10
92
(K10a
46
)
A knot diagram
1
Linearized knot diagam
5 10 7 6 2 9 3 1 4 8
Solving Sequence
1,5
2
6,8
9 4 10 3 7
c
1
c
5
c
8
c
4
c
10
c
2
c
7
c
3
, c
6
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h6.14745 × 10
22
u
43
+ 1.68640 × 10
23
u
42
+ ··· + 4.10626 × 10
23
b + 5.65855 × 10
23
,
− 1.07830 × 10
23
u
43
− 7.28908 × 10
23
u
42
+ ··· + 4.10626 × 10
23
a − 8.55134 × 10
23
, u
44
+ 3u
43
+ ··· + 4u + 1i
* 1 irreducible components of dim
C
= 0, with total 44 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
= h6.15×10
22
u
43
+1.69×10
23
u
42
+· · ·+4.11×10
23
b+5.66×10
23
, −1.08×
10
23
u
43
−7.29×10
23
u
42
+· · ·+4.11×10
23
a−8.55×10
23
, u
44
+3u
43
+· · ·+4u+1i
(i) Arc colorings
a
1
=
1
0
a
5
=
0
u
a
2
=
1
u
2
a
6
=
−u
−u
3
+ u
a
8
=
0.262600u
43
+ 1.77511u
42
+ ··· + 2.77682u + 2.08251
−0.149709u
43
− 0.410691u
42
+ ··· − 1.54325u − 1.37803
a
9
=
0.412309u
43
+ 2.18580u
42
+ ··· + 4.32007u + 3.46054
−0.149709u
43
− 0.410691u
42
+ ··· − 1.54325u − 1.37803
a
4
=
u
3
u
5
− u
3
+ u
a
10
=
0.313341u
43
+ 1.90111u
42
+ ··· + 3.81262u + 3.26735
−0.334825u
43
− 0.772241u
42
+ ··· − 1.55972u − 1.27556
a
3
=
1.07273u
43
+ 1.65129u
42
+ ··· + 0.120109u − 0.207377
−0.415470u
43
− 0.355187u
42
+ ··· − 2.46813u + 0.118486
a
7
=
0.942379u
43
+ 5.64956u
42
+ ··· − 4.55203u + 0.322394
−0.801791u
43
− 2.31053u
42
+ ··· − 2.19230u − 1.54713
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
299808041105979204994396
136875388103549877144643
u
43
−
848702959623216598779576
136875388103549877144643
u
42
+ ··· −
27052211834725271707812
19553626871935696734949
u −
1351235298619022041529338
136875388103549877144643
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
44
+ 3u
43
+ ··· + 4u + 1
c
2
u
44
+ 11u
43
+ ··· + 2050u − 319
c
3
, c
7
u
44
+ 3u
43
+ ··· + 4u + 1
c
4
u
44
+ 19u
43
+ ··· + 10u + 1
c
6
u
44
+ u
43
+ ··· − 28u + 7
c
8
, c
10
u
44
− u
43
+ ··· − 16u − 1
c
9
u
44
+ u
43
+ ··· + 10u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
44
− 19y
43
+ ··· − 10y + 1
c
2
y
44
− 107y
43
+ ··· − 1901234y + 101761
c
3
, c
7
y
44
+ 33y
43
+ ··· − 10y + 1
c
4
y
44
+ 13y
43
+ ··· − 10y + 1
c
6
y
44
+ 77y
43
+ ··· − 1078y + 49
c
8
, c
10
y
44
− 31y
43
+ ··· − 122y + 1
c
9
y
44
− 3y
43
+ ··· − 50y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.363757 + 0.931801I
a = 0.574314 + 0.152690I
b = 1.051760 − 0.377630I
0.93507 + 3.55591I −4.27504 − 5.80144I
u = 0.363757 − 0.931801I
a = 0.574314 − 0.152690I
b = 1.051760 + 0.377630I
0.93507 − 3.55591I −4.27504 + 5.80144I
u = 0.918123 + 0.411939I
a = −2.57013 + 0.48465I
b = −1.186550 + 0.092828I
−2.84407 − 1.62243I −4.14582 + 4.55154I
u = 0.918123 − 0.411939I
a = −2.57013 − 0.48465I
b = −1.186550 − 0.092828I
−2.84407 + 1.62243I −4.14582 − 4.55154I
u = −0.441228 + 0.915243I
a = 0.398119 − 0.217535I
b = 1.34117 + 0.51864I
−4.18962 − 9.08760I −8.08222 + 5.03295I
u = −0.441228 − 0.915243I
a = 0.398119 + 0.217535I
b = 1.34117 − 0.51864I
−4.18962 + 9.08760I −8.08222 − 5.03295I
u = 0.822616 + 0.487506I
a = 2.41823 − 5.79626I
b = −0.962457 − 0.015339I
−3.21593 − 2.04361I −52.4053 − 14.7990I
u = 0.822616 − 0.487506I
a = 2.41823 + 5.79626I
b = −0.962457 + 0.015339I
−3.21593 + 2.04361I −52.4053 + 14.7990I
u = 0.614573 + 0.715877I
a = 0.648178 − 0.462248I
b = 0.352533 + 0.684267I
3.04550 − 0.49268I −0.12697 + 2.02865I
u = 0.614573 − 0.715877I
a = 0.648178 + 0.462248I
b = 0.352533 − 0.684267I
3.04550 + 0.49268I −0.12697 − 2.02865I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.925118 + 0.134958I
a = 0.268380 + 0.914669I
b = −0.612800 + 0.910777I
−4.44447 + 2.34717I −13.36025 − 3.31347I
u = 0.925118 − 0.134958I
a = 0.268380 − 0.914669I
b = −0.612800 − 0.910777I
−4.44447 − 2.34717I −13.36025 + 3.31347I
u = −1.006040 + 0.358502I
a = −1.64888 − 1.39073I
b = −1.72272 − 0.34047I
−7.32531 + 1.01598I −16.3773 − 1.5947I
u = −1.006040 − 0.358502I
a = −1.64888 + 1.39073I
b = −1.72272 + 0.34047I
−7.32531 − 1.01598I −16.3773 + 1.5947I
u = −0.923394 + 0.545105I
a = 0.892868 − 0.453112I
b = −0.1085090 + 0.0372733I
−1.80992 + 2.06451I −8.33506 − 2.58557I
u = −0.923394 − 0.545105I
a = 0.892868 + 0.453112I
b = −0.1085090 − 0.0372733I
−1.80992 − 2.06451I −8.33506 + 2.58557I
u = −0.975696 + 0.495658I
a = −1.58974 − 1.81328I
b = −1.045760 + 0.398242I
−2.16678 + 3.71837I −7.18001 − 4.79801I
u = −0.975696 − 0.495658I
a = −1.58974 + 1.81328I
b = −1.045760 − 0.398242I
−2.16678 − 3.71837I −7.18001 + 4.79801I
u = 1.036360 + 0.480257I
a = −1.99121 + 1.16563I
b = −1.49224 − 0.83332I
−6.51425 − 5.38013I −14.5306 + 6.8865I
u = 1.036360 − 0.480257I
a = −1.99121 − 1.16563I
b = −1.49224 + 0.83332I
−6.51425 + 5.38013I −14.5306 − 6.8865I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.509147 + 0.682421I
a = 0.748061 + 0.578286I
b = 0.040117 − 1.082950I
−0.05957 − 3.45708I −5.25205 + 3.26607I
u = −0.509147 − 0.682421I
a = 0.748061 − 0.578286I
b = 0.040117 + 1.082950I
−0.05957 + 3.45708I −5.25205 − 3.26607I
u = 1.005360 + 0.620641I
a = −0.379272 − 0.130111I
b = 0.152753 − 0.830976I
1.86298 − 4.63552I −2.63874 + 4.34296I
u = 1.005360 − 0.620641I
a = −0.379272 + 0.130111I
b = 0.152753 + 0.830976I
1.86298 + 4.63552I −2.63874 − 4.34296I
u = −0.630444 + 1.006790I
a = 0.515707 + 0.251954I
b = 1.091770 − 0.179141I
−3.10073 + 4.10126I −10.8949 − 11.0256I
u = −0.630444 − 1.006790I
a = 0.515707 − 0.251954I
b = 1.091770 + 0.179141I
−3.10073 − 4.10126I −10.8949 + 11.0256I
u = −1.043400 + 0.593727I
a = −1.020580 + 0.191405I
b = −0.060111 + 1.315520I
−1.62830 + 8.40873I −8.69535 − 8.26732I
u = −1.043400 − 0.593727I
a = −1.020580 − 0.191405I
b = −0.060111 − 1.315520I
−1.62830 − 8.40873I −8.69535 + 8.26732I
u = −0.677683 + 0.298861I
a = 0.440425 + 0.337840I
b = −0.653219 − 0.324097I
−1.057920 + 0.069554I −6.35507 + 0.09655I
u = −0.677683 − 0.298861I
a = 0.440425 − 0.337840I
b = −0.653219 + 0.324097I
−1.057920 − 0.069554I −6.35507 − 0.09655I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.279390 + 0.043840I
a = 2.10525 − 0.31617I
b = 1.39686 − 0.31540I
−10.47240 + 6.33527I −14.2462 − 4.4391I
u = 1.279390 − 0.043840I
a = 2.10525 + 0.31617I
b = 1.39686 + 0.31540I
−10.47240 − 6.33527I −14.2462 + 4.4391I
u = −1.141180 + 0.657704I
a = 1.77431 + 1.29931I
b = 1.42524 − 0.56997I
−6.3237 + 14.8554I −10.29546 − 8.59158I
u = −1.141180 − 0.657704I
a = 1.77431 − 1.29931I
b = 1.42524 + 0.56997I
−6.3237 − 14.8554I −10.29546 + 8.59158I
u = 1.161630 + 0.643448I
a = 1.67963 − 1.04513I
b = 1.220440 + 0.442442I
−1.45853 − 9.28321I −6.00000 + 7.80258I
u = 1.161630 − 0.643448I
a = 1.67963 + 1.04513I
b = 1.220440 − 0.442442I
−1.45853 + 9.28321I −6.00000 − 7.80258I
u = −0.354494 + 0.530250I
a = 1.064660 − 0.138642I
b = 0.127335 + 0.413006I
−0.54354 + 1.79828I −3.49440 − 3.19528I
u = −0.354494 − 0.530250I
a = 1.064660 + 0.138642I
b = 0.127335 − 0.413006I
−0.54354 − 1.79828I −3.49440 + 3.19528I
u = −1.38103
a = 1.82513
b = 1.18122
−5.51547 −19.3220
u = −1.23100 + 0.72005I
a = 1.18995 + 0.81794I
b = 1.144640 − 0.060756I
−5.05123 + 2.61575I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.23100 − 0.72005I
a = 1.18995 − 0.81794I
b = 1.144640 + 0.060756I
−5.05123 − 2.61575I 0
u = 0.206659 + 0.446571I
a = 1.139280 − 0.241376I
b = −1.248780 + 0.511630I
−4.48946 + 1.55296I −10.02584 − 1.50927I
u = 0.206659 − 0.446571I
a = 1.139280 + 0.241376I
b = −1.248780 − 0.511630I
−4.48946 − 1.55296I −10.02584 + 1.50927I
u = −0.418735
a = 0.859759
b = −0.684180
−1.08485 −8.34540
9
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
5
u
44
+ 3u
43
+ ··· + 4u + 1
c
2
u
44
+ 11u
43
+ ··· + 2050u − 319
c
3
, c
7
u
44
+ 3u
43
+ ··· + 4u + 1
c
4
u
44
+ 19u
43
+ ··· + 10u + 1
c
6
u
44
+ u
43
+ ··· − 28u + 7
c
8
, c
10
u
44
− u
43
+ ··· − 16u − 1
c
9
u
44
+ u
43
+ ··· + 10u − 1
10
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
44
− 19y
43
+ ··· − 10y + 1
c
2
y
44
− 107y
43
+ ··· − 1901234y + 101761
c
3
, c
7
y
44
+ 33y
43
+ ··· − 10y + 1
c
4
y
44
+ 13y
43
+ ··· − 10y + 1
c
6
y
44
+ 77y
43
+ ··· − 1078y + 49
c
8
, c
10
y
44
− 31y
43
+ ··· − 122y + 1
c
9
y
44
− 3y
43
+ ··· − 50y + 1
11
