12a
0456
(K12a
0456
)
A knot diagram
1
Linearized knot diagam
3 6 10 12 7 2 1 11 5 8 4 9
Solving Sequence
4,11
12
5,9
1 8 7 10 3 2 6
c
11
c
4
c
12
c
8
c
7
c
10
c
3
c
1
c
6
c
2
, c
5
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−2.53175 × 10
313
u
115
+ 2.92436 × 10
313
u
114
+ ··· + 2.25234 × 10
314
b + 8.23829 × 10
313
,
− 2.24989 × 10
314
u
115
+ 2.20110 × 10
314
u
114
+ ··· + 3.60375 × 10
315
a − 2.99578 × 10
315
,
u
116
+ 2u
115
+ ··· + 4u + 1i
I
u
2
= hb − 1, 3u
3
+ 2u
2
+ 16a + 7u + 11, u
4
− u
3
+ 3u
2
− 2u + 1i
* 2 irreducible components of dim
C
= 0, with total 120 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−2.53 × 10
313
u
115
+ 2.92 × 10
313
u
114
+ · · · + 2.25 × 10
314
b + 8.24 ×
10
313
, −2.25 × 10
314
u
115
+ 2.20 × 10
314
u
114
+ · · · + 3.60 × 10
315
a − 3.00 ×
10
315
, u
116
+ 2u
115
+ · · · + 4u + 1i
(i) Arc colorings
a
4
=
0
u
a
11
=
1
0
a
12
=
1
u
2
a
5
=
−u
−u
3
+ u
a
9
=
0.0624320u
115
− 0.0610780u
114
+ ··· − 0.624844u + 0.831296
0.112405u
115
− 0.129836u
114
+ ··· − 3.13673u − 0.365765
a
1
=
−1.36566u
115
− 0.966684u
114
+ ··· − 0.101173u + 0.236304
−0.0575097u
115
+ 0.109899u
114
+ ··· + 3.11321u + 0.437787
a
8
=
−0.0499731u
115
+ 0.0687581u
114
+ ··· + 2.51188u + 1.19706
0.112405u
115
− 0.129836u
114
+ ··· − 3.13673u − 0.365765
a
7
=
0.376542u
115
+ 0.0535687u
114
+ ··· + 0.455051u + 0.877028
−0.313567u
115
− 1.13025u
114
+ ··· − 9.22734u − 2.08951
a
10
=
−0.0577405u
115
− 0.359290u
114
+ ··· − 2.23769u + 0.421032
0.277384u
115
+ 0.258423u
114
+ ··· − 1.17224u + 0.102366
a
3
=
1.10683u
115
+ 1.22497u
114
+ ··· + 5.46904u + 1.96029
−0.608411u
115
− 1.03975u
114
+ ··· − 1.36203u − 0.474932
a
2
=
−0.448108u
115
+ 1.00733u
114
+ ··· + 7.64578u + 1.31221
0.191247u
115
+ 0.929848u
114
+ ··· + 9.34460u + 2.37131
a
6
=
0.269740u
115
+ 0.274312u
114
+ ··· − 2.62641u − 1.27309
2.08463u
115
+ 3.62773u
114
+ ··· + 8.91773u + 0.133485
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4.00070u
115
− 9.56340u
114
+ ··· − 41.1381u − 13.7651
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
116
+ 38u
115
+ ··· − 2u + 1
c
2
, c
6
u
116
− 2u
115
+ ··· − u
2
+ 1
c
3
16(16u
116
− 117u
115
+ ··· − 5135u + 3001)
c
4
, c
11
u
116
+ 2u
115
+ ··· + 4u + 1
c
7
u
116
+ 10u
115
+ ··· + 1233680u + 97600
c
8
, c
10
u
116
+ 5u
115
+ ··· + 2505u + 256
c
9
u
116
+ 3u
115
+ ··· + 26496u + 4096
c
12
16(16u
116
+ 237u
115
+ ··· − 7715u + 289)
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
116
+ 82y
115
+ ··· − 14y + 1
c
2
, c
6
y
116
+ 38y
115
+ ··· − 2y + 1
c
3
256(256y
116
+ 3815y
115
+ ··· − 5.95490 × 10
8
y + 9006001)
c
4
, c
11
y
116
− 62y
115
+ ··· − 2y + 1
c
7
y
116
+ 14y
115
+ ··· + 306040470400y + 9525760000
c
8
, c
10
y
116
− 67y
115
+ ··· − 938449y + 65536
c
9
y
116
− 27y
115
+ ··· + 438878208y + 16777216
c
12
256(256y
116
+ 14007y
115
+ ··· − 1.71712 × 10
7
y + 83521)
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.932975 + 0.380055I
a = 0.50615 − 1.93295I
b = 1.18511 − 0.91051I
3.59446 − 4.25759I 0
u = 0.932975 − 0.380055I
a = 0.50615 + 1.93295I
b = 1.18511 + 0.91051I
3.59446 + 4.25759I 0
u = −0.942443 + 0.386528I
a = 0.48712 + 1.95718I
b = 1.16351 + 0.96120I
2.72521 + 9.87166I 0
u = −0.942443 − 0.386528I
a = 0.48712 − 1.95718I
b = 1.16351 − 0.96120I
2.72521 − 9.87166I 0
u = −1.015520 + 0.079924I
a = 2.86594 + 5.65897I
b = 0.943003 − 0.008732I
1.51330 − 0.01120I 0
u = −1.015520 − 0.079924I
a = 2.86594 − 5.65897I
b = 0.943003 + 0.008732I
1.51330 + 0.01120I 0
u = 0.921677 + 0.322581I
a = 0.47350 − 1.83013I
b = 1.102010 − 0.674058I
1.18239 − 2.90297I 0
u = 0.921677 − 0.322581I
a = 0.47350 + 1.83013I
b = 1.102010 + 0.674058I
1.18239 + 2.90297I 0
u = −0.966971 + 0.356693I
a = 0.42098 + 1.89144I
b = 0.991776 + 0.891367I
−2.25470 + 4.58566I 0
u = −0.966971 − 0.356693I
a = 0.42098 − 1.89144I
b = 0.991776 − 0.891367I
−2.25470 − 4.58566I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.025030 + 0.133441I
a = 2.16050 − 2.96069I
b = 0.820014 − 0.004042I
−3.74478 − 0.00361I 0
u = 1.025030 − 0.133441I
a = 2.16050 + 2.96069I
b = 0.820014 + 0.004042I
−3.74478 + 0.00361I 0
u = 1.032360 + 0.089616I
a = 3.52581 − 4.46017I
b = 0.924511 + 0.036679I
0.64084 + 5.41192I 0
u = 1.032360 − 0.089616I
a = 3.52581 + 4.46017I
b = 0.924511 − 0.036679I
0.64084 − 5.41192I 0
u = −0.933101 + 0.165578I
a = 0.15820 + 2.41425I
b = 0.963208 + 0.212678I
0.097528 + 0.717924I 0
u = −0.933101 − 0.165578I
a = 0.15820 − 2.41425I
b = 0.963208 − 0.212678I
0.097528 − 0.717924I 0
u = 1.040820 + 0.176639I
a = 1.70112 − 1.62243I
b = 0.587537 − 0.040637I
−0.10015 − 5.28988I 0
u = 1.040820 − 0.176639I
a = 1.70112 + 1.62243I
b = 0.587537 + 0.040637I
−0.10015 + 5.28988I 0
u = −1.051100 + 0.195133I
a = 1.13277 + 1.30258I
b = 0.433420 + 0.197090I
0.514456 + 0.135291I 0
u = −1.051100 − 0.195133I
a = 1.13277 − 1.30258I
b = 0.433420 − 0.197090I
0.514456 − 0.135291I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.168018 + 1.071190I
a = 0.338703 + 0.172300I
b = −1.151900 + 0.484030I
−1.45169 − 6.87895I 0
u = −0.168018 − 1.071190I
a = 0.338703 − 0.172300I
b = −1.151900 − 0.484030I
−1.45169 + 6.87895I 0
u = 0.837697 + 0.351028I
a = 0.63116 − 1.69354I
b = 1.40819 − 0.57266I
4.57854 − 2.68459I 0
u = 0.837697 − 0.351028I
a = 0.63116 + 1.69354I
b = 1.40819 + 0.57266I
4.57854 + 2.68459I 0
u = −0.133686 + 1.084940I
a = 0.288829 + 0.186794I
b = −1.250560 + 0.482907I
4.19362 − 13.02090I 0
u = −0.133686 − 1.084940I
a = 0.288829 − 0.186794I
b = −1.250560 − 0.482907I
4.19362 + 13.02090I 0
u = −0.255673 + 1.064880I
a = 0.403088 + 0.100874I
b = −1.002170 + 0.401779I
0.405726 − 0.191311I 0
u = −0.255673 − 1.064880I
a = 0.403088 − 0.100874I
b = −1.002170 − 0.401779I
0.405726 + 0.191311I 0
u = 0.139068 + 1.094320I
a = 0.288556 − 0.170981I
b = −1.242370 − 0.453261I
5.30484 + 7.16529I 0
u = 0.139068 − 1.094320I
a = 0.288556 + 0.170981I
b = −1.242370 + 0.453261I
5.30484 − 7.16529I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.064290 + 0.320997I
a = 0.25708 + 1.62401I
b = 0.484658 + 0.861383I
0.553410 − 0.120359I 0
u = −1.064290 − 0.320997I
a = 0.25708 − 1.62401I
b = 0.484658 − 0.861383I
0.553410 + 0.120359I 0
u = −0.815607 + 0.351086I
a = 0.66682 + 1.62768I
b = 1.45666 + 0.51569I
4.00667 − 2.83899I 0
u = −0.815607 − 0.351086I
a = 0.66682 − 1.62768I
b = 1.45666 − 0.51569I
4.00667 + 2.83899I 0
u = 0.197323 + 1.109430I
a = 0.334392 − 0.117534I
b = −1.125740 − 0.385168I
2.84490 + 4.28893I 0
u = 0.197323 − 1.109430I
a = 0.334392 + 0.117534I
b = −1.125740 + 0.385168I
2.84490 − 4.28893I 0
u = 1.108580 + 0.330328I
a = 0.07789 − 1.50159I
b = 0.268886 − 0.939607I
0.73853 − 5.21162I 0
u = 1.108580 − 0.330328I
a = 0.07789 + 1.50159I
b = 0.268886 + 0.939607I
0.73853 + 5.21162I 0
u = 1.030480 + 0.600228I
a = 0.787511 + 0.802602I
b = −0.629673 + 0.394217I
−1.91929 + 4.20741I 0
u = 1.030480 − 0.600228I
a = 0.787511 − 0.802602I
b = −0.629673 − 0.394217I
−1.91929 − 4.20741I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.033930 + 0.672720I
a = 0.632515 − 0.738424I
b = −0.713327 − 0.320995I
−0.60389 + 1.31728I 0
u = −1.033930 − 0.672720I
a = 0.632515 + 0.738424I
b = −0.713327 + 0.320995I
−0.60389 − 1.31728I 0
u = −0.712038 + 0.268205I
a = 0.544099 + 1.124880I
b = 1.41778 + 0.18424I
−0.13211 + 1.45451I −1.69686 − 4.01852I
u = −0.712038 − 0.268205I
a = 0.544099 − 1.124880I
b = 1.41778 − 0.18424I
−0.13211 − 1.45451I −1.69686 + 4.01852I
u = 0.239199 + 0.710424I
a = 0.779803 − 0.124579I
b = −0.398169 − 0.538145I
−1.17035 + 3.60756I −3.17763 − 3.80286I
u = 0.239199 − 0.710424I
a = 0.779803 + 0.124579I
b = −0.398169 + 0.538145I
−1.17035 − 3.60756I −3.17763 + 3.80286I
u = 1.190100 + 0.393431I
a = −0.50179 − 1.42134I
b = −0.195049 − 1.264670I
−1.98641 − 6.48143I 0
u = 1.190100 − 0.393431I
a = −0.50179 + 1.42134I
b = −0.195049 + 1.264670I
−1.98641 + 6.48143I 0
u = 1.205200 + 0.360020I
a = −0.401169 − 1.223780I
b = −0.236390 − 1.062780I
−3.83829 − 4.36811I 0
u = 1.205200 − 0.360020I
a = −0.401169 + 1.223780I
b = −0.236390 + 1.062780I
−3.83829 + 4.36811I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.193840 + 0.399946I
a = −0.54952 + 1.42991I
b = −0.225922 + 1.298760I
−3.05221 + 12.12590I 0
u = −1.193840 − 0.399946I
a = −0.54952 − 1.42991I
b = −0.225922 − 1.298760I
−3.05221 − 12.12590I 0
u = −1.211410 + 0.388213I
a = −0.559229 + 1.294670I
b = −0.310138 + 1.203680I
−8.10394 + 6.21848I 0
u = −1.211410 − 0.388213I
a = −0.559229 − 1.294670I
b = −0.310138 − 1.203680I
−8.10394 − 6.21848I 0
u = 1.133830 + 0.616400I
a = 0.594258 + 1.041120I
b = −0.797894 + 0.496771I
−6.67592 − 2.20639I 0
u = 1.133830 − 0.616400I
a = 0.594258 − 1.041120I
b = −0.797894 − 0.496771I
−6.67592 + 2.20639I 0
u = −1.238500 + 0.366883I
a = −0.541186 + 1.087490I
b = −0.411510 + 1.043980I
−5.39668 + 0.15552I 0
u = −1.238500 − 0.366883I
a = −0.541186 − 1.087490I
b = −0.411510 − 1.043980I
−5.39668 − 0.15552I 0
u = −0.619178 + 0.338799I
a = 0.942625 + 0.930733I
b = 1.57822 + 0.02039I
4.51489 + 6.13738I 5.17778 − 7.54514I
u = −0.619178 − 0.338799I
a = 0.942625 − 0.930733I
b = 1.57822 − 0.02039I
4.51489 − 6.13738I 5.17778 + 7.54514I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.593224 + 0.328294I
a = 0.945133 − 0.834395I
b = 1.54650 + 0.02847I
5.21239 − 0.58460I 6.91499 + 2.03694I
u = 0.593224 − 0.328294I
a = 0.945133 + 0.834395I
b = 1.54650 − 0.02847I
5.21239 + 0.58460I 6.91499 − 2.03694I
u = 1.287070 + 0.320286I
a = −0.445671 − 0.757330I
b = −0.517943 − 0.762187I
−4.95775 − 3.95723I 0
u = 1.287070 − 0.320286I
a = −0.445671 + 0.757330I
b = −0.517943 + 0.762187I
−4.95775 + 3.95723I 0
u = −1.314910 + 0.223822I
a = −0.192367 + 0.486790I
b = −0.469371 + 0.450322I
−3.07974 + 0.33761I 0
u = −1.314910 − 0.223822I
a = −0.192367 − 0.486790I
b = −0.469371 − 0.450322I
−3.07974 − 0.33761I 0
u = 0.107181 + 0.653140I
a = 0.906215 − 0.203840I
b = −0.147931 − 0.713160I
−4.33398 − 2.39690I −5.75709 + 3.17963I
u = 0.107181 − 0.653140I
a = 0.906215 + 0.203840I
b = −0.147931 + 0.713160I
−4.33398 + 2.39690I −5.75709 − 3.17963I
u = 0.178790 + 1.338570I
a = 0.266652 − 0.006836I
b = −1.120380 − 0.115989I
8.74835 + 3.17154I 0
u = 0.178790 − 1.338570I
a = 0.266652 + 0.006836I
b = −1.120380 + 0.115989I
8.74835 − 3.17154I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.206210 + 0.613574I
a = 0.384852 + 1.227350I
b = −0.959000 + 0.561231I
−3.65725 − 8.87599I 0
u = 1.206210 − 0.613574I
a = 0.384852 − 1.227350I
b = −0.959000 − 0.561231I
−3.65725 + 8.87599I 0
u = 0.033600 + 0.642239I
a = 0.985142 − 0.244254I
b = 0.011037 − 0.835334I
0.46430 − 8.24496I 0.50974 + 7.18818I
u = 0.033600 − 0.642239I
a = 0.985142 + 0.244254I
b = 0.011037 + 0.835334I
0.46430 + 8.24496I 0.50974 − 7.18818I
u = −1.193650 + 0.658691I
a = 0.345947 − 1.049920I
b = −0.944344 − 0.451052I
−1.78250 + 4.18645I 0
u = −1.193650 − 0.658691I
a = 0.345947 + 1.049920I
b = −0.944344 + 0.451052I
−1.78250 − 4.18645I 0
u = −0.034663 + 0.616794I
a = 0.998131 + 0.215645I
b = 0.056574 + 0.777691I
1.50714 + 2.68871I 2.49575 − 2.58539I
u = −0.034663 − 0.616794I
a = 0.998131 − 0.215645I
b = 0.056574 − 0.777691I
1.50714 − 2.68871I 2.49575 + 2.58539I
u = −0.340191 + 0.489590I
a = 0.901844 − 0.007398I
b = −0.213986 + 0.244163I
0.011500 + 1.083370I −2.30792 − 3.75059I
u = −0.340191 − 0.489590I
a = 0.901844 + 0.007398I
b = −0.213986 − 0.244163I
0.011500 − 1.083370I −2.30792 + 3.75059I
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.275660 + 0.593237I
a = 0.06995 − 1.46230I
b = −1.192240 − 0.626878I
−2.86858 + 6.11454I 0
u = −1.275660 − 0.593237I
a = 0.06995 + 1.46230I
b = −1.192240 + 0.626878I
−2.86858 − 6.11454I 0
u = 1.381390 + 0.301986I
a = −0.486626 − 0.402298I
b = −0.726966 − 0.529704I
−6.88096 + 1.98077I 0
u = 1.381390 − 0.301986I
a = −0.486626 + 0.402298I
b = −0.726966 + 0.529704I
−6.88096 − 1.98077I 0
u = −1.29250 + 0.58088I
a = −0.03961 − 1.57216I
b = −1.28137 − 0.66517I
−4.98176 + 12.74390I 0
u = −1.29250 − 0.58088I
a = −0.03961 + 1.57216I
b = −1.28137 + 0.66517I
−4.98176 − 12.74390I 0
u = 1.29226 + 0.59404I
a = −0.04653 + 1.47058I
b = −1.261460 + 0.604557I
−0.62576 − 10.29630I 0
u = 1.29226 − 0.59404I
a = −0.04653 − 1.47058I
b = −1.261460 − 0.604557I
−0.62576 + 10.29630I 0
u = −1.30349 + 0.57782I
a = −0.13130 − 1.60635I
b = −1.34309 − 0.66340I
0.5378 + 18.9008I 0
u = −1.30349 − 0.57782I
a = −0.13130 + 1.60635I
b = −1.34309 + 0.66340I
0.5378 − 18.9008I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.30373 + 0.58142I
a = −0.13459 + 1.57454I
b = −1.33738 + 0.64400I
1.66025 − 13.08200I 0
u = 1.30373 − 0.58142I
a = −0.13459 − 1.57454I
b = −1.33738 − 0.64400I
1.66025 + 13.08200I 0
u = −0.386795 + 0.388376I
a = 1.229680 + 0.337965I
b = 1.35766 − 0.42189I
4.14545 − 6.42366I 5.06027 + 4.33078I
u = −0.386795 − 0.388376I
a = 1.229680 − 0.337965I
b = 1.35766 + 0.42189I
4.14545 + 6.42366I 5.06027 − 4.33078I
u = 0.405228 + 0.367597I
a = 1.185670 − 0.375547I
b = 1.37406 + 0.36367I
4.93612 + 0.86391I 6.86019 + 1.04991I
u = 0.405228 − 0.367597I
a = 1.185670 + 0.375547I
b = 1.37406 − 0.36367I
4.93612 − 0.86391I 6.86019 − 1.04991I
u = 1.31376 + 0.62961I
a = −0.158778 + 1.224320I
b = −1.266390 + 0.437367I
5.12704 − 9.72281I 0
u = 1.31376 − 0.62961I
a = −0.158778 − 1.224320I
b = −1.266390 − 0.437367I
5.12704 + 9.72281I 0
u = −1.31432 + 0.64276I
a = −0.140832 − 1.155560I
b = −1.239700 − 0.403441I
5.00542 + 3.74494I 0
u = −1.31432 − 0.64276I
a = −0.140832 + 1.155560I
b = −1.239700 + 0.403441I
5.00542 − 3.74494I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.26974 + 1.46073I
a = 0.262189 − 0.026077I
b = −1.054360 + 0.082304I
8.58527 + 3.04895I 0
u = −0.26974 − 1.46073I
a = 0.262189 + 0.026077I
b = −1.054360 − 0.082304I
8.58527 − 3.04895I 0
u = 1.46981 + 0.32497I
a = −0.532496 − 0.175783I
b = −0.886516 − 0.390567I
−1.19925 + 7.69678I 0
u = 1.46981 − 0.32497I
a = −0.532496 + 0.175783I
b = −0.886516 + 0.390567I
−1.19925 − 7.69678I 0
u = 0.459714 + 0.168334I
a = 0.786644 − 0.302575I
b = 1.281580 + 0.086509I
2.35130 + 0.01962I 6.92796 + 1.30693I
u = 0.459714 − 0.168334I
a = 0.786644 + 0.302575I
b = 1.281580 − 0.086509I
2.35130 − 0.01962I 6.92796 − 1.30693I
u = −0.162843 + 0.460600I
a = 0.963740 + 0.056991I
b = −0.004343 + 0.338203I
−0.011505 + 1.030340I 0.09970 − 5.57726I
u = −0.162843 − 0.460600I
a = 0.963740 − 0.056991I
b = −0.004343 − 0.338203I
−0.011505 − 1.030340I 0.09970 + 5.57726I
u = −1.48354 + 0.29138I
a = −0.463830 + 0.164782I
b = −0.843739 + 0.340266I
−0.22909 − 1.82469I 0
u = −1.48354 − 0.29138I
a = −0.463830 − 0.164782I
b = −0.843739 − 0.340266I
−0.22909 + 1.82469I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.163731 + 0.440161I
a = 1.185900 − 0.001397I
b = 0.819743 − 0.557047I
2.94920 + 3.29370I 5.18784 − 3.60846I
u = −0.163731 − 0.440161I
a = 1.185900 + 0.001397I
b = 0.819743 + 0.557047I
2.94920 − 3.29370I 5.18784 + 3.60846I
u = 0.116072 + 0.451977I
a = 1.153390 + 0.040725I
b = 0.680537 + 0.544028I
3.42477 + 2.02673I 6.58023 − 3.04514I
u = 0.116072 − 0.451977I
a = 1.153390 − 0.040725I
b = 0.680537 − 0.544028I
3.42477 − 2.02673I 6.58023 + 3.04514I
u = −0.291018 + 0.355390I
a = 1.161280 + 0.179300I
b = 1.145130 − 0.402487I
−0.58774 − 1.37393I −0.877677 + 0.764145I
u = −0.291018 − 0.355390I
a = 1.161280 − 0.179300I
b = 1.145130 + 0.402487I
−0.58774 + 1.37393I −0.877677 − 0.764145I
16
II. I
u
2
= hb − 1, 3u
3
+ 2u
2
+ 16a + 7u + 11, u
4
− u
3
+ 3u
2
− 2u + 1i
(i) Arc colorings
a
4
=
0
u
a
11
=
1
0
a
12
=
1
u
2
a
5
=
−u
−u
3
+ u
a
9
=
−
3
16
u
3
−
1
8
u
2
−
7
16
u −
11
16
1
a
1
=
0.347656u
3
+ 0.0234375u
2
+ 0.832031u + 1.31641
−
3
16
u
3
+
7
8
u
2
−
7
16
u −
11
16
a
8
=
−
3
16
u
3
−
1
8
u
2
−
7
16
u −
27
16
1
a
7
=
−0.347656u
3
− 1.02344u
2
− 0.832031u − 1.31641
−0.812500u
3
+ 3.12500u
2
− 1.56250u + 1.68750
a
10
=
−
3
16
u
3
−
1
8
u
2
−
7
16
u −
11
16
1
a
3
=
0.371094u
3
− 0.210938u
2
+ 1.01172u − 0.347656
−
5
16
u
3
+
1
8
u
2
−
1
16
u +
3
16
a
2
=
0.507813u
3
− 0.0781250u
2
+ 1.22656u + 0.945313
−
3
8
u
3
+
7
4
u
2
−
7
8
u −
3
8
a
6
=
−1.37109u
3
+ 0.210938u
2
− 3.01172u + 0.347656
21
16
u
3
+
7
8
u
2
+
17
16
u +
13
16
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
631
256
u
3
+
1427
128
u
2
−
187
256
u +
1025
256
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
11
u
4
− u
3
+ 3u
2
− 2u + 1
c
2
u
4
− u
3
+ u
2
+ 1
c
3
16(16u
4
− 5u
3
+ 8u
2
− u + 1)
c
4
u
4
+ u
3
+ 3u
2
+ 2u + 1
c
6
u
4
+ u
3
+ u
2
+ 1
c
7
u
4
− 5u
3
+ 7u
2
− 2u + 1
c
8
(u + 1)
4
c
9
u
4
c
10
(u − 1)
4
c
12
16(16u
4
− 35u
3
+ 28u
2
− 9u + 1)
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
5
c
11
y
4
+ 5y
3
+ 7y
2
+ 2y + 1
c
2
, c
6
y
4
+ y
3
+ 3y
2
+ 2y + 1
c
3
256(256y
4
+ 231y
3
+ 86y
2
+ 15y + 1)
c
7
y
4
− 11y
3
+ 31y
2
+ 10y + 1
c
8
, c
10
(y −1)
4
c
9
y
4
c
12
256(256y
4
− 329y
3
+ 186y
2
− 25y + 1)
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.395123 + 0.506844I
a = −0.802241 − 0.291908I
b = 1.00000
1.43393 − 1.41510I 3.19039 + 3.83087I
u = 0.395123 − 0.506844I
a = −0.802241 + 0.291908I
b = 1.00000
1.43393 + 1.41510I 3.19039 − 3.83087I
u = 0.10488 + 1.55249I
a = −0.291509 − 0.027926I
b = 1.00000
8.43568 − 3.16396I −20.9541 + 11.5932I
u = 0.10488 − 1.55249I
a = −0.291509 + 0.027926I
b = 1.00000
8.43568 + 3.16396I −20.9541 − 11.5932I
20
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
5
(u
4
− u
3
+ 3u
2
− 2u + 1)(u
116
+ 38u
115
+ ··· − 2u + 1)
c
2
(u
4
− u
3
+ u
2
+ 1)(u
116
− 2u
115
+ ··· − u
2
+ 1)
c
3
256(16u
4
− 5u
3
+ ··· − u + 1)(16u
116
− 117u
115
+ ··· − 5135u + 3001)
c
4
(u
4
+ u
3
+ 3u
2
+ 2u + 1)(u
116
+ 2u
115
+ ··· + 4u + 1)
c
6
(u
4
+ u
3
+ u
2
+ 1)(u
116
− 2u
115
+ ··· − u
2
+ 1)
c
7
(u
4
− 5u
3
+ 7u
2
− 2u + 1)(u
116
+ 10u
115
+ ··· + 1233680u + 97600)
c
8
((u + 1)
4
)(u
116
+ 5u
115
+ ··· + 2505u + 256)
c
9
u
4
(u
116
+ 3u
115
+ ··· + 26496u + 4096)
c
10
((u − 1)
4
)(u
116
+ 5u
115
+ ··· + 2505u + 256)
c
11
(u
4
− u
3
+ 3u
2
− 2u + 1)(u
116
+ 2u
115
+ ··· + 4u + 1)
c
12
256(16u
4
− 35u
3
+ 28u
2
− 9u + 1)
· (16u
116
+ 237u
115
+ ··· − 7715u + 289)
21
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
(y
4
+ 5y
3
+ 7y
2
+ 2y + 1)(y
116
+ 82y
115
+ ··· − 14y + 1)
c
2
, c
6
(y
4
+ y
3
+ 3y
2
+ 2y + 1)(y
116
+ 38y
115
+ ··· − 2y + 1)
c
3
65536(256y
4
+ 231y
3
+ 86y
2
+ 15y + 1)
· (256y
116
+ 3815y
115
+ ··· − 595489869y + 9006001)
c
4
, c
11
(y
4
+ 5y
3
+ 7y
2
+ 2y + 1)(y
116
− 62y
115
+ ··· − 2y + 1)
c
7
(y
4
− 11y
3
+ 31y
2
+ 10y + 1)
· (y
116
+ 14y
115
+ ··· + 306040470400y + 9525760000)
c
8
, c
10
((y −1)
4
)(y
116
− 67y
115
+ ··· − 938449y + 65536)
c
9
y
4
(y
116
− 27y
115
+ ··· + 4.38878 × 10
8
y + 1.67772 × 10
7
)
c
12
65536(256y
4
− 329y
3
+ 186y
2
− 25y + 1)
· (256y
116
+ 14007y
115
+ ··· − 17171165y + 83521)
22
