12a
0438
(K12a
0438
)
A knot diagram
1
Linearized knot diagam
3 6 10 8 9 2 11 5 1 12 7 4
Solving Sequence
7,11
8
2,12
6 3 1 10 4 9 5
c
7
c
11
c
6
c
2
c
1
c
10
c
3
c
9
c
5
c
4
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= hb − u, −111497u
26
+ 189910u
25
+ ··· + 191887a − 257923, u
27
− u
26
+ ··· + 3u − 1i
I
u
2
= h−5.40927 × 10
221
u
103
− 1.66221 × 10
222
u
102
+ ··· + 5.33227 × 10
221
b − 3.81465 × 10
223
,
− 3.26612 × 10
223
u
103
− 1.05210 × 10
224
u
102
+ ··· + 6.45205 × 10
223
a − 7.33788 × 10
224
,
u
104
+ 2u
103
+ ··· − 17u + 121i
I
u
3
= hb + u, 2u
12
− 2u
11
+ 6u
10
− 5u
9
+ 12u
8
− 9u
7
+ 13u
6
− 8u
5
+ 8u
4
− 5u
3
− u
2
+ a + u − 1,
u
13
− u
12
+ 4u
11
− 3u
10
+ 9u
9
− 6u
8
+ 13u
7
− 7u
6
+ 12u
5
− 6u
4
+ 6u
3
− 3u
2
+ u − 1i
I
u
4
= h−u
13
+ u
12
− 4u
11
+ 3u
10
− 8u
9
+ 6u
8
− 10u
7
+ 7u
6
− 10u
5
+ 6u
4
− 8u
3
+ 3u
2
+ b − 4u + 1,
3u
12
− 3u
11
+ 10u
10
− 8u
9
+ 18u
8
− 15u
7
+ 19u
6
− 14u
5
+ 19u
4
− 10u
3
+ 12u
2
+ a − 5u + 4,
u
14
− u
13
+ 4u
12
− 3u
11
+ 8u
10
− 6u
9
+ 10u
8
− 7u
7
+ 10u
6
− 6u
5
+ 8u
4
− 3u
3
+ 4u
2
− u + 1i
* 4 irreducible components of dim
C
= 0, with total 158 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
= hb − u, −1.11 × 10
5
u
26
+ 1.90 × 10
5
u
25
+ · · · + 1.92 × 10
5
a − 2.58 ×
10
5
, u
27
− u
26
+ · · · + 3u − 1i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
u
a
8
=
1
−u
2
a
2
=
0.581056u
26
− 0.989697u
25
+ ··· + 1.16938u + 1.34414
u
a
12
=
u
u
a
6
=
−0.408642u
26
− 0.985012u
25
+ ··· − 0.399027u + 1.58106
u
2
a
3
=
−0.812598u
26
+ 0.389719u
25
+ ··· + 3.97636u + 0.935498
u
3
+ u
a
1
=
0.423645u
26
− 0.450249u
25
+ ··· + 1.62541u + 0.921261
u
5
+ u
3
+ u
a
10
=
u
3
u
3
+ u
a
4
=
−0.920328u
26
+ 0.782815u
25
+ ··· + 4.86559u + 0.300943
−1.12217u
26
+ 0.772976u
25
+ ··· + 2.73671u − 0.593714
a
9
=
−0.240814u
26
+ 0.615836u
25
+ ··· + 1.05933u − 1.48438
−0.245436u
26
+ 0.0573358u
25
+ ··· + 1.36645u − 0.289717
a
5
=
−0.462053u
26
+ 0.0205433u
25
+ ··· + 2.63666u + 1.03217
−0.245436u
26
+ 0.0573358u
25
+ ··· + 1.36645u − 0.289717
(ii) Obstruction class = −1
(iii) Cusp Shapes =
922784
191887
u
26
−
996775
191887
u
25
+ ··· −
2303468
191887
u +
1548666
191887
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
10
u
27
+ 13u
26
+ ··· + 3u − 1
c
2
, c
6
, c
7
c
11
u
27
− u
26
+ ··· + 3u − 1
c
3
u
27
− 22u
26
+ ··· + 24576u − 2560
c
4
, c
5
, c
8
u
27
+ 12u
26
+ ··· + 16u − 32
c
9
, c
12
u
27
− u
26
+ ··· − 3u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
y
27
+ 5y
26
+ ··· + 87y −1
c
2
, c
6
, c
7
c
11
y
27
+ 13y
26
+ ··· + 3y −1
c
3
y
27
− 6y
26
+ ··· − 262144y −6553600
c
4
, c
5
, c
8
y
27
− 24y
26
+ ··· + 12032y −1024
c
9
, c
12
y
27
+ 11y
26
+ ··· − 5y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.798209 + 0.530470I
a = 0.734106 + 0.052162I
b = −0.798209 + 0.530470I
4.09001 + 3.06443I 6.85135 − 1.90892I
u = −0.798209 − 0.530470I
a = 0.734106 − 0.052162I
b = −0.798209 − 0.530470I
4.09001 − 3.06443I 6.85135 + 1.90892I
u = −0.426161 + 0.952205I
a = 4.12175 + 1.75502I
b = −0.426161 + 0.952205I
−9.45283 − 3.29114I −3.58272 + 7.60756I
u = −0.426161 − 0.952205I
a = 4.12175 − 1.75502I
b = −0.426161 − 0.952205I
−9.45283 + 3.29114I −3.58272 − 7.60756I
u = 0.954879 + 0.448921I
a = −0.281262 + 0.163354I
b = 0.954879 + 0.448921I
−1.43373 − 6.86787I 2.22098 + 3.48109I
u = 0.954879 − 0.448921I
a = −0.281262 − 0.163354I
b = 0.954879 − 0.448921I
−1.43373 + 6.86787I 2.22098 − 3.48109I
u = 0.385727 + 1.023230I
a = −0.12490 + 3.10427I
b = 0.385727 + 1.023230I
−2.90362 + 4.50575I −7.37031 − 4.71426I
u = 0.385727 − 1.023230I
a = −0.12490 − 3.10427I
b = 0.385727 − 1.023230I
−2.90362 − 4.50575I −7.37031 + 4.71426I
u = −0.212212 + 1.078960I
a = 0.50612 + 2.28652I
b = −0.212212 + 1.078960I
−5.61409 − 0.39405I −7.57855 − 0.70200I
u = −0.212212 − 1.078960I
a = 0.50612 − 2.28652I
b = −0.212212 − 1.078960I
−5.61409 + 0.39405I −7.57855 + 0.70200I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.582844 + 0.672430I
a = −1.96986 − 0.14069I
b = 0.582844 + 0.672430I
2.10068 + 1.61837I 4.51956 − 4.09176I
u = 0.582844 − 0.672430I
a = −1.96986 + 0.14069I
b = 0.582844 − 0.672430I
2.10068 − 1.61837I 4.51956 + 4.09176I
u = 0.580393 + 1.018610I
a = −2.37719 + 1.54830I
b = 0.580393 + 1.018610I
−0.15243 + 7.74596I −1.13140 − 8.56215I
u = 0.580393 − 1.018610I
a = −2.37719 − 1.54830I
b = 0.580393 − 1.018610I
−0.15243 − 7.74596I −1.13140 + 8.56215I
u = 0.156183 + 1.196450I
a = −1.03361 + 2.66772I
b = 0.156183 + 1.196450I
−13.26850 − 1.40447I −9.24996 + 0.64080I
u = 0.156183 − 1.196450I
a = −1.03361 − 2.66772I
b = 0.156183 − 1.196450I
−13.26850 + 1.40447I −9.24996 − 0.64080I
u = −0.486526 + 1.105720I
a = 0.71115 + 2.96516I
b = −0.486526 + 1.105720I
−7.98758 − 9.88572I −5.51020 + 9.99998I
u = −0.486526 − 1.105720I
a = 0.71115 − 2.96516I
b = −0.486526 − 1.105720I
−7.98758 + 9.88572I −5.51020 − 9.99998I
u = −0.698815 + 0.260905I
a = −0.249931 + 0.254046I
b = −0.698815 + 0.260905I
−3.08031 + 1.04158I 0.697827 + 0.089058I
u = −0.698815 − 0.260905I
a = −0.249931 − 0.254046I
b = −0.698815 − 0.260905I
−3.08031 − 1.04158I 0.697827 − 0.089058I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.646787 + 1.102220I
a = 1.64707 + 1.85074I
b = −0.646787 + 1.102220I
0.59333 − 14.04150I 0.79014 + 10.59403I
u = −0.646787 − 1.102220I
a = 1.64707 − 1.85074I
b = −0.646787 − 1.102220I
0.59333 + 14.04150I 0.79014 − 10.59403I
u = 0.282967 + 0.645901I
a = 0.678786 + 0.641978I
b = 0.282967 + 0.645901I
−0.20845 + 1.57682I −2.21035 − 5.49069I
u = 0.282967 − 0.645901I
a = 0.678786 − 0.641978I
b = 0.282967 − 0.645901I
−0.20845 − 1.57682I −2.21035 + 5.49069I
u = 0.663935 + 1.182010I
a = −1.32463 + 2.15062I
b = 0.663935 + 1.182010I
−6.0186 + 18.7694I −2.19898 − 10.24193I
u = 0.663935 − 1.182010I
a = −1.32463 − 2.15062I
b = 0.663935 − 1.182010I
−6.0186 − 18.7694I −2.19898 + 10.24193I
u = 0.323566
a = 1.92480
b = 0.323566
1.13556 9.50520
7
II. I
u
2
= h−5.41 × 10
221
u
103
− 1.66 × 10
222
u
102
+ · · · + 5.33 × 10
221
b − 3.81 ×
10
223
, −3.27 × 10
223
u
103
− 1.05 × 10
224
u
102
+ · · · + 6.45 × 10
223
a − 7.34 ×
10
224
, u
104
+ 2u
103
+ · · · − 17u + 121i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
u
a
8
=
1
−u
2
a
2
=
0.506215u
103
+ 1.63064u
102
+ ··· + 29.3200u + 11.3730
1.01444u
103
+ 3.11726u
102
+ ··· + 221.790u + 71.5390
a
12
=
u
u
a
6
=
−1.01826u
103
− 1.89566u
102
+ ··· − 98.4955u + 153.705
−0.962126u
103
− 1.98060u
102
+ ··· − 150.377u + 97.0479
a
3
=
−0.104590u
103
− 0.264231u
102
+ ··· − 275.043u − 157.743
0.835266u
103
+ 1.18555u
102
+ ··· − 72.8082u − 246.443
a
1
=
−0.758472u
103
− 1.35795u
102
+ ··· − 193.645u + 109.101
0.136944u
103
+ 0.870777u
102
+ ··· − 101.859u + 34.2650
a
10
=
u
3
u
3
+ u
a
4
=
−0.0375614u
103
− 0.896782u
102
+ ··· − 369.104u − 256.644
1.79450u
103
+ 3.15476u
102
+ ··· − 75.5459u − 381.742
a
9
=
−0.129934u
103
− 0.0682942u
102
+ ··· + 180.501u + 129.995
0.351406u
103
+ 1.08238u
102
+ ··· + 73.6035u + 75.0223
a
5
=
−1.05156u
103
− 1.82989u
102
+ ··· − 284.135u + 25.6770
0.0400246u
103
− 0.880599u
102
+ ··· − 216.852u − 249.262
(ii) Obstruction class = −1
(iii) Cusp Shapes = 1.64573u
103
+ 4.55387u
102
+ ··· + 785.939u + 299.162
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
10
u
104
+ 46u
103
+ ··· + 249939u + 14641
c
2
, c
6
, c
7
c
11
u
104
+ 2u
103
+ ··· − 17u + 121
c
3
(u
52
+ 10u
51
+ ··· − 3u − 1)
2
c
4
, c
5
, c
8
(u
52
− 5u
51
+ ··· + 7u + 1)
2
c
9
, c
12
u
104
+ 13u
103
+ ··· + 3452u + 283
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
y
104
+ 34y
103
+ ··· + 3659910927y + 214358881
c
2
, c
6
, c
7
c
11
y
104
+ 46y
103
+ ··· + 249939y + 14641
c
3
(y
52
− 12y
51
+ ··· − 43y + 1)
2
c
4
, c
5
, c
8
(y
52
− 53y
51
+ ··· − 37y + 1)
2
c
9
, c
12
y
104
− 5y
103
+ ··· + 215340y + 80089
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.601006 + 0.783368I
a = 0.0584591 + 0.0734378I
b = 0.723694 + 1.004170I
1.55323 + 1.66347I 0
u = −0.601006 − 0.783368I
a = 0.0584591 − 0.0734378I
b = 0.723694 − 1.004170I
1.55323 − 1.66347I 0
u = −0.625964 + 0.763245I
a = 0.130359 − 0.723406I
b = 0.924850 + 0.421097I
3.26376 − 0.55062I 0
u = −0.625964 − 0.763245I
a = 0.130359 + 0.723406I
b = 0.924850 − 0.421097I
3.26376 + 0.55062I 0
u = 0.924850 + 0.421097I
a = 0.646631 + 0.302782I
b = −0.625964 + 0.763245I
3.26376 − 0.55062I 0
u = 0.924850 − 0.421097I
a = 0.646631 − 0.302782I
b = −0.625964 − 0.763245I
3.26376 + 0.55062I 0
u = 0.031250 + 0.980911I
a = −0.235677 + 0.376852I
b = −0.635597 + 0.291200I
−1.55506 + 2.06501I 0
u = 0.031250 − 0.980911I
a = −0.235677 − 0.376852I
b = −0.635597 − 0.291200I
−1.55506 − 2.06501I 0
u = −0.851961 + 0.480235I
a = 0.859609 − 0.480965I
b = −0.641480 − 1.066260I
2.47458 + 8.47773I 0
u = −0.851961 − 0.480235I
a = 0.859609 + 0.480965I
b = −0.641480 + 1.066260I
2.47458 − 8.47773I 0
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.029580 + 0.075923I
a = −0.916980 + 1.015670I
b = 0.480542 + 0.932970I
−1.46501 + 2.48222I 0
u = −1.029580 − 0.075923I
a = −0.916980 − 1.015670I
b = 0.480542 − 0.932970I
−1.46501 − 2.48222I 0
u = 0.295716 + 0.919872I
a = −0.32064 − 2.78318I
b = 0.487555 − 1.059280I
−2.18861 − 2.12521I 0
u = 0.295716 − 0.919872I
a = −0.32064 + 2.78318I
b = 0.487555 + 1.059280I
−2.18861 + 2.12521I 0
u = 0.425973 + 0.861359I
a = 0.528034 + 0.144800I
b = 0.441668 + 0.214876I
−0.11368 + 1.81640I 0
u = 0.425973 − 0.861359I
a = 0.528034 − 0.144800I
b = 0.441668 − 0.214876I
−0.11368 − 1.81640I 0
u = 0.480542 + 0.932970I
a = −0.566525 − 1.221080I
b = −1.029580 + 0.075923I
−1.46501 + 2.48222I 0
u = 0.480542 − 0.932970I
a = −0.566525 + 1.221080I
b = −1.029580 − 0.075923I
−1.46501 − 2.48222I 0
u = 0.429770 + 0.968741I
a = −1.21282 + 1.70756I
b = −0.546527 + 1.284080I
−5.52629 − 2.94682I 0
u = 0.429770 − 0.968741I
a = −1.21282 − 1.70756I
b = −0.546527 − 1.284080I
−5.52629 + 2.94682I 0
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.986696 + 0.396692I
a = −0.624859 − 0.884889I
b = 0.672647 − 1.153190I
−3.60087 − 12.79700I 0
u = 0.986696 − 0.396692I
a = −0.624859 + 0.884889I
b = 0.672647 + 1.153190I
−3.60087 + 12.79700I 0
u = −0.922258 + 0.122473I
a = −0.424499 + 0.044620I
b = 0.438182 − 0.776661I
−0.90908 − 1.34820I 0
u = −0.922258 − 0.122473I
a = −0.424499 − 0.044620I
b = 0.438182 + 0.776661I
−0.90908 + 1.34820I 0
u = 0.902428 + 0.580570I
a = 0.944671 − 0.522436I
b = −0.606198 − 0.907558I
2.81324 + 4.29790I 0
u = 0.902428 − 0.580570I
a = 0.944671 + 0.522436I
b = −0.606198 + 0.907558I
2.81324 − 4.29790I 0
u = 0.776726 + 0.758218I
a = −0.363743 − 0.173713I
b = −1.103830 + 0.728123I
−0.184790 − 0.909141I 0
u = 0.776726 − 0.758218I
a = −0.363743 + 0.173713I
b = −1.103830 − 0.728123I
−0.184790 + 0.909141I 0
u = −0.606198 + 0.907558I
a = −0.646877 − 0.841459I
b = 0.902428 − 0.580570I
2.81324 − 4.29790I 0
u = −0.606198 − 0.907558I
a = −0.646877 + 0.841459I
b = 0.902428 + 0.580570I
2.81324 + 4.29790I 0
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.499516 + 0.974559I
a = 1.75948 − 2.30223I
b = −0.64443 − 1.29302I
−5.06786 + 8.46879I 0
u = 0.499516 − 0.974559I
a = 1.75948 + 2.30223I
b = −0.64443 + 1.29302I
−5.06786 − 8.46879I 0
u = −0.633873 + 0.899833I
a = −1.40684 − 1.55880I
b = 0.710426 − 1.119870I
1.20873 − 6.54051I 0
u = −0.633873 − 0.899833I
a = −1.40684 + 1.55880I
b = 0.710426 + 1.119870I
1.20873 + 6.54051I 0
u = 0.438182 + 0.776661I
a = 0.303685 − 0.325708I
b = −0.922258 − 0.122473I
−0.90908 + 1.34820I 0
u = 0.438182 − 0.776661I
a = 0.303685 + 0.325708I
b = −0.922258 + 0.122473I
−0.90908 − 1.34820I 0
u = −0.354334 + 0.817967I
a = 1.38616 + 3.19989I
b = −0.354334 − 0.817967I
−8.87842 0
u = −0.354334 − 0.817967I
a = 1.38616 − 3.19989I
b = −0.354334 + 0.817967I
−8.87842 0
u = 0.785536 + 0.418604I
a = −0.544261 + 1.279960I
b = 0.008149 + 1.329420I
−8.10565 − 3.93282I 0
u = 0.785536 − 0.418604I
a = −0.544261 − 1.279960I
b = 0.008149 − 1.329420I
−8.10565 + 3.93282I 0
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.558791 + 0.968003I
a = −0.063595 + 1.107100I
b = 0.641644 − 0.575513I
1.18258 + 2.94175I 0
u = 0.558791 − 0.968003I
a = −0.063595 − 1.107100I
b = 0.641644 + 0.575513I
1.18258 − 2.94175I 0
u = −0.504260 + 1.007480I
a = −0.41215 − 2.73765I
b = −0.366905 − 1.121840I
−8.78594 − 2.32359I 0
u = −0.504260 − 1.007480I
a = −0.41215 + 2.73765I
b = −0.366905 + 1.121840I
−8.78594 + 2.32359I 0
u = 0.641644 + 0.575513I
a = −1.38782 + 0.37658I
b = 0.558791 − 0.968003I
1.18258 − 2.94175I 0
u = 0.641644 − 0.575513I
a = −1.38782 − 0.37658I
b = 0.558791 + 0.968003I
1.18258 + 2.94175I 0
u = 0.487555 + 1.059280I
a = 1.75487 − 1.51966I
b = 0.295716 − 0.919872I
−2.18861 + 2.12521I 0
u = 0.487555 − 1.059280I
a = 1.75487 + 1.51966I
b = 0.295716 + 0.919872I
−2.18861 − 2.12521I 0
u = −0.252289 + 1.144220I
a = −0.90905 + 1.41665I
b = −0.547375 + 0.522103I
−7.35313 − 1.89826I 0
u = −0.252289 − 1.144220I
a = −0.90905 − 1.41665I
b = −0.547375 − 0.522103I
−7.35313 + 1.89826I 0
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.442489 + 0.697558I
a = −0.0215440 + 0.0999968I
b = −0.673127 + 1.235190I
−4.12299 − 4.50302I 0
u = 0.442489 − 0.697558I
a = −0.0215440 − 0.0999968I
b = −0.673127 − 1.235190I
−4.12299 + 4.50302I 0
u = −0.366905 + 1.121840I
a = −1.55841 − 2.13414I
b = −0.504260 − 1.007480I
−8.78594 + 2.32359I 0
u = −0.366905 − 1.121840I
a = −1.55841 + 2.13414I
b = −0.504260 + 1.007480I
−8.78594 − 2.32359I 0
u = 0.037861 + 1.180360I
a = 0.16520 − 1.99220I
b = −0.536637 − 1.062390I
−3.63796 + 6.54304I 0
u = 0.037861 − 1.180360I
a = 0.16520 + 1.99220I
b = −0.536637 + 1.062390I
−3.63796 − 6.54304I 0
u = −0.536637 + 1.062390I
a = −0.98281 − 1.72288I
b = 0.037861 − 1.180360I
−3.63796 − 6.54304I 0
u = −0.536637 − 1.062390I
a = −0.98281 + 1.72288I
b = 0.037861 + 1.180360I
−3.63796 + 6.54304I 0
u = 0.724416 + 0.947735I
a = 0.52725 − 1.41910I
b = −1.058660 − 0.927148I
−0.76003 + 6.57704I 0
u = 0.724416 − 0.947735I
a = 0.52725 + 1.41910I
b = −1.058660 + 0.927148I
−0.76003 − 6.57704I 0
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.409809 + 1.125960I
a = 0.05894 + 1.41666I
b = −0.217013 + 0.721229I
−1.44654 + 2.79038I 0
u = 0.409809 − 1.125960I
a = 0.05894 − 1.41666I
b = −0.217013 − 0.721229I
−1.44654 − 2.79038I 0
u = −0.543575 + 1.094100I
a = −0.769980 + 0.146024I
b = −0.598812 − 0.128338I
−5.39609 − 5.71097I 0
u = −0.543575 − 1.094100I
a = −0.769980 − 0.146024I
b = −0.598812 + 0.128338I
−5.39609 + 5.71097I 0
u = 0.723694 + 1.004170I
a = −0.0426830 + 0.0615170I
b = −0.601006 + 0.783368I
1.55323 + 1.66347I 0
u = 0.723694 − 1.004170I
a = −0.0426830 − 0.0615170I
b = −0.601006 − 0.783368I
1.55323 − 1.66347I 0
u = −0.547375 + 0.522103I
a = 0.05604 + 2.60664I
b = −0.252289 + 1.144220I
−7.35313 − 1.89826I −3.11574 + 3.33363I
u = −0.547375 − 0.522103I
a = 0.05604 − 2.60664I
b = −0.252289 − 1.144220I
−7.35313 + 1.89826I −3.11574 − 3.33363I
u = −0.641480 + 1.066260I
a = −0.358729 + 0.686039I
b = −0.851961 − 0.480235I
2.47458 − 8.47773I 0
u = −0.641480 − 1.066260I
a = −0.358729 − 0.686039I
b = −0.851961 + 0.480235I
2.47458 + 8.47773I 0
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.217013 + 0.721229I
a = 1.42348 + 1.74983I
b = 0.409809 + 1.125960I
−1.44654 + 2.79038I −3.18108 − 7.81868I
u = −0.217013 − 0.721229I
a = 1.42348 − 1.74983I
b = 0.409809 − 1.125960I
−1.44654 − 2.79038I −3.18108 + 7.81868I
u = 0.269989 + 0.699887I
a = 0.79505 − 1.96652I
b = −0.531628 − 1.197670I
−4.54291 + 6.20206I −3.22343 − 7.94187I
u = 0.269989 − 0.699887I
a = 0.79505 + 1.96652I
b = −0.531628 + 1.197670I
−4.54291 − 6.20206I −3.22343 + 7.94187I
u = 0.617899 + 1.107080I
a = 1.03560 − 1.95299I
b = 0.079207 − 1.395880I
−10.12590 + 9.22402I 0
u = 0.617899 − 1.107080I
a = 1.03560 + 1.95299I
b = 0.079207 + 1.395880I
−10.12590 − 9.22402I 0
u = 0.223884 + 0.677776I
a = 1.02403 − 3.10009I
b = 0.223884 − 0.677776I
0.423251 −1.45472 + 0.I
u = 0.223884 − 0.677776I
a = 1.02403 + 3.10009I
b = 0.223884 + 0.677776I
0.423251 −1.45472 + 0.I
u = −0.635597 + 0.291200I
a = 0.359559 + 0.509922I
b = 0.031250 + 0.980911I
−1.55506 + 2.06501I −1.16113 − 4.48303I
u = −0.635597 − 0.291200I
a = 0.359559 − 0.509922I
b = 0.031250 − 0.980911I
−1.55506 − 2.06501I −1.16113 + 4.48303I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.531628 + 1.197670I
a = −0.510395 − 1.101850I
b = 0.269989 − 0.699887I
−4.54291 − 6.20206I 0
u = −0.531628 − 1.197670I
a = −0.510395 + 1.101850I
b = 0.269989 + 0.699887I
−4.54291 + 6.20206I 0
u = −1.103830 + 0.728123I
a = −0.075822 + 0.322076I
b = 0.776726 + 0.758218I
−0.184790 − 0.909141I 0
u = −1.103830 − 0.728123I
a = −0.075822 − 0.322076I
b = 0.776726 − 0.758218I
−0.184790 + 0.909141I 0
u = 0.710426 + 1.119870I
a = 1.10367 − 1.34867I
b = −0.633873 − 0.899833I
1.20873 + 6.54051I 0
u = 0.710426 − 1.119870I
a = 1.10367 + 1.34867I
b = −0.633873 + 0.899833I
1.20873 − 6.54051I 0
u = 0.008149 + 1.329420I
a = 0.580472 + 0.728186I
b = 0.785536 + 0.418604I
−8.10565 − 3.93282I 0
u = 0.008149 − 1.329420I
a = 0.580472 − 0.728186I
b = 0.785536 − 0.418604I
−8.10565 + 3.93282I 0
u = 0.672647 + 1.153190I
a = 0.625101 + 0.594864I
b = 0.986696 − 0.396692I
−3.60087 + 12.79700I 0
u = 0.672647 − 1.153190I
a = 0.625101 − 0.594864I
b = 0.986696 + 0.396692I
−3.60087 − 12.79700I 0
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.598812 + 0.128338I
a = −0.09774 − 1.56034I
b = −0.543575 − 1.094100I
−5.39609 + 5.71097I −1.75805 − 4.99375I
u = −0.598812 − 0.128338I
a = −0.09774 + 1.56034I
b = −0.543575 + 1.094100I
−5.39609 − 5.71097I −1.75805 + 4.99375I
u = −0.546527 + 1.284080I
a = 0.31967 + 1.55809I
b = 0.429770 + 0.968741I
−5.52629 − 2.94682I 0
u = −0.546527 − 1.284080I
a = 0.31967 − 1.55809I
b = 0.429770 − 0.968741I
−5.52629 + 2.94682I 0
u = 0.079207 + 1.395880I
a = 0.15657 − 1.99846I
b = 0.617899 − 1.107080I
−10.12590 − 9.22402I 0
u = 0.079207 − 1.395880I
a = 0.15657 + 1.99846I
b = 0.617899 + 1.107080I
−10.12590 + 9.22402I 0
u = −0.673127 + 1.235190I
a = 0.0452102 + 0.0395523I
b = 0.442489 + 0.697558I
−4.12299 − 4.50302I 0
u = −0.673127 − 1.235190I
a = 0.0452102 − 0.0395523I
b = 0.442489 − 0.697558I
−4.12299 + 4.50302I 0
u = −1.058660 + 0.927148I
a = −0.675806 − 1.090900I
b = 0.724416 − 0.947735I
−0.76003 − 6.57704I 0
u = −1.058660 − 0.927148I
a = −0.675806 + 1.090900I
b = 0.724416 + 0.947735I
−0.76003 + 6.57704I 0
20
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.64443 + 1.29302I
a = −1.31394 − 1.76007I
b = 0.499516 − 0.974559I
−5.06786 − 8.46879I 0
u = −0.64443 − 1.29302I
a = −1.31394 + 1.76007I
b = 0.499516 + 0.974559I
−5.06786 + 8.46879I 0
u = 0.441668 + 0.214876I
a = 0.643509 + 0.856375I
b = 0.425973 + 0.861359I
−0.11368 + 1.81640I 0.19208 − 3.30081I
u = 0.441668 − 0.214876I
a = 0.643509 − 0.856375I
b = 0.425973 − 0.861359I
−0.11368 − 1.81640I 0.19208 + 3.30081I
21
III. I
u
3
= hb + u, 2u
12
− 2u
11
+ · · · + a − 1, u
13
− u
12
+ · · · + u − 1i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
u
a
8
=
1
−u
2
a
2
=
−2u
12
+ 2u
11
+ ··· − u + 1
−u
a
12
=
u
u
a
6
=
−2u
11
+ u
10
+ ··· − 3u + 3
u
2
a
3
=
u
11
+ 2u
9
+ u
8
+ 3u
7
+ 3u
6
+ u
5
+ 5u
4
− 2u
3
+ 4u
2
− 4u + 1
−u
3
− u
a
1
=
−u
12
− 2u
10
− u
9
− 3u
8
− 3u
7
− u
6
− 6u
5
+ 2u
4
− 5u
3
+ 5u
2
− 2u + 2
−u
5
− u
3
− u
a
10
=
u
3
u
3
+ u
a
4
=
u
10
− 2u
9
+ 4u
8
− 5u
7
+ 8u
6
− 9u
5
+ 10u
4
− 9u
3
+ 7u
2
− 5u + 2
−u
9
+ u
8
− 3u
7
+ 2u
6
− 5u
5
+ 3u
4
− 6u
3
+ 2u
2
− 3u + 1
a
9
=
u
11
− u
10
+ 4u
9
− 3u
8
+ 9u
7
− 6u
6
+ 12u
5
− 7u
4
+ 11u
3
− 6u
2
+ 3u − 3
u
12
− u
11
+ 3u
10
− 2u
9
+ 6u
8
− 3u
7
+ 7u
6
− 2u
5
+ 5u
4
+ u
2
+ u
a
5
=
−u
12
+ 2u
11
+ ··· − 2u + 1
−u
12
+ u
11
− 3u
10
+ 2u
9
− 6u
8
+ 3u
7
− 7u
6
+ 2u
5
− 5u
4
− u
2
− u
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −6u
12
+8u
11
−21u
10
+21u
9
−42u
8
+42u
7
−55u
6
+47u
5
−41u
4
+41u
3
−18u
2
+14u −4
22
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
10
u
13
− 7u
12
+ ··· − 5u + 1
c
2
, c
7
u
13
− u
12
+ ··· + u − 1
c
3
u
13
− 5u
12
+ ··· − u − 1
c
4
, c
5
u
13
+ u
12
+ ··· − u − 1
c
6
, c
11
u
13
+ u
12
+ ··· + u + 1
c
8
u
13
− u
12
+ ··· − u + 1
c
9
, c
12
u
13
− u
12
+ ··· − u + 1
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
y
13
+ 7y
12
+ ··· + 7y −1
c
2
, c
6
, c
7
c
11
y
13
+ 7y
12
+ ··· − 5y −1
c
3
y
13
− 5y
12
+ ··· + 7y −1
c
4
, c
5
, c
8
y
13
− 15y
12
+ ··· + 7y −1
c
9
, c
12
y
13
+ y
12
+ ··· − y −1
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.253183 + 0.920765I
a = −2.52282 − 0.15008I
b = −0.253183 − 0.920765I
−9.61431 + 2.16485I −6.94667 − 1.68072I
u = 0.253183 − 0.920765I
a = −2.52282 + 0.15008I
b = −0.253183 + 0.920765I
−9.61431 − 2.16485I −6.94667 + 1.68072I
u = −0.385741 + 1.009650I
a = −0.05256 − 2.10788I
b = 0.385741 − 1.009650I
−2.05382 − 5.10474I 1.17110 + 8.30767I
u = −0.385741 − 1.009650I
a = −0.05256 + 2.10788I
b = 0.385741 + 1.009650I
−2.05382 + 5.10474I 1.17110 − 8.30767I
u = −0.704865 + 0.948521I
a = −1.23793 − 1.24160I
b = 0.704865 − 0.948521I
1.52123 − 5.50103I 5.31871 + 4.15235I
u = −0.704865 − 0.948521I
a = −1.23793 + 1.24160I
b = 0.704865 + 0.948521I
1.52123 + 5.50103I 5.31871 − 4.15235I
u = 0.451929 + 1.144740I
a = 1.05608 − 2.31391I
b = −0.451929 − 1.144740I
−6.73123 + 8.00105I −4.99764 − 6.83654I
u = 0.451929 − 1.144740I
a = 1.05608 + 2.31391I
b = −0.451929 + 1.144740I
−6.73123 − 8.00105I −4.99764 + 6.83654I
u = 0.848677 + 0.963431I
a = 0.61102 − 1.28409I
b = −0.848677 − 0.963431I
−1.55332 + 6.41919I −4.87371 − 5.93341I
u = 0.848677 − 0.963431I
a = 0.61102 + 1.28409I
b = −0.848677 + 0.963431I
−1.55332 − 6.41919I −4.87371 + 5.93341I
25
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.263568 + 0.615341I
a = 1.20381 − 2.39140I
b = 0.263568 − 0.615341I
0.672679 − 1.100140I 2.76274 + 4.26053I
u = −0.263568 − 0.615341I
a = 1.20381 + 2.39140I
b = 0.263568 + 0.615341I
0.672679 + 1.100140I 2.76274 − 4.26053I
u = 0.600770
a = 0.884799
b = −0.600770
−0.671001 3.13090
26
IV.
I
u
4
= h−u
13
+u
12
+· · · +b + 1, 3u
12
−3u
11
+· · · +a + 4, u
14
−u
13
+· · · −u + 1i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
u
a
8
=
1
−u
2
a
2
=
−3u
12
+ 3u
11
+ ··· + 5u − 4
u
13
− u
12
+ ··· + 4u − 1
a
12
=
u
u
a
6
=
−4u
13
+ 4u
12
+ ··· + 2u
2
− 4u
−u
13
− 3u
11
+ ··· − u − 3
a
3
=
u
12
− u
11
+ 3u
10
− u
9
+ 4u
8
− u
7
+ 3u
6
+ u
5
+ 2u
4
+ u
2
+ 3u
−2u
13
+ 3u
12
+ ··· − 3u + 3
a
1
=
−3u
13
− 9u
11
+ ··· − u
2
− 7u
u
13
− 4u
12
+ ··· + u − 5
a
10
=
u
3
u
3
+ u
a
4
=
u
12
+ 2u
10
+ 2u
9
+ 2u
8
+ 3u
7
+ 4u
5
+ 3u
3
+ 4u
−3u
13
+ 4u
12
+ ··· − 3u + 3
a
9
=
3u
12
− u
11
+ ··· + u + 3
−2u
13
+ 4u
12
+ ··· − 3u + 5
a
5
=
2u
13
− u
12
+ ··· + 6u − 2
−u
13
+ 3u
12
+ ··· − u + 3
(ii) Obstruction class = 1
(iii) Cusp Shapes
= 4u
13
−3u
12
+17u
11
−10u
10
+34u
9
−22u
8
+41u
7
−30u
6
+38u
5
−25u
4
+35u
3
−9u
2
+15u−4
27
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
10
u
14
− 7u
13
+ ··· − 7u + 1
c
2
, c
7
u
14
− u
13
+ ··· − u + 1
c
3
(u
7
+ 3u
6
+ 3u
5
− u
4
− 4u
3
− 2u
2
+ 1)
2
c
4
, c
5
(u
7
− 4u
5
− u
4
+ 4u
3
+ 2u
2
− 1)
2
c
6
, c
11
u
14
+ u
13
+ ··· + u + 1
c
8
(u
7
− 4u
5
+ u
4
+ 4u
3
− 2u
2
+ 1)
2
c
9
, c
12
u
14
− 2u
12
+ 3u
10
+ u
9
+ 3u
8
+ 7u
7
− 12u
5
− 11u
4
+ 6u
2
+ 4u + 1
28
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
y
14
+ 3y
13
+ ··· + 3y + 1
c
2
, c
6
, c
7
c
11
y
14
+ 7y
13
+ ··· + 7y + 1
c
3
(y
7
− 3y
6
+ 7y
5
− 13y
4
+ 6y
3
− 2y
2
+ 4y −1)
2
c
4
, c
5
, c
8
(y
7
− 8y
6
+ 24y
5
− 33y
4
+ 20y
3
− 6y
2
+ 4y −1)
2
c
9
, c
12
y
14
− 4y
13
+ ··· − 4y + 1
29
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.271534 + 0.962429I
a = −1.30581 + 4.62832I
b = −0.271534 + 0.962429I
−9.79470 −8.82578 + 0.I
u = 0.271534 − 0.962429I
a = −1.30581 − 4.62832I
b = −0.271534 − 0.962429I
−9.79470 −8.82578 + 0.I
u = 0.853858 + 0.520505I
a = 0.152789 − 0.093139I
b = −0.853858 + 0.520505I
−0.400829 3.59691 + 0.I
u = 0.853858 − 0.520505I
a = 0.152789 + 0.093139I
b = −0.853858 − 0.520505I
−0.400829 3.59691 + 0.I
u = −0.719129 + 0.694876I
a = −0.325329 − 0.314357I
b = 0.719129 + 0.694876I
2.28642 5.05433 + 0.I
u = −0.719129 − 0.694876I
a = −0.325329 + 0.314357I
b = 0.719129 − 0.694876I
2.28642 5.05433 + 0.I
u = −0.322303 + 0.789764I
a = 0.98249 + 2.38325I
b = 0.442964 + 1.085430I
−1.17508 + 2.13385I 2.42399 + 1.71411I
u = −0.322303 − 0.789764I
a = 0.98249 − 2.38325I
b = 0.442964 − 1.085430I
−1.17508 − 2.13385I 2.42399 − 1.71411I
u = −0.442964 + 1.085430I
a = 0.70254 + 1.73910I
b = 0.322303 + 0.789764I
−1.17508 − 2.13385I 2.42399 − 1.71411I
u = −0.442964 − 1.085430I
a = 0.70254 − 1.73910I
b = 0.322303 − 0.789764I
−1.17508 + 2.13385I 2.42399 + 1.71411I
30
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.292820 + 0.656840I
a = −0.599653 + 0.817113I
b = −0.566184 + 1.270040I
−4.73997 − 4.82255I −5.33672 + 5.53239I
u = 0.292820 − 0.656840I
a = −0.599653 − 0.817113I
b = −0.566184 − 1.270040I
−4.73997 + 4.82255I −5.33672 − 5.53239I
u = 0.566184 + 1.270040I
a = −0.107024 + 0.513141I
b = −0.292820 + 0.656840I
−4.73997 + 4.82255I −5.33672 − 5.53239I
u = 0.566184 − 1.270040I
a = −0.107024 − 0.513141I
b = −0.292820 − 0.656840I
−4.73997 − 4.82255I −5.33672 + 5.53239I
31
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
10
(u
13
− 7u
12
+ ··· − 5u + 1)(u
14
− 7u
13
+ ··· − 7u + 1)
· (u
27
+ 13u
26
+ ··· + 3u − 1)(u
104
+ 46u
103
+ ··· + 249939u + 14641)
c
2
, c
7
(u
13
− u
12
+ ··· + u − 1)(u
14
− u
13
+ ··· − u + 1)(u
27
− u
26
+ ··· + 3u − 1)
· (u
104
+ 2u
103
+ ··· − 17u + 121)
c
3
((u
7
+ 3u
6
+ ··· − 2u
2
+ 1)
2
)(u
13
− 5u
12
+ ··· − u − 1)
· (u
27
− 22u
26
+ ··· + 24576u − 2560)(u
52
+ 10u
51
+ ··· − 3u − 1)
2
c
4
, c
5
((u
7
− 4u
5
− u
4
+ 4u
3
+ 2u
2
− 1)
2
)(u
13
+ u
12
+ ··· − u − 1)
· (u
27
+ 12u
26
+ ··· + 16u − 32)(u
52
− 5u
51
+ ··· + 7u + 1)
2
c
6
, c
11
(u
13
+ u
12
+ ··· + u + 1)(u
14
+ u
13
+ ··· + u + 1)(u
27
− u
26
+ ··· + 3u − 1)
· (u
104
+ 2u
103
+ ··· − 17u + 121)
c
8
((u
7
− 4u
5
+ u
4
+ 4u
3
− 2u
2
+ 1)
2
)(u
13
− u
12
+ ··· − u + 1)
· (u
27
+ 12u
26
+ ··· + 16u − 32)(u
52
− 5u
51
+ ··· + 7u + 1)
2
c
9
, c
12
(u
13
− u
12
+ ··· − u + 1)
· (u
14
− 2u
12
+ 3u
10
+ u
9
+ 3u
8
+ 7u
7
− 12u
5
− 11u
4
+ 6u
2
+ 4u + 1)
· (u
27
− u
26
+ ··· − 3u − 1)(u
104
+ 13u
103
+ ··· + 3452u + 283)
32
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
10
(y
13
+ 7y
12
+ ··· + 7y −1)(y
14
+ 3y
13
+ ··· + 3y + 1)
· (y
27
+ 5y
26
+ ··· + 87y −1)
· (y
104
+ 34y
103
+ ··· + 3659910927y + 214358881)
c
2
, c
6
, c
7
c
11
(y
13
+ 7y
12
+ ··· − 5y −1)(y
14
+ 7y
13
+ ··· + 7y + 1)
· (y
27
+ 13y
26
+ ··· + 3y −1)(y
104
+ 46y
103
+ ··· + 249939y + 14641)
c
3
(y
7
− 3y
6
+ 7y
5
− 13y
4
+ 6y
3
− 2y
2
+ 4y −1)
2
· (y
13
− 5y
12
+ ··· + 7y −1)(y
27
− 6y
26
+ ··· − 262144y −6553600)
· (y
52
− 12y
51
+ ··· − 43y + 1)
2
c
4
, c
5
, c
8
(y
7
− 8y
6
+ 24y
5
− 33y
4
+ 20y
3
− 6y
2
+ 4y −1)
2
· (y
13
− 15y
12
+ ··· + 7y −1)(y
27
− 24y
26
+ ··· + 12032y −1024)
· (y
52
− 53y
51
+ ··· − 37y + 1)
2
c
9
, c
12
(y
13
+ y
12
+ ··· − y −1)(y
14
− 4y
13
+ ··· − 4y + 1)
· (y
27
+ 11y
26
+ ··· − 5y −1)(y
104
− 5y
103
+ ··· + 215340y + 80089)
33
