12n
0657
(K12n
0657
)
A knot diagram
1
Linearized knot diagam
3 8 9 12 8 10 2 11 3 6 4 5
Solving Sequence
4,11
12 5
1,9
3 8 6 2 7 10
c
11
c
4
c
12
c
3
c
8
c
5
c
2
c
7
c
10
c
1
, c
6
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.49961 × 10
89
u
57
− 4.30275 × 10
89
u
56
+ ··· + 1.84762 × 10
90
b − 3.84519 × 10
90
,
9.24565 × 10
90
u
57
+ 2.45942 × 10
91
u
56
+ ··· + 2.03238 × 10
91
a − 1.65302 × 10
91
, u
58
+ 4u
57
+ ··· + 32u + 11i
I
u
2
= h2u
17
+ u
16
+ ··· + b − 1,
u
16
− 11u
14
+ 50u
12
− u
11
− 121u
10
+ 5u
9
+ 168u
8
− 7u
7
− 135u
6
− u
5
+ 62u
4
+ 8u
3
− 17u
2
+ a − 5u + 2,
u
18
− u
17
+ ··· + 2u + 1i
* 2 irreducible components of dim
C
= 0, with total 76 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−1.50 × 10
89
u
57
− 4.30 × 10
89
u
56
+ · · · + 1.85 × 10
90
b − 3.85 ×
10
90
, 9.25 × 10
90
u
57
+ 2.46 × 10
91
u
56
+ · · · + 2.03 × 10
91
a − 1.65 ×
10
91
, u
58
+ 4u
57
+ · · · + 32u + 11i
(i) Arc colorings
a
4
=
0
u
a
11
=
1
0
a
12
=
1
−u
2
a
5
=
u
−u
3
+ u
a
1
=
−u
2
+ 1
u
4
− 2u
2
a
9
=
−0.454916u
57
− 1.21012u
56
+ ··· − 16.5801u + 0.813340
0.0811641u
57
+ 0.232880u
56
+ ··· − 0.624802u + 2.08115
a
3
=
−0.823019u
57
− 2.12734u
56
+ ··· + 7.49958u − 5.41326
0.711078u
57
+ 1.92531u
56
+ ··· + 19.8006u + 6.32004
a
8
=
−0.536080u
57
− 1.44300u
56
+ ··· − 15.9553u − 1.26781
0.0811641u
57
+ 0.232880u
56
+ ··· − 0.624802u + 2.08115
a
6
=
1.05675u
57
+ 2.85391u
56
+ ··· + 27.8234u + 9.33471
−0.544200u
57
− 1.45256u
56
+ ··· − 6.12029u − 4.46684
a
2
=
−0.132988u
57
− 0.334327u
56
+ ··· + 12.2892u − 3.37486
−0.0459035u
57
− 0.0804690u
56
+ ··· + 3.58707u − 1.18299
a
7
=
−1.48462u
57
− 3.93193u
56
+ ··· − 27.9977u − 11.9930
0.599967u
57
+ 1.56987u
56
+ ··· + 8.28968u + 4.81357
a
10
=
−1.04371u
57
− 2.79063u
56
+ ··· − 20.8363u − 7.03854
0.545357u
57
+ 1.43212u
56
+ ··· + 8.80444u + 4.70711
(ii) Obstruction class = −1
(iii) Cusp Shapes = −2.03502u
57
− 5.38837u
56
+ ··· − 45.6934u − 9.66794
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
58
+ 62u
57
+ ··· + 142553u + 3481
c
2
, c
7
u
58
− 31u
56
+ ··· + 3u + 59
c
3
, c
9
u
58
− u
57
+ ··· − 2798u + 691
c
4
, c
11
, c
12
u
58
− 4u
57
+ ··· − 32u + 11
c
5
u
58
+ 12u
57
+ ··· + 40669u + 11059
c
6
, c
10
u
58
+ 2u
57
+ ··· − 22u + 7
c
8
u
58
− 2u
57
+ ··· − 471u + 43
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
58
− 114y
57
+ ··· + 2999991563y + 12117361
c
2
, c
7
y
58
− 62y
57
+ ··· − 142553y + 3481
c
3
, c
9
y
58
+ 29y
57
+ ··· + 3857388y + 477481
c
4
, c
11
, c
12
y
58
− 58y
57
+ ··· + 8238y + 121
c
5
y
58
+ 24y
57
+ ··· − 2110306137y + 122301481
c
6
, c
10
y
58
+ 20y
57
+ ··· + 538y + 49
c
8
y
58
− 34y
57
+ ··· + 76235y + 1849
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.961036 + 0.344710I
a = 0.410562 − 0.361563I
b = 0.0577451 + 0.0746282I
1.63603 − 1.28858I 3.68914 − 2.65059I
u = −0.961036 − 0.344710I
a = 0.410562 + 0.361563I
b = 0.0577451 − 0.0746282I
1.63603 + 1.28858I 3.68914 + 2.65059I
u = −0.300610 + 0.983201I
a = −0.664168 + 0.542961I
b = −1.154320 + 0.289838I
2.11065 − 4.12734I 0. + 10.48560I
u = −0.300610 − 0.983201I
a = −0.664168 − 0.542961I
b = −1.154320 − 0.289838I
2.11065 + 4.12734I 0. − 10.48560I
u = 0.177176 + 1.016420I
a = 0.995049 + 0.839431I
b = 1.006590 + 0.559897I
−5.40198 + 2.14911I 0
u = 0.177176 − 1.016420I
a = 0.995049 − 0.839431I
b = 1.006590 − 0.559897I
−5.40198 − 2.14911I 0
u = 1.022550 + 0.300737I
a = 1.392440 − 0.121333I
b = −0.681814 − 0.288239I
−4.73896 − 0.44542I 0
u = 1.022550 − 0.300737I
a = 1.392440 + 0.121333I
b = −0.681814 + 0.288239I
−4.73896 + 0.44542I 0
u = 0.457539 + 1.028850I
a = −0.639770 − 1.028050I
b = −1.149000 − 0.599343I
−4.99783 + 9.61291I 0
u = 0.457539 − 1.028850I
a = −0.639770 + 1.028050I
b = −1.149000 + 0.599343I
−4.99783 − 9.61291I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.508367 + 0.560466I
a = 0.702577 − 1.074160I
b = 0.816859 − 0.437304I
0.87869 − 1.96952I −2.93815 + 3.59463I
u = −0.508367 − 0.560466I
a = 0.702577 + 1.074160I
b = 0.816859 + 0.437304I
0.87869 + 1.96952I −2.93815 − 3.59463I
u = −1.243480 + 0.160915I
a = −0.12542 + 1.47361I
b = −1.005060 + 0.654457I
8.10144 − 2.64219I 0
u = −1.243480 − 0.160915I
a = −0.12542 − 1.47361I
b = −1.005060 − 0.654457I
8.10144 + 2.64219I 0
u = 1.250380 + 0.115527I
a = −0.024680 + 0.709566I
b = 0.162747 + 1.279110I
2.43342 + 2.95295I 0
u = 1.250380 − 0.115527I
a = −0.024680 − 0.709566I
b = 0.162747 − 1.279110I
2.43342 − 2.95295I 0
u = 0.918632 + 0.898388I
a = −0.630878 − 0.202092I
b = −0.981209 + 0.316327I
−3.71484 − 3.13825I 0
u = 0.918632 − 0.898388I
a = −0.630878 + 0.202092I
b = −0.981209 − 0.316327I
−3.71484 + 3.13825I 0
u = −1.276100 + 0.238628I
a = 0.149526 + 0.895072I
b = 0.670232 + 1.202320I
−2.49632 − 0.10646I 0
u = −1.276100 − 0.238628I
a = 0.149526 − 0.895072I
b = 0.670232 − 1.202320I
−2.49632 + 0.10646I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.214091 + 0.659200I
a = 0.42003 + 1.64314I
b = −0.474121 + 0.960246I
−7.21101 + 3.94882I −5.14255 − 3.51346I
u = 0.214091 − 0.659200I
a = 0.42003 − 1.64314I
b = −0.474121 − 0.960246I
−7.21101 − 3.94882I −5.14255 + 3.51346I
u = −1.340150 + 0.006307I
a = −0.671961 − 0.615224I
b = 1.44910 − 0.06502I
6.41008 + 2.01791I 0
u = −1.340150 − 0.006307I
a = −0.671961 + 0.615224I
b = 1.44910 + 0.06502I
6.41008 − 2.01791I 0
u = 1.208760 + 0.634237I
a = 0.615633 + 0.389195I
b = 0.868802 − 0.223405I
−2.30604 + 3.66617I 0
u = 1.208760 − 0.634237I
a = 0.615633 − 0.389195I
b = 0.868802 + 0.223405I
−2.30604 − 3.66617I 0
u = 1.361830 + 0.160284I
a = −0.384112 + 0.899780I
b = 1.46541 + 0.58759I
6.81065 + 3.86139I 0
u = 1.361830 − 0.160284I
a = −0.384112 − 0.899780I
b = 1.46541 − 0.58759I
6.81065 − 3.86139I 0
u = 1.357900 + 0.198010I
a = −1.41096 − 0.24260I
b = 0.980223 + 0.173254I
−2.00761 + 5.36474I 0
u = 1.357900 − 0.198010I
a = −1.41096 + 0.24260I
b = 0.980223 − 0.173254I
−2.00761 − 5.36474I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.351158 + 0.438829I
a = −1.90822 + 1.84789I
b = −0.931746 − 0.128227I
5.20133 + 0.56913I 3.17376 + 3.13957I
u = −0.351158 − 0.438829I
a = −1.90822 − 1.84789I
b = −0.931746 + 0.128227I
5.20133 − 0.56913I 3.17376 − 3.13957I
u = −1.41665 + 0.25497I
a = −0.167580 − 0.716545I
b = −0.39722 − 1.42369I
−1.94189 − 7.25945I 0
u = −1.41665 − 0.25497I
a = −0.167580 + 0.716545I
b = −0.39722 + 1.42369I
−1.94189 + 7.25945I 0
u = −1.38880 + 0.42731I
a = 0.271840 + 0.657054I
b = −1.238430 + 0.075451I
5.55129 − 1.69307I 0
u = −1.38880 − 0.42731I
a = 0.271840 − 0.657054I
b = −1.238430 − 0.075451I
5.55129 + 1.69307I 0
u = −0.020913 + 0.538103I
a = −1.45595 − 2.11846I
b = 0.699320 − 0.714521I
−6.48919 − 2.77189I −4.31702 + 3.80378I
u = −0.020913 − 0.538103I
a = −1.45595 + 2.11846I
b = 0.699320 + 0.714521I
−6.48919 + 2.77189I −4.31702 − 3.80378I
u = −1.40623 + 0.43425I
a = −0.151715 − 1.142070I
b = 1.25232 − 0.77633I
−0.39560 − 7.30241I 0
u = −1.40623 − 0.43425I
a = −0.151715 + 1.142070I
b = 1.25232 + 0.77633I
−0.39560 + 7.30241I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.46204 + 0.36462I
a = 0.326405 − 0.912619I
b = −1.44645 − 0.46355I
7.77629 + 8.86284I 0
u = 1.46204 − 0.36462I
a = 0.326405 + 0.912619I
b = −1.44645 + 0.46355I
7.77629 − 8.86284I 0
u = 0.443286 + 0.212059I
a = −0.662346 + 0.537430I
b = 0.716948 + 0.729738I
0.67091 + 2.53345I −6.84359 − 5.09477I
u = 0.443286 − 0.212059I
a = −0.662346 − 0.537430I
b = 0.716948 − 0.729738I
0.67091 − 2.53345I −6.84359 + 5.09477I
u = 0.105029 + 0.468274I
a = 0.858036 − 0.852783I
b = −0.148908 − 0.554790I
−0.879280 − 0.837953I −6.06157 + 3.85318I
u = 0.105029 − 0.468274I
a = 0.858036 + 0.852783I
b = −0.148908 + 0.554790I
−0.879280 + 0.837953I −6.06157 − 3.85318I
u = 1.52144 + 0.16063I
a = 0.147683 − 1.054080I
b = −0.988171 − 0.419538I
11.65080 + 1.76628I 0
u = 1.52144 − 0.16063I
a = 0.147683 + 1.054080I
b = −0.988171 + 0.419538I
11.65080 − 1.76628I 0
u = −1.55510 + 0.06787I
a = −0.415660 − 0.379485I
b = 1.24881 − 0.70054I
7.53900 − 3.50491I 0
u = −1.55510 − 0.06787I
a = −0.415660 + 0.379485I
b = 1.24881 + 0.70054I
7.53900 + 3.50491I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.55296 + 0.10743I
a = −0.265564 + 0.772783I
b = 1.29007 + 0.93480I
7.76727 + 4.14815I 0
u = 1.55296 − 0.10743I
a = −0.265564 − 0.772783I
b = 1.29007 − 0.93480I
7.76727 − 4.14815I 0
u = −1.54876 + 0.39196I
a = 0.309319 + 1.063530I
b = −1.38659 + 0.73109I
1.4411 − 14.7651I 0
u = −1.54876 − 0.39196I
a = 0.309319 − 1.063530I
b = −1.38659 − 0.73109I
1.4411 + 14.7651I 0
u = −1.69455 + 0.13644I
a = 0.354754 + 0.421724I
b = −0.995880 + 0.147977I
5.71581 − 0.60212I 0
u = −1.69455 − 0.13644I
a = 0.354754 − 0.421724I
b = −0.995880 − 0.147977I
5.71581 + 0.60212I 0
u = −0.041702 + 0.155977I
a = 4.67058 − 1.41112I
b = 1.293750 − 0.398711I
2.00910 − 2.36209I 6.75260 − 1.70759I
u = −0.041702 − 0.155977I
a = 4.67058 + 1.41112I
b = 1.293750 + 0.398711I
2.00910 + 2.36209I 6.75260 + 1.70759I
10
II.
I
u
2
= h2u
17
+u
16
+· · ·+b −1, u
16
−11u
14
+· · ·+a +2, u
18
−u
17
+· · ·+2u +1i
(i) Arc colorings
a
4
=
0
u
a
11
=
1
0
a
12
=
1
−u
2
a
5
=
u
−u
3
+ u
a
1
=
−u
2
+ 1
u
4
− 2u
2
a
9
=
−u
16
+ 11u
14
+ ··· + 5u − 2
−2u
17
− u
16
+ ··· + 5u + 1
a
3
=
u
17
− 2u
16
+ ··· + 19u + 4
2u
17
− 21u
15
+ ··· − 10u
2
+ 2u
a
8
=
2u
17
− 20u
15
+ ··· + 2u
2
− 3
−2u
17
− u
16
+ ··· + 5u + 1
a
6
=
3u
17
− 31u
15
+ ··· − 7u
2
+ 7u
−u
17
+ 10u
15
+ ··· + 5u + 1
a
2
=
2u
17
− 2u
16
+ ··· + 18u + 1
2u
17
− 21u
15
+ ··· + 2u − 1
a
7
=
−u
17
+ u
16
+ ··· − 12u − 1
u
16
− 10u
14
+ ··· − 5u − 1
a
10
=
u
16
− u
15
+ ··· − u + 4
u
16
− 10u
14
+ ··· − u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −3u
17
− 7u
16
+ 30u
15
+ 69u
14
− 127u
13
− 279u
12
+ 295u
11
+
593u
10
− 398u
9
− 710u
8
+ 286u
7
+ 484u
6
− 61u
5
− 186u
4
− 42u
3
+ 33u
2
+ 27u + 8
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
18
− 19u
17
+ ··· + 7u + 1
c
2
u
18
+ u
17
+ ··· + u + 1
c
3
u
18
+ 6u
16
+ ··· + 12u
2
+ 1
c
4
u
18
+ u
17
+ ··· − 2u + 1
c
5
u
18
− u
17
+ ··· + 637u + 169
c
6
u
18
+ u
17
+ ··· + 9u
2
+ 1
c
7
u
18
− u
17
+ ··· − u + 1
c
8
u
18
+ 3u
17
+ ··· + 3u + 1
c
9
u
18
+ 6u
16
+ ··· + 12u
2
+ 1
c
10
u
18
− u
17
+ ··· + 9u
2
+ 1
c
11
, c
12
u
18
− u
17
+ ··· + 2u + 1
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
18
− 23y
17
+ ··· − 113y + 1
c
2
, c
7
y
18
− 19y
17
+ ··· + 7y + 1
c
3
, c
9
y
18
+ 12y
17
+ ··· + 24y + 1
c
4
, c
11
, c
12
y
18
− 23y
17
+ ··· + 10y + 1
c
5
y
18
− y
17
+ ··· + 80275y + 28561
c
6
, c
10
y
18
+ 15y
17
+ ··· + 18y + 1
c
8
y
18
− 11y
17
+ ··· + 3y + 1
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.887779 + 0.112048I
a = 0.089265 − 0.331367I
b = 0.461534 − 0.749043I
1.39736 − 2.22617I 1.56231 + 2.33825I
u = −0.887779 − 0.112048I
a = 0.089265 + 0.331367I
b = 0.461534 + 0.749043I
1.39736 + 2.22617I 1.56231 − 2.33825I
u = 0.758736 + 0.433252I
a = −0.977741 + 0.684412I
b = 0.369099 − 0.429483I
−5.13432 − 1.67601I −1.62747 + 2.23910I
u = 0.758736 − 0.433252I
a = −0.977741 − 0.684412I
b = 0.369099 + 0.429483I
−5.13432 + 1.67601I −1.62747 − 2.23910I
u = 1.143310 + 0.336155I
a = 0.949765 + 0.051215I
b = 0.058602 + 0.523758I
−3.76019 + 4.59860I −1.93853 − 3.26173I
u = 1.143310 − 0.336155I
a = 0.949765 − 0.051215I
b = 0.058602 − 0.523758I
−3.76019 − 4.59860I −1.93853 + 3.26173I
u = −0.383102 + 0.444250I
a = 0.823217 − 0.923482I
b = 1.133460 − 0.522137I
1.76189 − 2.88146I 1.41103 + 9.64361I
u = −0.383102 − 0.444250I
a = 0.823217 + 0.923482I
b = 1.133460 + 0.522137I
1.76189 + 2.88146I 1.41103 − 9.64361I
u = −1.45384 + 0.15707I
a = 0.292000 + 1.088040I
b = −1.046950 + 0.117848I
9.99566 − 0.53098I 4.50651 − 0.51925I
u = −1.45384 − 0.15707I
a = 0.292000 − 1.088040I
b = −1.046950 − 0.117848I
9.99566 + 0.53098I 4.50651 + 0.51925I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.48783 + 0.11385I
a = 0.078910 − 1.084200I
b = −1.091720 − 0.722143I
10.62920 + 2.91434I 4.17629 − 3.27745I
u = 1.48783 − 0.11385I
a = 0.078910 + 1.084200I
b = −1.091720 + 0.722143I
10.62920 − 2.91434I 4.17629 + 3.27745I
u = 1.54419 + 0.09001I
a = −0.288335 + 0.654660I
b = 1.44443 + 0.99383I
8.50423 + 4.51006I 9.09047 − 7.39147I
u = 1.54419 − 0.09001I
a = −0.288335 − 0.654660I
b = 1.44443 − 0.99383I
8.50423 − 4.51006I 9.09047 + 7.39147I
u = −1.64388 + 0.28012I
a = −0.301507 − 0.405678I
b = 1.183200 − 0.160247I
6.07303 − 1.21729I 10.42303 + 3.11644I
u = −1.64388 − 0.28012I
a = −0.301507 + 0.405678I
b = 1.183200 + 0.160247I
6.07303 + 1.21729I 10.42303 − 3.11644I
u = −0.065465 + 0.318414I
a = −4.66557 + 0.43662I
b = −1.011650 + 0.306442I
5.07676 − 1.32129I 0.89638 + 6.13933I
u = −0.065465 − 0.318414I
a = −4.66557 − 0.43662I
b = −1.011650 − 0.306442I
5.07676 + 1.32129I 0.89638 − 6.13933I
15
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
18
− 19u
17
+ ··· + 7u + 1)(u
58
+ 62u
57
+ ··· + 142553u + 3481)
c
2
(u
18
+ u
17
+ ··· + u + 1)(u
58
− 31u
56
+ ··· + 3u + 59)
c
3
(u
18
+ 6u
16
+ ··· + 12u
2
+ 1)(u
58
− u
57
+ ··· − 2798u + 691)
c
4
(u
18
+ u
17
+ ··· − 2u + 1)(u
58
− 4u
57
+ ··· − 32u + 11)
c
5
(u
18
− u
17
+ ··· + 637u + 169)(u
58
+ 12u
57
+ ··· + 40669u + 11059)
c
6
(u
18
+ u
17
+ ··· + 9u
2
+ 1)(u
58
+ 2u
57
+ ··· − 22u + 7)
c
7
(u
18
− u
17
+ ··· − u + 1)(u
58
− 31u
56
+ ··· + 3u + 59)
c
8
(u
18
+ 3u
17
+ ··· + 3u + 1)(u
58
− 2u
57
+ ··· − 471u + 43)
c
9
(u
18
+ 6u
16
+ ··· + 12u
2
+ 1)(u
58
− u
57
+ ··· − 2798u + 691)
c
10
(u
18
− u
17
+ ··· + 9u
2
+ 1)(u
58
+ 2u
57
+ ··· − 22u + 7)
c
11
, c
12
(u
18
− u
17
+ ··· + 2u + 1)(u
58
− 4u
57
+ ··· − 32u + 11)
16
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
18
− 23y
17
+ ··· − 113y + 1)
· (y
58
− 114y
57
+ ··· + 2999991563y + 12117361)
c
2
, c
7
(y
18
− 19y
17
+ ··· + 7y + 1)(y
58
− 62y
57
+ ··· − 142553y + 3481)
c
3
, c
9
(y
18
+ 12y
17
+ ··· + 24y + 1)
· (y
58
+ 29y
57
+ ··· + 3857388y + 477481)
c
4
, c
11
, c
12
(y
18
− 23y
17
+ ··· + 10y + 1)(y
58
− 58y
57
+ ··· + 8238y + 121)
c
5
(y
18
− y
17
+ ··· + 80275y + 28561)
· (y
58
+ 24y
57
+ ··· − 2110306137y + 122301481)
c
6
, c
10
(y
18
+ 15y
17
+ ··· + 18y + 1)(y
58
+ 20y
57
+ ··· + 538y + 49)
c
8
(y
18
− 11y
17
+ ··· + 3y + 1)(y
58
− 34y
57
+ ··· + 76235y + 1849)
17
