12a
0198
(K12a
0198
)
A knot diagram
1
Linearized knot diagam
3 5 10 7 2 9 12 4 6 1 8 11
Solving Sequence
2,6
5
3,10
4 1 11 9 7 8 12
c
5
c
2
c
3
c
1
c
10
c
9
c
6
c
8
c
12
c
4
, c
7
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h4.09817 × 10
213
u
103
+ 9.03681 × 10
212
u
102
+ ··· + 3.04803 × 10
213
b + 3.78252 × 10
213
,
2.98967 × 10
213
u
103
+ 1.28932 × 10
213
u
102
+ ··· + 3.04803 × 10
213
a + 1.33275 × 10
214
, u
104
+ u
103
+ ··· − 18u + 1i
* 1 irreducible components of dim
C
= 0, with total 104 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
= h4.10 × 10
213
u
103
+ 9.04 × 10
212
u
102
+ · · · + 3.05 × 10
213
b + 3.78 ×
10
213
, 2.99 × 10
213
u
103
+ 1.29 × 10
213
u
102
+ · · · + 3.05 × 10
213
a + 1.33 ×
10
214
, u
104
+ u
103
+ · · · − 18u + 1i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
5
=
1
u
2
a
3
=
u
u
3
+ u
a
10
=
−0.980852u
103
− 0.423002u
102
+ ··· − 301.358u − 4.37249
−1.34453u
103
− 0.296480u
102
+ ··· + 28.1294u − 1.24097
a
4
=
−0.165090u
103
+ 0.388729u
102
+ ··· − 249.973u + 34.5042
0.0825240u
103
− 0.759955u
102
+ ··· + 9.35599u − 2.04593
a
1
=
u
3
u
5
+ u
3
+ u
a
11
=
0.326890u
103
− 0.407412u
102
+ ··· − 304.926u − 4.11718
−0.930552u
103
− 0.197634u
102
+ ··· + 25.3578u − 1.01648
a
9
=
0.363680u
103
− 0.126522u
102
+ ··· − 329.487u − 3.13152
−1.34453u
103
− 0.296480u
102
+ ··· + 28.1294u − 1.24097
a
7
=
1.04068u
103
− 0.0442496u
102
+ ··· + 304.110u − 29.6838
1.60067u
103
+ 0.472640u
102
+ ··· − 11.4919u + 1.90007
a
8
=
0.203520u
103
+ 0.306686u
102
+ ··· − 469.111u + 0.852562
−1.74430u
103
− 0.392406u
102
+ ··· + 35.3865u − 1.76628
a
12
=
2.18547u
103
+ 1.17719u
102
+ ··· + 313.496u − 36.3829
0.863820u
103
+ 0.201308u
102
+ ··· − 1.30985u + 1.64945
(ii) Obstruction class = −1
(iii) Cusp Shapes = 3.21119u
103
− 3.19737u
102
+ ··· − 71.5495u + 0.533728
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
104
+ 41u
103
+ ··· + 124u + 1
c
2
, c
5
u
104
+ u
103
+ ··· − 18u + 1
c
3
u
104
+ 11u
103
+ ··· − 231098u + 177923
c
4
u
104
+ 23u
103
+ ··· + 128u + 41
c
6
, c
9
u
104
+ 5u
103
+ ··· + 10u
2
+ 1
c
7
, c
11
u
104
− 5u
103
+ ··· − 2u + 1
c
8
u
104
+ u
103
+ ··· − 10u + 1
c
10
, c
12
u
104
+ 29u
103
+ ··· + 20u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
104
+ 45y
103
+ ··· + 126804y + 1
c
2
, c
5
y
104
+ 41y
103
+ ··· + 124y + 1
c
3
y
104
− 455y
103
+ ··· + 1024648387080y + 31656593929
c
4
y
104
+ 425y
103
+ ··· + 199112y + 1681
c
6
, c
9
y
104
+ 65y
103
+ ··· + 20y + 1
c
7
, c
11
y
104
+ 29y
103
+ ··· + 20y + 1
c
8
y
104
+ 5y
103
+ ··· − 12y + 1
c
10
, c
12
y
104
+ 93y
103
+ ··· − 4y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.505387 + 0.862142I
a = −6.9147 − 13.2965I
b = −0.015623 + 1.032430I
1.40373 − 0.79963I 0
u = 0.505387 − 0.862142I
a = −6.9147 + 13.2965I
b = −0.015623 − 1.032430I
1.40373 + 0.79963I 0
u = 0.501219 + 0.873062I
a = 13.51170 + 2.65015I
b = 0.038652 − 1.005710I
1.36834 + 4.88130I 0
u = 0.501219 − 0.873062I
a = 13.51170 − 2.65015I
b = 0.038652 + 1.005710I
1.36834 − 4.88130I 0
u = 0.996201 + 0.173488I
a = 0.392374 + 0.187730I
b = 0.332779 − 0.565610I
5.81316 − 2.80924I 0
u = 0.996201 − 0.173488I
a = 0.392374 − 0.187730I
b = 0.332779 + 0.565610I
5.81316 + 2.80924I 0
u = −0.586727 + 0.827689I
a = −0.096700 + 1.025660I
b = 0.81719 + 1.39541I
2.94293 + 0.22991I 0
u = −0.586727 − 0.827689I
a = −0.096700 − 1.025660I
b = 0.81719 − 1.39541I
2.94293 − 0.22991I 0
u = 0.988414 + 0.247276I
a = −0.405864 − 0.194160I
b = −0.334041 + 0.546829I
5.78547 + 3.15535I 0
u = 0.988414 − 0.247276I
a = −0.405864 + 0.194160I
b = −0.334041 − 0.546829I
5.78547 − 3.15535I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.836334 + 0.599618I
a = −1.38843 − 0.45981I
b = −1.013470 + 0.146587I
7.69993 + 7.02828I 0
u = −0.836334 − 0.599618I
a = −1.38843 + 0.45981I
b = −1.013470 − 0.146587I
7.69993 − 7.02828I 0
u = 0.412346 + 0.942918I
a = 1.73833 − 2.45352I
b = 0.123181 + 1.085540I
−3.31178 + 1.98558I 0
u = 0.412346 − 0.942918I
a = 1.73833 + 2.45352I
b = 0.123181 − 1.085540I
−3.31178 − 1.98558I 0
u = −0.607552 + 0.837105I
a = 1.37091 + 0.92114I
b = 1.292200 − 0.191558I
3.03222 − 2.39899I 0
u = −0.607552 − 0.837105I
a = 1.37091 − 0.92114I
b = 1.292200 + 0.191558I
3.03222 + 2.39899I 0
u = −0.581639 + 0.858516I
a = 2.05036 + 0.18942I
b = 0.57922 − 1.63420I
2.85030 − 4.87673I 0
u = −0.581639 − 0.858516I
a = 2.05036 − 0.18942I
b = 0.57922 + 1.63420I
2.85030 + 4.87673I 0
u = −0.816116 + 0.645065I
a = 1.37577 + 0.50366I
b = 1.033450 − 0.153354I
8.39953 + 0.74620I 0
u = −0.816116 − 0.645065I
a = 1.37577 − 0.50366I
b = 1.033450 + 0.153354I
8.39953 − 0.74620I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.530773 + 0.778902I
a = −1.99026 − 0.06316I
b = −0.33699 + 1.68216I
2.11332 + 1.88283I 0
u = −0.530773 − 0.778902I
a = −1.99026 + 0.06316I
b = −0.33699 − 1.68216I
2.11332 − 1.88283I 0
u = −0.843149 + 0.398961I
a = −0.796579 − 0.889832I
b = −0.537396 − 1.228480I
−2.96530 + 7.47434I 0
u = −0.843149 − 0.398961I
a = −0.796579 + 0.889832I
b = −0.537396 + 1.228480I
−2.96530 − 7.47434I 0
u = −0.562569 + 0.913650I
a = 0.450930 − 0.767392I
b = −0.67940 − 1.58168I
1.65712 − 6.30829I 0
u = −0.562569 − 0.913650I
a = 0.450930 + 0.767392I
b = −0.67940 + 1.58168I
1.65712 + 6.30829I 0
u = −0.063215 + 1.078180I
a = −0.386819 − 0.988960I
b = 0.227112 + 1.304850I
−5.04325 + 2.34615I 0
u = −0.063215 − 1.078180I
a = −0.386819 + 0.988960I
b = 0.227112 − 1.304850I
−5.04325 − 2.34615I 0
u = −0.953692 + 0.515568I
a = 0.682831 + 0.711222I
b = 0.554982 + 1.263190I
4.94747 + 6.36433I 0
u = −0.953692 − 0.515568I
a = 0.682831 − 0.711222I
b = 0.554982 − 1.263190I
4.94747 − 6.36433I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.553236 + 0.727396I
a = −0.386426 + 0.064707I
b = −0.101505 + 0.353271I
0.11772 + 1.44824I 0
u = 0.553236 − 0.727396I
a = −0.386426 − 0.064707I
b = −0.101505 − 0.353271I
0.11772 − 1.44824I 0
u = −0.977564 + 0.488443I
a = −0.721488 − 0.693464I
b = −0.547978 − 1.264760I
4.22367 + 12.57380I 0
u = −0.977564 − 0.488443I
a = −0.721488 + 0.693464I
b = −0.547978 + 1.264760I
4.22367 − 12.57380I 0
u = 0.161347 + 1.083530I
a = −0.198232 − 0.559806I
b = −0.565720 − 0.200757I
1.13917 + 6.36070I 0
u = 0.161347 − 1.083530I
a = −0.198232 + 0.559806I
b = −0.565720 + 0.200757I
1.13917 − 6.36070I 0
u = 0.255973 + 1.066190I
a = 0.168535 + 0.484109I
b = 0.497613 + 0.161245I
1.62262 + 0.79893I 0
u = 0.255973 − 1.066190I
a = 0.168535 − 0.484109I
b = 0.497613 − 0.161245I
1.62262 − 0.79893I 0
u = −0.737290 + 0.506701I
a = 0.594472 + 0.998715I
b = 0.582907 + 1.204340I
0.12101 + 3.83292I 0
u = −0.737290 − 0.506701I
a = 0.594472 − 0.998715I
b = 0.582907 − 1.204340I
0.12101 − 3.83292I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.397803 + 0.796446I
a = 2.13538 − 1.07987I
b = 0.124948 − 0.824931I
−2.81189 + 1.48523I 0
u = 0.397803 − 0.796446I
a = 2.13538 + 1.07987I
b = 0.124948 + 0.824931I
−2.81189 − 1.48523I 0
u = −0.244913 + 1.089920I
a = 0.534481 + 0.533393I
b = −0.27978 − 1.39230I
−7.44706 − 1.35876I 0
u = −0.244913 − 1.089920I
a = 0.534481 − 0.533393I
b = −0.27978 + 1.39230I
−7.44706 + 1.35876I 0
u = −0.563984 + 0.974977I
a = −0.967704 − 1.012100I
b = −1.267190 − 0.108109I
−1.16734 − 6.56904I 0
u = −0.563984 − 0.974977I
a = −0.967704 + 1.012100I
b = −1.267190 + 0.108109I
−1.16734 + 6.56904I 0
u = 0.563323 + 0.976069I
a = 0.214860 + 0.203704I
b = 0.301646 − 0.087160I
−0.88605 + 3.09648I 0
u = 0.563323 − 0.976069I
a = 0.214860 − 0.203704I
b = 0.301646 + 0.087160I
−0.88605 − 3.09648I 0
u = 0.664866 + 0.555061I
a = 0.150859 + 0.411065I
b = 0.197184 + 0.715235I
0.20121 + 1.54957I 0
u = 0.664866 − 0.555061I
a = 0.150859 − 0.411065I
b = 0.197184 − 0.715235I
0.20121 − 1.54957I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.541563 + 1.038640I
a = −1.92835 − 0.47733I
b = −0.68081 + 1.34674I
−5.56704 − 5.39461I 0
u = −0.541563 − 1.038640I
a = −1.92835 + 0.47733I
b = −0.68081 − 1.34674I
−5.56704 + 5.39461I 0
u = −0.139441 + 0.815286I
a = −0.107784 − 0.995643I
b = −0.688124 − 0.558770I
−3.50757 + 1.44378I −7.49193 − 4.44049I
u = −0.139441 − 0.815286I
a = −0.107784 + 0.995643I
b = −0.688124 + 0.558770I
−3.50757 − 1.44378I −7.49193 + 4.44049I
u = 0.791541 + 0.865692I
a = −0.925362 − 0.291803I
b = −0.239348 − 0.862721I
−0.53591 + 3.95919I 0
u = 0.791541 − 0.865692I
a = −0.925362 + 0.291803I
b = −0.239348 + 0.862721I
−0.53591 − 3.95919I 0
u = 0.598103 + 1.032470I
a = −1.60013 + 0.38394I
b = −0.209568 − 0.988716I
−1.29854 + 3.50304I 0
u = 0.598103 − 1.032470I
a = −1.60013 − 0.38394I
b = −0.209568 + 0.988716I
−1.29854 − 3.50304I 0
u = −0.626822 + 1.054980I
a = 1.86254 + 0.41719I
b = 0.61435 − 1.37730I
−1.48010 − 9.03843I 0
u = −0.626822 − 1.054980I
a = 1.86254 − 0.41719I
b = 0.61435 + 1.37730I
−1.48010 + 9.03843I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.786160 + 0.943347I
a = −0.347310 − 0.183982I
b = −0.362772 + 0.261162I
4.64197 + 0.21423I 0
u = 0.786160 − 0.943347I
a = −0.347310 + 0.183982I
b = −0.362772 − 0.261162I
4.64197 − 0.21423I 0
u = 0.574664 + 0.511013I
a = −0.617338 − 0.139145I
b = −0.206183 + 0.494096I
0.254275 + 1.333160I 3.09253 − 3.95569I
u = 0.574664 − 0.511013I
a = −0.617338 + 0.139145I
b = −0.206183 − 0.494096I
0.254275 − 1.333160I 3.09253 + 3.95569I
u = −0.695804 + 1.019420I
a = 1.014300 + 0.770211I
b = 1.146680 + 0.007195I
7.25970 − 6.40842I 0
u = −0.695804 − 1.019420I
a = 1.014300 − 0.770211I
b = 1.146680 − 0.007195I
7.25970 + 6.40842I 0
u = 0.763291 + 0.985949I
a = 0.335597 + 0.197355I
b = 0.375401 − 0.234733I
4.46281 + 6.08285I 0
u = 0.763291 − 0.985949I
a = 0.335597 − 0.197355I
b = 0.375401 + 0.234733I
4.46281 − 6.08285I 0
u = 0.098837 + 0.743321I
a = 1.89127 + 0.34280I
b = 0.391631 − 0.750203I
0.25747 − 2.49818I −1.86836 + 3.61739I
u = 0.098837 − 0.743321I
a = 1.89127 − 0.34280I
b = 0.391631 + 0.750203I
0.25747 + 2.49818I −1.86836 − 3.61739I
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.050370 + 0.680338I
a = 0.563271 + 0.072512I
b = 0.318996 + 0.781931I
5.32160 + 0.40661I 0
u = 1.050370 − 0.680338I
a = 0.563271 − 0.072512I
b = 0.318996 − 0.781931I
5.32160 − 0.40661I 0
u = −0.687882 + 1.051100I
a = −0.974401 − 0.763916I
b = −1.133250 − 0.023746I
6.3250 − 12.7173I 0
u = −0.687882 − 1.051100I
a = −0.974401 + 0.763916I
b = −1.133250 + 0.023746I
6.3250 + 12.7173I 0
u = −0.097678 + 1.256820I
a = 0.096434 + 0.703259I
b = −0.307554 − 1.285720I
−8.65151 + 4.70512I 0
u = −0.097678 − 1.256820I
a = 0.096434 − 0.703259I
b = −0.307554 + 1.285720I
−8.65151 − 4.70512I 0
u = −0.276156 + 0.675129I
a = −1.84613 − 0.61832I
b = −0.753175 + 0.632458I
−0.01020 + 2.19701I −2.29099 − 5.45111I
u = −0.276156 − 0.675129I
a = −1.84613 + 0.61832I
b = −0.753175 − 0.632458I
−0.01020 − 2.19701I −2.29099 + 5.45111I
u = 1.048900 + 0.737652I
a = −0.604511 − 0.068297I
b = −0.320223 − 0.798682I
5.20836 + 6.36397I 0
u = 1.048900 − 0.737652I
a = −0.604511 + 0.068297I
b = −0.320223 + 0.798682I
5.20836 − 6.36397I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.625889 + 1.119740I
a = −1.82121 − 0.45820I
b = −0.59532 + 1.34507I
−5.09982 − 12.90830I 0
u = −0.625889 − 1.119740I
a = −1.82121 + 0.45820I
b = −0.59532 − 1.34507I
−5.09982 + 12.90830I 0
u = −0.435139 + 0.541580I
a = −1.75759 − 0.57039I
b = −0.843804 + 0.397536I
−0.03969 + 2.18859I 0. − 5.53183I
u = −0.435139 − 0.541580I
a = −1.75759 + 0.57039I
b = −0.843804 − 0.397536I
−0.03969 − 2.18859I 0. + 5.53183I
u = 0.538328 + 1.211250I
a = 1.020570 − 0.702140I
b = 0.269635 + 1.049080I
−3.27693 + 5.64208I 0
u = 0.538328 − 1.211250I
a = 1.020570 + 0.702140I
b = 0.269635 − 1.049080I
−3.27693 − 5.64208I 0
u = −0.702251 + 1.128830I
a = 1.77074 + 0.42168I
b = 0.56556 − 1.35944I
3.05623 − 12.40750I 0
u = −0.702251 − 1.128830I
a = 1.77074 − 0.42168I
b = 0.56556 + 1.35944I
3.05623 + 12.40750I 0
u = −0.699999 + 1.148730I
a = −1.76232 − 0.43473I
b = −0.56292 + 1.35286I
2.1837 − 18.6708I 0
u = −0.699999 − 1.148730I
a = −1.76232 + 0.43473I
b = −0.56292 − 1.35286I
2.1837 + 18.6708I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.084454 + 1.345260I
a = 0.215536 − 0.791522I
b = 0.312103 + 1.212010I
−2.26641 + 3.85361I 0
u = 0.084454 − 1.345260I
a = 0.215536 + 0.791522I
b = 0.312103 − 1.212010I
−2.26641 − 3.85361I 0
u = 0.035100 + 1.381650I
a = −0.180333 + 0.713414I
b = −0.328473 − 1.223950I
−2.91423 + 9.64392I 0
u = 0.035100 − 1.381650I
a = −0.180333 − 0.713414I
b = −0.328473 + 1.223950I
−2.91423 − 9.64392I 0
u = 0.570798 + 0.171210I
a = −0.024673 − 0.218918I
b = 0.225209 + 0.629606I
0.348138 + 1.250510I 4.33846 − 5.62577I
u = 0.570798 − 0.171210I
a = −0.024673 + 0.218918I
b = 0.225209 − 0.629606I
0.348138 − 1.250510I 4.33846 + 5.62577I
u = −0.512414 + 0.300789I
a = −0.80972 − 1.57315I
b = −0.481029 − 1.099690I
−3.73698 + 1.08033I −4.99609 − 1.21844I
u = −0.512414 − 0.300789I
a = −0.80972 + 1.57315I
b = −0.481029 + 1.099690I
−3.73698 − 1.08033I −4.99609 + 1.21844I
u = 0.74819 + 1.25033I
a = −0.918808 + 0.360469I
b = −0.317197 − 0.990579I
2.80756 + 3.24354I 0
u = 0.74819 − 1.25033I
a = −0.918808 − 0.360469I
b = −0.317197 + 0.990579I
2.80756 − 3.24354I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.71866 + 1.28682I
a = 0.892581 − 0.408496I
b = 0.321440 + 1.004820I
2.50531 + 9.13493I 0
u = 0.71866 − 1.28682I
a = 0.892581 + 0.408496I
b = 0.321440 − 1.004820I
2.50531 − 9.13493I 0
u = 0.0390323 + 0.0478117I
a = −15.0554 − 16.4608I
b = −0.035216 + 1.097540I
1.42493 + 2.89189I −2.46424 − 2.96057I
u = 0.0390323 − 0.0478117I
a = −15.0554 + 16.4608I
b = −0.035216 − 1.097540I
1.42493 − 2.89189I −2.46424 + 2.96057I
15
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
104
+ 41u
103
+ ··· + 124u + 1
c
2
, c
5
u
104
+ u
103
+ ··· − 18u + 1
c
3
u
104
+ 11u
103
+ ··· − 231098u + 177923
c
4
u
104
+ 23u
103
+ ··· + 128u + 41
c
6
, c
9
u
104
+ 5u
103
+ ··· + 10u
2
+ 1
c
7
, c
11
u
104
− 5u
103
+ ··· − 2u + 1
c
8
u
104
+ u
103
+ ··· − 10u + 1
c
10
, c
12
u
104
+ 29u
103
+ ··· + 20u + 1
16
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
104
+ 45y
103
+ ··· + 126804y + 1
c
2
, c
5
y
104
+ 41y
103
+ ··· + 124y + 1
c
3
y
104
− 455y
103
+ ··· + 1024648387080y + 31656593929
c
4
y
104
+ 425y
103
+ ··· + 199112y + 1681
c
6
, c
9
y
104
+ 65y
103
+ ··· + 20y + 1
c
7
, c
11
y
104
+ 29y
103
+ ··· + 20y + 1
c
8
y
104
+ 5y
103
+ ··· − 12y + 1
c
10
, c
12
y
104
+ 93y
103
+ ··· − 4y + 1
17
