5.38395 × 10
26
, u
80
+ 2u
79
+ ··· + 5u + 1i
I
u
2
= hb − 1, a + 1, u + 1i
* 2 irreducible components of dim
C
= 0, with total 81 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
= h7.83 × 10
25
u
79
− 2.57 × 10
25
u
78
+ · · · + 1.29 × 10
26
b − 2.50 × 10
25
, 2.29 ×
10
26
u
79
+3.33×10
26
u
78
+· · ·+6.46×10
25
a+5.38×10
26
, u
80
+2u
79
+· · ·+5u+1i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
5
=
1
−u
2
a
1
=
u
−u
3
+ u
a
3
=
−u
3
u
5
− u
3
+ u
a
7
=
u
8
− u
6
+ u
4
+ 1
−u
10
+ 2u
8
− 3u
6
+ 2u
4
− u
2
a
8
=
−3.55341u
79
− 5.15334u
78
+ ··· − 20.1149u − 8.33667
−0.606508u
79
+ 0.198767u
78
+ ··· + 0.990713u + 0.193492
a
11
=
u
3
−u
3
+ u
a
9
=
−3.78703u
79
− 5.38668u
78
+ ··· − 20.9985u − 8.55334
−0.572619u
79
+ 0.249326u
78
+ ··· + 1.94321u + 0.227381
a
10
=
−4.01996u
79
− 5.62000u
78
+ ··· − 20.4242u − 8.87000
−0.540079u
79
+ 0.255493u
78
+ ··· + 1.98965u + 0.259921
a
4
=
8.92076u
79
+ 10.5265u
78
+ ··· + 40.2493u + 13.8432
−1.55419u
79
− 2.35995u
78
+ ··· − 9.35652u − 2.35995
a
4
=
8.92076u
79
+ 10.5265u
78
+ ··· + 40.2493u + 13.8432
−1.55419u
79
− 2.35995u
78
+ ··· − 9.35652u − 2.35995
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
120968554523544040789727864
21527170222575090764609709
u
79
−
5739563596393551567527518
1025103343932147179267129
u
78
+
··· −
240609495551769451833935926
7175723407525030254869903
u −
236354186912654203058622196
21527170222575090764609709
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
80
+ 2u
79
+ ··· + 5u + 1
c
2
u
80
+ 38u
79
+ ··· + 5u + 1
c
3
u
80
+ 35u
78
+ ··· + 27u − 1
c
4
u
80
+ 2u
79
+ ··· + 89u + 19
c
6
u
80
− 15u
78
+ ··· + 56453u + 8017
c
7
u
80
+ 4u
79
+ ··· − u − 1
c
8
, c
10
u
80
− 2u
79
+ ··· + 5u − 1
c
9
u
80
+ 13u
79
+ ··· + 6u + 2
c
11
u
80
+ 3u
79
+ ··· − 1824u − 288
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
80
− 38y
79
+ ··· − 5y + 1
c
2
y
80
+ 10y
79
+ ··· − 73y + 1
c
3
y
80
+ 70y
79
+ ··· − 129y + 1
c
4
y
80
+ 78y
79
+ ··· + 10547y + 361
c
6
y
80
− 30y
79
+ ··· − 2160187985y + 64272289
c
7
y
80
− 14y
79
+ ··· − 5y + 1
c
8
, c
10
y
80
− 50y
79
+ ··· + 55y + 1
c
9
y
80
− 9y
79
+ ··· − 64y + 4
c
11
y
80
+ 15y
79
+ ··· + 2084544y + 82944
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.993582 + 0.219652I
a = −0.681629 + 0.056586I
b = −0.017242 − 0.156551I
−1.76831 + 0.41384I 0
u = −0.993582 − 0.219652I
a = −0.681629 − 0.056586I
b = −0.017242 + 0.156551I
−1.76831 − 0.41384I 0
u = −0.633725 + 0.710008I
a = 1.304580 + 0.456964I
b = −1.169060 − 0.469516I
1.10017 + 9.52896I 0. − 7.63149I
u = −0.633725 − 0.710008I
a = 1.304580 − 0.456964I
b = −1.169060 + 0.469516I
1.10017 − 9.52896I 0. + 7.63149I
u = 0.666948 + 0.650580I
a = −1.033680 + 0.452004I
b = 1.264010 − 0.241396I
2.84471 − 1.91218I 3.52882 + 5.17190I
u = 0.666948 − 0.650580I
a = −1.033680 − 0.452004I
b = 1.264010 + 0.241396I
2.84471 + 1.91218I 3.52882 − 5.17190I
u = −1.031480 + 0.286770I
a = 0.53377 − 6.02234I
b = 3.13018 + 2.41426I
−3.78449 + 0.73170I 0
u = −1.031480 − 0.286770I
a = 0.53377 + 6.02234I
b = 3.13018 − 2.41426I
−3.78449 − 0.73170I 0
u = −1.017560 + 0.366491I
a = 0.142352 + 1.380120I
b = −0.580624 − 0.069040I
−2.69872 + 1.44530I 0
u = −1.017560 − 0.366491I
a = 0.142352 − 1.380120I
b = −0.580624 + 0.069040I
−2.69872 − 1.44530I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.529228 + 0.750028I
a = −0.766967 + 0.360768I
b = 0.522843 + 0.472910I
3.02838 + 1.37936I 3.64616 − 3.11353I
u = 0.529228 − 0.750028I
a = −0.766967 − 0.360768I
b = 0.522843 − 0.472910I
3.02838 − 1.37936I 3.64616 + 3.11353I
u = 0.924365 + 0.563218I
a = −0.78920 + 1.35114I
b = 1.063890 − 0.643299I
2.08735 − 2.83654I 0
u = 0.924365 − 0.563218I
a = −0.78920 − 1.35114I
b = 1.063890 + 0.643299I
2.08735 + 2.83654I 0
u = 1.085720 + 0.197443I
a = −0.544690 − 0.850906I
b = 0.308390 + 1.048710I
−1.19443 + 3.73477I 0
u = 1.085720 − 0.197443I
a = −0.544690 + 0.850906I
b = 0.308390 − 1.048710I
−1.19443 − 3.73477I 0
u = 1.078910 + 0.266597I
a = −0.12207 − 2.82977I
b = −1.45556 + 1.85197I
−5.69690 + 1.47728I 0
u = 1.078910 − 0.266597I
a = −0.12207 + 2.82977I
b = −1.45556 − 1.85197I
−5.69690 − 1.47728I 0
u = −0.562648 + 0.677266I
a = 0.225635 + 0.785522I
b = −0.233404 + 0.503707I
4.34092 + 3.75201I 2.40820 − 5.29181I
u = −0.562648 − 0.677266I
a = 0.225635 − 0.785522I
b = −0.233404 − 0.503707I
4.34092 − 3.75201I 2.40820 + 5.29181I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.075990 + 0.321255I
a = −0.12764 − 2.13134I
b = −1.77154 + 1.40590I
−6.18593 − 2.21505I 0
u = 1.075990 − 0.321255I
a = −0.12764 + 2.13134I
b = −1.77154 − 1.40590I
−6.18593 + 2.21505I 0
u = −0.358068 + 0.799824I
a = 1.125740 − 0.036921I
b = −0.45145 + 2.59579I
−0.37727 − 12.19400I −2.40584 + 6.91147I
u = −0.358068 − 0.799824I
a = 1.125740 + 0.036921I
b = −0.45145 − 2.59579I
−0.37727 + 12.19400I −2.40584 − 6.91147I
u = 0.322943 + 0.804382I
a = −0.956715 − 0.093636I
b = 0.61338 + 2.12460I
0.97731 + 4.20187I −0.27939 − 7.34151I
u = 0.322943 − 0.804382I
a = −0.956715 + 0.093636I
b = 0.61338 − 2.12460I
0.97731 − 4.20187I −0.27939 + 7.34151I
u = −0.950417 + 0.625173I
a = 1.29330 + 0.99233I
b = −1.084190 − 0.511800I
0.16239 − 4.42235I 0
u = −0.950417 − 0.625173I
a = 1.29330 − 0.99233I
b = −1.084190 + 0.511800I
0.16239 + 4.42235I 0
u = 1.067680 + 0.392778I
a = 0.852018 + 0.414010I
b = −0.780612 − 0.671395I
−2.94524 − 4.81984I 0
u = 1.067680 − 0.392778I
a = 0.852018 − 0.414010I
b = −0.780612 + 0.671395I
−2.94524 + 4.81984I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.435068 + 0.737884I
a = −0.527799 − 0.057176I
b = 0.365706 + 0.271011I
2.69064 + 1.31991I 2.13735 + 0.80724I
u = 0.435068 − 0.737884I
a = −0.527799 + 0.057176I
b = 0.365706 − 0.271011I
2.69064 − 1.31991I 2.13735 − 0.80724I
u = −0.381093 + 0.751489I
a = 0.343576 − 0.594171I
b = 0.560845 − 0.405823I
3.42648 − 6.07271I 0.67730 + 5.78894I
u = −0.381093 − 0.751489I
a = 0.343576 + 0.594171I
b = 0.560845 + 0.405823I
3.42648 + 6.07271I 0.67730 − 5.78894I
u = −1.001240 + 0.581180I
a = −0.619113 + 0.338239I
b = −0.469007 − 0.810748I
3.04528 + 1.12254I 0
u = −1.001240 − 0.581180I
a = −0.619113 − 0.338239I
b = −0.469007 + 0.810748I
3.04528 − 1.12254I 0
u = −1.045000 + 0.507333I
a = −0.507155 + 0.270967I
b = −0.264182 + 0.152064I
−2.30319 + 1.88747I 0
u = −1.045000 − 0.507333I
a = −0.507155 − 0.270967I
b = −0.264182 − 0.152064I
−2.30319 − 1.88747I 0
u = 1.155910 + 0.191256I
a = 0.84276 + 2.60711I
b = 0.92267 − 1.69592I
−5.29538 + 9.47417I 0
u = 1.155910 − 0.191256I
a = 0.84276 − 2.60711I
b = 0.92267 + 1.69592I
−5.29538 − 9.47417I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.17701
a = −0.658231
b = −0.350023
−2.75709 0
u = 1.059010 + 0.544082I
a = 2.90298 − 0.23263I
b = −1.80671 − 1.04197I
−1.35793 − 4.93977I 0
u = 1.059010 − 0.544082I
a = 2.90298 + 0.23263I
b = −1.80671 + 1.04197I
−1.35793 + 4.93977I 0
u = 1.027730 + 0.623923I
a = 0.067095 + 0.674046I
b = 0.550499 − 0.967599I
1.55978 − 6.58436I 0
u = 1.027730 − 0.623923I
a = 0.067095 − 0.674046I
b = 0.550499 + 0.967599I
1.55978 + 6.58436I 0
u = −1.191150 + 0.227672I
a = −1.19083 + 2.01827I
b = −0.48127 − 1.42841I
−3.84602 − 1.16588I 0
u = −1.191150 − 0.227672I
a = −1.19083 − 2.01827I
b = −0.48127 + 1.42841I
−3.84602 + 1.16588I 0
u = −1.092080 + 0.530795I
a = 1.39607 − 1.94234I
b = 0.28338 + 2.77059I
−4.75974 + 4.95618I 0
u = −1.092080 − 0.530795I
a = 1.39607 + 1.94234I
b = 0.28338 − 2.77059I
−4.75974 − 4.95618I 0
u = 1.086100 + 0.555013I
a = −4.94326 − 3.14688I
b = 1.11810 + 5.15447I
−1.91081 − 6.16425I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.086100 − 0.555013I
a = −4.94326 + 3.14688I
b = 1.11810 − 5.15447I
−1.91081 + 6.16425I 0
u = −0.349116 + 0.697052I
a = −0.850598 − 0.586037I
b = 0.15313 − 1.96985I
−1.57621 − 3.96915I −5.87435 + 6.27693I
u = −0.349116 − 0.697052I
a = −0.850598 + 0.586037I
b = 0.15313 + 1.96985I
−1.57621 + 3.96915I −5.87435 − 6.27693I
u = 0.393973 + 0.671200I
a = 1.57723 + 0.77061I
b = 0.38961 − 3.89569I
0.103983 + 1.397740I 2.4292 + 14.3351I
u = 0.393973 − 0.671200I
a = 1.57723 − 0.77061I
b = 0.38961 + 3.89569I
0.103983 − 1.397740I 2.4292 − 14.3351I
u = 0.457682 + 0.625241I
a = 0.565879 − 1.280020I
b = −1.18834 + 1.90703I
0.412068 + 0.321069I −4.01206 − 8.91676I
u = 0.457682 − 0.625241I
a = 0.565879 + 1.280020I
b = −1.18834 − 1.90703I
0.412068 − 0.321069I −4.01206 + 8.91676I
u = −0.527849 + 0.562689I
a = −1.116260 + 0.212682I
b = 0.123198 + 0.451359I
−0.74428 + 2.39884I −3.80212 − 6.62818I
u = −0.527849 − 0.562689I
a = −1.116260 − 0.212682I
b = 0.123198 − 0.451359I
−0.74428 − 2.39884I −3.80212 + 6.62818I
u = 1.087300 + 0.584528I
a = −0.135380 + 0.626345I
b = 0.248701 − 0.450700I
0.75605 − 6.35925I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.087300 − 0.584528I
a = −0.135380 − 0.626345I
b = 0.248701 + 0.450700I
0.75605 + 6.35925I 0
u = 1.165950 + 0.406590I
a = 1.22632 + 2.77362I
b = 1.06424 − 2.33151I
−7.89762 − 8.83460I 0
u = 1.165950 − 0.406590I
a = 1.22632 − 2.77362I
b = 1.06424 + 2.33151I
−7.89762 + 8.83460I 0
u = −1.103750 + 0.554364I
a = 2.12163 − 1.90495I
b = 0.24110 + 2.88334I
−3.76245 + 8.78286I 0
u = −1.103750 − 0.554364I
a = 2.12163 + 1.90495I
b = 0.24110 − 2.88334I
−3.76245 − 8.78286I 0
u = −1.107910 + 0.578539I
a = 0.099912 − 0.828642I
b = 0.979490 + 0.450273I
1.28682 + 11.11430I 0
u = −1.107910 − 0.578539I
a = 0.099912 + 0.828642I
b = 0.979490 − 0.450273I
1.28682 − 11.11430I 0
u = −0.042883 + 0.748508I
a = 0.389740 + 0.269401I
b = 0.15170 + 2.06876I
−4.35199 + 4.81540I −6.00555 − 5.45939I
u = −0.042883 − 0.748508I
a = 0.389740 − 0.269401I
b = 0.15170 − 2.06876I
−4.35199 − 4.81540I −6.00555 + 5.45939I
u = −1.169170 + 0.443646I
a = −1.65396 + 2.53789I
b = −0.39135 − 2.65142I
−7.65032 − 0.52064I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.169170 − 0.443646I
a = −1.65396 − 2.53789I
b = −0.39135 + 2.65142I
−7.65032 + 0.52064I 0
u = −1.130220 + 0.587955I
a = −2.32464 + 2.60165I
b = −0.18193 − 3.46366I
−2.6682 + 17.3873I 0
u = −1.130220 − 0.587955I
a = −2.32464 − 2.60165I
b = −0.18193 + 3.46366I
−2.6682 − 17.3873I 0
u = 1.142030 + 0.580131I
a = 1.67421 + 2.51891I
b = 0.39837 − 2.90345I
−1.44455 − 9.36809I 0
u = 1.142030 − 0.580131I
a = 1.67421 − 2.51891I
b = 0.39837 + 2.90345I
−1.44455 + 9.36809I 0
u = −0.325329 + 0.604214I
a = −1.70297 − 0.69757I
b = 0.284162 − 1.334030I
−2.59935 − 0.42981I −7.94943 + 0.49689I
u = −0.325329 − 0.604214I
a = −1.70297 + 0.69757I
b = 0.284162 + 1.334030I
−2.59935 + 0.42981I −7.94943 − 0.49689I
u = 0.022176 + 0.470783I
a = −0.873811 − 0.515901I
b = −0.268577 + 0.473782I
−0.24724 + 1.52128I −2.36985 − 4.33953I
u = 0.022176 − 0.470783I
a = −0.873811 + 0.515901I
b = −0.268577 − 0.473782I
−0.24724 − 1.52128I −2.36985 + 4.33953I
u = −0.363856
a = −3.77464
b = 0.0649355
−2.38530 −2.53010
12
II. I
u
2
= hb − 1, a + 1, u + 1i
(i) Arc colorings
a
2
=
0
−1
a
6
=
1
0
a
5
=
1
−1
a
1
=
−1
0
a
3
=
1
−1
a
7
=
2
−1
a
8
=
−1
1
a
11
=
−1
0
a
9
=
−2
1
a
10
=
−2
1
a
4
=
3
−2
a
4
=
3
−2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −12
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
8
u − 1
c
2
, c
3
, c
4
c
5
, c
6
, c
7
c
10
u + 1
c
9
, c
11
u
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
6
c
7
, c
8
, c
10
y −1
c
9
, c
11
y
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = −1.00000
b = 1.00000
−3.28987 −12.0000
16
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u − 1)(u
80
+ 2u
79
+ ··· + 5u + 1)
c
2
(u + 1)(u
80
+ 38u
79
+ ··· + 5u + 1)
c
3
(u + 1)(u
80
+ 35u
78
+ ··· + 27u − 1)
c
4
(u + 1)(u
80
+ 2u
79
+ ··· + 89u + 19)
c
5
(u + 1)(u
80
+ 2u
79
+ ··· + 5u + 1)
c
6
(u + 1)(u
80
− 15u
78
+ ··· + 56453u + 8017)
c
7
(u + 1)(u
80
+ 4u
79
+ ··· − u − 1)
c
8
(u − 1)(u
80
− 2u
79
+ ··· + 5u − 1)
c
9
u(u
80
+ 13u
79
+ ··· + 6u + 2)
c
10
(u + 1)(u
80
− 2u
79
+ ··· + 5u − 1)
c
11
u(u
80
+ 3u
79
+ ··· − 1824u − 288)
17
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
(y −1)(y
80
− 38y
79
+ ··· − 5y + 1)
c
2
(y −1)(y
80
+ 10y
79
+ ··· − 73y + 1)
c
3
(y −1)(y
80
+ 70y
79
+ ··· − 129y + 1)
c
4
(y −1)(y
80
+ 78y
79
+ ··· + 10547y + 361)
c
6
(y −1)(y
80
− 30y
79
+ ··· − 2.16019 × 10
9
y + 6.42723 × 10
7
)
c
7
(y −1)(y
80
− 14y
79
+ ··· − 5y + 1)
c
8
, c
10
(y −1)(y
80
− 50y
79
+ ··· + 55y + 1)
c
9
y(y
80
− 9y
79
+ ··· − 64y + 4)
c
11
y(y
80
+ 15y
79
+ ··· + 2084544y + 82944)
18
