12a
0392
(K12a
0392
)
A knot diagram
1
Linearized knot diagam
3 6 9 11 2 10 12 4 1 5 8 7
Solving Sequence
8,11 5,12
4 9 3 7 1 10 6 2
c
11
c
4
c
8
c
3
c
7
c
12
c
10
c
6
c
2
c
1
, c
5
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h43u
38
+ 714u
37
+ ··· + 128b − 4224, −119u
38
− 2108u
37
+ ··· + 256a − 156160,
u
39
+ 18u
38
+ ··· + 5120u + 256i
I
u
2
= h−1.58971 × 10
86
a
15
u
3
+ 2.22794 × 10
86
a
14
u
3
+ ··· − 5.54346 × 10
88
a − 7.99467 × 10
88
,
− 2a
15
u
3
+ 5a
14
u
3
+ ··· + 348a − 417, u
4
− u
3
+ 3u
2
− 2u + 1i
I
u
3
= hu
26
+ u
25
+ ··· + b + 2, −3u
26
+ 2u
25
+ ··· + a − 2, u
27
− u
26
+ ··· − 2u + 1i
* 3 irreducible components of dim
C
= 0, with total 130 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
= h43u
38
+ 714u
37
+ · · · + 128b − 4224, −119u
38
− 2108u
37
+ · · · +
256a − 156160, u
39
+ 18u
38
+ · · · + 5120u + 256i
(i) Arc colorings
a
8
=
0
u
a
11
=
1
0
a
5
=
119
256
u
38
+
527
64
u
37
+ ··· +
20949
2
u + 610
−
43
128
u
38
−
357
64
u
37
+ ··· + 17u + 33
a
12
=
1
u
2
a
4
=
33
256
u
38
+
85
32
u
37
+ ··· +
20983
2
u + 643
−
43
128
u
38
−
357
64
u
37
+ ··· + 17u + 33
a
9
=
3
2
u
38
+
51
2
u
37
+ ··· + 4544u +
449
2
3
2
u
38
+ 26u
37
+ ··· +
14913
2
u + 384
a
3
=
−3.08594u
38
− 51.7266u
37
+ ··· + 4079u + 359.500
−
429
128
u
38
−
937
16
u
37
+ ··· −
28813
2
u − 704
a
7
=
u
u
3
+ u
a
1
=
u
2
+ 1
u
4
+ 2u
2
a
10
=
0.500000u
37
+ 8.25000u
36
+ ··· + 2911.50u + 160.500
−
3
2
u
38
− 26u
37
+ ··· −
14911
2
u − 384
a
6
=
1
2
u
38
+ 8u
37
+ ··· −
5947
4
u − 96
5
4
u
38
+
85
4
u
37
+ ··· + 7201u + 384
a
2
=
−6u
38
−
1669
16
u
37
+ ··· − 35327u −
3677
2
−
55
16
u
38
−
485
8
u
37
+ ··· −
48673
2
u − 1280
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
49
8
u
38
−
1605
16
u
37
+ ··· + 16358u + 1094
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
39
+ 18u
38
+ ··· + 5504u + 256
c
2
, c
5
u
39
+ 12u
38
+ ··· + 176u + 16
c
3
, c
4
, c
8
c
10
u
39
+ 20u
37
+ ··· + 4u + 1
c
6
, c
9
u
39
− u
38
+ ··· − 8u + 1
c
7
, c
11
, c
12
u
39
+ 18u
38
+ ··· + 5120u + 256
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
39
+ 10y
38
+ ··· + 19341312y −65536
c
2
, c
5
y
39
− 18y
38
+ ··· + 5504y −256
c
3
, c
4
, c
8
c
10
y
39
+ 40y
38
+ ··· + 20y
2
− 1
c
6
, c
9
y
39
+ 21y
38
+ ··· + 4y −1
c
7
, c
11
, c
12
y
39
+ 36y
38
+ ··· + 589824y −65536
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.400663 + 0.963427I
a = 0.451632 + 0.816397I
b = 0.369575 − 0.774310I
−0.15313 + 4.84342I 0
u = −0.400663 − 0.963427I
a = 0.451632 − 0.816397I
b = 0.369575 + 0.774310I
−0.15313 − 4.84342I 0
u = 0.451130 + 0.992863I
a = 0.138378 + 1.102670I
b = 0.280699 − 0.629532I
−1.18720 − 1.89318I 0
u = 0.451130 − 0.992863I
a = 0.138378 − 1.102670I
b = 0.280699 + 0.629532I
−1.18720 + 1.89318I 0
u = −0.052624 + 1.102050I
a = −0.168827 − 0.844431I
b = −0.347523 + 0.553746I
2.60173 + 1.38324I 0
u = −0.052624 − 1.102050I
a = −0.168827 + 0.844431I
b = −0.347523 − 0.553746I
2.60173 − 1.38324I 0
u = −0.864676 + 0.737942I
a = 0.729080 + 0.693284I
b = 0.35512 − 1.48245I
8.1445 + 12.7684I 0
u = −0.864676 − 0.737942I
a = 0.729080 − 0.693284I
b = 0.35512 + 1.48245I
8.1445 − 12.7684I 0
u = −1.052450 + 0.490837I
a = 0.533205 + 0.265820I
b = −0.112515 − 1.397090I
7.28855 − 6.50907I 0
u = −1.052450 − 0.490837I
a = 0.533205 − 0.265820I
b = −0.112515 + 1.397090I
7.28855 + 6.50907I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.910975 + 0.731798I
a = −0.702822 − 0.636181I
b = −0.26897 + 1.47836I
9.80197 + 6.44149I 0
u = −0.910975 − 0.731798I
a = −0.702822 + 0.636181I
b = −0.26897 − 1.47836I
9.80197 − 6.44149I 0
u = −1.061090 + 0.576155I
a = −0.567903 − 0.380804I
b = 0.01767 + 1.42483I
9.20680 + 0.05896I 0
u = −1.061090 − 0.576155I
a = −0.567903 + 0.380804I
b = 0.01767 − 1.42483I
9.20680 − 0.05896I 0
u = −0.690930 + 0.149615I
a = 0.021817 − 0.306127I
b = −0.353074 − 0.523995I
−2.57796 − 0.99729I −13.7858 + 6.1595I
u = −0.690930 − 0.149615I
a = 0.021817 + 0.306127I
b = −0.353074 + 0.523995I
−2.57796 + 0.99729I −13.7858 − 6.1595I
u = −0.255978 + 1.318020I
a = −0.463212 − 0.163607I
b = 0.218629 + 0.376986I
1.98110 + 2.40422I 0
u = −0.255978 − 1.318020I
a = −0.463212 + 0.163607I
b = 0.218629 − 0.376986I
1.98110 − 2.40422I 0
u = −0.537476 + 0.324278I
a = −0.171379 − 0.673239I
b = −0.761237 − 0.128475I
−0.73710 + 3.72784I −13.9761 − 6.1233I
u = −0.537476 − 0.324278I
a = −0.171379 + 0.673239I
b = −0.761237 + 0.128475I
−0.73710 − 3.72784I −13.9761 + 6.1233I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.115760 + 0.810029I
a = 0.508718 + 0.600988I
b = 0.130410 − 1.320350I
1.72502 + 3.78448I 0
u = −1.115760 − 0.810029I
a = 0.508718 − 0.600988I
b = 0.130410 + 1.320350I
1.72502 − 3.78448I 0
u = −0.149861 + 1.383670I
a = 0.469652 − 0.674866I
b = −0.672332 + 0.210913I
5.20966 + 1.40328I 0
u = −0.149861 − 1.383670I
a = 0.469652 + 0.674866I
b = −0.672332 − 0.210913I
5.20966 − 1.40328I 0
u = −0.190013 + 1.391680I
a = −0.653793 + 0.515105I
b = 0.726029 − 0.003275I
4.70756 + 6.35711I 0
u = −0.190013 − 1.391680I
a = −0.653793 − 0.515105I
b = 0.726029 + 0.003275I
4.70756 − 6.35711I 0
u = −0.399279 + 0.387480I
a = 0.394234 + 0.785740I
b = 0.665015 − 0.160987I
−0.299504 − 0.631618I −12.71997 − 1.63926I
u = −0.399279 − 0.387480I
a = 0.394234 − 0.785740I
b = 0.665015 + 0.160987I
−0.299504 + 0.631618I −12.71997 + 1.63926I
u = −0.27536 + 1.63405I
a = −0.50107 − 1.80207I
b = −0.53416 + 1.64963I
15.9909 + 17.0430I 0
u = −0.27536 − 1.63405I
a = −0.50107 + 1.80207I
b = −0.53416 − 1.64963I
15.9909 − 17.0430I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.28713 + 1.63936I
a = 0.54343 + 1.73997I
b = 0.47039 − 1.63060I
17.6388 + 10.9152I 0
u = −0.28713 − 1.63936I
a = 0.54343 − 1.73997I
b = 0.47039 + 1.63060I
17.6388 − 10.9152I 0
u = −0.308532
a = 0.796218
b = 0.355272
−0.538927 −18.2760
u = −0.35579 + 1.66576I
a = 0.62206 + 1.45371I
b = 0.26274 − 1.48497I
16.6078 + 5.4335I 0
u = −0.35579 − 1.66576I
a = 0.62206 − 1.45371I
b = 0.26274 + 1.48497I
16.6078 − 5.4335I 0
u = −0.41026 + 1.66303I
a = −0.64890 − 1.31609I
b = −0.17699 + 1.41341I
14.2343 − 0.9071I 0
u = −0.41026 − 1.66303I
a = −0.64890 + 1.31609I
b = −0.17699 − 1.41341I
14.2343 + 0.9071I 0
u = −0.28654 + 1.68929I
a = −0.43241 − 1.56815I
b = −0.44711 + 1.45266I
10.16570 + 8.90260I 0
u = −0.28654 − 1.68929I
a = −0.43241 + 1.56815I
b = −0.44711 − 1.45266I
10.16570 − 8.90260I 0
8
II. I
u
2
= h−1.59 × 10
86
a
15
u
3
+ 2.23 × 10
86
a
14
u
3
+ · · · − 5.54 × 10
88
a − 7.99 ×
10
88
, −2a
15
u
3
+ 5a
14
u
3
+ · · · + 348a − 417, u
4
− u
3
+ 3u
2
− 2u + 1i
(i) Arc colorings
a
8
=
0
u
a
11
=
1
0
a
5
=
a
0.00408887a
15
u
3
− 0.00573044a
14
u
3
+ ··· + 1.42582a + 2.05629
a
12
=
1
u
2
a
4
=
0.00408887a
15
u
3
− 0.00573044a
14
u
3
+ ··· + 2.42582a + 2.05629
0.00408887a
15
u
3
− 0.00573044a
14
u
3
+ ··· + 1.42582a + 2.05629
a
9
=
−0.00155418a
15
u
3
+ 0.00258699a
14
u
3
+ ··· + 0.0885681a + 1.18429
−0.00126205a
15
u
3
+ 0.000265938a
14
u
3
+ ··· + 1.25572a + 0.310048
a
3
=
−0.00131987a
15
u
3
+ 0.00795777a
14
u
3
+ ··· − 4.11698a − 0.379473
0.00514080a
15
u
3
− 0.000145096a
14
u
3
+ ··· + 1.65513a + 0.682050
a
7
=
u
u
3
+ u
a
1
=
u
2
+ 1
u
3
− u
2
+ 2u − 1
a
10
=
−0.000982963a
15
u
3
+ 0.00140342a
14
u
3
+ ··· − 0.640785a + 0.472882
0.00120849a
15
u
3
+ 0.00435844a
14
u
3
+ ··· + 0.567163a − 0.159396
a
6
=
0.00145898a
15
u
3
− 0.00366768a
14
u
3
+ ··· + 0.244446a + 0.563875
−0.00148404a
15
u
3
+ 0.00319394a
14
u
3
+ ··· − 0.647576a − 0.831641
a
2
=
0.000836775a
15
u
3
+ 0.00741350a
14
u
3
+ ··· − 2.24164a − 1.04569
0.00384949a
15
u
3
− 0.00353384a
14
u
3
+ ··· + 2.01767a − 1.78758
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.00740162a
15
u
3
−0.000148538a
14
u
3
+ ···− 0.708796a −10.4488
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
8
+ 3u
7
+ 7u
6
+ 10u
5
+ 11u
4
+ 10u
3
+ 6u
2
+ 4u + 1)
8
c
2
, c
5
(u
8
− u
7
− u
6
+ 2u
5
+ u
4
− 2u
3
+ 2u − 1)
8
c
3
, c
4
, c
8
c
10
u
64
− u
63
+ ··· − 56048u + 9017
c
6
, c
9
u
64
+ 9u
63
+ ··· − 186580u + 125537
c
7
, c
11
, c
12
(u
4
− u
3
+ 3u
2
− 2u + 1)
16
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
8
+ 5y
7
+ 11y
6
+ 6y
5
− 17y
4
− 34y
3
− 22y
2
− 4y + 1)
8
c
2
, c
5
(y
8
− 3y
7
+ 7y
6
− 10y
5
+ 11y
4
− 10y
3
+ 6y
2
− 4y + 1)
8
c
3
, c
4
, c
8
c
10
y
64
+ 63y
63
+ ··· + 550974992y + 81306289
c
6
, c
9
y
64
+ 23y
63
+ ··· + 140468688776y + 15759538369
c
7
, c
11
, c
12
(y
4
+ 5y
3
+ 7y
2
+ 2y + 1)
16
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.395123 + 0.506844I
a = 0.529964 − 0.894339I
b = −0.271440 + 1.194030I
3.68314 − 0.28387I −7.24196 + 4.39795I
u = 0.395123 + 0.506844I
a = −0.834931 − 0.385761I
b = −0.868179 − 0.429906I
3.68314 − 2.54634I −7.24196 + 5.41953I
u = 0.395123 + 0.506844I
a = −1.106250 + 0.193590I
b = −0.53504 − 1.55487I
6.88321 − 3.99360I −4.10382 + 8.47670I
u = 0.395123 + 0.506844I
a = 1.090130 − 0.270344I
b = 0.39737 + 1.63331I
6.88321 + 1.16339I −4.10382 + 1.34079I
u = 0.395123 + 0.506844I
a = 0.497578 + 0.719297I
b = 0.672533 − 0.182376I
−1.77893 − 1.41510I −13.6908 + 4.9087I
u = 0.395123 + 0.506844I
a = −0.325623 + 0.736979I
b = 0.516120 − 1.133730I
2.34412 + 5.02843I −9.25519 − 0.38543I
u = 0.395123 + 0.506844I
a = 0.692179 + 0.327627I
b = 1.083680 + 0.298282I
2.34412 − 7.85864I −9.25519 + 10.20291I
u = 0.395123 + 0.506844I
a = −1.51485 − 0.13034I
b = −0.280648 − 1.037500I
3.87876 − 1.41510I −11.72120 + 4.90874I
u = 0.395123 + 0.506844I
a = 1.42416 − 0.72333I
b = 0.117535 + 1.371480I
3.87876 − 1.41510I −11.72120 + 4.90874I
u = 0.395123 + 0.506844I
a = −1.25536 − 1.22597I
b = 0.049747 − 0.249446I
3.68314 − 0.28387I −7.24196 + 4.39795I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.395123 + 0.506844I
a = −0.22939 + 1.80501I
b = −0.190203 − 0.805214I
−1.77893 − 1.41510I −13.6908 + 4.9087I
u = 0.395123 + 0.506844I
a = 1.17390 + 1.65779I
b = −0.276362 + 0.060214I
2.34412 + 5.02843I −9.25519 − 0.38543I
u = 0.395123 + 0.506844I
a = 1.09863 − 1.83963I
b = 0.259522 + 1.185500I
3.68314 − 2.54634I −7.24196 + 5.41953I
u = 0.395123 + 0.506844I
a = −1.01834 + 2.19191I
b = −0.384446 − 1.147400I
2.34412 − 7.85864I −9.25519 + 10.20291I
u = 0.395123 + 0.506844I
a = −2.48760 + 0.21755I
b = 0.103066 − 1.292470I
6.88321 + 1.16339I −4.10382 + 1.34079I
u = 0.395123 + 0.506844I
a = 2.46143 − 0.53883I
b = −0.041443 + 1.369750I
6.88321 − 3.99360I −4.10382 + 8.47670I
u = 0.395123 − 0.506844I
a = 0.529964 + 0.894339I
b = −0.271440 − 1.194030I
3.68314 + 0.28387I −7.24196 − 4.39795I
u = 0.395123 − 0.506844I
a = −0.834931 + 0.385761I
b = −0.868179 + 0.429906I
3.68314 + 2.54634I −7.24196 − 5.41953I
u = 0.395123 − 0.506844I
a = −1.106250 − 0.193590I
b = −0.53504 + 1.55487I
6.88321 + 3.99360I −4.10382 − 8.47670I
u = 0.395123 − 0.506844I
a = 1.090130 + 0.270344I
b = 0.39737 − 1.63331I
6.88321 − 1.16339I −4.10382 − 1.34079I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.395123 − 0.506844I
a = 0.497578 − 0.719297I
b = 0.672533 + 0.182376I
−1.77893 + 1.41510I −13.6908 − 4.9087I
u = 0.395123 − 0.506844I
a = −0.325623 − 0.736979I
b = 0.516120 + 1.133730I
2.34412 − 5.02843I −9.25519 + 0.38543I
u = 0.395123 − 0.506844I
a = 0.692179 − 0.327627I
b = 1.083680 − 0.298282I
2.34412 + 7.85864I −9.25519 − 10.20291I
u = 0.395123 − 0.506844I
a = −1.51485 + 0.13034I
b = −0.280648 + 1.037500I
3.87876 + 1.41510I −11.72120 − 4.90874I
u = 0.395123 − 0.506844I
a = 1.42416 + 0.72333I
b = 0.117535 − 1.371480I
3.87876 + 1.41510I −11.72120 − 4.90874I
u = 0.395123 − 0.506844I
a = −1.25536 + 1.22597I
b = 0.049747 + 0.249446I
3.68314 + 0.28387I −7.24196 − 4.39795I
u = 0.395123 − 0.506844I
a = −0.22939 − 1.80501I
b = −0.190203 + 0.805214I
−1.77893 + 1.41510I −13.6908 − 4.9087I
u = 0.395123 − 0.506844I
a = 1.17390 − 1.65779I
b = −0.276362 − 0.060214I
2.34412 − 5.02843I −9.25519 + 0.38543I
u = 0.395123 − 0.506844I
a = 1.09863 + 1.83963I
b = 0.259522 − 1.185500I
3.68314 + 2.54634I −7.24196 − 5.41953I
u = 0.395123 − 0.506844I
a = −1.01834 − 2.19191I
b = −0.384446 + 1.147400I
2.34412 + 7.85864I −9.25519 − 10.20291I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.395123 − 0.506844I
a = −2.48760 − 0.21755I
b = 0.103066 + 1.292470I
6.88321 − 1.16339I −4.10382 − 1.34079I
u = 0.395123 − 0.506844I
a = 2.46143 + 0.53883I
b = −0.041443 − 1.369750I
6.88321 + 3.99360I −4.10382 − 8.47670I
u = 0.10488 + 1.55249I
a = 0.765534 + 0.529987I
b = −1.66280 − 0.43897I
9.34587 − 9.60750I −5.60171 + 7.85897I
u = 0.10488 + 1.55249I
a = −0.511096 − 0.652030I
b = 1.44154 + 0.59151I
10.68490 − 4.29520I −3.58849 + 3.07559I
u = 0.10488 + 1.55249I
a = 0.325514 − 1.328990I
b = 0.722005 + 1.189080I
10.88050 − 3.16396I −8.06773 + 2.56480I
u = 0.10488 + 1.55249I
a = −0.484520 − 0.281104I
b = −0.469711 − 0.025814I
9.34587 + 3.27957I −5.60171 − 2.72937I
u = 0.10488 + 1.55249I
a = 0.418737 − 0.128216I
b = 0.602408 + 0.299006I
10.68490 − 2.03273I −3.58849 + 2.05401I
u = 0.10488 + 1.55249I
a = 0.370887 + 0.007580I
b = −1.200660 − 0.042489I
5.22281 − 3.16396I −10.03730 + 2.56480I
u = 0.10488 + 1.55249I
a = 0.41331 − 1.81369I
b = −0.37641 + 1.51363I
9.34587 + 3.27957I −5.60171 − 2.72937I
u = 0.10488 + 1.55249I
a = −0.07999 − 1.98132I
b = 0.97084 + 1.91424I
13.8850 − 5.7425I −0.45034 + 6.13276I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.10488 + 1.55249I
a = −0.37587 + 1.97654I
b = 0.15806 − 1.60323I
10.68490 − 2.03273I −3.58849 + 2.05401I
u = 0.10488 + 1.55249I
a = 1.13639 − 1.69735I
b = 0.192108 + 1.283880I
13.88500 − 0.58547I −0.450339 − 1.003158I
u = 0.10488 + 1.55249I
a = 0.04642 − 2.05989I
b = 0.032827 + 1.291870I
5.22281 − 3.16396I −10.03730 + 2.56480I
u = 0.10488 + 1.55249I
a = −0.46664 + 2.02303I
b = −0.32707 − 1.61159I
10.88050 − 3.16396I −8.06773 + 2.56480I
u = 0.10488 + 1.55249I
a = −0.05031 + 2.08668I
b = −0.78123 − 2.01911I
13.88500 − 0.58547I −0.450339 − 1.003158I
u = 0.10488 + 1.55249I
a = −1.07189 + 1.91560I
b = −0.197571 − 1.376010I
13.8850 − 5.7425I −0.45034 + 6.13276I
u = 0.10488 + 1.55249I
a = −0.25019 + 2.33684I
b = −0.19153 − 1.43815I
10.68490 − 4.29520I −3.58849 + 3.07559I
u = 0.10488 + 1.55249I
a = 0.11810 − 2.43062I
b = 0.235399 + 1.383450I
9.34587 − 9.60750I −5.60171 + 7.85897I
u = 0.10488 − 1.55249I
a = 0.765534 − 0.529987I
b = −1.66280 + 0.43897I
9.34587 + 9.60750I −5.60171 − 7.85897I
u = 0.10488 − 1.55249I
a = −0.511096 + 0.652030I
b = 1.44154 − 0.59151I
10.68490 + 4.29520I −3.58849 − 3.07559I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.10488 − 1.55249I
a = 0.325514 + 1.328990I
b = 0.722005 − 1.189080I
10.88050 + 3.16396I −8.06773 − 2.56480I
u = 0.10488 − 1.55249I
a = −0.484520 + 0.281104I
b = −0.469711 + 0.025814I
9.34587 − 3.27957I −5.60171 + 2.72937I
u = 0.10488 − 1.55249I
a = 0.418737 + 0.128216I
b = 0.602408 − 0.299006I
10.68490 + 2.03273I −3.58849 − 2.05401I
u = 0.10488 − 1.55249I
a = 0.370887 − 0.007580I
b = −1.200660 + 0.042489I
5.22281 + 3.16396I −10.03730 − 2.56480I
u = 0.10488 − 1.55249I
a = 0.41331 + 1.81369I
b = −0.37641 − 1.51363I
9.34587 − 3.27957I −5.60171 + 2.72937I
u = 0.10488 − 1.55249I
a = −0.07999 + 1.98132I
b = 0.97084 − 1.91424I
13.8850 + 5.7425I −0.45034 − 6.13276I
u = 0.10488 − 1.55249I
a = −0.37587 − 1.97654I
b = 0.15806 + 1.60323I
10.68490 + 2.03273I −3.58849 − 2.05401I
u = 0.10488 − 1.55249I
a = 1.13639 + 1.69735I
b = 0.192108 − 1.283880I
13.88500 + 0.58547I −0.450339 + 1.003158I
u = 0.10488 − 1.55249I
a = 0.04642 + 2.05989I
b = 0.032827 − 1.291870I
5.22281 + 3.16396I −10.03730 − 2.56480I
u = 0.10488 − 1.55249I
a = −0.46664 − 2.02303I
b = −0.32707 + 1.61159I
10.88050 + 3.16396I −8.06773 − 2.56480I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.10488 − 1.55249I
a = −0.05031 − 2.08668I
b = −0.78123 + 2.01911I
13.88500 + 0.58547I −0.450339 + 1.003158I
u = 0.10488 − 1.55249I
a = −1.07189 − 1.91560I
b = −0.197571 + 1.376010I
13.8850 + 5.7425I −0.45034 − 6.13276I
u = 0.10488 − 1.55249I
a = −0.25019 − 2.33684I
b = −0.19153 + 1.43815I
10.68490 + 4.29520I −3.58849 − 3.07559I
u = 0.10488 − 1.55249I
a = 0.11810 + 2.43062I
b = 0.235399 − 1.383450I
9.34587 + 9.60750I −5.60171 − 7.85897I
18
III.
I
u
3
= hu
26
+u
25
+· · ·+b+2, −3u
26
+2u
25
+· · ·+a−2, u
27
−u
26
+· · ·−2u+1i
(i) Arc colorings
a
8
=
0
u
a
11
=
1
0
a
5
=
3u
26
− 2u
25
+ ··· − 2u
2
+ 2
−u
26
− u
25
+ ··· + 4u − 2
a
12
=
1
u
2
a
4
=
2u
26
− 3u
25
+ ··· − 10u
2
+ 4u
−u
26
− u
25
+ ··· + 4u − 2
a
9
=
−2u
26
+ u
25
+ ··· − 2u + 1
−u
26
+ u
25
+ ··· − 2u + 2
a
3
=
2u
26
− 2u
25
+ ··· + 4u − 1
2u
26
− 6u
25
+ ··· + 7u − 3
a
7
=
u
u
3
+ u
a
1
=
u
2
+ 1
u
4
+ 2u
2
a
10
=
−u
26
− 16u
24
+ ··· + 16u
2
+ u
−u
26
+ u
25
+ ··· − 3u + 2
a
6
=
u
25
− u
24
+ ··· + 8u + 1
−u
25
− u
24
+ ··· + 10u
2
+ u
a
2
=
2u
26
− 2u
25
+ ··· + 8u − 4
u
26
− 2u
25
+ ··· − 6u
2
− 2
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −2u
26
+ 13u
25
−44u
24
+ 188u
23
−384u
22
+ 1192u
21
−1840u
20
+ 4386u
19
−5485u
18
+
10446u
17
− 10749u
16
+ 16942u
15
− 14071u
14
+ 18932u
13
− 12062u
12
+ 14034u
11
−
6237u
10
+ 6033u
9
− 1389u
8
+ 873u
7
+ 287u
6
− 280u
5
+ 211u
4
− 111u
3
+ 26u
2
− 7u − 2
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
27
− 15u
26
+ ··· + 41u − 4
c
2
u
27
+ 3u
26
+ ··· − 7u − 2
c
3
, c
10
u
27
+ 15u
25
+ ··· − 2u − 1
c
4
, c
8
u
27
+ 15u
25
+ ··· − 2u + 1
c
5
u
27
− 3u
26
+ ··· − 7u + 2
c
6
, c
9
u
27
− u
26
+ ··· − 15u
2
− 1
c
7
u
27
+ u
26
+ ··· − 2u − 1
c
11
, c
12
u
27
− u
26
+ ··· − 2u + 1
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
27
+ 5y
26
+ ··· − 287y − 16
c
2
, c
5
y
27
− 15y
26
+ ··· + 41y − 4
c
3
, c
4
, c
8
c
10
y
27
+ 30y
26
+ ··· + 22y − 1
c
6
, c
9
y
27
+ 7y
26
+ ··· − 30y − 1
c
7
, c
11
, c
12
y
27
+ 31y
26
+ ··· − 8y − 1
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.535336 + 0.994922I
a = 0.298240 − 1.158590I
b = 0.182952 + 0.715794I
−0.88204 + 2.07531I 1.26343 − 6.37506I
u = −0.535336 − 0.994922I
a = 0.298240 + 1.158590I
b = 0.182952 − 0.715794I
−0.88204 − 2.07531I 1.26343 + 6.37506I
u = −0.102103 + 1.222710I
a = −0.972159 + 0.502576I
b = 0.349966 − 0.736841I
6.72383 + 1.77161I −2.45683 − 1.18119I
u = −0.102103 − 1.222710I
a = −0.972159 − 0.502576I
b = 0.349966 + 0.736841I
6.72383 − 1.77161I −2.45683 + 1.18119I
u = 0.899346 + 0.875420I
a = 0.645841 − 0.587993I
b = 0.100783 + 1.239900I
1.23298 − 3.24440I −10.48599 − 0.27157I
u = 0.899346 − 0.875420I
a = 0.645841 + 0.587993I
b = 0.100783 − 1.239900I
1.23298 + 3.24440I −10.48599 + 0.27157I
u = −0.108309 + 1.271070I
a = 1.023980 − 0.261267I
b = −0.508159 + 0.617101I
5.80839 + 7.31398I −4.63619 − 6.85556I
u = −0.108309 − 1.271070I
a = 1.023980 + 0.261267I
b = −0.508159 − 0.617101I
5.80839 − 7.31398I −4.63619 + 6.85556I
u = −0.071301 + 0.666496I
a = −1.13829 + 1.53614I
b = −0.270892 − 0.978942I
4.50988 − 0.90734I −1.77390 + 1.10931I
u = −0.071301 − 0.666496I
a = −1.13829 − 1.53614I
b = −0.270892 + 0.978942I
4.50988 + 0.90734I −1.77390 − 1.10931I
22
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.203728 + 1.326250I
a = 0.333870 + 0.252783I
b = −0.313098 − 0.019896I
1.67821 + 2.63001I −17.8057 − 7.4070I
u = −0.203728 − 1.326250I
a = 0.333870 − 0.252783I
b = −0.313098 + 0.019896I
1.67821 − 2.63001I −17.8057 + 7.4070I
u = 0.223381 + 0.562186I
a = −1.75447 + 0.86382I
b = −0.256191 − 1.207040I
4.66163 − 0.95382I −1.65126 − 0.42273I
u = 0.223381 − 0.562186I
a = −1.75447 − 0.86382I
b = −0.256191 + 1.207040I
4.66163 + 0.95382I −1.65126 + 0.42273I
u = −0.528649
a = −0.718645
b = 0.248527
−2.57061 −15.8870
u = 0.18505 + 1.50235I
a = −0.69475 + 1.58247I
b = −0.31292 − 1.49830I
11.92070 + 0.27365I −5.83893 − 1.94056I
u = 0.18505 − 1.50235I
a = −0.69475 − 1.58247I
b = −0.31292 + 1.49830I
11.92070 − 0.27365I −5.83893 + 1.94056I
u = 0.12626 + 1.50914I
a = 0.62770 − 1.77432I
b = 0.43321 + 1.57602I
12.57020 − 4.62331I −4.80697 + 3.41997I
u = 0.12626 − 1.50914I
a = 0.62770 + 1.77432I
b = 0.43321 − 1.57602I
12.57020 + 4.62331I −4.80697 − 3.41997I
u = −0.199491 + 0.422310I
a = 0.69405 − 2.61132I
b = 0.502701 + 0.855643I
2.78684 − 6.14062I −5.64523 + 6.93886I
23
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.199491 − 0.422310I
a = 0.69405 + 2.61132I
b = 0.502701 − 0.855643I
2.78684 + 6.14062I −5.64523 − 6.93886I
u = 0.07220 + 1.55296I
a = 0.33634 − 1.82029I
b = 0.62283 + 1.46382I
11.79130 − 2.01446I −3.76548 − 1.58387I
u = 0.07220 − 1.55296I
a = 0.33634 + 1.82029I
b = 0.62283 − 1.46382I
11.79130 + 2.01446I −3.76548 + 1.58387I
u = 0.414983 + 0.084128I
a = −0.80072 − 1.94175I
b = −0.07262 − 1.50298I
6.79655 − 2.68393I −4.55211 + 2.58746I
u = 0.414983 − 0.084128I
a = −0.80072 + 1.94175I
b = −0.07262 + 1.50298I
6.79655 + 2.68393I −4.55211 − 2.58746I
u = 0.06338 + 1.61476I
a = −0.24031 + 1.63696I
b = −0.58283 − 1.30833I
10.64370 − 5.89407I −5.40122 + 5.44504I
u = 0.06338 − 1.61476I
a = −0.24031 − 1.63696I
b = −0.58283 + 1.30833I
10.64370 + 5.89407I −5.40122 − 5.44504I
24
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
8
+ 3u
7
+ 7u
6
+ 10u
5
+ 11u
4
+ 10u
3
+ 6u
2
+ 4u + 1)
8
· (u
27
− 15u
26
+ ··· + 41u − 4)(u
39
+ 18u
38
+ ··· + 5504u + 256)
c
2
((u
8
− u
7
+ ··· + 2u − 1)
8
)(u
27
+ 3u
26
+ ··· − 7u − 2)
· (u
39
+ 12u
38
+ ··· + 176u + 16)
c
3
, c
10
(u
27
+ 15u
25
+ ··· − 2u − 1)(u
39
+ 20u
37
+ ··· + 4u + 1)
· (u
64
− u
63
+ ··· − 56048u + 9017)
c
4
, c
8
(u
27
+ 15u
25
+ ··· − 2u + 1)(u
39
+ 20u
37
+ ··· + 4u + 1)
· (u
64
− u
63
+ ··· − 56048u + 9017)
c
5
((u
8
− u
7
+ ··· + 2u − 1)
8
)(u
27
− 3u
26
+ ··· − 7u + 2)
· (u
39
+ 12u
38
+ ··· + 176u + 16)
c
6
, c
9
(u
27
− u
26
+ ··· − 15u
2
− 1)(u
39
− u
38
+ ··· − 8u + 1)
· (u
64
+ 9u
63
+ ··· − 186580u + 125537)
c
7
((u
4
− u
3
+ 3u
2
− 2u + 1)
16
)(u
27
+ u
26
+ ··· − 2u − 1)
· (u
39
+ 18u
38
+ ··· + 5120u + 256)
c
11
, c
12
((u
4
− u
3
+ 3u
2
− 2u + 1)
16
)(u
27
− u
26
+ ··· − 2u + 1)
· (u
39
+ 18u
38
+ ··· + 5120u + 256)
25
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
8
+ 5y
7
+ 11y
6
+ 6y
5
− 17y
4
− 34y
3
− 22y
2
− 4y + 1)
8
· (y
27
+ 5y
26
+ ··· − 287y − 16)
· (y
39
+ 10y
38
+ ··· + 19341312y − 65536)
c
2
, c
5
(y
8
− 3y
7
+ 7y
6
− 10y
5
+ 11y
4
− 10y
3
+ 6y
2
− 4y + 1)
8
· (y
27
− 15y
26
+ ··· + 41y − 4)(y
39
− 18y
38
+ ··· + 5504y − 256)
c
3
, c
4
, c
8
c
10
(y
27
+ 30y
26
+ ··· + 22y − 1)(y
39
+ 40y
38
+ ··· + 20y
2
− 1)
· (y
64
+ 63y
63
+ ··· + 550974992y + 81306289)
c
6
, c
9
(y
27
+ 7y
26
+ ··· − 30y − 1)(y
39
+ 21y
38
+ ··· + 4y − 1)
· (y
64
+ 23y
63
+ ··· + 140468688776y + 15759538369)
c
7
, c
11
, c
12
((y
4
+ 5y
3
+ 7y
2
+ 2y + 1)
16
)(y
27
+ 31y
26
+ ··· − 8y − 1)
· (y
39
+ 36y
38
+ ··· + 589824y − 65536)
26
