12a
0624
(K12a
0624
)
A knot diagram
1
Linearized knot diagam
3 7 10 8 11 2 12 4 1 6 5 9
Solving Sequence
2,6
7 3
1,11
5 12 8 4 10 9
c
6
c
2
c
1
c
5
c
11
c
7
c
4
c
10
c
9
c
3
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.10901 × 10
159
u
88
+ 2.62824 × 10
159
u
87
+ ··· + 1.74259 × 10
159
b − 7.22250 × 10
158
,
1.79918 × 10
161
u
88
− 4.32262 × 10
161
u
87
+ ··· + 5.75056 × 10
160
a + 7.55383 × 10
161
, u
89
− 3u
88
+ ··· + 25u − 3i
* 1 irreducible components of dim
C
= 0, with total 89 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−1.11 × 10
159
u
88
+ 2.63 × 10
159
u
87
+ · · · + 1.74 × 10
159
b − 7.22 ×
10
158
, 1.80 × 10
161
u
88
− 4.32 × 10
161
u
87
+ · · · + 5.75 × 10
160
a + 7.55 ×
10
161
, u
89
− 3u
88
+ · · · + 25u − 3i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
7
=
1
u
2
a
3
=
−u
−u
3
+ u
a
1
=
u
3
u
5
− u
3
+ u
a
11
=
−3.12871u
88
+ 7.51688u
87
+ ··· + 109.415u − 13.1358
0.636414u
88
− 1.50823u
87
+ ··· − 12.0674u + 0.414469
a
5
=
−0.231096u
88
+ 1.01234u
87
+ ··· + 61.7683u − 10.7288
2.08200u
88
− 5.19544u
87
+ ··· − 80.1291u + 10.3551
a
12
=
0.150566u
88
− 0.137480u
87
+ ··· + 30.2309u − 11.3078
0.986969u
88
− 2.61086u
87
+ ··· − 53.1782u + 9.36670
a
8
=
2.53343u
88
− 7.13992u
87
+ ··· − 147.071u + 17.9792
−1.56685u
88
+ 3.59942u
87
+ ··· + 37.5502u − 2.31927
a
4
=
−0.887414u
88
+ 1.10529u
87
+ ··· − 9.46301u + 6.49474
0.853902u
88
− 2.02191u
87
+ ··· − 14.8570u + 0.758719
a
10
=
−3.76513u
88
+ 9.02512u
87
+ ··· + 121.482u − 13.5503
0.636414u
88
− 1.50823u
87
+ ··· − 12.0674u + 0.414469
a
9
=
−3.82241u
88
+ 9.23994u
87
+ ··· + 126.692u − 14.4481
0.00747695u
88
+ 0.0854807u
87
+ ··· + 14.4719u − 3.62999
(ii) Obstruction class = −1
(iii) Cusp Shapes = 15.1083u
88
− 38.1525u
87
+ ··· − 579.178u + 94.3288
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
89
+ 37u
88
+ ··· + 229u + 9
c
2
, c
6
u
89
− 3u
88
+ ··· + 25u − 3
c
3
1089(1089u
89
+ 13233u
88
+ ··· + 2115u − 259)
c
4
, c
8
u
89
− 3u
88
+ ··· + 25u − 3
c
5
, c
10
, c
11
u
89
+ u
88
+ ··· − 15u − 1
c
7
1089(1089u
89
+ 9075u
88
+ ··· + 8757765u − 5706775)
c
9
, c
12
u
89
− u
88
+ ··· + 17u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
89
+ 31y
88
+ ··· − 20963y −81
c
2
, c
6
y
89
− 37y
88
+ ··· + 229y −9
c
3
1185921(1185921y
89
− 1.88147 × 10
7
y
88
+ ··· + 2227177y −67081)
c
4
, c
8
y
89
+ 63y
88
+ ··· − 59y −9
c
5
, c
10
, c
11
y
89
+ 91y
88
+ ··· + 53y −1
c
7
1185921(1185921y
89
+ 6.81921 × 10
7
y
88
+ ··· + 9.41156 × 10
13
y −3.25673 × 10
13
)
c
9
, c
12
y
89
− 57y
88
+ ··· + 53y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.532636 + 0.845551I
a = −0.329471 + 0.111426I
b = 0.777464 − 0.546287I
2.17262 − 7.81441I 0
u = −0.532636 − 0.845551I
a = −0.329471 − 0.111426I
b = 0.777464 + 0.546287I
2.17262 + 7.81441I 0
u = −0.697190 + 0.706132I
a = 0.852079 − 1.052030I
b = −0.434773 − 0.748501I
4.50784 + 1.34674I 0
u = −0.697190 − 0.706132I
a = 0.852079 + 1.052030I
b = −0.434773 + 0.748501I
4.50784 − 1.34674I 0
u = 0.880484 + 0.453167I
a = 0.53480 + 3.00940I
b = 0.05012 + 1.51610I
−3.69992 − 1.85198I 0
u = 0.880484 − 0.453167I
a = 0.53480 − 3.00940I
b = 0.05012 − 1.51610I
−3.69992 + 1.85198I 0
u = −0.376262 + 0.908508I
a = −0.164022 − 0.085627I
b = 0.384148 + 0.325837I
1.41143 + 3.84397I 0
u = −0.376262 − 0.908508I
a = −0.164022 + 0.085627I
b = 0.384148 − 0.325837I
1.41143 − 3.84397I 0
u = −0.938175 + 0.401004I
a = −1.55412 + 1.82139I
b = −0.17732 + 1.87270I
−7.13369 + 1.50478I 0
u = −0.938175 − 0.401004I
a = −1.55412 − 1.82139I
b = −0.17732 − 1.87270I
−7.13369 − 1.50478I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.550397 + 0.885902I
a = 0.256430 + 0.103414I
b = −0.613597 − 0.295317I
5.86436 + 2.38119I 0
u = 0.550397 − 0.885902I
a = 0.256430 − 0.103414I
b = −0.613597 + 0.295317I
5.86436 − 2.38119I 0
u = −0.990809 + 0.326016I
a = −0.298513 + 0.540908I
b = −0.057054 + 0.487891I
−1.55145 + 1.37502I 0
u = −0.990809 − 0.326016I
a = −0.298513 − 0.540908I
b = −0.057054 − 0.487891I
−1.55145 − 1.37502I 0
u = 0.905252 + 0.530463I
a = 4.64241 + 0.47408I
b = −0.197180 − 0.025948I
−0.10358 − 2.04661I 0
u = 0.905252 − 0.530463I
a = 4.64241 − 0.47408I
b = −0.197180 + 0.025948I
−0.10358 + 2.04661I 0
u = −0.938122 + 0.518125I
a = −2.25920 + 1.17993I
b = 0.190351 + 1.357710I
−3.10521 + 2.76714I 0
u = −0.938122 − 0.518125I
a = −2.25920 − 1.17993I
b = 0.190351 − 1.357710I
−3.10521 − 2.76714I 0
u = −0.782728 + 0.488112I
a = 0.342336 + 0.940192I
b = −0.246621 − 0.071250I
−1.50935 + 2.07388I 0
u = −0.782728 − 0.488112I
a = 0.342336 − 0.940192I
b = −0.246621 + 0.071250I
−1.50935 − 2.07388I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.480693 + 0.965063I
a = −0.269333 + 0.692506I
b = 0.26611 + 1.53970I
−4.63843 + 11.63310I 0
u = 0.480693 − 0.965063I
a = −0.269333 − 0.692506I
b = 0.26611 − 1.53970I
−4.63843 − 11.63310I 0
u = 0.876714 + 0.264843I
a = 1.106160 + 0.454993I
b = 0.640905 + 1.124090I
−5.48696 + 0.76037I 0
u = 0.876714 − 0.264843I
a = 1.106160 − 0.454993I
b = 0.640905 − 1.124090I
−5.48696 − 0.76037I 0
u = 0.979855 + 0.475807I
a = 1.52486 + 1.95549I
b = −0.54385 + 1.67907I
−6.57605 − 4.05853I 0
u = 0.979855 − 0.475807I
a = 1.52486 − 1.95549I
b = −0.54385 − 1.67907I
−6.57605 + 4.05853I 0
u = 0.370514 + 0.813878I
a = 0.199700 − 0.361091I
b = −0.27361 − 1.53199I
−8.84893 + 6.12735I 0
u = 0.370514 − 0.813878I
a = 0.199700 + 0.361091I
b = −0.27361 + 1.53199I
−8.84893 − 6.12735I 0
u = 0.977486 + 0.532227I
a = 0.550302 + 0.974106I
b = −0.613667 + 0.315224I
−0.16594 − 4.11744I 0
u = 0.977486 − 0.532227I
a = 0.550302 − 0.974106I
b = −0.613667 − 0.315224I
−0.16594 + 4.11744I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.776189 + 0.801927I
a = 0.608392 + 0.186860I
b = −0.05077 + 1.43405I
−6.71130 − 2.95857I 0
u = 0.776189 − 0.801927I
a = 0.608392 − 0.186860I
b = −0.05077 − 1.43405I
−6.71130 + 2.95857I 0
u = 0.592682 + 0.654546I
a = −0.968450 − 0.900276I
b = 0.824689 − 0.582850I
2.14298 + 2.52868I 0
u = 0.592682 − 0.654546I
a = −0.968450 + 0.900276I
b = 0.824689 + 0.582850I
2.14298 − 2.52868I 0
u = −1.005190 + 0.529887I
a = −0.43796 + 1.39245I
b = 1.077510 + 0.640281I
−3.80322 + 6.41139I 0
u = −1.005190 − 0.529887I
a = −0.43796 − 1.39245I
b = 1.077510 − 0.640281I
−3.80322 − 6.41139I 0
u = 1.144320 + 0.059059I
a = −0.398793 + 0.894332I
b = −0.516834 + 0.697007I
−4.07816 − 6.32536I 0
u = 1.144320 − 0.059059I
a = −0.398793 − 0.894332I
b = −0.516834 − 0.697007I
−4.07816 + 6.32536I 0
u = −0.964012 + 0.634990I
a = 0.133390 − 0.352220I
b = 0.590169 − 0.621489I
3.68544 + 3.81135I 0
u = −0.964012 − 0.634990I
a = 0.133390 + 0.352220I
b = 0.590169 + 0.621489I
3.68544 − 3.81135I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.420226 + 1.077630I
a = 0.121883 + 0.882947I
b = −0.17022 + 1.41805I
0.39074 − 5.12452I 0
u = −0.420226 − 1.077630I
a = 0.121883 − 0.882947I
b = −0.17022 − 1.41805I
0.39074 + 5.12452I 0
u = 1.003450 + 0.603777I
a = −0.356046 + 0.311967I
b = −1.014410 − 0.523135I
0.92594 − 7.45495I 0
u = 1.003450 − 0.603777I
a = −0.356046 − 0.311967I
b = −1.014410 + 0.523135I
0.92594 + 7.45495I 0
u = −0.663274 + 0.482007I
a = −0.383552 − 0.098579I
b = −0.081911 + 1.222220I
−2.31044 + 1.39236I 6.00000 − 4.34365I
u = −0.663274 − 0.482007I
a = −0.383552 + 0.098579I
b = −0.081911 − 1.222220I
−2.31044 − 1.39236I 6.00000 + 4.34365I
u = −1.112340 + 0.394289I
a = −0.322205 + 0.390018I
b = −0.003884 + 0.449466I
−1.56596 + 1.33194I 0
u = −1.112340 − 0.394289I
a = −0.322205 − 0.390018I
b = −0.003884 − 0.449466I
−1.56596 − 1.33194I 0
u = −1.206400 + 0.133026I
a = 0.43556 − 2.50716I
b = 0.15758 − 1.60691I
−14.1434 − 3.4037I 0
u = −1.206400 − 0.133026I
a = 0.43556 + 2.50716I
b = 0.15758 + 1.60691I
−14.1434 + 3.4037I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.781572 + 0.064438I
a = −0.076040 − 1.012340I
b = −0.766778 + 0.017173I
−2.05830 − 2.27656I 1.43905 + 3.82974I
u = −0.781572 − 0.064438I
a = −0.076040 + 1.012340I
b = −0.766778 − 0.017173I
−2.05830 + 2.27656I 1.43905 − 3.82974I
u = 0.638409 + 0.407830I
a = −0.756928 − 0.235077I
b = 0.545634 + 0.053149I
0.925151 − 0.025658I 11.59100 − 0.67651I
u = 0.638409 − 0.407830I
a = −0.756928 + 0.235077I
b = 0.545634 − 0.053149I
0.925151 + 0.025658I 11.59100 + 0.67651I
u = −0.277680 + 0.700999I
a = −0.473863 − 0.710002I
b = 0.126131 − 1.373140I
−3.64108 − 2.19676I 3.44360 + 2.93374I
u = −0.277680 − 0.700999I
a = −0.473863 + 0.710002I
b = 0.126131 + 1.373140I
−3.64108 + 2.19676I 3.44360 − 2.93374I
u = −1.115820 + 0.562928I
a = 1.68042 − 1.98048I
b = −0.19932 − 1.46094I
−5.99017 + 7.03073I 0
u = −1.115820 − 0.562928I
a = 1.68042 + 1.98048I
b = −0.19932 + 1.46094I
−5.99017 − 7.03073I 0
u = 0.719293 + 0.152338I
a = 1.93280 − 1.48228I
b = 0.040871 − 1.218320I
−5.14999 − 0.88242I −2.43783 − 0.67572I
u = 0.719293 − 0.152338I
a = 1.93280 + 1.48228I
b = 0.040871 + 1.218320I
−5.14999 + 0.88242I −2.43783 + 0.67572I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.999056 + 0.783476I
a = 0.419737 + 0.001742I
b = −0.173174 − 0.368674I
−0.89057 + 3.16272I 0
u = −0.999056 − 0.783476I
a = 0.419737 − 0.001742I
b = −0.173174 + 0.368674I
−0.89057 − 3.16272I 0
u = 1.118450 + 0.601095I
a = −1.60533 − 1.82197I
b = 0.33141 − 1.59528I
−11.0564 − 11.3845I 0
u = 1.118450 − 0.601095I
a = −1.60533 + 1.82197I
b = 0.33141 + 1.59528I
−11.0564 + 11.3845I 0
u = −1.081930 + 0.666173I
a = 0.589579 − 1.180870I
b = −0.849627 − 0.630203I
0.50737 + 13.44270I 0
u = −1.081930 − 0.666173I
a = 0.589579 + 1.180870I
b = −0.849627 + 0.630203I
0.50737 − 13.44270I 0
u = 1.081650 + 0.685039I
a = −0.436996 − 0.839442I
b = 0.679308 − 0.435513I
4.23970 − 8.17310I 0
u = 1.081650 − 0.685039I
a = −0.436996 + 0.839442I
b = 0.679308 + 0.435513I
4.23970 + 8.17310I 0
u = 0.515945 + 1.185570I
a = −0.281752 − 0.887380I
b = 0.08841 − 1.44924I
−4.35102 − 5.41923I 0
u = 0.515945 − 1.185570I
a = −0.281752 + 0.887380I
b = 0.08841 + 1.44924I
−4.35102 + 5.41923I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.327490 + 0.027957I
a = 0.10271 − 2.52885I
b = −0.16454 − 1.56585I
−11.5806 + 8.8691I 0
u = −1.327490 − 0.027957I
a = 0.10271 + 2.52885I
b = −0.16454 + 1.56585I
−11.5806 − 8.8691I 0
u = 1.147680 + 0.689108I
a = 1.65716 + 1.78257I
b = −0.29117 + 1.57845I
−6.7006 − 17.6575I 0
u = 1.147680 − 0.689108I
a = 1.65716 − 1.78257I
b = −0.29117 − 1.57845I
−6.7006 + 17.6575I 0
u = 1.267310 + 0.467819I
a = −0.91083 − 2.20761I
b = 0.01027 − 1.47606I
−7.83136 − 1.39336I 0
u = 1.267310 − 0.467819I
a = −0.91083 + 2.20761I
b = 0.01027 + 1.47606I
−7.83136 + 1.39336I 0
u = −1.189860 + 0.697067I
a = −1.37002 + 1.77825I
b = 0.22269 + 1.48583I
−2.01069 + 11.42240I 0
u = −1.189860 − 0.697067I
a = −1.37002 − 1.77825I
b = 0.22269 − 1.48583I
−2.01069 − 11.42240I 0
u = −0.418699 + 0.448760I
a = 0.404715 − 0.840956I
b = −0.796403 + 0.426983I
−2.30355 − 2.21445I 3.22069 + 4.46897I
u = −0.418699 − 0.448760I
a = 0.404715 + 0.840956I
b = −0.796403 − 0.426983I
−2.30355 + 2.21445I 3.22069 − 4.46897I
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.39312 + 0.29865I
a = −0.46862 − 2.25091I
b = 0.00664 − 1.48464I
−7.91900 − 1.38899I 0
u = 1.39312 − 0.29865I
a = −0.46862 + 2.25091I
b = 0.00664 + 1.48464I
−7.91900 + 1.38899I 0
u = 0.260475 + 0.428192I
a = −1.01332 + 2.07686I
b = 0.331226 + 0.424317I
1.05980 − 1.42675I 5.79067 − 2.39869I
u = 0.260475 − 0.428192I
a = −1.01332 − 2.07686I
b = 0.331226 − 0.424317I
1.05980 + 1.42675I 5.79067 + 2.39869I
u = 1.18916 + 0.92841I
a = 0.85483 + 1.23080I
b = −0.04060 + 1.47076I
−6.95103 − 3.87677I 0
u = 1.18916 − 0.92841I
a = 0.85483 − 1.23080I
b = −0.04060 − 1.47076I
−6.95103 + 3.87677I 0
u = 0.451678
a = −1.04395
b = 0.420289
0.782505 13.3570
u = 0.224099 + 0.200594I
a = 2.26767 − 2.14874I
b = 0.22553 + 1.43813I
−5.13057 + 0.63128I 1.44985 − 0.35366I
u = 0.224099 − 0.200594I
a = 2.26767 + 2.14874I
b = 0.22553 − 1.43813I
−5.13057 − 0.63128I 1.44985 + 0.35366I
13
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
89
+ 37u
88
+ ··· + 229u + 9
c
2
, c
6
u
89
− 3u
88
+ ··· + 25u − 3
c
3
1089(1089u
89
+ 13233u
88
+ ··· + 2115u − 259)
c
4
, c
8
u
89
− 3u
88
+ ··· + 25u − 3
c
5
, c
10
, c
11
u
89
+ u
88
+ ··· − 15u − 1
c
7
1089(1089u
89
+ 9075u
88
+ ··· + 8757765u − 5706775)
c
9
, c
12
u
89
− u
88
+ ··· + 17u − 1
14
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
89
+ 31y
88
+ ··· − 20963y −81
c
2
, c
6
y
89
− 37y
88
+ ··· + 229y −9
c
3
1185921(1185921y
89
− 1.88147 × 10
7
y
88
+ ··· + 2227177y −67081)
c
4
, c
8
y
89
+ 63y
88
+ ··· − 59y −9
c
5
, c
10
, c
11
y
89
+ 91y
88
+ ··· + 53y −1
c
7
1185921(1185921y
89
+ 6.81921 × 10
7
y
88
+ ··· + 9.41156 × 10
13
y −3.25673 × 10
13
)
c
9
, c
12
y
89
− 57y
88
+ ··· + 53y −1
15
