12n
0704
(K12n
0704
)
A knot diagram
1
Linearized knot diagam
4 10 11 9 1 3 4 1 12 7 6 9
Solving Sequence
4,9 5,12
10 1 2 6 8 7 11 3
c
4
c
9
c
12
c
1
c
5
c
8
c
7
c
11
c
3
c
2
, c
6
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h1.19445 × 10
198
u
45
− 6.74601 × 10
197
u
44
+ ··· + 4.55141 × 10
201
b − 1.33536 × 10
201
,
1.06146 × 10
200
u
45
+ 1.69938 × 10
199
u
44
+ ··· + 1.77505 × 10
203
a − 2.99606 × 10
203
,
u
46
+ 56u
44
+ ··· − 1378u + 507i
I
u
2
= h788638025662u
15
− 78518326905455u
14
+ ··· + 919477490510109b − 419677061820201,
73623372272275u
15
− 47637302039197u
14
+ ··· + 919477490510109a + 2632097779359569,
u
16
+ u
15
+ ··· + 15u + 9i
* 2 irreducible components of dim
C
= 0, with total 62 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
= h1.19 × 10
198
u
45
− 6.75 × 10
197
u
44
+ · · · + 4.55 × 10
201
b − 1.34 ×
10
201
, 1.06 × 10
200
u
45
+ 1.70 × 10
199
u
44
+ · · · + 1.78 × 10
203
a − 3.00 ×
10
203
, u
46
+ 56u
44
+ · · · − 1378u + 507i
(i) Arc colorings
a
4
=
1
0
a
9
=
0
u
a
5
=
1
−u
2
a
12
=
−0.000597989u
45
− 0.0000957369u
44
+ ··· − 1.97693u + 1.68787
−0.000262435u
45
+ 0.000148218u
44
+ ··· + 0.754607u + 0.293395
a
10
=
−0.000625366u
45
− 0.000355332u
44
+ ··· − 0.368332u + 1.08941
0.0000695995u
45
+ 0.000148080u
44
+ ··· + 1.20417u + 0.198918
a
1
=
−0.000597989u
45
− 0.0000957369u
44
+ ··· − 1.97693u + 1.68787
−0.000174434u
45
+ 0.000154808u
44
+ ··· + 0.583352u + 0.244856
a
2
=
−0.000423555u
45
− 0.000250544u
44
+ ··· − 2.56028u + 1.44302
−0.000174434u
45
+ 0.000154808u
44
+ ··· + 0.583352u + 0.244856
a
6
=
−0.000392342u
45
+ 0.0000695995u
44
+ ··· + 0.902157u + 1.74482
0.000138440u
45
+ 0.0000385594u
44
+ ··· + 0.267201u + 0.0758209
a
8
=
0.000625366u
45
+ 0.000355332u
44
+ ··· + 0.368332u − 1.08941
−0.0000243237u
45
− 0.000122334u
44
+ ··· + 0.623241u − 0.0187641
a
7
=
0.000649690u
45
+ 0.000477667u
44
+ ··· − 0.254909u − 1.07065
−0.0000243237u
45
− 0.000122334u
44
+ ··· + 0.623241u − 0.0187641
a
11
=
−0.000621843u
45
− 0.0000319284u
44
+ ··· + 1.04140u + 2.54422
−0.000195680u
45
+ 0.0000193035u
44
+ ··· + 1.10047u + 0.158773
a
3
=
0.000304275u
45
− 0.000150311u
44
+ ··· − 2.53168u + 0.571523
−0.000414380u
45
− 0.0000218287u
44
+ ··· − 0.337787u + 0.0757931
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.00268732u
45
+ 0.000514392u
44
+ ··· − 6.90355u + 4.66863
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
46
+ 9u
45
+ ··· − 598194u + 53041
c
2
u
46
+ 14u
44
+ ··· − 11u + 1
c
3
u
46
− 3u
45
+ ··· − 23u + 3
c
4
u
46
+ 56u
44
+ ··· − 1378u + 507
c
5
u
46
− 2u
45
+ ··· − 250u + 1279
c
6
u
46
+ 5u
45
+ ··· − 9u + 1
c
7
u
46
+ 15u
44
+ ··· − 3108u + 149
c
8
, c
9
, c
12
u
46
+ 33u
44
+ ··· − 141u + 19
c
10
u
46
− 5u
45
+ ··· − 51u + 31
c
11
u
46
− u
45
+ ··· + 65u + 49
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
46
− 93y
45
+ ··· − 17713407268y + 2813347681
c
2
y
46
+ 28y
45
+ ··· + 261y + 1
c
3
y
46
+ 3y
45
+ ··· + 5y + 9
c
4
y
46
+ 112y
45
+ ··· + 2295020y + 257049
c
5
y
46
− 108y
45
+ ··· − 67250928y + 1635841
c
6
y
46
+ 3y
45
+ ··· + 9y + 1
c
7
y
46
+ 30y
45
+ ··· − 4374634y + 22201
c
8
, c
9
, c
12
y
46
+ 66y
45
+ ··· + 8809y + 361
c
10
y
46
+ 13y
45
+ ··· + 21765y + 961
c
11
y
46
+ 19y
45
+ ··· + 55653y + 2401
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.722623 + 0.663783I
a = −0.189781 + 1.081440I
b = −0.761905 + 0.077110I
−4.43282 + 1.52715I −7.37334 − 5.22015I
u = −0.722623 − 0.663783I
a = −0.189781 − 1.081440I
b = −0.761905 − 0.077110I
−4.43282 − 1.52715I −7.37334 + 5.22015I
u = 1.042020 + 0.291189I
a = 0.311194 + 0.202668I
b = 0.527721 + 0.608546I
1.89860 + 0.93839I −4.03451 + 1.19726I
u = 1.042020 − 0.291189I
a = 0.311194 − 0.202668I
b = 0.527721 − 0.608546I
1.89860 − 0.93839I −4.03451 − 1.19726I
u = −0.594177 + 0.677482I
a = 0.97182 − 1.32120I
b = −0.344145 − 0.034677I
−4.23209 + 3.88598I −4.75603 − 4.49965I
u = −0.594177 − 0.677482I
a = 0.97182 + 1.32120I
b = −0.344145 + 0.034677I
−4.23209 − 3.88598I −4.75603 + 4.49965I
u = 0.181031 + 0.824245I
a = −0.373014 + 0.986862I
b = 0.386192 − 0.053287I
0.75821 + 4.93973I 1.37497 − 6.10201I
u = 0.181031 − 0.824245I
a = −0.373014 − 0.986862I
b = 0.386192 + 0.053287I
0.75821 − 4.93973I 1.37497 + 6.10201I
u = −0.168414 + 0.786367I
a = −1.019670 + 0.047056I
b = −0.890177 + 0.606122I
−4.06154 − 0.13020I −4.76095 − 0.53915I
u = −0.168414 − 0.786367I
a = −1.019670 − 0.047056I
b = −0.890177 − 0.606122I
−4.06154 + 0.13020I −4.76095 + 0.53915I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.685524 + 0.242386I
a = 0.634928 + 0.396219I
b = 0.266521 + 0.975007I
1.64805 + 1.08045I 3.15096 − 7.04605I
u = 0.685524 − 0.242386I
a = 0.634928 − 0.396219I
b = 0.266521 − 0.975007I
1.64805 − 1.08045I 3.15096 + 7.04605I
u = −0.606976 + 0.353597I
a = 1.06341 − 1.70650I
b = 0.169419 − 1.237650I
−4.39199 + 5.06705I −1.75956 − 6.04792I
u = −0.606976 − 0.353597I
a = 1.06341 + 1.70650I
b = 0.169419 + 1.237650I
−4.39199 − 5.06705I −1.75956 + 6.04792I
u = 0.082102 + 0.677726I
a = 0.469990 − 0.277050I
b = −0.29228 − 1.51820I
3.41907 − 4.27710I −1.86663 − 0.85536I
u = 0.082102 − 0.677726I
a = 0.469990 + 0.277050I
b = −0.29228 + 1.51820I
3.41907 + 4.27710I −1.86663 + 0.85536I
u = −0.099218 + 0.655160I
a = 1.85892 + 0.20385I
b = −1.099660 + 0.530114I
−2.02807 + 0.89669I −0.59333 − 2.63444I
u = −0.099218 − 0.655160I
a = 1.85892 − 0.20385I
b = −1.099660 − 0.530114I
−2.02807 − 0.89669I −0.59333 + 2.63444I
u = 0.213548 + 0.536576I
a = 1.94510 − 0.08651I
b = 0.391610 + 0.666555I
−1.18834 + 2.94575I 2.79513 − 7.62929I
u = 0.213548 − 0.536576I
a = 1.94510 + 0.08651I
b = 0.391610 − 0.666555I
−1.18834 − 2.94575I 2.79513 + 7.62929I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.225474 + 0.520584I
a = 0.860068 + 0.132577I
b = −0.575467 + 0.297341I
−1.20487 + 1.08188I −2.86879 − 1.93861I
u = −0.225474 − 0.520584I
a = 0.860068 − 0.132577I
b = −0.575467 − 0.297341I
−1.20487 − 1.08188I −2.86879 + 1.93861I
u = −0.529336 + 0.126590I
a = −0.73767 + 1.92374I
b = −0.833828 + 0.084948I
−3.13560 − 2.98726I −2.43600 + 6.69169I
u = −0.529336 − 0.126590I
a = −0.73767 − 1.92374I
b = −0.833828 − 0.084948I
−3.13560 + 2.98726I −2.43600 − 6.69169I
u = 0.362920 + 0.366463I
a = 0.70009 + 2.45399I
b = 0.875473 − 0.158897I
−3.13163 − 10.16720I −0.48934 + 7.57078I
u = 0.362920 − 0.366463I
a = 0.70009 − 2.45399I
b = 0.875473 + 0.158897I
−3.13163 + 10.16720I −0.48934 − 7.57078I
u = −1.47983 + 0.30015I
a = −0.113526 + 0.386179I
b = 0.466727 + 0.213716I
2.38652 − 5.13357I 0
u = −1.47983 − 0.30015I
a = −0.113526 − 0.386179I
b = 0.466727 − 0.213716I
2.38652 + 5.13357I 0
u = 0.206753 + 0.194399I
a = 2.05172 − 0.92917I
b = 0.347573 + 0.385865I
1.35869 + 0.69751I 4.29607 − 0.54875I
u = 0.206753 − 0.194399I
a = 2.05172 + 0.92917I
b = 0.347573 − 0.385865I
1.35869 − 0.69751I 4.29607 + 0.54875I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.82791 + 0.18540I
a = 0.095317 − 0.729148I
b = −0.550395 − 1.005790I
−1.73016 + 2.21015I 0
u = 1.82791 − 0.18540I
a = 0.095317 + 0.729148I
b = −0.550395 + 1.005790I
−1.73016 − 2.21015I 0
u = −0.19250 + 2.63308I
a = 0.671878 − 0.103363I
b = −2.71999 + 0.09262I
−11.36540 + 5.64381I 0
u = −0.19250 − 2.63308I
a = 0.671878 + 0.103363I
b = −2.71999 − 0.09262I
−11.36540 − 5.64381I 0
u = 0.30985 + 2.75631I
a = 0.666351 + 0.066193I
b = −2.79148 + 0.01630I
−17.1201 + 5.1887I 0
u = 0.30985 − 2.75631I
a = 0.666351 − 0.066193I
b = −2.79148 − 0.01630I
−17.1201 − 5.1887I 0
u = −0.49972 + 2.82464I
a = −0.642407 + 0.112172I
b = 2.42127 + 0.01216I
−14.4376 + 0.6038I 0
u = −0.49972 − 2.82464I
a = −0.642407 − 0.112172I
b = 2.42127 − 0.01216I
−14.4376 − 0.6038I 0
u = −0.11803 + 2.94113I
a = −0.598923 + 0.099596I
b = 2.73153 + 0.31584I
−13.8680 + 5.1464I 0
u = −0.11803 − 2.94113I
a = −0.598923 − 0.099596I
b = 2.73153 − 0.31584I
−13.8680 − 5.1464I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.00605 + 3.10643I
a = 0.580378 + 0.060548I
b = −2.92917 − 0.02937I
−13.5048 − 13.8523I 0
u = −0.00605 − 3.10643I
a = 0.580378 − 0.060548I
b = −2.92917 + 0.02937I
−13.5048 + 13.8523I 0
u = −0.37723 + 3.19003I
a = −0.548210 + 0.055625I
b = 2.97114 + 0.61922I
−13.65630 − 3.67082I 0
u = −0.37723 − 3.19003I
a = −0.548210 − 0.055625I
b = 2.97114 − 0.61922I
−13.65630 + 3.67082I 0
u = 0.70791 + 3.28454I
a = −0.491311 − 0.131780I
b = 3.23332 − 0.44420I
−13.12530 − 1.26369I 0
u = 0.70791 − 3.28454I
a = −0.491311 + 0.131780I
b = 3.23332 + 0.44420I
−13.12530 + 1.26369I 0
9
II.
I
u
2
= h7.89 × 10
11
u
15
− 7.85 × 10
13
u
14
+ · · · + 9.19 × 10
14
b − 4.20 × 10
14
, 7.36 ×
10
13
u
15
−4.76×10
13
u
14
+· · ·+9.19×10
14
a+2.63×10
15
, u
16
+u
15
+· · ·+15u+9i
(i) Arc colorings
a
4
=
1
0
a
9
=
0
u
a
5
=
1
−u
2
a
12
=
−0.0800709u
15
+ 0.0518091u
14
+ ··· − 1.62186u − 2.86260
−0.000857702u
15
+ 0.0853945u
14
+ ··· + 1.39867u + 0.456430
a
10
=
0.422782u
15
+ 0.157685u
14
+ ··· + 9.37781u + 2.87737
0.0444333u
15
+ 0.0205806u
14
+ ··· + 1.43880u + 1.35558
a
1
=
−0.0800709u
15
+ 0.0518091u
14
+ ··· − 1.62186u − 2.86260
0.270758u
15
− 0.0289705u
14
+ ··· + 2.65623u + 1.64335
a
2
=
−0.350829u
15
+ 0.0807796u
14
+ ··· − 4.27809u − 4.50595
0.270758u
15
− 0.0289705u
14
+ ··· + 2.65623u + 1.64335
a
6
=
−0.150620u
15
− 0.106187u
14
+ ··· − 4.01725u − 0.820503
−0.0851810u
15
− 0.0130518u
14
+ ··· − 0.872683u − 0.785729
a
8
=
−0.422782u
15
− 0.157685u
14
+ ··· − 9.37781u − 2.87737
0.198744u
15
− 0.0486526u
14
+ ··· + 0.732607u + 1.03028
a
7
=
−0.621526u
15
− 0.109033u
14
+ ··· − 10.1104u − 3.90765
0.198744u
15
− 0.0486526u
14
+ ··· + 0.732607u + 1.03028
a
11
=
0.0797236u
15
+ 0.0501001u
14
+ ··· − 2.52386u − 1.58118
0.0894444u
15
− 0.0458413u
14
+ ··· + 2.06356u + 0.413661
a
3
=
−0.194771u
15
+ 0.236670u
14
+ ··· + 4.93424u − 0.393951
0.175039u
15
− 0.121465u
14
+ ··· + 1.06866u + 1.69379
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −
541123579097900
306492496836703
u
15
+
279674211722222
306492496836703
u
14
+ ··· −
2560838929027227
306492496836703
u −
1228461990620122
306492496836703
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
16
− 10u
15
+ ··· − 11u + 1
c
2
u
16
− u
15
+ ··· + 6u + 1
c
3
u
16
+ 3u
14
+ ··· + 2u + 1
c
4
u
16
+ u
15
+ ··· + 15u + 9
c
5
u
16
− u
15
+ ··· + 91u + 17
c
6
u
16
− 2u
15
+ ··· + 2u + 1
c
7
u
16
+ u
15
+ ··· − 11u + 5
c
8
, c
9
u
16
+ u
15
+ ··· − 2u + 1
c
10
u
16
+ 2u
15
+ ··· + 2u + 1
c
11
u
16
+ 7u
14
+ ··· + 8u + 5
c
12
u
16
− u
15
+ ··· + 2u + 1
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
16
− 10y
15
+ ··· + 5y + 1
c
2
y
16
+ 15y
15
+ ··· − 34y + 1
c
3
y
16
+ 6y
15
+ ··· + 18y + 1
c
4
y
16
+ 3y
15
+ ··· + 513y + 81
c
5
y
16
− 5y
15
+ ··· − 427y + 289
c
6
y
16
+ 2y
15
+ ··· + 10y + 1
c
7
y
16
+ 5y
15
+ ··· − 161y + 25
c
8
, c
9
, c
12
y
16
+ 21y
15
+ ··· − 14y + 1
c
10
y
16
+ 4y
15
+ ··· + 6y + 1
c
11
y
16
+ 14y
15
+ ··· + 226y + 25
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.893310 + 0.263570I
a = −0.589954 + 0.134532I
b = −0.554370 + 0.638444I
2.21646 − 1.01376I 22.0835 + 5.4010I
u = −0.893310 − 0.263570I
a = −0.589954 − 0.134532I
b = −0.554370 − 0.638444I
2.21646 + 1.01376I 22.0835 − 5.4010I
u = 0.681825 + 0.479862I
a = −0.346166 + 0.209492I
b = 0.001679 + 1.263930I
3.85961 + 4.70319I 8.55831 − 7.51978I
u = 0.681825 − 0.479862I
a = −0.346166 − 0.209492I
b = 0.001679 − 1.263930I
3.85961 − 4.70319I 8.55831 + 7.51978I
u = −1.238650 + 0.203176I
a = 0.363333 − 1.017220I
b = −0.591621 − 0.222631I
−0.58691 + 2.51670I 3.45399 − 4.44673I
u = −1.238650 − 0.203176I
a = 0.363333 + 1.017220I
b = −0.591621 + 0.222631I
−0.58691 − 2.51670I 3.45399 + 4.44673I
u = 0.274389 + 0.600424I
a = −0.936590 − 1.009320I
b = −0.923402 + 0.053522I
−3.63004 − 1.23018I 1.45254 + 3.84800I
u = 0.274389 − 0.600424I
a = −0.936590 + 1.009320I
b = −0.923402 − 0.053522I
−3.63004 + 1.23018I 1.45254 − 3.84800I
u = −1.396590 + 0.109133I
a = 0.006693 − 0.834622I
b = −0.65590 − 1.38874I
−0.315524 + 0.953488I 0.808208 − 0.633683I
u = −1.396590 − 0.109133I
a = 0.006693 + 0.834622I
b = −0.65590 + 1.38874I
−0.315524 − 0.953488I 0.808208 + 0.633683I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.077983 + 0.460813I
a = −3.11541 + 0.03348I
b = 0.337699 + 0.657908I
−3.44078 − 3.74719I 4.59997 + 2.83303I
u = −0.077983 − 0.460813I
a = −3.11541 − 0.03348I
b = 0.337699 − 0.657908I
−3.44078 + 3.74719I 4.59997 − 2.83303I
u = 2.21181 + 0.23952I
a = 0.007267 + 0.633167I
b = −0.07038 + 1.95938I
−1.01719 − 6.39683I 0.14163 + 5.33600I
u = 2.21181 − 0.23952I
a = 0.007267 − 0.633167I
b = −0.07038 − 1.95938I
−1.01719 + 6.39683I 0.14163 − 5.33600I
u = −0.06149 + 3.20027I
a = −0.555836 − 0.009838I
b = 2.95629 + 0.20169I
−13.53500 − 2.98379I −1.59812 − 0.80751I
u = −0.06149 − 3.20027I
a = −0.555836 + 0.009838I
b = 2.95629 − 0.20169I
−13.53500 + 2.98379I −1.59812 + 0.80751I
14
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
16
− 10u
15
+ ··· − 11u + 1)(u
46
+ 9u
45
+ ··· − 598194u + 53041)
c
2
(u
16
− u
15
+ ··· + 6u + 1)(u
46
+ 14u
44
+ ··· − 11u + 1)
c
3
(u
16
+ 3u
14
+ ··· + 2u + 1)(u
46
− 3u
45
+ ··· − 23u + 3)
c
4
(u
16
+ u
15
+ ··· + 15u + 9)(u
46
+ 56u
44
+ ··· − 1378u + 507)
c
5
(u
16
− u
15
+ ··· + 91u + 17)(u
46
− 2u
45
+ ··· − 250u + 1279)
c
6
(u
16
− 2u
15
+ ··· + 2u + 1)(u
46
+ 5u
45
+ ··· − 9u + 1)
c
7
(u
16
+ u
15
+ ··· − 11u + 5)(u
46
+ 15u
44
+ ··· − 3108u + 149)
c
8
, c
9
(u
16
+ u
15
+ ··· − 2u + 1)(u
46
+ 33u
44
+ ··· − 141u + 19)
c
10
(u
16
+ 2u
15
+ ··· + 2u + 1)(u
46
− 5u
45
+ ··· − 51u + 31)
c
11
(u
16
+ 7u
14
+ ··· + 8u + 5)(u
46
− u
45
+ ··· + 65u + 49)
c
12
(u
16
− u
15
+ ··· + 2u + 1)(u
46
+ 33u
44
+ ··· − 141u + 19)
15
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
16
− 10y
15
+ ··· + 5y + 1)
· (y
46
− 93y
45
+ ··· − 17713407268y + 2813347681)
c
2
(y
16
+ 15y
15
+ ··· − 34y + 1)(y
46
+ 28y
45
+ ··· + 261y + 1)
c
3
(y
16
+ 6y
15
+ ··· + 18y + 1)(y
46
+ 3y
45
+ ··· + 5y + 9)
c
4
(y
16
+ 3y
15
+ ··· + 513y + 81)
· (y
46
+ 112y
45
+ ··· + 2295020y + 257049)
c
5
(y
16
− 5y
15
+ ··· − 427y + 289)
· (y
46
− 108y
45
+ ··· − 67250928y + 1635841)
c
6
(y
16
+ 2y
15
+ ··· + 10y + 1)(y
46
+ 3y
45
+ ··· + 9y + 1)
c
7
(y
16
+ 5y
15
+ ··· − 161y + 25)
· (y
46
+ 30y
45
+ ··· − 4374634y + 22201)
c
8
, c
9
, c
12
(y
16
+ 21y
15
+ ··· − 14y + 1)(y
46
+ 66y
45
+ ··· + 8809y + 361)
c
10
(y
16
+ 4y
15
+ ··· + 6y + 1)(y
46
+ 13y
45
+ ··· + 21765y + 961)
c
11
(y
16
+ 14y
15
+ ··· + 226y + 25)(y
46
+ 19y
45
+ ··· + 55653y + 2401)
16
