12a
1121
(K12a
1121
)
A knot diagram
1
Linearized knot diagam
4 7 1 9 10 11 12 3 6 5 2 8
Solving Sequence
6,9
10 5 11 7
1,4
2 3 8 12
c
9
c
5
c
10
c
6
c
4
c
1
c
3
c
8
c
12
c
2
, c
7
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h5.90630 × 10
49
u
89
+ 1.31991 × 10
50
u
88
+ ··· + 4.25606 × 10
49
b + 3.51669 × 10
49
,
− 1.65197 × 10
49
u
89
− 4.23977 × 10
48
u
88
+ ··· + 4.25606 × 10
49
a − 8.68845 × 10
48
, u
90
+ 3u
89
+ ··· + u + 1i
* 1 irreducible components of dim
C
= 0, with total 90 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
= h5.91×10
49
u
89
+1.32×10
50
u
88
+· · ·+4.26×10
49
b+3.52×10
49
, −1.65×
10
49
u
89
−4.24×10
48
u
88
+· · ·+4.26×10
49
a−8.69×10
48
, u
90
+3u
89
+· · ·+u+1i
(i) Arc colorings
a
6
=
0
u
a
9
=
1
0
a
10
=
1
−u
2
a
5
=
−u
u
3
+ u
a
11
=
u
2
+ 1
−u
4
− 2u
2
a
7
=
u
5
+ 2u
3
+ u
−u
7
− 3u
5
− 2u
3
+ u
a
1
=
0.388146u
89
+ 0.0996172u
88
+ ··· − 3.53913u + 0.204143
−1.38774u
89
− 3.10125u
88
+ ··· − 1.81453u − 0.826277
a
4
=
−u
3
− 2u
u
3
+ u
a
2
=
0.373224u
89
+ 0.168382u
88
+ ··· − 6.26564u − 0.00828401
−1.30287u
89
− 2.95085u
88
+ ··· − 0.411641u − 0.715405
a
3
=
0.384238u
89
+ 0.247633u
88
+ ··· − 6.17011u − 0.0491235
−1.23224u
89
− 2.80698u
88
+ ··· − 0.113134u − 0.765808
a
8
=
−0.326104u
89
− 1.12314u
88
+ ··· − 2.90218u + 0.138637
0.0488887u
89
− 0.0899770u
88
+ ··· − 5.97900u + 1.15368
a
12
=
0.905595u
89
+ 3.12820u
88
+ ··· − 6.17823u − 0.729495
−1.10592u
89
− 2.60082u
88
+ ··· − 3.75255u + 1.73185
(ii) Obstruction class = −1
(iii) Cusp Shapes = 2.39862u
89
+ 7.11016u
88
+ ··· − 12.9059u + 1.64968
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
u
90
− u
89
+ ··· − 31u + 1
c
2
u
90
+ 3u
89
+ ··· + u + 1
c
4
, c
6
u
90
+ 3u
89
+ ··· + 7251u + 1721
c
5
, c
9
, c
10
u
90
− 3u
89
+ ··· − u + 1
c
7
, c
12
u
90
− u
89
+ ··· + 3u + 1
c
8
u
90
− u
89
+ ··· + 65361u + 5017
c
11
u
90
+ 35u
89
+ ··· + 75u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
y
90
− 59y
89
+ ··· − 335y + 1
c
2
y
90
− 3y
89
+ ··· − 95y + 1
c
4
, c
6
y
90
− 67y
89
+ ··· + 48208201y + 2961841
c
5
, c
9
, c
10
y
90
+ 73y
89
+ ··· + 9y + 1
c
7
, c
12
y
90
− 67y
89
+ ··· + 9y + 1
c
8
y
90
− 255y
89
+ ··· + 4511974197y + 25170289
c
11
y
90
− 331y
89
+ ··· − 9007y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.937123
a = 1.90392
b = −0.917372
1.63736 19.5510
u = −0.261061 + 1.099980I
a = −0.436661 − 1.288730I
b = 0.922105 + 0.512288I
−1.31351 − 2.59617I 0
u = −0.261061 − 1.099980I
a = −0.436661 + 1.288730I
b = 0.922105 − 0.512288I
−1.31351 + 2.59617I 0
u = −0.849717 + 0.127541I
a = 2.58445 − 2.17478I
b = −1.05607 + 1.83759I
−0.89862 − 13.13250I 2.00000 + 7.64404I
u = −0.849717 − 0.127541I
a = 2.58445 + 2.17478I
b = −1.05607 − 1.83759I
−0.89862 + 13.13250I 2.00000 − 7.64404I
u = 0.841272 + 0.138052I
a = −2.63082 − 1.87687I
b = 1.16893 + 1.60792I
3.99372 + 7.68634I 5.01991 − 6.90086I
u = 0.841272 − 0.138052I
a = −2.63082 + 1.87687I
b = 1.16893 − 1.60792I
3.99372 − 7.68634I 5.01991 + 6.90086I
u = −0.819056 + 0.226853I
a = 2.33150 − 1.49762I
b = −1.03530 + 1.27468I
1.07734 − 1.28710I 11.1015 + 10.6083I
u = −0.819056 − 0.226853I
a = 2.33150 + 1.49762I
b = −1.03530 − 1.27468I
1.07734 + 1.28710I 11.1015 − 10.6083I
u = 0.827904 + 0.067788I
a = −0.308488 − 0.082776I
b = 0.014970 − 0.313093I
6.67284 + 2.65477I 9.38233 − 1.76568I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.827904 − 0.067788I
a = −0.308488 + 0.082776I
b = 0.014970 + 0.313093I
6.67284 − 2.65477I 9.38233 + 1.76568I
u = 0.403334 + 1.103620I
a = 0.18830 − 1.67878I
b = −0.99729 + 1.41348I
1.03582 − 3.19789I 0
u = 0.403334 − 1.103620I
a = 0.18830 + 1.67878I
b = −0.99729 − 1.41348I
1.03582 + 3.19789I 0
u = −0.814581 + 0.083546I
a = −0.330391 − 0.060506I
b = 0.333110 − 0.548293I
3.22864 − 6.64156I 4.09104 + 6.26285I
u = −0.814581 − 0.083546I
a = −0.330391 + 0.060506I
b = 0.333110 + 0.548293I
3.22864 + 6.64156I 4.09104 − 6.26285I
u = −0.466390 + 0.665000I
a = 0.68025 − 1.38405I
b = −0.07940 + 1.41778I
−0.55470 − 2.94063I 5.53893 + 10.70355I
u = −0.466390 − 0.665000I
a = 0.68025 + 1.38405I
b = −0.07940 − 1.41778I
−0.55470 + 2.94063I 5.53893 − 10.70355I
u = −0.803094
a = 1.70297
b = −1.03993
2.35076 4.70780
u = −0.415202 + 1.125870I
a = −0.07193 − 1.70685I
b = 0.94307 + 1.68550I
−3.95530 + 8.58651I 0
u = −0.415202 − 1.125870I
a = −0.07193 + 1.70685I
b = 0.94307 − 1.68550I
−3.95530 − 8.58651I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.780177
a = 28.8634
b = −17.3034
0.642195 236.630
u = −0.768657 + 0.045497I
a = −1.26138 + 2.23210I
b = 0.30449 − 1.66593I
2.11470 − 2.09203I 6.08144 + 3.20366I
u = −0.768657 − 0.045497I
a = −1.26138 − 2.23210I
b = 0.30449 + 1.66593I
2.11470 + 2.09203I 6.08144 − 3.20366I
u = −0.359082 + 1.182080I
a = −0.277386 − 0.260116I
b = −0.497689 − 0.461522I
−0.13150 + 2.39964I 0
u = −0.359082 − 1.182080I
a = −0.277386 + 0.260116I
b = −0.497689 + 0.461522I
−0.13150 − 2.39964I 0
u = 0.750884 + 0.074464I
a = 1.56606 + 1.08475I
b = −0.333629 − 1.250990I
−2.07688 + 4.03513I −0.77206 − 5.75428I
u = 0.750884 − 0.074464I
a = 1.56606 − 1.08475I
b = −0.333629 + 1.250990I
−2.07688 − 4.03513I −0.77206 + 5.75428I
u = 0.750322
a = 4.62706
b = −2.19293
0.926282 10.3150
u = 0.516388 + 0.539580I
a = −1.22279 − 1.21451I
b = 0.33652 + 1.68820I
−6.08532 + 8.60177I −2.05233 − 8.35929I
u = 0.516388 − 0.539580I
a = −1.22279 + 1.21451I
b = 0.33652 − 1.68820I
−6.08532 − 8.60177I −2.05233 + 8.35929I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.587527 + 0.460758I
a = −1.49865 − 1.57895I
b = 0.04068 + 1.52677I
−5.79931 − 4.64010I −2.15185 + 2.96139I
u = 0.587527 − 0.460758I
a = −1.49865 + 1.57895I
b = 0.04068 − 1.52677I
−5.79931 + 4.64010I −2.15185 − 2.96139I
u = 0.276456 + 1.222790I
a = −0.308998 + 0.239699I
b = 0.356193 − 1.081640I
−5.54460 − 0.31885I 0
u = 0.276456 − 1.222790I
a = −0.308998 − 0.239699I
b = 0.356193 + 1.081640I
−5.54460 + 0.31885I 0
u = 0.377586 + 1.200650I
a = 0.412056 − 0.409749I
b = 0.140629 − 0.207567I
3.19378 + 1.68551I 0
u = 0.377586 − 1.200650I
a = 0.412056 + 0.409749I
b = 0.140629 + 0.207567I
3.19378 − 1.68551I 0
u = −0.313949 + 1.237250I
a = −0.350967 + 0.874435I
b = −0.48753 − 1.41857I
−1.54414 − 1.81425I 0
u = −0.313949 − 1.237250I
a = −0.350967 − 0.874435I
b = −0.48753 + 1.41857I
−1.54414 + 1.81425I 0
u = 0.058868 + 1.282810I
a = −0.515422 − 0.374024I
b = −1.12297 − 1.06200I
−6.48452 − 0.22424I 0
u = 0.058868 − 1.282810I
a = −0.515422 + 0.374024I
b = −1.12297 + 1.06200I
−6.48452 + 0.22424I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.091814 + 1.294430I
a = −0.471118 + 0.058377I
b = 0.478551 − 0.284575I
−3.57869 − 2.12683I 0
u = −0.091814 − 1.294430I
a = −0.471118 − 0.058377I
b = 0.478551 + 0.284575I
−3.57869 + 2.12683I 0
u = 0.334734 + 1.267370I
a = 1.19920 + 10.92680I
b = 8.39728 − 6.86782I
−3.28894 + 4.01947I 0
u = 0.334734 − 1.267370I
a = 1.19920 − 10.92680I
b = 8.39728 + 6.86782I
−3.28894 − 4.01947I 0
u = 0.021231 + 1.312000I
a = −0.37337 + 1.68595I
b = −0.90144 + 1.52731I
−6.45174 + 1.00513I 0
u = 0.021231 − 1.312000I
a = −0.37337 − 1.68595I
b = −0.90144 − 1.52731I
−6.45174 − 1.00513I 0
u = −0.687457
a = −2.11270
b = 0.254874
−3.59454 −2.08330
u = 0.317138 + 1.278160I
a = −2.36082 + 1.97757I
b = 2.24217 + 0.55331I
−3.05253 + 3.84993I 0
u = 0.317138 − 1.278160I
a = −2.36082 − 1.97757I
b = 2.24217 − 0.55331I
−3.05253 − 3.84993I 0
u = −0.464583 + 1.233390I
a = −0.763414 − 0.959331I
b = 0.691780 + 0.454765I
−2.15640 − 4.97754I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.464583 − 1.233390I
a = −0.763414 + 0.959331I
b = 0.691780 − 0.454765I
−2.15640 + 4.97754I 0
u = −0.291881 + 1.294590I
a = 1.81902 + 0.69556I
b = −0.444399 + 0.401299I
−7.67966 − 3.54806I 0
u = −0.291881 − 1.294590I
a = 1.81902 − 0.69556I
b = −0.444399 − 0.401299I
−7.67966 + 3.54806I 0
u = −0.354603 + 1.280270I
a = −0.578559 − 0.882544I
b = 1.106940 + 0.030534I
−1.63707 − 4.16714I 0
u = −0.354603 − 1.280270I
a = −0.578559 + 0.882544I
b = 1.106940 − 0.030534I
−1.63707 + 4.16714I 0
u = 0.085495 + 1.336500I
a = 0.895958 + 0.606142I
b = −0.0647435 − 0.0674574I
−6.92803 + 5.33049I 0
u = 0.085495 − 1.336500I
a = 0.895958 − 0.606142I
b = −0.0647435 + 0.0674574I
−6.92803 − 5.33049I 0
u = −0.333079 + 1.300200I
a = 2.15159 − 0.17648I
b = −0.17385 + 1.88326I
−2.09133 − 6.07186I 0
u = −0.333079 − 1.300200I
a = 2.15159 + 0.17648I
b = −0.17385 − 1.88326I
−2.09133 + 6.07186I 0
u = −0.024488 + 1.344540I
a = −0.25708 + 1.78304I
b = 0.086305 + 1.139830I
−10.82350 − 2.16535I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.024488 − 1.344540I
a = −0.25708 − 1.78304I
b = 0.086305 − 1.139830I
−10.82350 + 2.16535I 0
u = 0.325021 + 1.315680I
a = −1.83650 + 0.60450I
b = 0.301394 + 1.359290I
−6.43488 + 7.93390I 0
u = 0.325021 − 1.315680I
a = −1.83650 − 0.60450I
b = 0.301394 − 1.359290I
−6.43488 − 7.93390I 0
u = 0.366790 + 1.314970I
a = 0.103265 + 0.202107I
b = −0.153689 + 0.371111I
2.34671 + 6.95130I 0
u = 0.366790 − 1.314970I
a = 0.103265 − 0.202107I
b = −0.153689 − 0.371111I
2.34671 − 6.95130I 0
u = −0.357962 + 1.323750I
a = 0.252483 + 0.656103I
b = −0.199867 + 0.595001I
−1.18201 − 10.86480I 0
u = −0.357962 − 1.323750I
a = 0.252483 − 0.656103I
b = −0.199867 − 0.595001I
−1.18201 + 10.86480I 0
u = −0.372698 + 1.353660I
a = −2.57177 − 0.28581I
b = 1.10000 − 1.96529I
−5.5579 − 17.5286I 0
u = −0.372698 − 1.353660I
a = −2.57177 + 0.28581I
b = 1.10000 + 1.96529I
−5.5579 + 17.5286I 0
u = 0.367205 + 1.358040I
a = 2.38128 − 0.41798I
b = −1.24184 − 1.76183I
−0.71612 + 12.03670I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.367205 − 1.358040I
a = 2.38128 + 0.41798I
b = −1.24184 + 1.76183I
−0.71612 − 12.03670I 0
u = 0.11948 + 1.41428I
a = 0.799214 − 0.923726I
b = −0.40851 − 2.07647I
−12.3236 + 10.6039I 0
u = 0.11948 − 1.41428I
a = 0.799214 + 0.923726I
b = −0.40851 + 2.07647I
−12.3236 − 10.6039I 0
u = 0.15556 + 1.42068I
a = 1.273220 − 0.518064I
b = −0.40014 − 1.78278I
−11.86630 − 2.13825I 0
u = 0.15556 − 1.42068I
a = 1.273220 + 0.518064I
b = −0.40014 + 1.78278I
−11.86630 + 2.13825I 0
u = −0.36575 + 1.39002I
a = −2.00001 − 0.37638I
b = 1.29946 − 1.37796I
−4.01462 − 5.61115I 0
u = −0.36575 − 1.39002I
a = −2.00001 + 0.37638I
b = 1.29946 + 1.37796I
−4.01462 + 5.61115I 0
u = −0.10871 + 1.43775I
a = −0.711700 − 0.571145I
b = 0.41423 − 2.05484I
−7.26188 − 4.73080I 0
u = −0.10871 − 1.43775I
a = −0.711700 + 0.571145I
b = 0.41423 + 2.05484I
−7.26188 + 4.73080I 0
u = 0.363666 + 0.367971I
a = −0.71092 − 1.39826I
b = −0.358401 + 0.121100I
−1.70262 + 3.89923I 0.47407 − 8.44781I
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.363666 − 0.367971I
a = −0.71092 + 1.39826I
b = −0.358401 − 0.121100I
−1.70262 − 3.89923I 0.47407 + 8.44781I
u = −0.443041 + 0.210244I
a = 1.115080 − 0.803627I
b = −0.243882 + 0.331160I
0.977445 − 0.443469I 9.13598 + 2.65028I
u = −0.443041 − 0.210244I
a = 1.115080 + 0.803627I
b = −0.243882 − 0.331160I
0.977445 + 0.443469I 9.13598 − 2.65028I
u = −0.128903 + 0.435158I
a = 0.05734 − 1.56254I
b = 0.210102 − 1.022530I
−5.45762 − 1.72264I −7.56446 + 4.36840I
u = −0.128903 − 0.435158I
a = 0.05734 + 1.56254I
b = 0.210102 + 1.022530I
−5.45762 + 1.72264I −7.56446 − 4.36840I
u = 0.296041 + 0.340592I
a = −0.266482 − 0.465775I
b = 0.669387 + 0.440484I
−1.76112 − 1.36605I 0.34312 − 1.73006I
u = 0.296041 − 0.340592I
a = −0.266482 + 0.465775I
b = 0.669387 − 0.440484I
−1.76112 + 1.36605I 0.34312 + 1.73006I
u = −0.352145
a = −0.773626
b = −1.24362
−4.02007 9.15390
u = 0.137293 + 0.265055I
a = 0.19984 − 1.40052I
b = 0.363542 − 0.923994I
−1.69230 + 0.56377I −4.96157 + 0.85721I
u = 0.137293 − 0.265055I
a = 0.19984 + 1.40052I
b = 0.363542 + 0.923994I
−1.69230 − 0.56377I −4.96157 − 0.85721I
13
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
3
u
90
− u
89
+ ··· − 31u + 1
c
2
u
90
+ 3u
89
+ ··· + u + 1
c
4
, c
6
u
90
+ 3u
89
+ ··· + 7251u + 1721
c
5
, c
9
, c
10
u
90
− 3u
89
+ ··· − u + 1
c
7
, c
12
u
90
− u
89
+ ··· + 3u + 1
c
8
u
90
− u
89
+ ··· + 65361u + 5017
c
11
u
90
+ 35u
89
+ ··· + 75u + 1
14
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
3
y
90
− 59y
89
+ ··· − 335y + 1
c
2
y
90
− 3y
89
+ ··· − 95y + 1
c
4
, c
6
y
90
− 67y
89
+ ··· + 48208201y + 2961841
c
5
, c
9
, c
10
y
90
+ 73y
89
+ ··· + 9y + 1
c
7
, c
12
y
90
− 67y
89
+ ··· + 9y + 1
c
8
y
90
− 255y
89
+ ··· + 4511974197y + 25170289
c
11
y
90
− 331y
89
+ ··· − 9007y + 1
15
