12a
0016
(K12a
0016
)
A knot diagram
1
Linearized knot diagam
3 5 6 9 2 10 11 4 1 12 7 8
Solving Sequence
7,11 4,8
9 5 12 1 10 6 3 2
c
7
c
8
c
4
c
11
c
12
c
10
c
6
c
3
c
2
c
1
, c
5
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h8u
109
− 22u
108
+ ··· + 2b + 6u, −8u
109
+ 24u
108
+ ··· + 2a + 11, u
110
− 3u
109
+ ··· − 2u + 1i
I
u
2
= h−u
2
a + b, u
4
− u
2
a + 2u
3
+ a
2
− au + 3u
2
− a + 2u + 1, u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1i
* 2 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
= h8u
109
− 22u
108
+ · · · + 2b + 6u, −8u
109
+ 24u
108
+ · · · + 2a +
11, u
110
− 3u
109
+ · · · − 2u + 1i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
u
a
4
=
4u
109
− 12u
108
+ ··· +
15
2
u −
11
2
−4u
109
+ 11u
108
+ ··· −
1
2
u
2
− 3u
a
8
=
1
u
2
a
9
=
−u
11
− 2u
9
− 2u
7
− u
3
−u
13
− 3u
11
− 5u
9
− 4u
7
− 2u
5
+ u
3
+ u
a
5
=
4u
108
− 8u
107
+ ··· −
3
2
u +
1
2
−2u
108
+
5
2
u
107
+ ··· −
11
2
u
2
+ 3u
a
12
=
−u
u
a
1
=
u
3
u
5
+ u
3
+ u
a
10
=
−u
3
u
3
+ u
a
6
=
−u
6
− u
4
+ 1
u
6
+ 2u
4
+ u
2
a
3
=
2u
109
−
11
2
u
108
+ ··· + 6u − 3
−2u
109
+
11
2
u
108
+ ··· −
3
2
u
2
−
1
2
u
a
2
=
−
1
2
u
108
+ u
107
+ ··· + 2u − 1
1
2
u
108
− u
107
+ ··· −
3
2
u
2
+
3
2
u
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
109
−
31
2
u
108
+ ··· +
47
2
u −
15
2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
110
+ 54u
109
+ ··· + 7u + 1
c
2
, c
5
u
110
+ 6u
109
+ ··· + 5u + 1
c
3
u
110
− 6u
109
+ ··· − 455049u + 73746
c
4
, c
8
u
110
− u
109
+ ··· − 10240u
2
+ 1024
c
6
, c
12
u
110
− 3u
109
+ ··· − 585u + 34
c
7
, c
11
u
110
+ 3u
109
+ ··· + 2u + 1
c
9
u
110
+ 13u
109
+ ··· + 74128u + 1669
c
10
u
110
− 59u
109
+ ··· − 8u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
110
+ 10y
109
+ ··· − 9y + 1
c
2
, c
5
y
110
+ 54y
109
+ ··· + 7y + 1
c
3
y
110
− 34y
109
+ ··· − 23865354441y + 5438472516
c
4
, c
8
y
110
− 55y
109
+ ··· − 20971520y + 1048576
c
6
, c
12
y
110
− 85y
109
+ ··· + 105147y + 1156
c
7
, c
11
y
110
+ 59y
109
+ ··· + 8y + 1
c
9
y
110
+ 15y
109
+ ··· − 1624602792y + 2785561
c
10
y
110
− 13y
109
+ ··· + 76y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.579982 + 0.823482I
a = −1.10813 − 1.57808I
b = 0.196290 + 1.248310I
−7.69991 + 3.23271I 0
u = −0.579982 − 0.823482I
a = −1.10813 + 1.57808I
b = 0.196290 − 1.248310I
−7.69991 − 3.23271I 0
u = −0.561599 + 0.852113I
a = 1.26319 + 1.80130I
b = 0.00553 − 1.44932I
−3.12530 + 6.60837I 0
u = −0.561599 − 0.852113I
a = 1.26319 − 1.80130I
b = 0.00553 + 1.44932I
−3.12530 − 6.60837I 0
u = 0.406550 + 0.888189I
a = −0.690850 − 0.195917I
b = 0.0799002 + 0.0496905I
0.19398 − 2.02003I 0
u = 0.406550 − 0.888189I
a = −0.690850 + 0.195917I
b = 0.0799002 − 0.0496905I
0.19398 + 2.02003I 0
u = 0.528135 + 0.808914I
a = 1.011690 − 0.239556I
b = 0.0721671 − 0.1011930I
−2.50066 − 5.75747I 0
u = 0.528135 − 0.808914I
a = 1.011690 + 0.239556I
b = 0.0721671 + 0.1011930I
−2.50066 + 5.75747I 0
u = −0.577603 + 0.864674I
a = −1.14476 − 1.89716I
b = −0.142767 + 1.339650I
−5.80226 + 11.67560I 0
u = −0.577603 − 0.864674I
a = −1.14476 + 1.89716I
b = −0.142767 − 1.339650I
−5.80226 − 11.67560I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.128950 + 1.034770I
a = −1.07011 − 1.42517I
b = 0.553854 + 0.773753I
1.55547 − 2.74435I 0
u = 0.128950 − 1.034770I
a = −1.07011 + 1.42517I
b = 0.553854 − 0.773753I
1.55547 + 2.74435I 0
u = −0.487300 + 0.806990I
a = 1.99235 + 1.41659I
b = −0.57504 − 1.94110I
−0.42932 + 4.54389I 0
u = −0.487300 − 0.806990I
a = 1.99235 − 1.41659I
b = −0.57504 + 1.94110I
−0.42932 − 4.54389I 0
u = 0.011304 + 0.929219I
a = −0.35995 − 1.94849I
b = −0.263245 + 1.087660I
2.57030 − 1.41361I 0
u = 0.011304 − 0.929219I
a = −0.35995 + 1.94849I
b = −0.263245 − 1.087660I
2.57030 + 1.41361I 0
u = −0.592873 + 0.707362I
a = 0.861643 + 0.645026I
b = −0.91828 − 1.09414I
−8.03143 + 1.39305I 0
u = −0.592873 − 0.707362I
a = 0.861643 − 0.645026I
b = −0.91828 + 1.09414I
−8.03143 − 1.39305I 0
u = 0.452920 + 0.800781I
a = −0.763988 + 0.178725I
b = 0.0478287 + 0.0879934I
−0.04986 − 1.88964I 0
u = 0.452920 − 0.800781I
a = −0.763988 − 0.178725I
b = 0.0478287 − 0.0879934I
−0.04986 + 1.88964I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.128527 + 1.087170I
a = 1.41312 + 1.45257I
b = −0.928389 − 0.812896I
−0.83737 − 7.40305I 0
u = 0.128527 − 1.087170I
a = 1.41312 − 1.45257I
b = −0.928389 + 0.812896I
−0.83737 + 7.40305I 0
u = 0.226104 + 1.082150I
a = 1.30997 + 0.79217I
b = −0.731357 − 0.110538I
−2.18609 + 0.20029I 0
u = 0.226104 − 1.082150I
a = 1.30997 − 0.79217I
b = −0.731357 + 0.110538I
−2.18609 − 0.20029I 0
u = 0.521951 + 0.724522I
a = 0.874689 − 0.434640I
b = −0.029472 − 0.261786I
−2.74492 + 1.47945I 0
u = 0.521951 − 0.724522I
a = 0.874689 + 0.434640I
b = −0.029472 + 0.261786I
−2.74492 − 1.47945I 0
u = −0.603428 + 0.653495I
a = 0.705508 + 0.281490I
b = −1.10269 − 1.10590I
−6.40282 − 7.03071I 0
u = −0.603428 − 0.653495I
a = 0.705508 − 0.281490I
b = −1.10269 + 1.10590I
−6.40282 + 7.03071I 0
u = −0.087587 + 0.882466I
a = −0.05146 + 2.36788I
b = 0.85301 − 1.20943I
1.34153 + 3.06537I 5.56421 + 0.I
u = −0.087587 − 0.882466I
a = −0.05146 − 2.36788I
b = 0.85301 + 1.20943I
1.34153 − 3.06537I 5.56421 + 0.I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.467459 + 0.752773I
a = −2.12256 − 0.69643I
b = 1.06350 + 1.76434I
−0.606282 − 0.555086I −5.95291 + 0.I
u = −0.467459 − 0.752773I
a = −2.12256 + 0.69643I
b = 1.06350 − 1.76434I
−0.606282 + 0.555086I −5.95291 + 0.I
u = −0.575057 + 0.665687I
a = −0.913960 − 0.314089I
b = 1.05186 + 1.16392I
−3.65420 − 2.08576I 0
u = −0.575057 − 0.665687I
a = −0.913960 + 0.314089I
b = 1.05186 − 1.16392I
−3.65420 + 2.08576I 0
u = 0.819934 + 0.162919I
a = −0.41914 − 1.36387I
b = 1.32289 − 1.67361I
−2.26724 + 12.52740I −2.80434 − 7.99531I
u = 0.819934 − 0.162919I
a = −0.41914 + 1.36387I
b = 1.32289 + 1.67361I
−2.26724 − 12.52740I −2.80434 + 7.99531I
u = −0.828291 + 0.028957I
a = 0.701648 − 0.191250I
b = 1.336090 − 0.429868I
1.62988 + 3.17856I −3.50751 − 5.52897I
u = −0.828291 − 0.028957I
a = 0.701648 + 0.191250I
b = 1.336090 + 0.429868I
1.62988 − 3.17856I −3.50751 + 5.52897I
u = 0.806530 + 0.157966I
a = 0.53866 + 1.33941I
b = −1.17343 + 1.59078I
0.21834 + 7.31585I 0. − 4.55869I
u = 0.806530 − 0.157966I
a = 0.53866 − 1.33941I
b = −1.17343 − 1.59078I
0.21834 − 7.31585I 0. + 4.55869I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.792107 + 0.182923I
a = −0.519053 − 1.102450I
b = 1.27628 − 1.28558I
−4.65166 + 4.23372I −5.98881 − 2.52410I
u = 0.792107 − 0.182923I
a = −0.519053 + 1.102450I
b = 1.27628 + 1.28558I
−4.65166 − 4.23372I −5.98881 + 2.52410I
u = 0.507208 + 1.073690I
a = 0.813220 + 1.009570I
b = −0.554966 − 0.329840I
−3.13792 + 0.92257I 0
u = 0.507208 − 1.073690I
a = 0.813220 − 1.009570I
b = −0.554966 + 0.329840I
−3.13792 − 0.92257I 0
u = −0.795193 + 0.053029I
a = −0.528875 + 0.373665I
b = −0.905963 + 0.770490I
3.25367 − 0.82072I 2.37894 − 1.72031I
u = −0.795193 − 0.053029I
a = −0.528875 − 0.373665I
b = −0.905963 − 0.770490I
3.25367 + 0.82072I 2.37894 + 1.72031I
u = 0.488937 + 1.104850I
a = −0.432111 − 1.066750I
b = 0.387961 + 0.735312I
−0.04787 − 3.54238I 0
u = 0.488937 − 1.104850I
a = −0.432111 + 1.066750I
b = 0.387961 − 0.735312I
−0.04787 + 3.54238I 0
u = −0.767663 + 0.149617I
a = 0.522352 − 0.771363I
b = 0.54928 − 1.61345I
0.28498 − 6.22966I −1.67005 + 5.40696I
u = −0.767663 − 0.149617I
a = 0.522352 + 0.771363I
b = 0.54928 + 1.61345I
0.28498 + 6.22966I −1.67005 − 5.40696I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.413961 + 1.146140I
a = 0.43422 + 2.07516I
b = 1.20426 − 1.84563I
2.54580 + 4.57308I 0
u = −0.413961 − 1.146140I
a = 0.43422 − 2.07516I
b = 1.20426 + 1.84563I
2.54580 − 4.57308I 0
u = 0.763221 + 0.125905I
a = 1.04676 + 1.31046I
b = −0.59709 + 1.37823I
2.27168 + 4.64244I 0.14088 − 6.23456I
u = 0.763221 − 0.125905I
a = 1.04676 − 1.31046I
b = −0.59709 − 1.37823I
2.27168 − 4.64244I 0.14088 + 6.23456I
u = −0.759138 + 0.112943I
a = −0.473360 + 0.674125I
b = −0.57188 + 1.33475I
2.55409 − 1.75029I 2.58514 + 1.16963I
u = −0.759138 − 0.112943I
a = −0.473360 − 0.674125I
b = −0.57188 − 1.33475I
2.55409 + 1.75029I 2.58514 − 1.16963I
u = 0.517547 + 1.118880I
a = 0.54435 + 1.49296I
b = −0.917306 − 0.885875I
−3.84920 − 7.45703I 0
u = 0.517547 − 1.118880I
a = 0.54435 − 1.49296I
b = −0.917306 + 0.885875I
−3.84920 + 7.45703I 0
u = 0.348172 + 1.192970I
a = −1.31970 + 0.77788I
b = −0.12251 − 1.61626I
−0.502173 + 0.513562I 0
u = 0.348172 − 1.192970I
a = −1.31970 − 0.77788I
b = −0.12251 + 1.61626I
−0.502173 − 0.513562I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.379263 + 1.186000I
a = −0.16882 + 2.36666I
b = 1.84998 − 1.82441I
4.19584 − 2.40976I 0
u = −0.379263 − 1.186000I
a = −0.16882 − 2.36666I
b = 1.84998 + 1.82441I
4.19584 + 2.40976I 0
u = 0.698012 + 0.281638I
a = 0.607096 + 0.269495I
b = −1.162940 + 0.229128I
−6.27859 + 2.81930I −7.65388 − 2.76519I
u = 0.698012 − 0.281638I
a = 0.607096 − 0.269495I
b = −1.162940 − 0.229128I
−6.27859 − 2.81930I −7.65388 + 2.76519I
u = 0.407392 + 1.179060I
a = −0.068976 + 0.937001I
b = −1.67160 − 0.80250I
5.23948 − 4.51130I 0
u = 0.407392 − 1.179060I
a = −0.068976 − 0.937001I
b = −1.67160 + 0.80250I
5.23948 + 4.51130I 0
u = 0.392928 + 1.189590I
a = 0.510361 − 1.133510I
b = 1.34113 + 1.39839I
6.09922 + 0.72292I 0
u = 0.392928 − 1.189590I
a = 0.510361 + 1.133510I
b = 1.34113 − 1.39839I
6.09922 − 0.72292I 0
u = 0.657190 + 0.353180I
a = 0.603599 − 0.062740I
b = −1.035640 − 0.145534I
−5.21588 − 5.43372I −6.35737 + 4.53160I
u = 0.657190 − 0.353180I
a = 0.603599 + 0.062740I
b = −1.035640 + 0.145534I
−5.21588 + 5.43372I −6.35737 − 4.53160I
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.399775 + 1.189730I
a = 0.21805 − 2.06307I
b = −1.73761 + 1.50516I
6.33069 + 2.21234I 0
u = −0.399775 − 1.189730I
a = 0.21805 + 2.06307I
b = −1.73761 − 1.50516I
6.33069 − 2.21234I 0
u = −0.491061 + 1.156340I
a = −1.35904 − 1.51080I
b = −0.38225 + 2.14323I
1.97040 + 3.53194I 0
u = −0.491061 − 1.156340I
a = −1.35904 + 1.51080I
b = −0.38225 − 2.14323I
1.97040 − 3.53194I 0
u = 0.732239 + 0.108513I
a = −1.38411 − 1.13292I
b = 0.307181 − 1.116300I
1.58615 − 0.58965I −2.07800 − 0.97177I
u = 0.732239 − 0.108513I
a = −1.38411 + 1.13292I
b = 0.307181 + 1.116300I
1.58615 + 0.58965I −2.07800 + 0.97177I
u = 0.365257 + 1.209930I
a = 1.26314 − 1.20974I
b = 0.51622 + 2.09356I
4.34795 + 3.40901I 0
u = 0.365257 − 1.209930I
a = 1.26314 + 1.20974I
b = 0.51622 − 2.09356I
4.34795 − 3.40901I 0
u = 0.359487 + 1.219040I
a = −1.46794 + 1.26755I
b = −0.30978 − 2.32417I
1.94636 + 8.59411I 0
u = 0.359487 − 1.219040I
a = −1.46794 − 1.26755I
b = −0.30978 + 2.32417I
1.94636 − 8.59411I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.490134 + 1.175270I
a = 0.75303 − 2.05112I
b = 0.57013 + 2.89728I
4.64951 − 3.96013I 0
u = 0.490134 − 1.175270I
a = 0.75303 + 2.05112I
b = 0.57013 − 2.89728I
4.64951 + 3.96013I 0
u = −0.494920 + 1.182490I
a = 1.55048 + 1.06172I
b = −0.12686 − 2.10588I
5.65654 + 6.38567I 0
u = −0.494920 − 1.182490I
a = 1.55048 − 1.06172I
b = −0.12686 + 2.10588I
5.65654 − 6.38567I 0
u = 0.499816 + 1.182010I
a = −0.56993 + 2.39465I
b = −1.18433 − 2.97646I
5.34282 − 9.31716I 0
u = 0.499816 − 1.182010I
a = −0.56993 − 2.39465I
b = −1.18433 + 2.97646I
5.34282 + 9.31716I 0
u = −0.507954 + 1.179230I
a = −1.76230 − 1.22811I
b = 0.06729 + 2.40466I
3.28961 + 10.96240I 0
u = −0.507954 − 1.179230I
a = −1.76230 + 1.22811I
b = 0.06729 − 2.40466I
3.28961 − 10.96240I 0
u = −0.428422 + 1.211720I
a = 0.67472 − 1.44248I
b = −1.73574 + 0.61936I
6.98159 + 3.47872I 0
u = −0.428422 − 1.211720I
a = 0.67472 + 1.44248I
b = −1.73574 − 0.61936I
6.98159 − 3.47872I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.523849 + 1.179140I
a = −0.03926 − 2.55082I
b = 1.91455 + 2.27803I
−1.71917 − 9.10568I 0
u = 0.523849 − 1.179140I
a = −0.03926 + 2.55082I
b = 1.91455 − 2.27803I
−1.71917 + 9.10568I 0
u = −0.477259 + 1.205010I
a = 1.362350 + 0.317722I
b = −0.73341 − 1.44993I
6.63442 + 5.43541I 0
u = −0.477259 − 1.205010I
a = 1.362350 − 0.317722I
b = −0.73341 + 1.44993I
6.63442 − 5.43541I 0
u = 0.519304 + 1.190370I
a = −0.14297 + 2.76693I
b = −2.07221 − 2.71035I
3.26514 − 12.19690I 0
u = 0.519304 − 1.190370I
a = −0.14297 − 2.76693I
b = −2.07221 + 2.71035I
3.26514 + 12.19690I 0
u = 0.628194 + 0.302021I
a = −0.782163 − 0.035357I
b = 0.902462 − 0.036429I
−2.36622 − 0.81836I −3.40956 + 0.70885I
u = 0.628194 − 0.302021I
a = −0.782163 + 0.035357I
b = 0.902462 + 0.036429I
−2.36622 + 0.81836I −3.40956 − 0.70885I
u = −0.440512 + 1.226900I
a = −1.18374 + 1.20119I
b = 2.00793 + 0.02526I
5.38653 + 7.66239I 0
u = −0.440512 − 1.226900I
a = −1.18374 − 1.20119I
b = 2.00793 − 0.02526I
5.38653 − 7.66239I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.524277 + 1.193940I
a = 0.05264 − 2.87689I
b = 2.30560 + 2.67048I
0.7867 − 17.4656I 0
u = 0.524277 − 1.193940I
a = 0.05264 + 2.87689I
b = 2.30560 − 2.67048I
0.7867 + 17.4656I 0
u = −0.676138 + 0.154497I
a = 0.362911 − 0.849043I
b = 0.08403 − 1.41391I
−0.888884 + 0.929390I −3.75477 − 1.10365I
u = −0.676138 − 0.154497I
a = 0.362911 + 0.849043I
b = 0.08403 + 1.41391I
−0.888884 − 0.929390I −3.75477 + 1.10365I
u = −0.469401 + 1.221640I
a = −1.52045 + 0.28914I
b = 1.44919 + 1.14088I
5.18083 + 1.47813I 0
u = −0.469401 − 1.221640I
a = −1.52045 − 0.28914I
b = 1.44919 − 1.14088I
5.18083 − 1.47813I 0
u = 0.344949 + 0.596122I
a = −0.728991 + 0.654589I
b = 0.346398 + 0.099866I
−0.61758 − 1.45216I −4.40076 + 4.02243I
u = 0.344949 − 0.596122I
a = −0.728991 − 0.654589I
b = 0.346398 − 0.099866I
−0.61758 + 1.45216I −4.40076 − 4.02243I
u = −0.229291 + 0.287793I
a = −0.89506 + 1.47855I
b = 0.523982 + 0.596248I
−0.31251 − 1.54411I −2.34290 + 4.88175I
u = −0.229291 − 0.287793I
a = −0.89506 − 1.47855I
b = 0.523982 − 0.596248I
−0.31251 + 1.54411I −2.34290 − 4.88175I
15
II. I
u
2
=
h−u
2
a+b, u
4
−u
2
a+2u
3
+a
2
−au+3u
2
−a+2u+1, u
5
+u
4
+2u
3
+u
2
+u+1i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
u
a
4
=
a
u
2
a
a
8
=
1
u
2
a
9
=
1
u
2
a
5
=
a
u
2
a
a
12
=
−u
u
a
1
=
u
3
−u
4
− u
3
− u
2
− 1
a
10
=
−u
3
u
3
+ u
a
6
=
−u
3
u
4
+ u
3
+ u
2
+ 1
a
3
=
−u
3
a
u
3
a + au
a
2
=
−u
3
a − u
2
− u − 1
u
3
a − u
4
− u
3
+ au − u
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −3u
3
a − u
4
+ 2u
3
− 2au + u
2
+ a + 2u + 1
16
(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
8
u
10
c
6
, c
9
(u
5
− u
4
− 2u
3
+ u
2
+ u + 1)
2
c
7
(u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1)
2
c
10
(u
5
+ 3u
4
+ 4u
3
+ u
2
− u − 1)
2
c
11
(u
5
− u
4
+ 2u
3
− u
2
+ u − 1)
2
c
12
(u
5
+ u
4
− 2u
3
− u
2
+ u − 1)
2
17
(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
8
y
10
c
6
, c
9
, c
12
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)
2
c
7
, c
11
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)
2
c
10
(y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1)
2
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.339110 + 0.822375I
a = −0.80632 + 1.36366I
b = −0.307991 − 1.215160I
0.32910 − 3.56046I −0.88631 + 6.04478I
u = 0.339110 + 0.822375I
a = 1.58413 + 0.01647I
b = −0.898363 + 0.874307I
0.329100 + 0.499304I 3.42267 + 1.01043I
u = 0.339110 − 0.822375I
a = −0.80632 − 1.36366I
b = −0.307991 + 1.215160I
0.32910 + 3.56046I −0.88631 − 6.04478I
u = 0.339110 − 0.822375I
a = 1.58413 − 0.01647I
b = −0.898363 − 0.874307I
0.329100 − 0.499304I 3.42267 − 1.01043I
u = −0.766826
a = 0.410598 + 0.711177I
b = 0.241441 + 0.418187I
2.40108 − 2.02988I 0.40252 + 2.76390I
u = −0.766826
a = 0.410598 − 0.711177I
b = 0.241441 − 0.418187I
2.40108 + 2.02988I 0.40252 − 2.76390I
u = −0.455697 + 1.200150I
a = −0.252108 + 0.649344I
b = 1.021040 − 0.524691I
5.87256 + 6.43072I 2.86519 − 5.89938I
u = −0.455697 + 1.200150I
a = −0.436295 − 0.543004I
b = −0.056121 + 1.146590I
5.87256 + 2.37095I 4.19593 − 1.57328I
u = −0.455697 − 1.200150I
a = −0.252108 − 0.649344I
b = 1.021040 + 0.524691I
5.87256 − 6.43072I 2.86519 + 5.89938I
u = −0.455697 − 1.200150I
a = −0.436295 + 0.543004I
b = −0.056121 − 1.146590I
5.87256 − 2.37095I 4.19593 + 1.57328I
19
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
2
− u + 1)
5
)(u
110
+ 54u
109
+ ··· + 7u + 1)
c
2
((u
2
+ u + 1)
5
)(u
110
+ 6u
109
+ ··· + 5u + 1)
c
3
((u
2
− u + 1)
5
)(u
110
− 6u
109
+ ··· − 455049u + 73746)
c
4
, c
8
u
10
(u
110
− u
109
+ ··· − 10240u
2
+ 1024)
c
5
((u
2
− u + 1)
5
)(u
110
+ 6u
109
+ ··· + 5u + 1)
c
6
((u
5
− u
4
− 2u
3
+ u
2
+ u + 1)
2
)(u
110
− 3u
109
+ ··· − 585u + 34)
c
7
((u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1)
2
)(u
110
+ 3u
109
+ ··· + 2u + 1)
c
9
((u
5
− u
4
− 2u
3
+ u
2
+ u + 1)
2
)(u
110
+ 13u
109
+ ··· + 74128u + 1669)
c
10
((u
5
+ 3u
4
+ 4u
3
+ u
2
− u − 1)
2
)(u
110
− 59u
109
+ ··· − 8u + 1)
c
11
((u
5
− u
4
+ 2u
3
− u
2
+ u − 1)
2
)(u
110
+ 3u
109
+ ··· + 2u + 1)
c
12
((u
5
+ u
4
− 2u
3
− u
2
+ u − 1)
2
)(u
110
− 3u
109
+ ··· − 585u + 34)
20
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
2
+ y + 1)
5
)(y
110
+ 10y
109
+ ··· − 9y + 1)
c
2
, c
5
((y
2
+ y + 1)
5
)(y
110
+ 54y
109
+ ··· + 7y + 1)
c
3
((y
2
+ y + 1)
5
)(y
110
− 34y
109
+ ··· − 2.38654 × 10
10
y + 5.43847 × 10
9
)
c
4
, c
8
y
10
(y
110
− 55y
109
+ ··· − 2.09715 × 10
7
y + 1048576)
c
6
, c
12
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)
2
· (y
110
− 85y
109
+ ··· + 105147y + 1156)
c
7
, c
11
((y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)
2
)(y
110
+ 59y
109
+ ··· + 8y + 1)
c
9
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)
2
· (y
110
+ 15y
109
+ ··· − 1624602792y + 2785561)
c
10
((y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1)
2
)(y
110
− 13y
109
+ ··· + 76y + 1)
21
