12a
0612
(K12a
0612
)
A knot diagram
1
Linearized knot diagam
3 7 9 12 11 2 10 6 1 8 5 4
Solving Sequence
4,12
5
1,9
10 3 2 11 6 8 7
c
4
c
12
c
9
c
3
c
1
c
11
c
5
c
8
c
7
c
2
, c
6
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−2.18462 × 10
73
u
73
+ 3.16063 × 10
73
u
72
+ ··· + 5.40007 × 10
73
b − 3.24788 × 10
72
,
− 2.10222 × 10
73
u
73
− 1.17709 × 10
73
u
72
+ ··· + 2.16003 × 10
74
a − 7.97915 × 10
74
, u
74
− 2u
73
+ ··· − 5u + 1i
I
u
2
= hb, 2a + 1, u
2
− u + 1i
* 2 irreducible components of dim
C
= 0, with total 76 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−2.18×10
73
u
73
+3.16×10
73
u
72
+· · ·+5.40×10
73
b−3.25×10
72
, −2.10×
10
73
u
73
−1.18×10
73
u
72
+· · ·+2.16×10
74
a−7.98×10
74
, u
74
−2u
73
+· · ·−5u+1i
(i) Arc colorings
a
4
=
1
0
a
12
=
0
u
a
5
=
1
−u
2
a
1
=
u
u
a
9
=
0.0973237u
73
+ 0.0544942u
72
+ ··· − 7.75879u + 3.69400
0.404554u
73
− 0.585294u
72
+ ··· + 2.13148u + 0.0601452
a
10
=
0.0724192u
73
+ 0.00246463u
72
+ ··· − 7.32492u + 3.66868
0.379649u
73
− 0.637323u
72
+ ··· + 2.56535u + 0.0348175
a
3
=
1.52542u
73
− 2.53855u
72
+ ··· + 1.82716u − 0.738325
0.550001u
73
− 0.984294u
72
+ ··· + 1.31434u − 0.000117455
a
2
=
−1.45206u
73
+ 3.42469u
72
+ ··· − 9.87487u + 1.52722
−0.301071u
73
+ 0.447914u
72
+ ··· + 0.617849u − 0.0822885
a
11
=
−u
u
3
+ u
a
6
=
u
2
+ 1
−u
4
− 2u
2
a
8
=
−0.317026u
73
+ 0.923011u
72
+ ··· − 6.65577u + 3.92960
0.433026u
73
− 1.09679u
72
+ ··· + 4.34853u − 0.519695
a
7
=
−0.512410u
73
+ 1.28277u
72
+ ··· + 1.89759u + 0.211662
0.0303919u
73
− 0.875961u
72
+ ··· + 5.08662u − 1.26747
(ii) Obstruction class = −1
(iii) Cusp Shapes = 6.42891u
73
− 17.1405u
72
+ ··· + 84.2991u − 27.4117
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
74
+ 30u
73
+ ··· + 11u + 1
c
2
, c
6
u
74
− 2u
73
+ ··· + u + 1
c
3
u
74
− u
73
+ ··· + 32u − 64
c
4
, c
5
, c
11
c
12
u
74
+ 2u
73
+ ··· + 5u + 1
c
7
, c
10
u
74
− 3u
73
+ ··· − 24u − 16
c
8
4(4u
74
+ 50u
73
+ ··· + 1.01760 × 10
7
u − 826861)
c
9
4(4u
74
+ 74u
73
+ ··· + 3578u + 331)
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
74
+ 22y
73
+ ··· − 11y + 1
c
2
, c
6
y
74
− 30y
73
+ ··· − 11y + 1
c
3
y
74
− 15y
73
+ ··· − 100864y + 4096
c
4
, c
5
, c
11
c
12
y
74
+ 90y
73
+ ··· − 11y + 1
c
7
, c
10
y
74
− 57y
73
+ ··· + 8928y + 256
c
8
16(16y
74
− 988y
73
+ ··· − 3.20264 × 10
13
y + 6.83699 × 10
11
)
c
9
16(16y
74
− 12y
73
+ ··· − 4095460y + 109561)
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.516398 + 0.937796I
a = 1.37934 + 0.47440I
b = 1.11519 − 1.02621I
−5.3318 + 13.4301I 0
u = 0.516398 − 0.937796I
a = 1.37934 − 0.47440I
b = 1.11519 + 1.02621I
−5.3318 − 13.4301I 0
u = 0.646355 + 0.860532I
a = −0.031559 + 0.651495I
b = 0.787715 + 0.427271I
−4.52765 − 4.39825I 0
u = 0.646355 − 0.860532I
a = −0.031559 − 0.651495I
b = 0.787715 − 0.427271I
−4.52765 + 4.39825I 0
u = −0.514593 + 0.957275I
a = −1.203500 + 0.319270I
b = −0.931893 − 0.901069I
−3.14453 − 7.64245I 0
u = −0.514593 − 0.957275I
a = −1.203500 − 0.319270I
b = −0.931893 + 0.901069I
−3.14453 + 7.64245I 0
u = −0.164439 + 1.088400I
a = −0.289406 − 0.798790I
b = 0.007352 − 0.649980I
−0.76278 − 2.78369I 0
u = −0.164439 − 1.088400I
a = −0.289406 + 0.798790I
b = 0.007352 + 0.649980I
−0.76278 + 2.78369I 0
u = 0.565708 + 0.953078I
a = 0.797027 + 0.611956I
b = 1.083310 − 0.435515I
−9.49521 + 4.75713I 0
u = 0.565708 − 0.953078I
a = 0.797027 − 0.611956I
b = 1.083310 + 0.435515I
−9.49521 − 4.75713I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.139200 + 0.868293I
a = 1.067450 − 0.566161I
b = 1.41905 − 1.07046I
−5.34190 − 5.03781I 0
u = −0.139200 − 0.868293I
a = 1.067450 + 0.566161I
b = 1.41905 + 1.07046I
−5.34190 + 5.03781I 0
u = −0.053293 + 0.873796I
a = 0.463556 − 0.288559I
b = 0.57959 − 1.54839I
−6.12072 + 1.15020I 0
u = −0.053293 − 0.873796I
a = 0.463556 + 0.288559I
b = 0.57959 + 1.54839I
−6.12072 − 1.15020I 0
u = 0.339838 + 0.799583I
a = −1.61362 − 0.26065I
b = −1.24870 + 1.11169I
−0.75369 + 7.61744I 0
u = 0.339838 − 0.799583I
a = −1.61362 + 0.26065I
b = −1.24870 − 1.11169I
−0.75369 − 7.61744I 0
u = 0.857154
a = 0.267986
b = −0.915149
−6.54255 −13.9400
u = −0.352195 + 0.760005I
a = 1.41551 − 0.20271I
b = 0.886656 + 1.011220I
0.71510 − 2.68070I 0
u = −0.352195 − 0.760005I
a = 1.41551 + 0.20271I
b = 0.886656 − 1.011220I
0.71510 + 2.68070I 0
u = −0.809015 + 0.119912I
a = −0.063657 − 0.319788I
b = 0.625904 + 0.637596I
0.12891 − 3.27306I 0. + 6.36577I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.809015 − 0.119912I
a = −0.063657 + 0.319788I
b = 0.625904 − 0.637596I
0.12891 + 3.27306I 0. − 6.36577I
u = 0.229003 + 0.780373I
a = −1.50737 − 0.57430I
b = −1.213480 + 0.110904I
−3.53186 + 1.82003I −12.85757 + 0.I
u = 0.229003 − 0.780373I
a = −1.50737 + 0.57430I
b = −1.213480 − 0.110904I
−3.53186 − 1.82003I −12.85757 + 0.I
u = 0.116450 + 0.799438I
a = −1.337450 − 0.093652I
b = −0.844614 − 0.673886I
−3.46518 + 1.28856I −10.13108 + 0.I
u = 0.116450 − 0.799438I
a = −1.337450 + 0.093652I
b = −0.844614 + 0.673886I
−3.46518 − 1.28856I −10.13108 + 0.I
u = −0.732025 + 0.956216I
a = −0.160761 + 0.324928I
b = −0.525729 + 0.071221I
−2.08683 − 1.93469I 0
u = −0.732025 − 0.956216I
a = −0.160761 − 0.324928I
b = −0.525729 − 0.071221I
−2.08683 + 1.93469I 0
u = 0.782596 + 0.075119I
a = 0.210771 − 0.453706I
b = −0.903700 + 0.805460I
−2.24768 + 9.11251I −6.74714 − 7.64665I
u = 0.782596 − 0.075119I
a = 0.210771 + 0.453706I
b = −0.903700 − 0.805460I
−2.24768 − 9.11251I −6.74714 + 7.64665I
u = 0.157717 + 0.755447I
a = −0.07570 − 1.57177I
b = −0.364346 − 0.324652I
−1.00910 − 2.34681I −6.98279 + 1.27218I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.157717 − 0.755447I
a = −0.07570 + 1.57177I
b = −0.364346 + 0.324652I
−1.00910 + 2.34681I −6.98279 − 1.27218I
u = −0.315752 + 0.567010I
a = 0.726247 − 0.417162I
b = 0.265687 + 0.485420I
−0.095251 − 1.249930I −1.34438 + 5.11849I
u = −0.315752 − 0.567010I
a = 0.726247 + 0.417162I
b = 0.265687 − 0.485420I
−0.095251 + 1.249930I −1.34438 − 5.11849I
u = 0.120112 + 0.600674I
a = −4.25050 − 3.90612I
b = −0.378236 + 0.135229I
−2.57143 + 1.88701I −22.8777 − 20.8815I
u = 0.120112 − 0.600674I
a = −4.25050 + 3.90612I
b = −0.378236 − 0.135229I
−2.57143 − 1.88701I −22.8777 + 20.8815I
u = −0.525480 + 0.097303I
a = 0.694323 − 0.276907I
b = −0.448154 + 0.890040I
2.69534 − 0.34676I 2.07291 + 1.95664I
u = −0.525480 − 0.097303I
a = 0.694323 + 0.276907I
b = −0.448154 − 0.890040I
2.69534 + 0.34676I 2.07291 − 1.95664I
u = 0.508981 + 0.034990I
a = −0.944097 − 0.159201I
b = 0.768623 + 0.882121I
1.52983 − 4.69247I −0.63478 + 4.64507I
u = 0.508981 − 0.034990I
a = −0.944097 + 0.159201I
b = 0.768623 − 0.882121I
1.52983 + 4.69247I −0.63478 − 4.64507I
u = −0.06618 + 1.61043I
a = −1.103590 − 0.029524I
b = −0.610671 − 0.632639I
−7.73703 − 2.51040I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.06618 − 1.61043I
a = −1.103590 + 0.029524I
b = −0.610671 + 0.632639I
−7.73703 + 2.51040I 0
u = 0.03509 + 1.61351I
a = 0.888518 + 0.804947I
b = 0.456223 − 0.165796I
−9.06255 − 1.74034I 0
u = 0.03509 − 1.61351I
a = 0.888518 − 0.804947I
b = 0.456223 + 0.165796I
−9.06255 + 1.74034I 0
u = 0.00915 + 1.62932I
a = 3.65614 − 2.49513I
b = 0.235207 + 0.261485I
−10.53390 + 2.15468I 0
u = 0.00915 − 1.62932I
a = 3.65614 + 2.49513I
b = 0.235207 − 0.261485I
−10.53390 − 2.15468I 0
u = −0.162962 + 0.325759I
a = 0.37499 − 5.29235I
b = −0.061683 + 0.638217I
−2.74823 + 1.72250I 2.01945 − 1.32528I
u = −0.162962 − 0.325759I
a = 0.37499 + 5.29235I
b = −0.061683 − 0.638217I
−2.74823 − 1.72250I 2.01945 + 1.32528I
u = −0.307838 + 0.186179I
a = 0.36310 − 3.03306I
b = −0.728206 + 0.583603I
−2.23234 − 3.57955I −4.32988 + 5.24615I
u = −0.307838 − 0.186179I
a = 0.36310 + 3.03306I
b = −0.728206 − 0.583603I
−2.23234 + 3.57955I −4.32988 − 5.24615I
u = −0.08246 + 1.64390I
a = −1.79296 − 0.55515I
b = −1.26542 − 1.17285I
−7.63678 − 4.24546I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.08246 − 1.64390I
a = −1.79296 + 0.55515I
b = −1.26542 + 1.17285I
−7.63678 + 4.24546I 0
u = 0.05737 + 1.65209I
a = 2.06972 + 0.11611I
b = 1.64431 − 0.28908I
−12.05210 + 2.87915I 0
u = 0.05737 − 1.65209I
a = 2.06972 − 0.11611I
b = 1.64431 + 0.28908I
−12.05210 − 2.87915I 0
u = 0.08286 + 1.65467I
a = 2.11845 − 0.66031I
b = 1.64239 − 1.35516I
−9.30194 + 9.17519I 0
u = 0.08286 − 1.65467I
a = 2.11845 + 0.66031I
b = 1.64239 + 1.35516I
−9.30194 − 9.17519I 0
u = 0.02506 + 1.66126I
a = 1.51899 + 0.63274I
b = 1.15850 + 1.07316I
−12.15050 + 1.78914I 0
u = 0.02506 − 1.66126I
a = 1.51899 − 0.63274I
b = 1.15850 − 1.07316I
−12.15050 − 1.78914I 0
u = 0.331439 + 0.062097I
a = 0.042259 − 1.155080I
b = 0.772329 + 0.069502I
−1.180990 − 0.117604I −4.18793 − 0.25289I
u = 0.331439 − 0.062097I
a = 0.042259 + 1.155080I
b = 0.772329 − 0.069502I
−1.180990 + 0.117604I −4.18793 + 0.25289I
u = −0.03137 + 1.67412I
a = −1.88894 + 1.15601I
b = −1.88611 + 1.43903I
−14.3020 − 5.6642I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.03137 − 1.67412I
a = −1.88894 − 1.15601I
b = −1.88611 − 1.43903I
−14.3020 + 5.6642I 0
u = −0.01286 + 1.67510I
a = −0.86416 + 1.39905I
b = −0.84742 + 2.08208I
−15.1137 + 0.9015I 0
u = −0.01286 − 1.67510I
a = −0.86416 − 1.39905I
b = −0.84742 − 2.08208I
−15.1137 − 0.9015I 0
u = 0.14686 + 1.69181I
a = −1.85665 + 0.23574I
b = −1.30389 + 1.18234I
−14.4226 + 16.0595I 0
u = 0.14686 − 1.69181I
a = −1.85665 − 0.23574I
b = −1.30389 − 1.18234I
−14.4226 − 16.0595I 0
u = −0.14591 + 1.69645I
a = 1.68010 + 0.24966I
b = 1.17315 + 1.05919I
−12.3248 − 10.2734I 0
u = −0.14591 − 1.69645I
a = 1.68010 − 0.24966I
b = 1.17315 − 1.05919I
−12.3248 + 10.2734I 0
u = 0.15685 + 1.69894I
a = −1.54459 − 0.10686I
b = −1.33263 + 0.70962I
−18.6532 + 7.6097I 0
u = 0.15685 − 1.69894I
a = −1.54459 + 0.10686I
b = −1.33263 − 0.70962I
−18.6532 − 7.6097I 0
u = 0.19047 + 1.71554I
a = −0.819798 − 0.305915I
b = −0.900938 + 0.096382I
−13.42310 − 0.97072I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.19047 − 1.71554I
a = −0.819798 + 0.305915I
b = −0.900938 − 0.096382I
−13.42310 + 0.97072I 0
u = −0.16188 + 1.72459I
a = 1.005060 + 0.026326I
b = 0.852608 + 0.458742I
−11.56300 − 5.35029I 0
u = −0.16188 − 1.72459I
a = 1.005060 − 0.026326I
b = 0.852608 − 0.458742I
−11.56300 + 5.35029I 0
u = 0.261116
a = 1.48550
b = 0.559178
−1.16884 −7.32880
12
II. I
u
2
= hb, 2a + 1, u
2
− u + 1i
(i) Arc colorings
a
4
=
1
0
a
12
=
0
u
a
5
=
1
−u + 1
a
1
=
u
u
a
9
=
−0.5
0
a
10
=
−
1
2
u
−
1
2
u +
1
2
a
3
=
1
0
a
2
=
0
u
a
11
=
−u
u − 1
a
6
=
u
−u + 2
a
8
=
1
2
u
−
3
2
u +
3
2
a
7
=
u
−u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4u −
7
4
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
, c
11
c
12
u
2
+ u + 1
c
2
, c
4
, c
5
u
2
− u + 1
c
3
u
2
c
7
(u − 1)
2
c
8
4(4u
2
+ 6u + 3)
c
9
4(4u
2
+ 2u + 1)
c
10
(u + 1)
2
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
5
, c
6
, c
11
c
12
y
2
+ y + 1
c
3
y
2
c
7
, c
10
(y −1)
2
c
8
16(16y
2
− 12y + 9)
c
9
16(16y
2
+ 4y + 1)
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500000 + 0.866025I
a = −0.500000
b = 0
−1.64493 + 2.02988I −3.75000 − 3.46410I
u = 0.500000 − 0.866025I
a = −0.500000
b = 0
−1.64493 − 2.02988I −3.75000 + 3.46410I
16
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
2
+ u + 1)(u
74
+ 30u
73
+ ··· + 11u + 1)
c
2
(u
2
− u + 1)(u
74
− 2u
73
+ ··· + u + 1)
c
3
u
2
(u
74
− u
73
+ ··· + 32u − 64)
c
4
, c
5
(u
2
− u + 1)(u
74
+ 2u
73
+ ··· + 5u + 1)
c
6
(u
2
+ u + 1)(u
74
− 2u
73
+ ··· + u + 1)
c
7
((u − 1)
2
)(u
74
− 3u
73
+ ··· − 24u − 16)
c
8
16(4u
2
+ 6u + 3)(4u
74
+ 50u
73
+ ··· + 1.01760 × 10
7
u − 826861)
c
9
16(4u
2
+ 2u + 1)(4u
74
+ 74u
73
+ ··· + 3578u + 331)
c
10
((u + 1)
2
)(u
74
− 3u
73
+ ··· − 24u − 16)
c
11
, c
12
(u
2
+ u + 1)(u
74
+ 2u
73
+ ··· + 5u + 1)
17
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
2
+ y + 1)(y
74
+ 22y
73
+ ··· − 11y + 1)
c
2
, c
6
(y
2
+ y + 1)(y
74
− 30y
73
+ ··· − 11y + 1)
c
3
y
2
(y
74
− 15y
73
+ ··· − 100864y + 4096)
c
4
, c
5
, c
11
c
12
(y
2
+ y + 1)(y
74
+ 90y
73
+ ··· − 11y + 1)
c
7
, c
10
((y −1)
2
)(y
74
− 57y
73
+ ··· + 8928y + 256)
c
8
256(16y
2
− 12y + 9)
· (16y
74
− 988y
73
+ ··· − 32026352041720y + 683699113321)
c
9
256(16y
2
+ 4y + 1)(16y
74
− 12y
73
+ ··· − 4095460y + 109561)
18
