11a
244
(K11a
244
)
A knot diagram
1
Linearized knot diagam
7 1 10 8 11 9 2 5 3 6 4
Solving Sequence
6,10 4,11
1 3 2 5 9 7 8
c
10
c
11
c
3
c
2
c
5
c
9
c
6
c
8
c
1
, c
4
, c
7
Ideals for irreducible components
2
of X
par
I
u
1
= h−4.39064 × 10
39
u
31
+ 4.83121 × 10
39
u
30
+ ··· + 3.73404 × 10
41
b + 3.85648 × 10
41
,
5.47363 × 10
41
u
31
− 1.44531 × 10
42
u
30
+ ··· + 1.94170 × 10
43
a + 9.06455 × 10
42
,
u
32
− 3u
31
+ ··· + 114u − 26i
I
u
2
= h2u
23
a + 2u
23
+ ··· + 3a + 2, 4u
23
a − 10u
23
+ ··· + 4a − 8, u
24
+ u
23
+ ··· + 2u + 1i
I
u
3
= hb + u, 4a
2
− 12au − 2a + 3u − 8, u
2
+ 1i
I
u
4
= hb + 1, 6a − u + 2, u
2
− 2i
I
v
1
= ha, b − 1, v + 1i
* 5 irreducible components of dim
C
= 0, with total 87 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−4.39 × 10
39
u
31
+ 4.83 × 10
39
u
30
+ · · · + 3.73 × 10
41
b + 3.86 ×
10
41
, 5.47 × 10
41
u
31
− 1.45 × 10
42
u
30
+ · · · + 1.94 × 10
43
a + 9.06 ×
10
42
, u
32
− 3u
31
+ · · · + 114u − 26i
(i) Arc colorings
a
6
=
0
u
a
10
=
1
0
a
4
=
−0.0281899u
31
+ 0.0744353u
30
+ ··· + 6.65054u − 0.466836
0.0117584u
31
− 0.0129383u
30
+ ··· + 4.93202u − 1.03279
a
11
=
1
u
2
a
1
=
0.0176665u
31
− 0.0552376u
30
+ ··· + 0.409548u + 0.504274
0.00785720u
31
− 0.0192778u
30
+ ··· + 0.867861u − 0.446163
a
3
=
−0.0164315u
31
+ 0.0614970u
30
+ ··· + 11.5826u − 1.49963
0.0117584u
31
− 0.0129383u
30
+ ··· + 4.93202u − 1.03279
a
2
=
0.0234202u
31
− 0.0628944u
30
+ ··· + 8.74105u − 1.33147
0.00391087u
31
+ 0.00194896u
30
+ ··· + 1.97724u − 0.532828
a
5
=
u
u
3
+ u
a
9
=
−0.0295883u
31
+ 0.0920957u
30
+ ··· + 1.53443u + 1.13656
0.0239060u
31
− 0.0827478u
30
+ ··· − 3.89581u + 0.819535
a
7
=
0.0149220u
31
− 0.0655790u
30
+ ··· − 10.0660u + 1.54772
−0.00696861u
31
+ 0.0183587u
30
+ ··· + 1.25096u − 0.0818115
a
8
=
−0.0519253u
31
+ 0.163878u
30
+ ··· + 3.90769u + 0.830841
0.0106080u
31
− 0.0452849u
30
+ ··· − 2.64731u + 0.637885
a
8
=
−0.0519253u
31
+ 0.163878u
30
+ ··· + 3.90769u + 0.830841
0.0106080u
31
− 0.0452849u
30
+ ··· − 2.64731u + 0.637885
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.141620u
31
+ 0.504992u
30
+ ··· + 51.3458u − 23.3173
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
u
32
+ 3u
31
+ ··· − 46u − 10
c
2
u
32
+ 17u
31
+ ··· + 596u + 100
c
3
, c
4
, c
8
c
9
u
32
+ u
31
+ ··· − 8u − 1
c
5
, c
10
u
32
+ 3u
31
+ ··· − 114u − 26
c
6
, c
11
16(16u
32
− 32u
31
+ ··· + 20u + 1)
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
32
− 17y
31
+ ··· − 596y + 100
c
2
y
32
− y
31
+ ··· − 264816y + 10000
c
3
, c
4
, c
8
c
9
y
32
− 11y
31
+ ··· − 24y + 1
c
5
, c
10
y
32
+ 13y
31
+ ··· + 8740y + 676
c
6
, c
11
256(256y
32
+ 1664y
31
+ ··· − 136y + 1)
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.247680 + 0.984503I
a = 0.230631 + 0.815096I
b = 0.374640 + 0.105048I
1.44688 − 2.10542I −10.64510 + 3.10426I
u = −0.247680 − 0.984503I
a = 0.230631 − 0.815096I
b = 0.374640 − 0.105048I
1.44688 + 2.10542I −10.64510 − 3.10426I
u = 0.322065 + 1.002960I
a = −0.79959 + 1.57315I
b = 0.494847 − 1.304260I
3.40906 − 3.86825I −10.66165 + 7.93865I
u = 0.322065 − 1.002960I
a = −0.79959 − 1.57315I
b = 0.494847 + 1.304260I
3.40906 + 3.86825I −10.66165 − 7.93865I
u = 0.749051 + 0.842571I
a = 0.838998 − 0.649336I
b = 0.805918 + 0.420403I
1.15662 − 1.21443I −10.34690 + 5.00886I
u = 0.749051 − 0.842571I
a = 0.838998 + 0.649336I
b = 0.805918 − 0.420403I
1.15662 + 1.21443I −10.34690 − 5.00886I
u = −0.261685 + 1.100560I
a = 0.69752 + 1.32278I
b = −0.560070 − 1.085440I
4.73730 − 0.53503I −5.59189 − 1.15953I
u = −0.261685 − 1.100560I
a = 0.69752 − 1.32278I
b = −0.560070 + 1.085440I
4.73730 + 0.53503I −5.59189 + 1.15953I
u = 1.159410 + 0.253577I
a = −0.235640 − 0.264464I
b = −1.242110 + 0.484247I
−6.13645 + 10.98730I −16.3430 − 7.4849I
u = 1.159410 − 0.253577I
a = −0.235640 + 0.264464I
b = −1.242110 − 0.484247I
−6.13645 − 10.98730I −16.3430 + 7.4849I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.140650 + 0.360946I
a = 0.307006 − 0.172337I
b = 1.128760 + 0.444978I
−3.38197 − 5.23032I −13.5291 + 4.8406I
u = −1.140650 − 0.360946I
a = 0.307006 + 0.172337I
b = 1.128760 − 0.444978I
−3.38197 + 5.23032I −13.5291 − 4.8406I
u = 0.141488 + 0.788388I
a = −0.36135 + 2.04053I
b = 0.099839 − 1.311650I
2.29463 + 1.59601I −17.2362 + 0.3937I
u = 0.141488 − 0.788388I
a = −0.36135 − 2.04053I
b = 0.099839 + 1.311650I
2.29463 − 1.59601I −17.2362 − 0.3937I
u = −0.736458 + 1.048230I
a = −0.625364 − 1.039090I
b = −0.962297 + 0.501826I
1.70241 + 7.23076I −10.37930 − 9.14942I
u = −0.736458 − 1.048230I
a = −0.625364 + 1.039090I
b = −0.962297 − 0.501826I
1.70241 − 7.23076I −10.37930 + 9.14942I
u = −0.097231 + 1.300930I
a = 0.428856 + 0.829956I
b = −0.638240 − 0.573688I
3.55297 − 1.35902I −6.22009 + 3.91725I
u = −0.097231 − 1.300930I
a = 0.428856 − 0.829956I
b = −0.638240 + 0.573688I
3.55297 + 1.35902I −6.22009 − 3.91725I
u = −0.66504 + 1.26287I
a = −0.08339 − 1.53240I
b = −1.242040 + 0.607992I
−0.46603 + 11.63550I −10.91066 − 6.70327I
u = −0.66504 − 1.26287I
a = −0.08339 + 1.53240I
b = −1.242040 − 0.607992I
−0.46603 − 11.63550I −10.91066 + 6.70327I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.64627 + 1.29426I
a = −0.04894 − 1.63210I
b = 1.30934 + 0.63525I
−2.8457 − 17.3477I −13.2852 + 10.0205I
u = 0.64627 − 1.29426I
a = −0.04894 + 1.63210I
b = 1.30934 − 0.63525I
−2.8457 + 17.3477I −13.2852 − 10.0205I
u = 1.38769 + 0.52320I
a = −0.203571 − 0.024919I
b = −1.092060 + 0.243675I
−9.14170 + 1.02273I −18.9526 − 6.3910I
u = 1.38769 − 0.52320I
a = −0.203571 + 0.024919I
b = −1.092060 − 0.243675I
−9.14170 − 1.02273I −18.9526 + 6.3910I
u = 0.75214 + 1.28922I
a = −0.023703 − 1.211370I
b = 1.242430 + 0.458182I
−6.39323 − 8.37491I −16.6922 + 6.0879I
u = 0.75214 − 1.28922I
a = −0.023703 + 1.211370I
b = 1.242430 − 0.458182I
−6.39323 + 8.37491I −16.6922 − 6.0879I
u = 0.15834 + 1.54684I
a = −0.519510 + 0.469576I
b = 0.921773 − 0.411908I
0.43477 + 5.74906I −12.0210 − 8.3466I
u = 0.15834 − 1.54684I
a = −0.519510 − 0.469576I
b = 0.921773 + 0.411908I
0.43477 − 5.74906I −12.0210 + 8.3466I
u = −1.61248
a = −0.366965
b = −0.861180
−7.60439 −2.56870
u = −0.027688 + 0.377024I
a = 0.62467 + 1.38038I
b = 0.136888 + 0.524281I
1.38354 − 2.30080I −9.19830 + 4.85013I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.027688 − 0.377024I
a = 0.62467 − 1.38038I
b = 0.136888 − 0.524281I
1.38354 + 2.30080I −9.19830 − 4.85013I
u = 0.332429
a = 0.529099
b = 0.305964
−0.575721 −17.4050
8
II. I
u
2
=
h2u
23
a+2u
23
+· · ·+3a+2, 4u
23
a−10u
23
+· · ·+4a−8, u
24
+u
23
+· · ·+2u+1i
(i) Arc colorings
a
6
=
0
u
a
10
=
1
0
a
4
=
a
−2u
23
a − 2u
23
+ ··· − 3a − 2
a
11
=
1
u
2
a
1
=
−2u
22
a + 12u
23
+ ··· + 2a + 11
2u
22
+ 2u
21
+ ··· + 4u + 5
a
3
=
−2u
23
a − 2u
23
+ ··· − 2a − 2
−2u
23
a − 2u
23
+ ··· − 3a − 2
a
2
=
−2u
22
a − 2u
23
+ ··· − a + 12
−2u
23
a − 4u
23
+ ··· − 3a − 2
a
5
=
u
u
3
+ u
a
9
=
−3u
23
a − 2u
23
+ ··· − 4a − 6
−u
23
a − 2u
23
+ ··· − 2a − 4
a
7
=
2u
23
a − 8u
23
+ ··· − 2a + 10
2u
23
a + u
22
a + ··· + 3a + 2
a
8
=
−2u
23
a − u
22
+ ··· − 2a − 4
−1
a
8
=
−2u
23
a − u
22
+ ··· − 2a − 4
−1
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −4u
23
− 4u
22
− 24u
21
− 20u
20
− 68u
19
− 52u
18
− 108u
17
− 80u
16
− 96u
15
− 84u
14
−
32u
13
− 52u
12
+ 24u
11
− 8u
10
+ 32u
9
+ 28u
8
+ 16u
7
+ 20u
6
+ 4u
4
+ 4u
3
− 4u
2
− 4u − 18
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
(u
24
− u
23
+ ··· − 2u
3
+ 1)
2
c
2
(u
24
+ 11u
23
+ ··· − 2u
2
+ 1)
2
c
3
, c
4
, c
8
c
9
u
48
+ u
47
+ ··· + 60u + 17
c
5
, c
10
(u
24
− u
23
+ ··· − 2u + 1)
2
c
6
, c
11
u
48
+ 19u
47
+ ··· − 5852u + 617
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
(y
24
− 11y
23
+ ··· − 2y
2
+ 1)
2
c
2
(y
24
+ 5y
23
+ ··· − 4y + 1)
2
c
3
, c
4
, c
8
c
9
y
48
− 29y
47
+ ··· − 2036y + 289
c
5
, c
10
(y
24
+ 13y
23
+ ··· − 2y
2
+ 1)
2
c
6
, c
11
y
48
− 17y
47
+ ··· + 4462208y + 380689
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.539628 + 0.849352I
a = 0.543922 + 0.247508I
b = −1.51045 + 0.21810I
−5.72979 − 5.71321I −16.1082 + 7.5036I
u = 0.539628 + 0.849352I
a = −0.33191 − 2.03598I
b = 1.039360 + 0.760521I
−5.72979 − 5.71321I −16.1082 + 7.5036I
u = 0.539628 − 0.849352I
a = 0.543922 − 0.247508I
b = −1.51045 − 0.21810I
−5.72979 + 5.71321I −16.1082 − 7.5036I
u = 0.539628 − 0.849352I
a = −0.33191 + 2.03598I
b = 1.039360 − 0.760521I
−5.72979 + 5.71321I −16.1082 − 7.5036I
u = −0.096397 + 0.986281I
a = 4.87120 + 4.00215I
b = 1.080380 + 0.019593I
−1.54603 + 2.05721I −7.72702 − 4.01793I
u = −0.096397 + 0.986281I
a = 4.84423 − 6.02369I
b = −0.896362 + 0.034778I
−1.54603 + 2.05721I −7.72702 − 4.01793I
u = −0.096397 − 0.986281I
a = 4.87120 − 4.00215I
b = 1.080380 − 0.019593I
−1.54603 − 2.05721I −7.72702 + 4.01793I
u = −0.096397 − 0.986281I
a = 4.84423 + 6.02369I
b = −0.896362 − 0.034778I
−1.54603 − 2.05721I −7.72702 + 4.01793I
u = −0.414627 + 0.808476I
a = 0.00257518 − 0.01121480I
b = 1.306580 + 0.198887I
−3.23391 + 1.77225I −11.98912 − 4.04184I
u = −0.414627 + 0.808476I
a = 0.35931 − 2.22876I
b = −0.979446 + 0.498112I
−3.23391 + 1.77225I −11.98912 − 4.04184I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.414627 − 0.808476I
a = 0.00257518 + 0.01121480I
b = 1.306580 − 0.198887I
−3.23391 − 1.77225I −11.98912 + 4.04184I
u = −0.414627 − 0.808476I
a = 0.35931 + 2.22876I
b = −0.979446 − 0.498112I
−3.23391 − 1.77225I −11.98912 + 4.04184I
u = 0.542169 + 0.664263I
a = 0.666243 − 0.437409I
b = −1.306800 + 0.469542I
−6.25412 + 1.34320I −18.0296 − 0.6200I
u = 0.542169 + 0.664263I
a = −0.14319 − 1.94467I
b = 1.290650 + 0.487392I
−6.25412 + 1.34320I −18.0296 − 0.6200I
u = 0.542169 − 0.664263I
a = 0.666243 + 0.437409I
b = −1.306800 − 0.469542I
−6.25412 − 1.34320I −18.0296 + 0.6200I
u = 0.542169 − 0.664263I
a = −0.14319 + 1.94467I
b = 1.290650 − 0.487392I
−6.25412 − 1.34320I −18.0296 + 0.6200I
u = −0.796432 + 0.144602I
a = −0.786039 − 0.575477I
b = −0.017969 + 0.851963I
−2.49287 − 6.17959I −13.7852 + 5.0455I
u = −0.796432 + 0.144602I
a = −0.197166 − 0.175593I
b = −1.233680 − 0.435221I
−2.49287 − 6.17959I −13.7852 + 5.0455I
u = −0.796432 − 0.144602I
a = −0.786039 + 0.575477I
b = −0.017969 − 0.851963I
−2.49287 + 6.17959I −13.7852 − 5.0455I
u = −0.796432 − 0.144602I
a = −0.197166 + 0.175593I
b = −1.233680 + 0.435221I
−2.49287 + 6.17959I −13.7852 − 5.0455I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.472424 + 1.121720I
a = −0.004693 − 1.220150I
b = −0.070699 + 0.850066I
−2.54173 + 3.77265I −13.8919 − 3.4911I
u = −0.472424 + 1.121720I
a = −0.225989 + 1.326630I
b = 1.276130 − 0.388706I
−2.54173 + 3.77265I −13.8919 − 3.4911I
u = −0.472424 − 1.121720I
a = −0.004693 + 1.220150I
b = −0.070699 − 0.850066I
−2.54173 − 3.77265I −13.8919 + 3.4911I
u = −0.472424 − 1.121720I
a = −0.225989 − 1.326630I
b = 1.276130 + 0.388706I
−2.54173 − 3.77265I −13.8919 + 3.4911I
u = 0.766849 + 0.083191I
a = 0.769852 − 0.382628I
b = 0.169700 + 0.594156I
−0.655501 + 1.182900I −10.60754 − 0.39910I
u = 0.766849 + 0.083191I
a = 0.400701 − 0.069987I
b = 1.032180 − 0.364777I
−0.655501 + 1.182900I −10.60754 − 0.39910I
u = 0.766849 − 0.083191I
a = 0.769852 + 0.382628I
b = 0.169700 − 0.594156I
−0.655501 − 1.182900I −10.60754 + 0.39910I
u = 0.766849 − 0.083191I
a = 0.400701 + 0.069987I
b = 1.032180 + 0.364777I
−0.655501 − 1.182900I −10.60754 + 0.39910I
u = −0.376287 + 1.204930I
a = 0.475135 + 0.983255I
b = 0.513121 − 0.339665I
1.53995 − 2.24524I −8.97303 + 1.89383I
u = −0.376287 + 1.204930I
a = −0.408284 + 0.298929I
b = 0.696267 + 0.307021I
1.53995 − 2.24524I −8.97303 + 1.89383I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.376287 − 1.204930I
a = 0.475135 − 0.983255I
b = 0.513121 + 0.339665I
1.53995 + 2.24524I −8.97303 − 1.89383I
u = −0.376287 − 1.204930I
a = −0.408284 − 0.298929I
b = 0.696267 − 0.307021I
1.53995 + 2.24524I −8.97303 − 1.89383I
u = 0.413902 + 1.197930I
a = −0.198548 + 1.325430I
b = −0.820849 − 0.486407I
3.07007 − 2.92383I −6.70980 + 3.29300I
u = 0.413902 + 1.197930I
a = 0.375753 − 0.333805I
b = −0.476232 + 0.580933I
3.07007 − 2.92383I −6.70980 + 3.29300I
u = 0.413902 − 1.197930I
a = −0.198548 − 1.325430I
b = −0.820849 + 0.486407I
3.07007 + 2.92383I −6.70980 − 3.29300I
u = 0.413902 − 1.197930I
a = 0.375753 + 0.333805I
b = −0.476232 − 0.580933I
3.07007 + 2.92383I −6.70980 − 3.29300I
u = 0.486243 + 1.189530I
a = 0.531403 − 1.075720I
b = −0.278243 + 1.022640I
2.55519 − 5.78082I −7.62473 + 3.72629I
u = 0.486243 + 1.189530I
a = 0.12458 + 1.60566I
b = −1.184610 − 0.672538I
2.55519 − 5.78082I −7.62473 + 3.72629I
u = 0.486243 − 1.189530I
a = 0.531403 + 1.075720I
b = −0.278243 − 1.022640I
2.55519 + 5.78082I −7.62473 − 3.72629I
u = 0.486243 − 1.189530I
a = 0.12458 − 1.60566I
b = −1.184610 + 0.672538I
2.55519 + 5.78082I −7.62473 − 3.72629I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.512242 + 1.189930I
a = −0.590726 − 1.274840I
b = 0.228910 + 1.166680I
0.58237 + 11.00000I −10.68175 − 8.05284I
u = −0.512242 + 1.189930I
a = −0.24364 + 1.67429I
b = 1.30033 − 0.72492I
0.58237 + 11.00000I −10.68175 − 8.05284I
u = −0.512242 − 1.189930I
a = −0.590726 + 1.274840I
b = 0.228910 − 1.166680I
0.58237 − 11.00000I −10.68175 + 8.05284I
u = −0.512242 − 1.189930I
a = −0.24364 − 1.67429I
b = 1.30033 + 0.72492I
0.58237 − 11.00000I −10.68175 + 8.05284I
u = −0.580381 + 0.259924I
a = −0.625985 − 0.961812I
b = −1.295020 − 0.005614I
−5.03285 + 0.40841I −17.8720 − 0.7556I
u = −0.580381 + 0.259924I
a = −1.20872 − 0.75067I
b = 0.636772 + 0.510637I
−5.03285 + 0.40841I −17.8720 − 0.7556I
u = −0.580381 − 0.259924I
a = −0.625985 + 0.961812I
b = −1.295020 + 0.005614I
−5.03285 − 0.40841I −17.8720 + 0.7556I
u = −0.580381 − 0.259924I
a = −1.20872 + 0.75067I
b = 0.636772 − 0.510637I
−5.03285 − 0.40841I −17.8720 + 0.7556I
16
III. I
u
3
= hb + u, 4a
2
− 12au − 2a + 3u − 8, u
2
+ 1i
(i) Arc colorings
a
6
=
0
u
a
10
=
1
0
a
4
=
a
−u
a
11
=
1
−1
a
1
=
2au +
1
2
a −
3
4
u + 3
−au − 2
a
3
=
a − u
−u
a
2
=
2au +
3
2
a −
11
4
u +
11
4
−au − a + u −
3
2
a
5
=
u
0
a
9
=
au + 2
1
a
7
=
1
2
au + a − 2u +
3
4
a − u
a
8
=
au + 1
1
a
8
=
au + 1
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 8a − 12u − 8
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
u
4
− u
2
+ 1
c
2
(u
2
+ u + 1)
2
c
3
, c
4
, c
5
c
8
, c
9
, c
10
(u
2
+ 1)
2
c
6
, c
11
16(16u
4
− 16u
3
+ 20u
2
− 8u + 1)
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
(y
2
− y + 1)
2
c
2
(y
2
+ y + 1)
2
c
3
, c
4
, c
5
c
8
, c
9
, c
10
(y + 1)
4
c
6
, c
11
256(256y
4
+ 384y
3
+ 176y
2
− 24y + 1)
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.000000I
a = 0.250000 + 1.066990I
b = − 1.000000I
3.28987 + 2.02988I −6.00000 − 3.46410I
u = 1.000000I
a = 0.25000 + 1.93301I
b = − 1.000000I
3.28987 − 2.02988I −6.00000 + 3.46410I
u = − 1.000000I
a = 0.250000 − 1.066990I
b = 1.000000I
3.28987 − 2.02988I −6.00000 + 3.46410I
u = − 1.000000I
a = 0.25000 − 1.93301I
b = 1.000000I
3.28987 + 2.02988I −6.00000 − 3.46410I
20
IV. I
u
4
= hb + 1, 6a − u + 2, u
2
− 2i
(i) Arc colorings
a
6
=
0
u
a
10
=
1
0
a
4
=
1
6
u −
1
3
−1
a
11
=
1
2
a
1
=
1
18
u + 1
1
3
u +
7
3
a
3
=
1
6
u −
4
3
−1
a
2
=
5
18
u +
2
3
2
3
u +
11
3
a
5
=
u
3u
a
9
=
1
6
u −
1
3
−1
a
7
=
−
1
6
u +
2
9
2
3
u +
1
3
a
8
=
−
5
6
u −
1
3
−3u − 1
a
8
=
−
5
6
u −
1
3
−3u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −20
21
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
7
c
10
u
2
− 2
c
2
(u + 2)
2
c
3
, c
8
(u − 1)
2
c
4
, c
9
(u + 1)
2
c
6
, c
11
9(9u
2
+ 6u − 1)
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
7
c
10
(y −2)
2
c
2
(y −4)
2
c
3
, c
4
, c
8
c
9
(y −1)
2
c
6
, c
11
81(81y
2
− 54y + 1)
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.41421
a = −0.0976311
b = −1.00000
−8.22467 −20.0000
u = −1.41421
a = −0.569036
b = −1.00000
−8.22467 −20.0000
24
V. I
v
1
= ha, b − 1, v + 1i
(i) Arc colorings
a
6
=
−1
0
a
10
=
1
0
a
4
=
0
1
a
11
=
1
0
a
1
=
1
1
a
3
=
1
1
a
2
=
1
1
a
5
=
−1
0
a
9
=
0
−1
a
7
=
−1
−1
a
8
=
−1
−1
a
8
=
−1
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −12
25
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
5
c
7
, c
10
u
c
3
, c
8
u + 1
c
4
, c
6
, c
9
c
11
u − 1
26
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
7
, c
10
y
c
3
, c
4
, c
6
c
8
, c
9
, c
11
y −1
27
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −1.00000
a = 0
b = 1.00000
−3.28987 −12.0000
28
VI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
7
u(u
2
− 2)(u
4
− u
2
+ 1)(u
24
− u
23
+ ··· − 2u
3
+ 1)
2
· (u
32
+ 3u
31
+ ··· − 46u − 10)
c
2
u(u + 2)
2
(u
2
+ u + 1)
2
(u
24
+ 11u
23
+ ··· − 2u
2
+ 1)
2
· (u
32
+ 17u
31
+ ··· + 596u + 100)
c
3
, c
8
((u − 1)
2
)(u + 1)(u
2
+ 1)
2
(u
32
+ u
31
+ ··· − 8u − 1)
· (u
48
+ u
47
+ ··· + 60u + 17)
c
4
, c
9
(u − 1)(u + 1)
2
(u
2
+ 1)
2
(u
32
+ u
31
+ ··· − 8u − 1)
· (u
48
+ u
47
+ ··· + 60u + 17)
c
5
, c
10
u(u
2
− 2)(u
2
+ 1)
2
(u
24
− u
23
+ ··· − 2u + 1)
2
· (u
32
+ 3u
31
+ ··· − 114u − 26)
c
6
, c
11
2304(u − 1)(9u
2
+ 6u − 1)(16u
4
− 16u
3
+ 20u
2
− 8u + 1)
· (16u
32
− 32u
31
+ ··· + 20u + 1)(u
48
+ 19u
47
+ ··· − 5852u + 617)
29
VII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
7
y(y −2)
2
(y
2
− y + 1)
2
(y
24
− 11y
23
+ ··· − 2y
2
+ 1)
2
· (y
32
− 17y
31
+ ··· − 596y + 100)
c
2
y(y −4)
2
(y
2
+ y + 1)
2
(y
24
+ 5y
23
+ ··· − 4y + 1)
2
· (y
32
− y
31
+ ··· − 264816y + 10000)
c
3
, c
4
, c
8
c
9
((y −1)
3
)(y + 1)
4
(y
32
− 11y
31
+ ··· − 24y + 1)
· (y
48
− 29y
47
+ ··· − 2036y + 289)
c
5
, c
10
y(y −2)
2
(y + 1)
4
(y
24
+ 13y
23
+ ··· − 2y
2
+ 1)
2
· (y
32
+ 13y
31
+ ··· + 8740y + 676)
c
6
, c
11
5308416(y −1)(81y
2
− 54y + 1)(256y
4
+ 384y
3
+ ··· − 24y + 1)
· (256y
32
+ 1664y
31
+ ··· − 136y + 1)
· (y
48
− 17y
47
+ ··· + 4462208y + 380689)
30
