11a
66
(K11a
66
)
A knot diagram
1
Linearized knot diagam
5 1 10 2 9 4 11 3 6 7 8
Solving Sequence
7,10
11 8
1,4
3 2 6 9 5
c
10
c
7
c
11
c
3
c
2
c
6
c
9
c
5
c
1
, c
4
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h4.83591 × 10
64
u
58
− 1.44015 × 10
65
u
57
+ ··· + 2.71331 × 10
65
b + 7.55669 × 10
64
,
− 4.47446 × 10
63
u
58
+ 4.62488 × 10
64
u
57
+ ··· + 2.71331 × 10
65
a + 7.20796 × 10
65
, u
59
− 5u
58
+ ··· + 5u
2
− 1i
* 1 irreducible components of dim
C
= 0, with total 59 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
= h4.84 × 10
64
u
58
− 1.44 × 10
65
u
57
+ · · · + 2.71 × 10
65
b + 7.56 ×
10
64
, −4.47 × 10
63
u
58
+ 4.62 × 10
64
u
57
+ · · · + 2.71 × 10
65
a + 7.21 ×
10
65
, u
59
− 5u
58
+ · · · + 5u
2
− 1i
(i) Arc colorings
a
7
=
0
u
a
10
=
1
0
a
11
=
1
−u
2
a
8
=
u
−u
3
+ u
a
1
=
−u
2
+ 1
u
4
− 2u
2
a
4
=
0.0164908u
58
− 0.170452u
57
+ ··· − 2.08113u − 2.65652
−0.178229u
58
+ 0.530775u
57
+ ··· + 0.638738u − 0.278505
a
3
=
0.194720u
58
− 0.701226u
57
+ ··· − 2.71987u − 2.37802
−0.178229u
58
+ 0.530775u
57
+ ··· + 0.638738u − 0.278505
a
2
=
0.00985244u
58
− 0.352681u
57
+ ··· − 2.73901u − 3.24048
−0.0389600u
58
+ 0.0920662u
57
+ ··· + 0.321451u − 0.113177
a
6
=
2.78334u
58
− 11.1287u
57
+ ··· − 2.34565u + 5.60971
0.818170u
58
− 2.82973u
57
+ ··· − 0.893777u + 0.202220
a
9
=
1.33059u
58
− 7.98023u
57
+ ··· + 2.66373u + 4.38104
−0.671853u
58
+ 2.30116u
57
+ ··· − 1.18700u − 0.702689
a
5
=
1.35895u
58
− 4.91224u
57
+ ··· − 7.98808u + 0.456873
−u
4
+ 2u
2
a
5
=
1.35895u
58
− 4.91224u
57
+ ··· − 7.98808u + 0.456873
−u
4
+ 2u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −3.13284u
58
+ 8.55288u
57
+ ··· − 6.92957u + 2.03395
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
59
+ u
58
+ ··· + 14u − 1
c
2
u
59
+ 23u
58
+ ··· + 198u − 1
c
3
u
59
− 3u
58
+ ··· − 4u + 1
c
5
, c
9
u
59
+ u
58
+ ··· + 5u
2
− 1
c
6
u
59
+ 11u
58
+ ··· + 286u
2
+ 8
c
7
, c
10
, c
11
u
59
− 5u
58
+ ··· + 5u
2
− 1
c
8
u
59
− 15u
58
+ ··· − 256u − 256
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
59
+ 23y
58
+ ··· + 198y −1
c
2
y
59
+ 27y
58
+ ··· + 45406y −1
c
3
y
59
− 5y
58
+ ··· − 18y −1
c
5
, c
9
y
59
− 37y
58
+ ··· + 10y −1
c
6
y
59
+ 279y
58
+ ··· − 4576y −64
c
7
, c
10
, c
11
y
59
− 61y
58
+ ··· + 10y −1
c
8
y
59
+ 287y
58
+ ··· + 1015808y −65536
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.602290 + 0.803555I
a = −0.12280 + 1.44745I
b = −0.907835 + 1.001240I
−2.44624 − 11.82370I 0. + 9.37680I
u = −0.602290 − 0.803555I
a = −0.12280 − 1.44745I
b = −0.907835 − 1.001240I
−2.44624 + 11.82370I 0. − 9.37680I
u = −0.513328 + 0.905605I
a = 0.836669 + 0.413786I
b = 0.607726 + 0.709697I
−2.77146 + 6.25200I 0
u = −0.513328 − 0.905605I
a = 0.836669 − 0.413786I
b = 0.607726 − 0.709697I
−2.77146 − 6.25200I 0
u = 0.780237 + 0.719781I
a = 0.262671 + 0.669150I
b = 0.668932 + 0.384075I
2.44555 + 0.67895I 0
u = 0.780237 − 0.719781I
a = 0.262671 − 0.669150I
b = 0.668932 − 0.384075I
2.44555 − 0.67895I 0
u = −0.610415 + 0.675553I
a = 0.09095 − 1.51512I
b = 0.869792 − 1.011370I
−0.53563 − 6.33799I 3.85891 + 5.79197I
u = −0.610415 − 0.675553I
a = 0.09095 + 1.51512I
b = 0.869792 + 1.011370I
−0.53563 + 6.33799I 3.85891 − 5.79197I
u = −0.738862 + 0.507440I
a = 0.784790 − 0.069867I
b = 0.451996 + 0.888554I
−5.18481 + 0.07298I −2.77397 + 1.06751I
u = −0.738862 − 0.507440I
a = 0.784790 + 0.069867I
b = 0.451996 − 0.888554I
−5.18481 − 0.07298I −2.77397 − 1.06751I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.610635 + 0.920920I
a = −0.371965 − 0.691396I
b = −0.678927 − 0.415007I
1.69330 + 5.46743I 0
u = 0.610635 − 0.920920I
a = −0.371965 + 0.691396I
b = −0.678927 + 0.415007I
1.69330 − 5.46743I 0
u = 1.179590 + 0.072832I
a = 0.023949 + 0.735583I
b = 0.504296 + 0.524843I
1.93352 − 0.03829I 0
u = 1.179590 − 0.072832I
a = 0.023949 − 0.735583I
b = 0.504296 − 0.524843I
1.93352 + 0.03829I 0
u = −0.298346 + 0.756487I
a = −1.040070 − 0.594848I
b = −0.539223 − 0.629121I
−1.35810 + 1.65554I 2.46202 − 2.77708I
u = −0.298346 − 0.756487I
a = −1.040070 + 0.594848I
b = −0.539223 + 0.629121I
−1.35810 − 1.65554I 2.46202 + 2.77708I
u = −0.331322 + 0.631890I
a = −0.28163 + 1.56746I
b = −0.92852 + 1.10882I
−6.37379 − 4.04787I −3.93072 + 5.51814I
u = −0.331322 − 0.631890I
a = −0.28163 − 1.56746I
b = −0.92852 − 1.10882I
−6.37379 + 4.04787I −3.93072 − 5.51814I
u = −1.384970 + 0.131008I
a = −0.737163 − 0.719110I
b = 1.026640 − 0.458872I
3.26189 − 3.67751I 0
u = −1.384970 − 0.131008I
a = −0.737163 + 0.719110I
b = 1.026640 + 0.458872I
3.26189 + 3.67751I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.42247 + 0.01167I
a = −4.44893 + 9.36868I
b = 0.072559 + 0.149112I
3.30587 − 2.05347I 0
u = −1.42247 − 0.01167I
a = −4.44893 − 9.36868I
b = 0.072559 − 0.149112I
3.30587 + 2.05347I 0
u = 0.009641 + 0.561258I
a = −0.84390 − 1.40804I
b = −0.499557 − 0.473604I
−1.27830 + 1.37033I −1.75929 − 4.49534I
u = 0.009641 − 0.561258I
a = −0.84390 + 1.40804I
b = −0.499557 + 0.473604I
−1.27830 − 1.37033I −1.75929 + 4.49534I
u = 1.43879 + 0.18099I
a = −0.623609 + 0.710901I
b = 1.51759 + 1.20583I
−0.67928 + 6.89950I 0
u = 1.43879 − 0.18099I
a = −0.623609 − 0.710901I
b = 1.51759 − 1.20583I
−0.67928 − 6.89950I 0
u = 1.45449
a = 0.915660
b = −0.262354
3.37740 0
u = 0.402436 + 0.343152I
a = −0.669541 + 0.915825I
b = −1.23192 + 0.73590I
−1.56344 + 4.78630I 2.02963 − 10.35215I
u = 0.402436 − 0.343152I
a = −0.669541 − 0.915825I
b = −1.23192 − 0.73590I
−1.56344 − 4.78630I 2.02963 + 10.35215I
u = 0.526798 + 0.021630I
a = 0.188140 + 0.404628I
b = 0.891983 + 0.249450I
1.131640 + 0.063901I 10.49402 + 0.56940I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.526798 − 0.021630I
a = 0.188140 − 0.404628I
b = 0.891983 − 0.249450I
1.131640 − 0.063901I 10.49402 − 0.56940I
u = 1.47328 + 0.05201I
a = −0.062797 − 0.841379I
b = 0.39778 − 1.37113I
6.50993 + 3.19293I 0
u = 1.47328 − 0.05201I
a = −0.062797 + 0.841379I
b = 0.39778 + 1.37113I
6.50993 − 3.19293I 0
u = −1.47786 + 0.08730I
a = −0.045066 + 0.186936I
b = 1.71673 + 1.40690I
4.61526 − 6.26348I 0
u = −1.47786 − 0.08730I
a = −0.045066 − 0.186936I
b = 1.71673 − 1.40690I
4.61526 + 6.26348I 0
u = −0.490640 + 0.130399I
a = −0.01807 − 2.09045I
b = 0.412044 − 1.147950I
0.68155 − 2.84567I 8.20760 + 7.93876I
u = −0.490640 − 0.130399I
a = −0.01807 + 2.09045I
b = 0.412044 + 1.147950I
0.68155 + 2.84567I 8.20760 − 7.93876I
u = 1.49940 + 0.03329I
a = 0.219999 − 0.701654I
b = −0.91452 − 1.88246I
7.24513 + 3.41415I 0
u = 1.49940 − 0.03329I
a = 0.219999 + 0.701654I
b = −0.91452 + 1.88246I
7.24513 − 3.41415I 0
u = −1.50177 + 0.00830I
a = 0.297564 + 0.231736I
b = −1.67755 + 0.55669I
7.78177 − 0.18045I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.50177 − 0.00830I
a = 0.297564 − 0.231736I
b = −1.67755 − 0.55669I
7.78177 + 0.18045I 0
u = 1.55701 + 0.22591I
a = 0.536066 − 0.912338I
b = −1.21260 − 1.20134I
6.60505 + 9.68161I 0
u = 1.55701 − 0.22591I
a = 0.536066 + 0.912338I
b = −1.21260 + 1.20134I
6.60505 − 9.68161I 0
u = 1.56490 + 0.27474I
a = −0.575143 + 0.964495I
b = 1.19103 + 1.13486I
4.6425 + 15.8011I 0
u = 1.56490 − 0.27474I
a = −0.575143 − 0.964495I
b = 1.19103 − 1.13486I
4.6425 − 15.8011I 0
u = −1.57947 + 0.22255I
a = 0.272883 + 0.711732I
b = −1.148480 + 0.713126I
10.09090 − 4.09953I 0
u = −1.57947 − 0.22255I
a = 0.272883 − 0.711732I
b = −1.148480 − 0.713126I
10.09090 + 4.09953I 0
u = 0.023287 + 0.400883I
a = −0.56139 − 3.63273I
b = −0.438386 − 0.419133I
−1.06640 + 1.39300I −4.87303 − 6.40557I
u = 0.023287 − 0.400883I
a = −0.56139 + 3.63273I
b = −0.438386 + 0.419133I
−1.06640 − 1.39300I −4.87303 + 6.40557I
u = −1.57430 + 0.29595I
a = −0.251509 − 0.797155I
b = 1.101890 − 0.732255I
8.82124 − 9.84696I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.57430 − 0.29595I
a = −0.251509 + 0.797155I
b = 1.101890 + 0.732255I
8.82124 + 9.84696I 0
u = −0.344914 + 0.168527I
a = 0.30650 − 2.60805I
b = −0.194817 − 0.606555I
0.46273 − 2.38122I 3.10427 + 1.63624I
u = −0.344914 − 0.168527I
a = 0.30650 + 2.60805I
b = −0.194817 + 0.606555I
0.46273 + 2.38122I 3.10427 − 1.63624I
u = 0.253207 + 0.285102I
a = −3.18179 + 4.75906I
b = 0.552194 + 0.272160I
−1.85782 − 2.60565I 2.86490 − 11.40100I
u = 0.253207 − 0.285102I
a = −3.18179 − 4.75906I
b = 0.552194 − 0.272160I
−1.85782 + 2.60565I 2.86490 + 11.40100I
u = 1.61782 + 0.39605I
a = 0.061041 + 0.323493I
b = 0.609284 + 0.193792I
4.33658 + 3.40939I 0
u = 1.61782 − 0.39605I
a = 0.061041 − 0.323493I
b = 0.609284 − 0.193792I
4.33658 − 3.40939I 0
u = 1.70668 + 0.24332I
a = −0.003673 − 0.211471I
b = −0.588967 − 0.121325I
4.61241 − 1.25946I 0
u = 1.70668 − 0.24332I
a = −0.003673 + 0.211471I
b = −0.588967 + 0.121325I
4.61241 + 1.25946I 0
10
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
4
u
59
+ u
58
+ ··· + 14u − 1
c
2
u
59
+ 23u
58
+ ··· + 198u − 1
c
3
u
59
− 3u
58
+ ··· − 4u + 1
c
5
, c
9
u
59
+ u
58
+ ··· + 5u
2
− 1
c
6
u
59
+ 11u
58
+ ··· + 286u
2
+ 8
c
7
, c
10
, c
11
u
59
− 5u
58
+ ··· + 5u
2
− 1
c
8
u
59
− 15u
58
+ ··· − 256u − 256
11
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
59
+ 23y
58
+ ··· + 198y −1
c
2
y
59
+ 27y
58
+ ··· + 45406y −1
c
3
y
59
− 5y
58
+ ··· − 18y −1
c
5
, c
9
y
59
− 37y
58
+ ··· + 10y −1
c
6
y
59
+ 279y
58
+ ··· − 4576y −64
c
7
, c
10
, c
11
y
59
− 61y
58
+ ··· + 10y −1
c
8
y
59
+ 287y
58
+ ··· + 1015808y −65536
12
