12a
0810
(K12a
0810
)
A knot diagram
1
Linearized knot diagam
4 5 6 10 9 11 12 3 2 1 8 7
Solving Sequence
8,11
12 7
1,4
2 6 3 9 5 10
c
11
c
7
c
12
c
1
c
6
c
3
c
8
c
5
c
10
c
2
, c
4
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−53291u
57
− 330291u
56
+ ··· + 14534b − 482502,
− 241251u
57
− 1340924u
56
+ ··· + 29068a − 1111355, u
58
+ 6u
57
+ ··· + 37u + 4i
I
u
2
= h−2u
40
+ 3u
39
+ ··· + b + 3, 3u
42
a + 11u
42
+ ··· − 6a − 25, u
43
− 2u
42
+ ··· − 6u + 1i
I
u
3
= h−u
15
+ u
14
− 7u
13
+ 6u
12
− 20u
11
+ 12u
10
− 29u
9
+ 6u
8
− 20u
7
− 8u
6
− 10u
4
+ 7u
3
− 5u
2
+ b + u − 2,
2u
16
− 2u
15
+ ··· + a − 3, u
17
− u
16
+ ··· − 2u + 1i
I
u
4
= hau − u
2
+ b − u − 1, u
2
a + a
2
+ 2u
2
+ a + u + 3, u
3
+ u
2
+ 2u + 1i
* 4 irreducible components of dim
C
= 0, with total 167 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−5.33 × 10
4
u
57
− 3.30 × 10
5
u
56
+ · · · + 1.45 × 10
4
b − 4.83 × 10
5
, −2.41 ×
10
5
u
57
−1.34×10
6
u
56
+· · ·+2.91×10
4
a−1.11×10
6
, u
58
+6u
57
+· · ·+37u+4i
(i) Arc colorings
a
8
=
0
u
a
11
=
1
0
a
12
=
1
u
2
a
7
=
u
u
3
+ u
a
1
=
u
2
+ 1
u
4
+ 2u
2
a
4
=
8.29954u
57
+ 46.1306u
56
+ ··· + 337.485u + 38.2329
3.66664u
57
+ 22.7254u
56
+ ··· + 268.850u + 33.1982
a
2
=
−2.89765u
57
− 15.3587u
56
+ ··· − 105.156u − 12.0214
−2.02725u
57
− 12.7218u
56
+ ··· − 94.1918u − 11.5906
a
6
=
u
3
+ 2u
u
3
+ u
a
3
=
3.21223u
57
+ 16.7379u
56
+ ··· + 84.4613u + 8.61301
2.41510u
57
+ 14.4401u
56
+ ··· + 114.725u + 14.5737
a
9
=
−2.60875u
57
− 12.7540u
56
+ ··· − 168.192u − 25.1931
−4.24625u
57
− 24.3533u
56
+ ··· − 130.976u − 17.3985
a
5
=
7.39765u
57
+ 42.3587u
56
+ ··· + 357.156u + 41.5214
1.63940u
57
+ 11.0036u
56
+ ··· + 286.658u + 36.6075
a
10
=
−u
6
− 3u
4
− 2u
2
+ 1
−u
8
− 4u
6
− 4u
4
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
47209
7267
u
57
−
39509
1118
u
56
+ ··· −
5750393
14534
u −
461504
7267
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
u
58
+ 10u
57
+ ··· − 5u + 1
c
2
u
58
+ 30u
57
+ ··· + 7u + 2
c
4
, c
8
u
58
+ 8u
56
+ ··· + 5u + 2
c
5
, c
9
u
58
− 2u
57
+ ··· − u + 1
c
6
u
58
− 6u
57
+ ··· + 10406u + 1768
c
7
, c
11
, c
12
u
58
+ 6u
57
+ ··· + 37u + 4
c
10
u
58
− 10u
57
+ ··· − 79407u + 9248
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
y
58
− 20y
57
+ ··· − 37y + 1
c
2
y
58
+ 12y
56
+ ··· − 17y + 4
c
4
, c
8
y
58
+ 16y
57
+ ··· + 47y + 4
c
5
, c
9
y
58
+ 32y
57
+ ··· + 67y + 1
c
6
y
58
+ 14y
57
+ ··· + 31546284y + 3125824
c
7
, c
11
, c
12
y
58
+ 54y
57
+ ··· − 89y + 16
c
10
y
58
+ 30y
57
+ ··· + 1679029599y + 85525504
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.486650 + 0.826191I
a = 0.344322 − 0.261471I
b = −0.048461 − 0.411721I
0.75504 + 4.17161I −17.2218 − 16.9606I
u = −0.486650 − 0.826191I
a = 0.344322 + 0.261471I
b = −0.048461 + 0.411721I
0.75504 − 4.17161I −17.2218 + 16.9606I
u = 0.305000 + 1.120370I
a = 0.337905 − 0.211727I
b = −0.340274 − 0.314004I
−0.40781 + 4.56651I 0
u = 0.305000 − 1.120370I
a = 0.337905 + 0.211727I
b = −0.340274 + 0.314004I
−0.40781 − 4.56651I 0
u = −0.683075 + 0.462128I
a = −0.542422 + 1.104780I
b = 0.140036 + 1.005320I
0.22278 + 2.22232I −13.09381 − 5.11160I
u = −0.683075 − 0.462128I
a = −0.542422 − 1.104780I
b = 0.140036 − 1.005320I
0.22278 − 2.22232I −13.09381 + 5.11160I
u = −0.537460 + 0.617600I
a = 1.94977 + 0.77515I
b = 1.52666 − 0.78757I
2.39350 − 11.33360I −3.90914 + 5.14948I
u = −0.537460 − 0.617600I
a = 1.94977 − 0.77515I
b = 1.52666 + 0.78757I
2.39350 + 11.33360I −3.90914 − 5.14948I
u = −0.729161 + 0.366582I
a = −1.28232 − 2.43009I
b = −1.82584 − 1.30185I
1.4886 + 15.6557I −5.70789 − 10.38760I
u = −0.729161 − 0.366582I
a = −1.28232 + 2.43009I
b = −1.82584 + 1.30185I
1.4886 − 15.6557I −5.70789 + 10.38760I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.013312 + 1.213490I
a = −1.198630 + 0.354187I
b = 0.41384 + 1.45923I
0.694497 + 0.076769I 0
u = −0.013312 − 1.213490I
a = −1.198630 − 0.354187I
b = 0.41384 − 1.45923I
0.694497 − 0.076769I 0
u = 0.188583 + 1.225570I
a = −0.795866 − 0.034391I
b = 0.107938 + 0.981875I
−0.66118 − 4.66603I 0
u = 0.188583 − 1.225570I
a = −0.795866 + 0.034391I
b = 0.107938 − 0.981875I
−0.66118 + 4.66603I 0
u = −0.667450 + 0.362079I
a = 1.42453 + 2.98943I
b = 2.03321 + 1.47950I
−0.49660 + 6.79598I −12.1715 − 9.4069I
u = −0.667450 − 0.362079I
a = 1.42453 − 2.98943I
b = 2.03321 − 1.47950I
−0.49660 − 6.79598I −12.1715 + 9.4069I
u = 0.748570 + 0.048874I
a = −0.400924 − 0.165680I
b = 0.292022 + 0.143618I
−3.68988 − 8.42336I −10.53471 + 7.87489I
u = 0.748570 − 0.048874I
a = −0.400924 + 0.165680I
b = 0.292022 − 0.143618I
−3.68988 + 8.42336I −10.53471 − 7.87489I
u = 0.182516 + 1.252480I
a = −0.460878 + 0.482200I
b = 0.688062 + 0.489231I
−0.537435 − 1.220210I 0
u = 0.182516 − 1.252480I
a = −0.460878 − 0.482200I
b = 0.688062 − 0.489231I
−0.537435 + 1.220210I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.716893 + 0.148103I
a = −0.586320 − 0.467569I
b = −0.489577 − 0.248361I
−1.46760 + 0.14646I −10.66155 − 6.45496I
u = −0.716893 − 0.148103I
a = −0.586320 + 0.467569I
b = −0.489577 + 0.248361I
−1.46760 − 0.14646I −10.66155 + 6.45496I
u = 0.598802 + 0.420280I
a = −0.056377 + 0.342481I
b = 0.177697 − 0.181384I
3.17991 − 1.93750I −0.05128 + 3.41899I
u = 0.598802 − 0.420280I
a = −0.056377 − 0.342481I
b = 0.177697 + 0.181384I
3.17991 + 1.93750I −0.05128 − 3.41899I
u = 0.296710 + 1.235000I
a = 0.503062 + 0.098001I
b = −0.028232 − 0.650361I
0.26982 − 12.21040I 0
u = 0.296710 − 1.235000I
a = 0.503062 − 0.098001I
b = −0.028232 + 0.650361I
0.26982 + 12.21040I 0
u = −0.498652 + 0.501751I
a = −2.45024 − 1.17096I
b = −1.80935 + 0.64551I
0.14979 − 2.90525I −9.74237 + 2.76855I
u = −0.498652 − 0.501751I
a = −2.45024 + 1.17096I
b = −1.80935 − 0.64551I
0.14979 + 2.90525I −9.74237 − 2.76855I
u = −0.068712 + 1.333800I
a = 0.769513 + 0.152421I
b = 0.256174 − 1.015900I
3.90944 + 2.10883I 0
u = −0.068712 − 1.333800I
a = 0.769513 − 0.152421I
b = 0.256174 + 1.015900I
3.90944 − 2.10883I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.554749 + 0.320999I
a = 0.363194 − 0.745212I
b = −0.440694 + 0.296820I
−1.24071 − 1.57402I −9.37561 + 4.19103I
u = 0.554749 − 0.320999I
a = 0.363194 + 0.745212I
b = −0.440694 − 0.296820I
−1.24071 + 1.57402I −9.37561 − 4.19103I
u = 0.620237 + 0.005952I
a = 0.684603 − 0.312047I
b = −0.426474 + 0.189468I
−4.34476 + 1.69097I −17.4074 − 4.2929I
u = 0.620237 − 0.005952I
a = 0.684603 + 0.312047I
b = −0.426474 − 0.189468I
−4.34476 − 1.69097I −17.4074 + 4.2929I
u = −0.552154 + 0.262175I
a = −0.00417 + 2.56788I
b = 0.67093 + 1.41896I
−1.55541 + 1.68524I −10.30877 − 5.83070I
u = −0.552154 − 0.262175I
a = −0.00417 − 2.56788I
b = 0.67093 − 1.41896I
−1.55541 − 1.68524I −10.30877 + 5.83070I
u = −0.247870 + 1.385030I
a = −0.001904 + 0.889063I
b = 1.230910 + 0.223010I
3.45219 + 3.47788I 0
u = −0.247870 − 1.385030I
a = −0.001904 − 0.889063I
b = 1.230910 − 0.223010I
3.45219 − 3.47788I 0
u = −0.21441 + 1.40281I
a = 0.99934 − 1.05859I
b = −1.27072 − 1.62886I
3.77827 + 4.51742I 0
u = −0.21441 − 1.40281I
a = 0.99934 + 1.05859I
b = −1.27072 + 1.62886I
3.77827 − 4.51742I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.21996 + 1.42291I
a = −0.231668 + 0.476881I
b = 0.729514 + 0.224747I
4.35313 − 4.46243I 0
u = 0.21996 − 1.42291I
a = −0.231668 − 0.476881I
b = 0.729514 − 0.224747I
4.35313 + 4.46243I 0
u = −0.18090 + 1.45437I
a = 0.24700 + 1.67631I
b = 2.48266 − 0.05598I
6.36667 − 0.42955I 0
u = −0.18090 − 1.45437I
a = 0.24700 − 1.67631I
b = 2.48266 + 0.05598I
6.36667 + 0.42955I 0
u = −0.25301 + 1.44537I
a = 0.91357 − 1.91598I
b = −2.53814 − 1.80521I
5.31051 + 10.16090I 0
u = −0.25301 − 1.44537I
a = 0.91357 + 1.91598I
b = −2.53814 + 1.80521I
5.31051 − 10.16090I 0
u = 0.22159 + 1.45553I
a = 0.072388 − 0.270086I
b = −0.409159 − 0.045515I
9.20820 − 4.94870I 0
u = 0.22159 − 1.45553I
a = 0.072388 + 0.270086I
b = −0.409159 + 0.045515I
9.20820 + 4.94870I 0
u = −0.27798 + 1.45411I
a = −0.70415 + 1.66871I
b = 2.23074 + 1.48777I
7.3380 + 19.3241I 0
u = −0.27798 − 1.45411I
a = −0.70415 − 1.66871I
b = 2.23074 − 1.48777I
7.3380 − 19.3241I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.14926 + 1.49263I
a = −0.200412 − 1.212690I
b = −1.84002 + 0.11814I
9.24070 − 8.97855I 0
u = −0.14926 − 1.49263I
a = −0.200412 + 1.212690I
b = −1.84002 − 0.11814I
9.24070 + 8.97855I 0
u = −0.25822 + 1.48249I
a = 0.628146 − 0.442430I
b = −0.493697 − 1.045470I
6.49112 + 5.68833I 0
u = −0.25822 − 1.48249I
a = 0.628146 + 0.442430I
b = −0.493697 + 1.045470I
6.49112 − 5.68833I 0
u = −0.11942 + 1.52627I
a = −0.327180 + 0.242381I
b = 0.330868 + 0.528310I
8.42211 + 6.12728I 0
u = −0.11942 − 1.52627I
a = −0.327180 − 0.242381I
b = 0.330868 − 0.528310I
8.42211 − 6.12728I 0
u = −0.282114 + 0.301857I
a = −1.86889 + 0.58508I
b = −0.350628 + 0.729197I
−0.937840 + 0.856649I −7.17209 − 5.06992I
u = −0.282114 − 0.301857I
a = −1.86889 − 0.58508I
b = −0.350628 − 0.729197I
−0.937840 − 0.856649I −7.17209 + 5.06992I
10
II. I
u
2
=
h−2u
40
+3u
39
+· · ·+b+3, 3u
42
a+11u
42
+· · ·−6a−25, u
43
−2u
42
+· · ·−6u+1i
(i) Arc colorings
a
8
=
0
u
a
11
=
1
0
a
12
=
1
u
2
a
7
=
u
u
3
+ u
a
1
=
u
2
+ 1
u
4
+ 2u
2
a
4
=
a
2u
40
− 3u
39
+ ··· + 12u − 3
a
2
=
u
42
a − u
42
+ ··· − 2a + 4
u
42
a − 3u
41
a + ··· − 2a − 1
a
6
=
u
3
+ 2u
u
3
+ u
a
3
=
u
42
− 2u
41
+ ··· + a − 2
3u
40
− 5u
39
+ ··· + 15u − 4
a
9
=
4u
42
− 5u
41
+ ··· − a − 9
−u
41
a + 3u
42
+ ··· + 17u − 4
a
5
=
−u
39
+ u
38
+ ··· + a + 1
2u
40
− 4u
39
+ ··· + 11u − 3
a
10
=
−u
6
− 3u
4
− 2u
2
+ 1
−u
8
− 4u
6
− 4u
4
(ii) Obstruction class = −1
(iii) Cusp Shapes = −u
42
− 4u
41
+ ··· + 25u − 15
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
u
86
− 7u
85
+ ··· + 79u − 4
c
2
(u
43
− 21u
42
+ ··· − 20u + 8)
2
c
4
, c
8
u
86
− 2u
85
+ ··· + 14276u + 1576
c
5
, c
9
u
86
− 4u
85
+ ··· − 3u + 2
c
6
(u
43
+ 2u
42
+ ··· − 189u + 26)
2
c
7
, c
11
, c
12
(u
43
− 2u
42
+ ··· − 6u + 1)
2
c
10
(u
43
− 8u
42
+ ··· − 160u + 25)
2
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
y
86
+ 33y
85
+ ··· + 551y + 16
c
2
(y
43
− 7y
42
+ ··· + 1296y −64)
2
c
4
, c
8
y
86
+ 12y
85
+ ··· + 61922032y + 2483776
c
5
, c
9
y
86
− 16y
85
+ ··· + 127y + 4
c
6
(y
43
+ 8y
42
+ ··· + 517y −676)
2
c
7
, c
11
, c
12
(y
43
+ 40y
42
+ ··· + 10y −1)
2
c
10
(y
43
+ 24y
42
+ ··· + 3550y −625)
2
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.166107 + 1.122630I
a = −0.943447 + 0.723919I
b = 0.485509 − 0.343469I
−0.25076 + 4.18783I −11.21753 − 7.87764I
u = −0.166107 + 1.122630I
a = 0.362014 + 0.378909I
b = 0.655982 + 1.179390I
−0.25076 + 4.18783I −11.21753 − 7.87764I
u = −0.166107 − 1.122630I
a = −0.943447 − 0.723919I
b = 0.485509 + 0.343469I
−0.25076 − 4.18783I −11.21753 + 7.87764I
u = −0.166107 − 1.122630I
a = 0.362014 − 0.378909I
b = 0.655982 − 1.179390I
−0.25076 − 4.18783I −11.21753 + 7.87764I
u = 0.728452 + 0.355363I
a = 1.30301 − 1.48050I
b = 1.53789 − 0.75478I
3.01372 − 7.42675I −1.58849 + 8.96440I
u = 0.728452 + 0.355363I
a = −1.29704 + 1.66888I
b = −1.47529 + 0.61543I
3.01372 − 7.42675I −1.58849 + 8.96440I
u = 0.728452 − 0.355363I
a = 1.30301 + 1.48050I
b = 1.53789 + 0.75478I
3.01372 + 7.42675I −1.58849 − 8.96440I
u = 0.728452 − 0.355363I
a = −1.29704 − 1.66888I
b = −1.47529 − 0.61543I
3.01372 + 7.42675I −1.58849 − 8.96440I
u = 0.515250 + 0.625157I
a = 1.146030 − 0.789959I
b = 1.253930 + 0.218600I
3.99431 + 3.15841I 1.13775 − 2.94710I
u = 0.515250 + 0.625157I
a = −1.19266 + 1.02280I
b = −1.084340 − 0.309421I
3.99431 + 3.15841I 1.13775 − 2.94710I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.515250 − 0.625157I
a = 1.146030 + 0.789959I
b = 1.253930 − 0.218600I
3.99431 − 3.15841I 1.13775 + 2.94710I
u = 0.515250 − 0.625157I
a = −1.19266 − 1.02280I
b = −1.084340 + 0.309421I
3.99431 − 3.15841I 1.13775 + 2.94710I
u = −0.298241 + 1.201080I
a = 0.413065 + 0.139598I
b = 0.384660 + 0.184593I
2.17074 + 3.81123I 5.45803 − 7.32123I
u = −0.298241 + 1.201080I
a = −0.069857 + 0.337608I
b = 0.290861 − 0.454491I
2.17074 + 3.81123I 5.45803 − 7.32123I
u = −0.298241 − 1.201080I
a = 0.413065 − 0.139598I
b = 0.384660 − 0.184593I
2.17074 − 3.81123I 5.45803 + 7.32123I
u = −0.298241 − 1.201080I
a = −0.069857 − 0.337608I
b = 0.290861 + 0.454491I
2.17074 − 3.81123I 5.45803 + 7.32123I
u = −0.749297
a = −0.634113
b = −0.306363
−1.51538 2.92720
u = −0.749297
a = −0.408867
b = −0.475139
−1.51538 2.92720
u = 0.072880 + 1.255020I
a = 0.367200 − 0.883639I
b = −0.17474 + 2.14293I
3.68125 − 5.05648I 0. + 9.54550I
u = 0.072880 + 1.255020I
a = −1.69368 − 0.23759I
b = −1.135750 − 0.396445I
3.68125 − 5.05648I 0. + 9.54550I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.072880 − 1.255020I
a = 0.367200 + 0.883639I
b = −0.17474 − 2.14293I
3.68125 + 5.05648I 0. − 9.54550I
u = 0.072880 − 1.255020I
a = −1.69368 + 0.23759I
b = −1.135750 + 0.396445I
3.68125 + 5.05648I 0. − 9.54550I
u = 0.594323 + 0.424749I
a = −0.000767 + 0.967530I
b = −0.050270 + 0.212676I
3.18915 − 1.94047I 0.07176 + 3.68376I
u = 0.594323 + 0.424749I
a = −0.113294 − 0.276878I
b = 0.411413 − 0.574699I
3.18915 − 1.94047I 0.07176 + 3.68376I
u = 0.594323 − 0.424749I
a = −0.000767 − 0.967530I
b = −0.050270 − 0.212676I
3.18915 + 1.94047I 0.07176 − 3.68376I
u = 0.594323 − 0.424749I
a = −0.113294 + 0.276878I
b = 0.411413 + 0.574699I
3.18915 + 1.94047I 0.07176 − 3.68376I
u = 0.662452 + 0.307770I
a = −1.04468 + 2.39874I
b = −1.81272 + 1.07558I
−1.07433 − 6.97867I −11.2100 + 9.9328I
u = 0.662452 + 0.307770I
a = 1.63018 − 2.38101I
b = 1.43031 − 1.26753I
−1.07433 − 6.97867I −11.2100 + 9.9328I
u = 0.662452 − 0.307770I
a = −1.04468 − 2.39874I
b = −1.81272 − 1.07558I
−1.07433 + 6.97867I −11.2100 − 9.9328I
u = 0.662452 − 0.307770I
a = 1.63018 + 2.38101I
b = 1.43031 + 1.26753I
−1.07433 + 6.97867I −11.2100 − 9.9328I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.602232 + 0.367369I
a = 2.52885 + 1.09942I
b = 2.22765 + 0.30146I
2.66264 + 6.12754I −1.33584 − 9.50761I
u = −0.602232 + 0.367369I
a = 2.47329 + 2.00931I
b = 1.92685 − 0.26692I
2.66264 + 6.12754I −1.33584 − 9.50761I
u = −0.602232 − 0.367369I
a = 2.52885 − 1.09942I
b = 2.22765 − 0.30146I
2.66264 − 6.12754I −1.33584 + 9.50761I
u = −0.602232 − 0.367369I
a = 2.47329 − 2.00931I
b = 1.92685 + 0.26692I
2.66264 − 6.12754I −1.33584 + 9.50761I
u = −0.668648 + 0.115442I
a = −0.589888 + 1.183360I
b = −0.814550 + 0.545174I
−3.17456 − 0.99810I −14.6431 + 6.0970I
u = −0.668648 + 0.115442I
a = −1.31964 + 0.58750I
b = −0.257818 + 0.859350I
−3.17456 − 0.99810I −14.6431 + 6.0970I
u = −0.668648 − 0.115442I
a = −0.589888 − 1.183360I
b = −0.814550 − 0.545174I
−3.17456 + 0.99810I −14.6431 − 6.0970I
u = −0.668648 − 0.115442I
a = −1.31964 − 0.58750I
b = −0.257818 − 0.859350I
−3.17456 + 0.99810I −14.6431 − 6.0970I
u = 0.010728 + 1.322970I
a = 1.244150 + 0.551389I
b = −0.648154 − 0.430906I
4.82449 + 2.56349I 0
u = 0.010728 + 1.322970I
a = 0.329663 − 0.487250I
b = 0.71612 − 1.65189I
4.82449 + 2.56349I 0
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.010728 − 1.322970I
a = 1.244150 − 0.551389I
b = −0.648154 + 0.430906I
4.82449 − 2.56349I 0
u = 0.010728 − 1.322970I
a = 0.329663 + 0.487250I
b = 0.71612 + 1.65189I
4.82449 − 2.56349I 0
u = −0.542094 + 0.403826I
a = −1.18402 − 2.00462I
b = −2.07820 − 0.81935I
2.88555 − 2.52090I 0.109990 + 1.127839I
u = −0.542094 + 0.403826I
a = −1.74137 − 2.80867I
b = −1.45137 − 0.60855I
2.88555 − 2.52090I 0.109990 + 1.127839I
u = −0.542094 − 0.403826I
a = −1.18402 + 2.00462I
b = −2.07820 + 0.81935I
2.88555 + 2.52090I 0.109990 − 1.127839I
u = −0.542094 − 0.403826I
a = −1.74137 + 2.80867I
b = −1.45137 + 0.60855I
2.88555 + 2.52090I 0.109990 − 1.127839I
u = −0.256969 + 1.321500I
a = 0.946134 + 0.516154I
b = 0.062124 − 0.663605I
1.32438 + 2.35380I 0
u = −0.256969 + 1.321500I
a = 0.492675 − 0.048791I
b = 0.92522 − 1.11768I
1.32438 + 2.35380I 0
u = −0.256969 − 1.321500I
a = 0.946134 − 0.516154I
b = 0.062124 + 0.663605I
1.32438 − 2.35380I 0
u = −0.256969 − 1.321500I
a = 0.492675 + 0.048791I
b = 0.92522 + 1.11768I
1.32438 − 2.35380I 0
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.324328 + 0.492223I
a = 0.89618 − 1.35706I
b = 1.249870 + 0.610441I
−0.04060 + 3.47279I −8.09430 − 4.02435I
u = 0.324328 + 0.492223I
a = −2.03136 + 1.20077I
b = −0.958632 − 0.000991I
−0.04060 + 3.47279I −8.09430 − 4.02435I
u = 0.324328 − 0.492223I
a = 0.89618 + 1.35706I
b = 1.249870 − 0.610441I
−0.04060 − 3.47279I −8.09430 + 4.02435I
u = 0.324328 − 0.492223I
a = −2.03136 − 1.20077I
b = −0.958632 + 0.000991I
−0.04060 − 3.47279I −8.09430 + 4.02435I
u = 0.17630 + 1.41651I
a = 0.096486 − 1.257610I
b = 2.50835 − 0.78501I
5.67023 + 1.42487I 0
u = 0.17630 + 1.41651I
a = 0.32870 + 1.81171I
b = −1.79843 + 0.08504I
5.67023 + 1.42487I 0
u = 0.17630 − 1.41651I
a = 0.096486 + 1.257610I
b = 2.50835 + 0.78501I
5.67023 − 1.42487I 0
u = 0.17630 − 1.41651I
a = 0.32870 − 1.81171I
b = −1.79843 − 0.08504I
5.67023 − 1.42487I 0
u = 0.25512 + 1.42436I
a = 0.48456 + 1.65129I
b = −2.06107 + 1.74576I
4.47634 − 10.32970I 0
u = 0.25512 + 1.42436I
a = −0.93642 − 1.61474I
b = 2.22840 − 1.11147I
4.47634 − 10.32970I 0
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.25512 − 1.42436I
a = 0.48456 − 1.65129I
b = −2.06107 − 1.74576I
4.47634 + 10.32970I 0
u = 0.25512 − 1.42436I
a = −0.93642 + 1.61474I
b = 2.22840 + 1.11147I
4.47634 + 10.32970I 0
u = −0.20779 + 1.44208I
a = −0.82626 + 1.33991I
b = 2.58288 + 0.93449I
8.79083 + 0.26279I 0
u = −0.20779 + 1.44208I
a = −0.38201 + 1.84612I
b = 1.76058 + 1.46995I
8.79083 + 0.26279I 0
u = −0.20779 − 1.44208I
a = −0.82626 − 1.33991I
b = 2.58288 − 0.93449I
8.79083 − 0.26279I 0
u = −0.20779 − 1.44208I
a = −0.38201 − 1.84612I
b = 1.76058 − 1.46995I
8.79083 − 0.26279I 0
u = −0.23021 + 1.43938I
a = −0.19100 − 1.45184I
b = −3.10116 − 0.20307I
8.45919 + 9.19448I 0
u = −0.23021 + 1.43938I
a = −0.19843 − 2.12276I
b = −2.13373 − 0.05931I
8.45919 + 9.19448I 0
u = −0.23021 − 1.43938I
a = −0.19100 + 1.45184I
b = −3.10116 + 0.20307I
8.45919 − 9.19448I 0
u = −0.23021 − 1.43938I
a = −0.19843 + 2.12276I
b = −2.13373 + 0.05931I
8.45919 − 9.19448I 0
20
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.21830 + 1.45337I
a = −0.229747 − 0.721592I
b = 0.186966 − 0.603079I
9.21760 − 4.91390I 0
u = 0.21830 + 1.45337I
a = 0.386900 + 0.186755I
b = −0.998591 + 0.491430I
9.21760 − 4.91390I 0
u = 0.21830 − 1.45337I
a = −0.229747 + 0.721592I
b = 0.186966 + 0.603079I
9.21760 + 4.91390I 0
u = 0.21830 − 1.45337I
a = 0.386900 − 0.186755I
b = −0.998591 − 0.491430I
9.21760 + 4.91390I 0
u = 0.27891 + 1.44938I
a = 0.293485 + 1.280960I
b = −2.00481 + 0.83557I
8.8077 − 11.0948I 0
u = 0.27891 + 1.44938I
a = −0.29925 − 1.44081I
b = 1.77473 − 0.78264I
8.8077 − 11.0948I 0
u = 0.27891 − 1.44938I
a = 0.293485 − 1.280960I
b = −2.00481 − 0.83557I
8.8077 + 11.0948I 0
u = 0.27891 − 1.44938I
a = −0.29925 + 1.44081I
b = 1.77473 + 0.78264I
8.8077 + 11.0948I 0
u = 0.14206 + 1.48462I
a = −0.127936 − 1.024860I
b = 1.232200 − 0.477498I
10.80640 + 0.93464I 0
u = 0.14206 + 1.48462I
a = 0.240014 + 0.852942I
b = −1.50335 + 0.33553I
10.80640 + 0.93464I 0
21
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.14206 − 1.48462I
a = −0.127936 + 1.024860I
b = 1.232200 + 0.477498I
10.80640 − 0.93464I 0
u = 0.14206 − 1.48462I
a = 0.240014 − 0.852942I
b = −1.50335 − 0.33553I
10.80640 − 0.93464I 0
u = 0.367839 + 0.121390I
a = −2.22244 + 1.37771I
b = −0.88352 + 1.20133I
0.28028 + 3.43207I −11.92037 − 3.46520I
u = 0.367839 + 0.121390I
a = 1.19410 − 3.65999I
b = 0.984742 − 0.236994I
0.28028 + 3.43207I −11.92037 − 3.46520I
u = 0.367839 − 0.121390I
a = −2.22244 − 1.37771I
b = −0.88352 − 1.20133I
0.28028 − 3.43207I −11.92037 + 3.46520I
u = 0.367839 − 0.121390I
a = 1.19410 + 3.65999I
b = 0.984742 + 0.236994I
0.28028 − 3.43207I −11.92037 + 3.46520I
22
III.
I
u
3
= h−u
15
+u
14
+· · ·+b−2, 2u
16
−2u
15
+· · ·+a−3, u
17
−u
16
+· · ·−2u+1i
(i) Arc colorings
a
8
=
0
u
a
11
=
1
0
a
12
=
1
u
2
a
7
=
u
u
3
+ u
a
1
=
u
2
+ 1
u
4
+ 2u
2
a
4
=
−2u
16
+ 2u
15
+ ··· − 5u + 3
u
15
− u
14
+ ··· − u + 2
a
2
=
−u
16
− 7u
14
+ ··· − u − 1
−u
16
+ 2u
15
+ ··· − 4u + 1
a
6
=
u
3
+ 2u
u
3
+ u
a
3
=
−u
16
+ u
15
+ ··· − 4u + 1
−u
15
+ u
14
+ ··· − u
2
+ u
a
9
=
u
16
− u
15
+ ··· − 3u
2
+ 3u
u
15
+ u
14
+ ··· + 2u − 1
a
5
=
−u
16
+ u
15
+ ··· − 2u + 1
u
11
+ 5u
9
+ 8u
7
+ 3u
5
− u
3
+ u
2
+ 1
a
10
=
−u
6
− 3u
4
− 2u
2
+ 1
−u
8
− 4u
6
− 4u
4
(ii) Obstruction class = 1
(iii) Cusp Shap es = −2u
15
− 6u
14
− 6u
13
− 42u
12
+ 12u
11
− 108u
10
+ 66u
9
− 114u
8
+
80u
7
− 26u
6
+ 17u
5
+ 30u
4
− 26u
3
+ 20u
2
− 13u + 4
23
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
u
17
− 4u
16
+ ··· + 4u − 1
c
2
u
17
+ 13u
16
+ ··· + 492u + 55
c
4
, c
8
u
17
− 2u
15
+ ··· + 2u
2
− 1
c
5
, c
9
u
17
− 2u
15
+ ··· + 2u
2
− 1
c
6
u
17
− u
16
+ ··· − 4u − 1
c
7
u
17
+ u
16
+ ··· − 2u − 1
c
10
u
17
+ 3u
16
+ ··· − 8u − 1
c
11
, c
12
u
17
− u
16
+ ··· − 2u + 1
24
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
y
17
+ 16y
16
+ ··· − 4y −1
c
2
y
17
+ 7y
16
+ ··· + 2704y −3025
c
4
, c
8
y
17
− 4y
16
+ ··· + 4y −1
c
5
, c
9
y
17
− 4y
16
+ ··· + 4y −1
c
6
y
17
+ 5y
16
+ ··· − 8y −1
c
7
, c
11
, c
12
y
17
+ 17y
16
+ ··· − 6y −1
c
10
y
17
+ 5y
16
+ ··· + 2y −1
25
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.226846 + 1.074950I
a = 0.280723 − 0.296179I
b = 0.254698 + 0.368951I
1.37776 + 4.07487I −4.75927 − 9.57829I
u = −0.226846 − 1.074950I
a = 0.280723 + 0.296179I
b = 0.254698 − 0.368951I
1.37776 − 4.07487I −4.75927 + 9.57829I
u = −0.826052
a = −0.125381
b = 0.103571
−1.78096 −36.8030
u = 0.657980 + 0.330013I
a = −2.04222 + 2.19942I
b = −2.06958 + 0.77322I
0.69054 − 6.88630I −4.75043 + 9.91438I
u = 0.657980 − 0.330013I
a = −2.04222 − 2.19942I
b = −2.06958 − 0.77322I
0.69054 + 6.88630I −4.75043 − 9.91438I
u = 0.008379 + 1.297160I
a = −1.128220 + 0.428770I
b = −0.56564 − 1.45988I
4.26670 − 3.72263I −1.66158 + 6.42655I
u = 0.008379 − 1.297160I
a = −1.128220 − 0.428770I
b = −0.56564 + 1.45988I
4.26670 + 3.72263I −1.66158 − 6.42655I
u = 0.434959 + 0.422256I
a = 1.70189 − 2.41770I
b = 1.76114 − 0.33297I
1.44897 + 3.32356I −2.50461 − 3.66335I
u = 0.434959 − 0.422256I
a = 1.70189 + 2.41770I
b = 1.76114 + 0.33297I
1.44897 − 3.32356I −2.50461 + 3.66335I
u = 0.18670 + 1.43747I
a = 0.29511 + 1.87628I
b = −2.64199 + 0.77451I
7.34687 + 0.89678I 1.38946 − 4.29809I
26
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.18670 − 1.43747I
a = 0.29511 − 1.87628I
b = −2.64199 − 0.77451I
7.34687 − 0.89678I 1.38946 + 4.29809I
u = −0.222618 + 0.502273I
a = −0.753888 − 0.350585I
b = 0.343918 − 0.300611I
1.26383 + 3.80210I −1.63515 − 6.00657I
u = −0.222618 − 0.502273I
a = −0.753888 + 0.350585I
b = 0.343918 + 0.300611I
1.26383 − 3.80210I −1.63515 + 6.00657I
u = 0.25256 + 1.43441I
a = −0.41060 − 1.90729I
b = 2.63214 − 1.07067I
6.35635 − 10.21900I −0.12977 + 9.37561I
u = 0.25256 − 1.43441I
a = −0.41060 + 1.90729I
b = 2.63214 + 1.07067I
6.35635 + 10.21900I −0.12977 − 9.37561I
u = −0.17808 + 1.48097I
a = 0.119877 − 0.172094I
b = 0.233518 + 0.208181I
7.74827 + 5.86104I −3.04695 − 6.97760I
u = −0.17808 − 1.48097I
a = 0.119877 + 0.172094I
b = 0.233518 − 0.208181I
7.74827 − 5.86104I −3.04695 + 6.97760I
27
IV. I
u
4
= hau − u
2
+ b − u − 1, u
2
a + a
2
+ 2u
2
+ a + u + 3, u
3
+ u
2
+ 2u + 1i
(i) Arc colorings
a
8
=
0
u
a
11
=
1
0
a
12
=
1
u
2
a
7
=
u
−u
2
− u − 1
a
1
=
u
2
+ 1
u
2
+ u + 1
a
4
=
a
−au + u
2
+ u + 1
a
2
=
u
2
+ a + 1
−au + 2u
2
+ 2u + 2
a
6
=
−u
2
− 1
−u
2
− u − 1
a
3
=
u
2
+ a + 1
−au + 2u
2
+ 2u + 2
a
9
=
u
2
a + au − u
2
+ a − u − 1
2au + 2a − u − 1
a
5
=
a
u
2
a − au + u
2
+ u + 1
a
10
=
0
u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −5u
2
− 8u − 16
28
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
(u − 1)
6
c
2
u
6
c
4
, c
5
, c
8
c
9
u
6
+ u
5
+ 3u
4
+ u
3
+ 3u
2
+ u + 1
c
6
, c
10
(u
3
+ u
2
− 1)
2
c
7
(u
3
− u
2
+ 2u − 1)
2
c
11
, c
12
(u
3
+ u
2
+ 2u + 1)
2
29
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
(y −1)
6
c
2
y
6
c
4
, c
5
, c
8
c
9
y
6
+ 5y
5
+ 13y
4
+ 17y
3
+ 13y
2
+ 5y + 1
c
6
, c
10
(y
3
− y
2
+ 2y −1)
2
c
7
, c
11
, c
12
(y
3
+ 3y
2
+ 2y −1)
2
30
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.215080 + 1.307140I
a = 1.086460 + 0.283545I
b = −0.273131 − 0.614306I
1.37919 + 2.82812I −5.96757 − 7.64573I
u = −0.215080 + 1.307140I
a = −0.424098 + 0.278735I
b = −0.60431 + 1.35917I
1.37919 + 2.82812I −5.96757 − 7.64573I
u = −0.215080 − 1.307140I
a = 1.086460 − 0.283545I
b = −0.273131 + 0.614306I
1.37919 − 2.82812I −5.96757 + 7.64573I
u = −0.215080 − 1.307140I
a = −0.424098 − 0.278735I
b = −0.60431 − 1.35917I
1.37919 − 2.82812I −5.96757 + 7.64573I
u = −0.569840
a = −0.66236 + 1.62508I
b = 0.377439 + 0.926035I
−2.75839 −13.0650
u = −0.569840
a = −0.66236 − 1.62508I
b = 0.377439 − 0.926035I
−2.75839 −13.0650
31
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
3
((u − 1)
6
)(u
17
− 4u
16
+ ··· + 4u − 1)(u
58
+ 10u
57
+ ··· − 5u + 1)
· (u
86
− 7u
85
+ ··· + 79u − 4)
c
2
u
6
(u
17
+ 13u
16
+ ··· + 492u + 55)(u
43
− 21u
42
+ ··· − 20u + 8)
2
· (u
58
+ 30u
57
+ ··· + 7u + 2)
c
4
, c
8
(u
6
+ u
5
+ 3u
4
+ u
3
+ 3u
2
+ u + 1)(u
17
− 2u
15
+ ··· + 2u
2
− 1)
· (u
58
+ 8u
56
+ ··· + 5u + 2)(u
86
− 2u
85
+ ··· + 14276u + 1576)
c
5
, c
9
(u
6
+ u
5
+ 3u
4
+ u
3
+ 3u
2
+ u + 1)(u
17
− 2u
15
+ ··· + 2u
2
− 1)
· (u
58
− 2u
57
+ ··· − u + 1)(u
86
− 4u
85
+ ··· − 3u + 2)
c
6
((u
3
+ u
2
− 1)
2
)(u
17
− u
16
+ ··· − 4u − 1)
· ((u
43
+ 2u
42
+ ··· − 189u + 26)
2
)(u
58
− 6u
57
+ ··· + 10406u + 1768)
c
7
((u
3
− u
2
+ 2u − 1)
2
)(u
17
+ u
16
+ ··· − 2u − 1)
· ((u
43
− 2u
42
+ ··· − 6u + 1)
2
)(u
58
+ 6u
57
+ ··· + 37u + 4)
c
10
((u
3
+ u
2
− 1)
2
)(u
17
+ 3u
16
+ ··· − 8u − 1)
· ((u
43
− 8u
42
+ ··· − 160u + 25)
2
)(u
58
− 10u
57
+ ··· − 79407u + 9248)
c
11
, c
12
((u
3
+ u
2
+ 2u + 1)
2
)(u
17
− u
16
+ ··· − 2u + 1)
· ((u
43
− 2u
42
+ ··· − 6u + 1)
2
)(u
58
+ 6u
57
+ ··· + 37u + 4)
32
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
3
((y −1)
6
)(y
17
+ 16y
16
+ ··· − 4y −1)(y
58
− 20y
57
+ ··· − 37y + 1)
· (y
86
+ 33y
85
+ ··· + 551y + 16)
c
2
y
6
(y
17
+ 7y
16
+ ··· + 2704y −3025)
· ((y
43
− 7y
42
+ ··· + 1296y −64)
2
)(y
58
+ 12y
56
+ ··· − 17y + 4)
c
4
, c
8
(y
6
+ 5y
5
+ ··· + 5y + 1)(y
17
− 4y
16
+ ··· + 4y −1)
· (y
58
+ 16y
57
+ ··· + 47y + 4)
· (y
86
+ 12y
85
+ ··· + 61922032y + 2483776)
c
5
, c
9
(y
6
+ 5y
5
+ ··· + 5y + 1)(y
17
− 4y
16
+ ··· + 4y −1)
· (y
58
+ 32y
57
+ ··· + 67y + 1)(y
86
− 16y
85
+ ··· + 127y + 4)
c
6
((y
3
− y
2
+ 2y −1)
2
)(y
17
+ 5y
16
+ ··· − 8y −1)
· (y
43
+ 8y
42
+ ··· + 517y −676)
2
· (y
58
+ 14y
57
+ ··· + 31546284y + 3125824)
c
7
, c
11
, c
12
((y
3
+ 3y
2
+ 2y −1)
2
)(y
17
+ 17y
16
+ ··· − 6y −1)
· ((y
43
+ 40y
42
+ ··· + 10y −1)
2
)(y
58
+ 54y
57
+ ··· − 89y + 16)
c
10
((y
3
− y
2
+ 2y −1)
2
)(y
17
+ 5y
16
+ ··· + 2y −1)
· (y
43
+ 24y
42
+ ··· + 3550y −625)
2
· (y
58
+ 30y
57
+ ··· + 1679029599y + 85525504)
33
