11a
147
(K11a
147
)
A knot diagram
1
Linearized knot diagam
5 1 10 8 2 9 11 3 7 4 6
Solving Sequence
2,5
6 1
3,8
9 4 11 7 10
c
5
c
1
c
2
c
8
c
4
c
11
c
7
c
10
c
3
, c
6
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h9.07204 × 10
41
u
77
+ 7.90148 × 10
41
u
76
+ ··· + 2.06037 × 10
42
b − 1.56482 × 10
41
,
1.17116 × 10
42
u
77
+ 1.73368 × 10
42
u
76
+ ··· + 2.06037 × 10
42
a − 6.11073 × 10
42
, u
78
+ 2u
77
+ ··· − 2u − 1i
I
u
2
= hb, −3u
2
+ 5a + 7u − 6, u
3
− u
2
+ 1i
* 2 irreducible components of dim
C
= 0, with total 81 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
= h9.07 × 10
41
u
77
+ 7.90 × 10
41
u
76
+ · · · + 2.06 × 10
42
b − 1.56 × 10
41
, 1.17 ×
10
42
u
77
+1.73×10
42
u
76
+· · ·+2.06×10
42
a−6.11×10
42
, u
78
+2u
77
+· · ·−2u−1i
(i) Arc colorings
a
2
=
0
u
a
5
=
1
0
a
6
=
1
u
2
a
1
=
u
u
a
3
=
−u
3
−u
3
+ u
a
8
=
−0.568420u
77
− 0.841443u
76
+ ··· + 7.36773u + 2.96584
−0.440311u
77
− 0.383498u
76
+ ··· + 0.720857u + 0.0759485
a
9
=
−1.82193u
77
− 2.29694u
76
+ ··· + 8.78768u + 3.83863
−1.36819u
77
− 2.06052u
76
+ ··· + 2.39639u + 1.90814
a
4
=
−1.18444u
77
− 2.09711u
76
+ ··· + 1.00657u + 1.49223
0.344158u
77
+ 1.17317u
76
+ ··· − 0.834190u − 1.22870
a
11
=
u
3
u
5
− u
3
+ u
a
7
=
−1.12364u
77
− 1.00031u
76
+ ··· + 7.99454u + 3.41779
−1.37767u
77
− 1.68487u
76
+ ··· + 2.56542u + 1.34481
a
10
=
1.18444u
77
+ 2.09711u
76
+ ··· − 1.00657u − 1.49223
0.380290u
77
+ 1.21706u
76
+ ··· − 0.193293u − 1.50047
a
10
=
1.18444u
77
+ 2.09711u
76
+ ··· − 1.00657u − 1.49223
0.380290u
77
+ 1.21706u
76
+ ··· − 0.193293u − 1.50047
(ii) Obstruction class = −1
(iii) Cusp Shapes = 3.52017u
77
+ 0.863610u
76
+ ··· − 23.9616u − 10.9917
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
78
+ 2u
77
+ ··· − 2u − 1
c
2
u
78
+ 38u
77
+ ··· + 4u + 1
c
3
, c
10
u
78
+ 2u
77
+ ··· + 4u + 1
c
4
u
78
+ 3u
77
+ ··· + 1620u + 200
c
6
, c
9
u
78
+ 4u
77
+ ··· − 349u − 25
c
7
5(5u
78
+ 22u
77
+ ··· − 2074u − 329)
c
8
5(5u
78
− 57u
77
+ ··· − 1179u − 1431)
c
11
u
78
+ 6u
77
+ ··· − 20170u − 4025
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
78
− 38y
77
+ ··· − 4y + 1
c
2
y
78
+ 6y
77
+ ··· + 8y + 1
c
3
, c
10
y
78
− 42y
77
+ ··· − 4y + 1
c
4
y
78
− 21y
77
+ ··· − 354000y + 40000
c
6
, c
9
y
78
− 44y
77
+ ··· − 59401y + 625
c
7
25(25y
78
+ 186y
77
+ ··· + 726960y + 108241)
c
8
25(25y
78
− 499y
77
+ ··· − 2.01676 × 10
7
y + 2047761)
c
11
y
78
+ 26y
77
+ ··· − 39169300y + 16200625
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.746844 + 0.705544I
a = −0.478258 − 0.846046I
b = −0.973201 + 0.859230I
1.84214 + 9.51725I 0
u = −0.746844 − 0.705544I
a = −0.478258 + 0.846046I
b = −0.973201 − 0.859230I
1.84214 − 9.51725I 0
u = 0.733786 + 0.768282I
a = −0.238190 + 0.368034I
b = −0.480787 − 0.550929I
5.29151 − 3.14059I 0
u = 0.733786 − 0.768282I
a = −0.238190 − 0.368034I
b = −0.480787 + 0.550929I
5.29151 + 3.14059I 0
u = −1.024600 + 0.336794I
a = 1.54401 − 1.42228I
b = 0.01866 − 1.42927I
−2.14618 − 1.33328I 0
u = −1.024600 − 0.336794I
a = 1.54401 + 1.42228I
b = 0.01866 + 1.42927I
−2.14618 + 1.33328I 0
u = −0.850399 + 0.683748I
a = −0.505972 + 0.523823I
b = 0.842741 + 0.745286I
1.54329 − 4.25093I 0
u = −0.850399 − 0.683748I
a = −0.505972 − 0.523823I
b = 0.842741 − 0.745286I
1.54329 + 4.25093I 0
u = −0.739719 + 0.511752I
a = 0.333454 + 0.752332I
b = 0.877805 − 0.981944I
−1.96956 + 4.60975I −4.54210 − 7.29697I
u = −0.739719 − 0.511752I
a = 0.333454 − 0.752332I
b = 0.877805 + 0.981944I
−1.96956 − 4.60975I −4.54210 + 7.29697I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.309437 + 0.842121I
a = −0.303870 − 0.378991I
b = −0.893991 + 0.759593I
2.88434 + 6.11355I 0.57263 − 4.98451I
u = 0.309437 − 0.842121I
a = −0.303870 + 0.378991I
b = −0.893991 − 0.759593I
2.88434 − 6.11355I 0.57263 + 4.98451I
u = 1.030610 + 0.412848I
a = 1.68779 − 0.30818I
b = 0.372068 + 0.975530I
−0.08665 − 1.81934I 0
u = 1.030610 − 0.412848I
a = 1.68779 + 0.30818I
b = 0.372068 − 0.975530I
−0.08665 + 1.81934I 0
u = −0.289191 + 0.831056I
a = −0.532023 + 0.563698I
b = −1.25627 − 0.93792I
−0.68796 − 12.03560I −2.39702 + 6.80252I
u = −0.289191 − 0.831056I
a = −0.532023 − 0.563698I
b = −1.25627 + 0.93792I
−0.68796 + 12.03560I −2.39702 − 6.80252I
u = 1.017100 + 0.476390I
a = 2.80013 − 1.11064I
b = 1.24917 + 0.87506I
0.76206 − 1.48191I 0
u = 1.017100 − 0.476390I
a = 2.80013 + 1.11064I
b = 1.24917 − 0.87506I
0.76206 + 1.48191I 0
u = −0.367142 + 0.771630I
a = 0.295260 + 0.430720I
b = −0.826296 − 0.097021I
−2.74670 − 1.03689I −6.52285 + 3.02306I
u = −0.367142 − 0.771630I
a = 0.295260 − 0.430720I
b = −0.826296 + 0.097021I
−2.74670 + 1.03689I −6.52285 − 3.02306I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.149695 + 0.830340I
a = 0.245507 − 0.296928I
b = 0.865089 − 0.200429I
−2.45171 + 2.55877I −5.85987 − 5.37138I
u = −0.149695 − 0.830340I
a = 0.245507 + 0.296928I
b = 0.865089 + 0.200429I
−2.45171 − 2.55877I −5.85987 + 5.37138I
u = −1.088040 + 0.413183I
a = −1.09001 + 0.98084I
b = −0.001009 − 0.600156I
−3.19952 + 3.59888I 0
u = −1.088040 − 0.413183I
a = −1.09001 − 0.98084I
b = −0.001009 + 0.600156I
−3.19952 − 3.59888I 0
u = 1.139890 + 0.236298I
a = 1.41756 + 0.21010I
b = 1.132930 + 0.048625I
−7.37477 − 1.65920I 0
u = 1.139890 − 0.236298I
a = 1.41756 − 0.21010I
b = 1.132930 − 0.048625I
−7.37477 + 1.65920I 0
u = −1.051900 + 0.501021I
a = 1.93452 + 1.70901I
b = 1.48871 + 0.16626I
1.14399 + 4.70367I 0
u = −1.051900 − 0.501021I
a = 1.93452 − 1.70901I
b = 1.48871 − 0.16626I
1.14399 − 4.70367I 0
u = −1.078790 + 0.507036I
a = 0.473785 + 1.201770I
b = 0.961578 + 0.893094I
0.70811 + 4.91347I 0
u = −1.078790 − 0.507036I
a = 0.473785 − 1.201770I
b = 0.961578 − 0.893094I
0.70811 − 4.91347I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.934335 + 0.746651I
a = −0.193081 − 0.276408I
b = 0.385335 − 0.321158I
4.74268 − 2.53637I 0
u = 0.934335 − 0.746651I
a = −0.193081 + 0.276408I
b = 0.385335 + 0.321158I
4.74268 + 2.53637I 0
u = 1.155640 + 0.314214I
a = −1.98719 + 1.54907I
b = −1.52907 + 0.68369I
−8.20158 + 2.35498I 0
u = 1.155640 − 0.314214I
a = −1.98719 − 1.54907I
b = −1.52907 − 0.68369I
−8.20158 − 2.35498I 0
u = 1.105230 + 0.476843I
a = −1.41172 + 3.06153I
b = 0.065078 − 0.438552I
−2.73306 − 3.75480I 0
u = 1.105230 − 0.476843I
a = −1.41172 − 3.06153I
b = 0.065078 + 0.438552I
−2.73306 + 3.75480I 0
u = −1.155380 + 0.357963I
a = −1.26784 − 0.83955I
b = −0.924109 − 0.405905I
−4.19189 + 1.50549I 0
u = −1.155380 − 0.357963I
a = −1.26784 + 0.83955I
b = −0.924109 + 0.405905I
−4.19189 − 1.50549I 0
u = −0.625614 + 0.475003I
a = 1.41445 − 0.35012I
b = −0.483183 − 0.492391I
−1.77605 − 0.65095I −5.05775 − 1.02917I
u = −0.625614 − 0.475003I
a = 1.41445 + 0.35012I
b = −0.483183 + 0.492391I
−1.77605 + 0.65095I −5.05775 + 1.02917I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.096640 + 0.524719I
a = −1.33967 − 1.54913I
b = 0.48017 − 1.76300I
−0.80322 − 8.33176I 0
u = 1.096640 − 0.524719I
a = −1.33967 + 1.54913I
b = 0.48017 + 1.76300I
−0.80322 + 8.33176I 0
u = −0.238423 + 0.742435I
a = 0.513424 − 0.435915I
b = 1.44532 + 0.92730I
−4.07487 − 5.63539I −5.32059 + 5.07237I
u = −0.238423 − 0.742435I
a = 0.513424 + 0.435915I
b = 1.44532 − 0.92730I
−4.07487 + 5.63539I −5.32059 − 5.07237I
u = −1.207250 + 0.220796I
a = 1.27897 + 0.72201I
b = 0.968015 + 0.543909I
−2.09592 − 2.91398I 0
u = −1.207250 − 0.220796I
a = 1.27897 − 0.72201I
b = 0.968015 − 0.543909I
−2.09592 + 2.91398I 0
u = 0.653825 + 0.410103I
a = 0.603104 − 0.900709I
b = 0.137771 + 0.795666I
1.09693 − 1.53880I 1.66479 + 5.08310I
u = 0.653825 − 0.410103I
a = 0.603104 + 0.900709I
b = 0.137771 − 0.795666I
1.09693 + 1.53880I 1.66479 − 5.08310I
u = 1.207280 + 0.247867I
a = 1.80061 − 1.10036I
b = 1.29376 − 0.79776I
−5.50516 + 8.73601I 0
u = 1.207280 − 0.247867I
a = 1.80061 + 1.10036I
b = 1.29376 + 0.79776I
−5.50516 − 8.73601I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.141590 + 0.513261I
a = −1.97225 + 0.58221I
b = −0.883958 − 0.783696I
−3.10971 − 6.53083I 0
u = 1.141590 − 0.513261I
a = −1.97225 − 0.58221I
b = −0.883958 + 0.783696I
−3.10971 + 6.53083I 0
u = 0.536973 + 0.520683I
a = −0.275984 − 0.550833I
b = −0.91164 + 1.14392I
2.17308 − 2.60159I 2.40455 + 6.09883I
u = 0.536973 − 0.520683I
a = −0.275984 + 0.550833I
b = −0.91164 − 1.14392I
2.17308 + 2.60159I 2.40455 − 6.09883I
u = −0.739477
a = 0.804258
b = 0.322518
−0.989802 −10.9810
u = 1.214520 + 0.340708I
a = −1.65330 − 0.02146I
b = −1.065870 − 0.267377I
−6.71121 − 6.46472I 0
u = 1.214520 − 0.340708I
a = −1.65330 + 0.02146I
b = −1.065870 + 0.267377I
−6.71121 + 6.46472I 0
u = −1.145480 + 0.533343I
a = −2.71029 − 1.10644I
b = −1.59668 + 0.98544I
−6.70525 + 10.43610I 0
u = −1.145480 − 0.533343I
a = −2.71029 + 1.10644I
b = −1.59668 − 0.98544I
−6.70525 − 10.43610I 0
u = −1.129540 + 0.584934I
a = 0.773398 + 1.151490I
b = 0.901036 − 0.260596I
−5.00368 + 6.17548I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.129540 − 0.584934I
a = 0.773398 − 1.151490I
b = 0.901036 + 0.260596I
−5.00368 − 6.17548I 0
u = 0.193316 + 0.691312I
a = 0.545322 + 0.428076I
b = 0.704072 − 0.657723I
−0.42144 + 1.94552I −2.30995 − 3.00822I
u = 0.193316 − 0.691312I
a = 0.545322 − 0.428076I
b = 0.704072 + 0.657723I
−0.42144 − 1.94552I −2.30995 + 3.00822I
u = 0.325468 + 0.636702I
a = −0.138810 + 0.488594I
b = −0.55951 − 1.52885I
1.40525 + 3.78104I 0.49759 − 6.55380I
u = 0.325468 − 0.636702I
a = −0.138810 − 0.488594I
b = −0.55951 + 1.52885I
1.40525 − 3.78104I 0.49759 + 6.55380I
u = −1.187200 + 0.508151I
a = −1.06426 − 1.06765I
b = −0.898331 − 0.033808I
−5.56201 + 2.30321I 0
u = −1.187200 − 0.508151I
a = −1.06426 + 1.06765I
b = −0.898331 + 0.033808I
−5.56201 − 2.30321I 0
u = −1.162450 + 0.573065I
a = 2.39742 + 1.05722I
b = 1.32796 − 0.97627I
−3.2894 + 17.2353I 0
u = −1.162450 − 0.573065I
a = 2.39742 − 1.05722I
b = 1.32796 + 0.97627I
−3.2894 − 17.2353I 0
u = 1.160070 + 0.582250I
a = 1.80074 − 0.72766I
b = 0.995785 + 0.824598I
0.33944 − 11.38210I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.160070 − 0.582250I
a = 1.80074 + 0.72766I
b = 0.995785 − 0.824598I
0.33944 + 11.38210I 0
u = −0.432470 + 0.537624I
a = −0.965637 + 0.005674I
b = −1.239030 − 0.068800I
2.94199 − 0.45731I 3.21783 + 1.77421I
u = −0.432470 − 0.537624I
a = −0.965637 − 0.005674I
b = −1.239030 + 0.068800I
2.94199 + 0.45731I 3.21783 − 1.77421I
u = −0.365285 + 0.557959I
a = −0.893897 − 0.608044I
b = −0.953283 + 0.561262I
2.76015 − 0.59113I 3.15854 − 1.26752I
u = −0.365285 − 0.557959I
a = −0.893897 + 0.608044I
b = −0.953283 − 0.561262I
2.76015 + 0.59113I 3.15854 + 1.26752I
u = 0.594731
a = 8.24266
b = 0.365566
0.210538 −40.2340
u = 0.152062 + 0.532162I
a = 3.33933 + 3.13837I
b = 0.119106 − 0.447244I
−0.213305 − 0.310477I 5.75572 − 9.22224I
u = 0.152062 − 0.532162I
a = 3.33933 − 3.13837I
b = 0.119106 + 0.447244I
−0.213305 + 0.310477I 5.75572 + 9.22224I
12
II. I
u
2
= hb, −3u
2
+ 5a + 7u − 6, u
3
− u
2
+ 1i
(i) Arc colorings
a
2
=
0
u
a
5
=
1
0
a
6
=
1
u
2
a
1
=
u
u
a
3
=
−u
2
+ 1
−u
2
+ u + 1
a
8
=
3
5
u
2
−
7
5
u +
6
5
0
a
9
=
2
5
u
2
−
8
5
u +
4
5
−
2
5
u
2
−
2
5
u +
1
5
a
4
=
1
0
a
11
=
u
2
− 1
−u
2
a
7
=
2
5
u
2
−
8
5
u +
9
5
3
5
u
2
−
2
5
u +
1
5
a
10
=
−1
−u
2
a
10
=
−1
−u
2
(ii) Obstruction class = 1
(iii) Cusp Shapes =
277
25
u
2
−
93
25
u −
181
25
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
3
+ u
2
− 1
c
2
, c
3
u
3
+ u
2
+ 2u + 1
c
4
u
3
c
5
u
3
− u
2
+ 1
c
6
(u + 1)
3
c
7
5(5u
3
+ 11u
2
+ 6u + 1)
c
8
5(5u
3
+ 4u
2
+ u + 1)
c
9
(u − 1)
3
c
10
u
3
− u
2
+ 2u − 1
c
11
u
3
+ 3u
2
+ 2u − 1
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
3
− y
2
+ 2y −1
c
2
, c
3
, c
10
y
3
+ 3y
2
+ 2y −1
c
4
y
3
c
6
, c
9
(y −1)
3
c
7
25(25y
3
− 61y
2
+ 14y −1)
c
8
25(25y
3
− 6y
2
− 7y −1)
c
11
y
3
− 5y
2
+ 10y −1
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.877439 + 0.744862I
a = 0.100634 − 0.258522I
b = 0
4.66906 − 2.82812I −8.1210 + 11.7122I
u = 0.877439 − 0.744862I
a = 0.100634 + 0.258522I
b = 0
4.66906 + 2.82812I −8.1210 − 11.7122I
u = −0.754878
a = 2.59873
b = 0
0.531480 1.88200
16
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
3
+ u
2
− 1)(u
78
+ 2u
77
+ ··· − 2u − 1)
c
2
(u
3
+ u
2
+ 2u + 1)(u
78
+ 38u
77
+ ··· + 4u + 1)
c
3
(u
3
+ u
2
+ 2u + 1)(u
78
+ 2u
77
+ ··· + 4u + 1)
c
4
u
3
(u
78
+ 3u
77
+ ··· + 1620u + 200)
c
5
(u
3
− u
2
+ 1)(u
78
+ 2u
77
+ ··· − 2u − 1)
c
6
((u + 1)
3
)(u
78
+ 4u
77
+ ··· − 349u − 25)
c
7
25(5u
3
+ 11u
2
+ 6u + 1)(5u
78
+ 22u
77
+ ··· − 2074u − 329)
c
8
25(5u
3
+ 4u
2
+ u + 1)(5u
78
− 57u
77
+ ··· − 1179u − 1431)
c
9
((u − 1)
3
)(u
78
+ 4u
77
+ ··· − 349u − 25)
c
10
(u
3
− u
2
+ 2u − 1)(u
78
+ 2u
77
+ ··· + 4u + 1)
c
11
(u
3
+ 3u
2
+ 2u − 1)(u
78
+ 6u
77
+ ··· − 20170u − 4025)
17
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
(y
3
− y
2
+ 2y −1)(y
78
− 38y
77
+ ··· − 4y + 1)
c
2
(y
3
+ 3y
2
+ 2y −1)(y
78
+ 6y
77
+ ··· + 8y + 1)
c
3
, c
10
(y
3
+ 3y
2
+ 2y −1)(y
78
− 42y
77
+ ··· − 4y + 1)
c
4
y
3
(y
78
− 21y
77
+ ··· − 354000y + 40000)
c
6
, c
9
((y −1)
3
)(y
78
− 44y
77
+ ··· − 59401y + 625)
c
7
625(25y
3
− 61y
2
+ 14y −1)
· (25y
78
+ 186y
77
+ ··· + 726960y + 108241)
c
8
625(25y
3
− 6y
2
− 7y −1)
· (25y
78
− 499y
77
+ ··· − 20167623y + 2047761)
c
11
(y
3
− 5y
2
+ 10y −1)(y
78
+ 26y
77
+ ··· − 3.91693 × 10
7
y + 1.62006 × 10
7
)
18
