12a
0008
(K12a
0008
)
A knot diagram
1
Linearized knot diagam
3 5 6 8 2 11 4 12 1 7 10 9
Solving Sequence
4,7
8
5,11
6 3 2 1 10 12 9
c
7
c
4
c
6
c
3
c
2
c
1
c
10
c
11
c
8
c
5
, c
9
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−3.82254 × 10
339
u
104
− 5.03783 × 10
339
u
103
+ ··· + 5.84724 × 10
339
b − 5.55902 × 10
342
,
1.82294 × 10
340
u
104
+ 2.22909 × 10
340
u
103
+ ··· + 2.33889 × 10
340
a + 2.44212 × 10
343
,
u
105
+ 2u
104
+ ··· + 2048u + 1024i
I
u
2
= hb, −u
4
+ 2u
3
+ u
2
+ a − 3u, u
5
− u
4
− 2u
3
+ u
2
+ u + 1i
I
v
1
= ha, −152v
9
+ 36v
8
− 216v
7
+ 881v
6
− 468v
5
+ 684v
4
− 1376v
3
+ 252v
2
+ 115b − 144v + 219,
v
10
− v
9
+ 2v
8
− 7v
7
+ 8v
6
− 9v
5
+ 14v
4
− 10v
3
+ 5v
2
− 3v + 1i
* 3 irreducible components of dim
C
= 0, with total 120 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−3.82 × 10
339
u
104
− 5.04 × 10
339
u
103
+ · · · + 5.85 × 10
339
b − 5.56 ×
10
342
, 1.82 × 10
340
u
104
+ 2.23 × 10
340
u
103
+ · · · + 2.34 × 10
340
a + 2.44 ×
10
343
, u
105
+ 2u
104
+ · · · + 2048u + 1024i
(i) Arc colorings
a
4
=
0
u
a
7
=
1
0
a
8
=
1
u
2
a
5
=
−u
−u
3
+ u
a
11
=
−0.779404u
104
− 0.953053u
103
+ ··· − 752.424u − 1044.13
0.653735u
104
+ 0.861575u
103
+ ··· + 591.500u + 950.710
a
6
=
1.76035u
104
+ 1.98543u
103
+ ··· + 1749.68u + 2063.65
−0.847121u
104
− 1.09653u
103
+ ··· − 781.787u − 1191.48
a
3
=
0.959231u
104
+ 1.22999u
103
+ ··· + 905.222u + 1333.17
−1.35472u
104
− 1.62405u
103
+ ··· − 1278.29u − 1734.35
a
2
=
1.51533u
104
+ 1.88583u
103
+ ··· + 1422.48u + 2030.46
−1.52651u
104
− 1.83959u
103
+ ··· − 1430.38u − 1964.33
a
1
=
−0.913226u
104
− 0.888902u
103
+ ··· − 967.888u − 872.162
−1.79713u
104
− 2.06159u
103
+ ··· − 1766.75u − 2151.53
a
10
=
−0.125669u
104
− 0.0914777u
103
+ ··· − 160.924u − 93.4241
0.653735u
104
+ 0.861575u
103
+ ··· + 591.500u + 950.710
a
12
=
−1.50997u
104
− 1.64956u
103
+ ··· − 1556.56u − 1732.04
−0.184220u
104
− 0.158133u
103
+ ··· − 191.728u − 159.602
a
9
=
−0.561315u
104
− 0.724978u
103
+ ··· − 476.369u − 771.780
1.00686u
104
+ 1.15100u
103
+ ··· + 1010.56u + 1206.98
(ii) Obstruction class = −1
(iii) Cusp Shapes = −1.68427u
104
− 1.92328u
103
+ ··· − 1794.45u − 2081.91
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
105
+ 53u
104
+ ··· − 7u − 1
c
2
, c
5
u
105
+ 7u
104
+ ··· + 7u + 1
c
3
u
105
− 7u
104
+ ··· + 40669u + 23377
c
4
, c
7
u
105
+ 2u
104
+ ··· + 2048u + 1024
c
6
, c
10
u
105
+ 3u
104
+ ··· + 96u + 32
c
8
, c
9
, c
12
u
105
+ 8u
104
+ ··· + 2u + 1
c
11
u
105
− 39u
104
+ ··· − 14848u + 1024
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
105
+ 5y
104
+ ··· − 47y −1
c
2
, c
5
y
105
+ 53y
104
+ ··· − 7y −1
c
3
y
105
− 43y
104
+ ··· + 5130220969y −546484129
c
4
, c
7
y
105
− 60y
104
+ ··· + 25165824y −1048576
c
6
, c
10
y
105
+ 39y
104
+ ··· − 14848y −1024
c
8
, c
9
, c
12
y
105
− 90y
104
+ ··· − 206y −1
c
11
y
105
+ 47y
104
+ ··· − 210108416y −1048576
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.966623 + 0.262000I
a = 1.84206 − 0.44039I
b = 0.613331 + 0.897632I
−0.62620 − 5.04939I 0
u = 0.966623 − 0.262000I
a = 1.84206 + 0.44039I
b = 0.613331 − 0.897632I
−0.62620 + 5.04939I 0
u = −0.994592 + 0.126675I
a = −0.11789 + 1.79257I
b = −0.244604 − 1.112200I
−1.41343 + 1.12338I 0
u = −0.994592 − 0.126675I
a = −0.11789 − 1.79257I
b = −0.244604 + 1.112200I
−1.41343 − 1.12338I 0
u = −0.156135 + 0.971665I
a = 0.04677 − 1.83355I
b = 0.595883 + 0.703683I
0.09747 − 2.29231I 0
u = −0.156135 − 0.971665I
a = 0.04677 + 1.83355I
b = 0.595883 − 0.703683I
0.09747 + 2.29231I 0
u = 0.996817 + 0.231114I
a = −0.119338 − 0.216906I
b = 1.148970 + 0.105590I
0.82031 − 3.49410I 0
u = 0.996817 − 0.231114I
a = −0.119338 + 0.216906I
b = 1.148970 − 0.105590I
0.82031 + 3.49410I 0
u = 0.830770 + 0.624559I
a = 0.50740 − 1.47941I
b = 0.195587 + 1.292660I
8.20664 − 3.74731I 0
u = 0.830770 − 0.624559I
a = 0.50740 + 1.47941I
b = 0.195587 − 1.292660I
8.20664 + 3.74731I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.06842
a = −0.124114
b = −0.549124
−1.78436 0
u = 0.289155 + 1.029210I
a = 0.010911 − 1.335340I
b = 0.859812 + 0.584753I
0.42759 + 4.73730I 0
u = 0.289155 − 1.029210I
a = 0.010911 + 1.335340I
b = 0.859812 − 0.584753I
0.42759 − 4.73730I 0
u = −0.765537 + 0.753961I
a = 1.22243 + 0.93816I
b = −0.075655 − 1.140690I
6.95108 − 3.58416I 0
u = −0.765537 − 0.753961I
a = 1.22243 − 0.93816I
b = −0.075655 + 1.140690I
6.95108 + 3.58416I 0
u = 0.298691 + 1.037650I
a = −0.200218 + 1.183490I
b = 0.621372 − 1.078950I
4.62024 + 5.96188I 0
u = 0.298691 − 1.037650I
a = −0.200218 − 1.183490I
b = 0.621372 + 1.078950I
4.62024 − 5.96188I 0
u = −0.915190 + 0.048307I
a = 1.57055 − 0.49914I
b = 0.606566 − 0.808414I
−0.915909 − 0.241093I 0
u = −0.915190 − 0.048307I
a = 1.57055 + 0.49914I
b = 0.606566 + 0.808414I
−0.915909 + 0.241093I 0
u = −0.951368 + 0.522622I
a = 0.38217 + 1.61581I
b = 0.252648 − 1.368440I
6.29716 + 8.47800I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.951368 − 0.522622I
a = 0.38217 − 1.61581I
b = 0.252648 + 1.368440I
6.29716 − 8.47800I 0
u = 0.771518 + 0.768489I
a = 0.94253 − 1.18145I
b = 0.017151 + 1.183720I
8.47050 − 1.50689I 0
u = 0.771518 − 0.768489I
a = 0.94253 + 1.18145I
b = 0.017151 − 1.183720I
8.47050 + 1.50689I 0
u = −1.075900 + 0.190627I
a = −1.365470 + 0.159370I
b = −0.603761 + 1.042000I
3.68939 + 3.33964I 0
u = −1.075900 − 0.190627I
a = −1.365470 − 0.159370I
b = −0.603761 − 1.042000I
3.68939 − 3.33964I 0
u = −0.651392 + 0.879936I
a = 0.393010 + 0.894053I
b = 0.194470 − 0.994625I
3.44940 + 2.87203I 0
u = −0.651392 − 0.879936I
a = 0.393010 − 0.894053I
b = 0.194470 + 0.994625I
3.44940 − 2.87203I 0
u = −1.050100 + 0.314666I
a = −0.22948 − 1.92157I
b = −0.037303 + 1.113740I
−0.96727 + 5.99715I 0
u = −1.050100 − 0.314666I
a = −0.22948 + 1.92157I
b = −0.037303 − 1.113740I
−0.96727 − 5.99715I 0
u = −0.835876 + 0.304185I
a = −1.05229 − 1.03238I
b = −0.825475 − 0.471650I
2.39540 + 3.43521I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.835876 − 0.304185I
a = −1.05229 + 1.03238I
b = −0.825475 + 0.471650I
2.39540 − 3.43521I 0
u = 0.082150 + 1.110590I
a = 0.169904 + 1.176230I
b = −0.700136 − 0.769483I
−3.28334 + 1.14216I 0
u = 0.082150 − 1.110590I
a = 0.169904 − 1.176230I
b = −0.700136 + 0.769483I
−3.28334 − 1.14216I 0
u = 0.208245 + 0.860687I
a = 0.059506 − 1.353310I
b = −0.575289 + 0.870092I
−0.20460 + 2.27131I 0
u = 0.208245 − 0.860687I
a = 0.059506 + 1.353310I
b = −0.575289 − 0.870092I
−0.20460 − 2.27131I 0
u = 1.096560 + 0.354630I
a = −1.50864 + 0.44399I
b = −0.649802 − 1.079910I
4.17470 − 8.90495I 0
u = 1.096560 − 0.354630I
a = −1.50864 − 0.44399I
b = −0.649802 + 1.079910I
4.17470 + 8.90495I 0
u = 0.771031 + 0.344389I
a = −0.34801 + 1.88152I
b = −0.033449 − 0.956974I
1.31907 − 1.85367I 0
u = 0.771031 − 0.344389I
a = −0.34801 − 1.88152I
b = −0.033449 + 0.956974I
1.31907 + 1.85367I 0
u = −0.303689 + 1.129670I
a = 0.198606 + 1.374610I
b = −0.673059 − 0.926013I
−2.80313 − 6.42495I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.303689 − 1.129670I
a = 0.198606 − 1.374610I
b = −0.673059 + 0.926013I
−2.80313 + 6.42495I 0
u = −0.323418 + 0.718994I
a = 0.351226 + 1.099770I
b = 0.817506 − 0.395832I
2.66939 − 0.70616I 3.86014 + 0.I
u = −0.323418 − 0.718994I
a = 0.351226 − 1.099770I
b = 0.817506 + 0.395832I
2.66939 + 0.70616I 3.86014 + 0.I
u = −0.783043 + 0.032782I
a = 0.05152 − 1.49817I
b = 0.456650 + 1.312500I
5.03761 − 2.14522I −2.62234 − 0.68124I
u = −0.783043 − 0.032782I
a = 0.05152 + 1.49817I
b = 0.456650 − 1.312500I
5.03761 + 2.14522I −2.62234 + 0.68124I
u = −0.069329 + 1.225860I
a = −0.207633 − 1.035880I
b = 0.608931 + 0.965031I
0.91219 − 2.50907I 0
u = −0.069329 − 1.225860I
a = −0.207633 + 1.035880I
b = 0.608931 − 0.965031I
0.91219 + 2.50907I 0
u = 1.170060 + 0.463549I
a = −1.10322 + 1.53284I
b = −0.553441 − 0.934425I
−0.62425 − 2.83456I 0
u = 1.170060 − 0.463549I
a = −1.10322 − 1.53284I
b = −0.553441 + 0.934425I
−0.62425 + 2.83456I 0
u = −0.476116 + 0.565252I
a = −0.304758 − 0.867417I
b = −0.445573 + 0.493036I
−0.87676 + 1.33458I −5.87002 − 4.06416I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.476116 − 0.565252I
a = −0.304758 + 0.867417I
b = −0.445573 − 0.493036I
−0.87676 − 1.33458I −5.87002 + 4.06416I
u = 0.454580 + 0.569119I
a = −0.43556 + 2.37608I
b = 0.170218 − 0.693124I
1.83393 − 1.25356I 7.30757 + 1.79196I
u = 0.454580 − 0.569119I
a = −0.43556 − 2.37608I
b = 0.170218 + 0.693124I
1.83393 + 1.25356I 7.30757 − 1.79196I
u = −0.408160 + 1.210580I
a = −0.294514 − 1.182610I
b = 0.694328 + 1.069540I
1.90832 − 10.51360I 0
u = −0.408160 − 1.210580I
a = −0.294514 + 1.182610I
b = 0.694328 − 1.069540I
1.90832 + 10.51360I 0
u = −0.608380 + 0.375672I
a = 0.257068 + 0.458626I
b = 0.964533 − 0.182230I
2.88842 − 0.29217I 2.82331 − 1.55863I
u = −0.608380 − 0.375672I
a = 0.257068 − 0.458626I
b = 0.964533 + 0.182230I
2.88842 + 0.29217I 2.82331 + 1.55863I
u = −1.190280 + 0.531474I
a = −0.038155 − 0.170848I
b = −1.015260 − 0.612676I
−0.03711 + 5.60715I 0
u = −1.190280 − 0.531474I
a = −0.038155 + 0.170848I
b = −1.015260 + 0.612676I
−0.03711 − 5.60715I 0
u = 1.296260 + 0.215123I
a = 0.0286880 + 0.1014560I
b = −0.625259 − 0.034743I
−5.00588 − 4.15826I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.296260 − 0.215123I
a = 0.0286880 − 0.1014560I
b = −0.625259 + 0.034743I
−5.00588 + 4.15826I 0
u = 0.540659 + 0.417528I
a = −0.08495 − 1.56537I
b = −0.396115 + 0.965766I
0.46462 + 2.21286I 0.18906 − 1.66288I
u = 0.540659 − 0.417528I
a = −0.08495 + 1.56537I
b = −0.396115 − 0.965766I
0.46462 − 2.21286I 0.18906 + 1.66288I
u = −1.262590 + 0.406275I
a = 0.043597 + 0.144135I
b = 0.808161 + 0.651447I
−4.49634 + 1.94814I 0
u = −1.262590 − 0.406275I
a = 0.043597 − 0.144135I
b = 0.808161 − 0.651447I
−4.49634 − 1.94814I 0
u = 0.501894 + 0.449298I
a = −0.061381 + 1.371720I
b = 0.532459 − 1.225220I
6.13895 + 5.63139I 4.44596 + 0.50184I
u = 0.501894 − 0.449298I
a = −0.061381 − 1.371720I
b = 0.532459 + 1.225220I
6.13895 − 5.63139I 4.44596 − 0.50184I
u = 0.538287 + 0.382734I
a = −2.47342 + 2.53276I
b = −0.174232 − 0.605006I
1.79965 − 1.45383I 6.85530 + 8.54654I
u = 0.538287 − 0.382734I
a = −2.47342 − 2.53276I
b = −0.174232 + 0.605006I
1.79965 + 1.45383I 6.85530 − 8.54654I
u = 0.650695 + 0.088990I
a = −3.07569 + 1.05876I
b = −0.634565 + 0.388641I
2.01640 + 1.51491I −4.95811 − 2.51475I
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.650695 − 0.088990I
a = −3.07569 − 1.05876I
b = −0.634565 − 0.388641I
2.01640 − 1.51491I −4.95811 + 2.51475I
u = −1.315550 + 0.292996I
a = −0.87266 − 1.20760I
b = −0.680138 + 0.916140I
−5.04079 − 0.55525I 0
u = −1.315550 − 0.292996I
a = −0.87266 + 1.20760I
b = −0.680138 − 0.916140I
−5.04079 + 0.55525I 0
u = 1.241410 + 0.559646I
a = 1.06522 − 1.30685I
b = 0.693688 + 1.030650I
−3.33108 − 7.60318I 0
u = 1.241410 − 0.559646I
a = 1.06522 + 1.30685I
b = 0.693688 − 1.030650I
−3.33108 + 7.60318I 0
u = 1.313810 + 0.373086I
a = −0.235478 − 0.167465I
b = −0.969130 + 0.703808I
−4.67411 − 2.30128I 0
u = 1.313810 − 0.373086I
a = −0.235478 + 0.167465I
b = −0.969130 − 0.703808I
−4.67411 + 2.30128I 0
u = −0.406323 + 0.472980I
a = −2.61611 − 2.10864I
b = 0.043443 + 0.684550I
0.98116 − 2.85208I 4.87688 + 0.20930I
u = −0.406323 − 0.472980I
a = −2.61611 + 2.10864I
b = 0.043443 − 0.684550I
0.98116 + 2.85208I 4.87688 − 0.20930I
u = −1.266110 + 0.561926I
a = −0.90672 − 1.64848I
b = −0.563296 + 1.011730I
−3.30268 + 7.81911I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.266110 − 0.561926I
a = −0.90672 + 1.64848I
b = −0.563296 − 1.011730I
−3.30268 − 7.81911I 0
u = 1.268350 + 0.617290I
a = 0.147260 + 0.059650I
b = −1.069350 + 0.631867I
−2.66171 − 10.71770I 0
u = 1.268350 − 0.617290I
a = 0.147260 − 0.059650I
b = −1.069350 − 0.631867I
−2.66171 + 10.71770I 0
u = 1.26411 + 0.64010I
a = −0.98809 + 1.20593I
b = −0.756688 − 1.129680I
1.61848 − 12.04680I 0
u = 1.26411 − 0.64010I
a = −0.98809 − 1.20593I
b = −0.756688 + 1.129680I
1.61848 + 12.04680I 0
u = −1.39616 + 0.27043I
a = −0.0275538 − 0.1189400I
b = −0.530086 − 0.789172I
−1.12946 − 1.52913I 0
u = −1.39616 − 0.27043I
a = −0.0275538 + 0.1189400I
b = −0.530086 + 0.789172I
−1.12946 + 1.52913I 0
u = −1.37101 + 0.42124I
a = 0.833638 + 1.030930I
b = 0.753137 − 0.991259I
−8.14449 + 4.19574I 0
u = −1.37101 − 0.42124I
a = 0.833638 − 1.030930I
b = 0.753137 + 0.991259I
−8.14449 − 4.19574I 0
u = 1.41210 + 0.25259I
a = 0.182134 + 0.133509I
b = 0.846007 − 0.737444I
−8.93146 + 1.75969I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.41210 − 0.25259I
a = 0.182134 − 0.133509I
b = 0.846007 + 0.737444I
−8.93146 − 1.75969I 0
u = −0.226596 + 0.512840I
a = −1.195050 + 0.039507I
b = 0.239764 + 0.183136I
−0.33339 + 1.65387I −2.68049 − 4.66999I
u = −0.226596 − 0.512840I
a = −1.195050 − 0.039507I
b = 0.239764 − 0.183136I
−0.33339 − 1.65387I −2.68049 + 4.66999I
u = 1.34885 + 0.52625I
a = −0.1255900 − 0.0557574I
b = 0.864727 − 0.616241I
−7.39202 − 6.95911I 0
u = 1.34885 − 0.52625I
a = −0.1255900 + 0.0557574I
b = 0.864727 + 0.616241I
−7.39202 + 6.95911I 0
u = −1.30284 + 0.65176I
a = 0.91312 + 1.44775I
b = 0.708405 − 1.069030I
−5.9958 + 12.8200I 0
u = −1.30284 − 0.65176I
a = 0.91312 − 1.44775I
b = 0.708405 + 1.069030I
−5.9958 − 12.8200I 0
u = −1.38919 + 0.53030I
a = −0.774216 − 0.940360I
b = −0.776331 + 1.071110I
−3.48041 + 8.68972I 0
u = −1.38919 − 0.53030I
a = −0.774216 + 0.940360I
b = −0.776331 − 1.071110I
−3.48041 − 8.68972I 0
u = −1.30301 + 0.72418I
a = −0.85428 − 1.34318I
b = −0.783365 + 1.149260I
−0.9805 + 17.4101I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.30301 − 0.72418I
a = −0.85428 + 1.34318I
b = −0.783365 − 1.149260I
−0.9805 − 17.4101I 0
u = 1.52631 + 0.11647I
a = −0.144120 − 0.089973I
b = −0.648982 + 0.791673I
−5.42904 + 5.71768I 0
u = 1.52631 − 0.11647I
a = −0.144120 + 0.089973I
b = −0.648982 − 0.791673I
−5.42904 − 5.71768I 0
u = 1.49316 + 0.40751I
a = 0.1032100 + 0.0283296I
b = −0.492837 + 0.689740I
−4.43944 − 3.45605I 0
u = 1.49316 − 0.40751I
a = 0.1032100 − 0.0283296I
b = −0.492837 − 0.689740I
−4.43944 + 3.45605I 0
15
II. I
u
2
= hb, −u
4
+ 2u
3
+ u
2
+ a − 3u, u
5
− u
4
− 2u
3
+ u
2
+ u + 1i
(i) Arc colorings
a
4
=
0
u
a
7
=
1
0
a
8
=
1
u
2
a
5
=
−u
−u
3
+ u
a
11
=
u
4
− 2u
3
− u
2
+ 3u
0
a
6
=
1
0
a
3
=
u
u
a
2
=
u
4
− u
2
− 1
u
4
− 2u
2
a
1
=
−1
−u
2
a
10
=
u
4
− 2u
3
− u
2
+ 3u
0
a
12
=
u
4
− 2u
3
− u
2
+ 3u
0
a
9
=
u
4
− 2u
3
− u
2
+ 3u + 1
u
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −2u
4
+ 7u
3
+ 7u
2
− 13u − 6
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
5
− 3u
4
+ 4u
3
− u
2
− u + 1
c
2
u
5
− u
4
+ 2u
3
− u
2
+ u − 1
c
3
, c
4
u
5
+ u
4
− 2u
3
− u
2
+ u − 1
c
5
u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1
c
6
, c
10
, c
11
u
5
c
7
u
5
− u
4
− 2u
3
+ u
2
+ u + 1
c
8
, c
9
(u + 1)
5
c
12
(u − 1)
5
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1
c
2
, c
5
y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1
c
3
, c
4
, c
7
y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1
c
6
, c
10
, c
11
y
5
c
8
, c
9
, c
12
(y −1)
5
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.21774
a = 0.674363
b = 0
−0.756147 3.17260
u = −0.309916 + 0.549911I
a = −1.29977 + 2.14694I
b = 0
1.31583 + 1.53058I −1.50865 − 9.87103I
u = −0.309916 − 0.549911I
a = −1.29977 − 2.14694I
b = 0
1.31583 − 1.53058I −1.50865 + 9.87103I
u = 1.41878 + 0.21917I
a = 0.462589 − 0.146410I
b = 0
−4.22763 − 4.40083I 0.92237 + 5.80708I
u = 1.41878 − 0.21917I
a = 0.462589 + 0.146410I
b = 0
−4.22763 + 4.40083I 0.92237 − 5.80708I
19
III. I
v
1
= ha, −152v
9
+ 36v
8
+ · · · + 115b + 219, v
10
− v
9
+ · · · − 3v + 1i
(i) Arc colorings
a
4
=
v
0
a
7
=
1
0
a
8
=
1
0
a
5
=
v
0
a
11
=
0
1.32174v
9
− 0.313043v
8
+ ··· + 1.25217v − 1.90435
a
6
=
1
1.35652v
9
− 0.373913v
8
+ ··· + 1.49565v − 0.191304
a
3
=
−0.982609v
9
+ 0.469565v
8
+ ··· − 2.87826v + 1.35652
−2.35652v
9
+ 1.37391v
8
+ ··· − 6.49565v + 3.19130
a
2
=
−0.469565v
9
+ 0.321739v
8
+ ··· − 2.28696v + 0.373913
−2.35652v
9
+ 1.37391v
8
+ ··· − 6.49565v + 3.19130
a
1
=
−1
−1.35652v
9
+ 0.373913v
8
+ ··· − 1.49565v + 0.191304
a
10
=
1.32174v
9
− 0.313043v
8
+ ··· + 1.25217v − 1.90435
1.32174v
9
− 0.313043v
8
+ ··· + 1.25217v − 1.90435
a
12
=
−0.808696v
9
+ 0.165217v
8
+ ··· − 0.660870v + 2.92174
0.513043v
9
− 0.147826v
8
+ ··· + 0.591304v + 1.01739
a
9
=
0.808696v
9
− 0.165217v
8
+ ··· + 0.660870v − 2.92174
−1.02609v
9
+ 0.295652v
8
+ ··· − 1.18261v − 1.03478
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −
281
115
v
9
+
118
115
v
8
−
363
115
v
7
+
1693
115
v
6
−
959
115
v
5
+
977
115
v
4
−
2683
115
v
3
+
251
115
v
2
+
793
115
v +
622
115
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
5
(u
2
− u + 1)
5
c
2
(u
2
+ u + 1)
5
c
4
, c
7
u
10
c
6
(u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1)
2
c
8
, c
9
(u
5
− u
4
− 2u
3
+ u
2
+ u + 1)
2
c
10
(u
5
− u
4
+ 2u
3
− u
2
+ u − 1)
2
c
11
(u
5
− 3u
4
+ 4u
3
− u
2
− u + 1)
2
c
12
(u
5
+ u
4
− 2u
3
− u
2
+ u − 1)
2
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
5
(y
2
+ y + 1)
5
c
4
, c
7
y
10
c
6
, c
10
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y − 1)
2
c
8
, c
9
, c
12
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y − 1)
2
c
11
(y
5
− y
4
+ 8y
3
− 3y
2
+ 3y − 1)
2
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 1.219640 + 0.330957I
a = 0
b = 0.339110 − 0.822375I
0.329100 − 0.499304I 2.43337 − 0.47576I
v = 1.219640 − 0.330957I
a = 0
b = 0.339110 + 0.822375I
0.329100 + 0.499304I 2.43337 + 0.47576I
v = −0.323203 + 1.221720I
a = 0
b = 0.339110 + 0.822375I
0.32910 − 3.56046I −1.41726 + 7.41465I
v = −0.323203 − 1.221720I
a = 0
b = 0.339110 − 0.822375I
0.32910 + 3.56046I −1.41726 − 7.41465I
v = 0.575710 + 0.191698I
a = 0
b = −0.455697 + 1.200150I
5.87256 + 2.37095I 7.21285 − 1.44195I
v = 0.575710 − 0.191698I
a = 0
b = −0.455697 − 1.200150I
5.87256 − 2.37095I 7.21285 + 1.44195I
v = −0.121840 + 0.594429I
a = 0
b = −0.455697 − 1.200150I
5.87256 − 6.43072I 1.90884 + 7.88634I
v = −0.121840 − 0.594429I
a = 0
b = −0.455697 + 1.200150I
5.87256 + 6.43072I 1.90884 − 7.88634I
v = −0.85031 + 1.47278I
a = 0
b = −0.766826
2.40108 + 2.02988I −0.13779 − 5.66929I
v = −0.85031 − 1.47278I
a = 0
b = −0.766826
2.40108 − 2.02988I −0.13779 + 5.66929I
23
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
2
− u + 1)
5
)(u
5
− 3u
4
+ ··· − u + 1)(u
105
+ 53u
104
+ ··· − 7u − 1)
c
2
((u
2
+ u + 1)
5
)(u
5
− u
4
+ ··· + u − 1)(u
105
+ 7u
104
+ ··· + 7u + 1)
c
3
(u
2
− u + 1)
5
(u
5
+ u
4
− 2u
3
− u
2
+ u − 1)
· (u
105
− 7u
104
+ ··· + 40669u + 23377)
c
4
u
10
(u
5
+ u
4
+ ··· + u − 1)(u
105
+ 2u
104
+ ··· + 2048u + 1024)
c
5
((u
2
− u + 1)
5
)(u
5
+ u
4
+ ··· + u + 1)(u
105
+ 7u
104
+ ··· + 7u + 1)
c
6
u
5
(u
5
+ u
4
+ ··· + u + 1)
2
(u
105
+ 3u
104
+ ··· + 96u + 32)
c
7
u
10
(u
5
− u
4
+ ··· + u + 1)(u
105
+ 2u
104
+ ··· + 2048u + 1024)
c
8
, c
9
((u + 1)
5
)(u
5
− u
4
+ ··· + u + 1)
2
(u
105
+ 8u
104
+ ··· + 2u + 1)
c
10
u
5
(u
5
− u
4
+ ··· + u − 1)
2
(u
105
+ 3u
104
+ ··· + 96u + 32)
c
11
u
5
(u
5
− 3u
4
+ ··· − u + 1)
2
(u
105
− 39u
104
+ ··· − 14848u + 1024)
c
12
((u − 1)
5
)(u
5
+ u
4
+ ··· + u − 1)
2
(u
105
+ 8u
104
+ ··· + 2u + 1)
24
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
2
+ y + 1)
5
)(y
5
− y
4
+ ··· + 3y − 1)(y
105
+ 5y
104
+ ··· − 47y − 1)
c
2
, c
5
((y
2
+ y + 1)
5
)(y
5
+ 3y
4
+ ··· − y − 1)(y
105
+ 53y
104
+ ··· − 7y − 1)
c
3
(y
2
+ y + 1)
5
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y − 1)
· (y
105
− 43y
104
+ ··· + 5130220969y − 546484129)
c
4
, c
7
y
10
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y − 1)
· (y
105
− 60y
104
+ ··· + 25165824y − 1048576)
c
6
, c
10
y
5
(y
5
+ 3y
4
+ ··· − y − 1)
2
(y
105
+ 39y
104
+ ··· − 14848y − 1024)
c
8
, c
9
, c
12
(y − 1)
5
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y − 1)
2
· (y
105
− 90y
104
+ ··· − 206y − 1)
c
11
y
5
(y
5
− y
4
+ 8y
3
− 3y
2
+ 3y − 1)
2
· (y
105
+ 47y
104
+ ··· − 210108416y − 1048576)
25
