12a
0872
(K12a
0872
)
A knot diagram
1
Linearized knot diagam
4 6 7 9 11 10 1 12 2 3 5 8
Solving Sequence
6,10 3,7
4 11 2 1 5 12 9 8
c
6
c
3
c
10
c
2
c
1
c
5
c
11
c
9
c
8
c
4
, c
7
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h1.30286 × 10
835
u
127
+ 6.91127 × 10
835
u
126
+ ··· + 1.24523 × 10
836
b + 3.82455 × 10
835
,
− 2.22805 × 10
837
u
127
− 3.94170 × 10
837
u
126
+ ··· + 1.24523 × 10
836
a + 1.79835 × 10
836
,
5u
128
+ 6u
127
+ ··· + 3u − 1i
I
u
2
= h−2.14762 × 10
46
u
29
− 1.35976 × 10
47
u
28
+ ··· + 8.51286 × 10
45
b − 1.05226 × 10
46
,
3.44982 × 10
46
u
29
+ 2.00343 × 10
47
u
28
+ ··· + 8.51286 × 10
45
a + 1.52741 × 10
46
, 5u
30
+ 33u
29
+ ··· + 2u + 1i
* 2 irreducible components of dim
C
= 0, with total 158 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
= h1.30 × 10
835
u
127
+ 6.91 × 10
835
u
126
+ · · · + 1.25 × 10
836
b + 3.82 ×
10
835
, −2.23 × 10
837
u
127
− 3.94 × 10
837
u
126
+ · · · + 1.25 × 10
836
a + 1.80 ×
10
836
, 5u
128
+ 6u
127
+ · · · + 3u − 1i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
u
a
3
=
17.8927u
127
+ 31.6544u
126
+ ··· − 38.4932u − 1.44419
−0.104628u
127
− 0.555020u
126
+ ··· + 3.04440u − 0.307136
a
7
=
1
u
2
a
4
=
23.8766u
127
+ 42.3995u
126
+ ··· − 44.0690u + 0.899592
2.07893u
127
+ 3.35288u
126
+ ··· + 2.10257u + 0.405735
a
11
=
56.8012u
127
+ 102.085u
126
+ ··· + 21.2724u + 9.74949
4.66762u
127
+ 7.89060u
126
+ ··· + 5.94744u + 1.35955
a
2
=
17.9973u
127
+ 32.2095u
126
+ ··· − 41.5376u − 1.13705
−0.104628u
127
− 0.555020u
126
+ ··· + 3.04440u − 0.307136
a
1
=
−9.39015u
127
− 13.4013u
126
+ ··· − 13.6158u − 9.85715
2.28571u
127
+ 4.94598u
126
+ ··· + 2.20477u − 0.129018
a
5
=
−51.8393u
127
− 102.851u
126
+ ··· − 104.441u − 18.1579
−8.81590u
127
− 16.5949u
126
+ ··· + 0.826844u − 3.72755
a
12
=
1.88284u
127
+ 10.1744u
126
+ ··· + 6.94980u + 3.35617
4.22223u
127
+ 8.39879u
126
+ ··· − 7.69204u + 0.894113
a
9
=
47.4844u
127
+ 86.0915u
126
+ ··· + 11.9416u + 7.09790
4.64910u
127
+ 8.10242u
126
+ ··· + 5.38331u + 1.29204
a
8
=
−33.4742u
127
− 65.6211u
126
+ ··· + 36.3065u − 9.46504
−12.7668u
127
− 24.5715u
126
+ ··· + 11.3679u − 3.58033
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4.75828u
127
− 9.80991u
126
+ ··· + 10.3737u + 5.73316
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
5(5u
128
+ 44u
127
+ ··· + 774818u − 401483)
c
2
u
128
− u
127
+ ··· + 181885u + 12725
c
3
u
128
− 4u
127
+ ··· − 11825779033u + 7211692781
c
4
u
128
+ u
127
+ ··· + 1190911161u + 121993295
c
5
, c
11
5(5u
128
− 6u
127
+ ··· + 40667u + 8021)
c
6
5(5u
128
− 6u
127
+ ··· − 3u − 1)
c
7
, c
8
, c
12
u
128
+ 69u
126
+ ··· + 3101u + 335
c
9
u
128
− u
127
+ ··· + 109650874u + 30512188
c
10
u
128
+ u
127
+ ··· − 86689u + 15995
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
25(25y
128
− 1586y
127
+ ··· − 2.34182 × 10
13
y + 1.61189 × 10
11
)
c
2
y
128
+ 29y
127
+ ··· + 3815485825y + 161925625
c
3
y
128
− 86y
127
+ ··· − 2.57 × 10
21
y + 5.20 × 10
19
c
4
y
128
+ 75y
127
+ ··· + 38410155386297739y + 14882364024957025
c
5
, c
11
25(25y
128
+ 2864y
127
+ ··· − 1.96260 × 10
9
y + 6.43364 × 10
7
)
c
6
25(25y
128
− 636y
127
+ ··· + 95y + 1)
c
7
, c
8
, c
12
y
128
+ 138y
127
+ ··· + 4645419y + 112225
c
9
y
128
− 41y
127
+ ··· − 25209093297032220y + 930993616547344
c
10
y
128
+ 49y
127
+ ··· + 19150857599y + 255840025
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.670057 + 0.755540I
a = −0.517959 − 1.274930I
b = 0.935974 − 0.837483I
−0.87146 − 4.99280I 0
u = 0.670057 − 0.755540I
a = −0.517959 + 1.274930I
b = 0.935974 + 0.837483I
−0.87146 + 4.99280I 0
u = −0.624462 + 0.755002I
a = 0.21457 − 1.66795I
b = −0.444985 − 0.450731I
−5.92544 + 6.29206I 0
u = −0.624462 − 0.755002I
a = 0.21457 + 1.66795I
b = −0.444985 + 0.450731I
−5.92544 − 6.29206I 0
u = −0.295858 + 0.985279I
a = 0.194219 − 0.597321I
b = −0.621681 − 0.280206I
1.70199 − 1.51235I 0
u = −0.295858 − 0.985279I
a = 0.194219 + 0.597321I
b = −0.621681 + 0.280206I
1.70199 + 1.51235I 0
u = −1.021420 + 0.130859I
a = 0.349460 − 0.779220I
b = 1.25324 − 1.28329I
−14.3831 − 5.4142I 0
u = −1.021420 − 0.130859I
a = 0.349460 + 0.779220I
b = 1.25324 + 1.28329I
−14.3831 + 5.4142I 0
u = 0.579786 + 0.772511I
a = 0.031052 + 1.173600I
b = −0.88407 + 1.68599I
−3.52416 − 6.28630I 0
u = 0.579786 − 0.772511I
a = 0.031052 − 1.173600I
b = −0.88407 − 1.68599I
−3.52416 + 6.28630I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.522546 + 0.810984I
a = −0.122581 − 0.663920I
b = 0.891034 − 0.999173I
1.01866 − 3.82875I 0
u = 0.522546 − 0.810984I
a = −0.122581 + 0.663920I
b = 0.891034 + 0.999173I
1.01866 + 3.82875I 0
u = 0.207432 + 0.930829I
a = −2.05658 − 0.82303I
b = 1.057120 − 0.241819I
−3.19236 − 3.86848I 0
u = 0.207432 − 0.930829I
a = −2.05658 + 0.82303I
b = 1.057120 + 0.241819I
−3.19236 + 3.86848I 0
u = 0.366467 + 0.870051I
a = 0.867940 + 1.015360I
b = −0.529045 + 0.284996I
0.95783 − 2.81467I 0
u = 0.366467 − 0.870051I
a = 0.867940 − 1.015360I
b = −0.529045 − 0.284996I
0.95783 + 2.81467I 0
u = 0.910977 + 0.022794I
a = −1.31716 − 1.54295I
b = −0.281869 − 0.748018I
−6.02235 + 2.51292I 0
u = 0.910977 − 0.022794I
a = −1.31716 + 1.54295I
b = −0.281869 + 0.748018I
−6.02235 − 2.51292I 0
u = 0.505895 + 0.753974I
a = −0.384177 − 0.535723I
b = −0.876631 − 0.195413I
−2.88825 − 1.05818I 0
u = 0.505895 − 0.753974I
a = −0.384177 + 0.535723I
b = −0.876631 + 0.195413I
−2.88825 + 1.05818I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.590777 + 0.655533I
a = −0.096733 + 1.240630I
b = 0.831556 + 0.810539I
1.69935 + 2.52168I 0
u = −0.590777 − 0.655533I
a = −0.096733 − 1.240630I
b = 0.831556 − 0.810539I
1.69935 − 2.52168I 0
u = 0.438393 + 1.029680I
a = 0.681582 + 0.508978I
b = −0.656703 + 0.349296I
0.86418 − 2.79224I 0
u = 0.438393 − 1.029680I
a = 0.681582 − 0.508978I
b = −0.656703 − 0.349296I
0.86418 + 2.79224I 0
u = 0.874260 + 0.063412I
a = 0.286911 + 0.810060I
b = 1.39969 + 1.48971I
−6.86492 + 0.90423I 0
u = 0.874260 − 0.063412I
a = 0.286911 − 0.810060I
b = 1.39969 − 1.48971I
−6.86492 − 0.90423I 0
u = 0.870242 + 0.081325I
a = 0.372337 − 0.669473I
b = −0.453377 − 0.627533I
−2.10764 − 0.31019I 0
u = 0.870242 − 0.081325I
a = 0.372337 + 0.669473I
b = −0.453377 + 0.627533I
−2.10764 + 0.31019I 0
u = −0.444130 + 0.751283I
a = −1.42413 + 2.16142I
b = 0.827220 + 0.523416I
−11.6274 + 9.0855I 0
u = −0.444130 − 0.751283I
a = −1.42413 − 2.16142I
b = 0.827220 − 0.523416I
−11.6274 − 9.0855I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.198236 + 1.123340I
a = −0.054559 + 0.576961I
b = −0.717832 + 0.266524I
−4.53083 + 4.28786I 0
u = 0.198236 − 1.123340I
a = −0.054559 − 0.576961I
b = −0.717832 − 0.266524I
−4.53083 − 4.28786I 0
u = −1.182480 + 0.015473I
a = −0.98519 + 1.35709I
b = −0.301076 + 0.771095I
−12.80370 − 3.50278I 0
u = −1.182480 − 0.015473I
a = −0.98519 − 1.35709I
b = −0.301076 − 0.771095I
−12.80370 + 3.50278I 0
u = 0.797207 + 0.152198I
a = 0.010654 + 1.374330I
b = −1.24385 + 1.28644I
−13.72010 − 0.71134I 0
u = 0.797207 − 0.152198I
a = 0.010654 − 1.374330I
b = −1.24385 − 1.28644I
−13.72010 + 0.71134I 0
u = 0.244448 + 0.764340I
a = 0.256468 − 1.357240I
b = −0.213982 + 0.538057I
−3.51522 − 1.36195I 0
u = 0.244448 − 0.764340I
a = 0.256468 + 1.357240I
b = −0.213982 − 0.538057I
−3.51522 + 1.36195I 0
u = −0.614296 + 1.031930I
a = 0.049824 + 0.701578I
b = 0.837621 + 1.089450I
−4.35521 + 5.20841I 0
u = −0.614296 − 1.031930I
a = 0.049824 − 0.701578I
b = 0.837621 − 1.089450I
−4.35521 − 5.20841I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.758094 + 0.068527I
a = 0.547819 − 0.754908I
b = 0.388808 − 0.978146I
−2.35008 − 1.38862I 0
u = 0.758094 − 0.068527I
a = 0.547819 + 0.754908I
b = 0.388808 + 0.978146I
−2.35008 + 1.38862I 0
u = −0.570739 + 1.100260I
a = −0.345455 + 0.400912I
b = −0.853665 + 0.129254I
−9.10526 + 1.63756I 0
u = −0.570739 − 1.100260I
a = −0.345455 − 0.400912I
b = −0.853665 − 0.129254I
−9.10526 − 1.63756I 0
u = −0.645405 + 1.078470I
a = 0.000837 − 1.151600I
b = −0.66228 − 1.56907I
−9.02052 + 9.15715I 0
u = −0.645405 − 1.078470I
a = 0.000837 + 1.151600I
b = −0.66228 + 1.56907I
−9.02052 − 9.15715I 0
u = 0.681254 + 0.286021I
a = 0.276682 + 0.912346I
b = 1.76338 + 1.19579I
−14.1256 − 9.6013I 0
u = 0.681254 − 0.286021I
a = 0.276682 − 0.912346I
b = 1.76338 − 1.19579I
−14.1256 + 9.6013I 0
u = −0.718832 + 0.147556I
a = 0.270402 − 0.863795I
b = 1.69870 − 1.43831I
−6.84689 + 5.14006I 0
u = −0.718832 − 0.147556I
a = 0.270402 + 0.863795I
b = 1.69870 + 1.43831I
−6.84689 − 5.14006I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.715567 + 0.101178I
a = −1.41896 − 1.71183I
b = 0.490263 − 0.767901I
−9.22915 − 5.13764I 0
u = 0.715567 − 0.101178I
a = −1.41896 + 1.71183I
b = 0.490263 + 0.767901I
−9.22915 + 5.13764I 0
u = −0.551613 + 0.419613I
a = 0.079826 − 1.258760I
b = −1.30518 − 1.65890I
−5.26385 + 2.17447I 0. − 6.45953I
u = −0.551613 − 0.419613I
a = 0.079826 + 1.258760I
b = −1.30518 + 1.65890I
−5.26385 − 2.17447I 0. + 6.45953I
u = 0.646911 + 0.234998I
a = 0.49123 − 1.43624I
b = −0.821114 − 1.137430I
−8.85813 − 5.71260I −5.31590 + 5.77023I
u = 0.646911 − 0.234998I
a = 0.49123 + 1.43624I
b = −0.821114 + 1.137430I
−8.85813 + 5.71260I −5.31590 − 5.77023I
u = 0.381787 + 0.548878I
a = 0.24918 − 1.52440I
b = 0.835516 − 0.649500I
−3.03550 − 1.02076I 4.00000 + 1.36709I
u = 0.381787 − 0.548878I
a = 0.24918 + 1.52440I
b = 0.835516 + 0.649500I
−3.03550 + 1.02076I 4.00000 − 1.36709I
u = −0.647217 + 0.166673I
a = 0.528516 + 1.159790I
b = −0.696240 + 1.031700I
−2.17972 + 3.31427I −1.58239 − 8.50857I
u = −0.647217 − 0.166673I
a = 0.528516 − 1.159790I
b = −0.696240 − 1.031700I
−2.17972 − 3.31427I −1.58239 + 8.50857I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.615583 + 0.251330I
a = −1.34050 + 2.75620I
b = −0.175714 + 0.930951I
−12.85860 − 1.12265I −8.29711 + 2.79143I
u = 0.615583 − 0.251330I
a = −1.34050 − 2.75620I
b = −0.175714 − 0.930951I
−12.85860 + 1.12265I −8.29711 − 2.79143I
u = −0.632472 + 0.150674I
a = −1.58365 − 2.46115I
b = −0.235162 − 0.823879I
−5.95201 + 1.33725I −10.32087 − 4.41817I
u = −0.632472 − 0.150674I
a = −1.58365 + 2.46115I
b = −0.235162 + 0.823879I
−5.95201 − 1.33725I −10.32087 + 4.41817I
u = 0.639803 + 0.067007I
a = 3.38721 + 2.28456I
b = 0.064049 + 0.603580I
−14.0527 − 8.5972I −12.9862 + 7.4232I
u = 0.639803 − 0.067007I
a = 3.38721 − 2.28456I
b = 0.064049 − 0.603580I
−14.0527 + 8.5972I −12.9862 − 7.4232I
u = −1.123890 + 0.784186I
a = −0.070071 − 1.122360I
b = −0.91195 − 1.25838I
−7.06870 + 7.42280I 0
u = −1.123890 − 0.784186I
a = −0.070071 + 1.122360I
b = −0.91195 + 1.25838I
−7.06870 − 7.42280I 0
u = 1.227420 + 0.668163I
a = −0.149805 + 1.140580I
b = −1.00939 + 1.22247I
−14.3901 − 8.1482I 0
u = 1.227420 − 0.668163I
a = −0.149805 − 1.140580I
b = −1.00939 − 1.22247I
−14.3901 + 8.1482I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.279680 + 0.523860I
a = −0.418095 + 0.037545I
b = 1.25432 + 0.85715I
−1.57984 + 2.50684I 7.10135 + 2.74151I
u = −0.279680 − 0.523860I
a = −0.418095 − 0.037545I
b = 1.25432 − 0.85715I
−1.57984 − 2.50684I 7.10135 − 2.74151I
u = −0.506778 + 0.252997I
a = 4.01838 + 0.09631I
b = −0.056855 − 0.537864I
−5.83710 + 5.47018I −6.5706 − 14.3078I
u = −0.506778 − 0.252997I
a = 4.01838 − 0.09631I
b = −0.056855 + 0.537864I
−5.83710 − 5.47018I −6.5706 + 14.3078I
u = −1.09221 + 0.96601I
a = −0.312852 + 1.071050I
b = 1.06807 + 1.19719I
−14.8073 + 3.4229I 0
u = −1.09221 − 0.96601I
a = −0.312852 − 1.071050I
b = 1.06807 − 1.19719I
−14.8073 − 3.4229I 0
u = −0.505308 + 0.187338I
a = −1.92448 + 0.93721I
b = 0.666295 + 0.531321I
−1.63986 + 3.32589I 0.57738 − 8.11329I
u = −0.505308 − 0.187338I
a = −1.92448 − 0.93721I
b = 0.666295 − 0.531321I
−1.63986 − 3.32589I 0.57738 + 8.11329I
u = −1.14072 + 0.91523I
a = 0.375350 − 0.863865I
b = −0.569570 − 0.902551I
−9.31994 + 2.57145I 0
u = −1.14072 − 0.91523I
a = 0.375350 + 0.863865I
b = −0.569570 + 0.902551I
−9.31994 − 2.57145I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.98163 + 1.11752I
a = −0.653006 − 0.326756I
b = −0.077346 − 0.697415I
−5.82983 − 0.92605I 0
u = 0.98163 − 1.11752I
a = −0.653006 + 0.326756I
b = −0.077346 + 0.697415I
−5.82983 + 0.92605I 0
u = 1.10777 + 1.02567I
a = 0.033171 + 1.133390I
b = −0.69881 + 1.27112I
−6.09605 − 6.88619I 0
u = 1.10777 − 1.02567I
a = 0.033171 − 1.133390I
b = −0.69881 − 1.27112I
−6.09605 + 6.88619I 0
u = 1.13485 + 1.02315I
a = −0.198966 − 1.003110I
b = 1.06301 − 1.29040I
−7.59653 − 8.63921I 0
u = 1.13485 − 1.02315I
a = −0.198966 + 1.003110I
b = 1.06301 + 1.29040I
−7.59653 + 8.63921I 0
u = −0.98455 + 1.18920I
a = 0.398469 − 0.329050I
b = 0.350678 − 1.128770I
−14.1479 + 4.2835I 0
u = −0.98455 − 1.18920I
a = 0.398469 + 0.329050I
b = 0.350678 + 1.128770I
−14.1479 − 4.2835I 0
u = −1.16189 + 1.04296I
a = −0.121335 + 1.033250I
b = 1.01373 + 1.30169I
−8.1926 + 14.6819I 0
u = −1.16189 − 1.04296I
a = −0.121335 − 1.033250I
b = 1.01373 − 1.30169I
−8.1926 − 14.6819I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.20161 + 1.01467I
a = −0.029505 − 0.653759I
b = 0.431105 − 0.931376I
−2.18056 − 3.50543I 0
u = 1.20161 − 1.01467I
a = −0.029505 + 0.653759I
b = 0.431105 + 0.931376I
−2.18056 + 3.50543I 0
u = −1.57696 + 0.02299I
a = 0.274018 + 0.289044I
b = −0.266637 + 0.314402I
−7.96524 − 0.86429I 0
u = −1.57696 − 0.02299I
a = 0.274018 − 0.289044I
b = −0.266637 − 0.314402I
−7.96524 + 0.86429I 0
u = 1.19446 + 1.04198I
a = 0.140629 + 0.733429I
b = −0.733077 + 0.886255I
−2.11721 − 5.16334I 0
u = 1.19446 − 1.04198I
a = 0.140629 − 0.733429I
b = −0.733077 − 0.886255I
−2.11721 + 5.16334I 0
u = −0.411280 + 0.052511I
a = 0.01973 + 1.56875I
b = −1.68869 + 0.64449I
−4.59765 − 1.10126I −10.42322 − 0.28122I
u = −0.411280 − 0.052511I
a = 0.01973 − 1.56875I
b = −1.68869 − 0.64449I
−4.59765 + 1.10126I −10.42322 + 0.28122I
u = 1.19148 + 1.05599I
a = −0.086033 − 1.072940I
b = 0.99364 − 1.29215I
−15.7178 − 18.8406I 0
u = 1.19148 − 1.05599I
a = −0.086033 + 1.072940I
b = 0.99364 + 1.29215I
−15.7178 + 18.8406I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.28775 + 0.95888I
a = −0.654482 + 0.669236I
b = −0.110160 + 0.822231I
−12.98490 + 1.73745I 0
u = −1.28775 − 0.95888I
a = −0.654482 − 0.669236I
b = −0.110160 − 0.822231I
−12.98490 − 1.73745I 0
u = −1.17113 + 1.12107I
a = 0.060923 − 1.173020I
b = −0.614574 − 1.269150I
−12.5200 + 6.9562I 0
u = −1.17113 − 1.12107I
a = 0.060923 + 1.173020I
b = −0.614574 + 1.269150I
−12.5200 − 6.9562I 0
u = 1.15319 + 1.18101I
a = 0.389296 + 0.304205I
b = 0.207194 + 1.078660I
−7.20819 + 0.38745I 0
u = 1.15319 − 1.18101I
a = 0.389296 − 0.304205I
b = 0.207194 − 1.078660I
−7.20819 − 0.38745I 0
u = −1.28089 + 1.04401I
a = −0.019449 − 0.753778I
b = −0.830707 − 0.907008I
−1.85528 + 9.47621I 0
u = −1.28089 − 1.04401I
a = −0.019449 + 0.753778I
b = −0.830707 + 0.907008I
−1.85528 − 9.47621I 0
u = −1.12744 + 1.20924I
a = −0.134245 + 0.738002I
b = 0.269905 + 1.069070I
−8.42042 + 5.63254I 0
u = −1.12744 − 1.20924I
a = −0.134245 − 0.738002I
b = 0.269905 − 1.069070I
−8.42042 − 5.63254I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.34657 + 1.02291I
a = −0.121299 + 0.785666I
b = −0.904184 + 0.923989I
−8.4020 − 12.4881I 0
u = 1.34657 − 1.02291I
a = −0.121299 − 0.785666I
b = −0.904184 − 0.923989I
−8.4020 + 12.4881I 0
u = −1.24191 + 1.26092I
a = 0.406986 − 0.282466I
b = 0.191166 − 0.941284I
−7.75939 − 6.10036I 0
u = −1.24191 − 1.26092I
a = 0.406986 + 0.282466I
b = 0.191166 + 0.941284I
−7.75939 + 6.10036I 0
u = 0.219734
a = −4.40302
b = 0.735094
0.649355 12.2090
u = −0.218333
a = 2.56125
b = 0.489078
0.832454 11.9890
u = −1.58238 + 0.85084I
a = 0.093494 + 0.469590I
b = 0.518979 + 0.676438I
−1.93470 + 0.48286I 0
u = −1.58238 − 0.85084I
a = 0.093494 − 0.469590I
b = 0.518979 − 0.676438I
−1.93470 − 0.48286I 0
u = 0.127676 + 0.133067I
a = −1.77453 + 7.62553I
b = −0.644227 + 0.919311I
−9.39443 − 4.84683I −0.04219 + 3.79481I
u = 0.127676 − 0.133067I
a = −1.77453 − 7.62553I
b = −0.644227 − 0.919311I
−9.39443 + 4.84683I −0.04219 − 3.79481I
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.27921 + 1.34533I
a = 0.426301 + 0.280019I
b = 0.244576 + 0.871817I
−15.1777 + 10.0042I 0
u = 1.27921 − 1.34533I
a = 0.426301 − 0.280019I
b = 0.244576 − 0.871817I
−15.1777 − 10.0042I 0
u = −0.0172012 + 0.0998655I
a = −11.26940 − 5.79803I
b = −0.799171 + 0.498445I
−3.34476 − 2.07319I 3.70739 + 2.71432I
u = −0.0172012 − 0.0998655I
a = −11.26940 + 5.79803I
b = −0.799171 − 0.498445I
−3.34476 + 2.07319I 3.70739 − 2.71432I
u = −1.18269 + 1.59050I
a = −0.0167657 + 0.0717750I
b = −0.423828 − 0.327854I
−7.77740 − 0.58428I 0
u = −1.18269 − 1.59050I
a = −0.0167657 − 0.0717750I
b = −0.423828 + 0.327854I
−7.77740 + 0.58428I 0
u = 2.04283 + 0.56784I
a = 0.239373 − 0.303133I
b = 0.654694 − 0.434222I
−7.94720 + 1.25723I 0
u = 2.04283 − 0.56784I
a = 0.239373 + 0.303133I
b = 0.654694 + 0.434222I
−7.94720 − 1.25723I 0
17
II. I
u
2
= h−2.15 × 10
46
u
29
− 1.36 × 10
47
u
28
+ · · · + 8.51 × 10
45
b − 1.05 ×
10
46
, 3.45 × 10
46
u
29
+ 2.00 × 10
47
u
28
+ · · · + 8.51 × 10
45
a + 1.53 ×
10
46
, 5u
30
+ 33u
29
+ · · · + 2u + 1i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
u
a
3
=
−4.05248u
29
− 23.5341u
28
+ ··· + 0.376398u − 1.79423
2.52279u
29
+ 15.9730u
28
+ ··· + 2.07229u + 1.23609
a
7
=
1
u
2
a
4
=
−6.94058u
29
− 41.5444u
28
+ ··· − 2.17028u − 3.67276
2.95865u
29
+ 18.3735u
28
+ ··· + 2.22942u + 1.02584
a
11
=
−5.84802u
29
− 35.8644u
28
+ ··· − 8.02089u − 3.17187
1.12877u
29
+ 7.33254u
28
+ ··· + 2.23703u + 0.342491
a
2
=
−6.57527u
29
− 39.5071u
28
+ ··· − 1.69589u − 3.03032
2.52279u
29
+ 15.9730u
28
+ ··· + 2.07229u + 1.23609
a
1
=
−0.0226501u
29
− 1.39650u
28
+ ··· − 0.953621u − 1.94678
2.09667u
29
+ 13.2323u
28
+ ··· + 0.942778u + 0.905006
a
5
=
1.68798u
29
+ 8.92987u
28
+ ··· − 3.68313u + 5.56772
−0.482655u
29
− 2.28074u
28
+ ··· − 0.583407u − 1.86820
a
12
=
1.28627u
29
+ 5.55865u
28
+ ··· + 10.3938u + 2.11451
−0.0898216u
29
− 0.368168u
28
+ ··· − 3.43140u − 0.247052
a
9
=
−8.19129u
29
− 51.0181u
28
+ ··· − 10.0302u − 3.64065
1.21450u
29
+ 7.82126u
28
+ ··· + 1.77229u + 0.126294
a
8
=
2.11707u
29
+ 16.6926u
28
+ ··· − 3.02830u − 0.257242
−1.88799u
29
− 12.7841u
28
+ ··· + 1.20749u + 0.210246
(ii) Obstruction class = 1
(iii) Cusp Shapes = −1.01805u
29
− 13.0484u
28
+ ··· − 1.40845u − 3.85011
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
5(5u
30
− 33u
29
+ ··· − 13u + 1)
c
2
u
30
− 4u
29
+ ··· + 22u + 5
c
3
u
30
+ 5u
29
+ ··· − 38u + 11
c
4
u
30
+ 7u
28
+ ··· + 18u + 5
c
5
5(5u
30
+ 23u
29
+ ··· − 14u + 1)
c
6
5(5u
30
+ 33u
29
+ ··· + 2u + 1)
c
7
, c
8
u
30
− u
29
+ ··· + 16u + 5
c
9
u
30
+ 5u
28
+ ··· + 14u + 4
c
10
u
30
+ 10u
28
+ ··· − 28u + 5
c
11
5(5u
30
− 23u
29
+ ··· + 14u + 1)
c
12
u
30
+ u
29
+ ··· − 16u + 5
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
25(25y
30
− 439y
29
+ ··· − 17y + 1)
c
2
y
30
+ 4y
29
+ ··· + 56y + 25
c
3
y
30
− 23y
29
+ ··· + 2494y + 121
c
4
y
30
+ 14y
29
+ ··· + 526y + 25
c
5
, c
11
25(25y
30
+ 611y
29
+ ··· + 244y
2
+ 1)
c
6
25(25y
30
− 189y
29
+ ··· − 6y + 1)
c
7
, c
8
, c
12
y
30
+ 33y
29
+ ··· + 314y + 25
c
9
y
30
+ 10y
29
+ ··· − 44y + 16
c
10
y
30
+ 20y
29
+ ··· + 606y + 25
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.569199 + 0.796831I
a = −0.416997 − 0.786658I
b = 0.720912 − 0.845806I
0.35841 − 3.58053I 1.95909 + 5.79681I
u = 0.569199 − 0.796831I
a = −0.416997 + 0.786658I
b = 0.720912 + 0.845806I
0.35841 + 3.58053I 1.95909 − 5.79681I
u = −0.548523 + 0.916219I
a = −0.515954 + 1.011370I
b = 0.183547 + 0.858650I
−6.74443 + 5.52946I −1.66846 − 5.08278I
u = −0.548523 − 0.916219I
a = −0.515954 − 1.011370I
b = 0.183547 − 0.858650I
−6.74443 − 5.52946I −1.66846 + 5.08278I
u = −1.029480 + 0.351847I
a = −0.717416 + 1.110250I
b = −0.382393 + 0.940448I
−12.21410 + 0.77384I −5.49839 + 0.47751I
u = −1.029480 − 0.351847I
a = −0.717416 − 1.110250I
b = −0.382393 − 0.940448I
−12.21410 − 0.77384I −5.49839 − 0.47751I
u = 0.321066 + 1.049190I
a = −0.896432 − 0.467798I
b = 0.614822 − 0.328859I
0.72579 − 2.96470I −12.5986 + 18.3028I
u = 0.321066 − 1.049190I
a = −0.896432 + 0.467798I
b = 0.614822 + 0.328859I
0.72579 + 2.96470I −12.5986 − 18.3028I
u = 0.351856 + 0.814791I
a = 1.88936 + 1.39790I
b = −0.961444 + 0.378370I
−2.86934 − 3.44062I 5.83200 + 0.99629I
u = 0.351856 − 0.814791I
a = 1.88936 − 1.39790I
b = −0.961444 − 0.378370I
−2.86934 + 3.44062I 5.83200 − 0.99629I
21
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.781091 + 0.395019I
a = −0.384993 − 0.714168I
b = −0.860550 − 0.920414I
−3.84586 + 0.18432I −4.14156 + 1.50496I
u = 0.781091 − 0.395019I
a = −0.384993 + 0.714168I
b = −0.860550 + 0.920414I
−3.84586 − 0.18432I −4.14156 − 1.50496I
u = 0.653623 + 0.309207I
a = −1.39552 − 0.58081I
b = −0.267290 − 1.008370I
−5.01891 + 0.72670I −2.38759 + 0.50812I
u = 0.653623 − 0.309207I
a = −1.39552 + 0.58081I
b = −0.267290 + 1.008370I
−5.01891 − 0.72670I −2.38759 − 0.50812I
u = −1.098530 + 0.773706I
a = 0.038400 − 1.397940I
b = −0.711510 − 1.057740I
−12.53450 + 5.60449I −5.42250 − 3.95249I
u = −1.098530 − 0.773706I
a = 0.038400 + 1.397940I
b = −0.711510 + 1.057740I
−12.53450 − 5.60449I −5.42250 + 3.95249I
u = −0.440725 + 0.466443I
a = −0.307751 + 0.910156I
b = 1.30016 + 1.09128I
−1.82886 + 2.86634I −3.21917 − 11.76445I
u = −0.440725 − 0.466443I
a = −0.307751 − 0.910156I
b = 1.30016 − 1.09128I
−1.82886 − 2.86634I −3.21917 + 11.76445I
u = 1.06291 + 0.95318I
a = 0.046619 + 1.115740I
b = −0.79757 + 1.28034I
−5.66490 − 6.69873I 4.19860 + 3.07617I
u = 1.06291 − 0.95318I
a = 0.046619 − 1.115740I
b = −0.79757 − 1.28034I
−5.66490 + 6.69873I 4.19860 − 3.07617I
22
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.274917 + 0.498694I
a = −0.431932 + 0.569688I
b = −1.57440 − 0.40294I
−4.12489 + 1.43960I 1.63216 − 6.49833I
u = −0.274917 − 0.498694I
a = −0.431932 − 0.569688I
b = −1.57440 + 0.40294I
−4.12489 − 1.43960I 1.63216 + 6.49833I
u = −1.02394 + 1.02607I
a = −0.072132 − 1.067560I
b = −0.68299 − 1.38636I
−9.90852 + 8.39660I −5.82890 − 6.07911I
u = −1.02394 − 1.02607I
a = −0.072132 + 1.067560I
b = −0.68299 + 1.38636I
−9.90852 − 8.39660I −5.82890 + 6.07911I
u = 0.373533 + 0.295071I
a = 0.23966 + 2.94764I
b = 0.701814 − 0.395561I
−13.2830 + 8.4783I −1.68666 − 4.27120I
u = 0.373533 − 0.295071I
a = 0.23966 − 2.94764I
b = 0.701814 + 0.395561I
−13.2830 − 8.4783I −1.68666 + 4.27120I
u = −0.361283 + 0.198894I
a = −2.07534 − 2.23336I
b = 0.434005 + 0.794969I
−5.54819 − 4.83112I −0.54326 + 3.53292I
u = −0.361283 − 0.198894I
a = −2.07534 + 2.23336I
b = 0.434005 − 0.794969I
−5.54819 + 4.83112I −0.54326 − 3.53292I
u = −2.63588 + 1.80949I
a = 0.0004245 + 0.1240620I
b = 0.282881 + 0.280638I
−7.97011 − 0.42223I 0
u = −2.63588 − 1.80949I
a = 0.0004245 − 0.1240620I
b = 0.282881 − 0.280638I
−7.97011 + 0.42223I 0
23
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
25(5u
30
− 33u
29
+ ··· − 13u + 1)
· (5u
128
+ 44u
127
+ ··· + 774818u − 401483)
c
2
(u
30
− 4u
29
+ ··· + 22u + 5)(u
128
− u
127
+ ··· + 181885u + 12725)
c
3
(u
30
+ 5u
29
+ ··· − 38u + 11)
· (u
128
− 4u
127
+ ··· − 11825779033u + 7211692781)
c
4
(u
30
+ 7u
28
+ ··· + 18u + 5)
· (u
128
+ u
127
+ ··· + 1190911161u + 121993295)
c
5
25(5u
30
+ 23u
29
+ ··· − 14u + 1)
· (5u
128
− 6u
127
+ ··· + 40667u + 8021)
c
6
25(5u
30
+ 33u
29
+ ··· + 2u + 1)(5u
128
− 6u
127
+ ··· − 3u − 1)
c
7
, c
8
(u
30
− u
29
+ ··· + 16u + 5)(u
128
+ 69u
126
+ ··· + 3101u + 335)
c
9
(u
30
+ 5u
28
+ ··· + 14u + 4)
· (u
128
− u
127
+ ··· + 109650874u + 30512188)
c
10
(u
30
+ 10u
28
+ ··· − 28u + 5)(u
128
+ u
127
+ ··· − 86689u + 15995)
c
11
25(5u
30
− 23u
29
+ ··· + 14u + 1)
· (5u
128
− 6u
127
+ ··· + 40667u + 8021)
c
12
(u
30
+ u
29
+ ··· − 16u + 5)(u
128
+ 69u
126
+ ··· + 3101u + 335)
24
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
625(25y
30
− 439y
29
+ ··· − 17y + 1)
· (25y
128
− 1586y
127
+ ··· − 23418200454280y + 161188599289)
c
2
(y
30
+ 4y
29
+ ··· + 56y + 25)
· (y
128
+ 29y
127
+ ··· + 3815485825y + 161925625)
c
3
(y
30
− 23y
29
+ ··· + 2494y + 121)
· (y
128
− 86y
127
+ ··· − 2.57 × 10
21
y + 5.20 × 10
19
)
c
4
(y
30
+ 14y
29
+ ··· + 526y + 25)
· (y
128
+ 75y
127
+ ··· + 38410155386297739y + 14882364024957025)
c
5
, c
11
625(25y
30
+ 611y
29
+ ··· + 244y
2
+ 1)
· (25y
128
+ 2864y
127
+ ··· − 1962597347y + 64336441)
c
6
625(25y
30
− 189y
29
+ ··· − 6y + 1)(25y
128
− 636y
127
+ ··· + 95y + 1)
c
7
, c
8
, c
12
(y
30
+ 33y
29
+ ··· + 314y + 25)
· (y
128
+ 138y
127
+ ··· + 4645419y + 112225)
c
9
(y
30
+ 10y
29
+ ··· − 44y + 16)
· (y
128
− 41y
127
+ ··· − 25209093297032220y + 930993616547344)
c
10
(y
30
+ 20y
29
+ ··· + 606y + 25)
· (y
128
+ 49y
127
+ ··· + 19150857599y + 255840025)
25
