12a
1197
(K12a
1197
)
A knot diagram
1
Linearized knot diagam
4 10 12 8 3 11 2 1 5 6 7 9
Solving Sequence
6,11
7
3,12
4 5 10 2 8 1 9
c
6
c
11
c
3
c
5
c
10
c
2
c
7
c
1
c
9
c
4
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.93169 × 10
465
u
150
+ 6.15703 × 10
464
u
149
+ ··· + 1.03741 × 10
462
b − 1.46910 × 10
465
,
2.56491 × 10
465
u
150
− 8.12627 × 10
464
u
149
+ ··· + 1.03741 × 10
462
a + 2.03425 × 10
465
, u
151
+ u
150
+ ··· + 32u + 1i
I
u
2
= h−7692162316330u
29
+ 11057540047927u
28
+ ··· + 19577401712437b − 8087783676063,
46327339192051u
29
− 8910173226523u
28
+ ··· + 19577401712437a + 35928041395928,
u
30
− u
29
+ ··· + 3u
2
+ 1i
I
u
3
= hb + 1, a
3
− 2a
2
+ a + 1, u + 1i
* 3 irreducible components of dim
C
= 0, with total 184 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−1.93 × 10
465
u
150
+ 6.16 × 10
464
u
149
+ · · · + 1.04 × 10
462
b − 1.47 ×
10
465
, 2.56 × 10
465
u
150
− 8.13 × 10
464
u
149
+ · · · + 1.04 × 10
462
a + 2.03 ×
10
465
, u
151
+ u
150
+ · · · + 32u + 1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
7
=
1
−u
2
a
3
=
−2472.41u
150
+ 783.321u
149
+ ··· − 60019.0u − 1960.89
1862.03u
150
− 593.499u
149
+ ··· + 44184.5u + 1416.12
a
12
=
u
−u
3
+ u
a
4
=
−2525.32u
150
+ 798.167u
149
+ ··· − 61301.5u − 2002.14
1896.33u
150
− 603.365u
149
+ ··· + 45017.4u + 1442.63
a
5
=
−1243.19u
150
+ 402.943u
149
+ ··· − 28715.3u − 917.733
1474.28u
150
− 472.125u
149
+ ··· + 34978.6u + 1121.68
a
10
=
−u
u
a
2
=
−1414.94u
150
+ 443.487u
149
+ ··· − 35022.8u − 1160.69
804.555u
150
− 253.665u
149
+ ··· + 19188.2u + 615.911
a
8
=
1246.81u
150
− 395.426u
149
+ ··· + 29898.5u + 949.873
−1586.95u
150
+ 506.441u
149
+ ··· − 37478.5u − 1197.23
a
1
=
1468.40u
150
− 478.505u
149
+ ··· + 33223.5u + 1016.63
−1479.74u
150
+ 476.894u
149
+ ··· − 34849.1u − 1112.88
a
9
=
410.152u
150
− 117.692u
149
+ ··· + 11541.2u + 398.278
30.8075u
150
− 12.2755u
149
+ ··· + 664.532u + 22.0427
(ii) Obstruction class = −1
(iii) Cusp Shapes = −1069.34u
150
+ 329.332u
149
+ ··· − 25627.6u − 819.257
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
151
+ 10u
150
+ ··· − 31u + 23
c
2
u
151
+ 3u
150
+ ··· + 17222u + 2203
c
3
u
151
− 3u
150
+ ··· − 514125u + 116356
c
4
u
151
− u
150
+ ··· + 64u + 16
c
5
u
151
+ 9u
150
+ ··· − 6313u + 9724
c
6
, c
10
, c
11
u
151
+ u
150
+ ··· + 32u + 1
c
7
u
151
− 4u
150
+ ··· − 2579090u + 234743
c
8
, c
12
u
151
− 2u
150
+ ··· + 4057u + 1279
c
9
u
151
− 2u
150
+ ··· + 492840u + 167911
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
151
+ 18y
150
+ ··· − 28249y −529
c
2
y
151
− 13y
150
+ ··· + 173229284y −4853209
c
3
y
151
− 21y
150
+ ··· − 752670674231y −13538718736
c
4
y
151
+ y
150
+ ··· − 11136y −256
c
5
y
151
+ 21y
150
+ ··· − 6011235647y −94556176
c
6
, c
10
, c
11
y
151
− 149y
150
+ ··· + 246y −1
c
7
y
151
+ 46y
150
+ ··· − 7705800129308y −55104276049
c
8
, c
12
y
151
+ 94y
150
+ ··· − 113123915y −1635841
c
9
y
151
− 56y
150
+ ··· + 725298561134y −28194103921
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.472050 + 0.884004I
a = −0.066559 − 0.608220I
b = −0.865778 + 0.742016I
−1.71499 + 3.44862I 0
u = 0.472050 − 0.884004I
a = −0.066559 + 0.608220I
b = −0.865778 − 0.742016I
−1.71499 − 3.44862I 0
u = 0.504245 + 0.856993I
a = 0.408980 + 0.667727I
b = 0.95994 − 1.03916I
0.0365 + 15.6382I 0
u = 0.504245 − 0.856993I
a = 0.408980 − 0.667727I
b = 0.95994 + 1.03916I
0.0365 − 15.6382I 0
u = 0.912866 + 0.388375I
a = 1.180150 − 0.056109I
b = −0.704000 − 0.782081I
1.12038 − 2.21817I 0
u = 0.912866 − 0.388375I
a = 1.180150 + 0.056109I
b = −0.704000 + 0.782081I
1.12038 + 2.21817I 0
u = −0.611081 + 0.775672I
a = −0.266528 + 1.168600I
b = −0.938329 − 1.024730I
−1.20004 − 5.85292I 0
u = −0.611081 − 0.775672I
a = −0.266528 − 1.168600I
b = −0.938329 + 1.024730I
−1.20004 + 5.85292I 0
u = −0.503327 + 0.841973I
a = 0.405727 − 0.542238I
b = 0.940020 + 0.870651I
−3.87850 − 9.51725I 0
u = −0.503327 − 0.841973I
a = 0.405727 + 0.542238I
b = 0.940020 − 0.870651I
−3.87850 + 9.51725I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.006270 + 0.228464I
a = 1.216270 + 0.711644I
b = −0.847046 + 0.388872I
−0.037294 + 1.011850I 0
u = −1.006270 − 0.228464I
a = 1.216270 − 0.711644I
b = −0.847046 − 0.388872I
−0.037294 − 1.011850I 0
u = 0.307987 + 1.007600I
a = 0.0145948 − 0.0417020I
b = −0.243767 + 0.424475I
−0.97150 + 2.88010I 0
u = 0.307987 − 1.007600I
a = 0.0145948 + 0.0417020I
b = −0.243767 − 0.424475I
−0.97150 − 2.88010I 0
u = 0.451480 + 0.831454I
a = 0.679184 + 0.277402I
b = 0.551251 − 0.635164I
2.01542 + 3.29869I 0
u = 0.451480 − 0.831454I
a = 0.679184 − 0.277402I
b = 0.551251 + 0.635164I
2.01542 − 3.29869I 0
u = 0.662919 + 0.657611I
a = −0.019360 − 0.205176I
b = −0.041555 + 0.763269I
2.82346 + 1.75052I 0
u = 0.662919 − 0.657611I
a = −0.019360 + 0.205176I
b = −0.041555 − 0.763269I
2.82346 − 1.75052I 0
u = −0.289908 + 0.878176I
a = −0.403446 + 0.003942I
b = −0.111239 − 1.043220I
4.09674 − 6.13896I 0
u = −0.289908 − 0.878176I
a = −0.403446 − 0.003942I
b = −0.111239 + 1.043220I
4.09674 + 6.13896I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.680650 + 0.853136I
a = −0.404161 − 0.241544I
b = 0.556428 − 0.537921I
−3.44023 + 3.92803I 0
u = −0.680650 − 0.853136I
a = −0.404161 + 0.241544I
b = 0.556428 + 0.537921I
−3.44023 − 3.92803I 0
u = 0.692681 + 0.848382I
a = −0.601898 + 0.126360I
b = 0.661284 + 0.730649I
0.52013 − 9.98699I 0
u = 0.692681 − 0.848382I
a = −0.601898 − 0.126360I
b = 0.661284 − 0.730649I
0.52013 + 9.98699I 0
u = −0.719832 + 0.492448I
a = 1.399660 − 0.089298I
b = −0.547746 + 0.373026I
1.12644 − 1.02234I 0
u = −0.719832 − 0.492448I
a = 1.399660 + 0.089298I
b = −0.547746 − 0.373026I
1.12644 + 1.02234I 0
u = 1.16581
a = 0.625214
b = 0.958492
−0.203933 0
u = −0.088671 + 0.819822I
a = 0.178460 − 0.665085I
b = 0.501925 − 0.506145I
1.03243 + 3.95432I 0
u = −0.088671 − 0.819822I
a = 0.178460 + 0.665085I
b = 0.501925 + 0.506145I
1.03243 − 3.95432I 0
u = 0.294379 + 0.769396I
a = −0.566559 − 0.276220I
b = −0.89715 + 1.15300I
−0.74749 + 6.51000I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.294379 − 0.769396I
a = −0.566559 + 0.276220I
b = −0.89715 − 1.15300I
−0.74749 − 6.51000I 0
u = 1.18028
a = 0.639260
b = 0.954322
−0.203875 0
u = 0.767722 + 0.269242I
a = −0.94336 − 2.30227I
b = −0.251496 + 1.103530I
2.38552 + 6.45222I 0
u = 0.767722 − 0.269242I
a = −0.94336 + 2.30227I
b = −0.251496 − 1.103530I
2.38552 − 6.45222I 0
u = 1.194630 + 0.039800I
a = −0.30353 − 2.67611I
b = 0.00986 + 1.76611I
2.58122 + 6.21762I 0
u = 1.194630 − 0.039800I
a = −0.30353 + 2.67611I
b = 0.00986 − 1.76611I
2.58122 − 6.21762I 0
u = −0.666938 + 0.432809I
a = 0.857628 − 0.684938I
b = 0.333070 + 1.027970I
5.90452 + 1.69142I 0
u = −0.666938 − 0.432809I
a = 0.857628 + 0.684938I
b = 0.333070 − 1.027970I
5.90452 − 1.69142I 0
u = 0.466756 + 0.642700I
a = 0.316550 + 0.923918I
b = 0.512069 − 0.068322I
0.36618 + 2.92618I 0
u = 0.466756 − 0.642700I
a = 0.316550 − 0.923918I
b = 0.512069 + 0.068322I
0.36618 − 2.92618I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.576637 + 0.541410I
a = 0.469384 + 0.295539I
b = 0.830869 − 0.401613I
0.83324 + 1.17258I 0
u = 0.576637 − 0.541410I
a = 0.469384 − 0.295539I
b = 0.830869 + 0.401613I
0.83324 − 1.17258I 0
u = 0.726822 + 0.968082I
a = 0.357375 + 0.005289I
b = −0.485392 − 0.257705I
−1.11296 + 2.52087I 0
u = 0.726822 − 0.968082I
a = 0.357375 − 0.005289I
b = −0.485392 + 0.257705I
−1.11296 − 2.52087I 0
u = 0.771651 + 0.143074I
a = 1.348220 − 0.330576I
b = −0.659980 + 0.317289I
1.47481 + 1.99247I 0
u = 0.771651 − 0.143074I
a = 1.348220 + 0.330576I
b = −0.659980 − 0.317289I
1.47481 − 1.99247I 0
u = 1.251800 + 0.039923I
a = 1.47364 − 0.18892I
b = −1.56675 + 0.30763I
1.83875 + 1.81155I 0
u = 1.251800 − 0.039923I
a = 1.47364 + 0.18892I
b = −1.56675 − 0.30763I
1.83875 − 1.81155I 0
u = −0.606001 + 0.422787I
a = 0.297448 − 0.682730I
b = 1.12975 + 0.89007I
2.97652 − 7.77376I 0
u = −0.606001 − 0.422787I
a = 0.297448 + 0.682730I
b = 1.12975 − 0.89007I
2.97652 + 7.77376I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.266550 + 0.008705I
a = 0.556477 − 0.495290I
b = 1.000120 + 0.422333I
3.57413 − 6.67964I 0
u = −1.266550 − 0.008705I
a = 0.556477 + 0.495290I
b = 1.000120 − 0.422333I
3.57413 + 6.67964I 0
u = −0.099423 + 0.717248I
a = 0.088176 + 0.562484I
b = −0.847484 − 1.026340I
−0.81884 − 2.99177I 0
u = −0.099423 − 0.717248I
a = 0.088176 − 0.562484I
b = −0.847484 + 1.026340I
−0.81884 + 2.99177I 0
u = −1.275840 + 0.028854I
a = 1.51296 + 0.05179I
b = −1.90289 + 0.18009I
1.19324 − 0.84761I 0
u = −1.275840 − 0.028854I
a = 1.51296 − 0.05179I
b = −1.90289 − 0.18009I
1.19324 + 0.84761I 0
u = −0.374955 + 0.586656I
a = 0.328445 + 0.196934I
b = −0.796211 + 0.663794I
−1.92772 + 0.99887I 0
u = −0.374955 − 0.586656I
a = 0.328445 − 0.196934I
b = −0.796211 − 0.663794I
−1.92772 − 0.99887I 0
u = −1.285530 + 0.224675I
a = 0.600454 − 0.994227I
b = 0.236056 + 1.049820I
6.60594 + 2.14914I 0
u = −1.285530 − 0.224675I
a = 0.600454 + 0.994227I
b = 0.236056 − 1.049820I
6.60594 − 2.14914I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.314366 + 0.611307I
a = −1.076990 + 0.329028I
b = −0.955686 − 0.827991I
−2.01575 − 4.12490I 0
u = −0.314366 − 0.611307I
a = −1.076990 − 0.329028I
b = −0.955686 + 0.827991I
−2.01575 + 4.12490I 0
u = 1.314370 + 0.054225I
a = 0.63928 − 1.81129I
b = −0.221124 + 0.619361I
2.21104 + 1.53029I 0
u = 1.314370 − 0.054225I
a = 0.63928 + 1.81129I
b = −0.221124 − 0.619361I
2.21104 − 1.53029I 0
u = −0.226306 + 0.644285I
a = 0.193572 + 0.017568I
b = −0.901110 + 0.749271I
−1.97131 + 0.98981I 0
u = −0.226306 − 0.644285I
a = 0.193572 − 0.017568I
b = −0.901110 − 0.749271I
−1.97131 − 0.98981I 0
u = −1.319580 + 0.000470I
a = 0.15449 + 2.89765I
b = −0.41715 − 2.16203I
0.74888 − 2.07009I 0
u = −1.319580 − 0.000470I
a = 0.15449 − 2.89765I
b = −0.41715 + 2.16203I
0.74888 + 2.07009I 0
u = −1.325950 + 0.072576I
a = −0.22273 − 2.02390I
b = 0.006077 + 0.210149I
0.33089 − 3.72354I 0
u = −1.325950 − 0.072576I
a = −0.22273 + 2.02390I
b = 0.006077 − 0.210149I
0.33089 + 3.72354I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.501132 + 0.424261I
a = 0.774921 + 0.176630I
b = 0.392521 − 0.225566I
1.02977 + 1.08869I 0
u = 0.501132 − 0.424261I
a = 0.774921 − 0.176630I
b = 0.392521 + 0.225566I
1.02977 − 1.08869I 0
u = 1.359840 + 0.106565I
a = 0.38150 − 2.26011I
b = −0.407501 + 1.332490I
2.43991 + 2.33188I 0
u = 1.359840 − 0.106565I
a = 0.38150 + 2.26011I
b = −0.407501 − 1.332490I
2.43991 − 2.33188I 0
u = −1.372460 + 0.115018I
a = −2.07479 + 0.74394I
b = 2.31167 − 0.86468I
4.50244 − 9.81798I 0
u = −1.372460 − 0.115018I
a = −2.07479 − 0.74394I
b = 2.31167 + 0.86468I
4.50244 + 9.81798I 0
u = −1.376410 + 0.053949I
a = 0.439738 − 0.430662I
b = −1.45268 + 0.38145I
2.51893 − 0.80202I 0
u = −1.376410 − 0.053949I
a = 0.439738 + 0.430662I
b = −1.45268 − 0.38145I
2.51893 + 0.80202I 0
u = 1.392990 + 0.092555I
a = −1.03769 + 2.11407I
b = 0.103443 − 0.346460I
5.20516 + 9.30317I 0
u = 1.392990 − 0.092555I
a = −1.03769 − 2.11407I
b = 0.103443 + 0.346460I
5.20516 − 9.30317I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.393310 + 0.092532I
a = 0.35300 + 2.65057I
b = −0.64454 − 1.55997I
3.56985 − 4.53824I 0
u = −1.393310 − 0.092532I
a = 0.35300 − 2.65057I
b = −0.64454 + 1.55997I
3.56985 + 4.53824I 0
u = 1.395620 + 0.092828I
a = −1.49502 − 1.58215I
b = 1.73103 + 1.54682I
2.26519 + 4.19440I 0
u = 1.395620 − 0.092828I
a = −1.49502 + 1.58215I
b = 1.73103 − 1.54682I
2.26519 − 4.19440I 0
u = 1.41149 + 0.12685I
a = −0.040753 − 1.036190I
b = −1.186810 + 0.482059I
3.47980 + 5.91274I 0
u = 1.41149 − 0.12685I
a = −0.040753 + 1.036190I
b = −1.186810 − 0.482059I
3.47980 − 5.91274I 0
u = 1.41753 + 0.01543I
a = −0.26012 + 1.98695I
b = −0.700504 − 1.140990I
8.08358 − 2.80885I 0
u = 1.41753 − 0.01543I
a = −0.26012 − 1.98695I
b = −0.700504 + 1.140990I
8.08358 + 2.80885I 0
u = 1.41337 + 0.32587I
a = 0.391511 + 0.900541I
b = 0.210075 − 0.759023I
2.96910 + 1.89636I 0
u = 1.41337 − 0.32587I
a = 0.391511 − 0.900541I
b = 0.210075 + 0.759023I
2.96910 − 1.89636I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.45986 + 0.04354I
a = 0.408620 + 0.933157I
b = 0.379155 − 0.667460I
8.29942 − 2.47433I 0
u = −1.45986 − 0.04354I
a = 0.408620 − 0.933157I
b = 0.379155 + 0.667460I
8.29942 + 2.47433I 0
u = 1.44853 + 0.23223I
a = 0.03102 − 1.82557I
b = −1.08265 + 1.19970I
3.72729 + 7.23890I 0
u = 1.44853 − 0.23223I
a = 0.03102 + 1.82557I
b = −1.08265 − 1.19970I
3.72729 − 7.23890I 0
u = −1.44057 + 0.29049I
a = −0.08711 + 1.97285I
b = −0.99032 − 1.49431I
4.83658 − 10.34260I 0
u = −1.44057 − 0.29049I
a = −0.08711 − 1.97285I
b = −0.99032 + 1.49431I
4.83658 + 10.34260I 0
u = −0.273659 + 0.438926I
a = −2.06869 + 0.18529I
b = −0.818659 − 0.523077I
−1.90487 − 3.92884I −7.58573 + 9.42654I
u = −0.273659 − 0.438926I
a = −2.06869 − 0.18529I
b = −0.818659 + 0.523077I
−1.90487 + 3.92884I −7.58573 − 9.42654I
u = −1.48690 + 0.16147I
a = −0.079299 − 0.792708I
b = 0.854653 + 0.548893I
7.49359 − 3.32401I 0
u = −1.48690 − 0.16147I
a = −0.079299 + 0.792708I
b = 0.854653 − 0.548893I
7.49359 + 3.32401I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.47731 + 0.34713I
a = −0.54860 − 1.36092I
b = −0.383801 + 1.301650I
9.8269 + 10.6093I 0
u = 1.47731 − 0.34713I
a = −0.54860 + 1.36092I
b = −0.383801 − 1.301650I
9.8269 − 10.6093I 0
u = 1.50967 + 0.15793I
a = −0.65385 + 2.02993I
b = 1.32504 − 1.60173I
9.83570 + 9.99284I 0
u = 1.50967 − 0.15793I
a = −0.65385 − 2.02993I
b = 1.32504 + 1.60173I
9.83570 − 9.99284I 0
u = −1.50985 + 0.16956I
a = −0.45650 − 1.40877I
b = 1.19697 + 1.06000I
7.65948 − 3.70739I 0
u = −1.50985 − 0.16956I
a = −0.45650 + 1.40877I
b = 1.19697 − 1.06000I
7.65948 + 3.70739I 0
u = 1.51617 + 0.14598I
a = 0.17637 + 1.74282I
b = 0.66376 − 1.32871I
12.95790 + 0.46142I 0
u = 1.51617 − 0.14598I
a = 0.17637 − 1.74282I
b = 0.66376 + 1.32871I
12.95790 − 0.46142I 0
u = −1.50184 + 0.32781I
a = 0.055125 + 1.190220I
b = −0.699659 − 0.996740I
5.09694 − 7.49634I 0
u = −1.50184 − 0.32781I
a = 0.055125 − 1.190220I
b = −0.699659 + 0.996740I
5.09694 + 7.49634I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.50712 + 0.31536I
a = 0.21669 + 1.69567I
b = −0.91742 − 1.22593I
4.64251 − 7.77080I 0
u = −1.50712 − 0.31536I
a = 0.21669 − 1.69567I
b = −0.91742 + 1.22593I
4.64251 + 7.77080I 0
u = 0.005081 + 0.459151I
a = 2.07821 + 2.22192I
b = 0.566295 + 0.122067I
−3.70803 + 2.01148I −16.7299 − 3.2259I
u = 0.005081 − 0.459151I
a = 2.07821 − 2.22192I
b = 0.566295 − 0.122067I
−3.70803 − 2.01148I −16.7299 + 3.2259I
u = 0.122429 + 0.441064I
a = 0.307074 − 0.852221I
b = 1.29383 + 1.07539I
−0.25921 + 7.91248I −8.42843 − 10.86566I
u = 0.122429 − 0.441064I
a = 0.307074 + 0.852221I
b = 1.29383 − 1.07539I
−0.25921 − 7.91248I −8.42843 + 10.86566I
u = −1.51485 + 0.29555I
a = 0.159193 − 1.316970I
b = 0.869395 + 0.890203I
8.41929 − 7.39030I 0
u = −1.51485 − 0.29555I
a = 0.159193 + 1.316970I
b = 0.869395 − 0.890203I
8.41929 + 7.39030I 0
u = 1.54114 + 0.15243I
a = 0.808180 + 0.527962I
b = 0.169963 − 0.381806I
8.54425 + 3.33001I 0
u = 1.54114 − 0.15243I
a = 0.808180 − 0.527962I
b = 0.169963 + 0.381806I
8.54425 − 3.33001I 0
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.54334 + 0.13218I
a = −0.46547 + 1.94357I
b = −0.508408 − 0.949189I
9.86209 − 8.16989I 0
u = −1.54334 − 0.13218I
a = −0.46547 − 1.94357I
b = −0.508408 + 0.949189I
9.86209 + 8.16989I 0
u = −1.54020 + 0.18959I
a = −0.11473 + 1.51017I
b = −0.213702 − 1.283790I
10.07000 − 4.73975I 0
u = −1.54020 − 0.18959I
a = −0.11473 − 1.51017I
b = −0.213702 + 1.283790I
10.07000 + 4.73975I 0
u = 1.52597 + 0.30174I
a = −0.13264 + 1.69925I
b = 1.09969 − 1.20329I
2.69365 + 13.68460I 0
u = 1.52597 − 0.30174I
a = −0.13264 − 1.69925I
b = 1.09969 + 1.20329I
2.69365 − 13.68460I 0
u = −1.53001 + 0.30855I
a = −0.07200 − 1.89106I
b = 1.06195 + 1.35725I
6.6245 − 19.8877I 0
u = −1.53001 − 0.30855I
a = −0.07200 + 1.89106I
b = 1.06195 − 1.35725I
6.6245 + 19.8877I 0
u = −1.54951 + 0.24361I
a = 0.185424 − 1.192490I
b = 0.339633 + 0.619390I
7.13558 − 6.16028I 0
u = −1.54951 − 0.24361I
a = 0.185424 + 1.192490I
b = 0.339633 − 0.619390I
7.13558 + 6.16028I 0
17
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.55092 + 0.28578I
a = 0.13231 − 2.05785I
b = −0.87798 + 1.37827I
5.81788 + 9.83437I 0
u = 1.55092 − 0.28578I
a = 0.13231 + 2.05785I
b = −0.87798 − 1.37827I
5.81788 − 9.83437I 0
u = −0.108555 + 0.402624I
a = −0.76794 + 1.54963I
b = −1.030070 − 0.682662I
−2.21467 − 0.54177I −9.73235 − 2.83144I
u = −0.108555 − 0.402624I
a = −0.76794 − 1.54963I
b = −1.030070 + 0.682662I
−2.21467 + 0.54177I −9.73235 + 2.83144I
u = 1.59611 + 0.08699I
a = 0.212658 − 0.852395I
b = −0.496177 + 0.758175I
5.16526 − 0.31579I 0
u = 1.59611 − 0.08699I
a = 0.212658 + 0.852395I
b = −0.496177 − 0.758175I
5.16526 + 0.31579I 0
u = 0.105740 + 0.346172I
a = −1.84978 − 1.14288I
b = −0.99826 + 1.06299I
−1.33844 + 3.06291I −5.43431 − 6.81720I
u = 0.105740 − 0.346172I
a = −1.84978 + 1.14288I
b = −0.99826 − 1.06299I
−1.33844 − 3.06291I −5.43431 + 6.81720I
u = −0.119394 + 0.340455I
a = 1.35948 − 4.85501I
b = 0.625960 + 0.177729I
0.27433 − 7.82240I −9.2796 + 15.5181I
u = −0.119394 − 0.340455I
a = 1.35948 + 4.85501I
b = 0.625960 − 0.177729I
0.27433 + 7.82240I −9.2796 − 15.5181I
18
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.60673 + 0.41665I
a = −0.087156 − 0.362531I
b = −0.323899 + 0.499991I
6.13843 + 1.53567I 0
u = 1.60673 − 0.41665I
a = −0.087156 + 0.362531I
b = −0.323899 − 0.499991I
6.13843 − 1.53567I 0
u = −0.159193 + 0.296546I
a = 0.882742 + 1.039190I
b = 0.73428 − 1.42709I
−2.79569 − 2.77242I −9.9283 + 14.3820I
u = −0.159193 − 0.296546I
a = 0.882742 − 1.039190I
b = 0.73428 + 1.42709I
−2.79569 + 2.77242I −9.9283 − 14.3820I
u = −1.67574 + 0.12556I
a = −0.320567 + 0.727525I
b = −0.036115 − 0.656702I
8.93364 + 6.05785I 0
u = −1.67574 − 0.12556I
a = −0.320567 − 0.727525I
b = −0.036115 + 0.656702I
8.93364 − 6.05785I 0
u = −0.022916 + 0.308042I
a = −1.15172 + 2.90897I
b = −0.840214 − 0.292102I
−1.91966 − 0.20692I −9.60004 + 1.25661I
u = −0.022916 − 0.308042I
a = −1.15172 − 2.90897I
b = −0.840214 + 0.292102I
−1.91966 + 0.20692I −9.60004 − 1.25661I
u = −0.232926
a = 2.86222
b = −0.993517
−1.47689 −7.48490
u = −0.0764654 + 0.0179802I
a = −10.9547 − 12.0482I
b = −0.306428 + 0.900968I
2.97613 + 2.97620I 6.05883 − 2.35222I
19
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.0764654 − 0.0179802I
a = −10.9547 + 12.0482I
b = −0.306428 − 0.900968I
2.97613 − 2.97620I 6.05883 + 2.35222I
20
II.
I
u
2
= h−7.69×10
12
u
29
+1.11×10
13
u
28
+· · ·+1.96×10
13
b−8.09×10
12
, 4.63×
10
13
u
29
−8.91×10
12
u
28
+· · ·+1.96 ×10
13
a+3.59×10
13
, u
30
−u
29
+· · ·+3u
2
+1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
7
=
1
−u
2
a
3
=
−2.36637u
29
+ 0.455125u
28
+ ··· + 2.85213u − 1.83518
0.392910u
29
− 0.564811u
28
+ ··· − 1.81298u + 0.413118
a
12
=
u
−u
3
+ u
a
4
=
−0.223320u
29
+ 1.48376u
28
+ ··· + 1.84450u − 3.66965
−1.34937u
29
− 1.47784u
28
+ ··· − 0.677567u + 1.75032
a
5
=
1.64840u
29
+ 2.33207u
28
+ ··· − 4.80812u + 0.368280
−1.76478u
29
− 2.03766u
28
+ ··· + 1.69144u + 2.10802
a
10
=
−u
u
a
2
=
0.517277u
29
+ 1.09914u
28
+ ··· + 0.878677u − 3.91832
−2.49074u
29
− 1.20883u
28
+ ··· + 0.160474u + 2.49626
a
8
=
−1.34852u
29
− 2.17782u
28
+ ··· − 1.08366u + 3.95248
0.670939u
29
+ 1.65264u
28
+ ··· + 0.818071u − 0.279740
a
1
=
0.432407u
29
− 0.373574u
28
+ ··· − 3.76950u − 0.401863
−0.861302u
29
+ 0.788713u
28
+ ··· + 1.29292u − 0.249427
a
9
=
−2.21167u
29
− 1.98166u
28
+ ··· + 5.04257u + 1.02655
1.82204u
29
+ 2.28955u
28
+ ··· + 0.868974u − 1.26941
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −
75435520361360
19577401712437
u
29
−
37163103293925
19577401712437
u
28
+ ··· −
152854444455780
19577401712437
u +
4516608067627
19577401712437
21
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
30
− 12u
29
+ ··· − 2u + 1
c
2
u
30
+ u
29
+ ··· + 3u + 1
c
3
u
30
− 5u
29
+ ··· − 5u + 1
c
4
u
30
+ 2u
29
+ ··· + 46u + 31
c
5
u
30
+ 9u
29
+ ··· + 5u + 1
c
6
u
30
− u
29
+ ··· + 3u
2
+ 1
c
7
u
30
+ 9u
28
+ ··· − 3u + 1
c
8
u
30
+ 2u
29
+ ··· + 4u + 1
c
9
u
30
+ u
29
+ ··· − 4u + 1
c
10
, c
11
u
30
+ u
29
+ ··· + 3u
2
+ 1
c
12
u
30
− 2u
29
+ ··· − 4u + 1
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
30
+ 6y
29
+ ··· + 28y
2
+ 1
c
2
y
30
+ 7y
29
+ ··· − 13y + 1
c
3
y
30
− 3y
29
+ ··· + 9y + 1
c
4
y
30
− 8y
29
+ ··· − 9370y + 961
c
5
y
30
+ 3y
29
+ ··· − 5y + 1
c
6
, c
10
, c
11
y
30
− 31y
29
+ ··· + 6y + 1
c
7
y
30
+ 18y
29
+ ··· + 7y + 1
c
8
, c
12
y
30
+ 22y
29
+ ··· + 6y + 1
c
9
y
30
− 19y
29
+ ··· − 20y + 1
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.989846 + 0.188369I
a = 1.206130 − 0.321311I
b = −0.887327 − 0.705380I
0.24373 − 1.95711I −4.33244 + 5.88609I
u = 0.989846 − 0.188369I
a = 1.206130 + 0.321311I
b = −0.887327 + 0.705380I
0.24373 + 1.95711I −4.33244 − 5.88609I
u = 0.442016 + 0.721148I
a = −0.538270 − 0.853835I
b = −0.934934 + 1.028010I
−0.92209 + 5.23366I −1.60069 − 4.30342I
u = 0.442016 − 0.721148I
a = −0.538270 + 0.853835I
b = −0.934934 − 1.028010I
−0.92209 − 5.23366I −1.60069 + 4.30342I
u = −0.283871 + 0.773743I
a = −0.884357 + 0.015524I
b = −0.445890 − 0.620166I
1.73260 − 3.73548I 2.68923 + 12.02592I
u = −0.283871 − 0.773743I
a = −0.884357 − 0.015524I
b = −0.445890 + 0.620166I
1.73260 + 3.73548I 2.68923 − 12.02592I
u = −0.620941 + 1.010250I
a = 0.341585 + 0.062165I
b = −0.269172 + 0.195766I
−0.90090 − 2.51387I 15.5859 − 3.9325I
u = −0.620941 − 1.010250I
a = 0.341585 − 0.062165I
b = −0.269172 − 0.195766I
−0.90090 + 2.51387I 15.5859 + 3.9325I
u = −1.268630 + 0.005990I
a = 0.943554 − 0.415590I
b = −1.42106 + 0.23943I
0.924843 − 0.028493I −4.88122 − 0.36452I
u = −1.268630 − 0.005990I
a = 0.943554 + 0.415590I
b = −1.42106 − 0.23943I
0.924843 + 0.028493I −4.88122 + 0.36452I
24
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.306870 + 0.096410I
a = 0.47285 − 2.07622I
b = −0.96983 + 1.16956I
2.09646 + 4.09367I −3.20107 − 5.19591I
u = 1.306870 − 0.096410I
a = 0.47285 + 2.07622I
b = −0.96983 − 1.16956I
2.09646 − 4.09367I −3.20107 + 5.19591I
u = −1.363160 + 0.072970I
a = −0.217801 + 1.330540I
b = 1.089230 − 0.490818I
4.75322 − 8.38730I 0.41943 + 5.10587I
u = −1.363160 − 0.072970I
a = −0.217801 − 1.330540I
b = 1.089230 + 0.490818I
4.75322 + 8.38730I 0.41943 − 5.10587I
u = 1.367220 + 0.065004I
a = −0.22762 − 2.55840I
b = 0.33368 + 1.66288I
1.52351 + 3.24753I −2.94159 − 3.47206I
u = 1.367220 − 0.065004I
a = −0.22762 + 2.55840I
b = 0.33368 − 1.66288I
1.52351 − 3.24753I −2.94159 + 3.47206I
u = −0.060763 + 0.618506I
a = −0.232594 + 0.319629I
b = −0.993911 − 0.639264I
−1.81239 − 1.85320I −8.10054 + 3.95646I
u = −0.060763 − 0.618506I
a = −0.232594 − 0.319629I
b = −0.993911 + 0.639264I
−1.81239 + 1.85320I −8.10054 − 3.95646I
u = −1.48783 + 0.29054I
a = 0.09984 + 1.99043I
b = −0.93099 − 1.42571I
5.30854 − 9.04232I 1.09446 + 5.67771I
u = −1.48783 − 0.29054I
a = 0.09984 − 1.99043I
b = −0.93099 + 1.42571I
5.30854 + 9.04232I 1.09446 − 5.67771I
25
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.49822 + 0.26471I
a = −0.28122 − 1.47445I
b = −0.719679 + 0.897739I
7.73993 + 7.39536I 0. − 8.76922I
u = 1.49822 − 0.26471I
a = −0.28122 + 1.47445I
b = −0.719679 − 0.897739I
7.73993 − 7.39536I 0. + 8.76922I
u = −1.60068 + 0.32668I
a = 0.086838 − 0.294584I
b = 0.365998 + 0.404602I
6.09798 − 1.37001I 0. − 16.1282I
u = −1.60068 − 0.32668I
a = 0.086838 + 0.294584I
b = 0.365998 − 0.404602I
6.09798 + 1.37001I 0. + 16.1282I
u = 1.63421 + 0.10685I
a = −0.123406 + 0.947575I
b = 0.411524 − 0.500133I
8.15025 + 6.77665I 0. − 9.54891I
u = 1.63421 − 0.10685I
a = −0.123406 − 0.947575I
b = 0.411524 + 0.500133I
8.15025 − 6.77665I 0. + 9.54891I
u = 0.177898 + 0.264606I
a = −2.16718 − 0.22962I
b = 0.142634 − 0.903384I
−2.70877 − 2.24454I −6.85300 + 0.37420I
u = 0.177898 − 0.264606I
a = −2.16718 + 0.22962I
b = 0.142634 + 0.903384I
−2.70877 + 2.24454I −6.85300 − 0.37420I
u = −0.230410 + 0.216371I
a = −3.97835 + 0.36788I
b = 0.729736 + 0.182828I
0.67176 + 7.39207I 1.02242 − 4.31377I
u = −0.230410 − 0.216371I
a = −3.97835 − 0.36788I
b = 0.729736 − 0.182828I
0.67176 − 7.39207I 1.02242 + 4.31377I
26
III. I
u
3
= hb + 1, a
3
− 2a
2
+ a + 1, u + 1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
−1
a
7
=
1
−1
a
3
=
a
−1
a
12
=
−1
0
a
4
=
a + 1
−1
a
5
=
a + 1
−1
a
10
=
1
−1
a
2
=
1
a − 2
a
8
=
−a + 2
−a
2
+ 3a − 3
a
1
=
2a
2
− 3a − 1
−a
2
+ 2a − 1
a
9
=
−a
2
− a + 1
a − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 9a
2
− 18a + 9
27
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
3
− 3u
2
+ 4u − 1
c
2
, c
12
u
3
− u
2
− 1
c
3
, c
5
, c
6
(u + 1)
3
c
4
u
3
c
7
, c
8
u
3
+ u
2
+ 1
c
9
u
3
− 2u
2
+ u + 1
c
10
, c
11
(u − 1)
3
28
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
3
− y
2
+ 10y −1
c
2
, c
7
, c
8
c
12
y
3
− y
2
− 2y −1
c
3
, c
5
, c
6
c
10
, c
11
(y −1)
3
c
4
y
3
c
9
y
3
− 2y
2
+ 5y −1
29
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = 1.23279 + 0.79255I
b = −1.00000
0 −5.16555 + 3.32090I
u = −1.00000
a = 1.23279 − 0.79255I
b = −1.00000
0 −5.16555 − 3.32090I
u = −1.00000
a = −0.465571
b = −1.00000
0 19.3310
30
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
3
− 3u
2
+ 4u − 1)(u
30
− 12u
29
+ ··· − 2u + 1)
· (u
151
+ 10u
150
+ ··· − 31u + 23)
c
2
(u
3
− u
2
− 1)(u
30
+ u
29
+ ··· + 3u + 1)
· (u
151
+ 3u
150
+ ··· + 17222u + 2203)
c
3
((u + 1)
3
)(u
30
− 5u
29
+ ··· − 5u + 1)
· (u
151
− 3u
150
+ ··· − 514125u + 116356)
c
4
u
3
(u
30
+ 2u
29
+ ··· + 46u + 31)(u
151
− u
150
+ ··· + 64u + 16)
c
5
((u + 1)
3
)(u
30
+ 9u
29
+ ··· + 5u + 1)(u
151
+ 9u
150
+ ··· − 6313u + 9724)
c
6
((u + 1)
3
)(u
30
− u
29
+ ··· + 3u
2
+ 1)(u
151
+ u
150
+ ··· + 32u + 1)
c
7
(u
3
+ u
2
+ 1)(u
30
+ 9u
28
+ ··· − 3u + 1)
· (u
151
− 4u
150
+ ··· − 2579090u + 234743)
c
8
(u
3
+ u
2
+ 1)(u
30
+ 2u
29
+ ··· + 4u + 1)
· (u
151
− 2u
150
+ ··· + 4057u + 1279)
c
9
(u
3
− 2u
2
+ u + 1)(u
30
+ u
29
+ ··· − 4u + 1)
· (u
151
− 2u
150
+ ··· + 492840u + 167911)
c
10
, c
11
((u − 1)
3
)(u
30
+ u
29
+ ··· + 3u
2
+ 1)(u
151
+ u
150
+ ··· + 32u + 1)
c
12
(u
3
− u
2
− 1)(u
30
− 2u
29
+ ··· − 4u + 1)
· (u
151
− 2u
150
+ ··· + 4057u + 1279)
31
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
3
− y
2
+ 10y −1)(y
30
+ 6y
29
+ ··· + 28y
2
+ 1)
· (y
151
+ 18y
150
+ ··· − 28249y −529)
c
2
(y
3
− y
2
− 2y −1)(y
30
+ 7y
29
+ ··· − 13y + 1)
· (y
151
− 13y
150
+ ··· + 173229284y −4853209)
c
3
((y −1)
3
)(y
30
− 3y
29
+ ··· + 9y + 1)
· (y
151
− 21y
150
+ ··· − 752670674231y −13538718736)
c
4
y
3
(y
30
− 8y
29
+ ··· − 9370y + 961)(y
151
+ y
150
+ ··· − 11136y −256)
c
5
((y −1)
3
)(y
30
+ 3y
29
+ ··· − 5y + 1)
· (y
151
+ 21y
150
+ ··· − 6011235647y −94556176)
c
6
, c
10
, c
11
((y −1)
3
)(y
30
− 31y
29
+ ··· + 6y + 1)(y
151
− 149y
150
+ ··· + 246y −1)
c
7
(y
3
− y
2
− 2y −1)(y
30
+ 18y
29
+ ··· + 7y + 1)
· (y
151
+ 46y
150
+ ··· − 7705800129308y −55104276049)
c
8
, c
12
(y
3
− y
2
− 2y −1)(y
30
+ 22y
29
+ ··· + 6y + 1)
· (y
151
+ 94y
150
+ ··· − 113123915y −1635841)
c
9
(y
3
− 2y
2
+ 5y −1)(y
30
− 19y
29
+ ··· − 20y + 1)
· (y
151
− 56y
150
+ ··· + 725298561134y −28194103921)
32
