12n
0699
(K12n
0699
)
A knot diagram
1
Linearized knot diagam
4 5 9 11 10 3 12 11 6 2 8 9
Solving Sequence
2,10 6,11
5 3 4 1 9 8 12 7
c
10
c
5
c
2
c
4
c
1
c
9
c
8
c
12
c
7
c
3
, c
6
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−4.48533 × 10
64
u
38
− 1.99110 × 10
65
u
37
+ ··· + 1.70583 × 10
66
b + 7.99429 × 10
65
,
2.92714 × 10
66
u
38
+ 1.55651 × 10
67
u
37
+ ··· + 4.94689 × 10
67
a + 4.66164 × 10
68
, u
39
+ 4u
38
+ ··· + 95u + 29i
I
u
2
= h−206u
15
+ 554u
14
+ ··· + 239b + 200, −339u
15
+ 914u
14
+ ··· + 239a + 53,
u
16
− 3u
15
+ 5u
14
− 4u
13
+ 3u
12
− 6u
11
+ 12u
10
− 10u
9
+ u
8
+ 6u
7
− 3u
5
+ 2u
4
+ 3u
3
− u + 1i
* 2 irreducible components of dim
C
= 0, with total 55 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−4.49 × 10
64
u
38
− 1.99 × 10
65
u
37
+ · · · + 1.71 × 10
66
b + 7.99 ×
10
65
, 2.93 × 10
66
u
38
+ 1.56 × 10
67
u
37
+ · · · + 4.95 × 10
67
a + 4.66 ×
10
68
, u
39
+ 4u
38
+ · · · + 95u + 29i
(i) Arc colorings
a
2
=
0
u
a
10
=
1
0
a
6
=
−0.0591713u
38
− 0.314643u
37
+ ··· − 24.3274u − 9.42337
0.0262942u
38
+ 0.116723u
37
+ ··· + 4.56393u − 0.468647
a
11
=
1
−u
2
a
5
=
−0.0854656u
38
− 0.431367u
37
+ ··· − 28.8913u − 8.95473
0.0262942u
38
+ 0.116723u
37
+ ··· + 4.56393u − 0.468647
a
3
=
0.517557u
38
+ 2.13119u
37
+ ··· + 67.6443u + 17.6022
0.128326u
38
+ 0.499772u
37
+ ··· + 14.8366u + 3.04010
a
4
=
0.0201548u
38
− 0.000488821u
37
+ ··· − 13.3460u − 6.82775
0.0712460u
38
+ 0.287520u
37
+ ··· + 8.42457u − 0.225151
a
1
=
0.120505u
38
+ 0.724667u
37
+ ··· + 51.9973u + 19.7269
−0.0193862u
38
+ 0.0323405u
37
+ ··· + 18.8628u + 7.88916
a
9
=
−0.170703u
38
− 0.565196u
37
+ ··· − 9.52828u + 2.61870
−0.0658720u
38
− 0.274198u
37
+ ··· − 13.3540u − 2.25891
a
8
=
−0.108782u
38
− 0.236844u
37
+ ··· + 10.0488u + 8.28847
−0.00548525u
38
− 0.0123701u
37
+ ··· − 3.89489u + 0.0804277
a
12
=
−0.406322u
38
− 1.94808u
37
+ ··· − 100.418u − 28.6038
−0.156580u
38
− 0.684622u
37
+ ··· − 24.5158u − 6.19127
a
7
=
0.518418u
38
+ 1.72726u
37
+ ··· + 17.1390u − 6.89267
0.124927u
38
+ 0.415220u
37
+ ··· − 0.251870u − 2.53467
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.432519u
38
− 1.98528u
37
+ ··· − 85.2061u − 12.7504
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
39
+ 6u
38
+ ··· + 68813u − 4453
c
2
u
39
+ 12u
38
+ ··· + 33u − 1
c
3
u
39
− u
38
+ ··· − 7950u − 6379
c
4
u
39
− 17u
37
+ ··· + 59051u − 25039
c
5
, c
9
u
39
− 3u
38
+ ··· − 8u − 1
c
6
u
39
− 4u
38
+ ··· + 621578u − 106361
c
7
, c
8
, c
11
u
39
+ u
38
+ ··· + 40u − 13
c
10
u
39
− 4u
38
+ ··· + 95u − 29
c
12
u
39
− u
38
+ ··· + 1387526u − 100009
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
39
− 86y
38
+ ··· + 1745564923y −19829209
c
2
y
39
+ 12y
38
+ ··· + 2135y −1
c
3
y
39
+ 77y
38
+ ··· − 133130362y −40691641
c
4
y
39
− 34y
38
+ ··· + 7818316899y −626951521
c
5
, c
9
y
39
+ 31y
38
+ ··· + 48y −1
c
6
y
39
+ 52y
38
+ ··· + 161820928428y −11312662321
c
7
, c
8
, c
11
y
39
+ 61y
38
+ ··· − 4614y −169
c
10
y
39
+ 12y
38
+ ··· − 9187y −841
c
12
y
39
+ 199y
38
+ ··· − 836738153944y −10001800081
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.443892 + 0.894212I
a = 0.136058 − 0.043126I
b = 1.102760 + 0.179428I
−4.34392 + 3.40044I 2.15847 − 4.15591I
u = 0.443892 − 0.894212I
a = 0.136058 + 0.043126I
b = 1.102760 − 0.179428I
−4.34392 − 3.40044I 2.15847 + 4.15591I
u = 0.584880 + 0.814792I
a = 1.18601 − 1.16107I
b = −0.391017 − 1.238900I
−2.68089 + 4.77988I 0.54174 − 3.58018I
u = 0.584880 − 0.814792I
a = 1.18601 + 1.16107I
b = −0.391017 + 1.238900I
−2.68089 − 4.77988I 0.54174 + 3.58018I
u = 0.388962 + 0.964036I
a = −0.68810 + 1.25836I
b = 0.080712 + 1.199870I
−3.44253 − 0.59700I 4.34930 + 3.15252I
u = 0.388962 − 0.964036I
a = −0.68810 − 1.25836I
b = 0.080712 − 1.199870I
−3.44253 + 0.59700I 4.34930 − 3.15252I
u = 0.724071 + 0.767036I
a = 0.527790 + 0.780046I
b = 0.123047 + 0.078516I
−3.74668 + 1.00507I 3.79526 − 1.05866I
u = 0.724071 − 0.767036I
a = 0.527790 − 0.780046I
b = 0.123047 − 0.078516I
−3.74668 − 1.00507I 3.79526 + 1.05866I
u = −0.181436 + 0.922500I
a = −0.74681 − 1.43570I
b = 0.57246 − 1.38204I
−8.18165 − 2.82026I −0.23535 + 2.51294I
u = −0.181436 − 0.922500I
a = −0.74681 + 1.43570I
b = 0.57246 + 1.38204I
−8.18165 + 2.82026I −0.23535 − 2.51294I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.215429 + 1.104370I
a = 0.271873 − 1.261790I
b = −0.70054 − 1.42784I
19.5709 − 0.0915I −0.041291 + 0.250584I
u = −0.215429 − 1.104370I
a = 0.271873 + 1.261790I
b = −0.70054 + 1.42784I
19.5709 + 0.0915I −0.041291 − 0.250584I
u = 0.869795 + 0.024295I
a = 0.313165 + 0.718063I
b = 0.524688 + 0.787160I
−3.32799 + 1.95686I 7.87158 − 4.03984I
u = 0.869795 − 0.024295I
a = 0.313165 − 0.718063I
b = 0.524688 − 0.787160I
−3.32799 − 1.95686I 7.87158 + 4.03984I
u = −0.567289 + 0.618604I
a = −0.642417 + 0.111976I
b = 0.429754 + 0.191974I
0.70753 − 1.66098I 4.28580 + 6.70295I
u = −0.567289 − 0.618604I
a = −0.642417 − 0.111976I
b = 0.429754 − 0.191974I
0.70753 + 1.66098I 4.28580 − 6.70295I
u = −0.958602 + 0.745202I
a = −0.176071 + 1.110370I
b = −0.507024 − 0.126186I
−14.7115 + 0.6008I 6.01609 + 0.22717I
u = −0.958602 − 0.745202I
a = −0.176071 − 1.110370I
b = −0.507024 + 0.126186I
−14.7115 − 0.6008I 6.01609 − 0.22717I
u = −0.016312 + 0.768909I
a = 1.61762 + 2.88519I
b = 0.085474 + 1.237340I
−7.68184 + 2.01879I −2.91621 − 3.56990I
u = −0.016312 − 0.768909I
a = 1.61762 − 2.88519I
b = 0.085474 − 1.237340I
−7.68184 − 2.01879I −2.91621 + 3.56990I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.202386 + 0.647908I
a = −0.94963 + 5.33367I
b = −0.170246 + 1.217870I
−17.9862 − 1.8167I −3.56636 + 4.57014I
u = −0.202386 − 0.647908I
a = −0.94963 − 5.33367I
b = −0.170246 − 1.217870I
−17.9862 + 1.8167I −3.56636 − 4.57014I
u = −0.710408 + 1.123780I
a = −0.072881 + 0.197480I
b = −1.171160 + 0.168197I
−16.1607 − 6.8649I 3.92588 + 3.99664I
u = −0.710408 − 1.123780I
a = −0.072881 − 0.197480I
b = −1.171160 − 0.168197I
−16.1607 + 6.8649I 3.92588 − 3.99664I
u = −0.958522 + 1.029410I
a = −0.881055 − 1.083290I
b = 0.205727 − 1.202210I
−2.36145 − 4.18202I 0
u = −0.958522 − 1.029410I
a = −0.881055 + 1.083290I
b = 0.205727 + 1.202210I
−2.36145 + 4.18202I 0
u = −0.68503 + 1.28773I
a = 0.274506 + 1.250660I
b = −0.317094 + 1.299910I
−3.61146 − 3.57309I 0
u = −0.68503 − 1.28773I
a = 0.274506 − 1.250660I
b = −0.317094 − 1.299910I
−3.61146 + 3.57309I 0
u = 0.060370 + 0.511531I
a = 0.280864 − 0.578455I
b = −0.835944 + 0.134295I
0.840144 + 0.301601I 5.20449 + 2.88042I
u = 0.060370 − 0.511531I
a = 0.280864 + 0.578455I
b = −0.835944 − 0.134295I
0.840144 − 0.301601I 5.20449 − 2.88042I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.85204 + 1.41437I
a = −0.370591 + 1.342560I
b = 0.43395 + 1.41226I
−9.43948 + 8.71487I 0
u = 0.85204 − 1.41437I
a = −0.370591 − 1.342560I
b = 0.43395 − 1.41226I
−9.43948 − 8.71487I 0
u = −0.335045
a = −0.614690
b = −0.549698
0.786782 11.7610
u = −0.98641 + 1.38943I
a = 0.58183 + 1.36840I
b = −0.49379 + 1.44935I
18.1844 − 12.7063I 0
u = −0.98641 − 1.38943I
a = 0.58183 − 1.36840I
b = −0.49379 − 1.44935I
18.1844 + 12.7063I 0
u = 1.51194 + 1.37229I
a = 0.442968 − 1.000110I
b = −0.020088 − 1.263070I
−7.39813 + 0.94271I 0
u = 1.51194 − 1.37229I
a = 0.442968 + 1.000110I
b = −0.020088 + 1.263070I
−7.39813 − 0.94271I 0
u = −1.78660 + 1.18481I
a = −0.263303 − 0.886923I
b = −0.176813 − 1.330570I
−19.3360 + 3.0576I 0
u = −1.78660 − 1.18481I
a = −0.263303 + 0.886923I
b = −0.176813 + 1.330570I
−19.3360 − 3.0576I 0
8
II. I
u
2
= h−206u
15
+ 554u
14
+ · · · + 239b + 200, −339u
15
+ 914u
14
+ · · · +
239a + 53, u
16
− 3u
15
+ · · · − u + 1i
(i) Arc colorings
a
2
=
0
u
a
10
=
1
0
a
6
=
1.41841u
15
− 3.82427u
14
+ ··· + 1.41423u − 0.221757
0.861925u
15
− 2.31799u
14
+ ··· + 0.393305u − 0.836820
a
11
=
1
−u
2
a
5
=
0.556485u
15
− 1.50628u
14
+ ··· + 1.02092u + 0.615063
0.861925u
15
− 2.31799u
14
+ ··· + 0.393305u − 0.836820
a
3
=
0.163180u
15
− 0.351464u
14
+ ··· + 2.17155u − 1.55649
−0.288703u
15
+ 0.698745u
14
+ ··· + 0.00418410u − 0.476987
a
4
=
1.55649u
15
− 4.50628u
14
+ ··· + 1.02092u − 0.384937
0.861925u
15
− 2.31799u
14
+ ··· + 1.39331u − 0.836820
a
1
=
−1.94979u
15
+ 5.66109u
14
+ ··· + 0.129707u − 1.78661
−1.01255u
15
+ 2.33473u
14
+ ··· − 1.78243u + 0.196653
a
9
=
−0.192469u
15
− 0.200837u
14
+ ··· − 1.33054u − 0.317992
−0.669456u
15
+ 1.51883u
14
+ ··· − 1.06276u + 0.154812
a
8
=
1.05858u
15
− 2.89540u
14
+ ··· + 0.317992u − 1.25105
−0.949791u
15
+ 2.66109u
14
+ ··· − 0.870293u + 1.21339
a
12
=
−0.163180u
15
+ 0.351464u
14
+ ··· − 2.17155u + 1.55649
0.288703u
15
− 0.698745u
14
+ ··· + 0.995816u + 1.47699
a
7
=
0.627615u
15
− 0.736402u
14
+ ··· + 2.12134u + 0.167364
0.899582u
15
− 2.32218u
14
+ ··· − 0.259414u − 0.426778
(ii) Obstruction class = 1
(iii) Cusp Shapes =
640
239
u
15
−
1930
239
u
14
+ ··· −
418
239
u +
91
239
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
16
− 13u
15
+ ··· − 41u + 5
c
2
u
16
+ 3u
15
+ ··· + u + 1
c
3
u
16
+ 5u
14
+ ··· − 3u
2
+ 1
c
4
u
16
− u
15
+ ··· − 3u + 1
c
5
u
16
− 2u
15
+ ··· − 8u + 5
c
6
u
16
+ 3u
15
+ ··· − 4u + 1
c
7
, c
8
u
16
+ 11u
14
+ ··· − 5u
2
+ 1
c
9
u
16
+ 2u
15
+ ··· + 8u + 5
c
10
u
16
− 3u
15
+ ··· − u + 1
c
11
u
16
+ 11u
14
+ ··· − 5u
2
+ 1
c
12
u
16
+ 18u
14
+ ··· + 4u + 1
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
16
− 13y
15
+ ··· + 129y + 25
c
2
y
16
− 3y
15
+ ··· − 7y + 1
c
3
y
16
+ 10y
15
+ ··· − 6y + 1
c
4
y
16
− y
15
+ ··· + y + 1
c
5
, c
9
y
16
+ 12y
15
+ ··· + 36y + 25
c
6
y
16
+ 9y
15
+ ··· − 4y + 1
c
7
, c
8
, c
11
y
16
+ 22y
15
+ ··· − 10y + 1
c
10
y
16
+ y
15
+ ··· − y + 1
c
12
y
16
+ 36y
15
+ ··· − 12y + 1
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.691915 + 0.809476I
a = −0.141371 − 0.368878I
b = −0.809947 − 0.085174I
−2.46403 + 2.62444I 6.23068 − 3.19231I
u = 0.691915 − 0.809476I
a = −0.141371 + 0.368878I
b = −0.809947 + 0.085174I
−2.46403 − 2.62444I 6.23068 + 3.19231I
u = −0.478310 + 0.598570I
a = −0.352507 + 0.241067I
b = 0.747607 + 0.372629I
1.24171 − 1.01060I 10.47599 + 2.54040I
u = −0.478310 − 0.598570I
a = −0.352507 − 0.241067I
b = 0.747607 − 0.372629I
1.24171 + 1.01060I 10.47599 − 2.54040I
u = −0.872633 + 0.901161I
a = −0.799950 − 1.113870I
b = 0.339325 − 1.214060I
−1.62684 − 5.00252I 9.33881 + 6.54924I
u = −0.872633 − 0.901161I
a = −0.799950 + 1.113870I
b = 0.339325 + 1.214060I
−1.62684 + 5.00252I 9.33881 − 6.54924I
u = −0.703248 + 0.221002I
a = 2.55456 + 1.15105I
b = 0.251764 + 1.099540I
−17.1600 + 1.1139I 3.03838 + 0.31992I
u = −0.703248 − 0.221002I
a = 2.55456 − 1.15105I
b = 0.251764 − 1.099540I
−17.1600 − 1.1139I 3.03838 − 0.31992I
u = 0.542037 + 1.148350I
a = −0.32058 + 1.58789I
b = −0.133199 + 1.270610I
−6.21575 − 0.64132I 1.39512 + 0.82339I
u = 0.542037 − 1.148350I
a = −0.32058 − 1.58789I
b = −0.133199 − 1.270610I
−6.21575 + 0.64132I 1.39512 − 0.82339I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.184320 + 0.475109I
a = 0.127955 − 0.290498I
b = −0.260397 − 1.111540I
−5.27072 + 2.33003I 1.62272 − 2.90954I
u = 1.184320 − 0.475109I
a = 0.127955 + 0.290498I
b = −0.260397 + 1.111540I
−5.27072 − 2.33003I 1.62272 + 2.90954I
u = 0.723742 + 1.105120I
a = 0.66985 − 1.77346I
b = −0.376215 − 1.341420I
−6.97182 + 6.95095I 2.09201 − 4.98121I
u = 0.723742 − 1.105120I
a = 0.66985 + 1.77346I
b = −0.376215 + 1.341420I
−6.97182 − 6.95095I 2.09201 + 4.98121I
u = 0.412174 + 0.462048I
a = 0.26204 + 1.56067I
b = −0.758938 + 0.847429I
−4.30084 − 1.41489I 0.806284 + 0.154147I
u = 0.412174 − 0.462048I
a = 0.26204 − 1.56067I
b = −0.758938 − 0.847429I
−4.30084 + 1.41489I 0.806284 − 0.154147I
13
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
16
− 13u
15
+ ··· − 41u + 5)(u
39
+ 6u
38
+ ··· + 68813u − 4453)
c
2
(u
16
+ 3u
15
+ ··· + u + 1)(u
39
+ 12u
38
+ ··· + 33u − 1)
c
3
(u
16
+ 5u
14
+ ··· − 3u
2
+ 1)(u
39
− u
38
+ ··· − 7950u − 6379)
c
4
(u
16
− u
15
+ ··· − 3u + 1)(u
39
− 17u
37
+ ··· + 59051u − 25039)
c
5
(u
16
− 2u
15
+ ··· − 8u + 5)(u
39
− 3u
38
+ ··· − 8u − 1)
c
6
(u
16
+ 3u
15
+ ··· − 4u + 1)(u
39
− 4u
38
+ ··· + 621578u − 106361)
c
7
, c
8
(u
16
+ 11u
14
+ ··· − 5u
2
+ 1)(u
39
+ u
38
+ ··· + 40u − 13)
c
9
(u
16
+ 2u
15
+ ··· + 8u + 5)(u
39
− 3u
38
+ ··· − 8u − 1)
c
10
(u
16
− 3u
15
+ ··· − u + 1)(u
39
− 4u
38
+ ··· + 95u − 29)
c
11
(u
16
+ 11u
14
+ ··· − 5u
2
+ 1)(u
39
+ u
38
+ ··· + 40u − 13)
c
12
(u
16
+ 18u
14
+ ··· + 4u + 1)(u
39
− u
38
+ ··· + 1387526u − 100009)
14
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
16
− 13y
15
+ ··· + 129y + 25)
· (y
39
− 86y
38
+ ··· + 1745564923y −19829209)
c
2
(y
16
− 3y
15
+ ··· − 7y + 1)(y
39
+ 12y
38
+ ··· + 2135y −1)
c
3
(y
16
+ 10y
15
+ ··· − 6y + 1)
· (y
39
+ 77y
38
+ ··· − 133130362y −40691641)
c
4
(y
16
− y
15
+ ··· + y + 1)
· (y
39
− 34y
38
+ ··· + 7818316899y −626951521)
c
5
, c
9
(y
16
+ 12y
15
+ ··· + 36y + 25)(y
39
+ 31y
38
+ ··· + 48y −1)
c
6
(y
16
+ 9y
15
+ ··· − 4y + 1)
· (y
39
+ 52y
38
+ ··· + 161820928428y −11312662321)
c
7
, c
8
, c
11
(y
16
+ 22y
15
+ ··· − 10y + 1)(y
39
+ 61y
38
+ ··· − 4614y −169)
c
10
(y
16
+ y
15
+ ··· − y + 1)(y
39
+ 12y
38
+ ··· − 9187y −841)
c
12
(y
16
+ 36y
15
+ ··· − 12y + 1)
· (y
39
+ 199y
38
+ ··· − 836738153944y −10001800081)
15
