12a
0410
(K12a
0410
)
A knot diagram
1
Linearized knot diagam
3 6 9 12 2 10 11 5 1 8 7 4
Solving Sequence
3,9 4,6
2 1 10 7 5 8 12 11
c
3
c
2
c
1
c
9
c
6
c
5
c
8
c
12
c
11
c
4
, c
7
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h4.25183 × 10
585
u
103
− 3.49672 × 10
585
u
102
+ ··· + 8.74093 × 10
585
b + 3.71015 × 10
586
,
6.16669 × 10
587
u
103
− 4.95476 × 10
587
u
102
+ ··· + 8.74093 × 10
585
a + 3.40901 × 10
588
, u
104
− u
103
+ ··· + 4u − 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
= h4.25 × 10
585
u
103
− 3.50 × 10
585
u
102
+ · · · + 8.74 × 10
585
b + 3.71 ×
10
586
, 6.17 × 10
587
u
103
− 4.95 × 10
587
u
102
+ · · · + 8.74 × 10
585
a + 3.41 ×
10
588
, u
104
− u
103
+ · · · + 4u − 1i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
u
2
a
6
=
−70.5495u
103
+ 56.6846u
102
+ ··· − 557.720u − 390.005
−0.486427u
103
+ 0.400040u
102
+ ··· − 5.53020u − 4.24457
a
2
=
−102.717u
103
+ 81.0025u
102
+ ··· − 543.733u − 496.837
−1.37667u
103
+ 1.15211u
102
+ ··· − 9.54433u − 8.96963
a
1
=
−104.094u
103
+ 82.1546u
102
+ ··· − 553.277u − 505.807
−1.37667u
103
+ 1.15211u
102
+ ··· − 9.54433u − 8.96963
a
10
=
−323.391u
103
+ 228.074u
102
+ ··· + 978.592u − 1309.82
−15.2283u
103
+ 12.0817u
102
+ ··· + 0.583226u − 70.8551
a
7
=
203.528u
103
− 157.623u
102
+ ··· − 787.570u + 388.116
9.83386u
103
− 7.22442u
102
+ ··· + 26.3806u + 44.1586
a
5
=
24.0836u
103
− 18.0365u
102
+ ··· − 147.484u + 38.3478
2.09265u
103
− 1.51733u
102
+ ··· + 0.457127u + 8.25296
a
8
=
−250.120u
103
+ 167.113u
102
+ ··· + 1343.51u − 959.073
−14.4955u
103
+ 11.4521u
102
+ ··· + 12.7671u − 66.7521
a
12
=
−106.712u
103
+ 84.1220u
102
+ ··· − 560.070u − 518.776
−1.53073u
103
+ 1.27128u
102
+ ··· − 9.55960u − 9.62036
a
11
=
−195.042u
103
+ 137.460u
102
+ ··· − 980.891u − 659.152
−5.95727u
103
+ 4.33298u
102
+ ··· + 14.3247u − 39.1433
(ii) Obstruction class = −1
(iii) Cusp Shapes = 8.88084u
103
− 5.44978u
102
+ ··· − 468.605u − 98.2415
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
104
+ 43u
103
+ ··· + 20u + 1
c
2
, c
5
u
104
+ 7u
103
+ ··· + 6u + 1
c
3
u
104
− u
103
+ ··· + 4u − 1
c
4
, c
12
u
104
+ 7u
103
+ ··· + 6u + 1
c
6
u
104
+ u
103
+ ··· − 159742u − 10001
c
7
, c
10
, c
11
u
104
− u
103
+ ··· − 16u − 1
c
8
u
104
+ 5u
103
+ ··· + 1611520u − 285184
c
9
u
104
+ 7u
103
+ ··· + 14816u + 928
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
104
+ 37y
103
+ ··· − 404y + 1
c
2
, c
5
y
104
− 43y
103
+ ··· − 20y + 1
c
3
y
104
− 7y
103
+ ··· − 84y + 1
c
4
, c
12
y
104
+ 73y
103
+ ··· − 20y + 1
c
6
y
104
− 35y
103
+ ··· − 15905585468y + 100020001
c
7
, c
10
, c
11
y
104
+ 89y
103
+ ··· − 156y + 1
c
8
y
104
− 199y
103
+ ··· − 3752188116992y + 81329913856
c
9
y
104
+ 145y
103
+ ··· − 51493888y + 861184
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.563363 + 0.821946I
a = 0.444185 − 0.891149I
b = −0.454391 + 0.989162I
6.57214 − 6.48719I 0
u = 0.563363 − 0.821946I
a = 0.444185 + 0.891149I
b = −0.454391 − 0.989162I
6.57214 + 6.48719I 0
u = −0.621126 + 0.769884I
a = −0.56396 − 1.81731I
b = −1.029360 + 0.485493I
1.01084 + 5.03860I 0
u = −0.621126 − 0.769884I
a = −0.56396 + 1.81731I
b = −1.029360 − 0.485493I
1.01084 − 5.03860I 0
u = 0.388922 + 0.904890I
a = 0.596870 − 0.870016I
b = −0.542166 + 0.717661I
2.80919 + 0.07810I 0
u = 0.388922 − 0.904890I
a = 0.596870 + 0.870016I
b = −0.542166 − 0.717661I
2.80919 − 0.07810I 0
u = 0.970515 + 0.147136I
a = 0.875999 − 0.444927I
b = 0.674437 + 0.541246I
4.46398 + 2.11638I 0
u = 0.970515 − 0.147136I
a = 0.875999 + 0.444927I
b = 0.674437 − 0.541246I
4.46398 − 2.11638I 0
u = −0.505334 + 0.804558I
a = 0.453957 + 0.831515I
b = −0.399937 − 0.890019I
1.50309 + 3.13338I 0
u = −0.505334 − 0.804558I
a = 0.453957 − 0.831515I
b = −0.399937 + 0.890019I
1.50309 − 3.13338I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.825078 + 0.437544I
a = 0.366274 − 0.209695I
b = 0.946141 − 0.486683I
−1.62694 + 3.28109I 0
u = 0.825078 − 0.437544I
a = 0.366274 + 0.209695I
b = 0.946141 + 0.486683I
−1.62694 − 3.28109I 0
u = −0.960850 + 0.560302I
a = 0.0740763 + 0.0415182I
b = 0.959373 + 0.560649I
3.58609 − 6.59895I 0
u = −0.960850 − 0.560302I
a = 0.0740763 − 0.0415182I
b = 0.959373 − 0.560649I
3.58609 + 6.59895I 0
u = −0.808529 + 0.272807I
a = −0.32342 − 2.08395I
b = −0.530241 − 0.185700I
1.61075 − 4.42335I 0
u = −0.808529 − 0.272807I
a = −0.32342 + 2.08395I
b = −0.530241 + 0.185700I
1.61075 + 4.42335I 0
u = −0.717693 + 0.898837I
a = −0.28560 − 1.56028I
b = −1.060130 + 0.592917I
1.24152 + 4.96360I 0
u = −0.717693 − 0.898837I
a = −0.28560 + 1.56028I
b = −1.060130 − 0.592917I
1.24152 − 4.96360I 0
u = −0.520163 + 1.029420I
a = 0.516539 + 0.934515I
b = −0.693321 − 0.824652I
8.89831 − 1.49693I 0
u = −0.520163 − 1.029420I
a = 0.516539 − 0.934515I
b = −0.693321 + 0.824652I
8.89831 + 1.49693I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.241022 + 0.772602I
a = 0.79562 + 2.59697I
b = −0.901827 − 0.433942I
−2.08746 − 1.73740I 0
u = 0.241022 − 0.772602I
a = 0.79562 − 2.59697I
b = −0.901827 + 0.433942I
−2.08746 + 1.73740I 0
u = 0.803988 + 0.896157I
a = −0.25183 + 1.43561I
b = −1.138880 − 0.645059I
−0.70178 − 8.77355I 0
u = 0.803988 − 0.896157I
a = −0.25183 − 1.43561I
b = −1.138880 + 0.645059I
−0.70178 + 8.77355I 0
u = 0.497385 + 0.621008I
a = 0.078179 − 0.664644I
b = 0.056824 + 0.865095I
4.05431 − 1.11668I 0
u = 0.497385 − 0.621008I
a = 0.078179 + 0.664644I
b = 0.056824 − 0.865095I
4.05431 + 1.11668I 0
u = −0.791300 + 0.046534I
a = 0.815917 − 0.154042I
b = 0.796187 + 0.354222I
−0.902576 − 0.388396I 0
u = −0.791300 − 0.046534I
a = 0.815917 + 0.154042I
b = 0.796187 − 0.354222I
−0.902576 + 0.388396I 0
u = −0.508719 + 0.607540I
a = 0.182981 + 1.047660I
b = 0.986634 + 0.373347I
1.059970 − 0.844026I 0
u = −0.508719 − 0.607540I
a = 0.182981 − 1.047660I
b = 0.986634 − 0.373347I
1.059970 + 0.844026I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.928727 + 0.802627I
a = −0.196145 + 1.138220I
b = −0.135690 − 0.300460I
−3.72257 + 0.98676I 0
u = 0.928727 − 0.802627I
a = −0.196145 − 1.138220I
b = −0.135690 + 0.300460I
−3.72257 − 0.98676I 0
u = −0.075525 + 0.763689I
a = 1.75244 − 1.84311I
b = −0.840944 + 0.347075I
2.01306 − 1.82511I 0
u = −0.075525 − 0.763689I
a = 1.75244 + 1.84311I
b = −0.840944 − 0.347075I
2.01306 + 1.82511I 0
u = −0.830605 + 0.911793I
a = −0.21117 − 1.42184I
b = −1.156170 + 0.688727I
4.41171 + 12.55190I 0
u = −0.830605 − 0.911793I
a = −0.21117 + 1.42184I
b = −1.156170 − 0.688727I
4.41171 − 12.55190I 0
u = −0.548337 + 0.469959I
a = −0.328853 + 1.044760I
b = 0.515000 − 1.053110I
2.07251 + 7.18772I −6.8037 − 12.4590I
u = −0.548337 − 0.469959I
a = −0.328853 − 1.044760I
b = 0.515000 + 1.053110I
2.07251 − 7.18772I −6.8037 + 12.4590I
u = 1.108980 + 0.641111I
a = −0.333073 + 0.138039I
b = −1.285360 − 0.021076I
−4.80953 − 10.09280I 0
u = 1.108980 − 0.641111I
a = −0.333073 − 0.138039I
b = −1.285360 + 0.021076I
−4.80953 + 10.09280I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.773737 + 1.036650I
a = −0.14378 + 1.50023I
b = −0.982973 − 0.702090I
7.99891 − 4.19713I 0
u = 0.773737 − 1.036650I
a = −0.14378 − 1.50023I
b = −0.982973 + 0.702090I
7.99891 + 4.19713I 0
u = −1.154320 + 0.625941I
a = −0.329904 − 0.003143I
b = −1.250860 − 0.033111I
−9.49573 + 5.97236I 0
u = −1.154320 − 0.625941I
a = −0.329904 + 0.003143I
b = −1.250860 + 0.033111I
−9.49573 − 5.97236I 0
u = 0.679111
a = 0.284649
b = 1.33147
−4.78114 −21.9600
u = −0.678215 + 0.013252I
a = 0.237565 + 0.197940I
b = 1.364900 − 0.142720I
−0.85837 + 3.39314I −16.6981 − 3.5212I
u = −0.678215 − 0.013252I
a = 0.237565 − 0.197940I
b = 1.364900 + 0.142720I
−0.85837 − 3.39314I −16.6981 + 3.5212I
u = 0.514461 + 0.432962I
a = −0.475888 − 1.078040I
b = 0.607901 + 0.957836I
−2.47422 − 3.90065I −12.9937 + 12.0198I
u = 0.514461 − 0.432962I
a = −0.475888 + 1.078040I
b = 0.607901 − 0.957836I
−2.47422 + 3.90065I −12.9937 − 12.0198I
u = −0.363724 + 0.562108I
a = −0.699635 + 0.105819I
b = 0.448049 − 0.543530I
−0.67399 + 1.89363I −4.47866 − 2.55693I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.363724 − 0.562108I
a = −0.699635 − 0.105819I
b = 0.448049 + 0.543530I
−0.67399 − 1.89363I −4.47866 + 2.55693I
u = 0.546846 + 0.348271I
a = 1.136730 + 0.190671I
b = 0.104676 + 0.374668I
3.28029 − 2.14163I −5.02286 + 4.41654I
u = 0.546846 − 0.348271I
a = 1.136730 − 0.190671I
b = 0.104676 − 0.374668I
3.28029 + 2.14163I −5.02286 − 4.41654I
u = −0.528143 + 0.344252I
a = −0.479136 + 1.328600I
b = 0.815535 − 0.943051I
0.934910 + 1.041190I −10.52989 − 8.15027I
u = −0.528143 − 0.344252I
a = −0.479136 − 1.328600I
b = 0.815535 + 0.943051I
0.934910 − 1.041190I −10.52989 + 8.15027I
u = 1.233470 + 0.601611I
a = −0.324632 − 0.186405I
b = −1.191290 + 0.103160I
−6.60481 − 1.68850I 0
u = 1.233470 − 0.601611I
a = −0.324632 + 0.186405I
b = −1.191290 − 0.103160I
−6.60481 + 1.68850I 0
u = 0.616964 + 0.103413I
a = 0.161187 − 1.006650I
b = 1.275880 + 0.605464I
−0.589345 + 0.680571I −17.4751 + 1.3227I
u = 0.616964 − 0.103413I
a = 0.161187 + 1.006650I
b = 1.275880 − 0.605464I
−0.589345 − 0.680571I −17.4751 − 1.3227I
u = −0.868038 + 1.069790I
a = −0.299836 − 0.985915I
b = 0.294814 + 0.475607I
−1.45640 + 3.06534I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.868038 − 1.069790I
a = −0.299836 + 0.985915I
b = 0.294814 − 0.475607I
−1.45640 − 3.06534I 0
u = 0.591931 + 0.186775I
a = −0.090390 − 1.313950I
b = 1.17202 + 0.80496I
−0.19970 − 5.86738I −15.9124 + 10.3490I
u = 0.591931 − 0.186775I
a = −0.090390 + 1.313950I
b = 1.17202 − 0.80496I
−0.19970 + 5.86738I −15.9124 − 10.3490I
u = −0.588394 + 0.142921I
a = 0.082609 + 1.246190I
b = 1.196880 − 0.701859I
−4.36091 + 2.54856I −22.8255 − 6.6552I
u = −0.588394 − 0.142921I
a = 0.082609 − 1.246190I
b = 1.196880 + 0.701859I
−4.36091 − 2.54856I −22.8255 + 6.6552I
u = −1.04004 + 1.03217I
a = −0.551356 − 0.879784I
b = 0.490615 + 0.933211I
1.92360 + 12.58100I 0
u = −1.04004 − 1.03217I
a = −0.551356 + 0.879784I
b = 0.490615 − 0.933211I
1.92360 − 12.58100I 0
u = 1.03517 + 1.04171I
a = −0.515586 + 0.900439I
b = 0.456752 − 0.891030I
−3.29144 − 8.47835I 0
u = 1.03517 − 1.04171I
a = −0.515586 − 0.900439I
b = 0.456752 + 0.891030I
−3.29144 + 8.47835I 0
u = −1.02615 + 1.06514I
a = −0.447832 − 0.911579I
b = 0.434256 + 0.795553I
−1.21263 + 4.04668I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.02615 − 1.06514I
a = −0.447832 + 0.911579I
b = 0.434256 − 0.795553I
−1.21263 − 4.04668I 0
u = −0.459257
a = 1.01669
b = 0.220418
−0.783430 −12.3850
u = 1.13472 + 1.07528I
a = −0.374927 + 0.755335I
b = 0.642091 − 0.737555I
6.67772 − 3.43727I 0
u = 1.13472 − 1.07528I
a = −0.374927 − 0.755335I
b = 0.642091 + 0.737555I
6.67772 + 3.43727I 0
u = −1.27994 + 0.93580I
a = −0.228492 − 1.201280I
b = −0.534879 + 0.497663I
1.69291 − 4.76934I 0
u = −1.27994 − 0.93580I
a = −0.228492 + 1.201280I
b = −0.534879 − 0.497663I
1.69291 + 4.76934I 0
u = 1.18881 + 1.11014I
a = 0.22480 − 1.52647I
b = 1.132280 + 0.683492I
−0.0478 − 18.5019I 0
u = 1.18881 − 1.11014I
a = 0.22480 + 1.52647I
b = 1.132280 − 0.683492I
−0.0478 + 18.5019I 0
u = −0.193816 + 0.301765I
a = −4.2506 − 14.1470I
b = −0.911434 + 0.459625I
1.36741 + 4.74474I 4.6304 − 28.6080I
u = −0.193816 − 0.301765I
a = −4.2506 + 14.1470I
b = −0.911434 − 0.459625I
1.36741 − 4.74474I 4.6304 + 28.6080I
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.12086 + 1.64891I
a = −0.237789 − 1.104930I
b = 0.876849 + 0.233377I
−1.58816 + 3.67691I 0
u = 0.12086 − 1.64891I
a = −0.237789 + 1.104930I
b = 0.876849 − 0.233377I
−1.58816 − 3.67691I 0
u = −1.20612 + 1.14721I
a = 0.19311 + 1.49297I
b = 1.126050 − 0.656619I
−5.3218 + 14.1793I 0
u = −1.20612 − 1.14721I
a = 0.19311 − 1.49297I
b = 1.126050 + 0.656619I
−5.3218 − 14.1793I 0
u = 0.318133 + 0.043089I
a = 2.36401 − 4.12070I
b = 0.918651 + 0.537939I
−1.80006 − 2.05759I −8.77434 + 2.54557I
u = 0.318133 − 0.043089I
a = 2.36401 + 4.12070I
b = 0.918651 − 0.537939I
−1.80006 + 2.05759I −8.77434 − 2.54557I
u = 1.25730 + 1.20177I
a = 0.16715 − 1.42834I
b = 1.100520 + 0.623230I
−3.17569 − 9.37700I 0
u = 1.25730 − 1.20177I
a = 0.16715 + 1.42834I
b = 1.100520 − 0.623230I
−3.17569 + 9.37700I 0
u = −0.172426 + 0.188300I
a = 23.8746 − 18.6316I
b = −0.847748 − 0.537795I
1.38082 + 0.72027I −1.7376 − 54.7659I
u = −0.172426 − 0.188300I
a = 23.8746 + 18.6316I
b = −0.847748 + 0.537795I
1.38082 − 0.72027I −1.7376 + 54.7659I
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.203979 + 0.019491I
a = −24.7660 + 37.7640I
b = −0.843694 + 0.490511I
−2.71693 + 2.03390I −94.2346 + 14.3841I
u = 0.203979 − 0.019491I
a = −24.7660 − 37.7640I
b = −0.843694 − 0.490511I
−2.71693 − 2.03390I −94.2346 − 14.3841I
u = −1.48989 + 1.04196I
a = 0.292330 + 1.277470I
b = 0.996033 − 0.647512I
5.60690 + 8.72189I 0
u = −1.48989 − 1.04196I
a = 0.292330 − 1.277470I
b = 0.996033 + 0.647512I
5.60690 − 8.72189I 0
u = 1.88590 + 0.28154I
a = −0.246019 − 0.815284I
b = −0.912559 + 0.304758I
−4.50986 − 1.24814I 0
u = 1.88590 − 0.28154I
a = −0.246019 + 0.815284I
b = −0.912559 − 0.304758I
−4.50986 + 1.24814I 0
u = 1.46046 + 1.60505I
a = 0.155240 − 0.823314I
b = −0.998169 + 0.552449I
0.38251 + 9.17605I 0
u = 1.46046 − 1.60505I
a = 0.155240 + 0.823314I
b = −0.998169 − 0.552449I
0.38251 − 9.17605I 0
u = 1.43763 + 1.70063I
a = 0.040194 − 1.224600I
b = 1.007560 + 0.505269I
−3.17734 − 7.04580I 0
u = 1.43763 − 1.70063I
a = 0.040194 + 1.224600I
b = 1.007560 − 0.505269I
−3.17734 + 7.04580I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.76981 + 2.17891I
a = −0.095447 + 1.148870I
b = 0.952498 − 0.398631I
−5.87156 + 1.43086I 0
u = −0.76981 − 2.17891I
a = −0.095447 − 1.148870I
b = 0.952498 + 0.398631I
−5.87156 − 1.43086I 0
u = −2.01108 + 1.27353I
a = 0.018017 + 0.800933I
b = −0.983353 − 0.460952I
−5.42846 − 4.28254I 0
u = −2.01108 − 1.27353I
a = 0.018017 − 0.800933I
b = −0.983353 + 0.460952I
−5.42846 + 4.28254I 0
15
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
104
+ 43u
103
+ ··· + 20u + 1
c
2
, c
5
u
104
+ 7u
103
+ ··· + 6u + 1
c
3
u
104
− u
103
+ ··· + 4u − 1
c
4
, c
12
u
104
+ 7u
103
+ ··· + 6u + 1
c
6
u
104
+ u
103
+ ··· − 159742u − 10001
c
7
, c
10
, c
11
u
104
− u
103
+ ··· − 16u − 1
c
8
u
104
+ 5u
103
+ ··· + 1611520u − 285184
c
9
u
104
+ 7u
103
+ ··· + 14816u + 928
16
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
104
+ 37y
103
+ ··· − 404y + 1
c
2
, c
5
y
104
− 43y
103
+ ··· − 20y + 1
c
3
y
104
− 7y
103
+ ··· − 84y + 1
c
4
, c
12
y
104
+ 73y
103
+ ··· − 20y + 1
c
6
y
104
− 35y
103
+ ··· − 15905585468y + 100020001
c
7
, c
10
, c
11
y
104
+ 89y
103
+ ··· − 156y + 1
c
8
y
104
− 199y
103
+ ··· − 3752188116992y + 81329913856
c
9
y
104
+ 145y
103
+ ··· − 51493888y + 861184
17
