12a
1038
(K12a
1038
)
A knot diagram
1
Linearized knot diagam
4 7 8 10 12 3 2 11 6 1 9 5
Solving Sequence
2,8
7 3
4,10
5 1 11 6 9 12
c
7
c
2
c
3
c
4
c
1
c
10
c
6
c
9
c
12
c
5
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−3.62076 × 10
53
u
97
+ 8.81180 × 10
53
u
96
+ ··· + 8.81449 × 10
53
b + 4.33084 × 10
53
,
1.67240 × 10
54
u
97
− 4.07185 × 10
54
u
96
+ ··· + 8.81449 × 10
53
a − 2.98740 × 10
54
, u
98
− 3u
97
+ ··· − 5u + 1i
* 1 irreducible components of dim
C
= 0, with total 98 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−3.62×10
53
u
97
+8.81×10
53
u
96
+· · ·+8.81×10
53
b+4.33×10
53
, 1.67×
10
54
u
97
−4.07×10
54
u
96
+· · ·+8.81×10
53
a−2.99×10
54
, u
98
−3u
97
+· · ·−5u+1i
(i) Arc colorings
a
2
=
0
u
a
8
=
1
0
a
7
=
1
−u
2
a
3
=
−u
u
3
+ u
a
4
=
−u
3
− 2u
u
3
+ u
a
10
=
−1.89733u
97
+ 4.61949u
96
+ ··· − 13.1123u + 3.38919
0.410774u
97
− 0.999695u
96
+ ··· + 4.99129u − 0.491331
a
5
=
0.222953u
97
− 1.13842u
96
+ ··· + 1.53433u − 1.07411
0.475801u
97
− 1.08428u
96
+ ··· + 1.54473u − 0.514952
a
1
=
u
7
+ 4u
5
+ 4u
3
−u
7
− 3u
5
− 2u
3
+ u
a
11
=
−0.469168u
97
+ 0.658638u
96
+ ··· − 3.66130u + 1.52455
−0.262625u
97
+ 0.897029u
96
+ ··· − 3.81810u + 1.84336
a
6
=
u
2
+ 1
−u
4
− 2u
2
a
9
=
−0.484597u
97
+ 0.957708u
96
+ ··· − 6.36097u + 3.14188
−0.393812u
97
+ 1.22529u
96
+ ··· − 4.19603u + 1.78580
a
12
=
0.00745162u
97
− 0.615653u
96
+ ··· + 4.96278u − 2.02379
0.381053u
97
− 0.953602u
96
+ ··· + 0.502513u + 0.295011
(ii) Obstruction class = −1
(iii) Cusp Shapes = 1.63646u
97
− 5.49263u
96
+ ··· + 8.71271u − 12.4499
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
98
− 19u
97
+ ··· − 841339u + 59603
c
2
, c
6
, c
7
u
98
+ 3u
97
+ ··· + 5u + 1
c
3
u
98
− 3u
97
+ ··· + 595u + 425
c
4
u
98
− u
97
+ ··· − u − 1
c
5
, c
12
u
98
− 3u
97
+ ··· + u + 1
c
8
, c
11
u
98
− u
97
+ ··· − 33u − 1
c
9
u
98
+ 5u
97
+ ··· − 3041767u − 195991
c
10
u
98
+ 9u
97
+ ··· + 4943u − 137
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
98
+ 45y
97
+ ··· + 84576889997y + 3552517609
c
2
, c
6
, c
7
y
98
+ 89y
97
+ ··· − 7y + 1
c
3
y
98
+ 13y
97
+ ··· + 6423025y + 180625
c
4
y
98
− 3y
97
+ ··· − 99y + 1
c
5
, c
12
y
98
+ 73y
97
+ ··· − 7y + 1
c
8
, c
11
y
98
− 67y
97
+ ··· − 179y + 1
c
9
y
98
− 203y
97
+ ··· − 3248967720299y + 38412472081
c
10
y
98
+ 137y
97
+ ··· − 6924923y + 18769
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.065339 + 1.097010I
a = −1.324380 − 0.441285I
b = 1.46093 + 1.29019I
−4.40512 − 2.11265I 0
u = 0.065339 − 1.097010I
a = −1.324380 + 0.441285I
b = 1.46093 − 1.29019I
−4.40512 + 2.11265I 0
u = 0.612404 + 0.652469I
a = −0.252396 − 0.753912I
b = −0.216088 + 0.660826I
−3.29048 − 3.02837I 0
u = 0.612404 − 0.652469I
a = −0.252396 + 0.753912I
b = −0.216088 − 0.660826I
−3.29048 + 3.02837I 0
u = 0.800888 + 0.357291I
a = 0.253454 + 0.756910I
b = 0.106025 − 0.595292I
−4.30667 − 1.74398I 0
u = 0.800888 − 0.357291I
a = 0.253454 − 0.756910I
b = 0.106025 + 0.595292I
−4.30667 + 1.74398I 0
u = −0.038346 + 1.161800I
a = −1.262120 − 0.527027I
b = 0.316673 − 1.090610I
−0.080038 + 0.981236I 0
u = −0.038346 − 1.161800I
a = −1.262120 + 0.527027I
b = 0.316673 + 1.090610I
−0.080038 − 0.981236I 0
u = −0.468868 + 0.684398I
a = −1.050430 − 0.676356I
b = 1.047240 − 0.388987I
0.46550 − 4.30305I −7.01592 + 4.36620I
u = −0.468868 − 0.684398I
a = −1.050430 + 0.676356I
b = 1.047240 + 0.388987I
0.46550 + 4.30305I −7.01592 − 4.36620I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.820805
a = −0.384972
b = −0.00973519
−4.50628 −26.0090
u = 0.486220 + 0.652272I
a = −2.00701 + 0.85445I
b = 1.61190 + 0.78207I
−4.55395 + 9.86790I −10.03674 − 4.17482I
u = 0.486220 − 0.652272I
a = −2.00701 − 0.85445I
b = 1.61190 − 0.78207I
−4.55395 − 9.86790I −10.03674 + 4.17482I
u = −0.741511 + 0.323631I
a = −1.21304 − 1.63056I
b = 1.42634 + 0.75096I
−0.79939 + 8.54144I −9.35248 − 8.62618I
u = −0.741511 − 0.323631I
a = −1.21304 + 1.63056I
b = 1.42634 − 0.75096I
−0.79939 − 8.54144I −9.35248 + 8.62618I
u = −0.154621 + 1.182450I
a = 0.442376 + 0.325025I
b = −0.24214 − 1.49177I
−0.62174 + 5.21555I 0
u = −0.154621 − 1.182450I
a = 0.442376 − 0.325025I
b = −0.24214 + 1.49177I
−0.62174 − 5.21555I 0
u = 0.734303 + 0.335173I
a = −1.56251 + 2.65545I
b = 1.95978 − 1.35725I
−5.6940 − 14.0982I −12.0008 + 9.3017I
u = 0.734303 − 0.335173I
a = −1.56251 − 2.65545I
b = 1.95978 + 1.35725I
−5.6940 + 14.0982I −12.0008 − 9.3017I
u = 0.347846 + 1.150340I
a = −0.326146 + 0.013567I
b = 0.146982 − 0.323227I
−0.98524 − 4.23518I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.347846 − 1.150340I
a = −0.326146 − 0.013567I
b = 0.146982 + 0.323227I
−0.98524 + 4.23518I 0
u = −0.298674 + 1.170600I
a = −0.755088 + 0.161129I
b = 0.215537 + 0.593171I
−6.09100 + 10.22850I 0
u = −0.298674 − 1.170600I
a = −0.755088 − 0.161129I
b = 0.215537 − 0.593171I
−6.09100 − 10.22850I 0
u = −0.077955 + 1.224770I
a = 1.109290 − 0.431612I
b = 1.41833 − 0.53377I
−0.161350 − 0.248342I 0
u = −0.077955 − 1.224770I
a = 1.109290 + 0.431612I
b = 1.41833 + 0.53377I
−0.161350 + 0.248342I 0
u = 0.117974 + 1.232200I
a = 0.425138 + 0.052215I
b = 0.113127 + 0.821566I
2.70749 − 2.08523I 0
u = 0.117974 − 1.232200I
a = 0.425138 − 0.052215I
b = 0.113127 − 0.821566I
2.70749 + 2.08523I 0
u = −0.754574 + 0.023137I
a = −0.666482 − 0.494419I
b = −0.142569 − 0.072822I
−9.60200 − 6.38751I −16.3307 + 4.5656I
u = −0.754574 − 0.023137I
a = −0.666482 + 0.494419I
b = −0.142569 + 0.072822I
−9.60200 + 6.38751I −16.3307 − 4.5656I
u = 0.673064 + 0.323027I
a = 1.06398 − 2.79653I
b = −1.86660 + 1.44175I
−1.10873 − 7.75152I −10.26708 + 9.05915I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.673064 − 0.323027I
a = 1.06398 + 2.79653I
b = −1.86660 − 1.44175I
−1.10873 + 7.75152I −10.26708 − 9.05915I
u = −0.659559 + 0.345898I
a = 1.45084 + 1.72925I
b = −1.62214 − 0.68769I
2.32911 + 3.95267I −4.15635 − 4.95765I
u = −0.659559 − 0.345898I
a = 1.45084 − 1.72925I
b = −1.62214 + 0.68769I
2.32911 − 3.95267I −4.15635 + 4.95765I
u = −0.313385 + 1.218800I
a = −0.294266 − 0.525040I
b = −0.311221 + 0.371550I
−5.77595 − 2.51906I 0
u = −0.313385 − 1.218800I
a = −0.294266 + 0.525040I
b = −0.311221 − 0.371550I
−5.77595 + 2.51906I 0
u = −0.648528 + 0.262294I
a = −2.67364 − 0.24168I
b = 1.08723 − 1.12029I
−5.97830 + 4.86271I −16.4498 − 7.8661I
u = −0.648528 − 0.262294I
a = −2.67364 + 0.24168I
b = 1.08723 + 1.12029I
−5.97830 − 4.86271I −16.4498 + 7.8661I
u = −0.486563 + 0.498299I
a = 1.29221 + 1.35928I
b = −1.247510 + 0.057218I
3.01687 − 0.15440I −1.87765 − 2.16900I
u = −0.486563 − 0.498299I
a = 1.29221 − 1.35928I
b = −1.247510 − 0.057218I
3.01687 + 0.15440I −1.87765 + 2.16900I
u = 0.616477 + 0.282636I
a = −0.118972 + 1.136580I
b = −0.122109 − 0.118162I
−1.70677 − 3.19543I −9.12410 + 5.81601I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.616477 − 0.282636I
a = −0.118972 − 1.136580I
b = −0.122109 + 0.118162I
−1.70677 + 3.19543I −9.12410 − 5.81601I
u = 0.427014 + 0.522919I
a = 1.85596 − 1.10388I
b = −1.45023 − 0.82297I
−0.18528 + 4.01394I −7.39455 − 2.93534I
u = 0.427014 − 0.522919I
a = 1.85596 + 1.10388I
b = −1.45023 + 0.82297I
−0.18528 − 4.01394I −7.39455 + 2.93534I
u = 0.592622 + 0.314755I
a = 0.90205 − 1.41462I
b = −0.756552 + 0.851099I
−1.42383 − 1.50400I −9.92069 + 3.68533I
u = 0.592622 − 0.314755I
a = 0.90205 + 1.41462I
b = −0.756552 − 0.851099I
−1.42383 + 1.50400I −9.92069 − 3.68533I
u = 0.614747 + 0.193180I
a = −1.70242 + 3.33964I
b = 1.98420 − 0.99309I
−6.79903 − 0.64790I −18.7159 + 2.4926I
u = 0.614747 − 0.193180I
a = −1.70242 − 3.33964I
b = 1.98420 + 0.99309I
−6.79903 + 0.64790I −18.7159 − 2.4926I
u = −0.530135 + 0.320976I
a = −2.6863 + 14.1321I
b = 0.55207 − 7.84865I
−2.93001 + 1.56016I −62.2549 + 71.6820I
u = −0.530135 − 0.320976I
a = −2.6863 − 14.1321I
b = 0.55207 + 7.84865I
−2.93001 − 1.56016I −62.2549 − 71.6820I
u = −0.176083 + 1.375290I
a = 1.319650 + 0.103630I
b = 1.15018 + 1.07723I
0.542290 − 0.074660I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.176083 − 1.375290I
a = 1.319650 − 0.103630I
b = 1.15018 − 1.07723I
0.542290 + 0.074660I 0
u = −0.562494 + 0.240160I
a = −2.44776 − 2.70868I
b = 1.86945 + 1.05664I
−2.43280 + 1.21285I −5.48234 − 6.16626I
u = −0.562494 − 0.240160I
a = −2.44776 + 2.70868I
b = 1.86945 − 1.05664I
−2.43280 − 1.21285I −5.48234 + 6.16626I
u = 0.232456 + 1.379630I
a = 1.02637 + 2.35893I
b = 2.47762 − 0.87478I
−1.78282 − 3.72107I 0
u = 0.232456 − 1.379630I
a = 1.02637 − 2.35893I
b = 2.47762 + 0.87478I
−1.78282 + 3.72107I 0
u = 0.107712 + 1.409150I
a = 0.737553 + 0.143732I
b = 0.003914 − 0.529307I
5.02738 − 2.93469I 0
u = 0.107712 − 1.409150I
a = 0.737553 − 0.143732I
b = 0.003914 + 0.529307I
5.02738 + 2.93469I 0
u = 0.19083 + 1.40218I
a = 0.135240 − 0.073939I
b = 0.934843 + 0.334737I
4.46155 − 2.13327I 0
u = 0.19083 − 1.40218I
a = 0.135240 + 0.073939I
b = 0.934843 − 0.334737I
4.46155 + 2.13327I 0
u = −0.22241 + 1.40043I
a = 0.43037 − 2.12672I
b = 2.89349 + 1.45814I
2.84029 + 4.11499I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.22241 − 1.40043I
a = 0.43037 + 2.12672I
b = 2.89349 − 1.45814I
2.84029 − 4.11499I 0
u = −0.25197 + 1.40362I
a = −1.23101 − 1.46628I
b = 0.99999 − 1.02640I
−0.65725 + 8.14961I 0
u = −0.25197 − 1.40362I
a = −1.23101 + 1.46628I
b = 0.99999 + 1.02640I
−0.65725 − 8.14961I 0
u = −0.570859 + 0.050835I
a = 0.840207 − 1.053810I
b = 0.446144 + 0.934977I
−3.95624 − 2.45671I −16.1151 + 3.1714I
u = −0.570859 − 0.050835I
a = 0.840207 + 1.053810I
b = 0.446144 − 0.934977I
−3.95624 + 2.45671I −16.1151 − 3.1714I
u = −0.21435 + 1.41488I
a = −5.17093 − 3.12191I
b = 9.88874 − 5.91330I
2.60671 + 4.35178I 0
u = −0.21435 − 1.41488I
a = −5.17093 + 3.12191I
b = 9.88874 + 5.91330I
2.60671 − 4.35178I 0
u = 0.24025 + 1.41099I
a = 0.208636 + 0.619895I
b = −0.315370 − 0.588894I
3.71345 − 6.34087I 0
u = 0.24025 − 1.41099I
a = 0.208636 − 0.619895I
b = −0.315370 + 0.588894I
3.71345 + 6.34087I 0
u = 0.22894 + 1.42766I
a = −0.214134 − 1.001530I
b = −1.56014 + 1.05291I
4.18239 − 4.52972I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.22894 − 1.42766I
a = −0.214134 + 1.001530I
b = −1.56014 − 1.05291I
4.18239 + 4.52972I 0
u = 0.15743 + 1.44043I
a = 0.03145 − 1.55183I
b = −1.93175 − 0.15846I
5.97894 + 1.89406I 0
u = 0.15743 − 1.44043I
a = 0.03145 + 1.55183I
b = −1.93175 + 0.15846I
5.97894 − 1.89406I 0
u = 0.25998 + 1.42918I
a = −1.05288 − 1.74902I
b = −2.32630 + 1.56569I
4.50338 − 11.15960I 0
u = 0.25998 − 1.42918I
a = −1.05288 + 1.74902I
b = −2.32630 − 1.56569I
4.50338 + 11.15960I 0
u = −0.25308 + 1.43624I
a = −0.34926 + 1.45938I
b = −2.13375 − 0.83125I
8.04215 + 7.29186I 0
u = −0.25308 − 1.43624I
a = −0.34926 − 1.45938I
b = −2.13375 + 0.83125I
8.04215 − 7.29186I 0
u = −0.17132 + 1.45219I
a = −0.264172 + 1.235620I
b = −1.60046 − 0.59631I
9.23042 + 2.23354I 0
u = −0.17132 − 1.45219I
a = −0.264172 − 1.235620I
b = −1.60046 + 0.59631I
9.23042 − 2.23354I 0
u = −0.28819 + 1.43675I
a = 0.35070 − 1.37830I
b = 1.79966 + 0.83955I
4.83747 + 12.28390I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.28819 − 1.43675I
a = 0.35070 + 1.37830I
b = 1.79966 − 0.83955I
4.83747 − 12.28390I 0
u = 0.28430 + 1.44095I
a = 0.69012 + 1.90557I
b = 2.38988 − 1.56515I
−0.0021 − 17.8042I 0
u = 0.28430 − 1.44095I
a = 0.69012 − 1.90557I
b = 2.38988 + 1.56515I
−0.0021 + 17.8042I 0
u = −0.10870 + 1.47116I
a = 0.280946 − 0.767506I
b = 1.190360 + 0.365704I
7.38329 − 2.52548I 0
u = −0.10870 − 1.47116I
a = 0.280946 + 0.767506I
b = 1.190360 − 0.365704I
7.38329 + 2.52548I 0
u = 0.31311 + 1.44342I
a = 0.398723 + 0.455278I
b = 0.431464 − 0.556617I
1.42609 − 5.78759I 0
u = 0.31311 − 1.44342I
a = 0.398723 − 0.455278I
b = 0.431464 + 0.556617I
1.42609 + 5.78759I 0
u = 0.12451 + 1.47990I
a = −0.087593 + 1.216800I
b = 2.04305 − 0.01678I
2.30951 + 7.86961I 0
u = 0.12451 − 1.47990I
a = −0.087593 − 1.216800I
b = 2.04305 + 0.01678I
2.30951 − 7.86961I 0
u = 0.291854 + 0.422173I
a = 1.45419 + 0.20833I
b = −0.109873 − 0.312516I
−0.66057 − 1.49579I −5.59034 + 3.83194I
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.291854 − 0.422173I
a = 1.45419 − 0.20833I
b = −0.109873 + 0.312516I
−0.66057 + 1.49579I −5.59034 − 3.83194I
u = −0.188505 + 0.460456I
a = 0.364513 − 0.286938I
b = 1.27520 + 1.02424I
−4.65808 − 1.73002I −12.40385 + 1.70424I
u = −0.188505 − 0.460456I
a = 0.364513 + 0.286938I
b = 1.27520 − 1.02424I
−4.65808 + 1.73002I −12.40385 − 1.70424I
u = 0.18126 + 1.50593I
a = −0.424240 − 0.456464I
b = −0.547878 + 0.934518I
3.71893 − 5.80434I 0
u = 0.18126 − 1.50593I
a = −0.424240 + 0.456464I
b = −0.547878 − 0.934518I
3.71893 + 5.80434I 0
u = 0.355795 + 0.303110I
a = 0.063077 − 0.722119I
b = 0.568919 − 0.030956I
−0.916385 + 0.195495I −7.80562 + 1.64458I
u = 0.355795 − 0.303110I
a = 0.063077 + 0.722119I
b = 0.568919 + 0.030956I
−0.916385 − 0.195495I −7.80562 − 1.64458I
u = 0.425920
a = 0.405168
b = 0.396583
−0.879709 −10.6710
14
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
98
− 19u
97
+ ··· − 841339u + 59603
c
2
, c
6
, c
7
u
98
+ 3u
97
+ ··· + 5u + 1
c
3
u
98
− 3u
97
+ ··· + 595u + 425
c
4
u
98
− u
97
+ ··· − u − 1
c
5
, c
12
u
98
− 3u
97
+ ··· + u + 1
c
8
, c
11
u
98
− u
97
+ ··· − 33u − 1
c
9
u
98
+ 5u
97
+ ··· − 3041767u − 195991
c
10
u
98
+ 9u
97
+ ··· + 4943u − 137
15
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
98
+ 45y
97
+ ··· + 84576889997y + 3552517609
c
2
, c
6
, c
7
y
98
+ 89y
97
+ ··· − 7y + 1
c
3
y
98
+ 13y
97
+ ··· + 6423025y + 180625
c
4
y
98
− 3y
97
+ ··· − 99y + 1
c
5
, c
12
y
98
+ 73y
97
+ ··· − 7y + 1
c
8
, c
11
y
98
− 67y
97
+ ··· − 179y + 1
c
9
y
98
− 203y
97
+ ··· − 3248967720299y + 38412472081
c
10
y
98
+ 137y
97
+ ··· − 6924923y + 18769
16
