12a
0476
(K12a
0476
)
A knot diagram
1
Linearized knot diagam
3 6 11 9 7 2 10 12 5 1 4 8
Solving Sequence
2,6
3
7,10
8 1 11 5 9 4 12
c
2
c
6
c
7
c
1
c
10
c
5
c
9
c
4
c
12
c
3
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−443u
40
− 3423u
39
+ ··· + 4b + 532, −955u
40
− 7773u
39
+ ··· + 8a + 3572,
u
41
+ 9u
40
+ ··· − 12u − 8i
I
u
2
= h1.43701 × 10
23
a
5
u
10
− 4.78586 × 10
23
a
4
u
10
+ ··· + 3.13902 × 10
22
a + 7.88174 × 10
22
,
− u
10
a
5
+ 3u
10
a
4
+ ··· + 13a + 49, u
11
− u
10
+ 2u
9
− u
8
+ 4u
7
− 2u
6
+ 4u
5
− u
4
+ 3u
3
+ u
2
+ 1i
I
u
3
= hu
26
+ 3u
24
+ ··· + b + 3, −u
26
+ 4u
25
+ ··· + a + 5, u
27
− 2u
26
+ ··· − 2u + 1i
* 3 irreducible components of dim
C
= 0, with total 134 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−443u
40
− 3423u
39
+ · · · + 4b + 532, −955u
40
− 7773u
39
+ · · · +
8a + 3572, u
41
+ 9u
40
+ · · · − 12u − 8i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
−u
2
a
7
=
u
u
a
10
=
119.375u
40
+ 971.625u
39
+ ··· − 884.750u − 446.500
443
4
u
40
+
3423
4
u
39
+ ··· − 708u − 133
a
8
=
−
327
8
u
40
−
2569
8
u
39
+ ··· +
1063
4
u + 107
−
121
4
u
40
−
863
4
u
39
+ ··· +
301
2
u − 47
a
1
=
u
2
+ 1
−u
4
a
11
=
40.1250u
40
+ 295.375u
39
+ ··· − 200.750u + 4.50000
79
4
u
40
+
479
4
u
39
+ ··· − 44u + 91
a
5
=
u
3
u
3
+ u
a
9
=
−3.62500u
40
− 21.3750u
39
+ ··· − 28.7500u + 17.5000
31
4
u
40
+
403
4
u
39
+ ··· − 158u − 163
a
4
=
9
8
u
40
−
57
8
u
39
+ ··· +
119
4
u + 92
−
75
4
u
40
−
669
4
u
39
+ ··· +
343
2
u + 159
a
12
=
−
473
8
u
40
−
3849
8
u
39
+ ··· +
915
2
u + 210
−46u
40
−
689
2
u
39
+ ··· +
575
2
u − 33
(ii) Obstruction class = −1
(iii) Cusp Shapes = 83u
40
+ 505u
39
+ ··· − 222u + 694
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
41
+ 13u
40
+ ··· − 432u − 64
c
2
, c
6
u
41
− 9u
40
+ ··· − 12u + 8
c
3
, c
4
, c
9
c
11
u
41
− u
40
+ ··· + 3u − 1
c
7
, c
10
u
41
+ 3u
40
+ ··· + 19u − 1
c
8
, c
12
u
41
+ 25u
40
+ ··· + 33792u + 2048
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
41
+ 33y
40
+ ··· − 307968y −4096
c
2
, c
6
y
41
+ 13y
40
+ ··· − 432y −64
c
3
, c
4
, c
9
c
11
y
41
− 41y
40
+ ··· + 5y −1
c
7
, c
10
y
41
− 25y
40
+ ··· + 113y −1
c
8
, c
12
y
41
+ 21y
40
+ ··· − 7340032y −4194304
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.606113 + 0.756260I
a = −0.527663 − 0.015390I
b = 0.186140 + 0.888970I
0.717698 − 0.435826I 11.97986 + 0.51850I
u = 0.606113 − 0.756260I
a = −0.527663 + 0.015390I
b = 0.186140 − 0.888970I
0.717698 + 0.435826I 11.97986 − 0.51850I
u = 0.962360
a = 0.390155
b = −0.736806
6.45252 14.5170
u = 0.584526 + 0.924292I
a = 0.334306 − 0.254126I
b = −0.533512 − 0.651963I
0.13835 + 5.13576I 6.76047 − 9.10266I
u = 0.584526 − 0.924292I
a = 0.334306 + 0.254126I
b = −0.533512 + 0.651963I
0.13835 − 5.13576I 6.76047 + 9.10266I
u = 0.077637 + 0.881616I
a = −0.045402 + 0.792739I
b = 0.775920 + 0.596071I
−2.56291 − 0.61927I −2.95076 + 3.56360I
u = 0.077637 − 0.881616I
a = −0.045402 − 0.792739I
b = 0.775920 − 0.596071I
−2.56291 + 0.61927I −2.95076 − 3.56360I
u = 0.876297 + 0.081630I
a = −0.504344 + 0.274789I
b = 0.887621 − 0.336651I
11.79550 − 7.37660I 13.37512 + 4.29558I
u = 0.876297 − 0.081630I
a = −0.504344 − 0.274789I
b = 0.887621 + 0.336651I
11.79550 + 7.37660I 13.37512 − 4.29558I
u = −0.486503 + 1.048500I
a = 0.157122 + 0.344419I
b = 0.221731 + 0.460231I
−0.68738 − 3.21872I 3.38786 − 5.31152I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.486503 − 1.048500I
a = 0.157122 − 0.344419I
b = 0.221731 − 0.460231I
−0.68738 + 3.21872I 3.38786 + 5.31152I
u = −0.749895 + 0.884257I
a = −1.04074 + 1.36900I
b = −1.61398 + 0.86725I
1.90930 − 2.84587I 2.86961 + 2.56736I
u = −0.749895 − 0.884257I
a = −1.04074 − 1.36900I
b = −1.61398 − 0.86725I
1.90930 + 2.84587I 2.86961 − 2.56736I
u = −0.794876 + 0.853954I
a = 1.81971 − 1.24727I
b = 2.25186 − 0.19647I
5.04339 + 0.55023I 7.93602 + 0.I
u = −0.794876 − 0.853954I
a = 1.81971 + 1.24727I
b = 2.25186 + 0.19647I
5.04339 − 0.55023I 7.93602 + 0.I
u = 0.208095 + 0.797419I
a = 0.076078 − 1.156830I
b = −1.277150 − 0.530691I
−0.86671 + 3.40698I −1.098484 + 0.234882I
u = 0.208095 − 0.797419I
a = 0.076078 + 1.156830I
b = −1.277150 + 0.530691I
−0.86671 − 3.40698I −1.098484 − 0.234882I
u = 0.360854 + 1.123230I
a = 0.328858 + 0.508397I
b = 1.236590 − 0.244211I
8.2770 + 11.6296I 7.90682 − 8.06324I
u = 0.360854 − 1.123230I
a = 0.328858 − 0.508397I
b = 1.236590 + 0.244211I
8.2770 − 11.6296I 7.90682 + 8.06324I
u = −0.963483 + 0.716288I
a = −0.336502 + 1.249250I
b = −1.013960 + 0.461474I
15.6786 − 2.9261I 14.2037 + 0.I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.963483 − 0.716288I
a = −0.336502 − 1.249250I
b = −1.013960 − 0.461474I
15.6786 + 2.9261I 14.2037 + 0.I
u = −0.923712 + 0.770216I
a = −1.41293 + 1.56615I
b = −1.95999 + 0.11724I
16.9602 + 10.9665I 12.30775 + 0.I
u = −0.923712 − 0.770216I
a = −1.41293 − 1.56615I
b = −1.95999 − 0.11724I
16.9602 − 10.9665I 12.30775 + 0.I
u = −0.780698 + 0.917269I
a = 0.98640 − 2.09195I
b = 2.07607 − 1.61034I
4.85004 − 6.47232I 0
u = −0.780698 − 0.917269I
a = 0.98640 + 2.09195I
b = 2.07607 + 1.61034I
4.85004 + 6.47232I 0
u = −0.953490 + 0.768002I
a = 1.00353 − 1.19789I
b = 1.47081 − 0.06065I
11.51350 + 4.53379I 0
u = −0.953490 − 0.768002I
a = 1.00353 + 1.19789I
b = 1.47081 + 0.06065I
11.51350 − 4.53379I 0
u = 0.228894 + 1.203420I
a = 0.445857 − 0.052905I
b = 0.427477 − 0.843919I
7.31681 − 3.62360I 10.12001 + 0.I
u = 0.228894 − 1.203420I
a = 0.445857 + 0.052905I
b = 0.427477 + 0.843919I
7.31681 + 3.62360I 10.12001 + 0.I
u = 0.361149 + 1.229680I
a = −0.269691 − 0.198156I
b = −0.694901 + 0.368948I
2.26659 + 4.57991I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.361149 − 1.229680I
a = −0.269691 + 0.198156I
b = −0.694901 − 0.368948I
2.26659 − 4.57991I 0
u = −0.496085 + 0.512183I
a = −0.677720 − 0.317935I
b = −0.348482 − 0.160165I
0.953433 − 0.876985I 9.19532 + 5.58347I
u = −0.496085 − 0.512183I
a = −0.677720 + 0.317935I
b = −0.348482 + 0.160165I
0.953433 + 0.876985I 9.19532 − 5.58347I
u = −0.810078 + 1.026960I
a = −1.29862 + 1.73461I
b = −2.67410 + 1.26920I
16.1484 − 17.3579I 0
u = −0.810078 − 1.026960I
a = −1.29862 − 1.73461I
b = −2.67410 − 1.26920I
16.1484 + 17.3579I 0
u = −0.823771 + 1.041760I
a = 0.95542 − 1.31971I
b = 2.06585 − 0.97932I
10.6436 − 11.0550I 0
u = −0.823771 − 1.041760I
a = 0.95542 + 1.31971I
b = 2.06585 + 0.97932I
10.6436 + 11.0550I 0
u = −0.805127 + 1.075830I
a = −1.014220 + 0.638818I
b = −1.75240 + 0.17374I
14.5492 − 3.5634I 0
u = −0.805127 − 1.075830I
a = −1.014220 − 0.638818I
b = −1.75240 − 0.17374I
14.5492 + 3.5634I 0
u = 0.302974 + 0.280498I
a = −0.424526 − 1.104140I
b = −0.363190 + 0.540241I
0.434000 − 1.344580I 4.71332 + 6.21686I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.302974 − 0.280498I
a = −0.424526 + 1.104140I
b = −0.363190 − 0.540241I
0.434000 + 1.344580I 4.71332 − 6.21686I
9
II. I
u
2
= h1.44 × 10
23
a
5
u
10
− 4.79 × 10
23
a
4
u
10
+ · · · + 3.14 × 10
22
a + 7.88 ×
10
22
, −u
10
a
5
+ 3u
10
a
4
+ · · · + 13a + 49, u
11
− u
10
+ · · · + u
2
+ 1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
−u
2
a
7
=
u
u
a
10
=
a
−0.401186a
5
u
10
+ 1.33612a
4
u
10
+ ··· − 0.0876356a − 0.220044
a
8
=
0.0710547a
5
u
10
+ 0.110918a
4
u
10
+ ··· − 0.483397a − 0.680125
−0.248190a
5
u
10
− 0.454501a
4
u
10
+ ··· + 0.984937a − 1.42088
a
1
=
u
2
+ 1
−u
4
a
11
=
−0.0141422a
5
u
10
− 0.246441a
4
u
10
+ ··· + 0.395981a − 0.0603578
0.105676a
5
u
10
+ 0.632640a
4
u
10
+ ··· + 0.257556a − 0.277155
a
5
=
u
3
u
3
+ u
a
9
=
1.72153a
5
u
10
+ 0.258802a
4
u
10
+ ··· + 1.44074a + 0.338467
0.105676a
5
u
10
+ 0.632640a
4
u
10
+ ··· + 0.257556a − 0.277155
a
4
=
0.0116912a
5
u
10
+ 0.202243a
4
u
10
+ ··· − 0.128390a + 0.338516
−0.0619103a
5
u
10
− 0.143534a
4
u
10
+ ··· − 0.866368a − 2.40128
a
12
=
0.450643a
5
u
10
+ 0.304819a
4
u
10
+ ··· + 2.01360a + 0.991347
−1.27156a
5
u
10
− 0.954263a
4
u
10
+ ··· + 0.757959a − 0.138853
(ii) Obstruction class = −1
(iii) Cusp Shapes =
1329200708568567847978968
358189792138919448707665
u
10
a
5
−
332490141090957910117688
71637958427783889741533
u
10
a
4
+
··· −
35259769041152257798896
358189792138919448707665
a +
1455974136897432947715906
358189792138919448707665
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
(u
11
+ 3u
10
+ ··· − 2u − 1)
6
c
2
, c
6
(u
11
+ u
10
+ 2u
9
+ u
8
+ 4u
7
+ 2u
6
+ 4u
5
+ u
4
+ 3u
3
− u
2
− 1)
6
c
3
, c
4
, c
9
c
11
u
66
− u
65
+ ··· − 19674u − 2411
c
7
, c
10
u
66
+ 13u
65
+ ··· − 4806258u − 401201
c
8
, c
12
(u
3
− u
2
+ 2u − 1)
22
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
(y
11
+ 11y
10
+ ··· + 6y −1)
6
c
2
, c
6
(y
11
+ 3y
10
+ ··· − 2y −1)
6
c
3
, c
4
, c
9
c
11
y
66
− 65y
65
+ ··· − 282043116y + 5812921
c
7
, c
10
y
66
− 29y
65
+ ··· − 4863460315404y + 160962242401
c
8
, c
12
(y
3
+ 3y
2
+ 2y −1)
22
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.274458 + 0.988557I
a = −0.895560 − 0.460248I
b = −0.83945 − 1.25577I
2.77731 − 0.11860I 5.71039 + 1.13842I
u = −0.274458 + 0.988557I
a = −0.146248 + 0.764571I
b = −0.599739 + 0.470580I
−1.36027 − 2.94672I −0.81888 + 4.11787I
u = −0.274458 + 0.988557I
a = 0.678240 − 1.161140I
b = 1.64509 − 0.59363I
2.77731 − 5.77484I 5.71039 + 7.09731I
u = −0.274458 + 0.988557I
a = 0.259736 − 0.356850I
b = −0.272876 + 0.578085I
2.77731 − 0.11860I 5.71039 + 1.13842I
u = −0.274458 + 0.988557I
a = 0.024785 + 0.401085I
b = −1.156990 − 0.613966I
2.77731 − 5.77484I 5.71039 + 7.09731I
u = −0.274458 + 0.988557I
a = 0.117340 − 0.086144I
b = 0.868259 + 0.340394I
−1.36027 − 2.94672I −0.81888 + 4.11787I
u = −0.274458 − 0.988557I
a = −0.895560 + 0.460248I
b = −0.83945 + 1.25577I
2.77731 + 0.11860I 5.71039 − 1.13842I
u = −0.274458 − 0.988557I
a = −0.146248 − 0.764571I
b = −0.599739 − 0.470580I
−1.36027 + 2.94672I −0.81888 − 4.11787I
u = −0.274458 − 0.988557I
a = 0.678240 + 1.161140I
b = 1.64509 + 0.59363I
2.77731 + 5.77484I 5.71039 − 7.09731I
u = −0.274458 − 0.988557I
a = 0.259736 + 0.356850I
b = −0.272876 − 0.578085I
2.77731 + 0.11860I 5.71039 − 1.13842I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.274458 − 0.988557I
a = 0.024785 − 0.401085I
b = −1.156990 + 0.613966I
2.77731 + 5.77484I 5.71039 − 7.09731I
u = −0.274458 − 0.988557I
a = 0.117340 + 0.086144I
b = 0.868259 − 0.340394I
−1.36027 + 2.94672I −0.81888 − 4.11787I
u = 0.838197 + 0.796762I
a = 1.00980 + 1.31331I
b = 1.56438 + 0.76313I
5.79840 − 1.41699I 5.77180 + 0.63373I
u = 0.838197 + 0.796762I
a = 0.34070 + 1.68447I
b = 0.787356 + 0.848265I
9.93598 + 1.41114I 12.30106 − 2.34572I
u = 0.838197 + 0.796762I
a = 0.05773 − 1.74594I
b = −1.27939 − 1.64219I
9.93598 + 1.41114I 12.30106 − 2.34572I
u = 0.838197 + 0.796762I
a = −1.23511 − 1.45168I
b = −1.65534 − 0.15732I
5.79840 − 1.41699I 5.77180 + 0.63373I
u = 0.838197 + 0.796762I
a = −1.73932 − 1.61488I
b = −2.01014 − 0.72785I
9.93598 − 4.24511I 12.30106 + 3.61318I
u = 0.838197 + 0.796762I
a = 1.86467 + 1.99803I
b = 2.71365 + 0.11345I
9.93598 − 4.24511I 12.30106 + 3.61318I
u = 0.838197 − 0.796762I
a = 1.00980 − 1.31331I
b = 1.56438 − 0.76313I
5.79840 + 1.41699I 5.77180 − 0.63373I
u = 0.838197 − 0.796762I
a = 0.34070 − 1.68447I
b = 0.787356 − 0.848265I
9.93598 − 1.41114I 12.30106 + 2.34572I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.838197 − 0.796762I
a = 0.05773 + 1.74594I
b = −1.27939 + 1.64219I
9.93598 − 1.41114I 12.30106 + 2.34572I
u = 0.838197 − 0.796762I
a = −1.23511 + 1.45168I
b = −1.65534 + 0.15732I
5.79840 + 1.41699I 5.77180 − 0.63373I
u = 0.838197 − 0.796762I
a = −1.73932 + 1.61488I
b = −2.01014 + 0.72785I
9.93598 + 4.24511I 12.30106 − 3.61318I
u = 0.838197 − 0.796762I
a = 1.86467 − 1.99803I
b = 2.71365 − 0.11345I
9.93598 + 4.24511I 12.30106 − 3.61318I
u = −0.813506 + 0.895281I
a = 0.651657 − 1.181340I
b = 1.93659 − 1.29451I
9.46395 − 3.04152I 9.04170 + 2.82242I
u = −0.813506 + 0.895281I
a = 1.34111 − 1.07926I
b = 1.231990 + 0.258257I
9.46395 − 3.04152I 9.04170 + 2.82242I
u = −0.813506 + 0.895281I
a = −1.86040 + 0.27694I
b = −2.50476 + 0.04665I
13.6015 − 5.8696I 15.5710 + 5.8019I
u = −0.813506 + 0.895281I
a = −0.41937 + 2.12452I
b = −0.67097 + 1.39619I
13.60150 − 0.21340I 15.5710 − 0.1570I
u = −0.813506 + 0.895281I
a = 0.33366 + 2.46944I
b = −1.98956 + 2.93484I
13.60150 − 0.21340I 15.5710 − 0.1570I
u = −0.813506 + 0.895281I
a = −2.68652 + 0.38435I
b = −2.20077 − 1.96869I
13.6015 − 5.8696I 15.5710 + 5.8019I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.813506 − 0.895281I
a = 0.651657 + 1.181340I
b = 1.93659 + 1.29451I
9.46395 + 3.04152I 9.04170 − 2.82242I
u = −0.813506 − 0.895281I
a = 1.34111 + 1.07926I
b = 1.231990 − 0.258257I
9.46395 + 3.04152I 9.04170 − 2.82242I
u = −0.813506 − 0.895281I
a = −1.86040 − 0.27694I
b = −2.50476 − 0.04665I
13.6015 + 5.8696I 15.5710 − 5.8019I
u = −0.813506 − 0.895281I
a = −0.41937 − 2.12452I
b = −0.67097 − 1.39619I
13.60150 + 0.21340I 15.5710 + 0.1570I
u = −0.813506 − 0.895281I
a = 0.33366 − 2.46944I
b = −1.98956 − 2.93484I
13.60150 + 0.21340I 15.5710 + 0.1570I
u = −0.813506 − 0.895281I
a = −2.68652 − 0.38435I
b = −2.20077 + 1.96869I
13.6015 + 5.8696I 15.5710 − 5.8019I
u = 0.783273 + 0.973706I
a = 1.326350 + 0.471754I
b = 2.04475 + 0.11364I
9.39071 + 4.64712I 11.28067 − 2.57516I
u = 0.783273 + 0.973706I
a = −1.67600 − 0.44303I
b = −1.81609 + 0.74728I
9.39071 + 4.64712I 11.28067 − 2.57516I
u = 0.783273 + 0.973706I
a = 1.18679 + 1.33645I
b = 1.77804 + 0.80841I
5.25313 + 7.47524I 4.75140 − 5.55460I
u = 0.783273 + 0.973706I
a = −1.02416 − 1.49922I
b = −2.25779 − 1.14181I
5.25313 + 7.47524I 4.75140 − 5.55460I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.783273 + 0.973706I
a = −1.45989 − 1.93026I
b = −2.33404 − 1.59863I
9.39071 + 10.30340I 11.2807 − 8.5341I
u = 0.783273 + 0.973706I
a = 1.43147 + 2.27994I
b = 3.22065 + 1.51278I
9.39071 + 10.30340I 11.2807 − 8.5341I
u = 0.783273 − 0.973706I
a = 1.326350 − 0.471754I
b = 2.04475 − 0.11364I
9.39071 − 4.64712I 11.28067 + 2.57516I
u = 0.783273 − 0.973706I
a = −1.67600 + 0.44303I
b = −1.81609 − 0.74728I
9.39071 − 4.64712I 11.28067 + 2.57516I
u = 0.783273 − 0.973706I
a = 1.18679 − 1.33645I
b = 1.77804 − 0.80841I
5.25313 − 7.47524I 4.75140 + 5.55460I
u = 0.783273 − 0.973706I
a = −1.02416 + 1.49922I
b = −2.25779 + 1.14181I
5.25313 − 7.47524I 4.75140 + 5.55460I
u = 0.783273 − 0.973706I
a = −1.45989 + 1.93026I
b = −2.33404 + 1.59863I
9.39071 − 10.30340I 11.2807 + 8.5341I
u = 0.783273 − 0.973706I
a = 1.43147 − 2.27994I
b = 3.22065 − 1.51278I
9.39071 − 10.30340I 11.2807 + 8.5341I
u = 0.267638 + 0.666716I
a = −0.623262 + 0.912471I
b = −1.52756 + 1.18198I
3.51662 + 1.13130I 4.96829 − 6.05785I
u = 0.267638 + 0.666716I
a = −0.668528 − 0.888572I
b = 1.61019 − 0.86088I
7.65420 − 1.69682I 11.49756 − 3.07840I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.267638 + 0.666716I
a = 0.04045 − 2.41478I
b = −0.071526 − 0.743532I
3.51662 + 1.13130I 4.96829 − 6.05785I
u = 0.267638 + 0.666716I
a = 2.08007 − 1.28478I
b = 1.93317 − 1.93185I
7.65420 + 3.95942I 11.4976 − 9.0373I
u = 0.267638 + 0.666716I
a = 0.07973 + 2.45592I
b = −0.507096 − 0.155654I
7.65420 + 3.95942I 11.4976 − 9.0373I
u = 0.267638 + 0.666716I
a = −0.13641 + 3.20987I
b = 0.68116 + 1.92911I
7.65420 − 1.69682I 11.49756 − 3.07840I
u = 0.267638 − 0.666716I
a = −0.623262 − 0.912471I
b = −1.52756 − 1.18198I
3.51662 − 1.13130I 4.96829 + 6.05785I
u = 0.267638 − 0.666716I
a = −0.668528 + 0.888572I
b = 1.61019 + 0.86088I
7.65420 + 1.69682I 11.49756 + 3.07840I
u = 0.267638 − 0.666716I
a = 0.04045 + 2.41478I
b = −0.071526 + 0.743532I
3.51662 − 1.13130I 4.96829 + 6.05785I
u = 0.267638 − 0.666716I
a = 2.08007 + 1.28478I
b = 1.93317 + 1.93185I
7.65420 − 3.95942I 11.4976 + 9.0373I
u = 0.267638 − 0.666716I
a = 0.07973 − 2.45592I
b = −0.507096 + 0.155654I
7.65420 − 3.95942I 11.4976 + 9.0373I
u = 0.267638 − 0.666716I
a = −0.13641 − 3.20987I
b = 0.68116 − 1.92911I
7.65420 + 1.69682I 11.49756 + 3.07840I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.602288
a = −0.203632 + 1.035930I
b = 0.985506 − 0.329928I
5.76356 − 2.82812I 11.88601 + 2.97945I
u = −0.602288
a = −0.203632 − 1.035930I
b = 0.985506 + 0.329928I
5.76356 + 2.82812I 11.88601 − 2.97945I
u = −0.602288
a = −1.09575
b = 0.378653
1.62597 5.35670
u = −0.602288
a = 1.51363 + 0.07613I
b = −0.671714 + 0.596308I
5.76356 − 2.82812I 11.88601 + 2.97945I
u = −0.602288
a = 1.51363 − 0.07613I
b = −0.671714 − 0.596308I
5.76356 + 2.82812I 11.88601 − 2.97945I
u = −0.602288
a = −0.0312656
b = −0.648614
1.62597 5.35670
19
III.
I
u
3
= hu
26
+3u
24
+· · ·+b+3, −u
26
+4u
25
+· · ·+a+5, u
27
−2u
26
+· · ·−2u+1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
−u
2
a
7
=
u
u
a
10
=
u
26
− 4u
25
+ ··· + 9u − 5
−u
26
− 3u
24
+ ··· + 2u − 3
a
8
=
−4u
26
+ 7u
25
+ ··· − 15u + 2
−2u
24
+ 2u
23
+ ··· − 7u + 3
a
1
=
u
2
+ 1
−u
4
a
11
=
u
26
− 4u
25
+ ··· + 9u − 6
−u
26
+ u
25
+ ··· − 3u
2
− 2
a
5
=
u
3
u
3
+ u
a
9
=
u
26
− 5u
25
+ ··· + 11u − 6
−u
26
− 4u
24
+ ··· − 5u
2
− 2
a
4
=
−3u
25
+ 6u
24
+ ··· + 15u − 7
−2u
26
+ 3u
25
+ ··· − u − 2
a
12
=
3u
26
− 2u
25
+ ··· − 4u + 7
3u
26
− 5u
25
+ ··· − 9u
2
+ 7u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −5u
26
+ 8u
25
− 28u
24
+ 32u
23
− 92u
22
+ 96u
21
− 220u
20
+
195u
19
− 398u
18
+ 309u
17
− 567u
16
+ 364u
15
− 635u
14
+ 328u
13
− 556u
12
+ 191u
11
−
353u
10
+ 38u
9
− 151u
8
− 44u
7
− 22u
6
− 61u
5
+ 18u
4
− 33u
3
+ 16u
2
− 8u + 11
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
27
− 10u
26
+ ··· − 10u + 1
c
2
u
27
− 2u
26
+ ··· − 2u + 1
c
3
, c
9
u
27
+ u
26
+ ··· − u − 1
c
4
, c
11
u
27
− u
26
+ ··· − u + 1
c
6
u
27
+ 2u
26
+ ··· − 2u − 1
c
7
, c
10
u
27
+ 3u
26
+ ··· + 9u + 1
c
8
u
27
+ 2u
26
+ ··· + 3u − 1
c
12
u
27
− 2u
26
+ ··· + 3u + 1
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
27
+ 22y
26
+ ··· − 6y −1
c
2
, c
6
y
27
+ 10y
26
+ ··· − 10y −1
c
3
, c
4
, c
9
c
11
y
27
− 31y
26
+ ··· + 25y −1
c
7
, c
10
y
27
− 7y
26
+ ··· + 17y −1
c
8
, c
12
y
27
+ 18y
26
+ ··· − 3y −1
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.098658 + 0.960080I
a = −0.689493 − 0.782416I
b = −0.093893 − 1.322120I
5.98500 − 2.27195I 5.47294 + 0.60584I
u = 0.098658 − 0.960080I
a = −0.689493 + 0.782416I
b = −0.093893 + 1.322120I
5.98500 + 2.27195I 5.47294 − 0.60584I
u = −0.371203 + 0.863799I
a = −0.127827 − 0.637731I
b = 0.929528 − 0.343631I
−0.32438 − 3.87037I 7.47138 + 7.61937I
u = −0.371203 − 0.863799I
a = −0.127827 + 0.637731I
b = 0.929528 + 0.343631I
−0.32438 + 3.87037I 7.47138 − 7.61937I
u = −0.475550 + 0.784868I
a = 0.543284 − 0.014973I
b = −0.023620 + 0.833245I
0.050415 + 0.292894I −0.32440 + 1.69769I
u = −0.475550 − 0.784868I
a = 0.543284 + 0.014973I
b = −0.023620 − 0.833245I
0.050415 − 0.292894I −0.32440 − 1.69769I
u = 0.763587 + 0.792484I
a = 0.20698 + 2.50246I
b = 1.21282 + 1.93690I
10.62880 − 1.45762I 13.10536 + 0.22687I
u = 0.763587 − 0.792484I
a = 0.20698 − 2.50246I
b = 1.21282 − 1.93690I
10.62880 + 1.45762I 13.10536 − 0.22687I
u = −0.403542 + 1.071660I
a = 0.152011 − 0.259503I
b = 0.591028 + 0.143334I
−0.51003 − 3.65390I 10.0399 + 10.0497I
u = −0.403542 − 1.071660I
a = 0.152011 + 0.259503I
b = 0.591028 − 0.143334I
−0.51003 + 3.65390I 10.0399 − 10.0497I
23
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.853885 + 0.812726I
a = −1.34378 − 1.57792I
b = −1.96292 − 0.46615I
7.38217 − 1.67242I 12.78278 + 1.33399I
u = 0.853885 − 0.812726I
a = −1.34378 + 1.57792I
b = −1.96292 + 0.46615I
7.38217 + 1.67242I 12.78278 − 1.33399I
u = −0.819337 + 0.863109I
a = −0.404025 + 0.055275I
b = 0.175393 − 0.961371I
12.22380 − 4.46615I 12.08548 + 2.98099I
u = −0.819337 − 0.863109I
a = −0.404025 − 0.055275I
b = 0.175393 + 0.961371I
12.22380 + 4.46615I 12.08548 − 2.98099I
u = 0.726432 + 0.962159I
a = 2.02402 + 0.40291I
b = 2.45152 − 0.42886I
10.09890 + 7.12276I 12.00767 − 6.24158I
u = 0.726432 − 0.962159I
a = 2.02402 − 0.40291I
b = 2.45152 + 0.42886I
10.09890 − 7.12276I 12.00767 + 6.24158I
u = 0.464339 + 1.114370I
a = −0.386128 + 0.482768I
b = −0.613914 + 0.688900I
1.74483 + 3.73772I 7.15988 − 1.11337I
u = 0.464339 − 1.114370I
a = −0.386128 − 0.482768I
b = −0.613914 − 0.688900I
1.74483 − 3.73772I 7.15988 + 1.11337I
u = −0.806430 + 0.927777I
a = 0.329921 + 0.150131I
b = −0.560569 + 0.710302I
12.02800 − 1.61473I 11.77298 + 2.04900I
u = −0.806430 − 0.927777I
a = 0.329921 − 0.150131I
b = −0.560569 − 0.710302I
12.02800 + 1.61473I 11.77298 − 2.04900I
24
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.798911 + 0.970282I
a = −1.28547 − 1.66984I
b = −2.38532 − 1.09469I
6.89307 + 7.82661I 11.65316 − 6.43233I
u = 0.798911 − 0.970282I
a = −1.28547 + 1.66984I
b = −2.38532 + 1.09469I
6.89307 − 7.82661I 11.65316 + 6.43233I
u = −0.681051
a = −0.614200
b = 0.703185
2.62920 15.1510
u = 0.078844 + 0.620759I
a = −0.42826 + 2.76821I
b = −1.64355 + 1.04383I
7.36770 + 3.04788I 7.32878 − 0.50531I
u = 0.078844 − 0.620759I
a = −0.42826 − 2.76821I
b = −1.64355 − 1.04383I
7.36770 − 3.04788I 7.32878 + 0.50531I
u = 0.431933 + 0.394463I
a = 1.21588 − 1.57109I
b = 0.571897 − 0.564666I
4.07392 + 0.22515I 11.36875 + 0.96100I
u = 0.431933 − 0.394463I
a = 1.21588 + 1.57109I
b = 0.571897 + 0.564666I
4.07392 − 0.22515I 11.36875 − 0.96100I
25
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
5
((u
11
+ 3u
10
+ ··· − 2u − 1)
6
)(u
27
− 10u
26
+ ··· − 10u + 1)
· (u
41
+ 13u
40
+ ··· − 432u − 64)
c
2
(u
11
+ u
10
+ 2u
9
+ u
8
+ 4u
7
+ 2u
6
+ 4u
5
+ u
4
+ 3u
3
− u
2
− 1)
6
· (u
27
− 2u
26
+ ··· − 2u + 1)(u
41
− 9u
40
+ ··· − 12u + 8)
c
3
, c
9
(u
27
+ u
26
+ ··· − u − 1)(u
41
− u
40
+ ··· + 3u − 1)
· (u
66
− u
65
+ ··· − 19674u − 2411)
c
4
, c
11
(u
27
− u
26
+ ··· − u + 1)(u
41
− u
40
+ ··· + 3u − 1)
· (u
66
− u
65
+ ··· − 19674u − 2411)
c
6
(u
11
+ u
10
+ 2u
9
+ u
8
+ 4u
7
+ 2u
6
+ 4u
5
+ u
4
+ 3u
3
− u
2
− 1)
6
· (u
27
+ 2u
26
+ ··· − 2u − 1)(u
41
− 9u
40
+ ··· − 12u + 8)
c
7
, c
10
(u
27
+ 3u
26
+ ··· + 9u + 1)(u
41
+ 3u
40
+ ··· + 19u − 1)
· (u
66
+ 13u
65
+ ··· − 4806258u − 401201)
c
8
((u
3
− u
2
+ 2u − 1)
22
)(u
27
+ 2u
26
+ ··· + 3u − 1)
· (u
41
+ 25u
40
+ ··· + 33792u + 2048)
c
12
((u
3
− u
2
+ 2u − 1)
22
)(u
27
− 2u
26
+ ··· + 3u + 1)
· (u
41
+ 25u
40
+ ··· + 33792u + 2048)
26
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
((y
11
+ 11y
10
+ ··· + 6y −1)
6
)(y
27
+ 22y
26
+ ··· − 6y −1)
· (y
41
+ 33y
40
+ ··· − 307968y −4096)
c
2
, c
6
((y
11
+ 3y
10
+ ··· − 2y −1)
6
)(y
27
+ 10y
26
+ ··· − 10y −1)
· (y
41
+ 13y
40
+ ··· − 432y −64)
c
3
, c
4
, c
9
c
11
(y
27
− 31y
26
+ ··· + 25y −1)(y
41
− 41y
40
+ ··· + 5y −1)
· (y
66
− 65y
65
+ ··· − 282043116y + 5812921)
c
7
, c
10
(y
27
− 7y
26
+ ··· + 17y −1)(y
41
− 25y
40
+ ··· + 113y −1)
· (y
66
− 29y
65
+ ··· − 4863460315404y + 160962242401)
c
8
, c
12
((y
3
+ 3y
2
+ 2y −1)
22
)(y
27
+ 18y
26
+ ··· − 3y −1)
· (y
41
+ 21y
40
+ ··· − 7340032y −4194304)
27
