11a
348
(K11a
348
)
A knot diagram
1
Linearized knot diagam
6 5 1 10 9 4 11 3 2 7 8
Solving Sequence
2,5 3,9
6 10 1 4 7 8 11
c
2
c
5
c
9
c
1
c
4
c
6
c
8
c
11
c
3
, c
7
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.83178 × 10
30
u
28
− 4.25498 × 10
31
u
27
+ ··· + 1.83797 × 10
31
b − 2.13808 × 10
31
,
− 2.13808 × 10
31
u
28
− 4.00799 × 10
32
u
27
+ ··· + 1.34172 × 10
33
a + 1.06235 × 10
34
,
u
29
+ 25u
28
+ ··· + 638u + 73i
I
u
2
= h−600u
14
a
3
− 936u
14
a
2
+ ··· − 1792a − 1217, 8u
14
a
3
+ 72u
14
a
2
+ ··· + 218a + 237,
u
15
− 7u
14
+ 23u
13
− 42u
12
+ 38u
11
+ 7u
10
− 61u
9
+ 62u
8
− 2u
7
− 50u
6
+ 38u
5
+ 4u
4
− 20u
3
+ 7u
2
+ 3u − 2i
I
u
3
= h−231789u
14
+ 1842380u
13
+ ··· + 808985b − 1813670,
− 362734u
14
+ 2468395u
13
+ ··· + 4044925a + 9070125, u
15
− 10u
14
+ ··· + 105u − 25i
I
v
1
= ha, b
2
− bv + 2b −v + 3, v
2
− 3v + 1i
I
v
2
= ha, b
2
+ b + 1, v −1i
* 5 irreducible components of dim
C
= 0, with total 110 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−1.83 × 10
30
u
28
− 4.25 × 10
31
u
27
+ · · · + 1.84 × 10
31
b − 2.14 ×
10
31
, −2.14 × 10
31
u
28
− 4.01 × 10
32
u
27
+ · · · + 1.34 × 10
33
a + 1.06 ×
10
34
, u
29
+ 25u
28
+ · · · + 638u + 73i
(i) Arc colorings
a
2
=
1
0
a
5
=
0
u
a
3
=
1
u
2
a
9
=
0.0159354u
28
+ 0.298722u
27
+ ··· − 40.6500u − 7.91783
0.0996632u
28
+ 2.31505u
27
+ ··· + 18.0846u + 1.16328
a
6
=
0.0368204u
28
+ 0.942895u
27
+ ··· + 43.0059u + 7.47915
−0.0223856u
28
− 0.491135u
27
+ ··· + 17.0122u + 2.68789
a
10
=
−0.0837278u
28
− 2.01633u
27
+ ··· − 58.7346u − 9.08111
0.0996632u
28
+ 2.31505u
27
+ ··· + 18.0846u + 1.16328
a
1
=
−0.107125u
28
− 2.64363u
27
+ ··· − 54.0442u − 5.41609
0.0340032u
28
+ 0.644747u
27
+ ··· − 44.9598u − 6.18598
a
4
=
0.0130859u
28
+ 0.295275u
27
+ ··· − 5.98849u + 0.469224
0.0461201u
28
+ 1.13875u
27
+ ··· + 33.9822u + 4.32204
a
7
=
0.0636554u
28
+ 1.58804u
27
+ ··· + 66.1229u + 10.2269
0.0414256u
28
+ 1.05896u
27
+ ··· + 53.1661u + 7.35249
a
8
=
0.0928024u
28
+ 2.19118u
27
+ ··· + 3.68727u − 1.80570
−0.0384173u
28
− 0.676173u
27
+ ··· + 31.1112u + 3.29583
a
11
=
−0.0973760u
28
− 2.33888u
27
+ ··· − 49.8137u − 6.44579
−0.0796577u
28
− 2.01645u
27
+ ··· − 84.2207u − 11.6200
a
11
=
−0.0973760u
28
− 2.33888u
27
+ ··· − 49.8137u − 6.44579
−0.0796577u
28
− 2.01645u
27
+ ··· − 84.2207u − 11.6200
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.174043u
28
+ 3.67857u
27
+ ··· − 96.9970u − 20.7731
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
29
− 29u
28
+ ··· − 131072u + 16384
c
2
u
29
− 25u
28
+ ··· + 638u − 73
c
3
, c
6
u
29
− u
28
+ ··· + 17u + 1
c
4
, c
8
u
29
− u
28
+ ··· + 21u + 9
c
5
, c
9
u
29
+ 2u
27
+ ··· + u + 1
c
7
, c
10
, c
11
u
29
+ 9u
28
+ ··· + 49u + 73
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
29
− 7y
28
+ ··· + 5100273664y −268435456
c
2
y
29
− 13y
28
+ ··· + 27006y −5329
c
3
, c
6
y
29
− 7y
28
+ ··· + 235y −1
c
4
, c
8
y
29
+ 17y
28
+ ··· − 225y −81
c
5
, c
9
y
29
+ 4y
28
+ ··· − 3y −1
c
7
, c
10
, c
11
y
29
− 31y
28
+ ··· − 8987y −5329
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.533215 + 0.743878I
a = 1.068930 − 0.077579I
b = 0.512259 − 0.836519I
2.89664 + 0.46546I 1.68040 + 0.26806I
u = −0.533215 − 0.743878I
a = 1.068930 + 0.077579I
b = 0.512259 + 0.836519I
2.89664 − 0.46546I 1.68040 − 0.26806I
u = −0.174221 + 0.891733I
a = −1.045550 − 0.239887I
b = −0.396072 + 0.890557I
−2.36877 − 2.03117I −4.15870 + 1.99602I
u = −0.174221 − 0.891733I
a = −1.045550 + 0.239887I
b = −0.396072 − 0.890557I
−2.36877 + 2.03117I −4.15870 − 1.99602I
u = −0.993675 + 0.553218I
a = −0.840807 + 0.404017I
b = −0.611979 + 0.866611I
1.00519 + 4.10843I −1.11851 − 6.27833I
u = −0.993675 − 0.553218I
a = −0.840807 − 0.404017I
b = −0.611979 − 0.866611I
1.00519 − 4.10843I −1.11851 + 6.27833I
u = 0.377713 + 0.751230I
a = 0.598055 + 0.080621I
b = −0.165328 − 0.479728I
−0.38938 − 1.51803I −2.55495 + 5.06805I
u = 0.377713 − 0.751230I
a = 0.598055 − 0.080621I
b = −0.165328 + 0.479728I
−0.38938 + 1.51803I −2.55495 − 5.06805I
u = −1.23159 + 0.78729I
a = −1.036980 + 0.164410I
b = −1.14770 + 1.01889I
−4.12024 + 7.78492I 0. − 5.99189I
u = −1.23159 − 0.78729I
a = −1.036980 − 0.164410I
b = −1.14770 − 1.01889I
−4.12024 − 7.78492I 0. + 5.99189I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.40924 + 0.62053I
a = 0.902693 − 0.279351I
b = 1.09876 − 0.95382I
−11.42010 + 3.19049I 0
u = −1.40924 − 0.62053I
a = 0.902693 + 0.279351I
b = 1.09876 + 0.95382I
−11.42010 − 3.19049I 0
u = 0.405846 + 0.192100I
a = −1.56669 − 1.76693I
b = 0.296405 + 1.018060I
−5.03403 − 2.22778I −7.47163 + 3.53534I
u = 0.405846 − 0.192100I
a = −1.56669 + 1.76693I
b = 0.296405 − 1.018060I
−5.03403 + 2.22778I −7.47163 − 3.53534I
u = −1.22083 + 0.96772I
a = 1.004960 − 0.047355I
b = 1.18107 − 1.03033I
−4.3561 + 13.4943I 0
u = −1.22083 − 0.96772I
a = 1.004960 + 0.047355I
b = 1.18107 + 1.03033I
−4.3561 − 13.4943I 0
u = 0.009310 + 0.427042I
a = 2.26846 + 1.69136I
b = 0.701162 − 0.984473I
−4.65620 + 1.98203I −8.58633 − 3.04801I
u = 0.009310 − 0.427042I
a = 2.26846 − 1.69136I
b = 0.701162 + 0.984473I
−4.65620 − 1.98203I −8.58633 + 3.04801I
u = −1.27872 + 1.09142I
a = −0.946459 + 0.001404I
b = −1.20873 + 1.03478I
−11.5069 + 17.5600I 0
u = −1.27872 − 1.09142I
a = −0.946459 − 0.001404I
b = −1.20873 − 1.03478I
−11.5069 − 17.5600I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.290088
a = −2.49108
b = −0.722632
−1.41973 −5.24450
u = −1.84285 + 0.37896I
a = −0.221920 + 0.459486I
b = −0.234839 + 0.930861I
−0.10408 + 3.63440I 0
u = −1.84285 − 0.37896I
a = −0.221920 − 0.459486I
b = −0.234839 − 0.930861I
−0.10408 − 3.63440I 0
u = −0.97578 + 1.61172I
a = 0.037347 + 0.297762I
b = 0.516352 + 0.230358I
−2.86261 − 4.93654I 0
u = −0.97578 − 1.61172I
a = 0.037347 − 0.297762I
b = 0.516352 − 0.230358I
−2.86261 + 4.93654I 0
u = −1.81822 + 1.09987I
a = 0.375121 − 0.181419I
b = 0.482516 − 0.742445I
−8.14903 + 8.41158I 0
u = −1.81822 − 1.09987I
a = 0.375121 + 0.181419I
b = 0.482516 + 0.742445I
−8.14903 − 8.41158I 0
u = −1.66948 + 1.64303I
a = −0.180391 − 0.219962I
b = −0.662563 − 0.070835I
−10.73200 − 7.71685I 0
u = −1.66948 − 1.64303I
a = −0.180391 + 0.219962I
b = −0.662563 + 0.070835I
−10.73200 + 7.71685I 0
7
II. I
u
2
= h−600u
14
a
3
− 936u
14
a
2
+ · · · − 1792a − 1217, 8u
14
a
3
+ 72u
14
a
2
+
· · · + 218a + 237, u
15
− 7u
14
+ · · · + 3u − 2i
(i) Arc colorings
a
2
=
1
0
a
5
=
0
u
a
3
=
1
u
2
a
9
=
a
0.669643a
3
u
14
+ 1.04464a
2
u
14
+ ··· + 2a + 1.35826
a
6
=
−a
2
u
−1.04464a
3
u
14
− 0.669643a
2
u
14
+ ··· + 6a + 1.00112
a
10
=
−0.669643a
3
u
14
− 1.04464a
2
u
14
+ ··· − a − 1.35826
0.669643a
3
u
14
+ 1.04464a
2
u
14
+ ··· + 2a + 1.35826
a
1
=
−0.477679a
3
u
14
+ 0.334821a
2
u
14
+ ··· − 2a + 0.499442
−1.04464a
3
u
14
− 0.669643a
2
u
14
+ ··· + 6a + 0.00111607
a
4
=
0.821429a
3
u
14
+ 0.321429a
2
u
14
+ ··· − 0.678571a
2
+ 0.00446429
0.223214a
3
u
14
+ 0.348214a
2
u
14
+ ··· − 6a − 1.00558
a
7
=
0.254464a
3
u
14
+ 0.316964a
2
u
14
+ ··· − 0.683036a
2
+ 0.506138
−0.866071a
3
u
14
+ 0.00892857a
2
u
14
+ ··· + 2.00893a
2
− 0.00334821
a
8
=
−0.669643a
3
u
14
− 1.04464a
2
u
14
+ ··· − a − 1.35826
0.991071a
3
u
14
− 0.133929a
2
u
14
+ ··· + 4a + 1.92522
a
11
=
−0.254464a
3
u
14
− 0.316964a
2
u
14
+ ··· − 3a − 0.506138
−
3
8
u
14
a
3
+
3
8
u
14
a
2
+ ··· + 6a +
63
64
a
11
=
−0.254464a
3
u
14
− 0.316964a
2
u
14
+ ··· − 3a − 0.506138
−
3
8
u
14
a
3
+
3
8
u
14
a
2
+ ··· + 6a +
63
64
(ii) Obstruction class = −1
(iii) Cusp Shapes =
117
28
u
14
a
3
+
75
28
u
14
a
2
+ ··· − 24a −
7393
224
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
2
+ u + 1)
30
c
2
(u
15
+ 7u
14
+ ··· + 3u + 2)
4
c
3
, c
6
u
60
+ 3u
59
+ ··· + 5800u + 1951
c
4
, c
8
u
60
+ 17u
58
+ ··· + 63147u + 112777
c
5
, c
9
u
60
− 9u
58
+ ··· + 5u + 1
c
7
, c
10
, c
11
(u
15
− 2u
14
+ ··· + 2u − 1)
4
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
2
+ y + 1)
30
c
2
(y
15
− 3y
14
+ ··· + 37y −4)
4
c
3
, c
6
y
60
− 31y
59
+ ··· − 116686266y + 3806401
c
4
, c
8
y
60
+ 34y
59
+ ··· + 352063429739y + 12718651729
c
5
, c
9
y
60
− 18y
59
+ ··· + 27y + 1
c
7
, c
10
, c
11
(y
15
− 16y
14
+ ··· + 10y −1)
4
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.602091 + 0.799295I
a = 0.967192 + 0.023712I
b = 1.46023 + 0.91520I
−0.38534 − 5.63362I −2.44329 + 10.98878I
u = 0.602091 + 0.799295I
a = 0.731075 + 0.157864I
b = −0.023707 − 0.161225I
−0.38534 − 1.57385I −2.44329 + 4.06057I
u = 0.602091 + 0.799295I
a = −1.60848 + 0.61527I
b = −0.563384 − 0.787348I
−0.38534 − 5.63362I −2.44329 + 10.98878I
u = 0.602091 + 0.799295I
a = 0.142942 + 0.078015I
b = −0.313994 − 0.679393I
−0.38534 − 1.57385I −2.44329 + 4.06057I
u = 0.602091 − 0.799295I
a = 0.967192 − 0.023712I
b = 1.46023 − 0.91520I
−0.38534 + 5.63362I −2.44329 − 10.98878I
u = 0.602091 − 0.799295I
a = 0.731075 − 0.157864I
b = −0.023707 + 0.161225I
−0.38534 + 1.57385I −2.44329 − 4.06057I
u = 0.602091 − 0.799295I
a = −1.60848 − 0.61527I
b = −0.563384 + 0.787348I
−0.38534 + 5.63362I −2.44329 − 10.98878I
u = 0.602091 − 0.799295I
a = 0.142942 − 0.078015I
b = −0.313994 + 0.679393I
−0.38534 + 1.57385I −2.44329 − 4.06057I
u = −0.754169 + 0.212783I
a = −0.910516 + 0.108757I
b = −1.26285 − 1.50931I
−10.63760 + 8.63903I −15.1406 − 9.1585I
u = −0.754169 + 0.212783I
a = 1.194270 + 0.576398I
b = 1.00815 − 1.23211I
−10.63760 + 4.57927I −15.1406 − 2.2303I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.754169 + 0.212783I
a = 1.66516 − 1.16392I
b = 1.023330 + 0.180581I
−10.63760 + 4.57927I −15.1406 − 2.2303I
u = −0.754169 + 0.212783I
a = −1.02801 − 2.29134I
b = −0.663541 + 0.275764I
−10.63760 + 8.63903I −15.1406 − 9.1585I
u = −0.754169 − 0.212783I
a = −0.910516 − 0.108757I
b = −1.26285 + 1.50931I
−10.63760 − 8.63903I −15.1406 + 9.1585I
u = −0.754169 − 0.212783I
a = 1.194270 − 0.576398I
b = 1.00815 + 1.23211I
−10.63760 − 4.57927I −15.1406 + 2.2303I
u = −0.754169 − 0.212783I
a = 1.66516 + 1.16392I
b = 1.023330 − 0.180581I
−10.63760 − 4.57927I −15.1406 + 2.2303I
u = −0.754169 − 0.212783I
a = −1.02801 + 2.29134I
b = −0.663541 − 0.275764I
−10.63760 − 8.63903I −15.1406 + 9.1585I
u = 0.671611 + 0.294946I
a = −0.839523 − 0.242865I
b = −1.36585 − 1.21898I
−2.26591 − 2.26892I −13.6402 + 6.9635I
u = 0.671611 + 0.294946I
a = −0.467370 + 0.332502I
b = −0.67510 + 1.24619I
−2.26591 + 1.79084I −13.64024 + 0.03534I
u = 0.671611 + 0.294946I
a = 0.15954 − 1.92560I
b = 0.411961 − 0.085463I
−2.26591 + 1.79084I −13.64024 + 0.03534I
u = 0.671611 + 0.294946I
a = 2.37310 + 0.77283I
b = 0.492201 + 0.410725I
−2.26591 − 2.26892I −13.6402 + 6.9635I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.671611 − 0.294946I
a = −0.839523 + 0.242865I
b = −1.36585 + 1.21898I
−2.26591 + 2.26892I −13.6402 − 6.9635I
u = 0.671611 − 0.294946I
a = −0.467370 − 0.332502I
b = −0.67510 − 1.24619I
−2.26591 − 1.79084I −13.64024 − 0.03534I
u = 0.671611 − 0.294946I
a = 0.15954 + 1.92560I
b = 0.411961 + 0.085463I
−2.26591 − 1.79084I −13.64024 − 0.03534I
u = 0.671611 − 0.294946I
a = 2.37310 − 0.77283I
b = 0.492201 − 0.410725I
−2.26591 + 2.26892I −13.6402 − 6.9635I
u = 0.581967 + 1.140370I
a = −0.962013 + 0.055914I
b = −1.43681 − 0.76472I
−5.74830 − 8.10302I −7.68774 + 10.38587I
u = 0.581967 + 1.140370I
a = −0.797951 + 0.360993I
b = −0.209830 − 0.145532I
−5.74830 − 4.04325I −7.68774 + 3.45767I
u = 0.581967 + 1.140370I
a = 1.042160 − 0.728098I
b = 0.623622 + 1.064510I
−5.74830 − 8.10302I −7.68774 + 10.38587I
u = 0.581967 + 1.140370I
a = 0.175748 − 0.094312I
b = 0.876048 + 0.699876I
−5.74830 − 4.04325I −7.68774 + 3.45767I
u = 0.581967 − 1.140370I
a = −0.962013 − 0.055914I
b = −1.43681 + 0.76472I
−5.74830 + 8.10302I −7.68774 − 10.38587I
u = 0.581967 − 1.140370I
a = −0.797951 − 0.360993I
b = −0.209830 + 0.145532I
−5.74830 + 4.04325I −7.68774 − 3.45767I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.581967 − 1.140370I
a = 1.042160 + 0.728098I
b = 0.623622 − 1.064510I
−5.74830 + 8.10302I −7.68774 − 10.38587I
u = 0.581967 − 1.140370I
a = 0.175748 + 0.094312I
b = 0.876048 − 0.699876I
−5.74830 + 4.04325I −7.68774 − 3.45767I
u = −0.643976 + 0.089739I
a = 1.093330 − 0.083941I
b = 1.33517 + 1.40617I
−3.68331 + 4.69916I −15.6538 − 8.3078I
u = −0.643976 + 0.089739I
a = −1.303550 − 0.278242I
b = −1.23743 + 1.19471I
−3.68331 + 0.63939I −15.6538 − 1.3796I
u = −0.643976 + 0.089739I
a = −2.13854 + 1.55720I
b = −0.864422 − 0.062203I
−3.68331 + 0.63939I −15.6538 − 1.3796I
u = −0.643976 + 0.089739I
a = 1.73533 + 2.42540I
b = 0.696542 − 0.152170I
−3.68331 + 4.69916I −15.6538 − 8.3078I
u = −0.643976 − 0.089739I
a = 1.093330 + 0.083941I
b = 1.33517 − 1.40617I
−3.68331 − 4.69916I −15.6538 + 8.3078I
u = −0.643976 − 0.089739I
a = −1.303550 + 0.278242I
b = −1.23743 − 1.19471I
−3.68331 − 0.63939I −15.6538 + 1.3796I
u = −0.643976 − 0.089739I
a = −2.13854 − 1.55720I
b = −0.864422 + 0.062203I
−3.68331 − 0.63939I −15.6538 + 1.3796I
u = −0.643976 − 0.089739I
a = 1.73533 − 2.42540I
b = 0.696542 + 0.152170I
−3.68331 − 4.69916I −15.6538 + 8.3078I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.36997
a = −0.907521 + 0.663747I
b = −0.787791 + 0.120392I
−10.12450 + 2.02988I −16.2012 − 3.4641I
u = 1.36997
a = −0.907521 − 0.663747I
b = −0.787791 − 0.120392I
−10.12450 − 2.02988I −16.2012 + 3.4641I
u = 1.36997
a = 0.575044 + 0.087879I
b = 1.24327 + 0.90931I
−10.12450 − 2.02988I −16.2012 + 3.4641I
u = 1.36997
a = 0.575044 − 0.087879I
b = 1.24327 − 0.90931I
−10.12450 + 2.02988I −16.2012 − 3.4641I
u = 1.07833 + 1.02126I
a = 1.015230 − 0.027169I
b = 1.121120 + 0.675049I
−3.06065 − 5.93358I −16.3852 + 11.3606I
u = 1.07833 + 1.02126I
a = −0.860624 + 0.189066I
b = −1.12250 − 1.00752I
−3.06065 − 5.93358I −16.3852 + 11.3606I
u = 1.07833 + 1.02126I
a = 0.449088 − 0.424366I
b = 0.630413 + 0.168459I
−3.06065 − 1.87382I −16.3852 + 4.4324I
u = 1.07833 + 1.02126I
a = −0.386184 + 0.209525I
b = −0.917652 − 0.001032I
−3.06065 − 1.87382I −16.3852 + 4.4324I
u = 1.07833 − 1.02126I
a = 1.015230 + 0.027169I
b = 1.121120 − 0.675049I
−3.06065 + 5.93358I −16.3852 − 11.3606I
u = 1.07833 − 1.02126I
a = −0.860624 − 0.189066I
b = −1.12250 + 1.00752I
−3.06065 + 5.93358I −16.3852 − 11.3606I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.07833 − 1.02126I
a = 0.449088 + 0.424366I
b = 0.630413 − 0.168459I
−3.06065 + 1.87382I −16.3852 − 4.4324I
u = 1.07833 − 1.02126I
a = −0.386184 − 0.209525I
b = −0.917652 + 0.001032I
−3.06065 + 1.87382I −16.3852 − 4.4324I
u = 1.27917 + 1.11829I
a = −0.961483 − 0.056576I
b = −1.189770 − 0.530548I
−9.45761 − 6.57584I −15.4486 + 8.3893I
u = 1.27917 + 1.11829I
a = 0.732710 − 0.225798I
b = 1.16663 + 1.14759I
−9.45761 − 6.57584I −15.4486 + 8.3893I
u = 1.27917 + 1.11829I
a = −0.508257 + 0.483174I
b = −0.644536 − 0.238801I
−9.45761 − 2.51607I −15.4486 + 1.4611I
u = 1.27917 + 1.11829I
a = 0.378101 − 0.143864I
b = 1.190480 − 0.049682I
−9.45761 − 2.51607I −15.4486 + 1.4611I
u = 1.27917 − 1.11829I
a = −0.961483 + 0.056576I
b = −1.189770 + 0.530548I
−9.45761 + 6.57584I −15.4486 − 8.3893I
u = 1.27917 − 1.11829I
a = 0.732710 + 0.225798I
b = 1.16663 − 1.14759I
−9.45761 + 6.57584I −15.4486 − 8.3893I
u = 1.27917 − 1.11829I
a = −0.508257 − 0.483174I
b = −0.644536 + 0.238801I
−9.45761 + 2.51607I −15.4486 − 1.4611I
u = 1.27917 − 1.11829I
a = 0.378101 + 0.143864I
b = 1.190480 + 0.049682I
−9.45761 + 2.51607I −15.4486 − 1.4611I
16
III. I
u
3
=
h−2.32×10
5
u
14
+1.84×10
6
u
13
+· · ·+8.09×10
5
b−1.81×10
6
, −3.63×10
5
u
14
+
2.47 × 10
6
u
13
+ · · · + 4.04 × 10
6
a + 9.07 × 10
6
, u
15
− 10u
14
+ · · · + 105u − 25i
(i) Arc colorings
a
2
=
1
0
a
5
=
0
u
a
3
=
1
u
2
a
9
=
0.0896763u
14
− 0.610245u
13
+ ··· + 1.19544u − 2.24235
0.286518u
14
− 2.27740u
13
+ ··· − 11.6584u + 2.24191
a
6
=
−0.0634041u
14
+ 0.785474u
13
+ ··· + 18.1892u − 7.38808
0.151433u
14
− 1.22656u
13
+ ··· + 0.269354u − 1.58510
a
10
=
−0.196842u
14
+ 1.66715u
13
+ ··· + 12.8538u − 4.48425
0.286518u
14
− 2.27740u
13
+ ··· − 11.6584u + 2.24191
a
1
=
−0.0471991u
14
+ 0.401388u
13
+ ··· − 3.38516u + 3.00810
0.217171u
14
− 1.82237u
13
+ ··· − 10.5216u + 2.60585
a
4
=
−0.0784959u
14
+ 0.629353u
13
+ ··· + 2.16490u − 0.432050
−0.136341u
14
+ 1.38268u
13
+ ··· + 17.7549u − 5.37093
a
7
=
0.0557345u
14
− 0.347574u
13
+ ··· + 4.78295u − 3.26033
−0.102577u
14
+ 0.766448u
13
+ ··· + 3.70070u − 1.06673
a
8
=
0.390944u
14
− 3.21782u
13
+ ··· − 14.9887u + 2.67870
0.631661u
14
− 5.74144u
13
+ ··· − 46.6622u + 12.3694
a
11
=
−0.252441u
14
+ 2.08510u
13
+ ··· + 10.5167u − 2.17291
−0.417515u
14
+ 3.68088u
13
+ ··· + 30.7038u − 9.58932
a
11
=
−0.252441u
14
+ 2.08510u
13
+ ··· + 10.5167u − 2.17291
−0.417515u
14
+ 3.68088u
13
+ ··· + 30.7038u − 9.58932
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
18347
808985
u
14
−
110489
161797
u
13
+ ··· −
11086343
808985
u −
1503188
161797
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
15
− 5u
14
+ ··· + 5u − 1
c
2
u
15
− 10u
14
+ ··· + 105u − 25
c
3
, c
6
u
15
+ 4u
14
+ ··· + 6u + 1
c
4
, c
8
u
15
+ 4u
13
+ ··· + 4u − 1
c
5
, c
9
u
15
+ u
14
+ ··· − 2u
2
+ 1
c
7
u
15
+ 4u
14
+ ··· + 4u + 1
c
10
, c
11
u
15
− 4u
14
+ ··· + 4u − 1
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
15
− 7y
14
+ ··· + 3y −1
c
2
y
15
− 10y
14
+ ··· + 1225y −625
c
3
, c
6
y
15
− 8y
14
+ ··· + 10y −1
c
4
, c
8
y
15
+ 8y
14
+ ··· − 6y −1
c
5
, c
9
y
15
− 5y
14
+ ··· + 4y −1
c
7
, c
10
, c
11
y
15
− 16y
14
+ ··· + 4y −1
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.993740 + 0.424598I
a = 0.556645 − 0.290398I
b = −0.429858 + 0.524931I
−9.75332 − 7.47692I −9.95866 + 4.06635I
u = −0.993740 − 0.424598I
a = 0.556645 + 0.290398I
b = −0.429858 − 0.524931I
−9.75332 + 7.47692I −9.95866 − 4.06635I
u = −0.342459 + 0.777675I
a = −0.626853 − 0.459197I
b = 0.571778 − 0.330232I
−2.51489 − 4.15156I −7.90898 + 4.64816I
u = −0.342459 − 0.777675I
a = −0.626853 + 0.459197I
b = 0.571778 + 0.330232I
−2.51489 + 4.15156I −7.90898 − 4.64816I
u = 0.693947 + 0.386253I
a = −0.953726 + 0.652169I
b = −0.913738 + 0.084191I
−2.48193 − 0.47503I −11.90735 + 0.90266I
u = 0.693947 − 0.386253I
a = −0.953726 − 0.652169I
b = −0.913738 − 0.084191I
−2.48193 + 0.47503I −11.90735 − 0.90266I
u = 0.789581 + 1.095750I
a = 1.006360 − 0.300538I
b = 1.12392 + 0.86542I
−6.71287 − 6.73017I −11.94424 + 5.36549I
u = 0.789581 − 1.095750I
a = 1.006360 + 0.300538I
b = 1.12392 − 0.86542I
−6.71287 + 6.73017I −11.94424 − 5.36549I
u = 1.020310 + 0.946886I
a = −0.990350 + 0.084939I
b = −1.090890 − 0.851084I
−2.45761 − 5.54387I −4.63100 + 3.66871I
u = 1.020310 − 0.946886I
a = −0.990350 − 0.084939I
b = −1.090890 + 0.851084I
−2.45761 + 5.54387I −4.63100 − 3.66871I
20
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.46936
a = 0.734892
b = 1.07982
−10.0492 −16.2980
u = 1.36954 + 1.00006I
a = 0.746523 − 0.031553I
b = 1.053950 + 0.703353I
−8.96044 − 5.01992I −12.46416 + 4.02360I
u = 1.36954 − 1.00006I
a = 0.746523 + 0.031553I
b = 1.053950 − 0.703353I
−8.96044 + 5.01992I −12.46416 − 4.02360I
u = 1.72814 + 0.40102I
a = −0.306044 − 0.433458I
b = −0.355064 − 0.871805I
0.07214 − 3.29542I −1.53653 − 2.69469I
u = 1.72814 − 0.40102I
a = −0.306044 + 0.433458I
b = −0.355064 + 0.871805I
0.07214 + 3.29542I −1.53653 + 2.69469I
21
IV. I
v
1
= ha, b
2
− bv + 2b − v + 3, v
2
− 3v + 1i
(i) Arc colorings
a
2
=
1
0
a
5
=
v
0
a
3
=
1
0
a
9
=
0
b
a
6
=
v
bv − b − 1
a
10
=
−b
b
a
1
=
2bv − b − v + 1
−bv + b
a
4
=
−bv + b + v + 1
bv − b − 1
a
7
=
−2bv + b + v − 1
bv − b
a
8
=
−b
b
a
11
=
2bv − 2b − v + 1
−bv + 2b
a
11
=
2bv − 2b − v + 1
−bv + 2b
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4bv − 4b − 3
22
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
6
(u
2
+ u + 1)
2
c
2
u
4
c
4
, c
5
, c
8
c
9
u
4
− u
3
+ 2u
2
+ u + 1
c
7
(u − 1)
4
c
10
, c
11
(u + 1)
4
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
6
(y
2
+ y + 1)
2
c
2
y
4
c
4
, c
5
, c
8
c
9
y
4
+ 3y
3
+ 8y
2
+ 3y + 1
c
7
, c
10
, c
11
(y − 1)
4
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 0.381966
a = 0
b = −0.80902 + 1.40126I
−1.64493 + 2.02988I −1.0000 − 3.46410I
v = 0.381966
a = 0
b = −0.80902 − 1.40126I
−1.64493 − 2.02988I −1.0000 + 3.46410I
v = 2.61803
a = 0
b = 0.309017 + 0.535233I
−1.64493 − 2.02988I −1.0000 + 3.46410I
v = 2.61803
a = 0
b = 0.309017 − 0.535233I
−1.64493 + 2.02988I −1.0000 − 3.46410I
25
V. I
v
2
= ha, b
2
+ b + 1, v − 1i
(i) Arc colorings
a
2
=
1
0
a
5
=
1
0
a
3
=
1
0
a
9
=
0
b
a
6
=
1
−b − 1
a
10
=
−b
b
a
1
=
−b
b
a
4
=
b + 2
−b − 1
a
7
=
b
−b
a
8
=
−b
b
a
11
=
−b
b
a
11
=
−b
b
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4b − 2
26
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
2
− u + 1
c
2
, c
7
, c
10
c
11
u
2
c
3
, c
4
, c
5
c
6
, c
8
, c
9
u
2
+ u + 1
27
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
5
, c
6
, c
8
c
9
y
2
+ y + 1
c
2
, c
7
, c
10
c
11
y
2
28
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
2
√
−1(vol +
√
−1CS) Cusp shape
v = 1.00000
a = 0
b = −0.500000 + 0.866025I
2.02988I 0. − 3.46410I
v = 1.00000
a = 0
b = −0.500000 − 0.866025I
− 2.02988I 0. + 3.46410I
29
VI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
2
− u + 1)(u
2
+ u + 1)
32
(u
15
− 5u
14
+ ··· + 5u − 1)
· (u
29
− 29u
28
+ ··· − 131072u + 16384)
c
2
u
6
(u
15
− 10u
14
+ ··· + 105u − 25)(u
15
+ 7u
14
+ ··· + 3u + 2)
4
· (u
29
− 25u
28
+ ··· + 638u − 73)
c
3
, c
6
((u
2
+ u + 1)
3
)(u
15
+ 4u
14
+ ··· + 6u + 1)(u
29
− u
28
+ ··· + 17u + 1)
· (u
60
+ 3u
59
+ ··· + 5800u + 1951)
c
4
, c
8
(u
2
+ u + 1)(u
4
− u
3
+ 2u
2
+ u + 1)(u
15
+ 4u
13
+ ··· + 4u − 1)
· (u
29
− u
28
+ ··· + 21u + 9)(u
60
+ 17u
58
+ ··· + 63147u + 112777)
c
5
, c
9
(u
2
+ u + 1)(u
4
− u
3
+ 2u
2
+ u + 1)(u
15
+ u
14
+ ··· − 2u
2
+ 1)
· (u
29
+ 2u
27
+ ··· + u + 1)(u
60
− 9u
58
+ ··· + 5u + 1)
c
7
u
2
(u − 1)
4
(u
15
− 2u
14
+ ··· + 2u − 1)
4
(u
15
+ 4u
14
+ ··· + 4u + 1)
· (u
29
+ 9u
28
+ ··· + 49u + 73)
c
10
, c
11
u
2
(u + 1)
4
(u
15
− 4u
14
+ ··· + 4u − 1)(u
15
− 2u
14
+ ··· + 2u − 1)
4
· (u
29
+ 9u
28
+ ··· + 49u + 73)
30
VII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
2
+ y + 1)
33
)(y
15
− 7y
14
+ ··· + 3y − 1)
· (y
29
− 7y
28
+ ··· + 5100273664y − 268435456)
c
2
y
6
(y
15
− 10y
14
+ ··· + 1225y − 625)(y
15
− 3y
14
+ ··· + 37y − 4)
4
· (y
29
− 13y
28
+ ··· + 27006y − 5329)
c
3
, c
6
((y
2
+ y + 1)
3
)(y
15
− 8y
14
+ ··· + 10y − 1)(y
29
− 7y
28
+ ··· + 235y − 1)
· (y
60
− 31y
59
+ ··· − 116686266y + 3806401)
c
4
, c
8
(y
2
+ y + 1)(y
4
+ 3y
3
+ ··· + 3y + 1)(y
15
+ 8y
14
+ ··· − 6y − 1)
· (y
29
+ 17y
28
+ ··· − 225y − 81)
· (y
60
+ 34y
59
+ ··· + 352063429739y + 12718651729)
c
5
, c
9
(y
2
+ y + 1)(y
4
+ 3y
3
+ ··· + 3y + 1)(y
15
− 5y
14
+ ··· + 4y − 1)
· (y
29
+ 4y
28
+ ··· − 3y − 1)(y
60
− 18y
59
+ ··· + 27y + 1)
c
7
, c
10
, c
11
y
2
(y − 1)
4
(y
15
− 16y
14
+ ··· + 10y − 1)
4
(y
15
− 16y
14
+ ··· + 4y − 1)
· (y
29
− 31y
28
+ ··· − 8987y − 5329)
31
