12a
0451
(K12a
0451
)
A knot diagram
1
Linearized knot diagam
3 6 10 9 8 2 12 1 11 4 7 5
Solving Sequence
3,10
4
6,11
2 7 12 1 9 8 5
c
3
c
10
c
2
c
6
c
11
c
1
c
9
c
8
c
5
c
4
, c
7
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h2.15850 × 10
215
u
141
+ 1.12135 × 10
215
u
140
+ ··· + 1.47358 × 10
214
b + 4.27986 × 10
215
,
− 1.02103 × 10
216
u
141
− 3.98145 × 10
215
u
140
+ ··· + 1.47358 × 10
214
a − 1.65816 × 10
216
,
u
142
+ u
141
+ ··· + 2u + 1i
I
u
2
= h−5u
29
+ 37u
27
+ ··· + b + 1, u
29
− 6u
28
+ ··· + a + 16, u
30
− 8u
28
+ ··· − 6u
2
+ 1i
I
u
3
= h−u
2
+ b, u
2
+ a − 1, u
9
− u
7
+ u
5
+ u − 1i
* 3 irreducible components of dim
C
= 0, with total 181 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
= h2.16 × 10
215
u
141
+ 1.12 × 10
215
u
140
+ · · · + 1.47 × 10
214
b + 4.28 ×
10
215
, −1.02 × 10
216
u
141
− 3.98 × 10
215
u
140
+ · · · + 1.47 × 10
214
a − 1.66 ×
10
216
, u
142
+ u
141
+ · · · + 2u + 1i
(i) Arc colorings
a
3
=
1
0
a
10
=
0
u
a
4
=
1
u
2
a
6
=
69.2888u
141
+ 27.0189u
140
+ ··· + 60.3781u + 112.526
−14.6480u
141
− 7.60972u
140
+ ··· − 3.77923u − 29.0439
a
11
=
−u
−u
3
+ u
a
2
=
98.5271u
141
+ 51.8440u
140
+ ··· − 20.6958u + 209.268
−15.8723u
141
− 9.69013u
140
+ ··· + 8.74357u − 36.7595
a
7
=
70.6230u
141
+ 32.6381u
140
+ ··· + 24.8012u + 130.839
−3.19139u
141
− 1.99522u
140
+ ··· + 1.36837u − 7.21709
a
12
=
−105.596u
141
− 54.7390u
140
+ ··· + 20.3905u − 221.860
14.8864u
141
+ 8.90364u
140
+ ··· − 7.43228u + 33.9364
a
1
=
82.6547u
141
+ 42.1539u
140
+ ··· − 11.9522u + 172.509
−15.8723u
141
− 9.69013u
140
+ ··· + 8.74357u − 36.7595
a
9
=
u
3
u
5
− u
3
+ u
a
8
=
−12.2390u
141
− 10.0968u
140
+ ··· + 43.9408u − 42.9882
−12.0821u
141
− 4.24533u
140
+ ··· − 5.97197u − 18.4046
a
5
=
u
6
− u
4
+ 1
u
8
− 2u
6
+ 2u
4
(ii) Obstruction class = −1
(iii) Cusp Shapes = 5.34809u
141
+ 4.05326u
140
+ ··· − 19.7693u + 23.7811
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
142
+ 68u
141
+ ··· + 45485023u + 1940449
c
2
, c
6
u
142
− 2u
141
+ ··· + 793u + 1393
c
3
, c
10
u
142
− u
141
+ ··· − 2u + 1
c
4
u
142
− 3u
141
+ ··· − 3417185u + 423016
c
5
u
142
− 9u
141
+ ··· − 48u + 1
c
7
, c
11
u
142
− 10u
141
+ ··· − 1373392u + 119344
c
8
u
142
− 5u
141
+ ··· + 1486u + 347
c
9
u
142
+ 75u
141
+ ··· + 12u + 1
c
12
u
142
− u
141
+ ··· − 68944u + 61373
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
142
+ 28y
141
+ ··· + 136799040774219y + 3765342321601
c
2
, c
6
y
142
+ 68y
141
+ ··· + 45485023y + 1940449
c
3
, c
10
y
142
− 75y
141
+ ··· − 12y + 1
c
4
y
142
+ 81y
141
+ ··· − 614480347793y + 178942536256
c
5
y
142
− 11y
141
+ ··· − 96y + 1
c
7
, c
11
y
142
− 98y
141
+ ··· − 733475256192y + 14242990336
c
8
y
142
+ 17y
141
+ ··· + 8068556y + 120409
c
9
y
142
− 3y
141
+ ··· − 56y + 1
c
12
y
142
+ 37y
141
+ ··· + 186760312142y + 3766645129
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.819925 + 0.573197I
a = 0.879246 + 0.964168I
b = −0.686532 − 0.919738I
2.90346 + 1.92369I 0
u = 0.819925 − 0.573197I
a = 0.879246 − 0.964168I
b = −0.686532 + 0.919738I
2.90346 − 1.92369I 0
u = −0.998317 + 0.162663I
a = 0.15234 + 1.72026I
b = 0.429286 + 0.749945I
−1.98733 + 4.15694I 0
u = −0.998317 − 0.162663I
a = 0.15234 − 1.72026I
b = 0.429286 − 0.749945I
−1.98733 − 4.15694I 0
u = 0.983094 + 0.270642I
a = 0.329558 + 0.164084I
b = 0.379901 + 0.532584I
−1.85848 − 0.87645I 0
u = 0.983094 − 0.270642I
a = 0.329558 − 0.164084I
b = 0.379901 − 0.532584I
−1.85848 + 0.87645I 0
u = −0.336460 + 0.966769I
a = 1.40956 − 0.63858I
b = −0.552563 + 1.026870I
−3.12233 − 4.55892I 0
u = −0.336460 − 0.966769I
a = 1.40956 + 0.63858I
b = −0.552563 − 1.026870I
−3.12233 + 4.55892I 0
u = 0.769689 + 0.689370I
a = −1.24009 − 0.71557I
b = 0.760360 + 0.502335I
1.41703 − 6.24375I 0
u = 0.769689 − 0.689370I
a = −1.24009 + 0.71557I
b = 0.760360 − 0.502335I
1.41703 + 6.24375I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.752662 + 0.593812I
a = −2.39364 − 0.09867I
b = 0.661817 − 0.973208I
3.09116 − 6.54197I 0
u = 0.752662 − 0.593812I
a = −2.39364 + 0.09867I
b = 0.661817 + 0.973208I
3.09116 + 6.54197I 0
u = −0.102308 + 1.037670I
a = 0.804635 + 0.252765I
b = −0.341980 − 0.947064I
−4.69706 + 1.29869I 0
u = −0.102308 − 1.037670I
a = 0.804635 − 0.252765I
b = −0.341980 + 0.947064I
−4.69706 − 1.29869I 0
u = −0.886405 + 0.577385I
a = 1.92287 + 0.05036I
b = −0.710853 − 0.743340I
3.41659 + 3.40993I 0
u = −0.886405 − 0.577385I
a = 1.92287 − 0.05036I
b = −0.710853 + 0.743340I
3.41659 − 3.40993I 0
u = 0.827768 + 0.692948I
a = 1.78087 + 0.30538I
b = −0.626794 + 0.564260I
1.26246 + 1.00442I 0
u = 0.827768 − 0.692948I
a = 1.78087 − 0.30538I
b = −0.626794 − 0.564260I
1.26246 − 1.00442I 0
u = −0.262097 + 0.881582I
a = −1.56596 + 0.44079I
b = 0.647747 − 1.172540I
−3.7320 − 14.3288I 0
u = −0.262097 − 0.881582I
a = −1.56596 − 0.44079I
b = 0.647747 + 1.172540I
−3.7320 + 14.3288I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.675824 + 0.615061I
a = −0.95501 + 1.31977I
b = 0.714573 − 0.655402I
4.02613 + 1.27883I 0
u = −0.675824 − 0.615061I
a = −0.95501 − 1.31977I
b = 0.714573 + 0.655402I
4.02613 − 1.27883I 0
u = 0.981739 + 0.467961I
a = −0.83111 + 2.10000I
b = −0.290470 − 0.855232I
−4.11806 + 0.96122I 0
u = 0.981739 − 0.467961I
a = −0.83111 − 2.10000I
b = −0.290470 + 0.855232I
−4.11806 − 0.96122I 0
u = −1.061260 + 0.329465I
a = 0.516163 − 1.058550I
b = 0.471837 − 1.310330I
−5.43261 − 3.34267I 0
u = −1.061260 − 0.329465I
a = 0.516163 + 1.058550I
b = 0.471837 + 1.310330I
−5.43261 + 3.34267I 0
u = −0.825572 + 0.325567I
a = −0.102107 − 0.515957I
b = −0.239822 − 1.224430I
−4.72518 + 5.65170I 0
u = −0.825572 − 0.325567I
a = −0.102107 + 0.515957I
b = −0.239822 + 1.224430I
−4.72518 − 5.65170I 0
u = −0.835490 + 0.753017I
a = −1.91088 − 0.30285I
b = 0.606604 + 1.064330I
−0.26999 + 11.42200I 0
u = −0.835490 − 0.753017I
a = −1.91088 + 0.30285I
b = 0.606604 − 1.064330I
−0.26999 − 11.42200I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.796220 + 0.800451I
a = 0.638727 − 0.980874I
b = −0.560690 + 1.022220I
−0.12297 − 5.68905I 0
u = −0.796220 − 0.800451I
a = 0.638727 + 0.980874I
b = −0.560690 − 1.022220I
−0.12297 + 5.68905I 0
u = 0.265127 + 0.826576I
a = −1.42559 + 0.49190I
b = 0.950982 − 0.387299I
−1.32824 + 8.51203I 0
u = 0.265127 − 0.826576I
a = −1.42559 − 0.49190I
b = 0.950982 + 0.387299I
−1.32824 − 8.51203I 0
u = 1.038220 + 0.468696I
a = 0.143061 − 0.914417I
b = 0.907283 + 0.353856I
−0.461214 − 1.205920I 0
u = 1.038220 − 0.468696I
a = 0.143061 + 0.914417I
b = 0.907283 − 0.353856I
−0.461214 + 1.205920I 0
u = 0.357950 + 0.775515I
a = 1.41875 + 0.05983I
b = −0.335547 − 0.925700I
−1.48529 + 2.74039I 0
u = 0.357950 − 0.775515I
a = 1.41875 − 0.05983I
b = −0.335547 + 0.925700I
−1.48529 − 2.74039I 0
u = −1.120770 + 0.262113I
a = −0.22224 − 1.55747I
b = 0.165035 − 1.029870I
−5.95469 − 0.06109I 0
u = −1.120770 − 0.262113I
a = −0.22224 + 1.55747I
b = 0.165035 + 1.029870I
−5.95469 + 0.06109I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.120430 + 0.285920I
a = 0.030486 + 0.400743I
b = −0.547562 + 0.446101I
−1.94419 + 0.00486I 0
u = 1.120430 − 0.285920I
a = 0.030486 − 0.400743I
b = −0.547562 − 0.446101I
−1.94419 − 0.00486I 0
u = 0.587273 + 0.586722I
a = 1.68540 − 0.81948I
b = −0.631334 + 1.116390I
−0.58161 − 4.44960I 0. + 7.84954I
u = 0.587273 − 0.586722I
a = 1.68540 + 0.81948I
b = −0.631334 − 1.116390I
−0.58161 + 4.44960I 0. − 7.84954I
u = −1.058660 + 0.516485I
a = −0.598797 + 1.113080I
b = 0.876245 − 0.001895I
0.01537 + 5.05199I 0
u = −1.058660 − 0.516485I
a = −0.598797 − 1.113080I
b = 0.876245 + 0.001895I
0.01537 − 5.05199I 0
u = 0.219678 + 0.781394I
a = −1.59503 + 0.21320I
b = 0.582661 + 1.058010I
0.56062 + 7.88617I −2.00000 − 7.64027I
u = 0.219678 − 0.781394I
a = −1.59503 − 0.21320I
b = 0.582661 − 1.058010I
0.56062 − 7.88617I −2.00000 + 7.64027I
u = −0.810891 + 0.018995I
a = −0.44839 + 2.20459I
b = 0.442563 + 1.132130I
−4.66414 + 3.91640I −11.24169 + 0.I
u = −0.810891 − 0.018995I
a = −0.44839 − 2.20459I
b = 0.442563 − 1.132130I
−4.66414 − 3.91640I −11.24169 + 0.I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.106370 + 0.437420I
a = 2.29478 − 2.07878I
b = −0.380770 − 0.983522I
−4.77162 + 1.80859I 0
u = −1.106370 − 0.437420I
a = 2.29478 + 2.07878I
b = −0.380770 + 0.983522I
−4.77162 − 1.80859I 0
u = −1.061380 + 0.538697I
a = −1.18916 + 0.82215I
b = 0.782131 + 0.441989I
−0.10586 + 5.44582I 0
u = −1.061380 − 0.538697I
a = −1.18916 − 0.82215I
b = 0.782131 − 0.441989I
−0.10586 − 5.44582I 0
u = −1.124720 + 0.396145I
a = 0.693007 + 0.740985I
b = −0.539884 + 1.115230I
−7.31755 − 1.87859I 0
u = −1.124720 − 0.396145I
a = 0.693007 − 0.740985I
b = −0.539884 − 1.115230I
−7.31755 + 1.87859I 0
u = 1.120490 + 0.414286I
a = 0.431652 + 0.605235I
b = 0.452609 + 1.065390I
−3.01714 − 0.96511I 0
u = 1.120490 − 0.414286I
a = 0.431652 − 0.605235I
b = 0.452609 − 1.065390I
−3.01714 + 0.96511I 0
u = 1.101160 + 0.477897I
a = −1.59513 − 0.83858I
b = 1.065770 − 0.832707I
−1.30656 − 7.29187I 0
u = 1.101160 − 0.477897I
a = −1.59513 + 0.83858I
b = 1.065770 + 0.832707I
−1.30656 + 7.29187I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.146851 + 0.783292I
a = −0.306003 − 0.486855I
b = 0.100720 + 1.339030I
−7.52306 − 5.15147I −7.08476 + 4.50382I
u = −0.146851 − 0.783292I
a = −0.306003 + 0.486855I
b = 0.100720 − 1.339030I
−7.52306 + 5.15147I −7.08476 − 4.50382I
u = −1.118420 + 0.447051I
a = 0.38796 − 1.51839I
b = −0.672384 + 0.533733I
−5.05939 + 4.74367I 0
u = −1.118420 − 0.447051I
a = 0.38796 + 1.51839I
b = −0.672384 − 0.533733I
−5.05939 − 4.74367I 0
u = −0.284485 + 0.740309I
a = −0.781132 − 0.751379I
b = 0.692387 + 0.481448I
2.26299 − 2.95719I 2.44235 + 2.41736I
u = −0.284485 − 0.740309I
a = −0.781132 + 0.751379I
b = 0.692387 − 0.481448I
2.26299 + 2.95719I 2.44235 − 2.41736I
u = 1.115220 + 0.468441I
a = −0.55244 − 1.56579I
b = −0.242606 − 1.060950I
−4.53390 − 5.70007I 0
u = 1.115220 − 0.468441I
a = −0.55244 + 1.56579I
b = −0.242606 + 1.060950I
−4.53390 + 5.70007I 0
u = 0.044027 + 0.788764I
a = 0.147867 − 0.134067I
b = 0.327426 − 0.992104I
−5.35872 − 1.03966I −10.97184 + 1.37054I
u = 0.044027 − 0.788764I
a = 0.147867 + 0.134067I
b = 0.327426 + 0.992104I
−5.35872 + 1.03966I −10.97184 − 1.37054I
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.124070 + 0.450929I
a = 0.582151 − 0.061219I
b = −0.719681 + 0.339253I
−5.01892 − 2.92665I 0
u = 1.124070 − 0.450929I
a = 0.582151 + 0.061219I
b = −0.719681 − 0.339253I
−5.01892 + 2.92665I 0
u = −1.030980 + 0.639248I
a = −0.066615 + 0.964674I
b = 0.256363 − 0.901271I
−3.06581 + 5.46183I 0
u = −1.030980 − 0.639248I
a = −0.066615 − 0.964674I
b = 0.256363 + 0.901271I
−3.06581 − 5.46183I 0
u = −1.183630 + 0.278653I
a = −0.862551 + 0.065500I
b = 0.645704 + 0.218716I
−6.27261 + 3.16463I 0
u = −1.183630 − 0.278653I
a = −0.862551 − 0.065500I
b = 0.645704 − 0.218716I
−6.27261 − 3.16463I 0
u = −1.127760 + 0.468002I
a = −1.73382 + 1.41012I
b = 0.627158 + 1.114120I
−2.64743 + 6.77904I 0
u = −1.127760 − 0.468002I
a = −1.73382 − 1.41012I
b = 0.627158 − 1.114120I
−2.64743 − 6.77904I 0
u = −1.182600 + 0.328583I
a = 0.040553 + 1.247040I
b = −0.523046 + 1.043670I
−3.66226 − 4.36716I 0
u = −1.182600 − 0.328583I
a = 0.040553 − 1.247040I
b = −0.523046 − 1.043670I
−3.66226 + 4.36716I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.112390 + 0.534778I
a = −2.25516 − 1.06311I
b = 0.61062 − 1.32428I
−3.95389 − 10.65120I 0
u = 1.112390 − 0.534778I
a = −2.25516 + 1.06311I
b = 0.61062 + 1.32428I
−3.95389 + 10.65120I 0
u = 1.132030 + 0.495273I
a = 2.78786 + 0.82100I
b = −0.586312 + 1.047710I
−6.60530 − 9.65736I 0
u = 1.132030 − 0.495273I
a = 2.78786 − 0.82100I
b = −0.586312 − 1.047710I
−6.60530 + 9.65736I 0
u = −1.206510 + 0.271984I
a = 0.438591 − 0.468643I
b = −0.927115 − 0.288564I
−6.00510 − 5.09569I 0
u = −1.206510 − 0.271984I
a = 0.438591 + 0.468643I
b = −0.927115 + 0.288564I
−6.00510 + 5.09569I 0
u = −0.420856 + 0.623086I
a = 1.302530 − 0.322364I
b = −0.732698 + 0.315993I
1.74958 − 0.85826I 4.53301 − 0.84557I
u = −0.420856 − 0.623086I
a = 1.302530 + 0.322364I
b = −0.732698 − 0.315993I
1.74958 + 0.85826I 4.53301 + 0.84557I
u = 0.316242 + 0.681335I
a = 1.51703 + 0.62075I
b = −0.599099 − 1.263720I
−1.64838 + 5.95849I −1.86023 − 9.97228I
u = 0.316242 − 0.681335I
a = 1.51703 − 0.62075I
b = −0.599099 + 1.263720I
−1.64838 − 5.95849I −1.86023 + 9.97228I
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.204550 + 0.360848I
a = 1.10979 + 1.04467I
b = −0.192669 + 1.340680I
−11.58090 + 1.28812I 0
u = 1.204550 − 0.360848I
a = 1.10979 − 1.04467I
b = −0.192669 − 1.340680I
−11.58090 − 1.28812I 0
u = −1.134450 + 0.543154I
a = −0.123964 − 0.975497I
b = −0.722111 + 0.415523I
−0.21897 + 7.80995I 0
u = −1.134450 − 0.543154I
a = −0.123964 + 0.975497I
b = −0.722111 − 0.415523I
−0.21897 − 7.80995I 0
u = −0.435709 + 0.592879I
a = 1.350760 + 0.182256I
b = −0.785767 − 0.088874I
1.83512 − 0.62347I 6.22978 + 1.16653I
u = −0.435709 − 0.592879I
a = 1.350760 − 0.182256I
b = −0.785767 + 0.088874I
1.83512 + 0.62347I 6.22978 − 1.16653I
u = 1.133490 + 0.572512I
a = −2.03687 − 0.98690I
b = 0.365310 − 1.019860I
−3.80710 − 7.83125I 0
u = 1.133490 − 0.572512I
a = −2.03687 + 0.98690I
b = 0.365310 + 1.019860I
−3.80710 + 7.83125I 0
u = 0.578025 + 0.442992I
a = −2.22702 + 2.71668I
b = 0.418703 − 0.936982I
−2.89762 − 4.84473I −4.45896 + 8.40432I
u = 0.578025 − 0.442992I
a = −2.22702 − 2.71668I
b = 0.418703 + 0.936982I
−2.89762 + 4.84473I −4.45896 − 8.40432I
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.638347 + 0.344624I
a = 1.128900 + 0.503530I
b = −0.038917 + 0.902501I
−1.20928 − 1.53546I −3.16332 + 5.13059I
u = 0.638347 − 0.344624I
a = 1.128900 − 0.503530I
b = −0.038917 − 0.902501I
−1.20928 + 1.53546I −3.16332 − 5.13059I
u = 1.268260 + 0.172146I
a = −0.550571 + 0.487520I
b = 0.470552 + 1.105120I
−8.85021 + 1.09012I 0
u = 1.268260 − 0.172146I
a = −0.550571 − 0.487520I
b = 0.470552 − 1.105120I
−8.85021 − 1.09012I 0
u = −1.203140 + 0.436543I
a = 0.46505 − 1.38480I
b = −0.302401 − 1.041580I
−9.00666 + 5.34263I 0
u = −1.203140 − 0.436543I
a = 0.46505 + 1.38480I
b = −0.302401 + 1.041580I
−9.00666 − 5.34263I 0
u = −1.177010 + 0.511932I
a = −1.056080 + 0.529663I
b = −0.096574 + 1.406160I
−10.5281 + 9.9181I 0
u = −1.177010 − 0.511932I
a = −1.056080 − 0.529663I
b = −0.096574 − 1.406160I
−10.5281 − 9.9181I 0
u = 1.166720 + 0.535906I
a = 2.03104 + 1.48485I
b = −0.578682 + 1.093820I
−2.21982 − 12.79480I 0
u = 1.166720 − 0.535906I
a = 2.03104 − 1.48485I
b = −0.578682 − 1.093820I
−2.21982 + 12.79480I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.261150 + 0.262650I
a = 0.256746 − 0.677907I
b = −0.602673 − 1.185480I
−8.71799 + 10.63660I 0
u = 1.261150 − 0.262650I
a = 0.256746 + 0.677907I
b = −0.602673 + 1.185480I
−8.71799 − 10.63660I 0
u = 1.206220 + 0.470147I
a = −1.145850 − 0.708872I
b = −0.285763 − 0.968912I
−8.77226 − 3.52818I 0
u = 1.206220 − 0.470147I
a = −1.145850 + 0.708872I
b = −0.285763 + 0.968912I
−8.77226 + 3.52818I 0
u = 1.168320 + 0.562737I
a = 0.378377 + 1.120870I
b = −1.004580 − 0.384344I
−4.0150 − 13.6539I 0
u = 1.168320 − 0.562737I
a = 0.378377 − 1.120870I
b = −1.004580 + 0.384344I
−4.0150 + 13.6539I 0
u = 1.165290 + 0.572245I
a = −0.548802 − 0.853736I
b = 0.720267 + 0.515487I
−4.21037 − 5.21554I 0
u = 1.165290 − 0.572245I
a = −0.548802 + 0.853736I
b = 0.720267 − 0.515487I
−4.21037 + 5.21554I 0
u = −1.188740 + 0.577791I
a = 2.13432 − 0.95302I
b = −0.662890 − 1.194780I
−6.5211 + 19.6728I 0
u = −1.188740 − 0.577791I
a = 2.13432 + 0.95302I
b = −0.662890 + 1.194780I
−6.5211 − 19.6728I 0
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.183180 + 0.623411I
a = −2.82260 − 0.68473I
b = 0.528925 + 1.041150I
−3.95708 + 5.28566I −7.65386 − 6.06353I
u = 0.183180 − 0.623411I
a = −2.82260 + 0.68473I
b = 0.528925 − 1.041150I
−3.95708 − 5.28566I −7.65386 + 6.06353I
u = −1.204110 + 0.613290I
a = −1.98739 + 0.58176I
b = 0.602557 + 1.058490I
−5.83477 + 10.29910I 0
u = −1.204110 − 0.613290I
a = −1.98739 − 0.58176I
b = 0.602557 − 1.058490I
−5.83477 − 10.29910I 0
u = 1.326160 + 0.345995I
a = −0.837092 − 0.801210I
b = 0.374168 − 1.056810I
−9.57865 − 6.09266I 0
u = 1.326160 − 0.345995I
a = −0.837092 + 0.801210I
b = 0.374168 + 1.056810I
−9.57865 + 6.09266I 0
u = 0.424473 + 0.459934I
a = 0.886035 − 0.618312I
b = −0.863375 + 0.576810I
1.27964 − 2.75816I 3.84353 + 4.77810I
u = 0.424473 − 0.459934I
a = 0.886035 + 0.618312I
b = −0.863375 − 0.576810I
1.27964 + 2.75816I 3.84353 − 4.77810I
u = −1.280760 + 0.498534I
a = 0.170811 − 0.501114I
b = 0.224304 − 0.941715I
−8.52722 + 4.11557I 0
u = −1.280760 − 0.498534I
a = 0.170811 + 0.501114I
b = 0.224304 + 0.941715I
−8.52722 − 4.11557I 0
17
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.073227 + 0.614228I
a = 1.218720 − 0.030606I
b = −0.603832 + 0.990875I
0.17547 − 2.67476I −0.35921 + 1.91691I
u = −0.073227 − 0.614228I
a = 1.218720 + 0.030606I
b = −0.603832 − 0.990875I
0.17547 + 2.67476I −0.35921 − 1.91691I
u = 0.051046 + 0.545236I
a = −0.58347 − 1.88291I
b = 0.519307 + 0.372756I
−2.18234 − 0.98648I −3.62310 + 1.27691I
u = 0.051046 − 0.545236I
a = −0.58347 + 1.88291I
b = 0.519307 − 0.372756I
−2.18234 + 0.98648I −3.62310 − 1.27691I
u = −0.518123 + 0.128146I
a = 2.59101 + 0.02205I
b = −0.835508 − 0.943250I
0.62409 + 3.22256I −4.92112 − 0.95785I
u = −0.518123 − 0.128146I
a = 2.59101 − 0.02205I
b = −0.835508 + 0.943250I
0.62409 − 3.22256I −4.92112 + 0.95785I
u = 0.249659 + 0.454698I
a = 1.56686 + 1.42274I
b = −0.957567 − 0.789185I
1.05703 + 3.26207I 0.45189 − 6.64532I
u = 0.249659 − 0.454698I
a = 1.56686 − 1.42274I
b = −0.957567 + 0.789185I
1.05703 − 3.26207I 0.45189 + 6.64532I
u = 0.156198 + 0.492346I
a = −0.43442 − 2.02699I
b = 0.202504 − 0.920440I
−1.94775 + 1.68927I −5.11970 − 2.70838I
u = 0.156198 − 0.492346I
a = −0.43442 + 2.02699I
b = 0.202504 + 0.920440I
−1.94775 − 1.68927I −5.11970 + 2.70838I
18
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.490158 + 0.040124I
a = −5.13907 + 1.02652I
b = 0.396678 − 0.727427I
−2.22107 + 1.42999I −3.99644 + 0.75307I
u = −0.490158 − 0.040124I
a = −5.13907 − 1.02652I
b = 0.396678 + 0.727427I
−2.22107 − 1.42999I −3.99644 − 0.75307I
19
II. I
u
2
=
h−5u
29
+37u
27
+· · ·+b+1, u
29
−6u
28
+· · ·+a+16, u
30
−8u
28
+· · ·−6u
2
+1i
(i) Arc colorings
a
3
=
1
0
a
10
=
0
u
a
4
=
1
u
2
a
6
=
−u
29
+ 6u
28
+ ··· + 4u − 16
5u
29
− 37u
27
+ ··· − 4u − 1
a
11
=
−u
−u
3
+ u
a
2
=
−4u
29
+ 29u
27
+ ··· − 29u
3
+ 5u
−2u
29
+ 13u
27
+ ··· + 4u
3
− 2u
a
7
=
2u
29
− 12u
27
+ ··· − u − 1
2u
29
− u
28
+ ··· + 4u + 1
a
12
=
−9u
29
+ 66u
27
+ ··· − 63u
3
+ 11u
−2u
29
+ 13u
27
+ ··· + 3u
3
− u
a
1
=
−6u
29
+ 42u
27
+ ··· − 25u
3
+ 3u
−2u
29
+ 13u
27
+ ··· + 4u
3
− 2u
a
9
=
u
3
u
5
− u
3
+ u
a
8
=
−15u
29
− u
28
+ ··· − 114u
3
+ 24u
−3u
29
− 2u
28
+ ··· + 9u + 2
a
5
=
u
6
− u
4
+ 1
u
8
− 2u
6
+ 2u
4
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −5u
29
+18u
28
+44u
27
−144u
26
−185u
25
+576u
24
+479u
23
−1426u
22
−846u
21
+2355u
20
+
1095u
19
−2559u
18
−1150u
17
+ 1602u
16
+ 1132u
15
−52u
14
−1071u
13
−1048u
12
+ 799u
11
+
1383u
10
−296u
9
−1263u
8
−115u
7
+ 982u
6
+ 211u
5
−584u
4
−103u
3
+ 244u
2
+ 21u −61
20
(iv) u-Polynomials at the component
21
Crossings u-Polynomials at each crossing
c
1
u
30
− 15u
29
+ ··· − 19u + 1
c
2
u
30
− u
29
+ ··· − u + 1
c
3
u
30
− 8u
28
+ ··· − 6u
2
+ 1
c
4
u
30
+ 8u
28
+ ··· − 10u
2
+ 1
c
5
u
30
− 4u
29
+ ··· − 2u
2
+ 1
c
6
u
30
+ u
29
+ ··· + u + 1
c
7
u
30
+ 2u
29
+ ··· + 2u + 1
c
8
u
30
+ 4u
28
+ ··· − 4u
4
+ 1
c
9
u
30
− 16u
29
+ ··· − 12u + 1
c
10
u
30
− 8u
28
+ ··· − 6u
2
+ 1
c
11
u
30
− 2u
29
+ ··· − 2u + 1
c
12
u
30
+ 8u
28
+ ··· + 7u
2
+ 1
22
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
30
+ 15y
29
+ ··· + 7y + 1
c
2
, c
6
y
30
+ 15y
29
+ ··· + 19y + 1
c
3
, c
10
y
30
− 16y
29
+ ··· − 12y + 1
c
4
y
30
+ 16y
29
+ ··· − 20y + 1
c
5
y
30
− 4y
29
+ ··· − 4y + 1
c
7
, c
11
y
30
− 26y
29
+ ··· − 26y + 1
c
8
y
30
+ 8y
29
+ ··· − 8y
2
+ 1
c
9
y
30
+ 32y
28
+ ··· + 4y + 1
c
12
y
30
+ 16y
29
+ ··· + 14y + 1
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.994467 + 0.353916I
a = −0.13957 − 1.41778I
b = 0.222604 + 0.612148I
−3.61074 + 0.45473I −6.93636 − 1.50595I
u = −0.994467 − 0.353916I
a = −0.13957 + 1.41778I
b = 0.222604 − 0.612148I
−3.61074 − 0.45473I −6.93636 + 1.50595I
u = −0.064011 + 0.940566I
a = 0.544351 + 0.162933I
b = −0.345063 − 0.914149I
−4.26161 + 1.42424I 0.50352 − 5.57942I
u = −0.064011 − 0.940566I
a = 0.544351 − 0.162933I
b = −0.345063 + 0.914149I
−4.26161 − 1.42424I 0.50352 + 5.57942I
u = −1.017560 + 0.448999I
a = 0.436222 + 1.072600I
b = 0.916579 − 0.881827I
−0.444250 − 0.254180I 2.26850 + 2.87479I
u = −1.017560 − 0.448999I
a = 0.436222 − 1.072600I
b = 0.916579 + 0.881827I
−0.444250 + 0.254180I 2.26850 − 2.87479I
u = 0.551713 + 0.688134I
a = 2.03216 − 0.74425I
b = −0.379573 + 0.645839I
−0.432727 + 0.842955I −0.87316 − 1.36840I
u = 0.551713 − 0.688134I
a = 2.03216 + 0.74425I
b = −0.379573 − 0.645839I
−0.432727 − 0.842955I −0.87316 + 1.36840I
u = 1.068000 + 0.342485I
a = −0.260910 + 1.386390I
b = 0.420339 + 1.169090I
−5.93334 + 2.39344I −9.77631 − 1.23550I
u = 1.068000 − 0.342485I
a = −0.260910 − 1.386390I
b = 0.420339 − 1.169090I
−5.93334 − 2.39344I −9.77631 + 1.23550I
25
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.406986 + 0.761142I
a = 1.60147 − 0.85711I
b = −0.516050 + 1.071810I
−2.07907 − 4.66119I −3.39761 + 4.57858I
u = −0.406986 − 0.761142I
a = 1.60147 + 0.85711I
b = −0.516050 − 1.071810I
−2.07907 + 4.66119I −3.39761 − 4.57858I
u = 1.028170 + 0.498788I
a = −1.40714 − 1.07504I
b = 0.900131 − 0.752158I
−0.07812 − 6.43302I −0.11395 + 9.43161I
u = 1.028170 − 0.498788I
a = −1.40714 + 1.07504I
b = 0.900131 + 0.752158I
−0.07812 + 6.43302I −0.11395 − 9.43161I
u = −0.791075 + 0.218782I
a = −2.88566 + 0.56757I
b = −0.215247 + 0.703613I
−2.68027 + 2.10521I −10.48037 − 7.05069I
u = −0.791075 − 0.218782I
a = −2.88566 − 0.56757I
b = −0.215247 − 0.703613I
−2.68027 − 2.10521I −10.48037 + 7.05069I
u = 1.051160 + 0.570107I
a = −0.540576 − 1.233710I
b = 0.351699 + 0.565930I
−1.98901 − 5.71256I −1.36845 + 5.76067I
u = 1.051160 − 0.570107I
a = −0.540576 + 1.233710I
b = 0.351699 − 0.565930I
−1.98901 + 5.71256I −1.36845 − 5.76067I
u = 0.592104 + 0.489364I
a = 1.173220 + 0.500106I
b = −0.804256 − 0.760321I
1.33625 + 2.32795I 0.115382 − 0.275012I
u = 0.592104 − 0.489364I
a = 1.173220 − 0.500106I
b = −0.804256 + 0.760321I
1.33625 − 2.32795I 0.115382 + 0.275012I
26
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.754778 + 0.131207I
a = −0.67105 + 2.14428I
b = −0.356741 + 1.111360I
−4.37931 − 4.59780I −7.80627 + 7.63028I
u = 0.754778 − 0.131207I
a = −0.67105 − 2.14428I
b = −0.356741 − 1.111360I
−4.37931 + 4.59780I −7.80627 − 7.63028I
u = −1.118810 + 0.557281I
a = −2.35393 + 0.82448I
b = 0.550027 + 1.148230I
−4.27699 + 9.64890I −6.76427 − 7.42984I
u = −1.118810 − 0.557281I
a = −2.35393 − 0.82448I
b = 0.550027 − 1.148230I
−4.27699 − 9.64890I −6.76427 + 7.42984I
u = −0.641717 + 0.369598I
a = 1.92513 + 0.81605I
b = −0.830917 − 0.913416I
0.87575 + 3.82370I 0.74649 − 11.26661I
u = −0.641717 − 0.369598I
a = 1.92513 − 0.81605I
b = −0.830917 + 0.913416I
0.87575 − 3.82370I 0.74649 + 11.26661I
u = 1.235430 + 0.411587I
a = −0.506147 − 0.937143I
b = 0.306226 − 0.980203I
−8.41986 − 5.93076I −6.32065 + 9.46541I
u = 1.235430 − 0.411587I
a = −0.506147 + 0.937143I
b = 0.306226 + 0.980203I
−8.41986 + 5.93076I −6.32065 − 9.46541I
u = −1.246730 + 0.463505I
a = 0.552435 − 0.730357I
b = 0.280242 − 0.887089I
−8.03990 + 3.51185I −3.79648 + 1.95941I
u = −1.246730 − 0.463505I
a = 0.552435 + 0.730357I
b = 0.280242 + 0.887089I
−8.03990 − 3.51185I −3.79648 − 1.95941I
27
III. I
u
3
= h−u
2
+ b, u
2
+ a − 1, u
9
− u
7
+ u
5
+ u − 1i
(i) Arc colorings
a
3
=
1
0
a
10
=
0
u
a
4
=
1
u
2
a
6
=
−u
2
+ 1
u
2
a
11
=
−u
−u
3
+ u
a
2
=
−u
4
+ u
2
+ 1
u
4
a
7
=
−u
6
+ u
4
+ 1
u
6
+ u
2
a
12
=
u
6
− u
4
− u − 1
−u
6
− u
3
− u
2
+ u
a
1
=
u
2
+ 1
u
4
a
9
=
u
3
u
5
− u
3
+ u
a
8
=
−u
−u
3
+ u
a
5
=
u
6
− u
4
+ 1
u
8
− 2u
6
+ 2u
4
(ii) Obstruction class = −1
(iii) Cusp Shapes = −6
28
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
9
+ 2u
8
+ 7u
7
+ 10u
6
+ 15u
5
+ 10u
4
+ 6u
3
+ u − 1
c
2
, c
6
, c
9
u
9
+ 2u
8
+ 3u
7
+ 2u
6
+ 3u
5
+ 2u
4
+ 2u
3
+ u + 1
c
3
, c
8
, c
10
u
9
− u
7
+ u
5
+ u + 1
c
4
u
9
− u
7
− 3u
6
+ 3u
5
+ 2u
4
+ 4u
3
+ 5u
2
+ 11u + 3
c
5
u
9
− 3u
7
− 4u
6
+ 5u
5
+ 4u
4
+ 10u
3
− 2u
2
− 3u + 1
c
7
, c
11
(u + 1)
9
c
12
u
9
− 2u
8
+ 7u
7
− 10u
6
+ 15u
5
− 10u
4
+ 6u
3
+ u + 1
29
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
12
y
9
+ 10y
8
+ 39y
7
+ 82y
6
+ 111y
5
+ 98y
4
+ 86y
3
+ 32y
2
+ y −1
c
2
, c
6
, c
9
y
9
+ 2y
8
+ 7y
7
+ 10y
6
+ 15y
5
+ 10y
4
+ 6y
3
+ y −1
c
3
, c
8
, c
10
y
9
− 2y
8
+ 3y
7
− 2y
6
+ 3y
5
− 2y
4
+ 2y
3
+ y −1
c
4
y
9
− 2y
8
+ 7y
7
− 7y
6
+ 35y
5
+ 28y
4
+ 80y
3
+ 51y
2
+ 91y −9
c
5
y
9
− 6y
8
+ 19y
7
− 26y
6
− 9y
5
+ 86y
4
+ 94y
3
− 72y
2
+ 13y −1
c
7
, c
11
(y −1)
9
30
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.569300 + 0.827941I
a = 1.36138 + 0.94269I
b = −0.361384 − 0.942694I
−1.64493 −6.00000
u = −0.569300 − 0.827941I
a = 1.36138 − 0.94269I
b = −0.361384 + 0.942694I
−1.64493 −6.00000
u = 0.951836 + 0.524109I
a = 0.368699 − 0.997731I
b = 0.631301 + 0.997731I
−1.64493 −6.00000
u = 0.951836 − 0.524109I
a = 0.368699 + 0.997731I
b = 0.631301 − 0.997731I
−1.64493 −6.00000
u = 0.318649 + 0.823858I
a = 1.57720 − 0.52504I
b = −0.577205 + 0.525043I
−1.64493 −6.00000
u = 0.318649 − 0.823858I
a = 1.57720 + 0.52504I
b = −0.577205 − 0.525043I
−1.64493 −6.00000
u = −1.091200 + 0.433183I
a = −0.003066 + 0.945378I
b = 1.003070 − 0.945378I
−1.64493 −6.00000
u = −1.091200 − 0.433183I
a = −0.003066 − 0.945378I
b = 1.003070 + 0.945378I
−1.64493 −6.00000
u = 0.780028
a = 0.391557
b = 0.608443
−1.64493 −6.00000
31
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
9
+ 2u
8
+ 7u
7
+ 10u
6
+ 15u
5
+ 10u
4
+ 6u
3
+ u − 1)
· (u
30
− 15u
29
+ ··· − 19u + 1)
· (u
142
+ 68u
141
+ ··· + 45485023u + 1940449)
c
2
(u
9
+ 2u
8
+ ··· + u + 1)(u
30
− u
29
+ ··· − u + 1)
· (u
142
− 2u
141
+ ··· + 793u + 1393)
c
3
(u
9
− u
7
+ u
5
+ u + 1)(u
30
− 8u
28
+ ··· − 6u
2
+ 1)
· (u
142
− u
141
+ ··· − 2u + 1)
c
4
(u
9
− u
7
− 3u
6
+ 3u
5
+ 2u
4
+ 4u
3
+ 5u
2
+ 11u + 3)
· (u
30
+ 8u
28
+ ··· − 10u
2
+ 1)(u
142
− 3u
141
+ ··· − 3417185u + 423016)
c
5
(u
9
− 3u
7
− 4u
6
+ 5u
5
+ 4u
4
+ 10u
3
− 2u
2
− 3u + 1)
· (u
30
− 4u
29
+ ··· − 2u
2
+ 1)(u
142
− 9u
141
+ ··· − 48u + 1)
c
6
(u
9
+ 2u
8
+ ··· + u + 1)(u
30
+ u
29
+ ··· + u + 1)
· (u
142
− 2u
141
+ ··· + 793u + 1393)
c
7
((u + 1)
9
)(u
30
+ 2u
29
+ ··· + 2u + 1)
· (u
142
− 10u
141
+ ··· − 1373392u + 119344)
c
8
(u
9
− u
7
+ u
5
+ u + 1)(u
30
+ 4u
28
+ ··· − 4u
4
+ 1)
· (u
142
− 5u
141
+ ··· + 1486u + 347)
c
9
(u
9
+ 2u
8
+ 3u
7
+ 2u
6
+ 3u
5
+ 2u
4
+ 2u
3
+ u + 1)
· (u
30
− 16u
29
+ ··· − 12u + 1)(u
142
+ 75u
141
+ ··· + 12u + 1)
c
10
(u
9
− u
7
+ u
5
+ u + 1)(u
30
− 8u
28
+ ··· − 6u
2
+ 1)
· (u
142
− u
141
+ ··· − 2u + 1)
c
11
((u + 1)
9
)(u
30
− 2u
29
+ ··· − 2u + 1)
· (u
142
− 10u
141
+ ··· − 1373392u + 119344)
c
12
(u
9
− 2u
8
+ 7u
7
− 10u
6
+ 15u
5
− 10u
4
+ 6u
3
+ u + 1)
· (u
30
+ 8u
28
+ ··· + 7u
2
+ 1)(u
142
− u
141
+ ··· − 68944u + 61373)
32
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
9
+ 10y
8
+ 39y
7
+ 82y
6
+ 111y
5
+ 98y
4
+ 86y
3
+ 32y
2
+ y −1)
· (y
30
+ 15y
29
+ ··· + 7y + 1)
· (y
142
+ 28y
141
+ ··· + 136799040774219y + 3765342321601)
c
2
, c
6
(y
9
+ 2y
8
+ 7y
7
+ 10y
6
+ 15y
5
+ 10y
4
+ 6y
3
+ y −1)
· (y
30
+ 15y
29
+ ··· + 19y + 1)
· (y
142
+ 68y
141
+ ··· + 45485023y + 1940449)
c
3
, c
10
(y
9
− 2y
8
+ 3y
7
− 2y
6
+ 3y
5
− 2y
4
+ 2y
3
+ y −1)
· (y
30
− 16y
29
+ ··· − 12y + 1)(y
142
− 75y
141
+ ··· − 12y + 1)
c
4
(y
9
− 2y
8
+ 7y
7
− 7y
6
+ 35y
5
+ 28y
4
+ 80y
3
+ 51y
2
+ 91y −9)
· (y
30
+ 16y
29
+ ··· − 20y + 1)
· (y
142
+ 81y
141
+ ··· − 614480347793y + 178942536256)
c
5
(y
9
− 6y
8
+ 19y
7
− 26y
6
− 9y
5
+ 86y
4
+ 94y
3
− 72y
2
+ 13y −1)
· (y
30
− 4y
29
+ ··· − 4y + 1)(y
142
− 11y
141
+ ··· − 96y + 1)
c
7
, c
11
((y −1)
9
)(y
30
− 26y
29
+ ··· − 26y + 1)
· (y
142
− 98y
141
+ ··· − 733475256192y + 14242990336)
c
8
(y
9
− 2y
8
+ 3y
7
− 2y
6
+ 3y
5
− 2y
4
+ 2y
3
+ y −1)
· (y
30
+ 8y
29
+ ··· − 8y
2
+ 1)(y
142
+ 17y
141
+ ··· + 8068556y + 120409)
c
9
(y
9
+ 2y
8
+ 7y
7
+ 10y
6
+ 15y
5
+ 10y
4
+ 6y
3
+ y −1)
· (y
30
+ 32y
28
+ ··· + 4y + 1)(y
142
− 3y
141
+ ··· − 56y + 1)
c
12
(y
9
+ 10y
8
+ 39y
7
+ 82y
6
+ 111y
5
+ 98y
4
+ 86y
3
+ 32y
2
+ y −1)
· (y
30
+ 16y
29
+ ··· + 14y + 1)
· (y
142
+ 37y
141
+ ··· + 186760312142y + 3766645129)
33
