12n
0297
(K12n
0297
)
A knot diagram
1
Linearized knot diagam
3 6 7 9 10 2 11 5 4 12 7 10
Solving Sequence
2,7
6 3 4
1,10
5 9 12 11 8
c
6
c
2
c
3
c
1
c
5
c
9
c
12
c
11
c
7
c
4
, c
8
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−u
3
+ b − u, u
13
− u
12
+ 5u
11
− 4u
10
+ 10u
9
− 7u
8
+ 7u
7
− 4u
6
− 4u
5
+ 2u
4
− 5u
3
+ 3u
2
+ 2a + u + 1,
u
17
− u
16
+ ··· − u + 1i
I
u
2
= h−6.01027 × 10
15
u
41
+ 4.38628 × 10
15
u
40
+ ··· + 4.85875 × 10
15
b − 1.83034 × 10
16
,
2907486392199263u
41
− 6406067892977536u
40
+ ··· + 2242499937318462a + 3116730258713323,
u
42
− 2u
41
+ ··· − 13u + 3i
I
u
3
= hb + u + 1, a
2
− 2a − 2u − 1, u
2
+ u + 1i
I
u
4
= hb + u − 1, a + 1, u
2
− u + 1i
I
u
5
= hb − u, a
2
+ 2au + 2a − u − 2, u
2
+ u + 1i
I
u
6
= hb − u, a + u − 1, u
2
− u + 1i
* 6 irreducible components of dim
C
= 0, with total 71 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−u
3
+ b − u, u
13
− u
12
+ · · · + 2a + 1, u
17
− u
16
+ · · · − u + 1i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
6
=
1
u
2
a
3
=
u
u
3
+ u
a
4
=
−u
3
u
3
+ u
a
1
=
u
3
u
5
+ u
3
+ u
a
10
=
−
1
2
u
13
+
1
2
u
12
+ ··· −
1
2
u −
1
2
u
3
+ u
a
5
=
u
16
− u
15
+ ··· − u +
3
2
1
2
u
14
−
1
2
u
13
+ ··· −
1
2
u
2
+
1
2
u
a
9
=
1
2
u
15
−
1
2
u
14
+ ··· −
1
2
u −
1
2
−
1
2
u
15
+
1
2
u
14
+ ··· +
3
2
u −
1
2
a
12
=
1
2
u
15
−
1
2
u
14
+ ··· +
3
2
u
3
+
1
2
u
2
u
a
11
=
1
2
u
15
−
1
2
u
14
+ ··· +
1
2
u
2
− u
u
a
8
=
−
1
2
u
16
+
1
2
u
15
+ ··· + u
2
+ 1
−u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −5u
16
+ 2u
15
− 24u
14
+ 5u
13
− 50u
12
+ 5u
11
− 42u
10
− 3u
9
+
8u
8
+ 33u
6
+ 4u
5
+ 8u
4
− 4u
3
− 11u
2
− 8u − 6
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
10
, c
12
u
17
+ 11u
16
+ ··· − 7u − 1
c
2
, c
6
, c
7
c
11
u
17
− u
16
+ ··· − u + 1
c
3
u
17
+ u
16
+ ··· + u + 1
c
4
, c
8
, c
9
u
17
+ 5u
16
+ ··· + 24u + 4
c
5
u
17
− 5u
16
+ ··· + 32u + 356
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
, c
12
y
17
− 5y
16
+ ··· + y −1
c
2
, c
6
, c
7
c
11
y
17
+ 11y
16
+ ··· − 7y −1
c
3
y
17
− 21y
16
+ ··· − 7y −1
c
4
, c
8
, c
9
y
17
+ 15y
16
+ ··· − 32y −16
c
5
y
17
− 5y
16
+ ··· − 685344y −126736
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.322943 + 1.038240I
a = −1.76695 − 1.17117I
b = 0.687713 + 0.243922I
2.86633 − 4.06837I −7.21746 + 4.92513I
u = −0.322943 − 1.038240I
a = −1.76695 + 1.17117I
b = 0.687713 − 0.243922I
2.86633 + 4.06837I −7.21746 − 4.92513I
u = 0.846972 + 0.190636I
a = 0.057316 + 0.298967I
b = 1.36222 + 0.59397I
1.50690 − 4.21109I 0.87343 + 2.53739I
u = 0.846972 − 0.190636I
a = 0.057316 − 0.298967I
b = 1.36222 − 0.59397I
1.50690 + 4.21109I 0.87343 − 2.53739I
u = 0.110349 + 1.142920I
a = 0.440223 − 0.492438I
b = −0.320742 − 0.308287I
−4.58609 + 2.21395I −10.42618 − 3.79439I
u = 0.110349 − 1.142920I
a = 0.440223 + 0.492438I
b = −0.320742 + 0.308287I
−4.58609 − 2.21395I −10.42618 + 3.79439I
u = −0.817813
a = −0.0448823
b = −1.36478
−2.55092 −3.29090
u = −0.430215 + 0.605602I
a = 1.58821 − 0.32847I
b = −0.036492 + 0.719758I
5.54966 − 2.41434I 1.92444 + 1.74579I
u = −0.430215 − 0.605602I
a = 1.58821 + 0.32847I
b = −0.036492 − 0.719758I
5.54966 + 2.41434I 1.92444 − 1.74579I
u = 0.432341 + 1.261340I
a = 1.58526 + 0.60200I
b = −1.55038 − 0.03811I
−6.94626 + 4.33928I −7.37666 − 2.73345I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.432341 − 1.261340I
a = 1.58526 − 0.60200I
b = −1.55038 + 0.03811I
−6.94626 − 4.33928I −7.37666 + 2.73345I
u = 0.581005 + 1.217160I
a = 1.92685 + 1.19674I
b = −1.80511 + 0.64658I
−4.4941 + 14.7863I −4.66375 − 8.62681I
u = 0.581005 − 1.217160I
a = 1.92685 − 1.19674I
b = −1.80511 − 0.64658I
−4.4941 − 14.7863I −4.66375 + 8.62681I
u = −0.523425 + 1.252060I
a = −1.77570 + 0.95237I
b = 1.79480 + 0.31837I
−9.65986 − 9.78843I −8.66609 + 6.57063I
u = −0.523425 − 1.252060I
a = −1.77570 − 0.95237I
b = 1.79480 − 0.31837I
−9.65986 + 9.78843I −8.66609 − 6.57063I
u = 0.214821 + 0.520126I
a = −0.532769 − 0.701691I
b = 0.050387 + 0.451424I
−0.232914 + 1.043600I −3.80228 − 6.41835I
u = 0.214821 − 0.520126I
a = −0.532769 + 0.701691I
b = 0.050387 − 0.451424I
−0.232914 − 1.043600I −3.80228 + 6.41835I
6
II. I
u
2
= h−6.01 × 10
15
u
41
+ 4.39 × 10
15
u
40
+ · · · + 4.86 × 10
15
b − 1.83 ×
10
16
, 2.91 × 10
15
u
41
− 6.41 × 10
15
u
40
+ · · · + 2.24 × 10
15
a + 3.12 ×
10
15
, u
42
− 2u
41
+ · · · − 13u + 3i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
6
=
1
u
2
a
3
=
u
u
3
+ u
a
4
=
−u
3
u
3
+ u
a
1
=
u
3
u
5
+ u
3
+ u
a
10
=
−1.29654u
41
+ 2.85666u
40
+ ··· − 2.89896u − 1.38985
1.23700u
41
− 0.902758u
40
+ ··· − 18.1061u + 3.76710
a
5
=
−1.28722u
41
+ 4.62863u
40
+ ··· − 72.8325u + 16.6384
0.929780u
41
− 2.10128u
40
+ ··· + 4.35029u + 1.40533
a
9
=
−0.801807u
41
+ 1.81747u
40
+ ··· + 6.37909u − 3.86212
0.263884u
41
+ 0.269109u
40
+ ··· − 18.9125u + 3.93233
a
12
=
−0.615799u
41
+ 0.348663u
40
+ ··· + 35.1901u − 10.2810
−0.211969u
41
+ 1.35987u
40
+ ··· − 12.2107u + 0.682808
a
11
=
−0.403831u
41
− 1.01121u
40
+ ··· + 47.4008u − 10.9638
−0.211969u
41
+ 1.35987u
40
+ ··· − 12.2107u + 0.682808
a
8
=
−3.43389u
41
+ 6.89021u
40
+ ··· − 2.02041u − 3.37620
1.03167u
41
− 1.32061u
40
+ ··· − 1.13275u + 0.551934
(ii) Obstruction class = −1
(iii) Cusp Shapes
=
14132658601726202
4858749864190001
u
41
−
2000261855343520
373749989553077
u
40
+ ···+
110747832601789324
4858749864190001
u −
19778111821628499
4858749864190001
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
10
, c
12
u
42
+ 22u
41
+ ··· + 59u + 9
c
2
, c
6
, c
7
c
11
u
42
− 2u
41
+ ··· − 13u + 3
c
3
u
42
+ 2u
41
+ ··· − 1001u + 375
c
4
, c
8
, c
9
(u
21
− 2u
20
+ ··· − 4u + 2)
2
c
5
(u
21
+ 2u
20
+ ··· − 4u + 2)
2
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
, c
12
y
42
− 2y
41
+ ··· − 2329y + 81
c
2
, c
6
, c
7
c
11
y
42
+ 22y
41
+ ··· + 59y + 9
c
3
y
42
− 26y
41
+ ··· + 2152499y + 140625
c
4
, c
8
, c
9
(y
21
+ 18y
20
+ ··· + 16y −4)
2
c
5
(y
21
− 22y
20
+ ··· + 40y −4)
2
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.648340 + 0.786994I
a = 0.520796 + 0.410581I
b = 0.600235 + 0.207579I
4.76959 − 2.48515I 1.90098 + 3.54281I
u = −0.648340 − 0.786994I
a = 0.520796 − 0.410581I
b = 0.600235 − 0.207579I
4.76959 + 2.48515I 1.90098 − 3.54281I
u = −0.281169 + 0.918116I
a = 1.66079 + 0.03172I
b = −0.705944 − 1.191570I
−0.82885 − 3.61332I −9.58837 + 1.89402I
u = −0.281169 − 0.918116I
a = 1.66079 − 0.03172I
b = −0.705944 + 1.191570I
−0.82885 + 3.61332I −9.58837 − 1.89402I
u = 0.919345 + 0.237233I
a = 0.139375 − 0.118273I
b = −1.65616 − 0.52114I
−1.52142 − 9.31938I −2.21398 + 5.58015I
u = 0.919345 − 0.237233I
a = 0.139375 + 0.118273I
b = −1.65616 + 0.52114I
−1.52142 + 9.31938I −2.21398 − 5.58015I
u = −0.918649 + 0.104898I
a = −0.159545 + 0.217864I
b = 1.52694 − 0.17361I
−6.16843 + 4.59035I −6.34834 − 3.42334I
u = −0.918649 − 0.104898I
a = −0.159545 − 0.217864I
b = 1.52694 + 0.17361I
−6.16843 − 4.59035I −6.34834 + 3.42334I
u = −0.746719 + 0.798648I
a = 0.124923 − 0.315475I
b = −1.083540 − 0.394401I
2.13930 − 6.31791I −2.69400 + 7.27088I
u = −0.746719 − 0.798648I
a = 0.124923 + 0.315475I
b = −1.083540 + 0.394401I
2.13930 + 6.31791I −2.69400 − 7.27088I
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.896010 + 0.063848I
a = 0.148702 − 0.571049I
b = −1.197580 − 0.165877I
−2.87260 − 0.28571I −3.90381 + 0.09482I
u = 0.896010 − 0.063848I
a = 0.148702 + 0.571049I
b = −1.197580 + 0.165877I
−2.87260 + 0.28571I −3.90381 − 0.09482I
u = 0.616574 + 0.917444I
a = −0.466225 + 0.312796I
b = 0.407626 − 0.361948I
−0.82885 + 3.61332I −9.58837 − 1.89402I
u = 0.616574 − 0.917444I
a = −0.466225 − 0.312796I
b = 0.407626 + 0.361948I
−0.82885 − 3.61332I −9.58837 + 1.89402I
u = −0.707790 + 0.857193I
a = −0.264002 − 1.060620I
b = −0.934767 + 0.363773I
1.95965 + 0.82852I −3.22814 − 1.28551I
u = −0.707790 − 0.857193I
a = −0.264002 + 1.060620I
b = −0.934767 − 0.363773I
1.95965 − 0.82852I −3.22814 + 1.28551I
u = −0.553188 + 0.964414I
a = 1.11387 + 1.08458I
b = 0.028624 − 0.375859I
4.51229 − 1.78805I −2.74245 + 3.28020I
u = −0.553188 − 0.964414I
a = 1.11387 − 1.08458I
b = 0.028624 + 0.375859I
4.51229 + 1.78805I −2.74245 − 3.28020I
u = 0.405897 + 1.075130I
a = 0.742962 − 1.081300I
b = 0.49784 + 1.51562I
1.95965 + 0.82852I −3.22814 − 1.28551I
u = 0.405897 − 1.075130I
a = 0.742962 + 1.081300I
b = 0.49784 − 1.51562I
1.95965 − 0.82852I −3.22814 + 1.28551I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.515102 + 0.670364I
a = −0.086404 − 0.577180I
b = 0.058588 + 0.436947I
−0.099396 + 1.054050I −5.09416 − 5.72302I
u = 0.515102 − 0.670364I
a = −0.086404 + 0.577180I
b = 0.058588 − 0.436947I
−0.099396 − 1.054050I −5.09416 + 5.72302I
u = 0.438792 + 1.104820I
a = −1.41623 + 0.50848I
b = 0.26578 − 1.62519I
2.13930 + 6.31791I −2.69400 − 7.27088I
u = 0.438792 − 1.104820I
a = −1.41623 − 0.50848I
b = 0.26578 + 1.62519I
2.13930 − 6.31791I −2.69400 + 7.27088I
u = 0.352371 + 1.227840I
a = −1.56964 − 0.94140I
b = 1.60440 + 0.21737I
−2.87260 − 0.28571I −4.00000 + 0.I
u = 0.352371 − 1.227840I
a = −1.56964 + 0.94140I
b = 1.60440 − 0.21737I
−2.87260 + 0.28571I −4.00000 + 0.I
u = −0.184003 + 0.671383I
a = −1.095080 − 0.579917I
b = −0.042669 + 0.902715I
−0.099396 + 1.054050I −5.09416 − 5.72302I
u = −0.184003 − 0.671383I
a = −1.095080 + 0.579917I
b = −0.042669 − 0.902715I
−0.099396 − 1.054050I −5.09416 + 5.72302I
u = −0.463537 + 1.225960I
a = 1.72317 − 0.93419I
b = −1.66359 − 0.36932I
−6.16843 − 4.59035I 0
u = −0.463537 − 1.225960I
a = 1.72317 + 0.93419I
b = −1.66359 + 0.36932I
−6.16843 + 4.59035I 0
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.073463 + 0.681917I
a = −2.84879 − 0.54672I
b = 0.821077 − 0.952800I
4.51229 + 1.78805I −2.74245 − 3.28020I
u = −0.073463 − 0.681917I
a = −2.84879 + 0.54672I
b = 0.821077 + 0.952800I
4.51229 − 1.78805I −2.74245 + 3.28020I
u = 0.542292 + 1.203890I
a = −1.84110 − 0.94344I
b = 1.54115 − 0.82541I
−1.52142 + 9.31938I 0. − 5.58015I
u = 0.542292 − 1.203890I
a = −1.84110 + 0.94344I
b = 1.54115 + 0.82541I
−1.52142 − 9.31938I 0. + 5.58015I
u = 0.301624 + 1.287530I
a = 1.83725 + 0.98743I
b = −1.71923 − 0.20551I
−6.49606 − 5.29485I 0
u = 0.301624 − 1.287530I
a = 1.83725 − 0.98743I
b = −1.71923 + 0.20551I
−6.49606 + 5.29485I 0
u = 0.495316 + 1.253840I
a = 1.39824 + 0.99998I
b = −1.170980 + 0.495445I
−6.49606 + 5.29485I 0
u = 0.495316 − 1.253840I
a = 1.39824 − 0.99998I
b = −1.170980 − 0.495445I
−6.49606 − 5.29485I 0
u = −0.404607 + 1.286580I
a = −1.64330 + 1.00540I
b = 1.53839 + 0.21123I
−10.5274 0
u = −0.404607 − 1.286580I
a = −1.64330 − 1.00540I
b = 1.53839 − 0.21123I
−10.5274 0
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.498140 + 0.119986I
a = 0.81356 + 1.59996I
b = 0.283799 + 1.291990I
4.76959 − 2.48515I 1.90098 + 3.54281I
u = 0.498140 − 0.119986I
a = 0.81356 − 1.59996I
b = 0.283799 − 1.291990I
4.76959 + 2.48515I 1.90098 − 3.54281I
14
III. I
u
3
= hb + u + 1, a
2
− 2a − 2u − 1, u
2
+ u + 1i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
6
=
1
−u − 1
a
3
=
u
u + 1
a
4
=
−1
u + 1
a
1
=
1
0
a
10
=
a
−u − 1
a
5
=
−au − a − u + 2
au − 2u − 1
a
9
=
au + 2a − u − 1
−au − 1
a
12
=
au + a + 1
−u
a
11
=
au + a + u + 1
−u
a
8
=
−a
u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 8u + 4
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
7
c
10
(u
2
− u + 1)
2
c
3
, c
6
, c
11
c
12
(u
2
+ u + 1)
2
c
4
, c
5
, c
8
c
9
(u
2
+ 2)
2
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
6
, c
7
, c
10
c
11
, c
12
(y
2
+ y + 1)
2
c
4
, c
5
, c
8
c
9
(y + 2)
4
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500000 + 0.866025I
a = −0.224745 − 0.707107I
b = −0.500000 − 0.866025I
4.93480 − 4.05977I 0. + 6.92820I
u = −0.500000 + 0.866025I
a = 2.22474 + 0.70711I
b = −0.500000 − 0.866025I
4.93480 − 4.05977I 0. + 6.92820I
u = −0.500000 − 0.866025I
a = −0.224745 + 0.707107I
b = −0.500000 + 0.866025I
4.93480 + 4.05977I 0. − 6.92820I
u = −0.500000 − 0.866025I
a = 2.22474 − 0.70711I
b = −0.500000 + 0.866025I
4.93480 + 4.05977I 0. − 6.92820I
18
IV. I
u
4
= hb + u − 1, a + 1, u
2
− u + 1i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
6
=
1
u − 1
a
3
=
u
u − 1
a
4
=
1
u − 1
a
1
=
−1
0
a
10
=
−1
−u + 1
a
5
=
1
u − 1
a
9
=
−1
−u + 1
a
12
=
u − 2
−u
a
11
=
2u − 2
−u
a
8
=
−1
−u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −8u + 4
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
6
c
10
, c
11
u
2
− u + 1
c
2
, c
7
, c
12
u
2
+ u + 1
c
4
, c
5
, c
8
c
9
u
2
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
6
, c
7
, c
10
c
11
, c
12
y
2
+ y + 1
c
4
, c
5
, c
8
c
9
y
2
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500000 + 0.866025I
a = −1.00000
b = 0.500000 − 0.866025I
4.05977I 0. − 6.92820I
u = 0.500000 − 0.866025I
a = −1.00000
b = 0.500000 + 0.866025I
− 4.05977I 0. + 6.92820I
22
V. I
u
5
= hb − u, a
2
+ 2au + 2a − u − 2, u
2
+ u + 1i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
6
=
1
−u − 1
a
3
=
u
u + 1
a
4
=
−1
u + 1
a
1
=
1
0
a
10
=
a
u
a
5
=
au − 2u
a
a
9
=
au + 2a + u
−au + u + 1
a
12
=
−au + 1
u + 1
a
11
=
−au − u
u + 1
a
8
=
−a
−u
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
23
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
7
c
10
(u
2
− u + 1)
2
c
3
, c
6
, c
11
c
12
(u
2
+ u + 1)
2
c
4
, c
5
, c
8
c
9
(u
2
+ 2)
2
24
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
6
, c
7
, c
10
c
11
, c
12
(y
2
+ y + 1)
2
c
4
, c
5
, c
8
c
9
(y + 2)
4
25
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500000 + 0.866025I
a = 0.724745 − 0.158919I
b = −0.500000 + 0.866025I
4.93480 0
u = −0.500000 + 0.866025I
a = −1.72474 − 1.57313I
b = −0.500000 + 0.866025I
4.93480 0
u = −0.500000 − 0.866025I
a = 0.724745 + 0.158919I
b = −0.500000 − 0.866025I
4.93480 0
u = −0.500000 − 0.866025I
a = −1.72474 + 1.57313I
b = −0.500000 − 0.866025I
4.93480 0
26
VI. I
u
6
= hb − u, a + u − 1, u
2
− u + 1i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
6
=
1
u − 1
a
3
=
u
u − 1
a
4
=
1
u − 1
a
1
=
−1
0
a
10
=
−u + 1
u
a
5
=
1
u − 1
a
9
=
−u + 1
u
a
12
=
0
u − 1
a
11
=
−u + 1
u − 1
a
8
=
−u + 1
u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −6
27
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
6
c
10
, c
11
u
2
− u + 1
c
2
, c
7
, c
12
u
2
+ u + 1
c
4
, c
5
, c
8
c
9
u
2
28
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
6
, c
7
, c
10
c
11
, c
12
y
2
+ y + 1
c
4
, c
5
, c
8
c
9
y
2
29
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500000 + 0.866025I
a = 0.500000 − 0.866025I
b = 0.500000 + 0.866025I
0 −6.00000
u = 0.500000 − 0.866025I
a = 0.500000 + 0.866025I
b = 0.500000 − 0.866025I
0 −6.00000
30
VII. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
10
((u
2
− u + 1)
6
)(u
17
+ 11u
16
+ ··· − 7u − 1)(u
42
+ 22u
41
+ ··· + 59u + 9)
c
2
, c
7
((u
2
− u + 1)
4
)(u
2
+ u + 1)
2
(u
17
− u
16
+ ··· − u + 1)
· (u
42
− 2u
41
+ ··· − 13u + 3)
c
3
((u
2
− u + 1)
2
)(u
2
+ u + 1)
4
(u
17
+ u
16
+ ··· + u + 1)
· (u
42
+ 2u
41
+ ··· − 1001u + 375)
c
4
, c
8
, c
9
u
4
(u
2
+ 2)
4
(u
17
+ 5u
16
+ ··· + 24u + 4)(u
21
− 2u
20
+ ··· − 4u + 2)
2
c
5
u
4
(u
2
+ 2)
4
(u
17
− 5u
16
+ ··· + 32u + 356)(u
21
+ 2u
20
+ ··· − 4u + 2)
2
c
6
, c
11
((u
2
− u + 1)
2
)(u
2
+ u + 1)
4
(u
17
− u
16
+ ··· − u + 1)
· (u
42
− 2u
41
+ ··· − 13u + 3)
c
12
((u
2
+ u + 1)
6
)(u
17
+ 11u
16
+ ··· − 7u − 1)(u
42
+ 22u
41
+ ··· + 59u + 9)
31
VIII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
10
, c
12
((y
2
+ y + 1)
6
)(y
17
− 5y
16
+ ··· + y −1)(y
42
− 2y
41
+ ··· − 2329y + 81)
c
2
, c
6
, c
7
c
11
((y
2
+ y + 1)
6
)(y
17
+ 11y
16
+ ··· − 7y −1)(y
42
+ 22y
41
+ ··· + 59y + 9)
c
3
((y
2
+ y + 1)
6
)(y
17
− 21y
16
+ ··· − 7y −1)
· (y
42
− 26y
41
+ ··· + 2152499y + 140625)
c
4
, c
8
, c
9
y
4
(y + 2)
8
(y
17
+ 15y
16
+ ··· − 32y −16)
· (y
21
+ 18y
20
+ ··· + 16y −4)
2
c
5
y
4
(y + 2)
8
(y
17
− 5y
16
+ ··· − 685344y −126736)
· (y
21
− 22y
20
+ ··· + 40y −4)
2
32
