12a
0278
(K12a
0278
)
A knot diagram
1
Linearized knot diagam
3 6 8 9 2 12 10 4 5 1 7 11
Solving Sequence
5,9 1,10
11 4 8 3 2 7 12 6
c
9
c
10
c
4
c
8
c
3
c
1
c
7
c
12
c
6
c
2
, c
5
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h9.38441 × 10
39
u
74
+ 5.67453 × 10
39
u
73
+ ··· + 1.90771 × 10
40
b − 5.20911 × 10
40
,
− 1.62029 × 10
40
u
74
− 8.80257 × 10
39
u
73
+ ··· + 1.90771 × 10
40
a + 1.14013 × 10
41
, u
75
+ u
74
+ ··· − 12u − 4i
I
u
2
= hb
2
− 2bu − b + u + 3, 2a + u, u
2
− 2i
I
v
1
= ha, b − v −1, v
2
+ v + 1i
* 3 irreducible components of dim
C
= 0, with total 81 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
= h9.38×10
39
u
74
+5.67×10
39
u
73
+· · ·+1.91×10
40
b−5.21×10
40
, −1.62×
10
40
u
74
−8.80×10
39
u
73
+· · ·+1.91×10
40
a+1.14×10
41
, u
75
+u
74
+· · ·−12u−4i
(i) Arc colorings
a
5
=
0
u
a
9
=
1
0
a
1
=
0.849339u
74
+ 0.461421u
73
+ ··· − 10.4833u − 5.97644
−0.491921u
74
− 0.297453u
73
+ ··· + 0.593748u + 2.73056
a
10
=
1
−u
2
a
11
=
0.524536u
74
− 0.696711u
73
+ ··· − 8.34076u − 5.63903
−1.23043u
74
+ 1.30629u
73
+ ··· + 12.6838u + 6.35323
a
4
=
−u
u
a
8
=
−u
2
+ 1
u
2
a
3
=
u
3
− 2u
−u
3
+ u
a
2
=
0.871842u
74
− 0.0410241u
73
+ ··· − 10.2878u − 6.19131
−0.374527u
74
+ 0.413670u
73
+ ··· + 1.18849u + 2.97556
a
7
=
u
4
− 3u
2
+ 1
−u
6
+ 2u
4
+ u
2
a
12
=
0.519955u
74
− 0.395542u
73
+ ··· − 8.23310u − 4.93826
−1.16106u
74
+ 0.963015u
73
+ ··· + 11.8087u + 6.08819
a
6
=
−0.174957u
74
− 0.182489u
73
+ ··· − 8.40404u + 0.258482
0.672272u
74
+ 0.555135u
73
+ ··· − 0.695264u − 3.47423
(ii) Obstruction class = −1
(iii) Cusp Shapes = −2.15821u
74
+ 0.754780u
73
+ ··· + 41.7200u + 28.2560
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
75
+ 39u
74
+ ··· + 417u + 49
c
2
, c
5
u
75
+ 3u
74
+ ··· − 9u − 7
c
3
, c
4
, c
8
c
9
u
75
+ u
74
+ ··· − 12u − 4
c
6
, c
11
u
75
− 2u
74
+ ··· + 6u + 1
c
7
u
75
+ 15u
74
+ ··· + 11264u + 1792
c
10
, c
12
u
75
+ 26u
74
+ ··· + 40u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
75
+ y
74
+ ··· − 65623y −2401
c
2
, c
5
y
75
− 39y
74
+ ··· + 417y −49
c
3
, c
4
, c
8
c
9
y
75
− 85y
74
+ ··· + 272y −16
c
6
, c
11
y
75
+ 26y
74
+ ··· + 40y −1
c
7
y
75
+ 19y
74
+ ··· + 128483328y −3211264
c
10
, c
12
y
75
+ 50y
74
+ ··· + 1936y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.992360 + 0.148515I
a = 0.576542 + 0.197096I
b = −0.309129 + 0.852785I
4.89966 − 0.48043I 0
u = 0.992360 − 0.148515I
a = 0.576542 − 0.197096I
b = −0.309129 − 0.852785I
4.89966 + 0.48043I 0
u = −0.931734 + 0.252335I
a = −0.485930 + 0.342374I
b = 0.456955 + 0.767589I
4.81883 − 5.04031I 0
u = −0.931734 − 0.252335I
a = −0.485930 − 0.342374I
b = 0.456955 − 0.767589I
4.81883 + 5.04031I 0
u = 0.653012 + 0.614677I
a = −2.17237 + 0.30058I
b = 0.915870 + 0.280175I
−0.19940 + 12.18710I 0
u = 0.653012 − 0.614677I
a = −2.17237 − 0.30058I
b = 0.915870 − 0.280175I
−0.19940 − 12.18710I 0
u = −0.665614 + 0.580959I
a = 1.80487 + 0.31047I
b = −0.671344 + 0.328501I
0.97505 − 6.50542I 0
u = −0.665614 − 0.580959I
a = 1.80487 − 0.31047I
b = −0.671344 − 0.328501I
0.97505 + 6.50542I 0
u = −0.675215 + 0.522999I
a = −1.99689 + 0.08186I
b = 0.802298 − 0.038855I
2.37245 − 7.04723I 0. + 7.05593I
u = −0.675215 − 0.522999I
a = −1.99689 − 0.08186I
b = 0.802298 + 0.038855I
2.37245 + 7.04723I 0. − 7.05593I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.697751 + 0.462610I
a = 1.71652 − 0.07976I
b = −0.612037 − 0.027947I
3.26431 + 1.50095I 7.89789 − 1.80538I
u = 0.697751 − 0.462610I
a = 1.71652 + 0.07976I
b = −0.612037 + 0.027947I
3.26431 − 1.50095I 7.89789 + 1.80538I
u = 0.567607 + 0.560344I
a = −1.81116 − 0.63783I
b = 0.795511 + 0.950961I
−5.29697 + 5.95713I −3.09818 − 7.38755I
u = 0.567607 − 0.560344I
a = −1.81116 + 0.63783I
b = 0.795511 − 0.950961I
−5.29697 − 5.95713I −3.09818 + 7.38755I
u = 0.323852 + 0.694398I
a = −0.48580 − 1.64617I
b = −0.386203 + 0.980438I
−1.18225 − 7.78836I 0.62681 + 5.55340I
u = 0.323852 − 0.694398I
a = −0.48580 + 1.64617I
b = −0.386203 − 0.980438I
−1.18225 + 7.78836I 0.62681 − 5.55340I
u = −0.591460 + 0.442465I
a = 0.851460 − 0.535667I
b = −0.167713 + 0.970251I
−0.68077 − 3.94349I 4.08468 + 7.42217I
u = −0.591460 − 0.442465I
a = 0.851460 + 0.535667I
b = −0.167713 − 0.970251I
−0.68077 + 3.94349I 4.08468 − 7.42217I
u = −0.282851 + 0.667116I
a = 0.407429 − 1.153780I
b = 0.460517 + 0.731193I
−0.16240 + 2.29905I 2.31301 − 0.75455I
u = −0.282851 − 0.667116I
a = 0.407429 + 1.153780I
b = 0.460517 − 0.731193I
−0.16240 − 2.29905I 2.31301 + 0.75455I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.399552 + 0.588174I
a = −1.69508 − 1.30618I
b = 0.152200 + 0.661165I
−5.79484 − 2.02438I −5.06771 + 0.43859I
u = 0.399552 − 0.588174I
a = −1.69508 + 1.30618I
b = 0.152200 − 0.661165I
−5.79484 + 2.02438I −5.06771 − 0.43859I
u = 1.287660 + 0.137546I
a = 0.108222 + 0.102118I
b = −0.041567 − 1.232660I
4.69216 + 0.68186I 0
u = 1.287660 − 0.137546I
a = 0.108222 − 0.102118I
b = −0.041567 + 1.232660I
4.69216 − 0.68186I 0
u = −0.477179 + 0.487322I
a = −1.37904 + 0.78397I
b = 0.597926 − 0.495834I
−2.38002 − 1.71377I −0.33796 + 4.28154I
u = −0.477179 − 0.487322I
a = −1.37904 − 0.78397I
b = 0.597926 + 0.495834I
−2.38002 + 1.71377I −0.33796 − 4.28154I
u = 0.511035 + 0.444098I
a = −2.87952 − 0.72570I
b = 0.418047 + 0.120094I
−2.37090 + 3.74638I 0.22703 − 6.74943I
u = 0.511035 − 0.444098I
a = −2.87952 + 0.72570I
b = 0.418047 − 0.120094I
−2.37090 − 3.74638I 0.22703 + 6.74943I
u = 0.473672 + 0.440581I
a = −0.80128 − 1.37475I
b = 0.17379 + 1.52146I
−2.48507 − 0.60256I −0.45284 − 3.01495I
u = 0.473672 − 0.440581I
a = −0.80128 + 1.37475I
b = 0.17379 − 1.52146I
−2.48507 + 0.60256I −0.45284 + 3.01495I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.342850 + 0.195956I
a = 0.162252 + 0.343427I
b = −0.00168 − 1.80697I
4.05099 + 4.57027I 0
u = −1.342850 − 0.195956I
a = 0.162252 − 0.343427I
b = −0.00168 + 1.80697I
4.05099 − 4.57027I 0
u = −0.208285 + 0.606015I
a = −0.37413 + 1.46044I
b = −0.050477 − 0.875409I
1.01708 + 3.22485I 3.29952 − 1.53483I
u = −0.208285 − 0.606015I
a = −0.37413 − 1.46044I
b = −0.050477 + 0.875409I
1.01708 − 3.22485I 3.29952 + 1.53483I
u = 0.107932 + 0.597520I
a = 0.058053 + 1.205490I
b = 0.304582 − 0.660951I
1.52734 + 2.01025I 4.15237 − 4.38381I
u = 0.107932 − 0.597520I
a = 0.058053 − 1.205490I
b = 0.304582 + 0.660951I
1.52734 − 2.01025I 4.15237 + 4.38381I
u = 0.574225 + 0.154605I
a = 0.895573 + 0.119935I
b = −0.453435 − 0.321110I
1.012190 + 0.224702I 10.07500 − 1.39244I
u = 0.574225 − 0.154605I
a = 0.895573 − 0.119935I
b = −0.453435 + 0.321110I
1.012190 − 0.224702I 10.07500 + 1.39244I
u = 1.44015
a = 0.864467
b = −1.81545
3.34202 0
u = −0.443389 + 0.313223I
a = 2.92248 − 0.01185I
b = −0.146346 + 0.009497I
−1.45213 + 1.13937I 2.80069 + 2.68006I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.443389 − 0.313223I
a = 2.92248 + 0.01185I
b = −0.146346 − 0.009497I
−1.45213 − 1.13937I 2.80069 − 2.68006I
u = −1.46267 + 0.14512I
a = −0.479150 + 1.024860I
b = 1.54755 − 2.32447I
0.219652 − 0.514414I 0
u = −1.46267 − 0.14512I
a = −0.479150 − 1.024860I
b = 1.54755 + 2.32447I
0.219652 + 0.514414I 0
u = −0.478987 + 0.106396I
a = −0.928822 − 0.554161I
b = 0.976701 + 0.733060I
−1.09010 − 2.70453I 5.06111 + 8.24534I
u = −0.478987 − 0.106396I
a = −0.928822 + 0.554161I
b = 0.976701 − 0.733060I
−1.09010 + 2.70453I 5.06111 − 8.24534I
u = 1.53018 + 0.01645I
a = −0.378473 − 0.019636I
b = 1.78911 + 0.93630I
5.67752 − 2.80166I 0
u = 1.53018 − 0.01645I
a = −0.378473 + 0.019636I
b = 1.78911 − 0.93630I
5.67752 + 2.80166I 0
u = −0.217271 + 0.415338I
a = 1.48058 + 0.60711I
b = 0.0853380 + 0.1067120I
−1.61290 + 0.93401I −1.58237 + 0.39943I
u = −0.217271 − 0.415338I
a = 1.48058 − 0.60711I
b = 0.0853380 − 0.1067120I
−1.61290 − 0.93401I −1.58237 − 0.39943I
u = 1.52988 + 0.11797I
a = −0.623400 − 0.558838I
b = 2.34549 + 1.16028I
4.31442 + 3.77841I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.52988 − 0.11797I
a = −0.623400 + 0.558838I
b = 2.34549 − 1.16028I
4.31442 − 3.77841I 0
u = −1.53683 + 0.11028I
a = −0.320595 + 0.307458I
b = 1.52621 − 1.97759I
4.29005 − 1.28143I 0
u = −1.53683 − 0.11028I
a = −0.320595 − 0.307458I
b = 1.52621 + 1.97759I
4.29005 + 1.28143I 0
u = 1.54396 + 0.08769I
a = 1.58184 + 1.09398I
b = −3.48311 − 1.98660I
5.37828 + 0.28224I 0
u = 1.54396 − 0.08769I
a = 1.58184 − 1.09398I
b = −3.48311 + 1.98660I
5.37828 − 0.28224I 0
u = −1.54768 + 0.11773I
a = −1.40777 + 1.47039I
b = 3.29966 − 2.66855I
4.57897 − 5.71211I 0
u = −1.54768 − 0.11773I
a = −1.40777 − 1.47039I
b = 3.29966 + 2.66855I
4.57897 + 5.71211I 0
u = −1.55261 + 0.16241I
a = −0.864693 + 0.634138I
b = 3.02044 − 1.66426I
1.77533 − 8.56700I 0
u = −1.55261 − 0.16241I
a = −0.864693 − 0.634138I
b = 3.02044 + 1.66426I
1.77533 + 8.56700I 0
u = −1.56486 + 0.06219I
a = 0.713620 − 0.067510I
b = −2.18755 + 0.52995I
8.30846 − 1.13053I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.56486 − 0.06219I
a = 0.713620 + 0.067510I
b = −2.18755 − 0.52995I
8.30846 + 1.13053I 0
u = 1.56721 + 0.12575I
a = 0.669514 + 0.170271I
b = −2.06471 − 1.12705I
6.60902 + 6.00545I 0
u = 1.56721 − 0.12575I
a = 0.669514 − 0.170271I
b = −2.06471 + 1.12705I
6.60902 − 6.00545I 0
u = −1.58541 + 0.18980I
a = −1.50518 + 0.63558I
b = 3.93186 − 0.97204I
7.2874 − 15.1719I 0
u = −1.58541 − 0.18980I
a = −1.50518 − 0.63558I
b = 3.93186 + 0.97204I
7.2874 + 15.1719I 0
u = 1.58960 + 0.17605I
a = 1.40524 + 0.42225I
b = −3.59162 − 0.75532I
8.54478 + 9.31535I 0
u = 1.58960 − 0.17605I
a = 1.40524 − 0.42225I
b = −3.59162 + 0.75532I
8.54478 − 9.31535I 0
u = 1.59206 + 0.15544I
a = −1.29051 − 0.83360I
b = 3.33436 + 1.24733I
10.01660 + 9.56671I 0
u = 1.59206 − 0.15544I
a = −1.29051 + 0.83360I
b = 3.33436 − 1.24733I
10.01660 − 9.56671I 0
u = −1.59672 + 0.13586I
a = 1.29653 − 0.58956I
b = −3.24169 + 0.91373I
11.02700 − 3.73205I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.59672 − 0.13586I
a = 1.29653 + 0.58956I
b = −3.24169 − 0.91373I
11.02700 + 3.73205I 0
u = −1.63713 + 0.01501I
a = 0.391869 − 0.910777I
b = −0.94477 + 1.07763I
13.79420 + 0.08438I 0
u = −1.63713 − 0.01501I
a = 0.391869 + 0.910777I
b = −0.94477 − 1.07763I
13.79420 − 0.08438I 0
u = 1.63715 + 0.03760I
a = −0.095026 − 0.954894I
b = 0.326676 + 1.124460I
13.6181 + 5.9211I 0
u = 1.63715 − 0.03760I
a = −0.095026 + 0.954894I
b = 0.326676 − 1.124460I
13.6181 − 5.9211I 0
12
II. I
u
2
= hb
2
− 2bu − b + u + 3, 2a + u, u
2
− 2i
(i) Arc colorings
a
5
=
0
u
a
9
=
1
0
a
1
=
−
1
2
u
b
a
10
=
1
−2
a
11
=
−
1
2
bu + 2
bu + b − u − 5
a
4
=
−u
u
a
8
=
−1
2
a
3
=
0
−u
a
2
=
−
1
2
u
b − u
a
7
=
−1
2
a
12
=
−
1
2
bu + b − u + 1
bu − b + u − 3
a
6
=
−
1
2
u
b
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4b − 4u
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
(u − 1)
4
c
2
(u + 1)
4
c
3
, c
4
, c
8
c
9
(u
2
− 2)
2
c
6
, c
10
(u
2
− u + 1)
2
c
7
u
4
c
11
, c
12
(u
2
+ u + 1)
2
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
(y −1)
4
c
3
, c
4
, c
8
c
9
(y −2)
4
c
6
, c
10
, c
11
c
12
(y
2
+ y + 1)
2
c
7
y
4
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.41421
a = −0.707107
b = 1.91421 + 0.86603I
3.28987 − 2.02988I 2.00000 + 3.46410I
u = 1.41421
a = −0.707107
b = 1.91421 − 0.86603I
3.28987 + 2.02988I 2.00000 − 3.46410I
u = −1.41421
a = 0.707107
b = −0.914214 + 0.866025I
3.28987 − 2.02988I 2.00000 + 3.46410I
u = −1.41421
a = 0.707107
b = −0.914214 − 0.866025I
3.28987 + 2.02988I 2.00000 − 3.46410I
16
III. I
v
1
= ha, b − v − 1, v
2
+ v + 1i
(i) Arc colorings
a
5
=
v
0
a
9
=
1
0
a
1
=
0
v + 1
a
10
=
1
0
a
11
=
1
v
a
4
=
v
0
a
8
=
1
0
a
3
=
v
0
a
2
=
v
v + 1
a
7
=
1
0
a
12
=
v + 1
v
a
6
=
0
−v − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4v + 2
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
2
c
3
, c
4
, c
7
c
8
, c
9
u
2
c
5
(u + 1)
2
c
6
, c
12
u
2
+ u + 1
c
10
, c
11
u
2
− u + 1
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
(y − 1)
2
c
3
, c
4
, c
7
c
8
, c
9
y
2
c
6
, c
10
, c
11
c
12
y
2
+ y + 1
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −0.500000 + 0.866025I
a = 0
b = 0.500000 + 0.866025I
−1.64493 − 2.02988I 0. + 3.46410I
v = −0.500000 − 0.866025I
a = 0
b = 0.500000 − 0.866025I
−1.64493 + 2.02988I 0. − 3.46410I
20
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
6
)(u
75
+ 39u
74
+ ··· + 417u + 49)
c
2
((u − 1)
2
)(u + 1)
4
(u
75
+ 3u
74
+ ··· − 9u − 7)
c
3
, c
4
, c
8
c
9
u
2
(u
2
− 2)
2
(u
75
+ u
74
+ ··· − 12u − 4)
c
5
((u − 1)
4
)(u + 1)
2
(u
75
+ 3u
74
+ ··· − 9u − 7)
c
6
((u
2
− u + 1)
2
)(u
2
+ u + 1)(u
75
− 2u
74
+ ··· + 6u + 1)
c
7
u
6
(u
75
+ 15u
74
+ ··· + 11264u + 1792)
c
10
((u
2
− u + 1)
3
)(u
75
+ 26u
74
+ ··· + 40u − 1)
c
11
(u
2
− u + 1)(u
2
+ u + 1)
2
(u
75
− 2u
74
+ ··· + 6u + 1)
c
12
((u
2
+ u + 1)
3
)(u
75
+ 26u
74
+ ··· + 40u − 1)
21
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y − 1)
6
)(y
75
+ y
74
+ ··· − 65623y − 2401)
c
2
, c
5
((y − 1)
6
)(y
75
− 39y
74
+ ··· + 417y − 49)
c
3
, c
4
, c
8
c
9
y
2
(y − 2)
4
(y
75
− 85y
74
+ ··· + 272y − 16)
c
6
, c
11
((y
2
+ y + 1)
3
)(y
75
+ 26y
74
+ ··· + 40y − 1)
c
7
y
6
(y
75
+ 19y
74
+ ··· + 1.28483 × 10
8
y − 3211264)
c
10
, c
12
((y
2
+ y + 1)
3
)(y
75
+ 50y
74
+ ··· + 1936y − 1)
22
