12a
0983
(K12a
0983
)
A knot diagram
1
Linearized knot diagam
4 6 11 9 2 12 10 5 1 7 3 8
Solving Sequence
4,9 2,5
6 1 10 8 7 11 3 12
c
4
c
5
c
1
c
9
c
8
c
7
c
10
c
3
c
12
c
2
, c
6
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h9.08439 × 10
636
u
154
− 5.67777 × 10
637
u
153
+ ··· + 4.26910 × 10
637
b + 4.02846 × 10
640
,
− 1.96555 × 10
640
u
154
+ 1.40998 × 10
641
u
153
+ ··· + 8.32047 × 10
640
a − 1.35238 × 10
644
,
u
155
− 5u
154
+ ··· + 5977u − 1949i
I
u
2
= h−2.54107 × 10
23
u
40
− 6.68625 × 10
24
u
39
+ ··· + 4.56220 × 10
23
b − 1.25601 × 10
25
,
− 6.16269 × 10
22
u
40
+ 3.14727 × 10
22
u
39
+ ··· + 6.42563 × 10
21
a + 4.53567 × 10
22
,
u
41
+ 12u
39
+ ··· + 2u + 1i
* 2 irreducible components of dim
C
= 0, with total 196 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
= h9.08 × 10
636
u
154
− 5.68 × 10
637
u
153
+ · · · + 4.27 × 10
637
b + 4.03 ×
10
640
, −1.97 × 10
640
u
154
+ 1.41 × 10
641
u
153
+ · · · + 8.32 × 10
640
a − 1.35 ×
10
644
, u
155
− 5u
154
+ · · · + 5977u − 1949i
(i) Arc colorings
a
4
=
1
0
a
9
=
0
u
a
2
=
0.236230u
154
− 1.69459u
153
+ ··· − 5692.37u + 1625.37
−0.212794u
154
+ 1.32997u
153
+ ··· + 3632.61u − 943.634
a
5
=
1
u
2
a
6
=
0.330331u
154
− 1.99549u
153
+ ··· − 3639.71u + 998.058
−0.237444u
154
+ 1.28575u
153
+ ··· + 2893.91u − 775.387
a
1
=
0.0234361u
154
− 0.364618u
153
+ ··· − 2059.76u + 681.735
−0.212794u
154
+ 1.32997u
153
+ ··· + 3632.61u − 943.634
a
10
=
0.189005u
154
− 0.898469u
153
+ ··· + 20.6553u + 13.2784
0.120685u
154
− 0.600088u
153
+ ··· + 209.357u − 96.8051
a
8
=
u
u
3
+ u
a
7
=
−0.0586751u
154
+ 0.174131u
153
+ ··· + 1462.55u − 207.295
0.109921u
154
− 0.579575u
153
+ ··· + 280.179u − 97.6014
a
11
=
0.116953u
154
− 0.407827u
153
+ ··· + 2171.07u − 811.638
0.166621u
154
− 0.966567u
153
+ ··· + 9.72642u − 32.9991
a
3
=
0.168718u
154
− 0.843287u
153
+ ··· − 375.424u − 120.580
0.275648u
154
− 1.63163u
153
+ ··· − 2328.86u + 541.989
a
12
=
0.108998u
154
− 0.940004u
153
+ ··· − 4609.36u + 1398.34
−0.194449u
154
+ 1.09618u
153
+ ··· + 2131.83u − 514.656
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.744791u
154
− 3.25700u
153
+ ··· − 2772.95u − 268.489
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
155
− 12u
154
+ ··· + 27570093u − 1107493
c
2
, c
5
u
155
+ 4u
154
+ ··· + 3352225u + 213761
c
3
, c
11
u
155
+ 46u
153
+ ··· + 141090u + 6263
c
4
, c
8
u
155
+ 5u
154
+ ··· + 5977u + 1949
c
6
u
155
+ 2u
154
+ ··· + 2055676577u + 258968363
c
7
, c
10
u
155
− 8u
154
+ ··· − 211061u + 8101
c
9
u
155
+ 6u
154
+ ··· − 6440321u + 1742611
c
12
u
155
− 2u
154
+ ··· − 75394u + 5489
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
155
+ 2y
154
+ ··· + 738368560502371y −1226540745049
c
2
, c
5
y
155
− 120y
154
+ ··· − 8858040695633y −45693765121
c
3
, c
11
y
155
+ 92y
154
+ ··· + 1224660764y −39225169
c
4
, c
8
y
155
+ 89y
154
+ ··· − 114983845y −3798601
c
6
y
155
− 34y
154
+ ··· + 849943741672138741y −67064613034899769
c
7
, c
10
y
155
+ 110y
154
+ ··· − 4992732509y −65626201
c
9
y
155
+ 52y
154
+ ··· − 183271361272113y −3036693097321
c
12
y
155
+ 50y
154
+ ··· + 2953027638y −30129121
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.632154 + 0.764495I
a = −1.18773 + 1.14589I
b = 0.656993 − 1.249390I
−1.52361 − 2.33822I 0
u = 0.632154 − 0.764495I
a = −1.18773 − 1.14589I
b = 0.656993 + 1.249390I
−1.52361 + 2.33822I 0
u = −0.332105 + 0.955418I
a = −0.88838 + 2.06421I
b = 0.428057 − 0.475116I
−5.98722 + 5.65625I 0
u = −0.332105 − 0.955418I
a = −0.88838 − 2.06421I
b = 0.428057 + 0.475116I
−5.98722 − 5.65625I 0
u = 0.320034 + 0.935213I
a = −1.44761 − 2.62074I
b = 1.58115 + 1.32042I
−2.69846 + 5.60305I 0
u = 0.320034 − 0.935213I
a = −1.44761 + 2.62074I
b = 1.58115 − 1.32042I
−2.69846 − 5.60305I 0
u = 0.165753 + 0.943595I
a = 0.586498 − 1.215400I
b = −1.55472 + 1.20228I
2.07947 − 3.25255I 0
u = 0.165753 − 0.943595I
a = 0.586498 + 1.215400I
b = −1.55472 − 1.20228I
2.07947 + 3.25255I 0
u = −0.336433 + 0.886864I
a = 0.49414 − 2.15802I
b = −0.475427 + 0.808420I
−2.73771 + 1.86517I 0
u = −0.336433 − 0.886864I
a = 0.49414 + 2.15802I
b = −0.475427 − 0.808420I
−2.73771 − 1.86517I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.947907 + 0.023227I
a = −0.254238 − 0.022444I
b = −0.412821 − 1.053730I
1.60910 − 8.22629I 0
u = −0.947907 − 0.023227I
a = −0.254238 + 0.022444I
b = −0.412821 + 1.053730I
1.60910 + 8.22629I 0
u = −0.388203 + 0.864670I
a = −0.31910 + 2.41589I
b = 0.63527 − 1.41490I
−6.60783 − 1.40063I 0
u = −0.388203 − 0.864670I
a = −0.31910 − 2.41589I
b = 0.63527 + 1.41490I
−6.60783 + 1.40063I 0
u = −0.308062 + 1.007630I
a = −0.28746 − 1.60359I
b = −1.00284 + 1.04042I
1.21740 + 4.03535I 0
u = −0.308062 − 1.007630I
a = −0.28746 + 1.60359I
b = −1.00284 − 1.04042I
1.21740 − 4.03535I 0
u = 1.060490 + 0.136755I
a = −0.395064 − 0.346887I
b = 0.941299 − 0.388243I
−6.64824 + 1.50984I 0
u = 1.060490 − 0.136755I
a = −0.395064 + 0.346887I
b = 0.941299 + 0.388243I
−6.64824 − 1.50984I 0
u = 0.464278 + 0.976770I
a = 0.30566 + 1.84213I
b = −0.728498 − 0.632407I
0.02278 − 5.80615I 0
u = 0.464278 − 0.976770I
a = 0.30566 − 1.84213I
b = −0.728498 + 0.632407I
0.02278 + 5.80615I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.440998 + 0.997274I
a = −0.68309 − 2.08178I
b = 1.040830 + 0.429714I
−3.47172 − 10.78400I 0
u = 0.440998 − 0.997274I
a = −0.68309 + 2.08178I
b = 1.040830 − 0.429714I
−3.47172 + 10.78400I 0
u = 0.630842 + 0.647374I
a = 1.07282 − 1.33346I
b = −0.292806 + 1.331150I
−1.80068 − 2.59274I 0
u = 0.630842 − 0.647374I
a = 1.07282 + 1.33346I
b = −0.292806 − 1.331150I
−1.80068 + 2.59274I 0
u = −0.902322 + 0.044640I
a = 0.418779 − 0.204155I
b = 0.275791 − 0.766068I
3.96728 + 3.58960I 0
u = −0.902322 − 0.044640I
a = 0.418779 + 0.204155I
b = 0.275791 + 0.766068I
3.96728 − 3.58960I 0
u = 0.155717 + 0.883135I
a = 1.05498 + 2.34477I
b = −0.271165 − 1.150490I
1.90724 + 1.69368I 0
u = 0.155717 − 0.883135I
a = 1.05498 − 2.34477I
b = −0.271165 + 1.150490I
1.90724 − 1.69368I 0
u = 0.407305 + 1.027460I
a = −0.59832 + 1.29563I
b = −1.23541 − 1.14072I
4.63415 − 5.45186I 0
u = 0.407305 − 1.027460I
a = −0.59832 − 1.29563I
b = −1.23541 + 1.14072I
4.63415 + 5.45186I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.655471 + 0.910338I
a = −0.331171 + 0.795825I
b = −0.369577 + 0.034401I
−3.65853 − 0.76921I 0
u = −0.655471 − 0.910338I
a = −0.331171 − 0.795825I
b = −0.369577 − 0.034401I
−3.65853 + 0.76921I 0
u = 0.219832 + 1.106170I
a = −0.968653 + 0.366699I
b = −0.622560 − 0.130561I
3.44823 − 2.86027I 0
u = 0.219832 − 1.106170I
a = −0.968653 − 0.366699I
b = −0.622560 + 0.130561I
3.44823 + 2.86027I 0
u = 0.665562 + 0.913944I
a = 1.15419 − 0.97993I
b = −0.28018 + 1.75138I
3.33744 + 0.06742I 0
u = 0.665562 − 0.913944I
a = 1.15419 + 0.97993I
b = −0.28018 − 1.75138I
3.33744 − 0.06742I 0
u = 0.853746 + 0.160759I
a = 0.386286 + 0.044218I
b = −0.445128 + 0.406798I
−1.042080 + 0.198583I 0
u = 0.853746 − 0.160759I
a = 0.386286 − 0.044218I
b = −0.445128 − 0.406798I
−1.042080 − 0.198583I 0
u = 1.104610 + 0.255028I
a = −0.507189 − 0.167972I
b = 0.936725 − 0.943509I
−3.47694 + 13.60270I 0
u = 1.104610 − 0.255028I
a = −0.507189 + 0.167972I
b = 0.936725 + 0.943509I
−3.47694 − 13.60270I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.145480 + 0.841695I
a = −0.42940 − 2.52384I
b = −0.503978 + 0.504682I
0.06024 + 4.12457I 0
u = −0.145480 − 0.841695I
a = −0.42940 + 2.52384I
b = −0.503978 − 0.504682I
0.06024 − 4.12457I 0
u = 0.210950 + 1.131710I
a = −0.07148 + 1.94014I
b = −0.64854 − 1.77286I
5.15722 − 4.94782I 0
u = 0.210950 − 1.131710I
a = −0.07148 − 1.94014I
b = −0.64854 + 1.77286I
5.15722 + 4.94782I 0
u = −0.217354 + 1.133410I
a = 0.433968 + 1.047940I
b = 0.497943 − 0.806490I
3.40378 + 0.05786I 0
u = −0.217354 − 1.133410I
a = 0.433968 − 1.047940I
b = 0.497943 + 0.806490I
3.40378 − 0.05786I 0
u = −0.379012 + 1.093380I
a = −0.971570 − 0.105723I
b = 0.135918 + 0.931279I
4.11695 − 0.46339I 0
u = −0.379012 − 1.093380I
a = −0.971570 + 0.105723I
b = 0.135918 − 0.931279I
4.11695 + 0.46339I 0
u = 0.174326 + 0.821465I
a = −2.40032 − 0.25977I
b = 2.98947 − 0.36087I
−3.37727 − 7.93787I 0
u = 0.174326 − 0.821465I
a = −2.40032 + 0.25977I
b = 2.98947 + 0.36087I
−3.37727 + 7.93787I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.279492 + 0.791159I
a = −0.052746 − 1.333800I
b = −0.697093 − 0.199773I
0.21819 − 1.92183I 0
u = −0.279492 − 0.791159I
a = −0.052746 + 1.333800I
b = −0.697093 + 0.199773I
0.21819 + 1.92183I 0
u = −0.667864 + 0.494882I
a = −0.199319 − 0.960026I
b = 0.803175 − 0.259614I
−4.77617 + 5.79352I 0
u = −0.667864 − 0.494882I
a = −0.199319 + 0.960026I
b = 0.803175 + 0.259614I
−4.77617 − 5.79352I 0
u = 0.593305 + 1.007890I
a = −0.88677 + 1.59849I
b = −0.32755 − 1.80236I
3.69654 − 5.06498I 0
u = 0.593305 − 1.007890I
a = −0.88677 − 1.59849I
b = −0.32755 + 1.80236I
3.69654 + 5.06498I 0
u = 0.064119 + 0.824612I
a = 1.13744 + 2.27781I
b = −0.005073 − 0.691467I
2.03577 + 1.68642I 0
u = 0.064119 − 0.824612I
a = 1.13744 − 2.27781I
b = −0.005073 + 0.691467I
2.03577 − 1.68642I 0
u = 0.782761 + 0.261434I
a = −0.298402 + 0.700222I
b = −0.517502 − 0.534657I
−3.70924 − 1.83954I 0
u = 0.782761 − 0.261434I
a = −0.298402 − 0.700222I
b = −0.517502 + 0.534657I
−3.70924 + 1.83954I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.398255 + 1.107460I
a = 0.297301 + 0.172591I
b = −0.837825 − 0.163613I
−1.32317 − 2.47298I 0
u = 0.398255 − 1.107460I
a = 0.297301 − 0.172591I
b = −0.837825 + 0.163613I
−1.32317 + 2.47298I 0
u = 0.548751 + 1.041890I
a = −0.533329 − 1.037770I
b = 0.316666 + 0.111508I
−3.73870 − 1.26130I 0
u = 0.548751 − 1.041890I
a = −0.533329 + 1.037770I
b = 0.316666 − 0.111508I
−3.73870 + 1.26130I 0
u = −0.328741 + 1.130950I
a = 0.890426 − 0.905705I
b = −1.72705 + 0.48694I
1.25479 + 6.54912I 0
u = −0.328741 − 1.130950I
a = 0.890426 + 0.905705I
b = −1.72705 − 0.48694I
1.25479 − 6.54912I 0
u = −0.315353 + 0.748878I
a = −1.54231 − 0.64173I
b = 1.82527 + 0.83218I
−7.05962 + 4.60091I 0
u = −0.315353 − 0.748878I
a = −1.54231 + 0.64173I
b = 1.82527 − 0.83218I
−7.05962 − 4.60091I 0
u = 1.164350 + 0.245956I
a = 0.447906 + 0.184566I
b = −0.781624 + 0.785430I
0.20952 + 6.87027I 0
u = 1.164350 − 0.245956I
a = 0.447906 − 0.184566I
b = −0.781624 − 0.785430I
0.20952 − 6.87027I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.442189 + 1.110960I
a = 0.98886 − 1.05193I
b = 0.649432 + 1.200950I
4.17031 − 1.59616I 0
u = 0.442189 − 1.110960I
a = 0.98886 + 1.05193I
b = 0.649432 − 1.200950I
4.17031 + 1.59616I 0
u = −0.309217 + 0.735277I
a = 0.341028 + 0.397452I
b = −1.335460 − 0.412926I
−3.24796 + 1.11316I 0
u = −0.309217 − 0.735277I
a = 0.341028 − 0.397452I
b = −1.335460 + 0.412926I
−3.24796 − 1.11316I 0
u = −0.768328 + 0.188401I
a = 0.275738 − 0.566334I
b = −0.871620 − 0.946838I
0.32900 − 2.38674I 0
u = −0.768328 − 0.188401I
a = 0.275738 + 0.566334I
b = −0.871620 + 0.946838I
0.32900 + 2.38674I 0
u = −0.354167 + 1.158710I
a = 1.059200 + 0.778046I
b = 0.067922 − 1.155330I
4.32208 + 1.17221I 0
u = −0.354167 − 1.158710I
a = 1.059200 − 0.778046I
b = 0.067922 + 1.155330I
4.32208 − 1.17221I 0
u = −1.175620 + 0.322537I
a = −0.465550 − 0.054229I
b = 0.779649 + 0.753123I
−8.26316 − 7.06323I 0
u = −1.175620 − 0.322537I
a = −0.465550 + 0.054229I
b = 0.779649 − 0.753123I
−8.26316 + 7.06323I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.622512 + 0.453662I
a = 0.0266475 − 0.0692873I
b = −1.227340 + 0.239113I
−1.47244 + 1.58934I 0
u = 0.622512 − 0.453662I
a = 0.0266475 + 0.0692873I
b = −1.227340 − 0.239113I
−1.47244 − 1.58934I 0
u = −1.142530 + 0.505732I
a = 0.523359 + 0.032096I
b = −0.543675 − 0.766771I
−2.87889 − 1.93304I 0
u = −1.142530 − 0.505732I
a = 0.523359 − 0.032096I
b = −0.543675 + 0.766771I
−2.87889 + 1.93304I 0
u = 0.043575 + 1.249060I
a = −0.435578 − 0.988161I
b = 1.08789 + 1.05730I
7.75572 + 1.57249I 0
u = 0.043575 − 1.249060I
a = −0.435578 + 0.988161I
b = 1.08789 − 1.05730I
7.75572 − 1.57249I 0
u = 0.289936 + 1.219130I
a = 0.99461 − 1.01004I
b = 0.393519 + 0.626484I
3.20983 − 4.81140I 0
u = 0.289936 − 1.219130I
a = 0.99461 + 1.01004I
b = 0.393519 − 0.626484I
3.20983 + 4.81140I 0
u = −0.506429 + 1.146790I
a = −0.35114 + 2.11186I
b = 1.70814 − 1.58659I
3.20415 + 8.25375I 0
u = −0.506429 − 1.146790I
a = −0.35114 − 2.11186I
b = 1.70814 + 1.58659I
3.20415 − 8.25375I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.698177 + 0.220233I
a = −0.419829 + 1.074660I
b = 1.31140 + 0.67801I
0.51455 − 3.66015I 0
u = −0.698177 − 0.220233I
a = −0.419829 − 1.074660I
b = 1.31140 − 0.67801I
0.51455 + 3.66015I 0
u = −0.278021 + 1.247040I
a = −0.98662 + 1.95880I
b = 1.43804 − 1.92991I
0.15735 + 8.43497I 0
u = −0.278021 − 1.247040I
a = −0.98662 − 1.95880I
b = 1.43804 + 1.92991I
0.15735 − 8.43497I 0
u = −0.514734 + 1.170450I
a = −0.08794 − 1.94033I
b = −1.30080 + 1.60796I
3.21663 + 7.16288I 0
u = −0.514734 − 1.170450I
a = −0.08794 + 1.94033I
b = −1.30080 − 1.60796I
3.21663 − 7.16288I 0
u = 0.412246 + 1.221430I
a = 0.438540 − 0.919186I
b = 0.574472 + 0.762339I
2.95233 − 3.87355I 0
u = 0.412246 − 1.221430I
a = 0.438540 + 0.919186I
b = 0.574472 − 0.762339I
2.95233 + 3.87355I 0
u = 0.426286 + 1.219960I
a = −0.66481 − 1.78704I
b = 1.43638 + 1.38473I
−2.26989 − 7.19888I 0
u = 0.426286 − 1.219960I
a = −0.66481 + 1.78704I
b = 1.43638 − 1.38473I
−2.26989 + 7.19888I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.243161 + 0.664104I
a = 0.523133 − 0.354393I
b = 1.323260 + 0.243075I
−6.99155 − 2.85050I 0
u = −0.243161 − 0.664104I
a = 0.523133 + 0.354393I
b = 1.323260 − 0.243075I
−6.99155 + 2.85050I 0
u = 0.515308 + 1.203210I
a = −0.09123 + 1.52106I
b = −0.76313 − 1.26992I
2.13886 − 5.12719I 0
u = 0.515308 − 1.203210I
a = −0.09123 − 1.52106I
b = −0.76313 + 1.26992I
2.13886 + 5.12719I 0
u = −0.335508 + 0.597688I
a = 0.865218 + 1.033820I
b = 0.331892 + 0.033728I
2.75467 + 1.57364I 0
u = −0.335508 − 0.597688I
a = 0.865218 − 1.033820I
b = 0.331892 − 0.033728I
2.75467 − 1.57364I 0
u = 0.664010 + 0.151032I
a = −0.178023 + 0.640797I
b = 1.199990 + 0.348926I
−6.07050 − 3.24646I 0
u = 0.664010 − 0.151032I
a = −0.178023 − 0.640797I
b = 1.199990 − 0.348926I
−6.07050 + 3.24646I 0
u = 0.037284 + 1.334640I
a = −0.465607 − 0.486813I
b = −0.147167 + 0.263317I
−0.95180 − 2.88072I 0
u = 0.037284 − 1.334640I
a = −0.465607 + 0.486813I
b = −0.147167 − 0.263317I
−0.95180 + 2.88072I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.467731 + 1.262170I
a = 0.308949 + 1.136310I
b = 0.882237 − 0.995385I
7.89563 + 8.39932I 0
u = −0.467731 − 1.262170I
a = 0.308949 − 1.136310I
b = 0.882237 + 0.995385I
7.89563 − 8.39932I 0
u = 0.454528 + 0.468295I
a = 0.466447 − 0.293460I
b = 1.55447 − 0.20447I
−5.00548 + 6.98572I −12.81869 + 0.I
u = 0.454528 − 0.468295I
a = 0.466447 + 0.293460I
b = 1.55447 + 0.20447I
−5.00548 − 6.98572I −12.81869 + 0.I
u = −0.495947 + 1.269820I
a = −0.48329 − 1.41042I
b = −0.80391 + 1.22983I
5.4234 + 13.3296I 0
u = −0.495947 − 1.269820I
a = −0.48329 + 1.41042I
b = −0.80391 − 1.22983I
5.4234 − 13.3296I 0
u = −0.480158 + 1.308130I
a = −0.238432 − 0.965969I
b = −0.344087 + 1.131670I
7.82001 + 1.55003I 0
u = −0.480158 − 1.308130I
a = −0.238432 + 0.965969I
b = −0.344087 − 1.131670I
7.82001 − 1.55003I 0
u = −0.435470 + 1.327730I
a = 0.579421 + 1.018310I
b = 0.060548 − 1.164660I
5.86004 − 3.19383I 0
u = −0.435470 − 1.327730I
a = 0.579421 − 1.018310I
b = 0.060548 + 1.164660I
5.86004 + 3.19383I 0
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.576786 + 0.166456I
a = 0.432897 − 0.994142I
b = −0.098592 − 0.980102I
1.55147 − 2.37026I −8.00000 + 3.44366I
u = 0.576786 − 0.166456I
a = 0.432897 + 0.994142I
b = −0.098592 + 0.980102I
1.55147 + 2.37026I −8.00000 − 3.44366I
u = −1.289590 + 0.546873I
a = −0.497506 − 0.030286I
b = 0.450415 + 0.496218I
−6.53330 + 4.97775I 0
u = −1.289590 − 0.546873I
a = −0.497506 + 0.030286I
b = 0.450415 − 0.496218I
−6.53330 − 4.97775I 0
u = 0.441209 + 1.329830I
a = −0.33967 + 1.44345I
b = −0.524598 − 1.002640I
1.17347 − 6.29813I 0
u = 0.441209 − 1.329830I
a = −0.33967 − 1.44345I
b = −0.524598 + 1.002640I
1.17347 + 6.29813I 0
u = −0.679370 + 1.231340I
a = −0.170929 − 1.330400I
b = −0.80144 + 1.29353I
−0.38329 + 8.43734I 0
u = −0.679370 − 1.231340I
a = −0.170929 + 1.330400I
b = −0.80144 − 1.29353I
−0.38329 − 8.43734I 0
u = 1.32290 + 0.51746I
a = −0.190207 + 0.430256I
b = 0.118271 − 0.626537I
−4.49216 − 1.70932I 0
u = 1.32290 − 0.51746I
a = −0.190207 − 0.430256I
b = 0.118271 + 0.626537I
−4.49216 + 1.70932I 0
17
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.375658 + 0.440001I
a = 0.64923 + 1.87094I
b = −0.314859 + 0.570720I
2.96714 + 1.99436I −4.69488 − 1.20406I
u = 0.375658 − 0.440001I
a = 0.64923 − 1.87094I
b = −0.314859 − 0.570720I
2.96714 − 1.99436I −4.69488 + 1.20406I
u = 0.62937 + 1.27748I
a = −0.00293 − 1.67751I
b = 1.18421 + 1.53311I
−0.2572 − 19.7583I 0
u = 0.62937 − 1.27748I
a = −0.00293 + 1.67751I
b = 1.18421 − 1.53311I
−0.2572 + 19.7583I 0
u = 0.54728 + 1.31582I
a = −0.47652 − 1.33782I
b = 1.32944 + 1.11610I
−2.91923 − 7.22256I 0
u = 0.54728 − 1.31582I
a = −0.47652 + 1.33782I
b = 1.32944 − 1.11610I
−2.91923 + 7.22256I 0
u = 0.573688
a = 0.646215
b = 0.0411893
−0.844639 −10.8360
u = −0.65115 + 1.27711I
a = 0.00968 + 1.52279I
b = 0.96355 − 1.30179I
−5.1619 + 13.4798I 0
u = −0.65115 − 1.27711I
a = 0.00968 − 1.52279I
b = 0.96355 + 1.30179I
−5.1619 − 13.4798I 0
u = 0.63931 + 1.29926I
a = 0.03131 + 1.44776I
b = −1.10638 − 1.37778I
3.55432 − 13.22140I 0
18
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.63931 − 1.29926I
a = 0.03131 − 1.44776I
b = −1.10638 + 1.37778I
3.55432 + 13.22140I 0
u = −0.74406 + 1.27530I
a = −0.012649 + 0.997902I
b = 0.716523 − 1.025500I
−3.93401 + 2.20930I 0
u = −0.74406 − 1.27530I
a = −0.012649 − 0.997902I
b = 0.716523 + 1.025500I
−3.93401 − 2.20930I 0
u = 0.19642 + 1.46631I
a = −0.626441 + 0.338435I
b = −0.069141 − 0.567483I
2.71989 + 8.77009I 0
u = 0.19642 − 1.46631I
a = −0.626441 − 0.338435I
b = −0.069141 + 0.567483I
2.71989 − 8.77009I 0
u = 0.01462 + 1.49692I
a = 1.333740 − 0.096824I
b = −1.78200 + 0.21594I
5.25755 − 0.08686I 0
u = 0.01462 − 1.49692I
a = 1.333740 + 0.096824I
b = −1.78200 − 0.21594I
5.25755 + 0.08686I 0
u = 0.71377 + 1.33251I
a = 0.147646 − 1.233320I
b = 0.401576 + 1.072580I
−1.44206 − 5.64572I 0
u = 0.71377 − 1.33251I
a = 0.147646 + 1.233320I
b = 0.401576 − 1.072580I
−1.44206 + 5.64572I 0
u = −0.363669 + 0.288021I
a = 0.14276 − 2.67673I
b = −1.082730 + 0.323822I
−1.20544 − 3.45426I −13.16867 + 2.70599I
19
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.363669 − 0.288021I
a = 0.14276 + 2.67673I
b = −1.082730 − 0.323822I
−1.20544 + 3.45426I −13.16867 − 2.70599I
u = −0.291358 + 0.296014I
a = 0.575723 − 1.044800I
b = −0.473802 − 0.521010I
−0.47265 − 1.36744I −4.36171 + 5.04399I
u = −0.291358 − 0.296014I
a = 0.575723 + 1.044800I
b = −0.473802 + 0.521010I
−0.47265 + 1.36744I −4.36171 − 5.04399I
u = 0.21801 + 1.57434I
a = 0.325810 − 0.105373I
b = 0.279738 + 0.297618I
6.68793 + 1.52866I 0
u = 0.21801 − 1.57434I
a = 0.325810 + 0.105373I
b = 0.279738 − 0.297618I
6.68793 − 1.52866I 0
20
II. I
u
2
= h−2.54 × 10
23
u
40
− 6.69 × 10
24
u
39
+ · · · + 4.56 × 10
23
b − 1.26 ×
10
25
, −6.16 × 10
22
u
40
+ 3.15 × 10
22
u
39
+ · · · + 6.43 × 10
21
a + 4.54 ×
10
22
, u
41
+ 12u
39
+ · · · + 2u + 1i
(i) Arc colorings
a
4
=
1
0
a
9
=
0
u
a
2
=
9.59079u
40
− 4.89800u
39
+ ··· + 25.8062u − 7.05871
0.556984u
40
+ 14.6558u
39
+ ··· + 55.0569u + 27.5308
a
5
=
1
u
2
a
6
=
11.5770u
40
− 23.1309u
39
+ ··· − 47.0461u − 39.1021
6.69245u
40
+ 15.0401u
39
+ ··· + 72.9557u + 31.4519
a
1
=
10.1478u
40
+ 9.75775u
39
+ ··· + 80.8630u + 20.4721
0.556984u
40
+ 14.6558u
39
+ ··· + 55.0569u + 27.5308
a
10
=
8.52349u
40
− 0.0137372u
39
+ ··· + 14.7889u + 2.84584
9.01292u
40
+ 16.7027u
39
+ ··· + 80.1114u + 34.9859
a
8
=
u
u
3
+ u
a
7
=
−13.5555u
40
+ 8.95947u
39
+ ··· + 14.4865u + 23.0814
−24.0536u
40
+ 0.177028u
39
+ ··· − 61.3343u − 4.03325
a
11
=
−2.54793u
40
+ 6.40265u
39
+ ··· + 41.9547u + 17.8120
14.7210u
40
− 2.51803u
39
+ ··· + 35.4520u − 1.53297
a
3
=
−35.2012u
40
+ 14.3882u
39
+ ··· + 20.0442u + 38.7408
−13.9457u
40
+ 2.32945u
39
+ ··· − 34.3077u − 2.32106
a
12
=
11.6105u
40
+ 4.51644u
39
+ ··· + 74.1057u + 11.6340
3.72732u
40
+ 12.6917u
39
+ ··· + 57.3194u + 23.9340
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
1064854346389677236939351
456219922362726537089049
u
40
−
10330854817279894643230856
456219922362726537089049
u
39
+
··· −
3932475944626848987645844
152073307454242179029683
u −
9054649088924496870698245
456219922362726537089049
21
(iv) u-Polynomials at the component
22
Crossings u-Polynomials at each crossing
c
1
u
41
− 3u
40
+ ··· − 14u − 1
c
2
u
41
+ 3u
40
+ ··· + 12u − 9
c
3
u
41
+ 3u
40
+ ··· − 3u + 1
c
4
u
41
+ 12u
39
+ ··· + 2u + 1
c
5
u
41
− 3u
40
+ ··· + 12u + 9
c
6
u
41
+ u
40
+ ··· + 14u − 1
c
7
u
41
− 3u
40
+ ··· + 16u − 7
c
8
u
41
+ 12u
39
+ ··· + 2u − 1
c
9
u
41
+ u
40
+ ··· + 6u − 1
c
10
u
41
+ 3u
40
+ ··· + 16u + 7
c
11
u
41
− 3u
40
+ ··· − 3u − 1
c
12
u
41
+ u
40
+ ··· + 15u + 9
23
24
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
41
− 19y
40
+ ··· − 148y −1
c
2
, c
5
y
41
− 33y
40
+ ··· + 2232y −81
c
3
, c
11
y
41
+ 19y
40
+ ··· − 23y −1
c
4
, c
8
y
41
+ 24y
40
+ ··· − 16y −1
c
6
y
41
+ 5y
40
+ ··· + 66y −1
c
7
, c
10
y
41
+ 33y
40
+ ··· − 1256y −49
c
9
y
41
+ 11y
40
+ ··· − 24y −1
c
12
y
41
+ 37y
40
+ ··· − 873y −81
25
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.294205 + 0.894932I
a = −0.96761 − 1.64787I
b = −0.54908 + 1.51961I
4.45682 + 3.64482I −3.20012 − 2.14168I
u = −0.294205 − 0.894932I
a = −0.96761 + 1.64787I
b = −0.54908 − 1.51961I
4.45682 − 3.64482I −3.20012 + 2.14168I
u = 0.814337 + 0.414835I
a = 0.363612 + 0.238097I
b = −0.586577 + 0.546664I
−1.39621 + 0.79226I −11.95934 − 3.79681I
u = 0.814337 − 0.414835I
a = 0.363612 − 0.238097I
b = −0.586577 − 0.546664I
−1.39621 − 0.79226I −11.95934 + 3.79681I
u = 0.284512 + 1.097740I
a = −0.139114 + 1.300540I
b = −1.094910 − 0.691279I
1.64334 − 4.87523I −5.35207 + 6.34777I
u = 0.284512 − 1.097740I
a = −0.139114 − 1.300540I
b = −1.094910 + 0.691279I
1.64334 + 4.87523I −5.35207 − 6.34777I
u = 0.314498 + 1.093850I
a = 1.047920 − 0.855485I
b = 0.689603 + 0.666465I
3.23575 − 3.64245I −6.22535 + 6.39839I
u = 0.314498 − 1.093850I
a = 1.047920 + 0.855485I
b = 0.689603 − 0.666465I
3.23575 + 3.64245I −6.22535 − 6.39839I
u = −0.432452 + 1.052920I
a = 1.175220 + 0.647057I
b = −0.132609 − 1.336900I
5.22222 − 0.62067I 0.39521 + 2.11145I
u = −0.432452 − 1.052920I
a = 1.175220 − 0.647057I
b = −0.132609 + 1.336900I
5.22222 + 0.62067I 0.39521 − 2.11145I
26
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.631279 + 0.952583I
a = −0.149338 + 0.889551I
b = −0.202560 − 0.349498I
−4.80982 − 0.17127I −14.1729 − 0.6369I
u = −0.631279 − 0.952583I
a = −0.149338 − 0.889551I
b = −0.202560 + 0.349498I
−4.80982 + 0.17127I −14.1729 + 0.6369I
u = −1.094450 + 0.385041I
a = −0.453292 − 0.179522I
b = 0.666315 − 0.025679I
−6.95193 + 5.59929I −13.8828 − 7.7228I
u = −1.094450 − 0.385041I
a = −0.453292 + 0.179522I
b = 0.666315 + 0.025679I
−6.95193 − 5.59929I −13.8828 + 7.7228I
u = 0.106906 + 0.784852I
a = 1.02361 + 2.35207I
b = −0.671203 − 0.248330I
0.11124 + 3.17137I −7.21953 − 2.12399I
u = 0.106906 − 0.784852I
a = 1.02361 − 2.35207I
b = −0.671203 + 0.248330I
0.11124 − 3.17137I −7.21953 + 2.12399I
u = −0.511264 + 1.134100I
a = 0.08397 − 2.02501I
b = −1.54546 + 1.59706I
4.36483 + 8.01871I 0. − 7.86201I
u = −0.511264 − 1.134100I
a = 0.08397 + 2.02501I
b = −1.54546 − 1.59706I
4.36483 − 8.01871I 0. + 7.86201I
u = −0.702660 + 0.244809I
a = 0.348138 − 0.998082I
b = −1.065380 − 0.708894I
1.79906 − 3.41018I −6.17250 + 3.51782I
u = −0.702660 − 0.244809I
a = 0.348138 + 0.998082I
b = −1.065380 + 0.708894I
1.79906 + 3.41018I −6.17250 − 3.51782I
27
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.290123 + 1.226800I
a = −1.36961 + 1.67442I
b = 1.87947 − 1.11725I
−0.98468 + 8.68675I −8.00000 − 8.68412I
u = −0.290123 − 1.226800I
a = −1.36961 − 1.67442I
b = 1.87947 + 1.11725I
−0.98468 − 8.68675I −8.00000 + 8.68412I
u = 0.482431 + 1.189810I
a = −0.21116 + 1.54018I
b = −0.78109 − 1.18139I
1.18945 − 5.41046I −8.00000 + 0.I
u = 0.482431 − 1.189810I
a = −0.21116 − 1.54018I
b = −0.78109 + 1.18139I
1.18945 + 5.41046I −8.00000 + 0.I
u = 0.155102 + 0.696565I
a = −1.18836 − 2.14248I
b = 0.0380708 + 0.0527682I
1.58556 + 1.42793I −14.2600 + 4.3907I
u = 0.155102 − 0.696565I
a = −1.18836 + 2.14248I
b = 0.0380708 − 0.0527682I
1.58556 − 1.42793I −14.2600 − 4.3907I
u = −0.183421 + 0.686680I
a = −0.48794 − 1.51808I
b = 1.33663 + 0.50535I
−6.63456 + 3.96308I −10.29153 − 1.24945I
u = −0.183421 − 0.686680I
a = −0.48794 + 1.51808I
b = 1.33663 − 0.50535I
−6.63456 − 3.96308I −10.29153 + 1.24945I
u = −0.046728 + 0.680660I
a = −2.16365 + 1.63985I
b = 2.45598 − 0.35924I
−3.52521 − 7.16247I −9.24661 + 2.38779I
u = −0.046728 − 0.680660I
a = −2.16365 − 1.63985I
b = 2.45598 + 0.35924I
−3.52521 + 7.16247I −9.24661 − 2.38779I
28
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.58523 + 1.29311I
a = −0.046071 − 1.308290I
b = 0.530935 + 1.132160I
−1.19838 − 5.21376I 0
u = 0.58523 − 1.29311I
a = −0.046071 + 1.308290I
b = 0.530935 − 1.132160I
−1.19838 + 5.21376I 0
u = 1.33959 + 0.50168I
a = −0.255393 + 0.410560I
b = 0.104528 − 0.645475I
−4.42992 − 1.79940I 0
u = 1.33959 − 0.50168I
a = −0.255393 − 0.410560I
b = 0.104528 + 0.645475I
−4.42992 + 1.79940I 0
u = −0.09651 + 1.43033I
a = 0.082930 + 0.159715I
b = 0.595667 − 0.347302I
7.08548 − 0.71231I 0
u = −0.09651 − 1.43033I
a = 0.082930 − 0.159715I
b = 0.595667 + 0.347302I
7.08548 + 0.71231I 0
u = 0.316887 + 0.397785I
a = 2.62350 − 1.06639I
b = −1.090340 + 0.726353I
0.70471 − 2.82051I −7.53028 + 3.18051I
u = 0.316887 − 0.397785I
a = 2.62350 + 1.06639I
b = −1.090340 − 0.726353I
0.70471 + 2.82051I −7.53028 − 3.18051I
u = 0.09794 + 1.49496I
a = 1.224090 + 0.383076I
b = −1.64412 − 0.49216I
5.23630 + 0.69959I 0
u = 0.09794 − 1.49496I
a = 1.224090 − 0.383076I
b = −1.64412 + 0.49216I
5.23630 − 0.69959I 0
29
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.428680
a = 1.91710
b = −0.867729
−3.53851 −12.1100
30
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
41
− 3u
40
+ ··· − 14u − 1)
· (u
155
− 12u
154
+ ··· + 27570093u − 1107493)
c
2
(u
41
+ 3u
40
+ ··· + 12u − 9)(u
155
+ 4u
154
+ ··· + 3352225u + 213761)
c
3
(u
41
+ 3u
40
+ ··· − 3u + 1)(u
155
+ 46u
153
+ ··· + 141090u + 6263)
c
4
(u
41
+ 12u
39
+ ··· + 2u + 1)(u
155
+ 5u
154
+ ··· + 5977u + 1949)
c
5
(u
41
− 3u
40
+ ··· + 12u + 9)(u
155
+ 4u
154
+ ··· + 3352225u + 213761)
c
6
(u
41
+ u
40
+ ··· + 14u − 1)
· (u
155
+ 2u
154
+ ··· + 2055676577u + 258968363)
c
7
(u
41
− 3u
40
+ ··· + 16u − 7)(u
155
− 8u
154
+ ··· − 211061u + 8101)
c
8
(u
41
+ 12u
39
+ ··· + 2u − 1)(u
155
+ 5u
154
+ ··· + 5977u + 1949)
c
9
(u
41
+ u
40
+ ··· + 6u − 1)(u
155
+ 6u
154
+ ··· − 6440321u + 1742611)
c
10
(u
41
+ 3u
40
+ ··· + 16u + 7)(u
155
− 8u
154
+ ··· − 211061u + 8101)
c
11
(u
41
− 3u
40
+ ··· − 3u − 1)(u
155
+ 46u
153
+ ··· + 141090u + 6263)
c
12
(u
41
+ u
40
+ ··· + 15u + 9)(u
155
− 2u
154
+ ··· − 75394u + 5489)
31
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
41
− 19y
40
+ ··· − 148y −1)
· (y
155
+ 2y
154
+ ··· + 738368560502371y −1226540745049)
c
2
, c
5
(y
41
− 33y
40
+ ··· + 2232y −81)
· (y
155
− 120y
154
+ ··· − 8858040695633y −45693765121)
c
3
, c
11
(y
41
+ 19y
40
+ ··· − 23y −1)
· (y
155
+ 92y
154
+ ··· + 1224660764y −39225169)
c
4
, c
8
(y
41
+ 24y
40
+ ··· − 16y −1)
· (y
155
+ 89y
154
+ ··· − 114983845y −3798601)
c
6
(y
41
+ 5y
40
+ ··· + 66y −1)
· (y
155
− 34y
154
+ ··· + 849943741672138741y −67064613034899769)
c
7
, c
10
(y
41
+ 33y
40
+ ··· − 1256y −49)
· (y
155
+ 110y
154
+ ··· − 4992732509y −65626201)
c
9
(y
41
+ 11y
40
+ ··· − 24y −1)
· (y
155
+ 52y
154
+ ··· − 183271361272113y −3036693097321)
c
12
(y
41
+ 37y
40
+ ··· − 873y −81)
· (y
155
+ 50y
154
+ ··· + 2953027638y −30129121)
32
