12n
0123
(K12n
0123
)
A knot diagram
1
Linearized knot diagam
3 5 8 2 10 9 3 11 1 12 8 6
Solving Sequence
3,8 7,12
11 9 6 1 10 5 2 4
c
7
c
11
c
8
c
6
c
12
c
10
c
5
c
2
c
4
c
1
, c
3
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h2.83838 × 10
326
u
84
+ 8.42548 × 10
326
u
83
+ ··· + 2.68317 × 10
328
b + 9.17623 × 10
328
,
6.23802 × 10
326
u
84
+ 1.74819 × 10
327
u
83
+ ··· + 5.36635 × 10
328
a − 1.85693 × 10
330
,
u
85
+ 3u
84
+ ··· + 2560u − 512i
I
u
2
= h2au + b + a + 2u + 1, a
2
+ 2au − a − 6u + 11, u
2
− u − 1i
I
v
1
= ha, 59103v
8
+ 362866v
7
+ ··· + 178147b + 551223, v
9
+ 5v
8
+ 10v
7
− v
5
+ 37v
4
+ 7v
3
+ 12v
2
+ v + 1i
* 3 irreducible components of dim
C
= 0, with total 98 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
= h2.84 × 10
326
u
84
+ 8.43 × 10
326
u
83
+ · · · + 2.68 × 10
328
b + 9.18 ×
10
328
, 6.24 × 10
326
u
84
+ 1.75 × 10
327
u
83
+ · · · + 5.37 × 10
328
a − 1.86 ×
10
330
, u
85
+ 3u
84
+ · · · + 2560u − 512i
(i) Arc colorings
a
3
=
0
u
a
8
=
1
0
a
7
=
1
−u
2
a
12
=
−0.0116243u
84
− 0.0325769u
83
+ ··· − 117.830u + 34.6031
−0.0105784u
84
− 0.0314011u
83
+ ··· + 28.9627u − 3.41991
a
11
=
−0.0222028u
84
− 0.0639781u
83
+ ··· − 88.8676u + 31.1832
−0.0105784u
84
− 0.0314011u
83
+ ··· + 28.9627u − 3.41991
a
9
=
0.0236744u
84
+ 0.0791102u
83
+ ··· − 302.193u + 68.4988
−0.00106759u
84
− 0.00464786u
83
+ ··· − 28.9121u + 6.35083
a
6
=
−0.105341u
84
− 0.352596u
83
+ ··· + 284.616u − 67.6484
−0.000678367u
84
+ 0.00363661u
83
+ ··· + 26.9996u − 3.21130
a
1
=
−0.00736711u
84
− 0.0243363u
83
+ ··· − 14.6299u + 2.91925
−0.00493845u
84
− 0.0150218u
83
+ ··· − 12.8311u + 5.37028
a
10
=
0.0322107u
84
+ 0.101321u
83
+ ··· − 331.012u + 70.6299
−0.00385472u
84
− 0.0102384u
83
+ ··· − 6.16248u + 2.58623
a
5
=
−0.0119640u
84
− 0.0392482u
83
+ ··· − 25.5114u + 7.14521
0.00459690u
84
+ 0.0149118u
83
+ ··· + 10.8814u − 4.22596
a
2
=
−0.00736711u
84
− 0.0243363u
83
+ ··· − 14.6299u + 2.91925
−0.00459690u
84
− 0.0149118u
83
+ ··· − 10.8814u + 4.22596
a
4
=
u
−u
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.381801u
84
+ 1.38285u
83
+ ··· − 1273.67u + 380.918
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
85
+ 38u
84
+ ··· − 213u + 1
c
2
, c
4
u
85
− 12u
84
+ ··· − u + 1
c
3
, c
7
u
85
− 3u
84
+ ··· + 2560u + 512
c
5
u
85
− u
84
+ ··· + 28266u + 22877
c
6
u
85
+ 3u
84
+ ··· + 112806u + 16279
c
8
, c
11
u
85
− 4u
84
+ ··· + 7u + 1
c
9
u
85
− 8u
84
+ ··· + 192u + 16
c
10
u
85
− 38u
84
+ ··· + 27u + 1
c
12
u
85
− 4u
84
+ ··· − 5u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
85
+ 30y
84
+ ··· + 27491y −1
c
2
, c
4
y
85
− 38y
84
+ ··· − 213y −1
c
3
, c
7
y
85
+ 51y
84
+ ··· − 3932160y −262144
c
5
y
85
− 57y
84
+ ··· − 21266860578y −523357129
c
6
y
85
− 81y
84
+ ··· + 5075593862y −265005841
c
8
, c
11
y
85
+ 38y
84
+ ··· + 27y −1
c
9
y
85
+ 20y
84
+ ··· + 12160y −256
c
10
y
85
+ 22y
84
+ ··· + 1735y −1
c
12
y
85
− 22y
84
+ ··· + 31y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.079250 + 0.084385I
a = 1.341430 + 0.023595I
b = −0.450037 − 0.371688I
−1.013250 + 0.170939I 0
u = 1.079250 − 0.084385I
a = 1.341430 − 0.023595I
b = −0.450037 + 0.371688I
−1.013250 − 0.170939I 0
u = −1.111280 + 0.071551I
a = 0.715294 + 0.590043I
b = −0.135819 − 1.144130I
3.33969 + 2.83227I 0
u = −1.111280 − 0.071551I
a = 0.715294 − 0.590043I
b = −0.135819 + 1.144130I
3.33969 − 2.83227I 0
u = −0.129045 + 1.113980I
a = −1.009610 − 0.472785I
b = 0.956465 + 0.931163I
0.094102 − 1.056740I 0
u = −0.129045 − 1.113980I
a = −1.009610 + 0.472785I
b = 0.956465 − 0.931163I
0.094102 + 1.056740I 0
u = −0.210154 + 1.114290I
a = 0.203823 − 0.103598I
b = −0.688869 − 0.426448I
−3.15620 + 2.51605I 0
u = −0.210154 − 1.114290I
a = 0.203823 + 0.103598I
b = −0.688869 + 0.426448I
−3.15620 − 2.51605I 0
u = 0.433540 + 1.050740I
a = 1.62226 − 0.79944I
b = −0.239254 − 1.010500I
0.982642 + 0.642938I 0
u = 0.433540 − 1.050740I
a = 1.62226 + 0.79944I
b = −0.239254 + 1.010500I
0.982642 − 0.642938I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.257695 + 1.109990I
a = −0.787822 − 0.341976I
b = 1.098020 + 0.136398I
−1.09681 + 2.37421I 0
u = −0.257695 − 1.109990I
a = −0.787822 + 0.341976I
b = 1.098020 − 0.136398I
−1.09681 − 2.37421I 0
u = 0.262541 + 1.168940I
a = −0.218677 − 0.885410I
b = 0.465838 + 0.484615I
2.10819 − 3.90878I 0
u = 0.262541 − 1.168940I
a = −0.218677 + 0.885410I
b = 0.465838 − 0.484615I
2.10819 + 3.90878I 0
u = 0.218930 + 1.186920I
a = −0.72368 + 1.66080I
b = 0.563973 − 0.682913I
2.18193 − 1.17088I 0
u = 0.218930 − 1.186920I
a = −0.72368 − 1.66080I
b = 0.563973 + 0.682913I
2.18193 + 1.17088I 0
u = −0.758522 + 0.188313I
a = −0.71807 − 1.77432I
b = 0.574022 + 1.099820I
−1.13123 − 4.17645I −11.8176 + 9.1818I
u = −0.758522 − 0.188313I
a = −0.71807 + 1.77432I
b = 0.574022 − 1.099820I
−1.13123 + 4.17645I −11.8176 − 9.1818I
u = −0.341078 + 1.170670I
a = −1.299470 + 0.134652I
b = 1.049370 − 0.766403I
−0.41725 + 6.01567I 0
u = −0.341078 − 1.170670I
a = −1.299470 − 0.134652I
b = 1.049370 + 0.766403I
−0.41725 − 6.01567I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.041071 + 1.235810I
a = −0.640152 + 0.371475I
b = 0.533714 + 1.299760I
3.32593 − 3.12666I 0
u = 0.041071 − 1.235810I
a = −0.640152 − 0.371475I
b = 0.533714 − 1.299760I
3.32593 + 3.12666I 0
u = −1.206060 + 0.339502I
a = 1.52169 − 0.13928I
b = −0.804789 + 0.394562I
−1.81678 − 5.27916I 0
u = −1.206060 − 0.339502I
a = 1.52169 + 0.13928I
b = −0.804789 − 0.394562I
−1.81678 + 5.27916I 0
u = −0.573407 + 0.367957I
a = 0.51933 − 3.19375I
b = 0.732207 + 0.631342I
−3.03530 − 2.32112I −18.2811 + 2.9821I
u = −0.573407 − 0.367957I
a = 0.51933 + 3.19375I
b = 0.732207 − 0.631342I
−3.03530 + 2.32112I −18.2811 − 2.9821I
u = 0.091692 + 1.317030I
a = −1.23007 − 1.63631I
b = 0.448877 − 0.989908I
3.52281 − 0.13174I 0
u = 0.091692 − 1.317030I
a = −1.23007 + 1.63631I
b = 0.448877 + 0.989908I
3.52281 + 0.13174I 0
u = −0.413209 + 1.277050I
a = −1.317440 − 0.293401I
b = 0.66453 − 1.29582I
2.39077 + 8.65291I 0
u = −0.413209 − 1.277050I
a = −1.317440 + 0.293401I
b = 0.66453 + 1.29582I
2.39077 − 8.65291I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.312068 + 1.307370I
a = −2.43711 + 1.16729I
b = 0.529124 + 0.972751I
3.08119 − 5.55867I 0
u = 0.312068 − 1.307370I
a = −2.43711 − 1.16729I
b = 0.529124 − 0.972751I
3.08119 + 5.55867I 0
u = −0.459021 + 0.459779I
a = −1.10908 − 1.88671I
b = 0.649790 − 0.402922I
−3.21369 + 0.63442I −17.2881 − 6.4476I
u = −0.459021 − 0.459779I
a = −1.10908 + 1.88671I
b = 0.649790 + 0.402922I
−3.21369 − 0.63442I −17.2881 + 6.4476I
u = 0.634951 + 0.073211I
a = 1.163640 + 0.016828I
b = 0.104936 − 0.148183I
−0.938890 − 0.000686I −9.17733 + 0.04419I
u = 0.634951 − 0.073211I
a = 1.163640 − 0.016828I
b = 0.104936 + 0.148183I
−0.938890 + 0.000686I −9.17733 − 0.04419I
u = 1.237320 + 0.581154I
a = 0.846750 − 0.577129I
b = −0.365370 + 1.037680I
1.88882 + 2.34511I 0
u = 1.237320 − 0.581154I
a = 0.846750 + 0.577129I
b = −0.365370 − 1.037680I
1.88882 − 2.34511I 0
u = −0.326856 + 1.339410I
a = 0.875245 + 0.373465I
b = −0.659177 − 0.135566I
4.34006 − 0.60753I 0
u = −0.326856 − 1.339410I
a = 0.875245 − 0.373465I
b = −0.659177 + 0.135566I
4.34006 + 0.60753I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.143186 + 1.381320I
a = 0.806814 + 0.741077I
b = −0.570387 + 1.078250I
−1.24862 + 7.38729I 0
u = −0.143186 − 1.381320I
a = 0.806814 − 0.741077I
b = −0.570387 − 1.078250I
−1.24862 − 7.38729I 0
u = 0.607638 + 0.026477I
a = −3.83486 − 6.56337I
b = 0.489160 − 0.868710I
−1.01649 + 2.08350I −108.2002 − 27.5787I
u = 0.607638 − 0.026477I
a = −3.83486 + 6.56337I
b = 0.489160 + 0.868710I
−1.01649 − 2.08350I −108.2002 + 27.5787I
u = 0.573976 + 0.144239I
a = −0.19466 − 6.06422I
b = 0.458798 + 0.876673I
−1.01583 − 1.80194I −34.3945 + 9.4437I
u = 0.573976 − 0.144239I
a = −0.19466 + 6.06422I
b = 0.458798 − 0.876673I
−1.01583 + 1.80194I −34.3945 − 9.4437I
u = 0.581059
a = 1.11628
b = 0.132880
−0.943887 −9.70520
u = 0.64849 + 1.26742I
a = 0.886065 − 0.572978I
b = −0.669667 + 0.411070I
2.43921 − 5.21595I 0
u = 0.64849 − 1.26742I
a = 0.886065 + 0.572978I
b = −0.669667 − 0.411070I
2.43921 + 5.21595I 0
u = −1.40213 + 0.33857I
a = 1.163050 + 0.534355I
b = −0.601473 − 1.118200I
0.33638 − 10.54090I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.40213 − 0.33857I
a = 1.163050 − 0.534355I
b = −0.601473 + 1.118200I
0.33638 + 10.54090I 0
u = −0.056938 + 0.544127I
a = 1.42278 − 0.39423I
b = −0.835208 + 0.748484I
−5.59621 − 1.18326I −2.58478 − 2.54783I
u = −0.056938 − 0.544127I
a = 1.42278 + 0.39423I
b = −0.835208 − 0.748484I
−5.59621 + 1.18326I −2.58478 + 2.54783I
u = −0.188367 + 0.482280I
a = 1.106380 − 0.209517I
b = 0.251302 + 1.017870I
1.59907 − 2.42394I −1.69948 + 4.54557I
u = −0.188367 − 0.482280I
a = 1.106380 + 0.209517I
b = 0.251302 − 1.017870I
1.59907 + 2.42394I −1.69948 − 4.54557I
u = 0.014000 + 0.513349I
a = 1.38502 + 0.50649I
b = −0.752798 − 0.984184I
−4.86894 − 7.11123I 0.90699 + 6.44296I
u = 0.014000 − 0.513349I
a = 1.38502 − 0.50649I
b = −0.752798 + 0.984184I
−4.86894 + 7.11123I 0.90699 − 6.44296I
u = 1.49443 + 0.02360I
a = 1.103380 + 0.416439I
b = −0.508069 − 1.060060I
0.90720 − 4.33616I 0
u = 1.49443 − 0.02360I
a = 1.103380 − 0.416439I
b = −0.508069 + 1.060060I
0.90720 + 4.33616I 0
u = 0.47007 + 1.42149I
a = 0.766976 − 0.387618I
b = −0.930414 + 0.340544I
3.61530 − 5.88108I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.47007 − 1.42149I
a = 0.766976 + 0.387618I
b = −0.930414 − 0.340544I
3.61530 + 5.88108I 0
u = −0.129721 + 0.460651I
a = 0.38178 − 8.17649I
b = 0.586175 − 0.964824I
−2.08258 + 2.71217I −0.93392 − 9.03807I
u = −0.129721 − 0.460651I
a = 0.38178 + 8.17649I
b = 0.586175 + 0.964824I
−2.08258 − 2.71217I −0.93392 + 9.03807I
u = −0.69533 + 1.35551I
a = 0.839067 + 0.683647I
b = −0.987614 − 0.425089I
1.45650 + 12.12210I 0
u = −0.69533 − 1.35551I
a = 0.839067 − 0.683647I
b = −0.987614 + 0.425089I
1.45650 − 12.12210I 0
u = 0.20084 + 1.51437I
a = 0.196514 + 0.358472I
b = −0.152432 + 1.330190I
9.43138 − 2.34122I 0
u = 0.20084 − 1.51437I
a = 0.196514 − 0.358472I
b = −0.152432 − 1.330190I
9.43138 + 2.34122I 0
u = −0.51519 + 1.44160I
a = −0.278437 − 0.202187I
b = −0.053028 − 1.378990I
8.12807 + 8.74738I 0
u = −0.51519 − 1.44160I
a = −0.278437 + 0.202187I
b = −0.053028 + 1.378990I
8.12807 − 8.74738I 0
u = −0.67286 + 1.43031I
a = 1.382550 + 0.212615I
b = −0.465319 + 1.120770I
7.12915 + 3.60494I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.67286 − 1.43031I
a = 1.382550 − 0.212615I
b = −0.465319 − 1.120770I
7.12915 − 3.60494I 0
u = 0.83986 + 1.36381I
a = 1.58928 − 0.15583I
b = −0.569092 − 1.079590I
4.36978 − 10.04380I 0
u = 0.83986 − 1.36381I
a = 1.58928 + 0.15583I
b = −0.569092 + 1.079590I
4.36978 + 10.04380I 0
u = −0.76822 + 1.41143I
a = 1.68389 + 0.29933I
b = −0.675369 + 1.176190I
3.7759 + 18.1504I 0
u = −0.76822 − 1.41143I
a = 1.68389 − 0.29933I
b = −0.675369 − 1.176190I
3.7759 − 18.1504I 0
u = 0.56721 + 1.54481I
a = 1.362350 − 0.354229I
b = −0.623855 − 1.176920I
6.15588 − 11.53790I 0
u = 0.56721 − 1.54481I
a = 1.362350 + 0.354229I
b = −0.623855 + 1.176920I
6.15588 + 11.53790I 0
u = −1.64677 + 0.04569I
a = 1.117370 − 0.194170I
b = −0.479694 + 0.856026I
−8.84126 + 1.96210I 0
u = −1.64677 − 0.04569I
a = 1.117370 + 0.194170I
b = −0.479694 − 0.856026I
−8.84126 − 1.96210I 0
u = 0.49039 + 1.61919I
a = 0.298433 + 0.301314I
b = −0.239444 + 1.049820I
6.55517 − 3.11546I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.49039 − 1.61919I
a = 0.298433 − 0.301314I
b = −0.239444 − 1.049820I
6.55517 + 3.11546I 0
u = 0.225615 + 0.193490I
a = 0.929610 + 0.057774I
b = 0.607173 + 0.840075I
−0.60683 − 2.35987I −1.70647 + 4.72969I
u = 0.225615 − 0.193490I
a = 0.929610 − 0.057774I
b = 0.607173 − 0.840075I
−0.60683 + 2.35987I −1.70647 − 4.72969I
u = −0.22938 + 1.72989I
a = 0.510244 − 0.261796I
b = −0.372735 − 1.103380I
7.76106 − 3.97762I 0
u = −0.22938 − 1.72989I
a = 0.510244 + 0.261796I
b = −0.372735 + 1.103380I
7.76106 + 3.97762I 0
13
II. I
u
2
= h2au + b + a + 2u + 1, a
2
+ 2au − a − 6u + 11, u
2
− u − 1i
(i) Arc colorings
a
3
=
0
u
a
8
=
1
0
a
7
=
1
−u − 1
a
12
=
a
−2au − a − 2u − 1
a
11
=
−2au − 2u − 1
−2au − a − 2u − 1
a
9
=
a + 2u − 2
−2au − a − 2u − 2
a
6
=
au − 2a + u − 1
au − 1
a
1
=
u
−3u − 2
a
10
=
a + 2u − 2
−2au − a − 2u − 2
a
5
=
1
−u − 1
a
2
=
u
−u − 1
a
4
=
−u
u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −92au − 67a − 113u − 94
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
12
(u
2
− 3u + 1)
2
c
2
, c
3
(u
2
+ u − 1)
2
c
4
, c
7
(u
2
− u − 1)
2
c
5
, c
6
u
4
+ 3u
3
+ 8u
2
+ 3u + 1
c
8
(u
2
− u + 1)
2
c
9
u
4
c
10
, c
11
(u
2
+ u + 1)
2
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
12
(y
2
− 7y + 1)
2
c
2
, c
3
, c
4
c
7
(y
2
− 3y + 1)
2
c
5
, c
6
y
4
+ 7y
3
+ 48y
2
+ 7y + 1
c
8
, c
10
, c
11
(y
2
+ y + 1)
2
c
9
y
4
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.618034
a = 1.11803 + 3.66854I
b = 0.500000 + 0.866025I
−0.98696 − 2.02988I −35.5000 − 37.2022I
u = −0.618034
a = 1.11803 − 3.66854I
b = 0.500000 − 0.866025I
−0.98696 + 2.02988I −35.5000 + 37.2022I
u = 1.61803
a = −1.118030 + 0.204441I
b = 0.500000 − 0.866025I
−8.88264 + 2.02988I −35.5000 − 44.1304I
u = 1.61803
a = −1.118030 − 0.204441I
b = 0.500000 + 0.866025I
−8.88264 − 2.02988I −35.5000 + 44.1304I
17
III.
I
v
1
= ha, 59103v
8
+ 362866v
7
+ · · · + 178147b + 551223, v
9
+ 5v
8
+ · · · + v + 1i
(i) Arc colorings
a
3
=
v
0
a
8
=
1
0
a
7
=
1
0
a
12
=
0
−0.331765v
8
− 2.03689v
7
+ ··· − 3.64641v −3.09420
a
11
=
−0.331765v
8
− 2.03689v
7
+ ··· − 3.64641v −3.09420
−0.331765v
8
− 2.03689v
7
+ ··· − 3.64641v −3.09420
a
9
=
0.727601v
8
+ 4.15347v
7
+ ··· + 6.59548v + 4.24127
0.727601v
8
+ 4.15347v
7
+ ··· + 6.59548v + 3.24127
a
6
=
0.704452v
8
+ 3.76495v
7
+ ··· + 3.53747v + 0.954251
−0.0231494v
8
− 0.388527v
7
+ ··· − 3.05801v −3.28702
a
1
=
−1.20067v
8
− 5.89924v
7
+ ··· − 2.68791v + 0.492840
v
8
+ 5v
7
+ 10v
6
− v
4
+ 37v
3
+ 7v
2
+ 12v + 1
a
10
=
−0.331765v
8
− 2.03689v
7
+ ··· − 3.64641v −3.09420
−1.07440v
8
− 6.00362v
7
+ ··· − 8.53879v −3.73749
a
5
=
1.20067v
8
+ 5.89924v
7
+ ··· + 2.68791v −0.492840
−v
8
− 5v
7
− 10v
6
+ v
4
− 37v
3
− 7v
2
− 12v −1
a
2
=
−1.20067v
8
− 5.89924v
7
+ ··· − 1.68791v + 0.492840
v
8
+ 5v
7
+ 10v
6
− v
4
+ 37v
3
+ 7v
2
+ 12v + 1
a
4
=
v
0
(ii) Obstruction class = 1
(iii) Cusp Shapes =
279551
178147
v
8
+
1437368
178147
v
7
+
2978743
178147
v
6
+
272298
178147
v
5
−
682691
178147
v
4
+
9851898
178147
v
3
+
3817557
178147
v
2
+
3775595
178147
v −
3107095
178147
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
9
c
3
, c
7
u
9
c
4
(u + 1)
9
c
5
, c
9
u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1
c
6
, c
10
u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1
c
8
u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1
c
11
u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1
c
12
u
9
+ 5u
8
+ 12u
7
+ 15u
6
+ 9u
5
− u
4
− 4u
3
− 2u
2
+ u + 1
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
9
c
3
, c
7
y
9
c
5
, c
9
y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1
c
6
, c
10
y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y −1
c
8
, c
11
y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y −1
c
12
y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y −1
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 0.939568 + 0.981640I
a = 0
b = 0.140343 + 0.966856I
0.13850 − 2.09337I −7.58955 + 5.46639I
v = 0.939568 − 0.981640I
a = 0
b = 0.140343 − 0.966856I
0.13850 + 2.09337I −7.58955 − 5.46639I
v = −0.119081 + 0.409451I
a = 0
b = −0.796005 + 0.733148I
−6.01628 − 1.33617I −20.0794 + 3.5537I
v = −0.119081 − 0.409451I
a = 0
b = −0.796005 − 0.733148I
−6.01628 + 1.33617I −20.0794 − 3.5537I
v = 0.016164 + 0.378317I
a = 0
b = −0.728966 − 0.986295I
−5.24306 − 7.08493I −20.6685 + 5.3307I
v = 0.016164 − 0.378317I
a = 0
b = −0.728966 + 0.986295I
−5.24306 + 7.08493I −20.6685 − 5.3307I
v = −2.14893
a = 0
b = 0.512358
−2.84338 −11.8180
v = −2.26219 + 2.13290I
a = 0
b = 0.628449 + 0.875112I
−2.26187 − 2.45442I −9.75362 − 6.63381I
v = −2.26219 − 2.13290I
a = 0
b = 0.628449 − 0.875112I
−2.26187 + 2.45442I −9.75362 + 6.63381I
21
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
9
)(u
2
− 3u + 1)
2
(u
85
+ 38u
84
+ ··· − 213u + 1)
c
2
((u − 1)
9
)(u
2
+ u − 1)
2
(u
85
− 12u
84
+ ··· − u + 1)
c
3
u
9
(u
2
+ u − 1)
2
(u
85
− 3u
84
+ ··· + 2560u + 512)
c
4
((u + 1)
9
)(u
2
− u − 1)
2
(u
85
− 12u
84
+ ··· − u + 1)
c
5
(u
4
+ 3u
3
+ 8u
2
+ 3u + 1)(u
9
+ u
8
+ ··· − u − 1)
· (u
85
− u
84
+ ··· + 28266u + 22877)
c
6
(u
4
+ 3u
3
+ 8u
2
+ 3u + 1)
· (u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1)
· (u
85
+ 3u
84
+ ··· + 112806u + 16279)
c
7
u
9
(u
2
− u − 1)
2
(u
85
− 3u
84
+ ··· + 2560u + 512)
c
8
(u
2
− u + 1)
2
(u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1)
· (u
85
− 4u
84
+ ··· + 7u + 1)
c
9
u
4
(u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1)
· (u
85
− 8u
84
+ ··· + 192u + 16)
c
10
(u
2
+ u + 1)
2
· (u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1)
· (u
85
− 38u
84
+ ··· + 27u + 1)
c
11
(u
2
+ u + 1)
2
(u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1)
· (u
85
− 4u
84
+ ··· + 7u + 1)
c
12
((u
2
− 3u + 1)
2
)(u
9
+ 5u
8
+ ··· + u + 1)
· (u
85
− 4u
84
+ ··· − 5u + 1)
22
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y −1)
9
)(y
2
− 7y + 1)
2
(y
85
+ 30y
84
+ ··· + 27491y −1)
c
2
, c
4
((y −1)
9
)(y
2
− 3y + 1)
2
(y
85
− 38y
84
+ ··· − 213y −1)
c
3
, c
7
y
9
(y
2
− 3y + 1)
2
(y
85
+ 51y
84
+ ··· − 3932160y −262144)
c
5
(y
4
+ 7y
3
+ 48y
2
+ 7y + 1)
· (y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1)
· (y
85
− 57y
84
+ ··· − 21266860578y −523357129)
c
6
(y
4
+ 7y
3
+ 48y
2
+ 7y + 1)
· (y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y −1)
· (y
85
− 81y
84
+ ··· + 5075593862y −265005841)
c
8
, c
11
(y
2
+ y + 1)
2
· (y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y −1)
· (y
85
+ 38y
84
+ ··· + 27y −1)
c
9
y
4
(y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1)
· (y
85
+ 20y
84
+ ··· + 12160y −256)
c
10
((y
2
+ y + 1)
2
)(y
9
+ 7y
8
+ ··· + 13y −1)
· (y
85
+ 22y
84
+ ··· + 1735y −1)
c
12
(y
2
− 7y + 1)
2
(y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y −1)
· (y
85
− 22y
84
+ ··· + 31y −1)
23
