11a
149
(K11a
149
)
A knot diagram
1
Linearized knot diagam
6 1 11 8 2 5 10 3 7 4 9
Solving Sequence
2,6
1 3 5
7,9
10 8 4 11
c
1
c
2
c
5
c
6
c
9
c
8
c
4
c
11
c
3
, c
7
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h6.59200 × 10
33
u
62
+ 1.26617 × 10
34
u
61
+ ··· + 9.14845 × 10
33
b − 6.13231 × 10
33
,
− 5.18869 × 10
30
u
62
− 4.60084 × 10
31
u
61
+ ··· + 1.51632 × 10
32
a + 4.89769 × 10
32
, u
63
+ 3u
62
+ ··· + 2u − 1i
* 1 irreducible components of dim
C
= 0, with total 63 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
= h6.59×10
33
u
62
+1.27×10
34
u
61
+· · ·+9.15×10
33
b−6.13×10
33
, −5.19×
10
30
u
62
−4.60×10
31
u
61
+· · ·+1.52×10
32
a+4.90×10
32
, u
63
+3u
62
+· · ·+2u−1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
1
=
1
u
2
a
3
=
u
2
+ 1
u
4
a
5
=
−u
u
a
7
=
−u
3
u
3
+ u
a
9
=
0.0342190u
62
+ 0.303422u
61
+ ··· − 0.970526u − 3.22999
−0.720560u
62
− 1.38403u
61
+ ··· + 0.258985u + 0.670312
a
10
=
0.163991u
62
+ 0.735688u
61
+ ··· − 0.518791u − 3.41101
−0.940033u
62
− 1.90438u
61
+ ··· − 0.942790u + 0.713453
a
8
=
0.167447u
62
+ 0.652868u
61
+ ··· + 1.09284u − 3.15598
−0.702143u
62
− 1.31297u
61
+ ··· + 0.508662u + 0.602596
a
4
=
−1.53220u
62
− 5.33133u
61
+ ··· − 6.95145u + 3.31985
0.408926u
62
+ 1.90611u
61
+ ··· − 1.94941u + 0.452963
a
11
=
−0.489880u
62
− 1.42153u
61
+ ··· + 3.35861u + 3.51142
−0.552392u
62
− 2.69530u
61
+ ··· + 2.86212u − 1.33768
a
11
=
−0.489880u
62
− 1.42153u
61
+ ··· + 3.35861u + 3.51142
−0.552392u
62
− 2.69530u
61
+ ··· + 2.86212u − 1.33768
(ii) Obstruction class = −1
(iii) Cusp Shapes = −2.55683u
62
− 9.47657u
61
+ ··· − 10.7932u − 4.31798
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
63
− 3u
62
+ ··· + 2u + 1
c
2
, c
6
u
63
+ 19u
62
+ ··· + 16u − 1
c
3
, c
10
u
63
+ 3u
62
+ ··· + 4u + 1
c
4
u
63
+ 11u
62
+ ··· + 26u + 529
c
7
, c
9
u
63
− u
62
+ ··· − 18u + 1
c
8
u
63
+ u
62
+ ··· − 10u + 1
c
11
u
63
+ 23u
62
+ ··· − 22u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
63
+ 19y
62
+ ··· + 16y −1
c
2
, c
6
y
63
+ 51y
62
+ ··· + 360y −1
c
3
, c
10
y
63
+ 47y
62
+ ··· + 16y −1
c
4
y
63
+ 127y
62
+ ··· − 1368376y −279841
c
7
, c
9
y
63
− 41y
62
+ ··· − 184y −1
c
8
y
63
+ 3y
62
+ ··· − 48y −1
c
11
y
63
− 177y
62
+ ··· − 84y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.202849 + 0.946044I
a = 1.94722 + 0.19778I
b = −0.928613 − 0.106351I
−3.81545 + 5.01176I −9.09327 − 7.69438I
u = 0.202849 − 0.946044I
a = 1.94722 − 0.19778I
b = −0.928613 + 0.106351I
−3.81545 − 5.01176I −9.09327 + 7.69438I
u = 0.695239 + 0.763843I
a = 0.75961 + 1.41295I
b = −1.63934 + 0.73836I
−2.73449 − 1.42844I −6.93697 + 2.22951I
u = 0.695239 − 0.763843I
a = 0.75961 − 1.41295I
b = −1.63934 − 0.73836I
−2.73449 + 1.42844I −6.93697 − 2.22951I
u = −0.058839 + 0.948485I
a = −1.17043 + 1.85637I
b = 0.45196 − 1.56324I
−7.69919 − 2.07381I −15.2166 + 3.4603I
u = −0.058839 − 0.948485I
a = −1.17043 − 1.85637I
b = 0.45196 + 1.56324I
−7.69919 + 2.07381I −15.2166 − 3.4603I
u = −0.763248 + 0.536252I
a = −0.200295 − 0.850847I
b = −0.612392 + 0.572188I
1.08095 − 1.39801I 4.18188 + 0.71132I
u = −0.763248 − 0.536252I
a = −0.200295 + 0.850847I
b = −0.612392 − 0.572188I
1.08095 + 1.39801I 4.18188 − 0.71132I
u = −0.726705 + 0.811867I
a = −1.18396 + 1.72005I
b = 2.18880 + 0.14253I
1.35473 − 0.62400I 0
u = −0.726705 − 0.811867I
a = −1.18396 − 1.72005I
b = 2.18880 − 0.14253I
1.35473 + 0.62400I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.643524 + 0.884288I
a = −0.670137 + 0.681552I
b = −0.214774 + 0.538469I
−4.63310 − 2.49365I 0
u = −0.643524 − 0.884288I
a = −0.670137 − 0.681552I
b = −0.214774 − 0.538469I
−4.63310 + 2.49365I 0
u = −0.810251 + 0.764677I
a = −0.614704 + 1.099300I
b = 2.27585 − 0.14042I
2.66441 + 3.76429I 0
u = −0.810251 − 0.764677I
a = −0.614704 − 1.099300I
b = 2.27585 + 0.14042I
2.66441 − 3.76429I 0
u = −0.247037 + 0.849494I
a = −1.142120 + 0.110784I
b = 0.398886 + 0.218053I
−0.62170 − 1.75556I −1.86458 + 4.77709I
u = −0.247037 − 0.849494I
a = −1.142120 − 0.110784I
b = 0.398886 − 0.218053I
−0.62170 + 1.75556I −1.86458 − 4.77709I
u = 0.879352 + 0.689382I
a = −0.766895 − 1.133880I
b = 1.80952 − 0.12559I
3.67279 − 4.73223I 0
u = 0.879352 − 0.689382I
a = −0.766895 + 1.133880I
b = 1.80952 + 0.12559I
3.67279 + 4.73223I 0
u = 0.702468 + 0.874127I
a = −1.37569 + 1.38479I
b = 0.83063 − 1.81611I
−0.03120 + 2.69612I 0
u = 0.702468 − 0.874127I
a = −1.37569 − 1.38479I
b = 0.83063 + 1.81611I
−0.03120 − 2.69612I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.057802 + 0.865842I
a = 1.039560 + 0.717759I
b = 0.212381 − 1.286120I
−3.45347 + 0.91963I −7.53722 + 0.57993I
u = 0.057802 − 0.865842I
a = 1.039560 − 0.717759I
b = 0.212381 + 1.286120I
−3.45347 − 0.91963I −7.53722 − 0.57993I
u = −0.888598 + 0.712739I
a = 1.23888 − 1.07985I
b = −2.21959 − 0.66956I
−1.25936 + 10.13510I 0
u = −0.888598 − 0.712739I
a = 1.23888 + 1.07985I
b = −2.21959 + 0.66956I
−1.25936 − 10.13510I 0
u = 0.737082 + 0.871113I
a = −4.8258 + 13.5054I
b = −5.4391 − 15.0888I
−0.27910 + 2.80205I 0. − 114.9176I
u = 0.737082 − 0.871113I
a = −4.8258 − 13.5054I
b = −5.4391 + 15.0888I
−0.27910 − 2.80205I 0. + 114.9176I
u = 0.249599 + 1.117340I
a = −0.933405 − 0.391979I
b = 0.083836 + 0.726791I
−8.93201 + 10.19930I 0
u = 0.249599 − 1.117340I
a = −0.933405 + 0.391979I
b = 0.083836 − 0.726791I
−8.93201 − 10.19930I 0
u = 0.825588 + 0.794026I
a = 0.471370 + 0.782650I
b = −1.65611 − 0.24031I
6.05392 + 0.28945I 0
u = 0.825588 − 0.794026I
a = 0.471370 − 0.782650I
b = −1.65611 + 0.24031I
6.05392 − 0.28945I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.171535 + 0.833363I
a = 0.472085 + 1.258500I
b = 0.192482 + 0.304858I
−3.56857 − 0.47654I −9.76423 − 1.75847I
u = 0.171535 − 0.833363I
a = 0.472085 − 1.258500I
b = 0.192482 − 0.304858I
−3.56857 + 0.47654I −9.76423 + 1.75847I
u = −0.716350 + 0.922760I
a = 0.58105 − 1.92526I
b = −2.53241 + 1.12922I
1.01466 − 4.89030I 0
u = −0.716350 − 0.922760I
a = 0.58105 + 1.92526I
b = −2.53241 − 1.12922I
1.01466 + 4.89030I 0
u = 0.693599 + 0.946330I
a = 0.34808 − 1.75912I
b = 1.94341 + 1.34022I
−3.28750 + 6.79142I 0
u = 0.693599 − 0.946330I
a = 0.34808 + 1.75912I
b = 1.94341 − 1.34022I
−3.28750 − 6.79142I 0
u = −0.765357 + 0.893742I
a = −0.888237 − 0.881040I
b = 0.160327 + 1.374950I
1.42211 − 2.89988I 0
u = −0.765357 − 0.893742I
a = −0.888237 + 0.881040I
b = 0.160327 − 1.374950I
1.42211 + 2.89988I 0
u = 0.818503 + 0.071595I
a = 0.947693 − 0.595880I
b = −0.190373 + 0.433337I
−4.90960 + 6.71055I −4.57662 − 5.93806I
u = 0.818503 − 0.071595I
a = 0.947693 + 0.595880I
b = −0.190373 − 0.433337I
−4.90960 − 6.71055I −4.57662 + 5.93806I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.330834 + 1.132940I
a = 0.122863 − 0.871157I
b = −0.389791 + 0.792565I
−8.44469 − 2.66782I 0
u = 0.330834 − 1.132940I
a = 0.122863 + 0.871157I
b = −0.389791 − 0.792565I
−8.44469 + 2.66782I 0
u = −0.213920 + 1.163890I
a = 0.446939 − 0.170107I
b = 0.032442 + 0.590549I
−3.79459 − 4.37631I 0
u = −0.213920 − 1.163890I
a = 0.446939 + 0.170107I
b = 0.032442 − 0.590549I
−3.79459 + 4.37631I 0
u = −0.750069 + 0.975450I
a = 0.85338 − 2.02212I
b = −2.24959 + 0.46334I
2.01737 − 9.62566I 0
u = −0.750069 − 0.975450I
a = 0.85338 + 2.02212I
b = −2.24959 − 0.46334I
2.01737 + 9.62566I 0
u = 0.769036 + 0.963922I
a = −0.64711 − 1.44598I
b = 1.56684 + 0.33213I
5.52656 + 5.67817I 0
u = 0.769036 − 0.963922I
a = −0.64711 + 1.44598I
b = 1.56684 − 0.33213I
5.52656 − 5.67817I 0
u = −0.693016 + 0.315312I
a = −0.289428 − 0.730127I
b = −0.310255 + 0.482151I
1.05806 − 1.32640I 4.87847 + 4.20428I
u = −0.693016 − 0.315312I
a = −0.289428 + 0.730127I
b = −0.310255 − 0.482151I
1.05806 + 1.32640I 4.87847 − 4.20428I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.754175 + 1.039690I
a = 0.72880 + 1.66445I
b = −2.16012 − 0.87201I
2.59510 + 10.79480I 0
u = 0.754175 − 1.039690I
a = 0.72880 − 1.66445I
b = −2.16012 + 0.87201I
2.59510 − 10.79480I 0
u = −0.765933 + 1.033730I
a = −0.51162 + 2.20505I
b = 2.40984 − 1.47160I
−2.2561 − 16.2663I 0
u = −0.765933 − 1.033730I
a = −0.51162 − 2.20505I
b = 2.40984 + 1.47160I
−2.2561 + 16.2663I 0
u = −0.933450 + 0.887239I
a = 0.182597 + 0.083461I
b = 0.164371 − 0.473416I
0.88299 − 3.37440I 0
u = −0.933450 − 0.887239I
a = 0.182597 − 0.083461I
b = 0.164371 + 0.473416I
0.88299 + 3.37440I 0
u = −0.730193 + 1.099430I
a = −0.467025 + 0.660302I
b = 1.157580 − 0.273573I
−0.60454 − 4.40493I 0
u = −0.730193 − 1.099430I
a = −0.467025 − 0.660302I
b = 1.157580 + 0.273573I
−0.60454 + 4.40493I 0
u = 0.516941 + 0.032452I
a = −0.286237 − 1.236950I
b = 0.641012 + 0.482457I
−1.03804 − 2.55802I −0.30006 + 3.39194I
u = 0.516941 − 0.032452I
a = −0.286237 + 1.236950I
b = 0.641012 − 0.482457I
−1.03804 + 2.55802I −0.30006 − 3.39194I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.309755 + 0.275620I
a = 1.19826 + 2.47111I
b = −0.692520 + 0.579657I
−4.36178 − 1.13101I −3.69450 + 1.07714I
u = −0.309755 − 0.275620I
a = 1.19826 − 2.47111I
b = −0.692520 − 0.579657I
−4.36178 + 1.13101I −3.69450 − 1.07714I
u = 0.223288
a = −3.73067
b = 0.429527
−1.26040 −8.85590
11
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
5
u
63
− 3u
62
+ ··· + 2u + 1
c
2
, c
6
u
63
+ 19u
62
+ ··· + 16u − 1
c
3
, c
10
u
63
+ 3u
62
+ ··· + 4u + 1
c
4
u
63
+ 11u
62
+ ··· + 26u + 529
c
7
, c
9
u
63
− u
62
+ ··· − 18u + 1
c
8
u
63
+ u
62
+ ··· − 10u + 1
c
11
u
63
+ 23u
62
+ ··· − 22u + 1
12
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
63
+ 19y
62
+ ··· + 16y −1
c
2
, c
6
y
63
+ 51y
62
+ ··· + 360y −1
c
3
, c
10
y
63
+ 47y
62
+ ··· + 16y −1
c
4
y
63
+ 127y
62
+ ··· − 1368376y −279841
c
7
, c
9
y
63
− 41y
62
+ ··· − 184y −1
c
8
y
63
+ 3y
62
+ ··· − 48y −1
c
11
y
63
− 177y
62
+ ··· − 84y −1
13
