12a
1066
(K12a
1066
)
A knot diagram
1
Linearized knot diagam
4 7 9 1 10 11 3 12 2 6 8 5
Solving Sequence
1,5
4
2,9
10 6 3 12 8 7 11
c
4
c
1
c
9
c
5
c
3
c
12
c
8
c
7
c
11
c
2
, c
6
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−6.17416 × 10
167
u
107
+ 1.20918 × 10
168
u
106
+ ··· + 4.51045 × 10
167
b + 1.01541 × 10
170
,
− 1.07213 × 10
170
u
107
+ 1.67093 × 10
170
u
106
+ ··· + 7.06637 × 10
168
a + 1.11521 × 10
172
,
u
108
− 2u
107
+ ··· − 299u + 47i
I
u
2
= h−u
26
− 3u
25
+ ··· + b − 1, −4u
26
− 10u
25
+ ··· + a + 5, u
27
+ 3u
26
+ ··· + 6u + 1i
* 2 irreducible components of dim
C
= 0, with total 135 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−6.17 × 10
167
u
107
+ 1.21 × 10
168
u
106
+ · · · + 4.51 × 10
167
b + 1.02 ×
10
170
, −1.07 × 10
170
u
107
+ 1.67 × 10
170
u
106
+ · · · + 7.07 × 10
168
a + 1.12 ×
10
172
, u
108
− 2u
107
+ · · · − 299u + 47i
(i) Arc colorings
a
1
=
0
u
a
5
=
1
0
a
4
=
1
−u
2
a
2
=
−u
u
3
+ u
a
9
=
15.1723u
107
− 23.6463u
106
+ ··· + 6660.78u − 1578.19
1.36886u
107
− 2.68085u
106
+ ··· + 921.712u − 225.124
a
10
=
20.0873u
107
− 30.6623u
106
+ ··· + 8396.19u − 2000.20
−3.49659u
107
+ 5.45677u
106
+ ··· − 1424.06u + 329.133
a
6
=
28.1414u
107
− 43.5083u
106
+ ··· + 11918.4u − 2851.74
−8.48372u
107
+ 13.3771u
106
+ ··· − 3599.41u + 861.349
a
3
=
6.47264u
107
− 9.65167u
106
+ ··· + 2937.00u − 738.000
5.66238u
107
− 8.30970u
106
+ ··· + 2515.37u − 615.722
a
12
=
u
u
a
8
=
12.6300u
107
− 19.1931u
106
+ ··· + 5323.74u − 1266.05
−1.17347u
107
+ 1.77231u
106
+ ··· − 415.326u + 87.0247
a
7
=
−0.134410u
107
+ 1.57897u
106
+ ··· − 199.017u + 71.6823
−8.59288u
107
+ 13.8267u
106
+ ··· − 3500.53u + 823.438
a
11
=
−17.2692u
107
+ 25.8300u
106
+ ··· − 7157.94u + 1718.79
11.0079u
107
− 17.3057u
106
+ ··· + 4803.68u − 1152.57
(ii) Obstruction class = −1
(iii) Cusp Shapes = 133.129u
107
− 204.954u
106
+ ··· + 56643.2u − 13565.8
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
12
u
108
− 2u
107
+ ··· − 299u + 47
c
2
, c
7
u
108
+ u
107
+ ··· + u + 1
c
3
u
108
− u
107
+ ··· − 28281u + 2677
c
5
, c
6
, c
10
u
108
− u
107
+ ··· + 575u − 103
c
8
, c
11
u
108
− 38u
106
+ ··· − 2046u + 89
c
9
u
108
+ 3u
107
+ ··· − 492579u + 108211
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
12
y
108
+ 102y
107
+ ··· − 95417y + 2209
c
2
, c
7
y
108
− 55y
107
+ ··· − 31y + 1
c
3
y
108
− 17y
107
+ ··· − 304371863y + 7166329
c
5
, c
6
, c
10
y
108
− 109y
107
+ ··· − 159233y + 10609
c
8
, c
11
y
108
− 76y
107
+ ··· − 3384048y + 7921
c
9
y
108
− 13y
107
+ ··· + 118667308219y + 11709620521
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.960885 + 0.291199I
a = −0.249799 + 0.319511I
b = 1.048870 + 0.325112I
−9.01540 + 5.66019I 0
u = −0.960885 − 0.291199I
a = −0.249799 − 0.319511I
b = 1.048870 − 0.325112I
−9.01540 − 5.66019I 0
u = 0.879867 + 0.356835I
a = 0.463996 + 0.497326I
b = −1.100970 + 0.398607I
−6.4421 − 12.9182I 0
u = 0.879867 − 0.356835I
a = 0.463996 − 0.497326I
b = −1.100970 − 0.398607I
−6.4421 + 12.9182I 0
u = 0.915261
a = −0.232583
b = −1.24242
−0.201236 0
u = −0.756019 + 0.477784I
a = 0.290448 − 0.199196I
b = 0.079001 − 0.498921I
−4.52075 + 2.63427I 0
u = −0.756019 − 0.477784I
a = 0.290448 + 0.199196I
b = 0.079001 + 0.498921I
−4.52075 − 2.63427I 0
u = 0.607423 + 0.651574I
a = −0.371400 + 0.981234I
b = 0.129075 − 0.255913I
0.66299 + 4.02428I 0
u = 0.607423 − 0.651574I
a = −0.371400 − 0.981234I
b = 0.129075 + 0.255913I
0.66299 − 4.02428I 0
u = −0.629163 + 0.913726I
a = 0.046330 + 0.624056I
b = −0.360205 − 0.065003I
−1.34592 + 1.86587I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.629163 − 0.913726I
a = 0.046330 − 0.624056I
b = −0.360205 + 0.065003I
−1.34592 − 1.86587I 0
u = −0.799233 + 0.384923I
a = 0.393026 − 0.191895I
b = −0.780162 − 0.402902I
−2.75619 + 3.19878I 0
u = −0.799233 − 0.384923I
a = 0.393026 + 0.191895I
b = −0.780162 + 0.402902I
−2.75619 − 3.19878I 0
u = 0.680217 + 0.881835I
a = 0.110805 − 0.836202I
b = −0.113620 + 0.333723I
−4.89449 + 7.56548I 0
u = 0.680217 − 0.881835I
a = 0.110805 + 0.836202I
b = −0.113620 − 0.333723I
−4.89449 − 7.56548I 0
u = −0.713702 + 0.467724I
a = 0.685472 − 0.609005I
b = −0.214722 − 0.196909I
−4.55568 + 2.15661I 0
u = −0.713702 − 0.467724I
a = 0.685472 + 0.609005I
b = −0.214722 + 0.196909I
−4.55568 − 2.15661I 0
u = 0.741551 + 0.400490I
a = −0.532830 − 0.358069I
b = 1.077380 − 0.535396I
−0.12708 − 8.61802I 0
u = 0.741551 − 0.400490I
a = −0.532830 + 0.358069I
b = 1.077380 + 0.535396I
−0.12708 + 8.61802I 0
u = −0.871367 + 0.785491I
a = −0.015895 − 0.166669I
b = 0.471406 − 0.061492I
−4.51827 + 3.11099I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.871367 − 0.785491I
a = −0.015895 + 0.166669I
b = 0.471406 + 0.061492I
−4.51827 − 3.11099I 0
u = 0.628602 + 0.514592I
a = 0.140119 + 0.038698I
b = −0.942555 − 0.441495I
−2.52085 + 2.11298I 0
u = 0.628602 − 0.514592I
a = 0.140119 − 0.038698I
b = −0.942555 + 0.441495I
−2.52085 − 2.11298I 0
u = 0.658355 + 0.427540I
a = −0.50852 − 1.37677I
b = 0.167600 + 0.058679I
−2.76561 − 6.36964I 0
u = 0.658355 − 0.427540I
a = −0.50852 + 1.37677I
b = 0.167600 − 0.058679I
−2.76561 + 6.36964I 0
u = −0.015750 + 1.241230I
a = −0.55862 − 1.97146I
b = −0.452918 − 0.930203I
1.21460 + 1.83268I 0
u = −0.015750 − 1.241230I
a = −0.55862 + 1.97146I
b = −0.452918 + 0.930203I
1.21460 − 1.83268I 0
u = −0.000500 + 1.271320I
a = −0.490111 − 0.034234I
b = −0.735300 + 1.164510I
1.49298 − 1.58324I 0
u = −0.000500 − 1.271320I
a = −0.490111 + 0.034234I
b = −0.735300 − 1.164510I
1.49298 + 1.58324I 0
u = −0.139816 + 1.267230I
a = −2.81942 − 0.52924I
b = −2.80141 − 1.17487I
−3.26505 − 2.41999I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.139816 − 1.267230I
a = −2.81942 + 0.52924I
b = −2.80141 + 1.17487I
−3.26505 + 2.41999I 0
u = −0.668451 + 1.095630I
a = 0.175348 − 0.759921I
b = 0.397156 + 0.121065I
−6.66351 + 0.05480I 0
u = −0.668451 − 1.095630I
a = 0.175348 + 0.759921I
b = 0.397156 − 0.121065I
−6.66351 − 0.05480I 0
u = −0.114982 + 1.283170I
a = −2.17584 − 0.88097I
b = −3.09042 − 1.67081I
−2.89688 + 5.98499I 0
u = −0.114982 − 1.283170I
a = −2.17584 + 0.88097I
b = −3.09042 + 1.67081I
−2.89688 − 5.98499I 0
u = 0.145553 + 1.285280I
a = 2.14352 − 0.14424I
b = 2.38908 − 1.20652I
−5.82754 − 2.11330I 0
u = 0.145553 − 1.285280I
a = 2.14352 + 0.14424I
b = 2.38908 + 1.20652I
−5.82754 + 2.11330I 0
u = 0.139891 + 1.303940I
a = 1.46519 − 0.44271I
b = 1.84127 − 1.77249I
−5.64315 − 2.18598I 0
u = 0.139891 − 1.303940I
a = 1.46519 + 0.44271I
b = 1.84127 + 1.77249I
−5.64315 + 2.18598I 0
u = 0.165819 + 1.311960I
a = 0.827554 + 0.648288I
b = 0.961060 − 0.559226I
−5.48555 − 2.56883I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.165819 − 1.311960I
a = 0.827554 − 0.648288I
b = 0.961060 + 0.559226I
−5.48555 + 2.56883I 0
u = −0.184266 + 1.314620I
a = −0.45129 + 1.65609I
b = −0.726779 + 0.686118I
−2.60615 + 7.32685I 0
u = −0.184266 − 1.314620I
a = −0.45129 − 1.65609I
b = −0.726779 − 0.686118I
−2.60615 − 7.32685I 0
u = 0.520457 + 0.421420I
a = 0.333578 + 1.304730I
b = −0.406578 + 0.125920I
3.42972 − 3.43786I 0. + 7.18170I
u = 0.520457 − 0.421420I
a = 0.333578 − 1.304730I
b = −0.406578 − 0.125920I
3.42972 + 3.43786I 0. − 7.18170I
u = −0.163049 + 1.336820I
a = 0.379416 + 0.145811I
b = 0.674270 − 1.070430I
−2.12910 − 1.69175I 0
u = −0.163049 − 1.336820I
a = 0.379416 − 0.145811I
b = 0.674270 + 1.070430I
−2.12910 + 1.69175I 0
u = 0.009254 + 1.382140I
a = −1.375880 + 0.064550I
b = −1.80279 + 0.63837I
3.07345 − 0.98640I 0
u = 0.009254 − 1.382140I
a = −1.375880 − 0.064550I
b = −1.80279 − 0.63837I
3.07345 + 0.98640I 0
u = 0.112915 + 1.384630I
a = 2.07144 + 0.39362I
b = 2.45982 + 0.63773I
8.06931 − 1.78241I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.112915 − 1.384630I
a = 2.07144 − 0.39362I
b = 2.45982 − 0.63773I
8.06931 + 1.78241I 0
u = 0.513028 + 0.316851I
a = 0.791650 + 0.093355I
b = −1.25958 + 0.75068I
−0.92372 − 3.05623I −6.12777 + 7.79662I
u = 0.513028 − 0.316851I
a = 0.791650 − 0.093355I
b = −1.25958 − 0.75068I
−0.92372 + 3.05623I −6.12777 − 7.79662I
u = 0.556846 + 0.210177I
a = 1.38483 − 0.74285I
b = −0.254810 + 0.168021I
−1.199540 + 0.252286I −7.51222 + 1.35320I
u = 0.556846 − 0.210177I
a = 1.38483 + 0.74285I
b = −0.254810 − 0.168021I
−1.199540 − 0.252286I −7.51222 − 1.35320I
u = 0.526995 + 0.270176I
a = 0.196728 − 0.611934I
b = 0.898486 + 0.021517I
3.10533 + 0.11149I 1.82107 + 0.90182I
u = 0.526995 − 0.270176I
a = 0.196728 + 0.611934I
b = 0.898486 − 0.021517I
3.10533 − 0.11149I 1.82107 − 0.90182I
u = 0.409524 + 1.347340I
a = −1.31749 − 0.89229I
b = −1.61711 − 0.28044I
4.06832 − 4.76863I 0
u = 0.409524 − 1.347340I
a = −1.31749 + 0.89229I
b = −1.61711 + 0.28044I
4.06832 + 4.76863I 0
u = −0.18631 + 1.40377I
a = 2.01754 + 0.72985I
b = 2.19802 + 1.28966I
3.95477 + 2.14843I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.18631 − 1.40377I
a = 2.01754 − 0.72985I
b = 2.19802 − 1.28966I
3.95477 − 2.14843I 0
u = −0.15134 + 1.41016I
a = 1.53834 + 0.42907I
b = 2.28622 + 1.00208I
4.08170 + 4.86816I 0
u = −0.15134 − 1.41016I
a = 1.53834 − 0.42907I
b = 2.28622 − 1.00208I
4.08170 − 4.86816I 0
u = 0.26018 + 1.40612I
a = 0.312189 + 0.489836I
b = 0.422413 + 1.152420I
3.95143 − 2.93911I 0
u = 0.26018 − 1.40612I
a = 0.312189 − 0.489836I
b = 0.422413 − 1.152420I
3.95143 + 2.93911I 0
u = 0.27858 + 1.40857I
a = 1.50777 + 0.66400I
b = 2.00793 + 0.23819I
8.27314 − 3.13426I 0
u = 0.27858 − 1.40857I
a = 1.50777 − 0.66400I
b = 2.00793 − 0.23819I
8.27314 + 3.13426I 0
u = 0.20327 + 1.42244I
a = −2.42805 + 0.22092I
b = −2.84613 + 1.06570I
4.66794 − 5.74198I 0
u = 0.20327 − 1.42244I
a = −2.42805 − 0.22092I
b = −2.84613 − 1.06570I
4.66794 + 5.74198I 0
u = −0.14687 + 1.43811I
a = 1.169270 + 0.044649I
b = 1.60540 − 0.16218I
5.57039 + 2.71636I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.14687 − 1.43811I
a = 1.169270 − 0.044649I
b = 1.60540 + 0.16218I
5.57039 − 2.71636I 0
u = −0.492215 + 0.249012I
a = −0.824121 + 0.198501I
b = 0.688523 + 1.133750I
−1.356930 − 0.364886I −7.63760 − 1.14677I
u = −0.492215 − 0.249012I
a = −0.824121 − 0.198501I
b = 0.688523 − 1.133750I
−1.356930 + 0.364886I −7.63760 + 1.14677I
u = 0.18750 + 1.45044I
a = −1.63241 − 0.36166I
b = −2.40745 − 0.61245I
9.45327 − 6.03947I 0
u = 0.18750 − 1.45044I
a = −1.63241 + 0.36166I
b = −2.40745 + 0.61245I
9.45327 + 6.03947I 0
u = −0.523236 + 0.062547I
a = 0.837529 + 0.934705I
b = −1.33607 + 1.11209I
−6.94722 + 4.75131I −11.69397 − 4.35447I
u = −0.523236 − 0.062547I
a = 0.837529 − 0.934705I
b = −1.33607 − 1.11209I
−6.94722 − 4.75131I −11.69397 + 4.35447I
u = 0.24247 + 1.46432I
a = 1.42620 + 0.45731I
b = 2.42437 + 0.79189I
3.32012 − 9.65966I 0
u = 0.24247 − 1.46432I
a = 1.42620 − 0.45731I
b = 2.42437 − 0.79189I
3.32012 + 9.65966I 0
u = −0.444548 + 0.248062I
a = −2.07093 + 0.35714I
b = 0.334505 + 0.408255I
−1.23188 + 2.67764I −8.00090 − 10.68725I
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.444548 − 0.248062I
a = −2.07093 − 0.35714I
b = 0.334505 − 0.408255I
−1.23188 − 2.67764I −8.00090 + 10.68725I
u = −0.28802 + 1.46360I
a = −1.63445 − 0.11403I
b = −2.09049 − 0.75480I
3.18901 + 7.09486I 0
u = −0.28802 − 1.46360I
a = −1.63445 + 0.11403I
b = −2.09049 + 0.75480I
3.18901 − 7.09486I 0
u = 0.27537 + 1.46680I
a = 2.08401 − 0.14935I
b = 2.65186 − 0.94698I
5.88295 − 12.31150I 0
u = 0.27537 − 1.46680I
a = 2.08401 + 0.14935I
b = 2.65186 + 0.94698I
5.88295 + 12.31150I 0
u = −0.28845 + 1.46832I
a = −0.844057 − 0.322078I
b = −1.006910 − 0.429078I
1.66920 + 6.47731I 0
u = −0.28845 − 1.46832I
a = −0.844057 + 0.322078I
b = −1.006910 + 0.429078I
1.66920 − 6.47731I 0
u = 0.18394 + 1.48641I
a = −1.45002 − 0.36108I
b = −2.13938 + 0.17582I
4.06961 − 0.77391I 0
u = 0.18394 − 1.48641I
a = −1.45002 + 0.36108I
b = −2.13938 − 0.17582I
4.06961 + 0.77391I 0
u = 0.498781 + 0.031813I
a = −1.83780 + 0.78218I
b = 1.200940 + 0.443882I
−9.72324 − 0.17260I −14.6955 − 1.6811I
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.498781 − 0.031813I
a = −1.83780 − 0.78218I
b = 1.200940 − 0.443882I
−9.72324 + 0.17260I −14.6955 + 1.6811I
u = −0.26046 + 1.47949I
a = −1.350680 − 0.064524I
b = −2.13964 − 0.22084I
1.70234 + 5.70571I 0
u = −0.26046 − 1.47949I
a = −1.350680 + 0.064524I
b = −2.13964 + 0.22084I
1.70234 − 5.70571I 0
u = −0.37688 + 1.45966I
a = 1.65237 − 0.15351I
b = 2.15867 + 0.62908I
−3.41289 + 10.44450I 0
u = −0.37688 − 1.45966I
a = 1.65237 + 0.15351I
b = 2.15867 − 0.62908I
−3.41289 − 10.44450I 0
u = 0.13345 + 1.50197I
a = −0.651574 − 0.494247I
b = −1.00228 − 1.08760I
7.84173 + 1.60885I 0
u = 0.13345 − 1.50197I
a = −0.651574 + 0.494247I
b = −1.00228 + 1.08760I
7.84173 − 1.60885I 0
u = 0.34024 + 1.47130I
a = −1.95397 − 0.02823I
b = −2.63237 + 0.78593I
−0.5823 − 17.3216I 0
u = 0.34024 − 1.47130I
a = −1.95397 + 0.02823I
b = −2.63237 − 0.78593I
−0.5823 + 17.3216I 0
u = 0.474941
a = −2.72071
b = 0.983847
−9.72586 −24.9570
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.465572 + 0.075078I
a = 1.94842 + 2.59870I
b = −0.579859 + 0.622820I
−6.63078 − 3.98358I −12.51677 + 2.81229I
u = −0.465572 − 0.075078I
a = 1.94842 − 2.59870I
b = −0.579859 − 0.622820I
−6.63078 + 3.98358I −12.51677 − 2.81229I
u = −0.326714 + 0.306052I
a = −0.490568 + 0.740050I
b = 0.055279 + 0.356898I
−0.167562 + 0.876730I −3.96855 − 7.53814I
u = −0.326714 − 0.306052I
a = −0.490568 − 0.740050I
b = 0.055279 − 0.356898I
−0.167562 − 0.876730I −3.96855 + 7.53814I
u = 0.441030
a = 1.00462
b = 1.11644
3.20630 6.32680
u = −0.01728 + 1.56600I
a = 0.999723 + 0.344621I
b = 1.54938 + 0.87919I
4.21990 + 5.75104I 0
u = −0.01728 − 1.56600I
a = 0.999723 − 0.344621I
b = 1.54938 − 0.87919I
4.21990 − 5.75104I 0
u = 0.338766
a = 1.91535
b = −0.532834
−1.44061 −6.16230
15
II. I
u
2
=
h−u
26
−3u
25
+· · ·+b −1, −4u
26
−10u
25
+· · ·+a +5, u
27
+3u
26
+· · ·+6u +1i
(i) Arc colorings
a
1
=
0
u
a
5
=
1
0
a
4
=
1
−u
2
a
2
=
−u
u
3
+ u
a
9
=
4u
26
+ 10u
25
+ ··· − 19u − 5
u
26
+ 3u
25
+ ··· + 7u + 1
a
10
=
7u
26
+ 17u
25
+ ··· − 19u − 5
4u
26
+ 10u
25
+ ··· − 2u − 1
a
6
=
−2u
26
− 6u
25
+ ··· − 39u − 7
2u
26
+ 12u
25
+ ··· + 24u + 4
a
3
=
−3u
26
− 12u
25
+ ··· − 40u − 6
−3u
25
− 7u
24
+ ··· + 4u
2
+ 3u
a
12
=
u
u
a
8
=
10u
26
+ 26u
25
+ ··· − 28u − 7
7u
26
+ 19u
25
+ ··· − 2u − 1
a
7
=
4u
26
+ 16u
25
+ ··· + 22u
2
− 3u
2u
26
+ 6u
25
+ ··· + 9u
2
+ 4u
a
11
=
−4u
26
− 12u
25
+ ··· − 18u − 6
−3u
26
− 7u
25
+ ··· + 13u + 4
(ii) Obstruction class = 1
(iii) Cusp Shapes
= 8u
26
+ 14u
25
+ 108u
24
+ 159u
23
+ 627u
22
+ 764u
21
+ 2034u
20
+ 1955u
19
+ 3971u
18
+
2638u
17
+ 4608u
16
+ 1110u
15
+ 2804u
14
− 1918u
13
+ 482u
12
− 3380u
11
− 123u
10
−
2436u
9
+ 250u
8
− 1025u
7
+ 301u
6
− 248u
5
+ 147u
4
− 6u
3
+ 29u
2
− u − 5
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
12
u
27
− 3u
26
+ ··· + 6u − 1
c
2
u
27
− 9u
25
+ ··· − 9u
2
+ 1
c
3
u
27
− 2u
24
+ ··· − 9u
2
− 1
c
4
u
27
+ 3u
26
+ ··· + 6u + 1
c
5
, c
6
u
27
− 16u
25
+ ··· − 6u + 1
c
7
u
27
− 9u
25
+ ··· + 9u
2
− 1
c
8
u
27
+ 5u
26
+ ··· − 5u − 1
c
9
u
27
+ 7u
24
+ ··· + 6u − 1
c
10
u
27
− 16u
25
+ ··· − 6u − 1
c
11
u
27
− 5u
26
+ ··· − 5u + 1
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
12
y
27
+ 27y
26
+ ··· − 8y −1
c
2
, c
7
y
27
− 18y
26
+ ··· + 18y −1
c
3
y
27
− 14y
25
+ ··· − 18y −1
c
5
, c
6
, c
10
y
27
− 32y
26
+ ··· + 16y −1
c
8
, c
11
y
27
− 27y
26
+ ··· + 23y −1
c
9
y
27
+ 4y
25
+ ··· − 32y −1
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.349187 + 0.950871I
a = −0.807587 + 0.771242I
b = −1.121300 − 0.478024I
−7.80198 + 1.43571I −9.19532 − 2.58353I
u = −0.349187 − 0.950871I
a = −0.807587 − 0.771242I
b = −1.121300 + 0.478024I
−7.80198 − 1.43571I −9.19532 + 2.58353I
u = −0.524782 + 0.805011I
a = −0.191943 − 0.585590I
b = 0.429680 + 0.206238I
−1.56889 + 2.18949I −7.93685 − 8.86415I
u = −0.524782 − 0.805011I
a = −0.191943 + 0.585590I
b = 0.429680 − 0.206238I
−1.56889 − 2.18949I −7.93685 + 8.86415I
u = 0.865146
a = 0.399939
b = 0.830267
0.961761 −1.58940
u = −0.894303 + 0.699265I
a = 0.343752 + 0.029060I
b = −0.168841 − 0.129023I
−4.88580 + 3.15924I −20.5341 − 9.3982I
u = −0.894303 − 0.699265I
a = 0.343752 − 0.029060I
b = −0.168841 + 0.129023I
−4.88580 − 3.15924I −20.5341 + 9.3982I
u = 0.029596 + 1.250160I
a = 2.13970 + 0.39451I
b = 2.65297 − 0.60411I
−2.85769 − 4.49481I −3.90049 + 2.81559I
u = 0.029596 − 1.250160I
a = 2.13970 − 0.39451I
b = 2.65297 + 0.60411I
−2.85769 + 4.49481I −3.90049 − 2.81559I
u = −0.032871 + 1.304030I
a = −0.160820 − 0.814359I
b = −0.329944 + 0.286174I
2.29000 − 1.19742I 2.58030 − 0.47093I
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.032871 − 1.304030I
a = −0.160820 + 0.814359I
b = −0.329944 − 0.286174I
2.29000 + 1.19742I 2.58030 + 0.47093I
u = −0.122293 + 1.328560I
a = −1.64806 − 0.35102I
b = −1.96596 − 1.71147I
−5.28712 + 1.88129I 3.03676 + 4.91413I
u = −0.122293 − 1.328560I
a = −1.64806 + 0.35102I
b = −1.96596 + 1.71147I
−5.28712 − 1.88129I 3.03676 − 4.91413I
u = 0.207564 + 1.370530I
a = −1.96759 − 0.60435I
b = −2.31426 − 0.20194I
7.35928 − 2.72940I −3.54297 + 2.72914I
u = 0.207564 − 1.370530I
a = −1.96759 + 0.60435I
b = −2.31426 + 0.20194I
7.35928 + 2.72940I −3.54297 − 2.72914I
u = 0.35746 + 1.38079I
a = 1.120110 + 0.669009I
b = 1.45233 + 0.47462I
5.42748 − 4.43200I 0.67537 + 3.40706I
u = 0.35746 − 1.38079I
a = 1.120110 − 0.669009I
b = 1.45233 − 0.47462I
5.42748 + 4.43200I 0.67537 − 3.40706I
u = −0.027004 + 0.563292I
a = 1.91164 + 1.44067I
b = 0.941661 − 0.329293I
−5.44454 + 4.33420I −5.60921 − 3.77384I
u = −0.027004 − 0.563292I
a = 1.91164 − 1.44067I
b = 0.941661 + 0.329293I
−5.44454 − 4.33420I −5.60921 + 3.77384I
u = −0.15542 + 1.44244I
a = 1.73021 + 0.57101I
b = 2.28253 + 1.18196I
4.64936 + 3.70031I 0.96546 − 2.09491I
20
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.15542 − 1.44244I
a = 1.73021 − 0.57101I
b = 2.28253 − 1.18196I
4.64936 − 3.70031I 0.96546 + 2.09491I
u = 0.542990
a = −0.340066
b = −1.35539
2.82244 −15.1650
u = −0.24899 + 1.51498I
a = −0.915730 − 0.316585I
b = −1.44310 − 0.51838I
2.29278 + 6.93609I −0.88072 − 10.03541I
u = −0.24899 − 1.51498I
a = −0.915730 + 0.316585I
b = −1.44310 + 0.51838I
2.29278 − 6.93609I −0.88072 + 10.03541I
u = −0.415767
a = 3.11726
b = −1.16114
−9.51393 13.4630
u = −0.235946 + 0.296409I
a = −2.14224 − 1.06325I
b = 0.427373 + 0.736804I
−1.17761 + 1.87746I −7.51263 − 1.01338I
u = −0.235946 − 0.296409I
a = −2.14224 + 1.06325I
b = 0.427373 − 0.736804I
−1.17761 − 1.87746I −7.51263 + 1.01338I
21
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
12
(u
27
− 3u
26
+ ··· + 6u − 1)(u
108
− 2u
107
+ ··· − 299u + 47)
c
2
(u
27
− 9u
25
+ ··· − 9u
2
+ 1)(u
108
+ u
107
+ ··· + u + 1)
c
3
(u
27
− 2u
24
+ ··· − 9u
2
− 1)(u
108
− u
107
+ ··· − 28281u + 2677)
c
4
(u
27
+ 3u
26
+ ··· + 6u + 1)(u
108
− 2u
107
+ ··· − 299u + 47)
c
5
, c
6
(u
27
− 16u
25
+ ··· − 6u + 1)(u
108
− u
107
+ ··· + 575u − 103)
c
7
(u
27
− 9u
25
+ ··· + 9u
2
− 1)(u
108
+ u
107
+ ··· + u + 1)
c
8
(u
27
+ 5u
26
+ ··· − 5u − 1)(u
108
− 38u
106
+ ··· − 2046u + 89)
c
9
(u
27
+ 7u
24
+ ··· + 6u − 1)(u
108
+ 3u
107
+ ··· − 492579u + 108211)
c
10
(u
27
− 16u
25
+ ··· − 6u − 1)(u
108
− u
107
+ ··· + 575u − 103)
c
11
(u
27
− 5u
26
+ ··· − 5u + 1)(u
108
− 38u
106
+ ··· − 2046u + 89)
22
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
12
(y
27
+ 27y
26
+ ··· − 8y −1)(y
108
+ 102y
107
+ ··· − 95417y + 2209)
c
2
, c
7
(y
27
− 18y
26
+ ··· + 18y −1)(y
108
− 55y
107
+ ··· − 31y + 1)
c
3
(y
27
− 14y
25
+ ··· − 18y −1)
· (y
108
− 17y
107
+ ··· − 304371863y + 7166329)
c
5
, c
6
, c
10
(y
27
− 32y
26
+ ··· + 16y −1)
· (y
108
− 109y
107
+ ··· − 159233y + 10609)
c
8
, c
11
(y
27
− 27y
26
+ ··· + 23y −1)(y
108
− 76y
107
+ ··· − 3384048y + 7921)
c
9
(y
27
+ 4y
25
+ ··· − 32y −1)
· (y
108
− 13y
107
+ ··· + 118667308219y + 11709620521)
23
