12a
0329
(K12a
0329
)
A knot diagram
1
Linearized knot diagam
3 6 8 11 7 2 5 12 1 4 10 9
Solving Sequence
2,7
6 3
1,9
10 5 8 4 12 11
c
6
c
2
c
1
c
9
c
5
c
7
c
3
c
12
c
11
c
4
, c
8
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= hu
72
+ u
71
+ ··· + b − u, u
72
+ u
71
+ ··· + a − 1, u
74
+ 2u
73
+ ··· − 3u + 1i
I
u
2
= hu
3
+ u
2
+ b, u
3
+ u
2
+ a + u, u
4
+ u
3
+ u
2
+ 1i
* 2 irreducible components of dim
C
= 0, with total 78 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
= hu
72
+ u
71
+ · · · + b − u, u
72
+ u
71
+ · · · + a − 1, u
74
+ 2u
73
+ · · · − 3u + 1i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
6
=
1
u
2
a
3
=
u
u
3
+ u
a
1
=
u
3
u
5
+ u
3
+ u
a
9
=
−u
72
− u
71
+ ··· + 2u + 1
−u
72
− u
71
+ ··· − u
2
+ u
a
10
=
−2u
72
− u
71
+ ··· − 7u
2
+ 6u
u
73
− u
72
+ ··· − 3u
2
+ 2u
a
5
=
u
2
+ 1
u
2
a
8
=
u
4
+ u
2
+ 1
u
4
a
4
=
−u
11
− 2u
9
− 4u
7
− 4u
5
− 3u
3
−u
11
− u
9
− 2u
7
− u
5
+ u
3
+ u
a
12
=
−u
71
− u
70
+ ··· − u + 1
−u
73
− u
72
+ ··· + 2u
2
+ u
a
11
=
−u
71
− u
70
+ ··· + u + 1
−u
73
− u
72
+ ··· + 3u
2
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
73
+ 33u
71
+ ··· + 26u − 15
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
7
u
74
+ 18u
73
+ ··· − 3u + 1
c
2
, c
6
u
74
− 2u
73
+ ··· + 3u + 1
c
3
u
74
− 2u
73
+ ··· + 9257u + 4777
c
4
, c
10
u
74
− u
73
+ ··· − 24u − 16
c
8
, c
9
, c
12
u
74
− 5u
73
+ ··· + 5u − 1
c
11
u
74
+ 27u
73
+ ··· + 1344u + 256
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
7
y
74
+ 78y
73
+ ··· − 75y + 1
c
2
, c
6
y
74
+ 18y
73
+ ··· − 3y + 1
c
3
y
74
+ 18y
73
+ ··· − 14218575y + 22819729
c
4
, c
10
y
74
− 27y
73
+ ··· − 1344y + 256
c
8
, c
9
, c
12
y
74
− 63y
73
+ ··· + 3y + 1
c
11
y
74
+ 33y
73
+ ··· − 20480y + 65536
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.370657 + 0.930941I
a = −1.27891 + 1.28820I
b = −0.48568 − 1.33658I
−3.10297 − 5.13562I −11.85911 + 6.70482I
u = −0.370657 − 0.930941I
a = −1.27891 − 1.28820I
b = −0.48568 + 1.33658I
−3.10297 + 5.13562I −11.85911 − 6.70482I
u = 0.262234 + 0.974045I
a = −1.51097 − 0.71110I
b = 0.13812 + 1.50691I
−10.11750 + 2.86955I −18.1096 + 0.I
u = 0.262234 − 0.974045I
a = −1.51097 + 0.71110I
b = 0.13812 − 1.50691I
−10.11750 − 2.86955I −18.1096 + 0.I
u = 0.391755 + 0.945458I
a = −0.120911 + 0.246009I
b = −0.073081 − 0.876023I
−0.03542 + 7.02498I 0
u = 0.391755 − 0.945458I
a = −0.120911 − 0.246009I
b = −0.073081 + 0.876023I
−0.03542 − 7.02498I 0
u = 0.101503 + 0.967548I
a = −1.333000 − 0.086551I
b = 0.51887 + 1.44531I
−6.74695 − 5.46594I −16.3389 + 3.3983I
u = 0.101503 − 0.967548I
a = −1.333000 + 0.086551I
b = 0.51887 − 1.44531I
−6.74695 + 5.46594I −16.3389 − 3.3983I
u = −0.539297 + 0.874713I
a = 1.41107 + 1.07868I
b = 1.43835 − 0.33243I
−3.04067 + 0.79446I 0
u = −0.539297 − 0.874713I
a = 1.41107 − 1.07868I
b = 1.43835 + 0.33243I
−3.04067 − 0.79446I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.423718 + 0.873936I
a = 0.058791 − 0.298637I
b = −0.105446 + 0.720386I
1.05241 − 2.06574I −5.32240 + 3.74687I
u = −0.423718 − 0.873936I
a = 0.058791 + 0.298637I
b = −0.105446 − 0.720386I
1.05241 + 2.06574I −5.32240 − 3.74687I
u = 0.358544 + 0.895439I
a = 0.987293 − 0.627444I
b = 0.663180 + 0.145591I
−2.38686 + 2.65510I −13.1205 − 6.3597I
u = 0.358544 − 0.895439I
a = 0.987293 + 0.627444I
b = 0.663180 − 0.145591I
−2.38686 − 2.65510I −13.1205 + 6.3597I
u = 0.394012 + 0.979247I
a = −1.11170 − 1.07359I
b = −0.296049 + 1.060090I
−5.08396 + 11.12460I 0
u = 0.394012 − 0.979247I
a = −1.11170 + 1.07359I
b = −0.296049 − 1.060090I
−5.08396 − 11.12460I 0
u = 0.103312 + 0.896931I
a = 0.887399 − 0.107134I
b = 0.1026740 + 0.0258890I
−1.62241 − 1.90988I −12.59659 + 2.96678I
u = 0.103312 − 0.896931I
a = 0.887399 + 0.107134I
b = 0.1026740 − 0.0258890I
−1.62241 + 1.90988I −12.59659 − 2.96678I
u = −0.162278 + 0.882080I
a = −1.86533 + 0.01556I
b = 0.61352 − 1.71143I
−4.28589 + 0.17592I −15.2224 + 1.2982I
u = −0.162278 − 0.882080I
a = −1.86533 − 0.01556I
b = 0.61352 + 1.71143I
−4.28589 − 0.17592I −15.2224 − 1.2982I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.228592 + 0.865642I
a = −0.205409 − 0.318538I
b = 0.393610 − 0.827305I
−3.11888 + 1.92265I −16.9691 − 4.8475I
u = 0.228592 − 0.865642I
a = −0.205409 + 0.318538I
b = 0.393610 + 0.827305I
−3.11888 − 1.92265I −16.9691 + 4.8475I
u = −0.793537 + 0.797011I
a = 1.20434 + 2.94943I
b = 3.24568 + 1.59448I
−3.39031 + 1.34510I 0
u = −0.793537 − 0.797011I
a = 1.20434 − 2.94943I
b = 3.24568 − 1.59448I
−3.39031 − 1.34510I 0
u = −0.800342 + 0.871137I
a = −0.361382 − 1.004460I
b = −1.018710 − 0.097940I
2.93090 − 0.84494I 0
u = −0.800342 − 0.871137I
a = −0.361382 + 1.004460I
b = −1.018710 + 0.097940I
2.93090 + 0.84494I 0
u = 0.787585 + 0.892783I
a = 3.73862 − 2.99484I
b = 5.51026 + 0.88946I
0.96592 + 2.96415I 0
u = 0.787585 − 0.892783I
a = 3.73862 + 2.99484I
b = 5.51026 − 0.88946I
0.96592 − 2.96415I 0
u = −0.648967 + 0.480188I
a = 0.67572 + 1.63606I
b = 1.05520 + 1.06991I
−1.82857 − 5.13657I −7.61220 + 5.78634I
u = −0.648967 − 0.480188I
a = 0.67572 − 1.63606I
b = 1.05520 − 1.06991I
−1.82857 + 5.13657I −7.61220 − 5.78634I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.792974 + 0.914514I
a = −0.925828 − 0.048708I
b = −1.136000 + 0.585010I
2.79856 − 5.13896I 0
u = −0.792974 − 0.914514I
a = −0.925828 + 0.048708I
b = −1.136000 − 0.585010I
2.79856 + 5.13896I 0
u = 0.871182 + 0.842854I
a = −0.43677 − 4.17578I
b = 3.19153 − 4.15521I
4.79039 − 2.56885I 0
u = 0.871182 − 0.842854I
a = −0.43677 + 4.17578I
b = 3.19153 + 4.15521I
4.79039 + 2.56885I 0
u = −0.865285 + 0.852184I
a = −0.446010 − 0.389569I
b = −1.374710 + 0.215281I
5.30374 − 0.19199I 0
u = −0.865285 − 0.852184I
a = −0.446010 + 0.389569I
b = −1.374710 − 0.215281I
5.30374 + 0.19199I 0
u = −0.889310 + 0.831084I
a = −0.58412 + 3.55348I
b = 2.51405 + 3.82161I
3.25231 + 8.92007I 0
u = −0.889310 − 0.831084I
a = −0.58412 − 3.55348I
b = 2.51405 − 3.82161I
3.25231 − 8.92007I 0
u = −0.880501 + 0.841506I
a = −0.09655 − 1.43175I
b = −0.96541 − 1.11206I
8.11567 + 4.50987I 0
u = −0.880501 − 0.841506I
a = −0.09655 + 1.43175I
b = −0.96541 + 1.11206I
8.11567 − 4.50987I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.768948 + 0.953815I
a = 3.60195 + 0.74895I
b = 3.28481 − 2.83553I
−3.85290 − 7.23015I 0
u = −0.768948 − 0.953815I
a = 3.60195 − 0.74895I
b = 3.28481 + 2.83553I
−3.85290 + 7.23015I 0
u = 0.875221 + 0.863661I
a = −0.24047 + 1.56679I
b = −1.32613 + 1.10874I
9.13605 + 1.16892I 0
u = 0.875221 − 0.863661I
a = −0.24047 − 1.56679I
b = −1.32613 − 1.10874I
9.13605 − 1.16892I 0
u = 0.836796 + 0.905566I
a = −0.976206 + 0.856643I
b = −1.69337 − 0.26275I
6.12773 + 3.11665I 0
u = 0.836796 − 0.905566I
a = −0.976206 − 0.856643I
b = −1.69337 + 0.26275I
6.12773 − 3.11665I 0
u = −0.284228 + 0.708232I
a = 0.571120 − 0.005427I
b = −0.023212 + 0.272923I
−0.344659 − 1.199220I −4.27090 + 5.42127I
u = −0.284228 − 0.708232I
a = 0.571120 + 0.005427I
b = −0.023212 − 0.272923I
−0.344659 + 1.199220I −4.27090 − 5.42127I
u = 0.884209 + 0.886388I
a = −0.453759 + 0.492959I
b = −1.44464 − 0.27372I
5.67600 + 4.74487I 0
u = 0.884209 − 0.886388I
a = −0.453759 − 0.492959I
b = −1.44464 + 0.27372I
5.67600 − 4.74487I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.824692 + 0.956473I
a = −0.430534 − 0.688248I
b = −1.273820 + 0.430919I
4.97545 − 6.08633I 0
u = −0.824692 − 0.956473I
a = −0.430534 + 0.688248I
b = −1.273820 − 0.430919I
4.97545 + 6.08633I 0
u = 0.823326 + 0.965058I
a = 4.31567 + 1.07074I
b = 2.38456 + 5.11677I
4.40603 + 8.85971I 0
u = 0.823326 − 0.965058I
a = 4.31567 − 1.07074I
b = 2.38456 − 5.11677I
4.40603 − 8.85971I 0
u = 0.837491 + 0.954895I
a = −1.59825 − 0.12438I
b = −1.24032 − 1.39697I
8.84737 + 5.18121I 0
u = 0.837491 − 0.954895I
a = −1.59825 + 0.12438I
b = −1.24032 + 1.39697I
8.84737 − 5.18121I 0
u = −0.827734 + 0.970843I
a = −1.44770 + 0.29178I
b = −0.93181 + 1.32597I
7.70752 − 10.84290I 0
u = −0.827734 − 0.970843I
a = −1.44770 − 0.29178I
b = −0.93181 − 1.32597I
7.70752 + 10.84290I 0
u = 0.858246 + 0.946417I
a = −0.453491 + 0.631410I
b = −1.39039 − 0.40883I
5.48554 + 1.70033I 0
u = 0.858246 − 0.946417I
a = −0.453491 − 0.631410I
b = −1.39039 + 0.40883I
5.48554 − 1.70033I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.826554 + 0.981242I
a = 3.64712 − 1.10764I
b = 1.77061 − 4.59589I
2.7778 − 15.2746I 0
u = −0.826554 − 0.981242I
a = 3.64712 + 1.10764I
b = 1.77061 + 4.59589I
2.7778 + 15.2746I 0
u = 0.660743 + 0.252301I
a = −0.786755 + 0.787997I
b = 1.110110 + 0.042205I
−2.78259 − 7.30543I −7.59550 + 5.05432I
u = 0.660743 − 0.252301I
a = −0.786755 − 0.787997I
b = 1.110110 − 0.042205I
−2.78259 + 7.30543I −7.59550 − 5.05432I
u = −0.573801 + 0.409204I
a = 0.527291 − 0.334649I
b = −0.483095 − 0.240497I
2.49523 − 1.66576I −1.39126 + 3.52161I
u = −0.573801 − 0.409204I
a = 0.527291 + 0.334649I
b = −0.483095 + 0.240497I
2.49523 + 1.66576I −1.39126 − 3.52161I
u = 0.602855 + 0.285159I
a = 0.583424 + 0.499225I
b = −0.364134 + 0.428826I
2.01747 − 3.35955I −2.79071 + 3.80374I
u = 0.602855 − 0.285159I
a = 0.583424 − 0.499225I
b = −0.364134 − 0.428826I
2.01747 + 3.35955I −2.79071 − 3.80374I
u = 0.611157
a = −1.22506
b = 1.19125
−7.12640 −11.6060
u = −0.543461 + 0.270079I
a = −1.07351 − 1.11244I
b = 1.135140 + 0.038101I
−1.09335 + 1.70677I −5.63790 − 1.01096I
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.543461 − 0.270079I
a = −1.07351 + 1.11244I
b = 1.135140 − 0.038101I
−1.09335 − 1.70677I −5.63790 + 1.01096I
u = 0.476340 + 0.362773I
a = 0.81595 − 1.63104I
b = 0.809668 − 0.738998I
−0.731866 + 0.571685I −5.61090 + 0.52362I
u = 0.476340 − 0.362773I
a = 0.81595 + 1.63104I
b = 0.809668 + 0.738998I
−0.731866 − 0.571685I −5.61090 − 0.52362I
u = 0.313519
a = 1.64868
b = 0.300888
−0.958769 −9.89680
12
II. I
u
2
= hu
3
+ u
2
+ b, u
3
+ u
2
+ a + u, u
4
+ u
3
+ u
2
+ 1i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
6
=
1
u
2
a
3
=
u
u
3
+ u
a
1
=
u
3
u
3
+ u
2
+ 1
a
9
=
−u
3
− u
2
− u
−u
3
− u
2
a
10
=
−u
2
− u
1
a
5
=
u
2
+ 1
u
2
a
8
=
−u
3
−u
3
− u
2
− 1
a
4
=
u
2
+ 1
u
2
a
12
=
−u
2
− u
1
a
11
=
−u
2
− u
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −3u
2
− 2u − 11
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
5
u
4
− u
3
+ 3u
2
− 2u + 1
c
2
u
4
− u
3
+ u
2
+ 1
c
4
, c
10
, c
11
u
4
c
6
u
4
+ u
3
+ u
2
+ 1
c
7
u
4
+ u
3
+ 3u
2
+ 2u + 1
c
8
, c
9
(u − 1)
4
c
12
(u + 1)
4
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
5
c
7
y
4
+ 5y
3
+ 7y
2
+ 2y + 1
c
2
, c
6
y
4
+ y
3
+ 3y
2
+ 2y + 1
c
4
, c
10
, c
11
y
4
c
8
, c
9
, c
12
(y −1)
4
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.351808 + 0.720342I
a = 0.547424 − 1.120870I
b = 0.899232 − 0.400532I
−1.85594 + 1.41510I −10.51825 − 2.96122I
u = 0.351808 − 0.720342I
a = 0.547424 + 1.120870I
b = 0.899232 + 0.400532I
−1.85594 − 1.41510I −10.51825 + 2.96122I
u = −0.851808 + 0.911292I
a = −0.547424 − 0.585652I
b = −1.39923 + 0.32564I
5.14581 − 3.16396I −8.98175 + 2.83489I
u = −0.851808 − 0.911292I
a = −0.547424 + 0.585652I
b = −1.39923 − 0.32564I
5.14581 + 3.16396I −8.98175 − 2.83489I
16
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
5
(u
4
− u
3
+ 3u
2
− 2u + 1)(u
74
+ 18u
73
+ ··· − 3u + 1)
c
2
(u
4
− u
3
+ u
2
+ 1)(u
74
− 2u
73
+ ··· + 3u + 1)
c
3
(u
4
− u
3
+ 3u
2
− 2u + 1)(u
74
− 2u
73
+ ··· + 9257u + 4777)
c
4
, c
10
u
4
(u
74
− u
73
+ ··· − 24u − 16)
c
6
(u
4
+ u
3
+ u
2
+ 1)(u
74
− 2u
73
+ ··· + 3u + 1)
c
7
(u
4
+ u
3
+ 3u
2
+ 2u + 1)(u
74
+ 18u
73
+ ··· − 3u + 1)
c
8
, c
9
((u − 1)
4
)(u
74
− 5u
73
+ ··· + 5u − 1)
c
11
u
4
(u
74
+ 27u
73
+ ··· + 1344u + 256)
c
12
((u + 1)
4
)(u
74
− 5u
73
+ ··· + 5u − 1)
17
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
7
(y
4
+ 5y
3
+ 7y
2
+ 2y + 1)(y
74
+ 78y
73
+ ··· − 75y + 1)
c
2
, c
6
(y
4
+ y
3
+ 3y
2
+ 2y + 1)(y
74
+ 18y
73
+ ··· − 3y + 1)
c
3
(y
4
+ 5y
3
+ 7y
2
+ 2y + 1)
· (y
74
+ 18y
73
+ ··· − 14218575y + 22819729)
c
4
, c
10
y
4
(y
74
− 27y
73
+ ··· − 1344y + 256)
c
8
, c
9
, c
12
((y −1)
4
)(y
74
− 63y
73
+ ··· + 3y + 1)
c
11
y
4
(y
74
+ 33y
73
+ ··· − 20480y + 65536)
18
