12n
0316
(K12n
0316
)
A knot diagram
1
Linearized knot diagam
3 6 12 7 2 10 3 12 1 5 7 9
Solving Sequence
3,6
2
1,9
10 7 5 4 12 8 11
c
2
c
1
c
9
c
6
c
5
c
4
c
12
c
8
c
11
c
3
, c
7
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h1.49187 × 10
37
u
44
− 1.01328 × 10
37
u
43
+ ··· + 2.01007 × 10
37
b − 7.03971 × 10
37
,
− 1.39776 × 10
38
u
44
+ 1.68461 × 10
38
u
43
+ ··· + 1.40705 × 10
38
a + 1.95501 × 10
39
,
u
45
− 2u
44
+ ··· − 63u + 7i
I
u
2
= h−3u
12
− 7u
11
+ 2u
10
+ 24u
9
+ 6u
8
− 43u
7
− 27u
6
+ 49u
5
+ 37u
4
− 29u
3
− 27u
2
+ b + 10u + 7,
5u
12
+ 13u
11
− 2u
10
− 44u
9
− 19u
8
+ 78u
7
+ 60u
6
− 84u
5
− 82u
4
+ 47u
3
+ 53u
2
+ a − 13u − 13,
u
13
+ 3u
12
+ u
11
− 8u
10
− 7u
9
+ 12u
8
+ 17u
7
− 9u
6
− 20u
5
+ u
4
+ 12u
3
+ 2u
2
− 3u − 1i
* 2 irreducible components of dim
C
= 0, with total 58 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
= h1.49 × 10
37
u
44
− 1.01 × 10
37
u
43
+ · · · + 2.01 × 10
37
b − 7.04 ×
10
37
, −1.40 × 10
38
u
44
+ 1.68 × 10
38
u
43
+ · · · + 1.41 × 10
38
a + 1.96 ×
10
39
, u
45
− 2u
44
+ · · · − 63u + 7i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
u
a
2
=
1
−u
2
a
1
=
−u
2
+ 1
−u
2
a
9
=
0.993395u
44
− 1.19726u
43
+ ··· + 89.5674u − 13.8944
−0.742197u
44
+ 0.504102u
43
+ ··· − 24.9174u + 3.50222
a
10
=
0.168633u
44
− 0.289227u
43
+ ··· + 40.1071u − 8.51481
−0.625412u
44
+ 0.0300369u
43
+ ··· + 0.0542180u − 0.00472178
a
7
=
−2.57523u
44
+ 2.47327u
43
+ ··· − 150.787u + 17.0513
−0.238127u
44
− 0.117959u
43
+ ··· + 25.4258u − 2.94147
a
5
=
u
−u
3
+ u
a
4
=
0.0434605u
44
− 0.501873u
43
+ ··· + 32.2099u − 4.00706
−1.00696u
44
+ 1.07716u
43
+ ··· − 66.0581u + 8.54528
a
12
=
−1.44259u
44
+ 2.27648u
43
+ ··· − 114.430u + 18.0623
0.842298u
44
− 0.861398u
43
+ ··· + 32.9618u − 4.57062
a
8
=
−2.81336u
44
+ 2.35531u
43
+ ··· − 125.361u + 14.1099
−0.238127u
44
− 0.117959u
43
+ ··· + 25.4258u − 2.94147
a
11
=
−0.991831u
44
+ 1.08676u
43
+ ··· − 88.6012u + 14.4109
0.546953u
44
− 0.100468u
43
+ ··· − 0.832675u − 0.0412010
(ii) Obstruction class = −1
(iii) Cusp Shapes = −1.33381u
44
+ 0.732754u
43
+ ··· − 88.2937u − 0.929056
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
45
+ 18u
44
+ ··· + 3381u + 49
c
2
, c
5
u
45
+ 2u
44
+ ··· − 63u − 7
c
3
, c
10
u
45
− u
44
+ ··· − 20u − 1
c
4
u
45
+ 7u
44
+ ··· + 15464u + 821
c
6
u
45
+ 4u
44
+ ··· − 22u − 4
c
7
u
45
− 3u
44
+ ··· + 22696u + 3551
c
8
, c
9
, c
12
u
45
+ u
44
+ ··· + 64u + 19
c
11
u
45
+ u
44
+ ··· − 63u + 9
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
45
+ 42y
44
+ ··· + 6542725y −2401
c
2
, c
5
y
45
− 18y
44
+ ··· + 3381y −49
c
3
, c
10
y
45
+ 57y
44
+ ··· + 198y −1
c
4
y
45
− 63y
44
+ ··· + 21028436y −674041
c
6
y
45
− 4y
44
+ ··· − 68y −16
c
7
y
45
− 53y
44
+ ··· + 550810170y −12609601
c
8
, c
9
, c
12
y
45
− 35y
44
+ ··· − 84y −361
c
11
y
45
+ 75y
44
+ ··· + 405y −81
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.352517 + 0.930511I
a = −2.09255 − 0.56873I
b = −1.53917 − 0.68803I
0.92371 − 3.61571I −7.30973 + 5.35358I
u = −0.352517 − 0.930511I
a = −2.09255 + 0.56873I
b = −1.53917 + 0.68803I
0.92371 + 3.61571I −7.30973 − 5.35358I
u = −0.622969 + 0.745341I
a = −0.498948 − 0.274339I
b = 0.0307757 + 0.1234220I
3.19833 + 0.47295I −2.90845 − 1.14935I
u = −0.622969 − 0.745341I
a = −0.498948 + 0.274339I
b = 0.0307757 − 0.1234220I
3.19833 − 0.47295I −2.90845 + 1.14935I
u = 0.852606 + 0.644697I
a = −1.60431 + 2.03212I
b = −0.66092 + 1.63965I
7.67151 − 0.54614I −7.14162 + 2.19289I
u = 0.852606 − 0.644697I
a = −1.60431 − 2.03212I
b = −0.66092 − 1.63965I
7.67151 + 0.54614I −7.14162 − 2.19289I
u = 0.870374 + 0.636220I
a = −1.51114 + 2.96200I
b = 0.84979 + 1.64164I
7.61467 − 4.45079I −7.29611 + 4.22653I
u = 0.870374 − 0.636220I
a = −1.51114 − 2.96200I
b = 0.84979 − 1.64164I
7.61467 + 4.45079I −7.29611 − 4.22653I
u = −0.706985 + 0.572515I
a = 1.61320 + 1.43432I
b = 0.612546 + 1.273340I
−0.603650 + 1.183020I −7.09381 − 2.18131I
u = −0.706985 − 0.572515I
a = 1.61320 − 1.43432I
b = 0.612546 − 1.273340I
−0.603650 − 1.183020I −7.09381 + 2.18131I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.017280 + 0.456940I
a = −0.20833 − 1.43339I
b = −1.77851 + 0.14760I
−2.41679 − 3.11933I −8.64263 + 5.00261I
u = 1.017280 − 0.456940I
a = −0.20833 + 1.43339I
b = −1.77851 − 0.14760I
−2.41679 + 3.11933I −8.64263 − 5.00261I
u = −0.837872 + 0.180212I
a = −0.719453 + 0.504755I
b = −0.475414 + 1.151620I
5.23022 + 2.95335I −10.41493 − 5.15699I
u = −0.837872 − 0.180212I
a = −0.719453 − 0.504755I
b = −0.475414 − 1.151620I
5.23022 − 2.95335I −10.41493 + 5.15699I
u = 0.829207 + 0.087175I
a = 2.10128 − 0.71672I
b = −0.375197 + 0.692927I
−6.31151 − 0.37732I −13.18619 − 0.42975I
u = 0.829207 − 0.087175I
a = 2.10128 + 0.71672I
b = −0.375197 − 0.692927I
−6.31151 + 0.37732I −13.18619 + 0.42975I
u = −0.780783 + 0.287291I
a = 0.16773 − 2.15348I
b = 1.01268 + 1.14500I
5.58706 − 0.92954I −9.44375 − 1.95517I
u = −0.780783 − 0.287291I
a = 0.16773 + 2.15348I
b = 1.01268 − 1.14500I
5.58706 + 0.92954I −9.44375 + 1.95517I
u = 0.741986 + 0.904888I
a = 1.232980 − 0.115587I
b = 0.350843 − 0.128409I
12.46620 + 1.15235I −3.81779 + 0.34527I
u = 0.741986 − 0.904888I
a = 1.232980 + 0.115587I
b = 0.350843 + 0.128409I
12.46620 − 1.15235I −3.81779 − 0.34527I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.822383
a = −2.63142
b = 0.371288
−10.1445 9.33710
u = 0.702661 + 0.398793I
a = −0.853897 + 0.310274I
b = −0.210564 + 0.967639I
−1.09811 − 1.39547I −6.56054 + 4.96588I
u = 0.702661 − 0.398793I
a = −0.853897 − 0.310274I
b = −0.210564 − 0.967639I
−1.09811 + 1.39547I −6.56054 − 4.96588I
u = −1.021490 + 0.633982I
a = 0.047816 − 0.193328I
b = −0.358831 − 0.204765I
1.97257 + 4.80081I −5.11482 − 5.89967I
u = −1.021490 − 0.633982I
a = 0.047816 + 0.193328I
b = −0.358831 + 0.204765I
1.97257 − 4.80081I −5.11482 + 5.89967I
u = 0.760787 + 0.239478I
a = 0.429130 − 0.024508I
b = 0.810532 − 0.368894I
−1.101730 − 0.180700I −6.28342 − 1.85189I
u = 0.760787 − 0.239478I
a = 0.429130 + 0.024508I
b = 0.810532 + 0.368894I
−1.101730 + 0.180700I −6.28342 + 1.85189I
u = −1.067050 + 0.679768I
a = 0.77890 + 2.44088I
b = −0.89344 + 1.68496I
−1.81546 + 3.64143I −8.00000 − 2.52158I
u = −1.067050 − 0.679768I
a = 0.77890 − 2.44088I
b = −0.89344 − 1.68496I
−1.81546 − 3.64143I −8.00000 + 2.52158I
u = 1.018190 + 0.768985I
a = −0.662287 − 0.442499I
b = −0.108103 − 0.271060I
11.57780 − 7.32875I −8.00000 + 4.62290I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.018190 − 0.768985I
a = −0.662287 + 0.442499I
b = −0.108103 + 0.271060I
11.57780 + 7.32875I −8.00000 − 4.62290I
u = 0.583636 + 1.148450I
a = 2.23765 − 1.83947I
b = 1.60697 − 1.61313I
8.75418 + 6.80607I −8.00000 − 4.07465I
u = 0.583636 − 1.148450I
a = 2.23765 + 1.83947I
b = 1.60697 + 1.61313I
8.75418 − 6.80607I −8.00000 + 4.07465I
u = −1.161870 + 0.639019I
a = 0.16411 − 2.14514I
b = 1.88266 − 1.13204I
−1.49977 + 9.31425I 0
u = −1.161870 − 0.639019I
a = 0.16411 + 2.14514I
b = 1.88266 + 1.13204I
−1.49977 − 9.31425I 0
u = 1.041350 + 0.853737I
a = −0.50445 + 1.98666I
b = 0.433982 + 1.234590I
−4.65783 − 3.47814I 0
u = 1.041350 − 0.853737I
a = −0.50445 − 1.98666I
b = 0.433982 − 1.234590I
−4.65783 + 3.47814I 0
u = 1.38604
a = 0.478642
b = 2.27111
−5.50304 −17.6960
u = 1.17910 + 0.78373I
a = 0.21212 − 2.72362I
b = −1.47078 − 1.85341I
6.8143 − 13.6617I 0
u = 1.17910 − 0.78373I
a = 0.21212 + 2.72362I
b = −1.47078 + 1.85341I
6.8143 + 13.6617I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.28910 + 0.63728I
a = 0.22407 + 2.43968I
b = −1.41146 + 2.05143I
−1.85160 + 3.71712I 0
u = −1.28910 − 0.63728I
a = 0.22407 − 2.43968I
b = −1.41146 − 2.05143I
−1.85160 − 3.71712I 0
u = −1.10756 + 0.93089I
a = 0.042729 + 1.301160I
b = −0.474464 + 0.759384I
0.57168 + 3.78059I 0
u = −1.10756 − 0.93089I
a = 0.042729 − 1.301160I
b = −0.474464 − 0.759384I
0.57168 − 3.78059I 0
u = 0.138369
a = −2.03994
b = 0.689748
−0.867384 −10.9880
9
II. I
u
2
=
h−3u
12
−7u
11
+· · ·+b+7, 5u
12
+13u
11
+· · ·+a−13, u
13
+3u
12
+· · ·−3u−1i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
u
a
2
=
1
−u
2
a
1
=
−u
2
+ 1
−u
2
a
9
=
−5u
12
− 13u
11
+ ··· + 13u + 13
3u
12
+ 7u
11
+ ··· − 10u − 7
a
10
=
−6u
12
− 15u
11
+ ··· + 16u + 14
5u
12
+ 12u
11
+ ··· − 13u − 9
a
7
=
−4u
12
− 9u
11
+ ··· + 8u + 3
−u
12
− 3u
11
+ ··· − u + 3
a
5
=
u
−u
3
+ u
a
4
=
10u
12
+ 23u
11
+ ··· − 25u − 13
u
12
+ 3u
11
+ ··· + 2u − 4
a
12
=
3u
12
+ 6u
11
+ ··· − 8u − 8
−6u
12
− 15u
11
+ ··· + 13u + 11
a
8
=
−5u
12
− 12u
11
+ ··· + 7u + 6
−u
12
− 3u
11
+ ··· − u + 3
a
11
=
−9u
12
− 23u
11
+ ··· + 23u + 20
2u
12
+ 5u
11
+ ··· − 6u − 4
(ii) Obstruction class = 1
(iii) Cusp Shapes
= 3u
12
+ u
11
−19u
10
−32u
9
+ 28u
8
+ 70u
7
−22u
6
−115u
5
−12u
4
+ 84u
3
+ 28u
2
−36u −23
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
13
− 7u
12
+ ··· + 13u − 1
c
2
u
13
+ 3u
12
+ ··· − 3u − 1
c
3
u
13
+ 8u
11
+ 24u
9
+ u
8
+ 33u
7
+ 4u
6
+ 20u
5
+ 5u
4
+ 5u
3
+ u
2
+ 2u − 1
c
4
u
13
+ 4u
11
+ ··· + 6u − 1
c
5
u
13
− 3u
12
+ ··· − 3u + 1
c
6
u
13
+ 3u
12
− 5u
10
+ u
8
− 5u
7
+ 3u
6
+ 8u
5
− u
4
− 6u
3
− u
2
+ 2u + 1
c
7
u
13
+ 3u
11
+ ··· + 6u − 1
c
8
, c
9
u
13
− 8u
11
+ ··· + 2u + 1
c
10
u
13
+ 8u
11
+ 24u
9
− u
8
+ 33u
7
− 4u
6
+ 20u
5
− 5u
4
+ 5u
3
− u
2
+ 2u + 1
c
11
u
13
− 2u
12
+ ··· − 13u − 1
c
12
u
13
− 8u
11
+ ··· + 2u − 1
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
13
+ 21y
12
+ ··· + 21y −1
c
2
, c
5
y
13
− 7y
12
+ ··· + 13y −1
c
3
, c
10
y
13
+ 16y
12
+ ··· + 6y −1
c
4
y
13
+ 8y
12
+ ··· + 4y −1
c
6
y
13
− 9y
12
+ ··· + 6y −1
c
7
y
13
+ 6y
12
+ ··· + 22y −1
c
8
, c
9
, c
12
y
13
− 16y
12
+ ··· + 8y −1
c
11
y
13
− 14y
12
+ ··· + 29y −1
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.881035 + 0.428633I
a = −1.93807 − 2.18231I
b = 0.402497 − 1.355330I
−5.55501 + 1.76839I −9.42733 − 3.99027I
u = −0.881035 − 0.428633I
a = −1.93807 + 2.18231I
b = 0.402497 + 1.355330I
−5.55501 − 1.76839I −9.42733 + 3.99027I
u = 0.910742
a = 2.11436
b = −0.698976
−10.3385 −32.2600
u = 0.988275 + 0.624685I
a = −0.18264 + 1.54866I
b = 0.822715 + 0.363964I
−4.28208 − 2.74184I −11.58472 + 0.68743I
u = 0.988275 − 0.624685I
a = −0.18264 − 1.54866I
b = 0.822715 − 0.363964I
−4.28208 + 2.74184I −11.58472 − 0.68743I
u = 0.786272 + 0.257302I
a = −1.165010 + 0.236660I
b = −0.544518 + 1.013380I
−1.90498 − 0.74935I −15.2105 + 0.6429I
u = 0.786272 − 0.257302I
a = −1.165010 − 0.236660I
b = −0.544518 − 1.013380I
−1.90498 + 0.74935I −15.2105 − 0.6429I
u = −1.010700 + 0.772169I
a = 0.445697 + 0.983245I
b = 0.008357 + 0.919135I
1.40993 + 3.16875I −4.51782 − 0.85705I
u = −1.010700 − 0.772169I
a = 0.445697 − 0.983245I
b = 0.008357 − 0.919135I
1.40993 − 3.16875I −4.51782 + 0.85705I
u = −0.501636 + 0.101564I
a = 0.96670 + 1.91810I
b = 0.581751 − 1.286380I
6.06288 + 2.09354I −6.13746 − 2.14572I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.501636 − 0.101564I
a = 0.96670 − 1.91810I
b = 0.581751 + 1.286380I
6.06288 − 2.09354I −6.13746 + 2.14572I
u = −1.33655 + 1.04817I
a = 0.31613 + 3.50034I
b = −0.92132 + 3.01182I
−2.07604 + 4.55409I −12.9921 − 8.8615I
u = −1.33655 − 1.04817I
a = 0.31613 − 3.50034I
b = −0.92132 − 3.01182I
−2.07604 − 4.55409I −12.9921 + 8.8615I
14
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
13
− 7u
12
+ ··· + 13u − 1)(u
45
+ 18u
44
+ ··· + 3381u + 49)
c
2
(u
13
+ 3u
12
+ ··· − 3u − 1)(u
45
+ 2u
44
+ ··· − 63u − 7)
c
3
(u
13
+ 8u
11
+ 24u
9
+ u
8
+ 33u
7
+ 4u
6
+ 20u
5
+ 5u
4
+ 5u
3
+ u
2
+ 2u − 1)
· (u
45
− u
44
+ ··· − 20u − 1)
c
4
(u
13
+ 4u
11
+ ··· + 6u − 1)(u
45
+ 7u
44
+ ··· + 15464u + 821)
c
5
(u
13
− 3u
12
+ ··· − 3u + 1)(u
45
+ 2u
44
+ ··· − 63u − 7)
c
6
(u
13
+ 3u
12
− 5u
10
+ u
8
− 5u
7
+ 3u
6
+ 8u
5
− u
4
− 6u
3
− u
2
+ 2u + 1)
· (u
45
+ 4u
44
+ ··· − 22u − 4)
c
7
(u
13
+ 3u
11
+ ··· + 6u − 1)(u
45
− 3u
44
+ ··· + 22696u + 3551)
c
8
, c
9
(u
13
− 8u
11
+ ··· + 2u + 1)(u
45
+ u
44
+ ··· + 64u + 19)
c
10
(u
13
+ 8u
11
+ 24u
9
− u
8
+ 33u
7
− 4u
6
+ 20u
5
− 5u
4
+ 5u
3
− u
2
+ 2u + 1)
· (u
45
− u
44
+ ··· − 20u − 1)
c
11
(u
13
− 2u
12
+ ··· − 13u − 1)(u
45
+ u
44
+ ··· − 63u + 9)
c
12
(u
13
− 8u
11
+ ··· + 2u − 1)(u
45
+ u
44
+ ··· + 64u + 19)
15
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
13
+ 21y
12
+ ··· + 21y −1)(y
45
+ 42y
44
+ ··· + 6542725y −2401)
c
2
, c
5
(y
13
− 7y
12
+ ··· + 13y −1)(y
45
− 18y
44
+ ··· + 3381y −49)
c
3
, c
10
(y
13
+ 16y
12
+ ··· + 6y −1)(y
45
+ 57y
44
+ ··· + 198y −1)
c
4
(y
13
+ 8y
12
+ ··· + 4y −1)(y
45
− 63y
44
+ ··· + 2.10284 × 10
7
y −674041)
c
6
(y
13
− 9y
12
+ ··· + 6y −1)(y
45
− 4y
44
+ ··· − 68y −16)
c
7
(y
13
+ 6y
12
+ ··· + 22y −1)
· (y
45
− 53y
44
+ ··· + 550810170y −12609601)
c
8
, c
9
, c
12
(y
13
− 16y
12
+ ··· + 8y −1)(y
45
− 35y
44
+ ··· − 84y −361)
c
11
(y
13
− 14y
12
+ ··· + 29y −1)(y
45
+ 75y
44
+ ··· + 405y −81)
16
