12a
0913
(K12a
0913
)
A knot diagram
1
Linearized knot diagam
4 6 9 7 11 2 12 3 1 8 5 10
Solving Sequence
5,11 2,6
3 7 12 8 9 4 1 10
c
5
c
2
c
6
c
11
c
7
c
8
c
4
c
1
c
10
c
3
, c
9
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.23675 × 10
864
u
158
+ 8.56639 × 10
864
u
157
+ ··· + 1.08073 × 10
866
b − 2.39792 × 10
869
,
9.55810 × 10
868
u
158
+ 2.76471 × 10
869
u
157
+ ··· + 6.48654 × 10
869
a − 4.53046 × 10
873
,
u
159
+ u
158
+ ··· − 95441u − 24008i
I
u
2
= h−7.72164 × 10
68
u
49
− 3.42499 × 10
69
u
48
+ ··· + 1.57649 × 10
69
b + 6.72123 × 10
70
,
5.04081 × 10
69
u
49
− 1.88268 × 10
70
u
48
+ ··· + 4.72946 × 10
69
a + 3.67110 × 10
71
, u
50
+ 11u
48
+ ··· + 15u − 9i
* 2 irreducible components of dim
C
= 0, with total 209 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−1.24 × 10
864
u
158
+ 8.57 × 10
864
u
157
+ · · · + 1.08 × 10
866
b − 2.40 ×
10
869
, 9.56 × 10
868
u
158
+ 2.76 × 10
869
u
157
+ · · · + 6.49 × 10
869
a − 4.53 ×
10
873
, u
159
+ u
158
+ · · · − 95441u − 24008i
(i) Arc colorings
a
5
=
1
0
a
11
=
0
u
a
2
=
−0.147353u
158
− 0.426224u
157
+ ··· + 31421.1u + 6984.41
0.0114437u
158
− 0.0792649u
157
+ ··· + 8457.34u + 2218.80
a
6
=
1
−u
2
a
3
=
0.00578855u
158
− 0.0950449u
157
+ ··· + 9725.12u + 2508.09
0.156936u
158
+ 0.237303u
157
+ ··· − 12211.3u − 2055.51
a
7
=
0.357898u
158
+ 0.241453u
157
+ ··· + 2030.58u + 2910.40
−0.0884457u
158
− 0.131877u
157
+ ··· + 7349.06u + 1277.73
a
12
=
u
u
a
8
=
−0.0431647u
158
− 0.0826383u
157
+ ··· + 5777.86u + 1157.47
−0.489509u
158
− 0.455968u
157
+ ··· + 11096.3u − 475.196
a
9
=
−0.00256598u
158
+ 0.0441083u
157
+ ··· − 4552.86u − 1152.68
−0.0179626u
158
+ 0.0140324u
157
+ ··· − 2580.84u − 742.756
a
4
=
−0.126198u
158
− 0.401253u
157
+ ··· + 31148.5u + 7083.44
0.0725043u
158
+ 0.0139851u
157
+ ··· + 3714.98u + 1451.08
a
1
=
0.0722265u
158
− 0.00605847u
157
+ ··· + 5929.89u + 1975.45
0.0504978u
158
− 0.0108585u
157
+ ··· + 5189.42u + 1635.88
a
10
=
0.0756881u
158
+ 0.122223u
157
+ ··· − 7580.53u − 1432.70
0.0634567u
158
+ 0.0797254u
157
+ ··· − 4471.11u − 724.940
(ii) Obstruction class = −1
(iii) Cusp Shapes = −2.37885u
158
+ 1.78647u
157
+ ··· − 358356.u − 105900.
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
159
− 8u
158
+ ··· + 80215197u − 1927186
c
2
, c
6
u
159
− 3u
158
+ ··· − 3046266u − 178861
c
3
, c
8
u
159
− u
158
+ ··· − 8744042u + 1097059
c
4
u
159
− 7u
158
+ ··· + 32390037u − 6440257
c
5
, c
11
u
159
+ u
158
+ ··· − 95441u − 24008
c
7
u
159
+ 15u
158
+ ··· + 43507681u − 2774953
c
9
, c
12
u
159
+ 5u
158
+ ··· + 159249u + 8893
c
10
u
159
− 15u
158
+ ··· − 333964577u + 95115071
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
159
− 82y
158
+ ··· + 3262006438404145y −3714045878596
c
2
, c
6
y
159
+ 115y
158
+ ··· + 126566005786y −31991257321
c
3
, c
8
y
159
− 105y
158
+ ··· + 42991384255528y −1203538449481
c
4
y
159
− 61y
158
+ ··· + 774738334454811y −41476910226049
c
5
, c
11
y
159
+ 97y
158
+ ··· − 15736846703y −576384064
c
7
y
159
− 57y
158
+ ··· + 1120931842505265y −7700364152209
c
9
, c
12
y
159
+ 127y
158
+ ··· + 291286079y −79085449
c
10
y
159
− 59y
158
+ ··· + 1754195507846337117y −9046876731335041
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.331449 + 0.959871I
a = −1.87562 − 0.22966I
b = −2.02429 − 0.05797I
−9.26485 + 9.17013I 0
u = 0.331449 − 0.959871I
a = −1.87562 + 0.22966I
b = −2.02429 + 0.05797I
−9.26485 − 9.17013I 0
u = −1.014430 + 0.098634I
a = 0.451232 − 0.570464I
b = 0.04601 + 1.78543I
−0.82025 + 3.44925I 0
u = −1.014430 − 0.098634I
a = 0.451232 + 0.570464I
b = 0.04601 − 1.78543I
−0.82025 − 3.44925I 0
u = −0.105746 + 1.013950I
a = −0.38849 − 3.37577I
b = 0.19676 − 2.47170I
−1.18179 − 3.20636I 0
u = −0.105746 − 1.013950I
a = −0.38849 + 3.37577I
b = 0.19676 + 2.47170I
−1.18179 + 3.20636I 0
u = 1.027040 + 0.093678I
a = 0.325147 + 0.603162I
b = 0.14935 − 1.94748I
−5.64108 − 7.19608I 0
u = 1.027040 − 0.093678I
a = 0.325147 − 0.603162I
b = 0.14935 + 1.94748I
−5.64108 + 7.19608I 0
u = −0.007128 + 0.966467I
a = −0.91257 − 3.00884I
b = 0.265736 − 0.196627I
−5.35993 − 0.16362I 0
u = −0.007128 − 0.966467I
a = −0.91257 + 3.00884I
b = 0.265736 + 0.196627I
−5.35993 + 0.16362I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.206168 + 1.014050I
a = 0.702066 + 0.183119I
b = −0.707965 + 0.099887I
−4.72393 + 1.17967I 0
u = −0.206168 − 1.014050I
a = 0.702066 − 0.183119I
b = −0.707965 − 0.099887I
−4.72393 − 1.17967I 0
u = 0.963567 + 0.007515I
a = 0.347493 − 0.236451I
b = 0.241095 + 1.028930I
−3.13062 − 0.11256I 0
u = 0.963567 − 0.007515I
a = 0.347493 + 0.236451I
b = 0.241095 − 1.028930I
−3.13062 + 0.11256I 0
u = 0.027589 + 1.039060I
a = 0.43849 + 2.47650I
b = 0.71163 + 1.31819I
−3.47849 + 0.04457I 0
u = 0.027589 − 1.039060I
a = 0.43849 − 2.47650I
b = 0.71163 − 1.31819I
−3.47849 − 0.04457I 0
u = 0.005856 + 0.947362I
a = 1.47155 + 1.25478I
b = 1.71025 + 0.16199I
−3.13181 + 0.06061I 0
u = 0.005856 − 0.947362I
a = 1.47155 − 1.25478I
b = 1.71025 − 0.16199I
−3.13181 − 0.06061I 0
u = −0.047301 + 1.053540I
a = −0.846698 + 0.406491I
b = 0.278061 − 0.181203I
−3.89278 − 1.46765I 0
u = −0.047301 − 1.053540I
a = −0.846698 − 0.406491I
b = 0.278061 + 0.181203I
−3.89278 + 1.46765I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.796936 + 0.498050I
a = −0.378245 + 0.302345I
b = −0.064321 + 0.714699I
−2.37488 + 1.85883I 0
u = −0.796936 − 0.498050I
a = −0.378245 − 0.302345I
b = −0.064321 − 0.714699I
−2.37488 − 1.85883I 0
u = 0.930792 + 0.099542I
a = −1.086010 − 0.411935I
b = −0.154613 + 0.497469I
−5.75841 + 7.93505I 0
u = 0.930792 − 0.099542I
a = −1.086010 + 0.411935I
b = −0.154613 − 0.497469I
−5.75841 − 7.93505I 0
u = −0.025548 + 1.073190I
a = 0.25346 + 1.95808I
b = −0.591747 + 0.924856I
−4.00735 + 0.66015I 0
u = −0.025548 − 1.073190I
a = 0.25346 − 1.95808I
b = −0.591747 − 0.924856I
−4.00735 − 0.66015I 0
u = 0.147611 + 0.907402I
a = −2.28013 + 3.50215I
b = −1.08327 + 2.58283I
−6.31757 + 6.13575I 0
u = 0.147611 − 0.907402I
a = −2.28013 − 3.50215I
b = −1.08327 − 2.58283I
−6.31757 − 6.13575I 0
u = −0.270464 + 1.053880I
a = 0.220215 + 0.410628I
b = 0.865549 + 0.010959I
−1.13430 − 5.16965I 0
u = −0.270464 − 1.053880I
a = 0.220215 − 0.410628I
b = 0.865549 − 0.010959I
−1.13430 + 5.16965I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.986643 + 0.464553I
a = 0.645433 + 0.557256I
b = −0.828812 − 0.697243I
−1.46392 − 1.72596I 0
u = −0.986643 − 0.464553I
a = 0.645433 − 0.557256I
b = −0.828812 + 0.697243I
−1.46392 + 1.72596I 0
u = 0.326680 + 1.043560I
a = −1.232940 + 0.026388I
b = −1.05491 + 1.16508I
−9.11718 + 3.78460I 0
u = 0.326680 − 1.043560I
a = −1.232940 − 0.026388I
b = −1.05491 − 1.16508I
−9.11718 − 3.78460I 0
u = −0.439715 + 1.019970I
a = −1.215290 − 0.543396I
b = −0.924564 − 0.546092I
−4.04313 − 6.43433I 0
u = −0.439715 − 1.019970I
a = −1.215290 + 0.543396I
b = −0.924564 + 0.546092I
−4.04313 + 6.43433I 0
u = 0.093402 + 1.111110I
a = −0.482507 − 0.125489I
b = −1.301650 + 0.417064I
−2.49562 + 2.39792I 0
u = 0.093402 − 1.111110I
a = −0.482507 + 0.125489I
b = −1.301650 − 0.417064I
−2.49562 − 2.39792I 0
u = 0.427649 + 0.770098I
a = 0.632864 + 0.592147I
b = 0.693759 + 0.434627I
0.27472 + 1.85275I 0
u = 0.427649 − 0.770098I
a = 0.632864 − 0.592147I
b = 0.693759 − 0.434627I
0.27472 − 1.85275I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.059139 + 1.118840I
a = −1.49842 − 0.15052I
b = −2.31279 − 0.94060I
−7.66974 − 5.81212I 0
u = −0.059139 − 1.118840I
a = −1.49842 + 0.15052I
b = −2.31279 + 0.94060I
−7.66974 + 5.81212I 0
u = 0.105934 + 1.115430I
a = −0.773443 + 0.267657I
b = −0.146736 + 0.819410I
−9.28250 + 3.60158I 0
u = 0.105934 − 1.115430I
a = −0.773443 − 0.267657I
b = −0.146736 − 0.819410I
−9.28250 − 3.60158I 0
u = 0.096505 + 1.121460I
a = −0.26282 − 2.56182I
b = −1.29469 − 2.13196I
−9.49062 − 2.16955I 0
u = 0.096505 − 1.121460I
a = −0.26282 + 2.56182I
b = −1.29469 + 2.13196I
−9.49062 + 2.16955I 0
u = −0.812851 + 0.308744I
a = 0.321515 − 0.416491I
b = −0.08798 + 1.64851I
−10.39250 − 0.95844I 0
u = −0.812851 − 0.308744I
a = 0.321515 + 0.416491I
b = −0.08798 − 1.64851I
−10.39250 + 0.95844I 0
u = −0.383628 + 0.770829I
a = 1.63748 − 1.40119I
b = 1.70091 − 0.66882I
−3.04898 − 1.72781I 0
u = −0.383628 − 0.770829I
a = 1.63748 + 1.40119I
b = 1.70091 + 0.66882I
−3.04898 + 1.72781I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.814637 + 0.806006I
a = −0.194321 + 0.413504I
b = 0.379575 − 0.762055I
−3.73916 + 3.05466I 0
u = 0.814637 − 0.806006I
a = −0.194321 − 0.413504I
b = 0.379575 + 0.762055I
−3.73916 − 3.05466I 0
u = 0.316018 + 0.780735I
a = 0.760174 + 0.065560I
b = 0.803027 + 0.272314I
0.21168 + 1.77831I 0
u = 0.316018 − 0.780735I
a = 0.760174 − 0.065560I
b = 0.803027 − 0.272314I
0.21168 − 1.77831I 0
u = 0.144941 + 1.170880I
a = 0.85577 − 2.13653I
b = 1.06163 − 1.93733I
−11.88590 + 1.90553I 0
u = 0.144941 − 1.170880I
a = 0.85577 + 2.13653I
b = 1.06163 + 1.93733I
−11.88590 − 1.90553I 0
u = −0.206468 + 1.161840I
a = 0.45549 + 2.11009I
b = 0.26222 + 1.54340I
−7.22920 − 5.91815I 0
u = −0.206468 − 1.161840I
a = 0.45549 − 2.11009I
b = 0.26222 − 1.54340I
−7.22920 + 5.91815I 0
u = 0.266217 + 1.150440I
a = 0.38049 − 2.22730I
b = −0.26969 − 1.42529I
−11.0945 + 10.2461I 0
u = 0.266217 − 1.150440I
a = 0.38049 + 2.22730I
b = −0.26969 + 1.42529I
−11.0945 − 10.2461I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.522240 + 0.627796I
a = −1.15089 − 1.09931I
b = −0.788166 − 0.577690I
−8.38649 − 5.65854I 0
u = 0.522240 − 0.627796I
a = −1.15089 + 1.09931I
b = −0.788166 + 0.577690I
−8.38649 + 5.65854I 0
u = 0.499932 + 0.643166I
a = 0.400852 + 0.726008I
b = 0.366515 − 0.076701I
0.60801 + 1.85316I 0
u = 0.499932 − 0.643166I
a = 0.400852 − 0.726008I
b = 0.366515 + 0.076701I
0.60801 − 1.85316I 0
u = −0.769962 + 0.163866I
a = 0.547244 + 0.349551I
b = 0.317116 + 0.011355I
−1.68423 + 3.19160I 0
u = −0.769962 − 0.163866I
a = 0.547244 − 0.349551I
b = 0.317116 − 0.011355I
−1.68423 − 3.19160I 0
u = −0.736684 + 0.276291I
a = 0.83859 + 1.19214I
b = −0.194284 − 0.743319I
−2.35427 − 4.71025I 0
u = −0.736684 − 0.276291I
a = 0.83859 − 1.19214I
b = −0.194284 + 0.743319I
−2.35427 + 4.71025I 0
u = 0.725780 + 0.250756I
a = 0.937083 − 0.554393I
b = −0.000028 + 0.163275I
1.81915 + 0.50684I 0
u = 0.725780 − 0.250756I
a = 0.937083 + 0.554393I
b = −0.000028 − 0.163275I
1.81915 − 0.50684I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.358578 + 1.183900I
a = 0.298937 − 0.398434I
b = −0.013537 − 0.528845I
−5.68724 − 0.48018I 0
u = −0.358578 − 1.183900I
a = 0.298937 + 0.398434I
b = −0.013537 + 0.528845I
−5.68724 + 0.48018I 0
u = 0.452125 + 1.162110I
a = 0.223636 + 0.406651I
b = −0.209376 + 0.349866I
−1.00597 + 3.92740I 0
u = 0.452125 − 1.162110I
a = 0.223636 − 0.406651I
b = −0.209376 − 0.349866I
−1.00597 − 3.92740I 0
u = −1.249640 + 0.080816I
a = −0.392212 + 0.379652I
b = 0.02648 − 2.03225I
−10.1461 + 13.3814I 0
u = −1.249640 − 0.080816I
a = −0.392212 − 0.379652I
b = 0.02648 + 2.03225I
−10.1461 − 13.3814I 0
u = 1.25488
a = 1.22864
b = −0.765551
2.41642 0
u = −0.485103 + 1.159700I
a = 0.137615 − 0.648439I
b = 0.000805 − 0.370392I
−4.64518 − 7.83372I 0
u = −0.485103 − 1.159700I
a = 0.137615 + 0.648439I
b = 0.000805 + 0.370392I
−4.64518 + 7.83372I 0
u = −1.157900 + 0.515482I
a = 0.208762 + 1.102190I
b = −1.40204 − 1.74039I
−1.84246 − 3.96352I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.157900 − 0.515482I
a = 0.208762 − 1.102190I
b = −1.40204 + 1.74039I
−1.84246 + 3.96352I 0
u = 0.446897 + 1.189680I
a = −0.67328 + 1.39673I
b = 0.089031 + 1.397490I
−6.84887 + 4.76569I 0
u = 0.446897 − 1.189680I
a = −0.67328 − 1.39673I
b = 0.089031 − 1.397490I
−6.84887 − 4.76569I 0
u = −0.544295 + 1.168160I
a = −0.149684 + 0.322845I
b = −0.873873 − 0.247173I
−3.77096 − 3.90843I 0
u = −0.544295 − 1.168160I
a = −0.149684 − 0.322845I
b = −0.873873 + 0.247173I
−3.77096 + 3.90843I 0
u = −0.703908 + 0.068401I
a = 0.655831 + 0.062267I
b = −0.273470 − 0.810045I
−1.62859 − 1.50701I 0
u = −0.703908 − 0.068401I
a = 0.655831 − 0.062267I
b = −0.273470 + 0.810045I
−1.62859 + 1.50701I 0
u = −1.187970 + 0.599390I
a = −0.348339 − 0.089925I
b = −0.18388 − 1.81300I
−9.33762 − 1.89266I 0
u = −1.187970 − 0.599390I
a = −0.348339 + 0.089925I
b = −0.18388 + 1.81300I
−9.33762 + 1.89266I 0
u = −0.358853 + 1.296280I
a = 0.52674 + 2.09742I
b = −0.92398 + 2.21765I
−15.1255 − 4.9139I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.358853 − 1.296280I
a = 0.52674 − 2.09742I
b = −0.92398 − 2.21765I
−15.1255 + 4.9139I 0
u = 1.334110 + 0.189473I
a = 0.191326 + 0.767859I
b = 0.15389 − 2.46775I
−1.93289 + 0.56643I 0
u = 1.334110 − 0.189473I
a = 0.191326 − 0.767859I
b = 0.15389 + 2.46775I
−1.93289 − 0.56643I 0
u = −0.678068 + 1.171080I
a = −0.454534 − 0.691144I
b = 0.471631 − 0.549554I
−4.97588 − 6.92931I 0
u = −0.678068 − 1.171080I
a = −0.454534 + 0.691144I
b = 0.471631 + 0.549554I
−4.97588 + 6.92931I 0
u = 0.261169 + 1.343400I
a = 0.31448 − 2.13252I
b = −0.62595 − 2.56704I
−10.09370 + 5.75820I 0
u = 0.261169 − 1.343400I
a = 0.31448 + 2.13252I
b = −0.62595 + 2.56704I
−10.09370 − 5.75820I 0
u = 0.418902 + 1.310450I
a = 0.66726 − 1.73551I
b = −1.01145 − 2.17863I
−10.26850 − 2.21343I 0
u = 0.418902 − 1.310450I
a = 0.66726 + 1.73551I
b = −1.01145 + 2.17863I
−10.26850 + 2.21343I 0
u = −0.138378 + 1.371850I
a = 0.04900 + 2.32700I
b = −0.39554 + 3.10585I
−13.5028 − 7.4928I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.138378 − 1.371850I
a = 0.04900 − 2.32700I
b = −0.39554 − 3.10585I
−13.5028 + 7.4928I 0
u = 0.484571 + 1.301100I
a = −1.00744 + 1.75593I
b = 0.19767 + 2.66554I
−8.22695 + 5.38031I 0
u = 0.484571 − 1.301100I
a = −1.00744 − 1.75593I
b = 0.19767 − 2.66554I
−8.22695 − 5.38031I 0
u = 0.514271 + 1.290290I
a = 0.393656 − 0.290781I
b = −0.418409 − 0.383558I
−7.06348 + 5.40793I 0
u = 0.514271 − 1.290290I
a = 0.393656 + 0.290781I
b = −0.418409 + 0.383558I
−7.06348 − 5.40793I 0
u = −0.676149 + 1.214900I
a = −1.21194 − 1.21304I
b = 0.60213 − 1.94702I
−12.84130 − 4.72638I 0
u = −0.676149 − 1.214900I
a = −1.21194 + 1.21304I
b = 0.60213 + 1.94702I
−12.84130 + 4.72638I 0
u = 1.104720 + 0.845440I
a = −0.574985 + 0.444823I
b = 1.078000 − 0.300541I
−3.50591 + 3.71554I 0
u = 1.104720 − 0.845440I
a = −0.574985 − 0.444823I
b = 1.078000 + 0.300541I
−3.50591 − 3.71554I 0
u = 1.392200 + 0.169807I
a = −0.289656 − 0.252465I
b = −0.01486 + 2.08062I
−4.50660 − 6.68866I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.392200 − 0.169807I
a = −0.289656 + 0.252465I
b = −0.01486 − 2.08062I
−4.50660 + 6.68866I 0
u = −0.016723 + 0.584676I
a = 1.47371 + 0.73503I
b = 0.079377 + 1.328000I
−9.63223 − 0.95108I −10.46124 + 0.I
u = −0.016723 − 0.584676I
a = 1.47371 − 0.73503I
b = 0.079377 − 1.328000I
−9.63223 + 0.95108I −10.46124 + 0.I
u = 0.46543 + 1.33926I
a = −0.335241 − 0.437237I
b = 0.265474 − 0.392860I
−10.1685 + 12.9580I 0
u = 0.46543 − 1.33926I
a = −0.335241 + 0.437237I
b = 0.265474 + 0.392860I
−10.1685 − 12.9580I 0
u = 0.54048 + 1.31131I
a = −0.92608 + 1.82847I
b = 0.81114 + 2.54043I
−9.4493 + 12.7977I 0
u = 0.54048 − 1.31131I
a = −0.92608 − 1.82847I
b = 0.81114 − 2.54043I
−9.4493 − 12.7977I 0
u = −0.53000 + 1.32665I
a = −0.86269 − 1.74973I
b = 0.69431 − 2.50874I
−4.72793 − 9.02952I 0
u = −0.53000 − 1.32665I
a = −0.86269 + 1.74973I
b = 0.69431 + 2.50874I
−4.72793 + 9.02952I 0
u = −0.50395 + 1.34036I
a = 0.58035 + 1.63104I
b = −1.30116 + 2.12303I
−5.00891 − 1.72048I 0
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.50395 − 1.34036I
a = 0.58035 − 1.63104I
b = −1.30116 − 2.12303I
−5.00891 + 1.72048I 0
u = 0.558638 + 0.050830I
a = 1.60432 − 0.88463I
b = −0.048843 + 1.277850I
−4.43341 + 1.09517I −2.80268 + 0.I
u = 0.558638 − 0.050830I
a = 1.60432 + 0.88463I
b = −0.048843 − 1.277850I
−4.43341 − 1.09517I −2.80268 + 0.I
u = −0.23743 + 1.42321I
a = −0.33158 − 1.55068I
b = 0.79303 − 1.57660I
−16.2757 − 6.0964I 0
u = −0.23743 − 1.42321I
a = −0.33158 + 1.55068I
b = 0.79303 + 1.57660I
−16.2757 + 6.0964I 0
u = −0.182188 + 0.507554I
a = 2.20846 − 0.34747I
b = −0.0700079 − 0.0114904I
0.74518 + 2.70199I 6.09705 + 8.93008I
u = −0.182188 − 0.507554I
a = 2.20846 + 0.34747I
b = −0.0700079 + 0.0114904I
0.74518 − 2.70199I 6.09705 − 8.93008I
u = 0.361036 + 0.387708I
a = 1.051040 − 0.113076I
b = −0.877468 + 0.107129I
−5.23563 + 1.85567I −2.02141 − 1.19335I
u = 0.361036 − 0.387708I
a = 1.051040 + 0.113076I
b = −0.877468 − 0.107129I
−5.23563 − 1.85567I −2.02141 + 1.19335I
u = −0.142352 + 0.484741I
a = 1.051240 + 0.024653I
b = 0.629964 + 0.953936I
−0.05898 + 1.76305I − 60.10 − 1.214412I
17
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.142352 − 0.484741I
a = 1.051240 − 0.024653I
b = 0.629964 − 0.953936I
−0.05898 − 1.76305I − 60.10 + 1.214412I
u = −0.44547 + 1.42740I
a = −0.243968 + 0.362423I
b = 0.561793 + 0.533218I
−4.31898 − 6.38185I 0
u = −0.44547 − 1.42740I
a = −0.243968 − 0.362423I
b = 0.561793 − 0.533218I
−4.31898 + 6.38185I 0
u = 0.67665 + 1.35112I
a = 0.055448 − 0.412412I
b = 0.575394 − 1.202040I
−8.96580 − 2.11243I 0
u = 0.67665 − 1.35112I
a = 0.055448 + 0.412412I
b = 0.575394 + 1.202040I
−8.96580 + 2.11243I 0
u = −0.60416 + 1.39048I
a = 0.88208 + 1.59689I
b = −0.65436 + 2.57122I
−14.3110 − 19.8553I 0
u = −0.60416 − 1.39048I
a = 0.88208 − 1.59689I
b = −0.65436 − 2.57122I
−14.3110 + 19.8553I 0
u = 0.47358 + 1.44323I
a = 0.40606 − 1.66453I
b = −1.41660 − 2.43899I
−7.38131 + 6.64518I 0
u = 0.47358 − 1.44323I
a = 0.40606 + 1.66453I
b = −1.41660 + 2.43899I
−7.38131 − 6.64518I 0
u = −0.451952 + 0.009408I
a = −1.37248 − 2.65345I
b = −0.264259 + 0.444034I
1.22543 + 2.80185I 7.98617 − 7.63935I
18
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.451952 − 0.009408I
a = −1.37248 + 2.65345I
b = −0.264259 − 0.444034I
1.22543 − 2.80185I 7.98617 + 7.63935I
u = 0.63779 + 1.41946I
a = 0.83727 − 1.44537I
b = −0.62558 − 2.38067I
−8.6527 + 13.6977I 0
u = 0.63779 − 1.41946I
a = 0.83727 + 1.44537I
b = −0.62558 + 2.38067I
−8.6527 − 13.6977I 0
u = −1.56092
a = −1.01979
b = 0.866671
1.33123 0
u = 0.368719 + 0.199742I
a = 1.072920 − 0.233054I
b = −0.675568 + 1.126810I
−8.25598 − 7.54835I −3.36824 + 2.59907I
u = 0.368719 − 0.199742I
a = 1.072920 + 0.233054I
b = −0.675568 − 1.126810I
−8.25598 + 7.54835I −3.36824 − 2.59907I
u = −0.44914 + 1.51551I
a = −0.47028 − 1.74603I
b = 0.98007 − 3.27749I
−8.48613 − 9.33687I 0
u = −0.44914 − 1.51551I
a = −0.47028 + 1.74603I
b = 0.98007 + 3.27749I
−8.48613 + 9.33687I 0
u = 0.64281 + 1.45091I
a = −0.71312 + 1.46158I
b = 1.23147 + 2.66153I
−6.12500 + 6.57118I 0
u = 0.64281 − 1.45091I
a = −0.71312 − 1.46158I
b = 1.23147 − 2.66153I
−6.12500 − 6.57118I 0
19
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.26432 + 1.59023I
a = −0.255582 + 1.366950I
b = 0.79208 + 1.94667I
−11.21150 − 0.32736I 0
u = 0.26432 − 1.59023I
a = −0.255582 − 1.366950I
b = 0.79208 − 1.94667I
−11.21150 + 0.32736I 0
u = −0.78903 + 1.41569I
a = 0.92434 + 1.13763I
b = −0.47686 + 2.14895I
−11.98310 − 5.76392I 0
u = −0.78903 − 1.41569I
a = 0.92434 − 1.13763I
b = −0.47686 − 2.14895I
−11.98310 + 5.76392I 0
u = −0.361658
a = 0.935815
b = −0.676241
−1.78112 −4.44940
u = −0.147459 + 0.317174I
a = 1.208160 + 0.004539I
b = −0.412265 − 1.044270I
−4.54719 + 4.06090I −8.21161 − 0.21669I
u = −0.147459 − 0.317174I
a = 1.208160 − 0.004539I
b = −0.412265 + 1.044270I
−4.54719 − 4.06090I −8.21161 + 0.21669I
u = −0.43090 + 1.60042I
a = −0.348510 − 1.254540I
b = 1.20446 − 2.00710I
−15.7144 + 6.9339I 0
u = −0.43090 − 1.60042I
a = −0.348510 + 1.254540I
b = 1.20446 + 2.00710I
−15.7144 − 6.9339I 0
20
II. I
u
2
= h−7.72 × 10
68
u
49
− 3.42 × 10
69
u
48
+ · · · + 1.58 × 10
69
b + 6.72 ×
10
70
, 5.04 × 10
69
u
49
− 1.88 × 10
70
u
48
+ · · · + 4.73 × 10
69
a + 3.67 ×
10
71
, u
50
+ 11u
48
+ · · · + 15u − 9i
(i) Arc colorings
a
5
=
1
0
a
11
=
0
u
a
2
=
−1.06583u
49
+ 3.98075u
48
+ ··· + 167.968u − 77.6219
0.489801u
49
+ 2.17255u
48
+ ··· + 71.1491u − 42.6342
a
6
=
1
−u
2
a
3
=
−0.453371u
49
+ 4.16901u
48
+ ··· + 169.813u − 84.4294
0.831377u
49
+ 2.11906u
48
+ ··· + 68.4608u − 44.3286
a
7
=
−1.21875u
49
− 0.152259u
48
+ ··· + 14.4083u − 1.78993
−0.723126u
49
+ 0.0129383u
48
+ ··· + 21.8285u − 4.87126
a
12
=
u
u
a
8
=
−0.639172u
49
+ 0.0452825u
48
+ ··· + 12.4257u − 3.27671
−0.143548u
49
+ 0.210480u
48
+ ··· + 19.8459u − 6.35804
a
9
=
0.596353u
49
− 7.42853u
48
+ ··· − 300.553u + 145.738
0.152023u
49
− 4.81843u
48
+ ··· − 164.313u + 86.4276
a
4
=
4.63476u
49
− 2.40970u
48
+ ··· − 151.038u + 45.9067
2.79752u
49
− 0.421708u
48
+ ··· − 56.8794u + 12.3998
a
1
=
−7.25554u
49
+ 4.08207u
48
+ ··· + 309.336u − 84.0007
−3.98731u
49
+ 2.42343u
48
+ ··· + 162.524u − 41.5434
a
10
=
2.95626u
49
+ 2.84311u
48
+ ··· + 16.0102u − 38.3289
−0.430049u
49
+ 2.21506u
48
+ ··· + 53.6672u − 29.5231
(ii) Obstruction class = 1
(iii) Cusp Shapes = −8.42932u
49
− 9.35486u
48
+ ··· − 28.8372u + 141.918
21
(iv) u-Polynomials at the component
22
Crossings u-Polynomials at each crossing
c
1
u
50
− 13u
49
+ ··· + 10u − 1
c
2
u
50
− 2u
49
+ ··· − 3u − 1
c
3
u
50
− 10u
48
+ ··· − 21u + 9
c
4
u
50
− 12u
49
+ ··· + 2u
2
+ 1
c
5
u
50
+ 11u
48
+ ··· + 15u − 9
c
6
u
50
+ 2u
49
+ ··· + 3u − 1
c
7
u
50
+ 14u
49
+ ··· − 2u − 1
c
8
u
50
− 10u
48
+ ··· + 21u + 9
c
9
u
50
+ 6u
49
+ ··· + 8u + 1
c
10
u
50
+ 6u
49
+ ··· + 32u + 1
c
11
u
50
+ 11u
48
+ ··· − 15u − 9
c
12
u
50
− 6u
49
+ ··· − 8u + 1
23
24
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
50
− 13y
49
+ ··· − 430y + 1
c
2
, c
6
y
50
+ 36y
49
+ ··· + 37y + 1
c
3
, c
8
y
50
− 20y
49
+ ··· − 2421y + 81
c
4
y
50
− 10y
48
+ ··· + 4y + 1
c
5
, c
11
y
50
+ 22y
49
+ ··· + 1953y + 81
c
7
y
50
− 8y
49
+ ··· − 30y + 1
c
9
, c
12
y
50
+ 36y
49
+ ··· + 68y + 1
c
10
y
50
− 22y
49
+ ··· − 322y + 1
25
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.024155 + 0.972597I
a = −0.35773 − 2.60424I
b = 0.407123 − 0.280918I
−5.45309 − 0.15110I −27.0239 − 3.5878I
u = −0.024155 − 0.972597I
a = −0.35773 + 2.60424I
b = 0.407123 + 0.280918I
−5.45309 + 0.15110I −27.0239 + 3.5878I
u = −0.668218 + 0.693303I
a = 0.534504 − 0.007795I
b = 0.162062 − 0.350560I
−0.30424 − 2.42087I −3.48746 + 5.64938I
u = −0.668218 − 0.693303I
a = 0.534504 + 0.007795I
b = 0.162062 + 0.350560I
−0.30424 + 2.42087I −3.48746 − 5.64938I
u = 0.866391 + 0.414495I
a = −0.627600 + 0.401747I
b = 0.297437 − 1.001000I
−4.07301 + 5.09628I −5.43623 − 6.15272I
u = 0.866391 − 0.414495I
a = −0.627600 − 0.401747I
b = 0.297437 + 1.001000I
−4.07301 − 5.09628I −5.43623 + 6.15272I
u = 0.511700 + 0.916661I
a = 0.269401 − 1.111660I
b = −0.20588 − 1.46272I
−7.72208 − 1.29849I −5.55816 − 0.60071I
u = 0.511700 − 0.916661I
a = 0.269401 + 1.111660I
b = −0.20588 + 1.46272I
−7.72208 + 1.29849I −5.55816 + 0.60071I
u = −0.543856 + 0.918032I
a = −0.166101 + 0.917175I
b = −0.652030 − 0.126106I
−2.43996 − 2.59796I −0.080780 + 1.341039I
u = −0.543856 − 0.918032I
a = −0.166101 − 0.917175I
b = −0.652030 + 0.126106I
−2.43996 + 2.59796I −0.080780 − 1.341039I
26
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.029513 + 1.068900I
a = 0.77541 + 1.95628I
b = −0.392468 + 0.586181I
−4.32905 + 0.46272I −27.1904 + 13.5249I
u = −0.029513 − 1.068900I
a = 0.77541 − 1.95628I
b = −0.392468 − 0.586181I
−4.32905 − 0.46272I −27.1904 − 13.5249I
u = −1.047460 + 0.281927I
a = 0.475716 + 0.878790I
b = −0.65299 − 1.54935I
−1.62321 − 2.73602I −4.04148 + 3.95768I
u = −1.047460 − 0.281927I
a = 0.475716 − 0.878790I
b = −0.65299 + 1.54935I
−1.62321 + 2.73602I −4.04148 − 3.95768I
u = 1.086390 + 0.112084I
a = 0.073264 + 0.509095I
b = 0.25870 − 1.46656I
−1.075830 + 0.278293I 1.49120 + 1.67846I
u = 1.086390 − 0.112084I
a = 0.073264 − 0.509095I
b = 0.25870 + 1.46656I
−1.075830 − 0.278293I 1.49120 − 1.67846I
u = 0.288248 + 0.859360I
a = 2.22859 + 1.53941I
b = 2.29907 + 0.68456I
−2.32073 + 1.32145I 1.73202 − 2.95234I
u = 0.288248 − 0.859360I
a = 2.22859 − 1.53941I
b = 2.29907 − 0.68456I
−2.32073 − 1.32145I 1.73202 + 2.95234I
u = −0.727438 + 0.899779I
a = −0.156658 − 0.364035I
b = −0.27527 − 1.39724I
−8.92290 − 0.74157I −8.21818 + 0.I
u = −0.727438 − 0.899779I
a = −0.156658 + 0.364035I
b = −0.27527 + 1.39724I
−8.92290 + 0.74157I −8.21818 + 0.I
27
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.549320 + 1.073620I
a = −0.729401 + 0.857467I
b = −0.021701 + 0.650873I
−4.19332 + 5.65802I −4.15222 − 3.61822I
u = 0.549320 − 1.073620I
a = −0.729401 − 0.857467I
b = −0.021701 − 0.650873I
−4.19332 − 5.65802I −4.15222 + 3.61822I
u = −0.167786 + 0.742490I
a = −1.69949 − 0.70322I
b = −1.171950 + 0.415321I
−9.38363 − 8.02808I −9.76145 + 4.70173I
u = −0.167786 − 0.742490I
a = −1.69949 + 0.70322I
b = −1.171950 − 0.415321I
−9.38363 + 8.02808I −9.76145 − 4.70173I
u = −0.326179 + 1.238510I
a = −1.49182 − 0.80294I
b = −1.61369 − 1.69935I
−8.50056 − 7.12637I 0
u = −0.326179 − 1.238510I
a = −1.49182 + 0.80294I
b = −1.61369 + 1.69935I
−8.50056 + 7.12637I 0
u = −0.026484 + 0.692646I
a = −2.74877 + 3.08030I
b = −1.43183 + 1.94402I
−5.84946 + 5.63915I 0.116877 − 0.973543I
u = −0.026484 − 0.692646I
a = −2.74877 − 3.08030I
b = −1.43183 − 1.94402I
−5.84946 − 5.63915I 0.116877 + 0.973543I
u = 0.394685 + 1.265650I
a = −0.119376 + 0.326422I
b = −0.770242 + 0.474796I
−2.95351 + 5.15507I 0
u = 0.394685 − 1.265650I
a = −0.119376 − 0.326422I
b = −0.770242 − 0.474796I
−2.95351 − 5.15507I 0
28
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.156810 + 0.650952I
a = 0.311852 + 0.975471I
b = −1.79222 − 1.16273I
−1.66487 − 3.54014I 0
u = −1.156810 − 0.650952I
a = 0.311852 − 0.975471I
b = −1.79222 + 1.16273I
−1.66487 + 3.54014I 0
u = 0.658545 + 0.118591I
a = −0.441800 + 0.347843I
b = 0.508996 − 0.999955I
−0.953803 + 0.368954I 0.072599 + 0.543637I
u = 0.658545 − 0.118591I
a = −0.441800 − 0.347843I
b = 0.508996 + 0.999955I
−0.953803 − 0.368954I 0.072599 − 0.543637I
u = 0.122190 + 1.327720I
a = −0.16813 − 2.12984I
b = −0.68210 − 2.31055I
−12.1831 + 7.6724I 0
u = 0.122190 − 1.327720I
a = −0.16813 + 2.12984I
b = −0.68210 + 2.31055I
−12.1831 − 7.6724I 0
u = 0.659604 + 1.218730I
a = 0.185879 − 0.616255I
b = −0.876829 − 0.328789I
−4.69384 + 6.27766I 0
u = 0.659604 − 1.218730I
a = 0.185879 + 0.616255I
b = −0.876829 + 0.328789I
−4.69384 − 6.27766I 0
u = 1.39521
a = 1.12172
b = −0.925932
2.20804 0
u = −0.394346 + 1.340360I
a = 0.75329 + 1.80412I
b = −0.16140 + 2.34788I
−11.14450 − 4.24832I 0
29
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.394346 − 1.340360I
a = 0.75329 − 1.80412I
b = −0.16140 − 2.34788I
−11.14450 + 4.24832I 0
u = −1.39861
a = −1.10302
b = 0.655693
1.56008 0
u = 0.599018 + 1.266510I
a = −1.19997 + 1.53324I
b = 0.25400 + 2.67846I
−9.05380 + 6.20174I 0
u = 0.599018 − 1.266510I
a = −1.19997 − 1.53324I
b = 0.25400 − 2.67846I
−9.05380 − 6.20174I 0
u = −0.152690 + 0.538735I
a = −0.94185 − 1.44847I
b = 0.186922 − 1.217670I
0.12355 − 2.69515I 2.04952 + 8.48009I
u = −0.152690 − 0.538735I
a = −0.94185 + 1.44847I
b = 0.186922 + 1.217670I
0.12355 + 2.69515I 2.04952 − 8.48009I
u = 0.044496 + 0.526118I
a = −2.53212 − 0.30146I
b = −0.110035 − 0.307794I
0.57351 − 2.92968I −10.9611 + 12.8773I
u = 0.044496 − 0.526118I
a = −2.53212 + 0.30146I
b = −0.110035 + 0.307794I
0.57351 + 2.92968I −10.9611 − 12.8773I
u = −0.51395 + 1.47597I
a = −0.56977 − 1.66117I
b = 1.07144 − 2.87859I
−7.24314 − 8.51394I 0
u = −0.51395 − 1.47597I
a = −0.56977 + 1.66117I
b = 1.07144 + 2.87859I
−7.24314 + 8.51394I 0
30
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
50
− 13u
49
+ ··· + 10u − 1)
· (u
159
− 8u
158
+ ··· + 80215197u − 1927186)
c
2
(u
50
− 2u
49
+ ··· − 3u − 1)(u
159
− 3u
158
+ ··· − 3046266u − 178861)
c
3
(u
50
− 10u
48
+ ··· − 21u + 9)
· (u
159
− u
158
+ ··· − 8744042u + 1097059)
c
4
(u
50
− 12u
49
+ ··· + 2u
2
+ 1)
· (u
159
− 7u
158
+ ··· + 32390037u − 6440257)
c
5
(u
50
+ 11u
48
+ ··· + 15u − 9)(u
159
+ u
158
+ ··· − 95441u − 24008)
c
6
(u
50
+ 2u
49
+ ··· + 3u − 1)(u
159
− 3u
158
+ ··· − 3046266u − 178861)
c
7
(u
50
+ 14u
49
+ ··· − 2u − 1)
· (u
159
+ 15u
158
+ ··· + 43507681u − 2774953)
c
8
(u
50
− 10u
48
+ ··· + 21u + 9)
· (u
159
− u
158
+ ··· − 8744042u + 1097059)
c
9
(u
50
+ 6u
49
+ ··· + 8u + 1)(u
159
+ 5u
158
+ ··· + 159249u + 8893)
c
10
(u
50
+ 6u
49
+ ··· + 32u + 1)
· (u
159
− 15u
158
+ ··· − 333964577u + 95115071)
c
11
(u
50
+ 11u
48
+ ··· − 15u − 9)(u
159
+ u
158
+ ··· − 95441u − 24008)
c
12
(u
50
− 6u
49
+ ··· − 8u + 1)(u
159
+ 5u
158
+ ··· + 159249u + 8893)
31
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
50
− 13y
49
+ ··· − 430y + 1)
· (y
159
− 82y
158
+ ··· + 3262006438404145y −3714045878596)
c
2
, c
6
(y
50
+ 36y
49
+ ··· + 37y + 1)
· (y
159
+ 115y
158
+ ··· + 126566005786y −31991257321)
c
3
, c
8
(y
50
− 20y
49
+ ··· − 2421y + 81)
· (y
159
− 105y
158
+ ··· + 42991384255528y −1203538449481)
c
4
(y
50
− 10y
48
+ ··· + 4y + 1)
· (y
159
− 61y
158
+ ··· + 774738334454811y −41476910226049)
c
5
, c
11
(y
50
+ 22y
49
+ ··· + 1953y + 81)
· (y
159
+ 97y
158
+ ··· − 15736846703y −576384064)
c
7
(y
50
− 8y
49
+ ··· − 30y + 1)
· (y
159
− 57y
158
+ ··· + 1120931842505265y −7700364152209)
c
9
, c
12
(y
50
+ 36y
49
+ ··· + 68y + 1)
· (y
159
+ 127y
158
+ ··· + 291286079y −79085449)
c
10
(y
50
− 22y
49
+ ··· − 322y + 1)
· (y
159
− 59y
158
+ ··· + 1754195507846337117y −9046876731335041)
32
