12a
0412
(K12a
0412
)
A knot diagram
1
Linearized knot diagam
3 6 9 12 2 10 11 1 5 8 7 4
Solving Sequence
2,6 3,9
4 1 5 10 7 8 12 11
c
2
c
3
c
1
c
5
c
9
c
6
c
8
c
12
c
11
c
4
, c
7
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h4.20170 × 10
176
u
104
− 3.69872 × 10
177
u
103
+ ··· + 1.98967 × 10
177
b − 1.56965 × 10
177
,
− 1.93657 × 10
177
u
104
+ 3.13804 × 10
178
u
103
+ ··· + 2.18864 × 10
178
a − 3.72446 × 10
178
,
u
105
− 7u
104
+ ··· + 3u + 1i
* 1 irreducible components of dim
C
= 0, with total 105 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
= h4.20 × 10
176
u
104
− 3.70 × 10
177
u
103
+ · · · + 1.99 × 10
177
b − 1.57 ×
10
177
, −1.94 × 10
177
u
104
+ 3.14 × 10
178
u
103
+ · · · + 2.19 × 10
178
a − 3.72 ×
10
178
, u
105
− 7u
104
+ · · · + 3u + 1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
u
2
a
9
=
0.0884829u
104
− 1.43379u
103
+ ··· + 0.687210u + 1.70173
−0.211175u
104
+ 1.85896u
103
+ ··· + 0.342478u + 0.788902
a
4
=
−0.165696u
104
− 0.198162u
103
+ ··· − 5.72062u − 1.82003
0.0402541u
104
− 0.944412u
103
+ ··· − 2.78766u − 0.617942
a
1
=
−u
2
+ 1
−u
4
a
5
=
u
u
a
10
=
2.15833u
104
− 14.1242u
103
+ ··· − 2.59855u + 0.506586
1.85867u
104
− 10.8314u
103
+ ··· − 2.94328u − 0.406239
a
7
=
1.13726u
104
− 6.38343u
103
+ ··· − 8.00594u − 2.72657
0.380524u
104
− 2.29143u
103
+ ··· + 3.83633u + 0.123900
a
8
=
2.25309u
104
− 14.9010u
103
+ ··· − 2.19648u − 0.0146111
1.96367u
104
− 11.9280u
103
+ ··· − 5.85996u − 0.890655
a
12
=
1.97598u
104
− 11.9594u
103
+ ··· − 9.62283u − 1.09953
2.39398u
104
− 15.0162u
103
+ ··· − 6.27032u − 2.03812
a
11
=
1.58757u
104
− 9.31152u
103
+ ··· + 0.980426u + 1.41068
1.26723u
104
− 7.07029u
103
+ ··· − 0.922253u − 0.284019
(ii) Obstruction class = −1
(iii) Cusp Shapes = 5.01196u
104
− 31.9283u
103
+ ··· − 6.46734u + 9.94137
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
105
+ 41u
104
+ ··· + 13u + 1
c
2
, c
5
u
105
+ 7u
104
+ ··· + 3u − 1
c
3
u
105
− u
104
+ ··· − 3u − 1
c
4
, c
12
u
105
+ 7u
104
+ ··· + 3u − 1
c
6
u
105
− u
104
+ ··· + 625275u − 85457
c
7
, c
10
, c
11
u
105
+ u
104
+ ··· + u − 1
c
8
u
105
+ 3u
104
+ ··· − 31u − 3
c
9
u
105
+ u
104
+ ··· + 413u − 2359
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
105
+ 47y
104
+ ··· + 245y −1
c
2
, c
5
y
105
− 41y
104
+ ··· + 13y −1
c
3
y
105
+ 7y
104
+ ··· + 69y −1
c
4
, c
12
y
105
+ 67y
104
+ ··· + 13y −1
c
6
y
105
− 25y
104
+ ··· + 228484645933y −7302898849
c
7
, c
10
, c
11
y
105
+ 91y
104
+ ··· + 45y −1
c
8
y
105
+ 231y
104
+ ··· − 3743y −9
c
9
y
105
− 209y
104
+ ··· + 318380797y −5564881
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.784644 + 0.598937I
a = 2.25636 − 0.88903I
b = 1.36159 − 1.31807I
1.85369 − 0.14305I 0
u = −0.784644 − 0.598937I
a = 2.25636 + 0.88903I
b = 1.36159 + 1.31807I
1.85369 + 0.14305I 0
u = −0.858240 + 0.539535I
a = 7.28815 + 2.86509I
b = 6.10302 − 5.61999I
−4.68800 − 0.72454I 0
u = −0.858240 − 0.539535I
a = 7.28815 − 2.86509I
b = 6.10302 + 5.61999I
−4.68800 + 0.72454I 0
u = 0.564992 + 0.806358I
a = −0.88945 − 1.11350I
b = 0.24954 − 1.51542I
−0.43187 + 4.02094I 0
u = 0.564992 − 0.806358I
a = −0.88945 + 1.11350I
b = 0.24954 + 1.51542I
−0.43187 − 4.02094I 0
u = −0.881792 + 0.510724I
a = −10.51730 + 2.00682I
b = −3.80678 + 10.52150I
−0.56771 + 2.03241I 0
u = −0.881792 − 0.510724I
a = −10.51730 − 2.00682I
b = −3.80678 − 10.52150I
−0.56771 − 2.03241I 0
u = 0.387986 + 0.950406I
a = 0.482022 − 0.428068I
b = 0.468486 + 0.163848I
0.84097 − 3.95845I 0
u = 0.387986 − 0.950406I
a = 0.482022 + 0.428068I
b = 0.468486 − 0.163848I
0.84097 + 3.95845I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.913124 + 0.476644I
a = 4.58490 − 3.63846I
b = −0.09300 − 6.06609I
−4.71244 + 4.76569I 0
u = −0.913124 − 0.476644I
a = 4.58490 + 3.63846I
b = −0.09300 + 6.06609I
−4.71244 − 4.76569I 0
u = 0.839840 + 0.597226I
a = −1.246410 + 0.445955I
b = −0.759419 + 0.644703I
2.38346 − 2.36277I 0
u = 0.839840 − 0.597226I
a = −1.246410 − 0.445955I
b = −0.759419 − 0.644703I
2.38346 + 2.36277I 0
u = 0.850571 + 0.587804I
a = −0.605447 + 0.275364I
b = −0.121760 + 0.829135I
2.36909 − 2.33534I 0
u = 0.850571 − 0.587804I
a = −0.605447 − 0.275364I
b = −0.121760 − 0.829135I
2.36909 + 2.33534I 0
u = 0.542109 + 0.888877I
a = 0.989633 + 0.984793I
b = −0.40355 + 1.51977I
1.65020 + 8.48448I 0
u = 0.542109 − 0.888877I
a = 0.989633 − 0.984793I
b = −0.40355 − 1.51977I
1.65020 − 8.48448I 0
u = 0.987126 + 0.357010I
a = 0.172002 − 0.826380I
b = 1.364530 − 0.094449I
−5.21470 − 0.78396I 0
u = 0.987126 − 0.357010I
a = 0.172002 + 0.826380I
b = 1.364530 + 0.094449I
−5.21470 + 0.78396I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.715044 + 0.618340I
a = −0.20679 − 1.46973I
b = 0.09366 − 1.70389I
−0.37710 + 2.65093I 0
u = 0.715044 − 0.618340I
a = −0.20679 + 1.46973I
b = 0.09366 + 1.70389I
−0.37710 − 2.65093I 0
u = 0.513664 + 0.931812I
a = −1.057000 − 0.935885I
b = 0.50411 − 1.49044I
−3.58129 + 12.58550I 0
u = 0.513664 − 0.931812I
a = −1.057000 + 0.935885I
b = 0.50411 + 1.49044I
−3.58129 − 12.58550I 0
u = −0.648758 + 0.845940I
a = 0.890042 − 0.645854I
b = 0.009504 − 1.305990I
2.52519 + 1.13520I 0
u = −0.648758 − 0.845940I
a = 0.890042 + 0.645854I
b = 0.009504 + 1.305990I
2.52519 − 1.13520I 0
u = −0.733179 + 0.561323I
a = 1.41999 − 0.77213I
b = 0.74850 − 1.44176I
1.39941 + 0.38540I 0
u = −0.733179 − 0.561323I
a = 1.41999 + 0.77213I
b = 0.74850 + 1.44176I
1.39941 − 0.38540I 0
u = −0.552779 + 0.925006I
a = −0.823336 + 0.551394I
b = 0.127984 + 1.085750I
5.43319 − 2.63646I 0
u = −0.552779 − 0.925006I
a = −0.823336 − 0.551394I
b = 0.127984 − 1.085750I
5.43319 + 2.63646I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.891298 + 0.610073I
a = −0.99689 + 1.67821I
b = −0.53902 + 2.37842I
1.52100 + 4.93000I 0
u = −0.891298 − 0.610073I
a = −0.99689 − 1.67821I
b = −0.53902 − 2.37842I
1.52100 − 4.93000I 0
u = 0.719718 + 0.566081I
a = 0.971659 + 0.472938I
b = −0.066367 − 0.169388I
−1.45824 + 1.82741I 0
u = 0.719718 − 0.566081I
a = 0.971659 − 0.472938I
b = −0.066367 + 0.169388I
−1.45824 − 1.82741I 0
u = −0.489338 + 0.987991I
a = 0.773874 − 0.512163I
b = −0.225468 − 0.939865I
0.79628 − 6.39354I 0
u = −0.489338 − 0.987991I
a = 0.773874 + 0.512163I
b = −0.225468 + 0.939865I
0.79628 + 6.39354I 0
u = 0.939075 + 0.580606I
a = 0.0878441 − 0.0304630I
b = −0.480576 − 0.945992I
−2.14023 − 6.43595I 0
u = 0.939075 − 0.580606I
a = 0.0878441 + 0.0304630I
b = −0.480576 + 0.945992I
−2.14023 + 6.43595I 0
u = −1.105020 + 0.003986I
a = −0.463514 + 0.579517I
b = −0.081000 − 0.445193I
−6.23158 − 2.80589I 0
u = −1.105020 − 0.003986I
a = −0.463514 − 0.579517I
b = −0.081000 + 0.445193I
−6.23158 + 2.80589I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.930889 + 0.606222I
a = −1.55877 + 0.85888I
b = −0.88224 + 1.58561I
0.76571 + 4.31173I 0
u = −0.930889 − 0.606222I
a = −1.55877 − 0.85888I
b = −0.88224 − 1.58561I
0.76571 − 4.31173I 0
u = 0.928998 + 0.618976I
a = 2.04545 + 0.23803I
b = 1.58004 + 0.66760I
−1.01275 − 7.53557I 0
u = 0.928998 − 0.618976I
a = 2.04545 − 0.23803I
b = 1.58004 − 0.66760I
−1.01275 + 7.53557I 0
u = 0.108711 + 0.871393I
a = −0.513219 + 0.308942I
b = −0.280446 + 0.170757I
−2.21809 − 1.17141I 0
u = 0.108711 − 0.871393I
a = −0.513219 − 0.308942I
b = −0.280446 − 0.170757I
−2.21809 + 1.17141I 0
u = 0.748138 + 0.456711I
a = −0.454893 + 1.287700I
b = −1.47842 + 0.24559I
−1.42263 − 2.10421I 0
u = 0.748138 − 0.456711I
a = −0.454893 − 1.287700I
b = −1.47842 − 0.24559I
−1.42263 + 2.10421I 0
u = 1.113190 + 0.197962I
a = 0.203752 + 0.323619I
b = 0.092885 − 0.183534I
−2.01882 − 1.15814I 0
u = 1.113190 − 0.197962I
a = 0.203752 − 0.323619I
b = 0.092885 + 0.183534I
−2.01882 + 1.15814I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.804192 + 0.313985I
a = −2.00216 + 0.54358I
b = −1.58425 + 1.27138I
−3.99118 − 2.00596I 0
u = −0.804192 − 0.313985I
a = −2.00216 − 0.54358I
b = −1.58425 − 1.27138I
−3.99118 + 2.00596I 0
u = 0.855335 + 0.112245I
a = 0.80652 + 1.60498I
b = 1.62206 + 1.22184I
−7.40410 + 4.25720I 0
u = 0.855335 − 0.112245I
a = 0.80652 − 1.60498I
b = 1.62206 − 1.22184I
−7.40410 − 4.25720I 0
u = −0.974317 + 0.592288I
a = 0.27144 − 1.61288I
b = 0.01068 − 2.47838I
−4.69892 + 9.33676I 0
u = −0.974317 − 0.592288I
a = 0.27144 + 1.61288I
b = 0.01068 + 2.47838I
−4.69892 − 9.33676I 0
u = −0.635040 + 0.567354I
a = −2.48560 + 0.33455I
b = −1.101240 + 0.509213I
−3.69404 − 4.64409I 0
u = −0.635040 − 0.567354I
a = −2.48560 − 0.33455I
b = −1.101240 − 0.509213I
−3.69404 + 4.64409I 0
u = 0.476371 + 1.053510I
a = −0.507456 + 0.437799I
b = −0.474779 − 0.347760I
−3.81811 − 7.20822I 0
u = 0.476371 − 1.053510I
a = −0.507456 − 0.437799I
b = −0.474779 + 0.347760I
−3.81811 + 7.20822I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.155890 + 0.151746I
a = 0.508318 − 0.111207I
b = 0.032423 + 0.975592I
−13.01170 − 1.06028I 0
u = −1.155890 − 0.151746I
a = 0.508318 + 0.111207I
b = 0.032423 − 0.975592I
−13.01170 + 1.06028I 0
u = −1.079920 + 0.483105I
a = 1.05608 − 1.02881I
b = 0.67251 − 1.36232I
−5.45759 + 5.13104I 0
u = −1.079920 − 0.483105I
a = 1.05608 + 1.02881I
b = 0.67251 + 1.36232I
−5.45759 − 5.13104I 0
u = 1.099770 + 0.484541I
a = 0.561303 + 0.185309I
b = 0.372907 + 0.221075I
−2.01746 − 1.41013I 0
u = 1.099770 − 0.484541I
a = 0.561303 − 0.185309I
b = 0.372907 − 0.221075I
−2.01746 + 1.41013I 0
u = −1.209830 + 0.064571I
a = 0.106577 + 0.547653I
b = −0.339099 − 0.297583I
−5.02520 + 6.71923I 0
u = −1.209830 − 0.064571I
a = 0.106577 − 0.547653I
b = −0.339099 + 0.297583I
−5.02520 − 6.71923I 0
u = 1.070970 + 0.573366I
a = −1.93630 − 0.77675I
b = −1.95721 − 1.69398I
−10.33900 − 8.37585I 0
u = 1.070970 − 0.573366I
a = −1.93630 + 0.77675I
b = −1.95721 + 1.69398I
−10.33900 + 8.37585I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.331960 + 0.691775I
a = 1.36501 + 1.42750I
b = −0.088717 + 1.079180I
−8.31773 + 3.57839I 0.49395 − 2.97375I
u = 0.331960 − 0.691775I
a = 1.36501 − 1.42750I
b = −0.088717 − 1.079180I
−8.31773 − 3.57839I 0.49395 + 2.97375I
u = −1.028750 + 0.688724I
a = −1.39282 + 0.64457I
b = −0.88861 + 1.57623I
1.34242 + 4.57879I 0
u = −1.028750 − 0.688724I
a = −1.39282 − 0.64457I
b = −0.88861 − 1.57623I
1.34242 − 4.57879I 0
u = 1.061750 + 0.666652I
a = 1.85225 + 0.61655I
b = 1.48698 + 1.73016I
−1.93050 − 9.56236I 0
u = 1.061750 − 0.666652I
a = 1.85225 − 0.61655I
b = 1.48698 − 1.73016I
−1.93050 + 9.56236I 0
u = 0.851397 + 0.934773I
a = 0.585957 − 0.403561I
b = 0.883007 + 0.461434I
−5.23518 − 0.97848I 0
u = 0.851397 − 0.934773I
a = 0.585957 + 0.403561I
b = 0.883007 − 0.461434I
−5.23518 + 0.97848I 0
u = −1.279860 + 0.048073I
a = −0.013258 − 0.408102I
b = 0.563062 + 0.424866I
−10.4637 + 10.2771I 0
u = −1.279860 − 0.048073I
a = −0.013258 + 0.408102I
b = 0.563062 − 0.424866I
−10.4637 − 10.2771I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.026340 + 0.782336I
a = −0.648271 + 0.252540I
b = −0.903269 − 0.402288I
−1.47950 − 3.15939I 0
u = 1.026340 − 0.782336I
a = −0.648271 − 0.252540I
b = −0.903269 + 0.402288I
−1.47950 + 3.15939I 0
u = 1.096650 + 0.689552I
a = −1.80294 − 0.63195I
b = −1.43879 − 1.94992I
−0.0438 − 14.3168I 0
u = 1.096650 − 0.689552I
a = −1.80294 + 0.63195I
b = −1.43879 + 1.94992I
−0.0438 + 14.3168I 0
u = −1.100720 + 0.704461I
a = 1.281180 − 0.579729I
b = 0.96217 − 1.58767I
3.74576 + 8.60988I 0
u = −1.100720 − 0.704461I
a = 1.281180 + 0.579729I
b = 0.96217 + 1.58767I
3.74576 − 8.60988I 0
u = 1.123730 + 0.693230I
a = 1.78117 + 0.64669I
b = 1.47918 + 2.08470I
−5.4572 − 18.5419I 0
u = 1.123730 − 0.693230I
a = 1.78117 − 0.64669I
b = 1.47918 − 2.08470I
−5.4572 + 18.5419I 0
u = −1.145170 + 0.703645I
a = −1.216640 + 0.551669I
b = −1.02688 + 1.57913I
−1.22739 + 12.51770I 0
u = −1.145170 − 0.703645I
a = −1.216640 − 0.551669I
b = −1.02688 − 1.57913I
−1.22739 − 12.51770I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.357540 + 0.184763I
a = −0.140088 − 0.106922I
b = −0.217060 + 0.411317I
−6.88882 − 3.53968I 0
u = 1.357540 − 0.184763I
a = −0.140088 + 0.106922I
b = −0.217060 − 0.411317I
−6.88882 + 3.53968I 0
u = 1.285270 + 0.572998I
a = −0.429502 + 0.031586I
b = −0.707482 + 0.030623I
−6.66935 + 0.80668I 0
u = 1.285270 − 0.572998I
a = −0.429502 − 0.031586I
b = −0.707482 − 0.030623I
−6.66935 − 0.80668I 0
u = 0.516771 + 0.279860I
a = 0.104453 + 1.197220I
b = −1.045920 + 0.531522I
−1.45581 − 2.03254I 1.98699 + 4.69397I
u = 0.516771 − 0.279860I
a = 0.104453 − 1.197220I
b = −1.045920 − 0.531522I
−1.45581 + 2.03254I 1.98699 − 4.69397I
u = 1.148910 + 0.824600I
a = 0.547230 − 0.223458I
b = 0.971811 + 0.306781I
−6.17233 − 5.96120I 0
u = 1.148910 − 0.824600I
a = 0.547230 + 0.223458I
b = 0.971811 − 0.306781I
−6.17233 + 5.96120I 0
u = −0.393907 + 0.222200I
a = −2.31125 − 2.68310I
b = −1.094040 + 0.870164I
−4.27194 + 4.28516I −0.73417 − 1.61280I
u = −0.393907 − 0.222200I
a = −2.31125 + 2.68310I
b = −1.094040 − 0.870164I
−4.27194 − 4.28516I −0.73417 + 1.61280I
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.062800 + 0.374522I
a = −1.00837 − 1.66128I
b = −0.164422 + 0.714048I
−2.90409 − 2.08093I 3.46783 + 4.41904I
u = 0.062800 − 0.374522I
a = −1.00837 + 1.66128I
b = −0.164422 − 0.714048I
−2.90409 + 2.08093I 3.46783 − 4.41904I
u = −0.107754 + 0.232769I
a = 0.65259 + 3.66655I
b = 0.687564 − 0.832329I
0.279130 + 0.757424I 6.19556 − 0.41609I
u = −0.107754 − 0.232769I
a = 0.65259 − 3.66655I
b = 0.687564 + 0.832329I
0.279130 − 0.757424I 6.19556 + 0.41609I
u = −0.240618
a = 2.16389
b = 0.603280
0.744592 13.6290
15
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
105
+ 41u
104
+ ··· + 13u + 1
c
2
, c
5
u
105
+ 7u
104
+ ··· + 3u − 1
c
3
u
105
− u
104
+ ··· − 3u − 1
c
4
, c
12
u
105
+ 7u
104
+ ··· + 3u − 1
c
6
u
105
− u
104
+ ··· + 625275u − 85457
c
7
, c
10
, c
11
u
105
+ u
104
+ ··· + u − 1
c
8
u
105
+ 3u
104
+ ··· − 31u − 3
c
9
u
105
+ u
104
+ ··· + 413u − 2359
16
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
105
+ 47y
104
+ ··· + 245y −1
c
2
, c
5
y
105
− 41y
104
+ ··· + 13y −1
c
3
y
105
+ 7y
104
+ ··· + 69y −1
c
4
, c
12
y
105
+ 67y
104
+ ··· + 13y −1
c
6
y
105
− 25y
104
+ ··· + 228484645933y −7302898849
c
7
, c
10
, c
11
y
105
+ 91y
104
+ ··· + 45y −1
c
8
y
105
+ 231y
104
+ ··· − 3743y −9
c
9
y
105
− 209y
104
+ ··· + 318380797y −5564881
17
