11a
216
(K11a
216
)
A knot diagram
1
Linearized knot diagam
6 1 10 8 9 2 4 11 3 5 7
Solving Sequence
2,7
6 1
3,9
5 11 8 4 10
c
6
c
1
c
2
c
5
c
11
c
8
c
4
c
10
c
3
, c
7
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.00850 × 10
59
u
80
− 3.71314 × 10
58
u
79
+ ··· + 1.36235 × 10
58
b − 1.35990 × 10
59
,
1.76890 × 10
59
u
80
+ 8.72974 × 10
58
u
79
+ ··· + 1.36235 × 10
58
a + 2.94938 × 10
59
, u
81
+ u
80
+ ··· + 2u + 1i
I
u
2
= h−2u
14
+ 2u
13
+ 7u
12
− 7u
11
− 12u
10
+ 12u
9
+ 9u
8
− 7u
7
− 4u
6
− 3u
5
+ 3u
4
+ 6u
3
− 5u
2
+ b − 2u + 3,
− 3u
13
+ u
12
+ 10u
11
− 3u
10
− 17u
9
+ 4u
8
+ 12u
7
+ u
6
− 4u
5
− 7u
4
+ 7u
2
+ a − 2u − 4,
u
15
− 4u
13
+ 8u
11
− 8u
9
− u
8
+ 4u
7
+ 3u
6
− 4u
4
+ 3u
2
− 1i
I
u
3
= hu
2
+ b, −u
2
+ a − 1, u
6
+ u
5
+ 1i
I
u
4
= hb + 1, a − 2, u − 1i
* 4 irreducible components of dim
C
= 0, with total 103 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−1.01×10
59
u
80
−3.71×10
58
u
79
+· · ·+1.36×10
58
b−1.36×10
59
, 1.77×
10
59
u
80
+8.73×10
58
u
79
+· · ·+1.36×10
58
a+2.95×10
59
, u
81
+u
80
+· · ·+2u+1i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
6
=
1
−u
2
a
1
=
u
−u
3
+ u
a
3
=
−u
3
u
5
− u
3
+ u
a
9
=
−12.9842u
80
− 6.40783u
79
+ ··· − 2.14853u − 21.6491
7.40264u
80
+ 2.72553u
79
+ ··· + 4.39790u + 9.98198
a
5
=
−13.3712u
80
− 5.09999u
79
+ ··· − 2.91497u − 20.5076
0.0913650u
80
− 0.813439u
79
+ ··· − 2.45718u − 2.62055
a
11
=
u
3
−u
3
+ u
a
8
=
−14.4485u
80
− 7.48009u
79
+ ··· − 2.78649u − 23.7611
5.28092u
80
+ 2.32374u
79
+ ··· + 4.14897u + 5.26440
a
4
=
−8.40559u
80
− 5.75051u
79
+ ··· + 2.69355u − 17.0429
−6.46426u
80
− 2.78674u
79
+ ··· − 6.07564u − 10.4024
a
10
=
−13.0257u
80
− 6.50801u
79
+ ··· − 1.60601u − 20.8812
6.96235u
80
+ 2.92923u
79
+ ··· + 6.10527u + 7.49207
a
10
=
−13.0257u
80
− 6.50801u
79
+ ··· − 1.60601u − 20.8812
6.96235u
80
+ 2.92923u
79
+ ··· + 6.10527u + 7.49207
(ii) Obstruction class = −1
(iii) Cusp Shapes = 14.5586u
80
+ 7.70676u
79
+ ··· − 1.69347u + 19.4046
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
81
− u
80
+ ··· + 2u − 1
c
2
u
81
+ 43u
80
+ ··· + 6u + 1
c
3
, c
9
u
81
− 7u
80
+ ··· − 1188u + 216
c
4
, c
7
u
81
− 2u
80
+ ··· − 77u + 79
c
5
u
81
+ u
80
+ ··· − 16528u − 1781
c
8
u
81
+ 13u
80
+ ··· − 34u + 11
c
10
u
81
− u
80
+ ··· + 14u + 3
c
11
u
81
− 3u
80
+ ··· + 4942u − 1947
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
81
− 43y
80
+ ··· + 6y −1
c
2
y
81
+ y
80
+ ··· + 38y −1
c
3
, c
9
y
81
− 57y
80
+ ··· + 1333584y −46656
c
4
, c
7
y
81
− 50y
80
+ ··· − 1813y −6241
c
5
y
81
− 27y
80
+ ··· + 148198452y −3171961
c
8
y
81
− 7y
80
+ ··· + 9032y −121
c
10
y
81
− 3y
80
+ ··· + 232y −9
c
11
y
81
+ 41y
80
+ ··· + 38652040y −3790809
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.353486 + 0.936121I
a = 0.145670 − 0.210945I
b = −0.684489 + 0.183324I
−1.81799 + 2.40695I 0
u = 0.353486 − 0.936121I
a = 0.145670 + 0.210945I
b = −0.684489 − 0.183324I
−1.81799 − 2.40695I 0
u = 0.764070 + 0.573116I
a = 0.019145 − 0.599281I
b = 0.294520 + 0.973700I
−1.65399 − 4.34598I 0. + 7.39263I
u = 0.764070 − 0.573116I
a = 0.019145 + 0.599281I
b = 0.294520 − 0.973700I
−1.65399 + 4.34598I 0. − 7.39263I
u = 0.897471 + 0.585786I
a = −0.426738 − 0.251752I
b = 0.378705 − 0.463704I
4.21372 − 0.52225I 0
u = 0.897471 − 0.585786I
a = −0.426738 + 0.251752I
b = 0.378705 + 0.463704I
4.21372 + 0.52225I 0
u = −0.255625 + 0.871069I
a = −0.322424 + 0.317539I
b = −1.67729 − 0.85921I
−0.92282 − 11.98720I −2.33004 + 6.68936I
u = −0.255625 − 0.871069I
a = −0.322424 − 0.317539I
b = −1.67729 + 0.85921I
−0.92282 + 11.98720I −2.33004 − 6.68936I
u = 0.887015 + 0.179085I
a = 1.247820 + 0.507202I
b = −0.406240 − 0.514609I
−1.382340 − 0.196561I −8.40096 + 0.94389I
u = 0.887015 − 0.179085I
a = 1.247820 − 0.507202I
b = −0.406240 + 0.514609I
−1.382340 + 0.196561I −8.40096 − 0.94389I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.666327 + 0.609855I
a = −1.056000 + 0.794212I
b = 0.120020 − 0.152491I
4.88164 − 4.17734I 2.92030 + 4.97430I
u = 0.666327 − 0.609855I
a = −1.056000 − 0.794212I
b = 0.120020 + 0.152491I
4.88164 + 4.17734I 2.92030 − 4.97430I
u = −0.772892 + 0.442862I
a = 0.911132 + 0.522504I
b = −0.563301 − 0.466917I
1.33705 + 1.90417I 2.60969 − 4.16146I
u = −0.772892 − 0.442862I
a = 0.911132 − 0.522504I
b = −0.563301 + 0.466917I
1.33705 − 1.90417I 2.60969 + 4.16146I
u = −0.833248 + 0.735410I
a = −0.309844 − 0.449602I
b = −0.203212 + 0.411021I
2.49951 + 9.29172I 0
u = −0.833248 − 0.735410I
a = −0.309844 + 0.449602I
b = −0.203212 − 0.411021I
2.49951 − 9.29172I 0
u = −0.839590 + 0.291084I
a = −0.45851 + 2.35188I
b = −0.61804 − 1.59554I
0.06939 + 4.39534I −6.51221 − 9.24323I
u = −0.839590 − 0.291084I
a = −0.45851 − 2.35188I
b = −0.61804 + 1.59554I
0.06939 − 4.39534I −6.51221 + 9.24323I
u = −0.789832 + 0.783125I
a = −0.465566 + 0.452295I
b = 0.0687710 − 0.1002050I
2.65976 − 3.66135I 0
u = −0.789832 − 0.783125I
a = −0.465566 − 0.452295I
b = 0.0687710 + 0.1002050I
2.65976 + 3.66135I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.032810 + 0.447989I
a = 2.83612 − 0.49189I
b = −1.53996 − 1.53611I
0.275846 − 0.630932I 0
u = 1.032810 − 0.447989I
a = 2.83612 + 0.49189I
b = −1.53996 + 1.53611I
0.275846 + 0.630932I 0
u = −1.111980 + 0.324340I
a = 1.80235 + 1.20589I
b = −2.24237 + 0.27267I
−0.79545 − 2.68846I 0
u = −1.111980 − 0.324340I
a = 1.80235 − 1.20589I
b = −2.24237 − 0.27267I
−0.79545 + 2.68846I 0
u = −0.453414 + 0.691603I
a = −0.0996573 − 0.0433267I
b = −0.996987 + 0.338045I
2.86402 − 1.12377I 1.82611 − 2.82977I
u = −0.453414 − 0.691603I
a = −0.0996573 + 0.0433267I
b = −0.996987 − 0.338045I
2.86402 + 1.12377I 1.82611 + 2.82977I
u = 0.231721 + 0.787238I
a = 0.250689 + 0.388970I
b = 1.75641 − 0.82207I
−4.21937 + 5.70269I −5.14699 − 5.02778I
u = 0.231721 − 0.787238I
a = 0.250689 − 0.388970I
b = 1.75641 + 0.82207I
−4.21937 − 5.70269I −5.14699 + 5.02778I
u = −1.065070 + 0.538991I
a = 1.40242 + 1.59557I
b = −1.70328 + 0.12611I
1.05312 + 5.61889I 0
u = −1.065070 − 0.538991I
a = 1.40242 − 1.59557I
b = −1.70328 − 0.12611I
1.05312 − 5.61889I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.111370 + 0.438228I
a = 1.385970 + 0.267580I
b = −0.64009 + 1.54321I
−5.57621 + 3.25113I 0
u = −1.111370 − 0.438228I
a = 1.385970 − 0.267580I
b = −0.64009 − 1.54321I
−5.57621 − 3.25113I 0
u = 1.125260 + 0.410648I
a = −1.34414 + 1.12484I
b = 1.69461 + 0.27601I
−3.69078 − 1.82728I 0
u = 1.125260 − 0.410648I
a = −1.34414 − 1.12484I
b = 1.69461 − 0.27601I
−3.69078 + 1.82728I 0
u = −0.447441 + 0.661185I
a = −0.088570 + 0.150125I
b = −1.232070 − 0.219872I
2.87684 − 0.94366I 3.19851 + 0.58211I
u = −0.447441 − 0.661185I
a = −0.088570 − 0.150125I
b = −1.232070 + 0.219872I
2.87684 + 0.94366I 3.19851 − 0.58211I
u = −1.065000 + 0.572695I
a = 0.18457 + 1.55186I
b = −1.040630 − 0.428971I
1.06746 + 6.00583I 0
u = −1.065000 − 0.572695I
a = 0.18457 − 1.55186I
b = −1.040630 + 0.428971I
1.06746 − 6.00583I 0
u = −1.197790 + 0.191469I
a = 1.080480 + 0.170748I
b = −0.489918 + 0.440340I
−7.30328 + 0.66829I 0
u = −1.197790 − 0.191469I
a = 1.080480 − 0.170748I
b = −0.489918 − 0.440340I
−7.30328 − 0.66829I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.120360 + 0.467251I
a = 1.24527 − 1.30896I
b = −1.96104 + 0.66304I
−5.35302 − 4.32976I 0
u = 1.120360 − 0.467251I
a = 1.24527 + 1.30896I
b = −1.96104 − 0.66304I
−5.35302 + 4.32976I 0
u = 1.115380 + 0.480964I
a = −0.90946 − 1.83248I
b = −0.309442 + 0.841468I
−1.19632 − 7.51167I 0
u = 1.115380 − 0.480964I
a = −0.90946 + 1.83248I
b = −0.309442 − 0.841468I
−1.19632 + 7.51167I 0
u = 0.268475 + 0.723594I
a = −1.083920 − 0.186754I
b = −1.39346 + 0.97561I
3.18792 + 5.71030I 0.53106 − 5.73349I
u = 0.268475 − 0.723594I
a = −1.083920 + 0.186754I
b = −1.39346 − 0.97561I
3.18792 − 5.71030I 0.53106 + 5.73349I
u = −1.188380 + 0.311281I
a = −1.75719 − 1.47102I
b = 1.79283 − 0.05490I
−8.54999 − 2.22876I 0
u = −1.188380 − 0.311281I
a = −1.75719 + 1.47102I
b = 1.79283 + 0.05490I
−8.54999 + 2.22876I 0
u = −1.137500 + 0.475476I
a = −2.17624 − 0.33439I
b = 1.72783 − 1.32004I
−3.22394 + 6.00881I 0
u = −1.137500 − 0.475476I
a = −2.17624 + 0.33439I
b = 1.72783 + 1.32004I
−3.22394 − 6.00881I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.078476 + 0.744812I
a = 0.704380 − 0.993703I
b = 1.305590 − 0.047937I
−2.16071 − 3.34222I −4.83017 + 7.08778I
u = −0.078476 − 0.744812I
a = 0.704380 + 0.993703I
b = 1.305590 + 0.047937I
−2.16071 + 3.34222I −4.83017 − 7.08778I
u = 1.137170 + 0.533166I
a = 2.28675 − 0.59226I
b = −2.03696 − 1.61104I
0.65865 − 10.48350I 0
u = 1.137170 − 0.533166I
a = 2.28675 + 0.59226I
b = −2.03696 + 1.61104I
0.65865 + 10.48350I 0
u = 1.186600 + 0.412439I
a = −1.40354 + 0.43387I
b = 1.19145 + 1.27355I
−5.80693 − 0.69674I 0
u = 1.186600 − 0.412439I
a = −1.40354 − 0.43387I
b = 1.19145 − 1.27355I
−5.80693 + 0.69674I 0
u = −1.178410 + 0.480916I
a = −1.70444 − 1.06176I
b = 2.40022 − 0.13432I
−5.32246 + 7.84641I 0
u = −1.178410 − 0.480916I
a = −1.70444 + 1.06176I
b = 2.40022 + 0.13432I
−5.32246 − 7.84641I 0
u = 1.251330 + 0.270280I
a = 1.54437 − 1.19181I
b = −1.72788 + 0.01203I
−5.81796 + 8.31263I 0
u = 1.251330 − 0.270280I
a = 1.54437 + 1.19181I
b = −1.72788 − 0.01203I
−5.81796 − 8.31263I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.163560 + 0.542163I
a = −2.49355 + 1.01995I
b = 2.30668 + 1.00700I
−6.95659 − 10.65130I 0
u = 1.163560 − 0.542163I
a = −2.49355 − 1.01995I
b = 2.30668 − 1.00700I
−6.95659 + 10.65130I 0
u = −0.686699 + 0.054430I
a = 1.53780 + 0.66922I
b = −0.66950 − 1.40480I
0.82340 + 2.75519I −4.46449 − 1.61172I
u = −0.686699 − 0.054430I
a = 1.53780 − 0.66922I
b = −0.66950 + 1.40480I
0.82340 − 2.75519I −4.46449 + 1.61172I
u = −1.186750 + 0.572166I
a = 2.24475 + 0.84767I
b = −2.15764 + 1.11820I
−3.7190 + 17.2795I 0
u = −1.186750 − 0.572166I
a = 2.24475 − 0.84767I
b = −2.15764 − 1.11820I
−3.7190 − 17.2795I 0
u = 1.288520 + 0.326107I
a = −0.977917 + 0.363557I
b = 0.859230 + 0.498217I
−6.39093 − 4.34959I 0
u = 1.288520 − 0.326107I
a = −0.977917 − 0.363557I
b = 0.859230 − 0.498217I
−6.39093 + 4.34959I 0
u = 1.186810 + 0.605790I
a = 1.066820 − 0.511590I
b = −1.075190 − 0.313808I
−4.42307 − 8.03198I 0
u = 1.186810 − 0.605790I
a = 1.066820 + 0.511590I
b = −1.075190 + 0.313808I
−4.42307 + 8.03198I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.230620 + 0.525995I
a = −1.38150 − 0.39729I
b = 1.41856 − 0.61959I
−5.01528 + 5.22835I 0
u = −1.230620 − 0.525995I
a = −1.38150 + 0.39729I
b = 1.41856 + 0.61959I
−5.01528 − 5.22835I 0
u = −0.122761 + 0.636850I
a = 0.773920 − 0.056125I
b = 0.994606 + 0.698230I
−0.40315 − 1.75468I −2.66947 + 3.58305I
u = −0.122761 − 0.636850I
a = 0.773920 + 0.056125I
b = 0.994606 − 0.698230I
−0.40315 + 1.75468I −2.66947 − 3.58305I
u = 0.491013 + 0.385970I
a = −1.318490 + 0.085313I
b = −0.86028 + 1.57846I
1.91014 − 3.07747I 3.39105 + 3.81953I
u = 0.491013 − 0.385970I
a = −1.318490 − 0.085313I
b = −0.86028 − 1.57846I
1.91014 + 3.07747I 3.39105 − 3.81953I
u = 0.180434 + 0.529501I
a = −0.662704 + 1.127170I
b = −0.591412 − 1.215950I
1.34431 + 3.37389I −0.27532 − 5.21535I
u = 0.180434 − 0.529501I
a = −0.662704 − 1.127170I
b = −0.591412 + 1.215950I
1.34431 − 3.37389I −0.27532 + 5.21535I
u = 0.144994 + 0.507790I
a = 0.36150 − 2.09518I
b = −0.958492 − 0.271503I
−2.71152 + 0.29912I −4.85977 + 1.99528I
u = 0.144994 − 0.507790I
a = 0.36150 + 2.09518I
b = −0.958492 + 0.271503I
−2.71152 − 0.29912I −4.85977 − 1.99528I
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.479949
a = −4.18306
b = −0.0617552
−2.92420 0.818700
13
II. I
u
2
=
h−2u
14
+2u
13
+· · · +b+3, −3u
13
+u
12
+· · · +a−4, u
15
−4u
13
+· · · +3u
2
−1i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
6
=
1
−u
2
a
1
=
u
−u
3
+ u
a
3
=
−u
3
u
5
− u
3
+ u
a
9
=
3u
13
− u
12
+ ··· + 2u + 4
2u
14
− 2u
13
+ ··· + 2u − 3
a
5
=
−u
14
− 2u
13
+ ··· − u − 3
u
14
− u
13
− 3u
12
+ 2u
11
+ 5u
10
− 2u
9
− 3u
8
− 2u
7
+ 2u
6
+ 3u
5
− 3u
3
+ 1
a
11
=
u
3
−u
3
+ u
a
8
=
3u
13
− u
12
+ ··· + 2u + 5
2u
14
− u
13
+ ··· + 2u − 2
a
4
=
−2u
14
− 2u
13
+ ··· − 3u − 4
u
12
− 3u
10
+ 4u
8
− u
6
− u
5
− u
4
+ 2u
3
− u + 1
a
10
=
2u
13
− u
12
+ ··· + 2u + 3
2u
14
− u
13
+ ··· + 3u − 2
a
10
=
2u
13
− u
12
+ ··· + 2u + 3
2u
14
− u
13
+ ··· + 3u − 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = u
14
−11u
13
−3u
12
+ 43u
11
+ 5u
10
−78u
9
−4u
8
+ 61u
7
+ 13u
6
−
11u
5
− 31u
4
− 13u
3
+ 35u
2
− 3u − 22
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
15
− 4u
13
+ 8u
11
− 8u
9
+ u
8
+ 4u
7
− 3u
6
+ 4u
4
− 3u
2
+ 1
c
2
u
15
+ 8u
14
+ ··· + 6u + 1
c
3
u
15
− u
14
+ ··· − u + 1
c
4
u
15
− u
14
+ ··· − u + 1
c
5
u
15
+ 2u
13
+ u
12
+ 3u
11
+ u
10
+ 2u
9
+ u
7
− 2u
6
− 3u
5
− 4u
4
− 1
c
6
u
15
− 4u
13
+ 8u
11
− 8u
9
− u
8
+ 4u
7
+ 3u
6
− 4u
4
+ 3u
2
− 1
c
7
u
15
+ u
14
+ ··· − u − 1
c
8
u
15
− 2u
13
+ ··· − 4u − 1
c
9
u
15
+ u
14
+ ··· − u − 1
c
10
u
15
+ 4u
11
+ 3u
10
+ 2u
9
− u
8
− 2u
6
− u
5
− 3u
4
− u
3
− 2u
2
− 1
c
11
u
15
+ 4u
13
+ ··· − 6u
2
+ 1
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
15
− 8y
14
+ ··· + 6y −1
c
2
y
15
+ 16y
13
+ ··· + 2y −1
c
3
, c
9
y
15
− 15y
14
+ ··· + 11y −1
c
4
, c
7
y
15
− 11y
14
+ ··· + 15y −1
c
5
y
15
+ 4y
14
+ ··· − 8y
2
− 1
c
8
y
15
− 4y
14
+ ··· + 4y −1
c
10
y
15
+ 8y
13
+ ··· − 4y −1
c
11
y
15
+ 8y
14
+ ··· + 12y −1
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.997247 + 0.392970I
a = 2.71489 − 0.62809I
b = −1.29145 + 1.40184I
−0.044369 − 0.633415I −1.08788 + 2.48026I
u = −0.997247 − 0.392970I
a = 2.71489 + 0.62809I
b = −1.29145 − 1.40184I
−0.044369 + 0.633415I −1.08788 − 2.48026I
u = −0.221545 + 0.858385I
a = −0.066551 − 0.561702I
b = 0.651943 − 0.003032I
−1.82195 − 1.76571I −4.04745 − 0.75169I
u = −0.221545 − 0.858385I
a = −0.066551 + 0.561702I
b = 0.651943 + 0.003032I
−1.82195 + 1.76571I −4.04745 + 0.75169I
u = 0.589578 + 0.609250I
a = 0.026910 − 0.340226I
b = −0.852572 − 0.777911I
2.48631 + 2.07411I −0.45705 − 2.34926I
u = 0.589578 − 0.609250I
a = 0.026910 + 0.340226I
b = −0.852572 + 0.777911I
2.48631 − 2.07411I −0.45705 + 2.34926I
u = 1.030730 + 0.548115I
a = −0.26464 − 1.93296I
b = −1.17743 + 0.81712I
1.09684 − 6.66891I −2.05979 + 11.69980I
u = 1.030730 − 0.548115I
a = −0.26464 + 1.93296I
b = −1.17743 − 0.81712I
1.09684 + 6.66891I −2.05979 − 11.69980I
u = −0.734119 + 0.278311I
a = 0.018935 + 1.247810I
b = −0.75789 − 1.70123I
1.01287 + 3.62441I −1.97748 − 8.82225I
u = −0.734119 − 0.278311I
a = 0.018935 − 1.247810I
b = −0.75789 + 1.70123I
1.01287 − 3.62441I −1.97748 + 8.82225I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.162560 + 0.361615I
a = −1.017670 + 0.054285I
b = 0.415367 + 1.176280I
−6.03108 − 1.76748I −8.58457 + 2.09679I
u = 1.162560 − 0.361615I
a = −1.017670 − 0.054285I
b = 0.415367 − 1.176280I
−6.03108 + 1.76748I −8.58457 − 2.09679I
u = 0.729970
a = 3.59045
b = −0.927345
−3.42072 −16.5640
u = −1.194930 + 0.516966I
a = −1.207100 − 0.512386I
b = 1.47569 − 0.21174I
−4.85785 + 6.78722I −6.00355 − 4.69104I
u = −1.194930 − 0.516966I
a = −1.207100 + 0.512386I
b = 1.47569 + 0.21174I
−4.85785 − 6.78722I −6.00355 + 4.69104I
18
III. I
u
3
= hu
2
+ b, −u
2
+ a − 1, u
6
+ u
5
+ 1i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
6
=
1
−u
2
a
1
=
u
−u
3
+ u
a
3
=
−u
3
u
5
− u
3
+ u
a
9
=
u
2
+ 1
−u
2
a
5
=
u
5
− u
4
+ 2
−u
5
− u
2
− 1
a
11
=
u
3
−u
3
+ u
a
8
=
u
4
+ u
2
+ 1
−u
4
a
4
=
u
2
+ 1
−u
2
a
10
=
−u
3
+ u
2
+ 1
u
5
− u
3
− u
2
+ u
a
10
=
−u
3
+ u
2
+ 1
u
5
− u
3
− u
2
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −6
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
, c
8
u
6
− u
5
+ 1
c
2
, c
4
, c
7
u
6
+ u
5
− 2u
3
+ 1
c
3
, c
9
(u + 1)
6
c
5
u
6
+ u
5
+ 4u
4
+ 2u
3
+ 1
c
10
, c
11
u
6
+ 3u
4
+ 4u
3
+ 2u
2
+ 4u + 3
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
, c
8
y
6
− y
5
+ 2y
3
+ 1
c
2
, c
4
, c
7
y
6
− y
5
+ 4y
4
− 2y
3
+ 1
c
3
, c
9
(y −1)
6
c
5
y
6
+ 7y
5
+ 12y
4
− 2y
3
+ 8y
2
+ 1
c
10
, c
11
y
6
+ 6y
5
+ 13y
4
+ 2y
3
− 10y
2
− 4y + 9
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.140390 + 0.942117I
a = 0.132124 − 0.264528I
b = 0.867876 + 0.264528I
−1.64493 −6.00000
u = −0.140390 − 0.942117I
a = 0.132124 + 0.264528I
b = 0.867876 − 0.264528I
−1.64493 −6.00000
u = 0.745509 + 0.482472I
a = 1.32300 + 0.71937I
b = −0.323005 − 0.719374I
−1.64493 −6.00000
u = 0.745509 − 0.482472I
a = 1.32300 − 0.71937I
b = −0.323005 + 0.719374I
−1.64493 −6.00000
u = −1.105120 + 0.420020I
a = 2.04487 − 0.92834I
b = −1.044870 + 0.928343I
−1.64493 −6.00000
u = −1.105120 − 0.420020I
a = 2.04487 + 0.92834I
b = −1.044870 − 0.928343I
−1.64493 −6.00000
22
IV. I
u
4
= hb + 1, a − 2, u − 1i
(i) Arc colorings
a
2
=
0
1
a
7
=
1
0
a
6
=
1
−1
a
1
=
1
0
a
3
=
−1
1
a
9
=
2
−1
a
5
=
−1
0
a
11
=
1
0
a
8
=
3
−1
a
4
=
2
−1
a
10
=
1
0
a
10
=
1
0
(ii) Obstruction class = −1
(iii) Cusp Shapes = −6
23
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
6
c
7
, c
8
, c
9
u + 1
c
10
, c
11
u
24
(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
9
y −1
c
10
, c
11
y
25
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = 2.00000
b = −1.00000
−1.64493 −6.00000
26
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u + 1)(u
6
− u
5
+ 1)
· (u
15
− 4u
13
+ 8u
11
− 8u
9
+ u
8
+ 4u
7
− 3u
6
+ 4u
4
− 3u
2
+ 1)
· (u
81
− u
80
+ ··· + 2u − 1)
c
2
(u + 1)(u
6
+ u
5
− 2u
3
+ 1)(u
15
+ 8u
14
+ ··· + 6u + 1)
· (u
81
+ 43u
80
+ ··· + 6u + 1)
c
3
((u + 1)
7
)(u
15
− u
14
+ ··· − u + 1)(u
81
− 7u
80
+ ··· − 1188u + 216)
c
4
(u + 1)(u
6
+ u
5
− 2u
3
+ 1)(u
15
− u
14
+ ··· − u + 1)
· (u
81
− 2u
80
+ ··· − 77u + 79)
c
5
(u + 1)(u
6
+ u
5
+ 4u
4
+ 2u
3
+ 1)
· (u
15
+ 2u
13
+ u
12
+ 3u
11
+ u
10
+ 2u
9
+ u
7
− 2u
6
− 3u
5
− 4u
4
− 1)
· (u
81
+ u
80
+ ··· − 16528u − 1781)
c
6
(u + 1)(u
6
− u
5
+ 1)
· (u
15
− 4u
13
+ 8u
11
− 8u
9
− u
8
+ 4u
7
+ 3u
6
− 4u
4
+ 3u
2
− 1)
· (u
81
− u
80
+ ··· + 2u − 1)
c
7
(u + 1)(u
6
+ u
5
− 2u
3
+ 1)(u
15
+ u
14
+ ··· − u − 1)
· (u
81
− 2u
80
+ ··· − 77u + 79)
c
8
(u + 1)(u
6
− u
5
+ 1)(u
15
− 2u
13
+ ··· − 4u − 1)
· (u
81
+ 13u
80
+ ··· − 34u + 11)
c
9
((u + 1)
7
)(u
15
+ u
14
+ ··· − u − 1)(u
81
− 7u
80
+ ··· − 1188u + 216)
c
10
u(u
6
+ 3u
4
+ 4u
3
+ 2u
2
+ 4u + 3)
· (u
15
+ 4u
11
+ 3u
10
+ 2u
9
− u
8
− 2u
6
− u
5
− 3u
4
− u
3
− 2u
2
− 1)
· (u
81
− u
80
+ ··· + 14u + 3)
c
11
u(u
6
+ 3u
4
+ ··· + 4u + 3)(u
15
+ 4u
13
+ ··· − 6u
2
+ 1)
· (u
81
− 3u
80
+ ··· + 4942u − 1947)
27
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
6
(y −1)(y
6
− y
5
+ 2y
3
+ 1)(y
15
− 8y
14
+ ··· + 6y −1)
· (y
81
− 43y
80
+ ··· + 6y −1)
c
2
(y −1)(y
6
− y
5
+ 4y
4
− 2y
3
+ 1)(y
15
+ 16y
13
+ ··· + 2y −1)
· (y
81
+ y
80
+ ··· + 38y −1)
c
3
, c
9
((y −1)
7
)(y
15
− 15y
14
+ ··· + 11y −1)
· (y
81
− 57y
80
+ ··· + 1333584y −46656)
c
4
, c
7
(y −1)(y
6
− y
5
+ 4y
4
− 2y
3
+ 1)(y
15
− 11y
14
+ ··· + 15y −1)
· (y
81
− 50y
80
+ ··· − 1813y −6241)
c
5
(y −1)(y
6
+ 7y
5
+ ··· + 8y
2
+ 1)(y
15
+ 4y
14
+ ··· − 8y
2
− 1)
· (y
81
− 27y
80
+ ··· + 148198452y −3171961)
c
8
(y −1)(y
6
− y
5
+ 2y
3
+ 1)(y
15
− 4y
14
+ ··· + 4y −1)
· (y
81
− 7y
80
+ ··· + 9032y −121)
c
10
y(y
6
+ 6y
5
+ ··· − 4y + 9)(y
15
+ 8y
13
+ ··· − 4y −1)
· (y
81
− 3y
80
+ ··· + 232y −9)
c
11
y(y
6
+ 6y
5
+ ··· − 4y + 9)(y
15
+ 8y
14
+ ··· + 12y −1)
· (y
81
+ 41y
80
+ ··· + 38652040y −3790809)
28
