11a
112
(K11a
112
)
A knot diagram
1
Linearized knot diagam
6 1 8 11 2 10 3 4 5 7 9
Solving Sequence
6,10
7
2,11
1 3 5 4 9 8
c
6
c
10
c
1
c
2
c
5
c
4
c
9
c
8
c
3
, c
7
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−8.66742 × 10
142
u
65
− 1.85341 × 10
143
u
64
+ ··· + 5.23974 × 10
142
b − 3.98318 × 10
145
,
− 2.38832 × 10
145
u
65
− 5.07173 × 10
145
u
64
+ ··· + 2.04874 × 10
145
a − 1.06078 × 10
148
,
u
66
+ 3u
65
+ ··· − 698u + 391i
I
u
2
= hu
12
− 2u
11
− 5u
10
+ 12u
9
+ 8u
8
− 29u
7
+ 34u
5
− 13u
4
− 18u
3
+ 13u
2
+ b + 3u − 3,
− u
13
+ 4u
12
+ u
11
− 22u
10
+ 16u
9
+ 45u
8
− 58u
7
− 35u
6
+ 83u
5
− 6u
4
− 54u
3
+ 23u
2
+ a + 11u − 7,
u
14
− 2u
13
− 5u
12
+ 12u
11
+ 8u
10
− 29u
9
+ 35u
7
− 14u
6
− 21u
5
+ 16u
4
+ 5u
3
− 6u
2
+ 1i
I
u
3
= h−u
5
+ 2u
4
+ u
3
− 2u
2
+ b − u, −u
5
+ 2u
4
+ 2u
3
− 4u
2
+ a − u,
u
10
− 4u
9
+ 2u
8
+ 8u
7
− 5u
6
− 7u
5
+ 3u
3
+ 3u
2
+ u + 1i
* 3 irreducible components of dim
C
= 0, with total 90 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−8.67 × 10
142
u
65
− 1.85 × 10
143
u
64
+ · · · + 5.24 × 10
142
b − 3.98 ×
10
145
, −2.39 × 10
145
u
65
− 5.07 × 10
145
u
64
+ · · · + 2.05 × 10
145
a − 1.06 ×
10
148
, u
66
+ 3u
65
+ · · · − 698u + 391i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
u
a
7
=
1
−u
2
a
2
=
1.16575u
65
+ 2.47554u
64
+ ··· − 1496.97u + 517.772
1.65417u
65
+ 3.53723u
64
+ ··· − 2227.88u + 760.187
a
11
=
u
−u
3
+ u
a
1
=
−0.488417u
65
− 1.06169u
64
+ ··· + 730.907u − 242.415
1.65417u
65
+ 3.53723u
64
+ ··· − 2227.88u + 760.187
a
3
=
−4.63396u
65
− 9.87610u
64
+ ··· + 6180.95u − 2106.10
3.44579u
65
+ 7.31099u
64
+ ··· − 4516.19u + 1545.50
a
5
=
−1.21103u
65
− 2.58621u
64
+ ··· + 1614.03u − 550.273
2.65367u
65
+ 5.65967u
64
+ ··· − 3544.37u + 1207.93
a
4
=
−3.44270u
65
− 7.34774u
64
+ ··· + 4580.96u − 1560.01
2.08906u
65
+ 4.45851u
64
+ ··· − 2799.61u + 954.194
a
9
=
1.82812u
65
+ 3.88511u
64
+ ··· − 2437.77u + 836.494
−1.49101u
65
− 3.16113u
64
+ ··· + 1941.13u − 660.317
a
8
=
6.19671u
65
+ 13.2052u
64
+ ··· − 8254.78u + 2813.85
−4.20938u
65
− 8.93733u
64
+ ··· + 5543.38u − 1893.47
a
8
=
6.19671u
65
+ 13.2052u
64
+ ··· − 8254.78u + 2813.85
−4.20938u
65
− 8.93733u
64
+ ··· + 5543.38u − 1893.47
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4.78436u
65
− 10.2758u
64
+ ··· + 6384.50u − 2162.36
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
66
+ 5u
65
+ ··· + 34u + 4
c
2
u
66
+ 27u
65
+ ··· − 12u + 16
c
3
, c
7
, c
8
u
66
− u
65
+ ··· − 56u + 11
c
4
u
66
− 3u
65
+ ··· − 250u + 71
c
6
, c
10
u
66
− 3u
65
+ ··· + 698u + 391
c
9
u
66
+ u
65
+ ··· − 470u + 241
c
11
u
66
− 7u
65
+ ··· − 102u − 67
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
66
+ 27y
65
+ ··· − 12y + 16
c
2
y
66
+ 27y
65
+ ··· − 164976y + 256
c
3
, c
7
, c
8
y
66
− 69y
65
+ ··· + 3574y + 121
c
4
y
66
+ 13y
65
+ ··· + 99380y + 5041
c
6
, c
10
y
66
− 41y
65
+ ··· − 3193706y + 152881
c
9
y
66
− 21y
65
+ ··· − 54610y + 58081
c
11
y
66
− 3y
65
+ ··· − 228020y + 4489
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.553994 + 0.817132I
a = 0.58544 + 1.58860I
b = 0.070442 + 0.432736I
−4.89628 + 4.04600I 0. − 7.91470I
u = 0.553994 − 0.817132I
a = 0.58544 − 1.58860I
b = 0.070442 − 0.432736I
−4.89628 − 4.04600I 0. + 7.91470I
u = 0.044651 + 1.027560I
a = −0.03585 − 1.60708I
b = 0.595192 − 0.987582I
−0.53608 − 6.26556I 0. + 8.67399I
u = 0.044651 − 1.027560I
a = −0.03585 + 1.60708I
b = 0.595192 + 0.987582I
−0.53608 + 6.26556I 0. − 8.67399I
u = −1.057280 + 0.123271I
a = −0.299700 + 0.067824I
b = 1.073380 − 0.701395I
0.04052 − 3.80627I 0
u = −1.057280 − 0.123271I
a = −0.299700 − 0.067824I
b = 1.073380 + 0.701395I
0.04052 + 3.80627I 0
u = 0.580719 + 0.732261I
a = −0.07117 + 1.86879I
b = 0.428988 + 1.124710I
−7.34513 + 3.69328I −5.70329 − 3.99766I
u = 0.580719 − 0.732261I
a = −0.07117 − 1.86879I
b = 0.428988 − 1.124710I
−7.34513 − 3.69328I −5.70329 + 3.99766I
u = −0.546154 + 0.917664I
a = 1.02255 + 1.19790I
b = −0.178208 + 1.154380I
−9.63085 + 2.05112I 0
u = −0.546154 − 0.917664I
a = 1.02255 − 1.19790I
b = −0.178208 − 1.154380I
−9.63085 − 2.05112I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.024070 + 0.311697I
a = 0.41730 − 1.46428I
b = −0.032613 − 1.192350I
−1.28697 + 4.18216I 0
u = 1.024070 − 0.311697I
a = 0.41730 + 1.46428I
b = −0.032613 + 1.192350I
−1.28697 − 4.18216I 0
u = −0.197995 + 0.874170I
a = 0.140181 + 0.842371I
b = 0.574376 + 0.595359I
0.60022 − 1.53805I 2.72682 + 4.17703I
u = −0.197995 − 0.874170I
a = 0.140181 − 0.842371I
b = 0.574376 − 0.595359I
0.60022 + 1.53805I 2.72682 − 4.17703I
u = 0.057515 + 1.110030I
a = 0.176652 + 0.885390I
b = −0.641007 + 0.405819I
−5.13042 + 4.43339I 0
u = 0.057515 − 1.110030I
a = 0.176652 − 0.885390I
b = −0.641007 − 0.405819I
−5.13042 − 4.43339I 0
u = −0.866529 + 0.013355I
a = −1.33674 + 0.64592I
b = 0.873691 + 1.006930I
−0.89589 + 3.10402I 0.54343 − 3.05170I
u = −0.866529 − 0.013355I
a = −1.33674 − 0.64592I
b = 0.873691 − 1.006930I
−0.89589 − 3.10402I 0.54343 + 3.05170I
u = 0.853665 + 0.135106I
a = −2.43454 + 0.28897I
b = 0.505356 − 0.698814I
−4.10664 + 2.85933I 0.363943 − 0.476166I
u = 0.853665 − 0.135106I
a = −2.43454 − 0.28897I
b = 0.505356 + 0.698814I
−4.10664 − 2.85933I 0.363943 + 0.476166I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.032450 + 0.507113I
a = −0.217969 − 1.258850I
b = 0.038438 − 1.392570I
−8.05212 − 7.21112I 0
u = −1.032450 − 0.507113I
a = −0.217969 + 1.258850I
b = 0.038438 + 1.392570I
−8.05212 + 7.21112I 0
u = 1.144210 + 0.214797I
a = 0.961366 − 0.866826I
b = −0.744120 − 1.117900I
2.95387 + 4.62224I 0
u = 1.144210 − 0.214797I
a = 0.961366 + 0.866826I
b = −0.744120 + 1.117900I
2.95387 − 4.62224I 0
u = 1.136700 + 0.303584I
a = −1.56569 − 0.14302I
b = 0.543699 + 0.963909I
−4.97139 + 7.17182I 0
u = 1.136700 − 0.303584I
a = −1.56569 + 0.14302I
b = 0.543699 − 0.963909I
−4.97139 − 7.17182I 0
u = −0.809325 + 0.115865I
a = −0.52327 − 2.10152I
b = −0.215765 − 1.035700I
−0.545532 + 0.599797I 1.64339 + 2.56314I
u = −0.809325 − 0.115865I
a = −0.52327 + 2.10152I
b = −0.215765 + 1.035700I
−0.545532 − 0.599797I 1.64339 − 2.56314I
u = −1.118470 + 0.456780I
a = 1.17750 + 1.75389I
b = −0.605458 + 1.064560I
2.13300 − 6.10455I 0
u = −1.118470 − 0.456780I
a = 1.17750 − 1.75389I
b = −0.605458 − 1.064560I
2.13300 + 6.10455I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.209870 + 0.001472I
a = 0.291036 − 0.003235I
b = −0.958064 − 0.487956I
4.84160 + 1.58290I 0
u = 1.209870 − 0.001472I
a = 0.291036 + 0.003235I
b = −0.958064 + 0.487956I
4.84160 − 1.58290I 0
u = 0.992580 + 0.743807I
a = 0.829585 − 0.896312I
b = 0.333033 − 0.931189I
−6.28712 + 1.90390I 0
u = 0.992580 − 0.743807I
a = 0.829585 + 0.896312I
b = 0.333033 + 0.931189I
−6.28712 − 1.90390I 0
u = 0.661473 + 0.362026I
a = 0.388489 − 0.220994I
b = 0.758076 + 0.048117I
−3.94345 − 0.27627I −0.20377 − 1.42170I
u = 0.661473 − 0.362026I
a = 0.388489 + 0.220994I
b = 0.758076 − 0.048117I
−3.94345 + 0.27627I −0.20377 + 1.42170I
u = −1.217260 + 0.293215I
a = −0.209546 + 0.352710I
b = −0.699865 − 0.501839I
3.79937 − 1.04615I 0
u = −1.217260 − 0.293215I
a = −0.209546 − 0.352710I
b = −0.699865 + 0.501839I
3.79937 + 1.04615I 0
u = 0.289729 + 0.632525I
a = −1.20205 + 2.02084I
b = 0.099360 + 0.983650I
−3.46107 − 0.67912I −7.42755 + 0.90755I
u = 0.289729 − 0.632525I
a = −1.20205 − 2.02084I
b = 0.099360 − 0.983650I
−3.46107 + 0.67912I −7.42755 − 0.90755I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.31931
a = −0.452314
b = 0.200297
2.96244 0
u = −1.33669
a = −0.327933
b = 1.10352
1.97498 0
u = −1.336450 + 0.216760I
a = −0.754740 − 0.809320I
b = 0.69935 − 1.27364I
−1.61048 − 6.33014I 0
u = −1.336450 − 0.216760I
a = −0.754740 + 0.809320I
b = 0.69935 + 1.27364I
−1.61048 + 6.33014I 0
u = 1.313190 + 0.421616I
a = −0.007522 + 0.224374I
b = 0.882628 − 0.511949I
5.12672 + 6.11193I 0
u = 1.313190 − 0.421616I
a = −0.007522 − 0.224374I
b = 0.882628 + 0.511949I
5.12672 − 6.11193I 0
u = −0.138682 + 1.399980I
a = 0.020109 − 1.269570I
b = −0.589344 − 1.066960I
−6.95817 + 9.29076I 0
u = −0.138682 − 1.399980I
a = 0.020109 + 1.269570I
b = −0.589344 + 1.066960I
−6.95817 − 9.29076I 0
u = 1.30750 + 0.54957I
a = −1.06901 + 1.35517I
b = 0.673865 + 1.105880I
3.31701 + 11.86690I 0
u = 1.30750 − 0.54957I
a = −1.06901 − 1.35517I
b = 0.673865 − 1.105880I
3.31701 − 11.86690I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.35147 + 0.54191I
a = 0.063163 + 0.131606I
b = −0.988314 − 0.489276I
−0.83745 − 10.20370I 0
u = −1.35147 − 0.54191I
a = 0.063163 − 0.131606I
b = −0.988314 + 0.489276I
−0.83745 + 10.20370I 0
u = −0.368991 + 0.379736I
a = −0.719106 + 0.942094I
b = −0.194366 + 0.419596I
0.210341 − 1.088940I 2.71206 + 6.43281I
u = −0.368991 − 0.379736I
a = −0.719106 − 0.942094I
b = −0.194366 − 0.419596I
0.210341 + 1.088940I 2.71206 − 6.43281I
u = −1.36359 + 0.61753I
a = −0.881623 − 1.082620I
b = 0.636156 − 0.930272I
3.70447 − 4.43878I 0
u = −1.36359 − 0.61753I
a = −0.881623 + 1.082620I
b = 0.636156 + 0.930272I
3.70447 + 4.43878I 0
u = 1.28331 + 0.78007I
a = 0.160169 + 0.274884I
b = −0.762107 + 0.779221I
0.022290 + 1.139270I 0
u = 1.28331 − 0.78007I
a = 0.160169 − 0.274884I
b = −0.762107 − 0.779221I
0.022290 − 1.139270I 0
u = −1.47641 + 0.39183I
a = −0.248686 + 0.207203I
b = 0.644167 + 0.746103I
4.27222 + 0.57322I 0
u = −1.47641 − 0.39183I
a = −0.248686 − 0.207203I
b = 0.644167 − 0.746103I
4.27222 − 0.57322I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.411878 + 0.216634I
a = −0.83054 − 2.42396I
b = 0.446886 − 1.198200I
−7.34762 − 4.66083I −3.40198 − 1.35385I
u = 0.411878 − 0.216634I
a = −0.83054 + 2.42396I
b = 0.446886 + 1.198200I
−7.34762 + 4.66083I −3.40198 + 1.35385I
u = −1.40430 + 0.66218I
a = 0.92865 + 1.22021I
b = −0.703220 + 1.153400I
−2.8953 − 16.3430I 0
u = −1.40430 − 0.66218I
a = 0.92865 − 1.22021I
b = −0.703220 − 1.153400I
−2.8953 + 16.3430I 0
u = 1.24829 + 0.96945I
a = 0.789126 − 1.086330I
b = −0.716542 − 0.934610I
−0.45544 + 6.74104I 0
u = 1.24829 − 0.96945I
a = 0.789126 + 1.086330I
b = −0.716542 + 0.934610I
−0.45544 − 6.74104I 0
11
II.
I
u
2
= hu
12
−2u
11
+· · ·+b−3, −u
13
+4u
12
+· · ·+a−7, u
14
−2u
13
+· · ·−6u
2
+1i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
u
a
7
=
1
−u
2
a
2
=
u
13
− 4u
12
+ ··· − 11u + 7
−u
12
+ 2u
11
+ ··· − 3u + 3
a
11
=
u
−u
3
+ u
a
1
=
u
13
− 3u
12
+ ··· − 8u + 4
−u
12
+ 2u
11
+ ··· − 3u + 3
a
3
=
u
13
− 4u
12
+ ··· − 6u + 6
u
7
− u
6
− 3u
5
+ 3u
4
+ 2u
3
− 3u
2
+ u + 1
a
5
=
4u
13
− 9u
12
+ ··· − 9u + 3
u
13
− 2u
12
+ ··· − 3u − 1
a
4
=
5u
13
− 11u
12
+ ··· − 11u + 3
2u
13
− 4u
12
+ ··· − 4u − 1
a
9
=
−u
13
+ 3u
12
+ ··· + 10u − 5
u
12
− 2u
11
+ ··· + 4u − 4
a
8
=
−2u
13
+ 3u
12
+ ··· + 5u + 1
u
12
− u
11
− 6u
10
+ 6u
9
+ 14u
8
− 15u
7
− 15u
6
+ 20u
5
+ 6u
4
− 14u
3
+ 4u
a
8
=
−2u
13
+ 3u
12
+ ··· + 5u + 1
u
12
− u
11
− 6u
10
+ 6u
9
+ 14u
8
− 15u
7
− 15u
6
+ 20u
5
+ 6u
4
− 14u
3
+ 4u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −7u
13
+ 11u
12
+ 40u
11
−69u
10
−84u
9
+ 177u
8
+ 62u
7
−230u
6
+
27u
5
+ 152u
4
− 64u
3
− 43u
2
+ 19u
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
14
− u
13
+ ··· − u + 1
c
2
u
14
+ 7u
13
+ ··· + 7u + 1
c
3
u
14
− 7u
12
+ ··· − 6u
2
+ 1
c
4
u
14
+ 3u
11
+ 2u
10
+ u
8
+ 3u
6
− u
5
− u
4
− 2u
3
+ u
2
+ 1
c
5
u
14
+ u
13
+ ··· + u + 1
c
6
u
14
− 2u
13
+ ··· − 6u
2
+ 1
c
7
, c
8
u
14
− 7u
12
+ ··· − 6u
2
+ 1
c
9
u
14
+ u
12
− 2u
11
− u
10
− u
9
+ 3u
8
+ u
6
+ 2u
4
+ 3u
3
+ 1
c
10
u
14
+ 2u
13
+ ··· − 6u
2
+ 1
c
11
u
14
− 2u
12
+ 3u
10
− u
9
+ u
8
+ 7u
7
+ 2u
6
− 2u
5
+ 2u
4
+ 2u
3
+ u
2
+ 2u + 1
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
14
+ 7y
13
+ ··· + 7y + 1
c
2
y
14
+ 7y
13
+ ··· + 3y + 1
c
3
, c
7
, c
8
y
14
− 14y
13
+ ··· − 12y + 1
c
4
y
14
+ 4y
12
+ ··· + 2y + 1
c
6
, c
10
y
14
− 14y
13
+ ··· − 12y + 1
c
9
y
14
+ 2y
13
+ ··· + 4y
2
+ 1
c
11
y
14
− 4y
13
+ ··· − 2y + 1
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.596231 + 0.643046I
a = −0.81845 + 2.50573I
b = −0.203371 + 0.690149I
−5.26561 + 3.25287I −6.82202 − 1.57098I
u = 0.596231 − 0.643046I
a = −0.81845 − 2.50573I
b = −0.203371 − 0.690149I
−5.26561 − 3.25287I −6.82202 + 1.57098I
u = −1.086550 + 0.327347I
a = −1.11518 − 1.19569I
b = 0.646482 − 1.025240I
2.26991 − 4.07125I 0.78077 + 2.79812I
u = −1.086550 − 0.327347I
a = −1.11518 + 1.19569I
b = 0.646482 + 1.025240I
2.26991 + 4.07125I 0.78077 − 2.79812I
u = 1.250560 + 0.436225I
a = 0.826732 − 0.714819I
b = −0.790207 − 1.045030I
−0.94118 + 5.35545I 0.99788 − 4.06151I
u = 1.250560 − 0.436225I
a = 0.826732 + 0.714819I
b = −0.790207 + 1.045030I
−0.94118 − 5.35545I 0.99788 + 4.06151I
u = 0.548029 + 0.362087I
a = −0.82146 − 1.24943I
b = −0.324639 − 1.160970I
−7.21557 + 5.51825I −2.78614 − 6.97305I
u = 0.548029 − 0.362087I
a = −0.82146 + 1.24943I
b = −0.324639 + 1.160970I
−7.21557 − 5.51825I −2.78614 + 6.97305I
u = −1.337530 + 0.185973I
a = −0.156832 − 0.018857I
b = 0.586268 + 0.660807I
3.49025 + 0.87643I 1.45603 − 4.57034I
u = −1.337530 − 0.185973I
a = −0.156832 + 0.018857I
b = 0.586268 − 0.660807I
3.49025 − 0.87643I 1.45603 + 4.57034I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.534535 + 0.096454I
a = 2.05204 + 2.53274I
b = 0.253909 + 0.916694I
−1.18133 + 1.08400I −6.90405 − 2.11871I
u = −0.534535 − 0.096454I
a = 2.05204 − 2.53274I
b = 0.253909 − 0.916694I
−1.18133 − 1.08400I −6.90405 + 2.11871I
u = 1.56380 + 0.18585I
a = 0.533141 + 0.309692I
b = −0.668443 + 0.547497I
0.618868 − 0.444831I 2.27753 + 0.29534I
u = 1.56380 − 0.18585I
a = 0.533141 − 0.309692I
b = −0.668443 − 0.547497I
0.618868 + 0.444831I 2.27753 − 0.29534I
16
III. I
u
3
=
h−u
5
+2u
4
+u
3
−2u
2
+b−u, −u
5
+2u
4
+2u
3
−4u
2
+a−u, u
10
−4u
9
+· · ·+u+1i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
u
a
7
=
1
−u
2
a
2
=
u
5
− 2u
4
− 2u
3
+ 4u
2
+ u
u
5
− 2u
4
− u
3
+ 2u
2
+ u
a
11
=
u
−u
3
+ u
a
1
=
−u
3
+ 2u
2
u
5
− 2u
4
− u
3
+ 2u
2
+ u
a
3
=
u
8
− 4u
7
+ 3u
6
+ 5u
5
− 5u
4
− 3u
3
+ 2u
2
+ u
u
5
− 2u
4
− u
3
+ 2u
2
+ u + 1
a
5
=
−u
8
+ 4u
7
− 3u
6
− 5u
5
+ 5u
4
+ 3u
3
− 2u
2
− u
−u
5
+ 2u
4
+ u
3
− 2u
2
− u − 1
a
4
=
u
9
− 4u
8
+ 4u
7
+ 2u
6
− 5u
5
+ 2u
4
+ 2u
3
− 2u
2
− u
−u
9
+ 2u
8
+ 3u
7
− 4u
6
− 7u
5
+ 2u
4
+ 6u
3
+ 2u
2
+ u
a
9
=
−u
2
+ 2u − 1
u
4
− 2u
3
+ 2u
a
8
=
u
−u
3
+ u
a
8
=
u
−u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
5
− 8u
4
− 4u
3
+ 8u
2
+ 4u + 2
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
(u
2
− u + 1)
5
c
2
(u
2
+ u + 1)
5
c
3
, c
4
, c
7
c
8
u
10
− 2u
8
− u
6
− u
5
+ 2u
4
+ u
3
+ u
2
+ u + 1
c
6
, c
10
u
10
+ 4u
9
+ 2u
8
− 8u
7
− 5u
6
+ 7u
5
− 3u
3
+ 3u
2
− u + 1
c
9
u
10
+ 2u
8
+ 4u
7
− 3u
6
+ u
5
+ 12u
4
+ u
3
− 5u
2
+ 3u + 3
c
11
u
10
− 4u
9
+ 2u
8
+ 8u
7
− 5u
6
− 7u
5
+ 3u
3
+ 3u
2
+ u + 1
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
(y
2
+ y + 1)
5
c
3
, c
4
, c
7
c
8
y
10
− 4y
9
+ 2y
8
+ 8y
7
− 5y
6
− 7y
5
+ 3y
3
+ 3y
2
+ y + 1
c
6
, c
10
, c
11
y
10
− 12y
9
+ 58y
8
− 140y
7
+ 167y
6
− 75y
5
− 5y
3
+ 3y
2
+ 5y + 1
c
9
y
10
+ 4y
9
+ ··· − 39y + 9
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.976073 + 0.147815I
a = 2.22768 − 0.13034I
b = −0.500000 + 0.866025I
− 2.02988I 0. + 3.46410I
u = −0.976073 − 0.147815I
a = 2.22768 + 0.13034I
b = −0.500000 − 0.866025I
2.02988I 0. − 3.46410I
u = −0.427474 + 0.537706I
a = −1.00546 − 1.92475I
b = −0.500000 − 0.866025I
2.02988I 0. − 3.46410I
u = −0.427474 − 0.537706I
a = −1.00546 + 1.92475I
b = −0.500000 + 0.866025I
− 2.02988I 0. + 3.46410I
u = 0.064556 + 0.510596I
a = −0.96286 + 1.12461I
b = −0.500000 + 0.866025I
− 2.02988I 0. + 3.46410I
u = 0.064556 − 0.510596I
a = −0.96286 − 1.12461I
b = −0.500000 − 0.866025I
2.02988I 0. − 3.46410I
u = 1.52905 + 0.35576I
a = 0.92852 − 1.14039I
b = −0.500000 − 0.866025I
2.02988I 0. − 3.46410I
u = 1.52905 − 0.35576I
a = 0.92852 + 1.14039I
b = −0.500000 + 0.866025I
− 2.02988I 0. + 3.46410I
u = 1.80994 + 0.23506I
a = 0.312112 + 0.270713I
b = −0.500000 + 0.866025I
− 2.02988I 0. + 3.46410I
u = 1.80994 − 0.23506I
a = 0.312112 − 0.270713I
b = −0.500000 − 0.866025I
2.02988I 0. − 3.46410I
20
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
2
− u + 1)
5
)(u
14
− u
13
+ ··· − u + 1)(u
66
+ 5u
65
+ ··· + 34u + 4)
c
2
((u
2
+ u + 1)
5
)(u
14
+ 7u
13
+ ··· + 7u + 1)(u
66
+ 27u
65
+ ··· − 12u + 16)
c
3
(u
10
− 2u
8
+ ··· + u + 1)(u
14
− 7u
12
+ ··· − 6u
2
+ 1)
· (u
66
− u
65
+ ··· − 56u + 11)
c
4
(u
10
− 2u
8
− u
6
− u
5
+ 2u
4
+ u
3
+ u
2
+ u + 1)
· (u
14
+ 3u
11
+ 2u
10
+ u
8
+ 3u
6
− u
5
− u
4
− 2u
3
+ u
2
+ 1)
· (u
66
− 3u
65
+ ··· − 250u + 71)
c
5
((u
2
− u + 1)
5
)(u
14
+ u
13
+ ··· + u + 1)(u
66
+ 5u
65
+ ··· + 34u + 4)
c
6
(u
10
+ 4u
9
+ 2u
8
− 8u
7
− 5u
6
+ 7u
5
− 3u
3
+ 3u
2
− u + 1)
· (u
14
− 2u
13
+ ··· − 6u
2
+ 1)(u
66
− 3u
65
+ ··· + 698u + 391)
c
7
, c
8
(u
10
− 2u
8
+ ··· + u + 1)(u
14
− 7u
12
+ ··· − 6u
2
+ 1)
· (u
66
− u
65
+ ··· − 56u + 11)
c
9
(u
10
+ 2u
8
+ 4u
7
− 3u
6
+ u
5
+ 12u
4
+ u
3
− 5u
2
+ 3u + 3)
· (u
14
+ u
12
− 2u
11
− u
10
− u
9
+ 3u
8
+ u
6
+ 2u
4
+ 3u
3
+ 1)
· (u
66
+ u
65
+ ··· − 470u + 241)
c
10
(u
10
+ 4u
9
+ 2u
8
− 8u
7
− 5u
6
+ 7u
5
− 3u
3
+ 3u
2
− u + 1)
· (u
14
+ 2u
13
+ ··· − 6u
2
+ 1)(u
66
− 3u
65
+ ··· + 698u + 391)
c
11
(u
10
− 4u
9
+ 2u
8
+ 8u
7
− 5u
6
− 7u
5
+ 3u
3
+ 3u
2
+ u + 1)
· (u
14
− 2u
12
+ 3u
10
− u
9
+ u
8
+ 7u
7
+ 2u
6
− 2u
5
+ 2u
4
+ 2u
3
+ u
2
+ 2u + 1)
· (u
66
− 7u
65
+ ··· − 102u − 67)
21
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
((y
2
+ y + 1)
5
)(y
14
+ 7y
13
+ ··· + 7y + 1)(y
66
+ 27y
65
+ ··· − 12y + 16)
c
2
((y
2
+ y + 1)
5
)(y
14
+ 7y
13
+ ··· + 3y + 1)
· (y
66
+ 27y
65
+ ··· − 164976y + 256)
c
3
, c
7
, c
8
(y
10
− 4y
9
+ 2y
8
+ 8y
7
− 5y
6
− 7y
5
+ 3y
3
+ 3y
2
+ y + 1)
· (y
14
− 14y
13
+ ··· − 12y + 1)(y
66
− 69y
65
+ ··· + 3574y + 121)
c
4
(y
10
− 4y
9
+ 2y
8
+ 8y
7
− 5y
6
− 7y
5
+ 3y
3
+ 3y
2
+ y + 1)
· (y
14
+ 4y
12
+ ··· + 2y + 1)(y
66
+ 13y
65
+ ··· + 99380y + 5041)
c
6
, c
10
(y
10
− 12y
9
+ 58y
8
− 140y
7
+ 167y
6
− 75y
5
− 5y
3
+ 3y
2
+ 5y + 1)
· (y
14
− 14y
13
+ ··· − 12y + 1)
· (y
66
− 41y
65
+ ··· − 3193706y + 152881)
c
9
(y
10
+ 4y
9
+ ··· − 39y + 9)(y
14
+ 2y
13
+ ··· + 4y
2
+ 1)
· (y
66
− 21y
65
+ ··· − 54610y + 58081)
c
11
(y
10
− 12y
9
+ 58y
8
− 140y
7
+ 167y
6
− 75y
5
− 5y
3
+ 3y
2
+ 5y + 1)
· (y
14
− 4y
13
+ ··· − 2y + 1)(y
66
− 3y
65
+ ··· − 228020y + 4489)
22
