12a
0107
(K12a
0107
)
A knot diagram
1
Linearized knot diagam
3 5 8 2 11 9 4 12 6 1 7 10
Solving Sequence
8,12 4,9
3 7 6 10 1 11 5 2
c
8
c
3
c
7
c
6
c
9
c
12
c
11
c
5
c
2
c
1
, c
4
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h2.20020 × 10
1302
u
128
+ 2.69244 × 10
1303
u
127
+ ··· + 4.96534 × 10
1303
b + 3.24071 × 10
1304
,
− 1.21845 × 10
1305
u
128
− 1.49391 × 10
1306
u
127
+ ··· + 1.27609 × 10
1306
a − 1.08044 × 10
1307
,
9u
129
+ 111u
128
+ ··· + 5137u + 257i
I
u
2
= hb, u
7
− u
6
− u
5
+ 3u
4
+ u
3
− 3u
2
+ a + 3, u
8
− u
7
− u
6
+ 2u
5
+ u
4
− 2u
3
+ 2u − 1i
I
u
3
= hb + 3u − 2, a + 3u − 1, 9u
2
− 9u + 1i
* 3 irreducible components of dim
C
= 0, with total 139 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
= h2.20 × 10
1302
u
128
+ 2.69 × 10
1303
u
127
+ · · · + 4.97 × 10
1303
b + 3.24 ×
10
1304
, −1.22 × 10
1305
u
128
− 1.49 × 10
1306
u
127
+ · · · + 1.28 × 10
1306
a −
1.08 × 10
1307
, 9u
129
+ 111u
128
+ · · · + 5137u + 257i
(i) Arc colorings
a
8
=
1
0
a
12
=
0
u
a
4
=
0.0954827u
128
+ 1.17069u
127
+ ··· + 214.507u + 8.46678
−0.0443112u
128
− 0.542246u
127
+ ··· − 109.842u − 6.52665
a
9
=
1
u
2
a
3
=
0.0511715u
128
+ 0.628443u
127
+ ··· + 104.665u + 1.94013
−0.0443112u
128
− 0.542246u
127
+ ··· − 109.842u − 6.52665
a
7
=
−0.0215808u
128
− 0.258363u
127
+ ··· + 48.4855u + 2.98364
−0.0222185u
128
− 0.268499u
127
+ ··· − 34.2702u − 2.52990
a
6
=
−0.0441534u
128
− 0.530839u
127
+ ··· + 18.0513u + 0.676483
−0.0235416u
128
− 0.284565u
127
+ ··· − 37.0038u − 2.69891
a
10
=
0.111352u
128
+ 1.36964u
127
+ ··· + 358.049u + 23.5975
0.113475u
128
+ 1.37895u
127
+ ··· + 245.872u + 16.0714
a
1
=
−0.00229959u
128
− 0.0237417u
127
+ ··· + 219.055u + 21.4240
0.117650u
128
+ 1.43086u
127
+ ··· + 231.967u + 14.9510
a
11
=
−0.104777u
128
− 1.26102u
127
+ ··· + 120.845u + 11.5128
0.0147018u
128
+ 0.177405u
127
+ ··· − 5.72762u − 0.818042
a
5
=
0.0126662u
128
+ 0.150899u
127
+ ··· − 201.626u − 14.2603
−0.0271052u
128
− 0.326635u
127
+ ··· − 25.7115u − 2.71321
a
2
=
−0.0261881u
128
− 0.309924u
127
+ ··· + 241.686u + 17.6947
0.0271052u
128
+ 0.326635u
127
+ ··· + 25.7115u + 2.71321
(ii) Obstruction class = −1
(iii) Cusp Shapes = −5.34482u
128
− 65.0381u
127
+ ··· − 12750.8u − 927.585
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
129
+ 68u
128
+ ··· + 31u + 1
c
2
, c
4
u
129
− 10u
128
+ ··· + 5u − 1
c
3
, c
7
u
129
+ 2u
128
+ ··· + 896u + 256
c
5
9(9u
129
− 72u
128
+ ··· − 1416882u + 58007)
c
6
, c
9
u
129
− 3u
128
+ ··· + 3u − 1
c
8
9(9u
129
− 111u
128
+ ··· + 5137u − 257)
c
10
, c
12
u
129
− 4u
128
+ ··· + 810u − 81
c
11
u
129
− 2u
128
+ ··· − 5940u + 324
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
129
− 4y
128
+ ··· + 1563y −1
c
2
, c
4
y
129
− 68y
128
+ ··· + 31y −1
c
3
, c
7
y
129
+ 48y
128
+ ··· − 933888y −65536
c
5
81(81y
129
− 1926y
128
+ ··· + 4.58236 × 10
11
y −3.36481 × 10
9
)
c
6
, c
9
y
129
+ 69y
128
+ ··· + 31y −1
c
8
81(81y
129
+ 1953y
128
+ ··· − 1315317y −66049)
c
10
, c
12
y
129
− 82y
128
+ ··· + 92178y −6561
c
11
y
129
+ 12y
128
+ ··· + 12906216y −104976
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.435964 + 0.912114I
a = −0.00814 + 1.87832I
b = −0.191368 − 1.227640I
7.90256 − 0.75255I 0
u = −0.435964 − 0.912114I
a = −0.00814 − 1.87832I
b = −0.191368 + 1.227640I
7.90256 + 0.75255I 0
u = 0.411533 + 0.926967I
a = 0.32805 − 1.69283I
b = 0.476647 + 1.106970I
2.20983 − 3.68482I 0
u = 0.411533 − 0.926967I
a = 0.32805 + 1.69283I
b = 0.476647 − 1.106970I
2.20983 + 3.68482I 0
u = −0.874519 + 0.547704I
a = 0.637430 − 0.368145I
b = 0.025470 − 0.914503I
1.88599 + 4.20801I 0
u = −0.874519 − 0.547704I
a = 0.637430 + 0.368145I
b = 0.025470 + 0.914503I
1.88599 − 4.20801I 0
u = 0.955609
a = −3.36955
b = −0.414891
−2.95218 0
u = −0.174007 + 1.038510I
a = −0.514443 − 1.168250I
b = −0.433681 + 1.273930I
4.44411 − 0.29904I 0
u = −0.174007 − 1.038510I
a = −0.514443 + 1.168250I
b = −0.433681 − 1.273930I
4.44411 + 0.29904I 0
u = 0.938888 + 0.091208I
a = −1.97734 + 0.30823I
b = −0.423058 − 0.813762I
−1.62544 − 1.74532I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.938888 − 0.091208I
a = −1.97734 − 0.30823I
b = −0.423058 + 0.813762I
−1.62544 + 1.74532I 0
u = −0.409205 + 0.847594I
a = 0.52684 + 1.35884I
b = 0.302427 − 1.316010I
3.08304 + 4.83288I 0
u = −0.409205 − 0.847594I
a = 0.52684 − 1.35884I
b = 0.302427 + 1.316010I
3.08304 − 4.83288I 0
u = −0.902376 + 0.560219I
a = −0.88592 − 1.39955I
b = −0.575630 + 1.056400I
−6.90472 + 4.00909I 0
u = −0.902376 − 0.560219I
a = −0.88592 + 1.39955I
b = −0.575630 − 1.056400I
−6.90472 − 4.00909I 0
u = −0.775280 + 0.509017I
a = 0.0796447 + 0.0901063I
b = 1.081100 + 0.460110I
−3.92344 + 1.90005I 0
u = −0.775280 − 0.509017I
a = 0.0796447 − 0.0901063I
b = 1.081100 − 0.460110I
−3.92344 − 1.90005I 0
u = 1.047190 + 0.246665I
a = 1.76430 − 0.43224I
b = 0.616968 + 0.997278I
−4.00569 − 6.12775I 0
u = 1.047190 − 0.246665I
a = 1.76430 + 0.43224I
b = 0.616968 − 0.997278I
−4.00569 + 6.12775I 0
u = 0.965899 + 0.483062I
a = −0.0049121 + 0.0725376I
b = 0.408056 + 0.524170I
−4.20368 − 6.98905I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.965899 − 0.483062I
a = −0.0049121 − 0.0725376I
b = 0.408056 − 0.524170I
−4.20368 + 6.98905I 0
u = 0.493740 + 0.967666I
a = −0.1282740 − 0.0462710I
b = −1.115560 − 0.163228I
0.43091 − 5.89606I 0
u = 0.493740 − 0.967666I
a = −0.1282740 + 0.0462710I
b = −1.115560 + 0.163228I
0.43091 + 5.89606I 0
u = 1.091460 + 0.062412I
a = 1.35457 − 0.40708I
b = 0.693163 − 0.634356I
−5.11123 − 1.06296I 0
u = 1.091460 − 0.062412I
a = 1.35457 + 0.40708I
b = 0.693163 + 0.634356I
−5.11123 + 1.06296I 0
u = −0.697529 + 0.570729I
a = 0.099959 − 0.426434I
b = −0.665378 + 0.313323I
2.70854 + 2.21222I 0
u = −0.697529 − 0.570729I
a = 0.099959 + 0.426434I
b = −0.665378 − 0.313323I
2.70854 − 2.21222I 0
u = 0.482006 + 0.750145I
a = 0.224125 − 0.373842I
b = −0.899239 + 0.478152I
−2.15161 − 3.15660I 0
u = 0.482006 − 0.750145I
a = 0.224125 + 0.373842I
b = −0.899239 − 0.478152I
−2.15161 + 3.15660I 0
u = −0.766376 + 0.813066I
a = 0.193598 − 0.250455I
b = −0.817315 − 0.177510I
3.03000 + 2.69910I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.766376 − 0.813066I
a = 0.193598 + 0.250455I
b = −0.817315 + 0.177510I
3.03000 − 2.69910I 0
u = 1.068990 + 0.329115I
a = −0.566873 + 0.321498I
b = 0.108140 − 0.878237I
−0.309030 − 0.975544I 0
u = 1.068990 − 0.329115I
a = −0.566873 − 0.321498I
b = 0.108140 + 0.878237I
−0.309030 + 0.975544I 0
u = −0.142097 + 0.868320I
a = −0.41314 − 1.54711I
b = −0.084954 + 1.241910I
3.87976 − 0.76203I 0
u = −0.142097 − 0.868320I
a = −0.41314 + 1.54711I
b = −0.084954 − 1.241910I
3.87976 + 0.76203I 0
u = −0.544754 + 0.991787I
a = 0.647921 + 1.000990I
b = 0.601075 − 1.204190I
2.43301 + 5.31759I 0
u = −0.544754 − 0.991787I
a = 0.647921 − 1.000990I
b = 0.601075 + 1.204190I
2.43301 − 5.31759I 0
u = 0.332468 + 0.800674I
a = 0.54037 + 1.51501I
b = 0.310620 − 1.117390I
−1.93394 − 3.59448I 0
u = 0.332468 − 0.800674I
a = 0.54037 − 1.51501I
b = 0.310620 + 1.117390I
−1.93394 + 3.59448I 0
u = −0.945160 + 0.633454I
a = −0.0520476 − 0.0964746I
b = −1.099790 − 0.642821I
−6.23959 + 6.98143I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.945160 − 0.633454I
a = −0.0520476 + 0.0964746I
b = −1.099790 + 0.642821I
−6.23959 − 6.98143I 0
u = 0.559506 + 1.002350I
a = −0.48378 + 1.51997I
b = −0.659661 − 1.130090I
−0.14095 − 8.90764I 0
u = 0.559506 − 1.002350I
a = −0.48378 − 1.51997I
b = −0.659661 + 1.130090I
−0.14095 + 8.90764I 0
u = −1.131530 + 0.201429I
a = −0.0311714 − 0.0473643I
b = −0.505843 − 0.549552I
−8.55610 − 0.51653I 0
u = −1.131530 − 0.201429I
a = −0.0311714 + 0.0473643I
b = −0.505843 + 0.549552I
−8.55610 + 0.51653I 0
u = 1.152590 + 0.028082I
a = 1.81868 − 0.12420I
b = 0.748745 + 0.603153I
−5.03711 + 1.30340I 0
u = 1.152590 − 0.028082I
a = 1.81868 + 0.12420I
b = 0.748745 − 0.603153I
−5.03711 − 1.30340I 0
u = −0.592741 + 0.989525I
a = −0.29184 − 1.86030I
b = −0.043017 + 1.232660I
8.20160 + 4.60896I 0
u = −0.592741 − 0.989525I
a = −0.29184 + 1.86030I
b = −0.043017 − 1.232660I
8.20160 − 4.60896I 0
u = 0.992014 + 0.612550I
a = 0.391172 − 0.270225I
b = −0.501622 + 0.961337I
−1.85468 + 3.08743I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.992014 − 0.612550I
a = 0.391172 + 0.270225I
b = −0.501622 − 0.961337I
−1.85468 − 3.08743I 0
u = −0.792368 + 0.190746I
a = 0.67979 − 1.40241I
b = 0.628497 + 0.648119I
−0.107532 + 1.168680I 0
u = −0.792368 − 0.190746I
a = 0.67979 + 1.40241I
b = 0.628497 − 0.648119I
−0.107532 − 1.168680I 0
u = 0.105855 + 0.786102I
a = 0.184417 + 0.085720I
b = 1.189990 + 0.367385I
−0.722498 − 0.774565I 0
u = 0.105855 − 0.786102I
a = 0.184417 − 0.085720I
b = 1.189990 − 0.367385I
−0.722498 + 0.774565I 0
u = −0.960305 + 0.733846I
a = 0.84021 + 1.21591I
b = 0.690131 − 1.183640I
−1.58958 + 8.19357I 0
u = −0.960305 − 0.733846I
a = 0.84021 − 1.21591I
b = 0.690131 + 1.183640I
−1.58958 − 8.19357I 0
u = 1.219140 + 0.051643I
a = −0.940811 − 0.016798I
b = −0.452221 − 0.908343I
−1.30643 − 1.95102I 0
u = 1.219140 − 0.051643I
a = −0.940811 + 0.016798I
b = −0.452221 + 0.908343I
−1.30643 + 1.95102I 0
u = −0.872889 + 0.860169I
a = 1.24217 + 2.06389I
b = 0.451396 − 0.833928I
0.59629 + 4.24180I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.872889 − 0.860169I
a = 1.24217 − 2.06389I
b = 0.451396 + 0.833928I
0.59629 − 4.24180I 0
u = 0.517133 + 0.558525I
a = −0.86433 + 2.38447I
b = −0.426177 − 0.694272I
−2.75849 − 0.86457I 0
u = 0.517133 − 0.558525I
a = −0.86433 − 2.38447I
b = −0.426177 + 0.694272I
−2.75849 + 0.86457I 0
u = −1.028690 + 0.700070I
a = −0.286840 + 0.288830I
b = 0.461373 + 0.896592I
0.818942 + 0.469421I 0
u = −1.028690 − 0.700070I
a = −0.286840 − 0.288830I
b = 0.461373 − 0.896592I
0.818942 − 0.469421I 0
u = −0.895085 + 0.923482I
a = −0.207578 + 0.242694I
b = 0.963931 + 0.522551I
1.25794 + 6.76486I 0
u = −0.895085 − 0.923482I
a = −0.207578 − 0.242694I
b = 0.963931 − 0.522551I
1.25794 − 6.76486I 0
u = −1.065860 + 0.746555I
a = −0.89931 − 1.13648I
b = −0.793606 + 1.164820I
−4.5214 + 13.8088I 0
u = −1.065860 − 0.746555I
a = −0.89931 + 1.13648I
b = −0.793606 − 1.164820I
−4.5214 − 13.8088I 0
u = 1.301420 + 0.035128I
a = 0.834859 − 0.212634I
b = 0.637709 − 1.032430I
−3.72158 + 6.59471I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.301420 − 0.035128I
a = 0.834859 + 0.212634I
b = 0.637709 + 1.032430I
−3.72158 − 6.59471I 0
u = −0.398473 + 1.281640I
a = 1.54081 + 0.69231I
b = 0.666855 + 0.083688I
−1.00084 + 1.88868I 0
u = −0.398473 − 1.281640I
a = 1.54081 − 0.69231I
b = 0.666855 − 0.083688I
−1.00084 − 1.88868I 0
u = −0.892562 + 1.005700I
a = −0.93267 − 1.64956I
b = −0.538338 + 1.124520I
5.71587 + 7.50058I 0
u = −0.892562 − 1.005700I
a = −0.93267 + 1.64956I
b = −0.538338 − 1.124520I
5.71587 − 7.50058I 0
u = −0.570094 + 0.164046I
a = 0.78526 − 1.91154I
b = 0.513844 − 0.972227I
0.08922 + 5.31573I −12.0000 − 7.7377I
u = −0.570094 − 0.164046I
a = 0.78526 + 1.91154I
b = 0.513844 + 0.972227I
0.08922 − 5.31573I −12.0000 + 7.7377I
u = −0.975735 + 1.019780I
a = 1.02579 + 1.47641I
b = 0.693994 − 1.139140I
3.20116 + 12.82290I 0
u = −0.975735 − 1.019780I
a = 1.02579 − 1.47641I
b = 0.693994 + 1.139140I
3.20116 − 12.82290I 0
u = −0.584597 + 0.016376I
a = 0.10923 − 2.03567I
b = −0.666782 − 1.057980I
−2.44628 − 10.17080I −12.0000 + 10.9484I
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.584597 − 0.016376I
a = 0.10923 + 2.03567I
b = −0.666782 + 1.057980I
−2.44628 + 10.17080I −12.0000 − 10.9484I
u = 1.22060 + 0.80886I
a = 0.0633373 − 0.0188740I
b = 0.515312 − 0.615281I
−4.58140 − 5.74757I 0
u = 1.22060 − 0.80886I
a = 0.0633373 + 0.0188740I
b = 0.515312 + 0.615281I
−4.58140 + 5.74757I 0
u = 0.54817 + 1.36880I
a = −0.000295 − 1.321590I
b = 0.000328 + 1.373620I
6.49374 − 4.63447I 0
u = 0.54817 − 1.36880I
a = −0.000295 + 1.321590I
b = 0.000328 − 1.373620I
6.49374 + 4.63447I 0
u = 0.235054 + 0.435527I
a = −0.44541 + 2.70629I
b = 0.313701 + 0.441055I
−1.13956 + 1.32806I −11.56070 − 1.59690I
u = 0.235054 − 0.435527I
a = −0.44541 − 2.70629I
b = 0.313701 − 0.441055I
−1.13956 − 1.32806I −11.56070 + 1.59690I
u = 1.03024 + 1.12779I
a = −0.0909527 + 0.0034040I
b = −1.021900 + 0.393108I
−0.41432 − 8.09825I 0
u = 1.03024 − 1.12779I
a = −0.0909527 − 0.0034040I
b = −1.021900 − 0.393108I
−0.41432 + 8.09825I 0
u = 0.215053 + 0.376805I
a = 1.15910 − 1.68096I
b = 0.831125 + 1.109170I
0.78134 − 8.18503I −11.0423 + 10.8586I
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.215053 − 0.376805I
a = 1.15910 + 1.68096I
b = 0.831125 − 1.109170I
0.78134 + 8.18503I −11.0423 − 10.8586I
u = −0.387457 + 0.149103I
a = −4.72172 − 0.28820I
b = −0.828826 − 0.592006I
−3.89027 + 4.57234I −17.0773 − 7.0245I
u = −0.387457 − 0.149103I
a = −4.72172 + 0.28820I
b = −0.828826 + 0.592006I
−3.89027 − 4.57234I −17.0773 + 7.0245I
u = 0.362965 + 0.162049I
a = −3.25229 + 2.00494I
b = 0.194051 + 0.668016I
−1.14181 + 1.35551I −11.47001 − 3.30210I
u = 0.362965 − 0.162049I
a = −3.25229 − 2.00494I
b = 0.194051 − 0.668016I
−1.14181 − 1.35551I −11.47001 + 3.30210I
u = −0.028016 + 0.389254I
a = −0.86778 + 2.14055I
b = −0.731170 − 1.053620I
3.98035 − 2.83956I −4.97619 + 5.97507I
u = −0.028016 − 0.389254I
a = −0.86778 − 2.14055I
b = −0.731170 + 1.053620I
3.98035 + 2.83956I −4.97619 − 5.97507I
u = 0.389939
a = −0.687099
b = 0.395152
−0.675214 −14.6290
u = 0.000187 + 0.387852I
a = 0.107141 + 0.910785I
b = 0.736606 + 0.101583I
−0.839116 + 0.254597I −10.56987 + 0.84875I
u = 0.000187 − 0.387852I
a = 0.107141 − 0.910785I
b = 0.736606 − 0.101583I
−0.839116 − 0.254597I −10.56987 − 0.84875I
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.78522 + 1.40814I
a = −0.222654 + 1.317030I
b = −0.204658 − 1.363680I
6.10627 − 10.54450I 0
u = 0.78522 − 1.40814I
a = −0.222654 − 1.317030I
b = −0.204658 + 1.363680I
6.10627 + 10.54450I 0
u = 1.14927 + 1.14541I
a = 0.82442 − 1.44113I
b = 0.541886 + 1.019480I
−3.27476 − 10.10590I 0
u = 1.14927 − 1.14541I
a = 0.82442 + 1.44113I
b = 0.541886 − 1.019480I
−3.27476 + 10.10590I 0
u = 1.20230 + 1.20093I
a = 0.0903320 − 0.0153408I
b = 1.081690 − 0.612879I
−2.58803 − 12.99720I 0
u = 1.20230 − 1.20093I
a = 0.0903320 + 0.0153408I
b = 1.081690 + 0.612879I
−2.58803 + 12.99720I 0
u = −0.232112 + 0.164649I
a = −3.39764 + 4.61356I
b = −0.619424 + 0.699430I
−4.15839 + 2.13695I −17.5319 − 6.2575I
u = −0.232112 − 0.164649I
a = −3.39764 − 4.61356I
b = −0.619424 − 0.699430I
−4.15839 − 2.13695I −17.5319 + 6.2575I
u = 0.93590 + 1.48686I
a = −0.90016 + 2.49308I
b = −0.193008 − 0.474455I
−2.43184 + 0.84245I 0
u = 0.93590 − 1.48686I
a = −0.90016 − 2.49308I
b = −0.193008 + 0.474455I
−2.43184 − 0.84245I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.76516 + 0.21267I
a = 0.312954 + 0.516295I
b = 0.494219 − 1.032940I
1.26936 + 5.44661I 0
u = −1.76516 − 0.21267I
a = 0.312954 − 0.516295I
b = 0.494219 + 1.032940I
1.26936 − 5.44661I 0
u = 1.23776 + 1.28958I
a = −0.736692 + 1.195200I
b = −0.659884 − 1.184340I
2.0610 − 14.1160I 0
u = 1.23776 − 1.28958I
a = −0.736692 − 1.195200I
b = −0.659884 + 1.184340I
2.0610 + 14.1160I 0
u = −0.037150 + 0.176825I
a = −0.16567 − 10.12740I
b = −0.586562 + 0.959572I
−3.34466 + 2.62448I −15.9889 − 1.0472I
u = −0.037150 − 0.176825I
a = −0.16567 + 10.12740I
b = −0.586562 − 0.959572I
−3.34466 − 2.62448I −15.9889 + 1.0472I
u = −0.112443 + 0.133560I
a = −2.23281 + 0.77149I
b = 0.919315 − 0.803419I
−0.19016 − 1.46770I −5.26638 + 3.44001I
u = −0.112443 − 0.133560I
a = −2.23281 − 0.77149I
b = 0.919315 + 0.803419I
−0.19016 + 1.46770I −5.26638 − 3.44001I
u = −0.162629
a = −0.241003
b = −1.60820
−10.5373 −421.260
u = 1.33820 + 1.27595I
a = 0.812233 − 1.096010I
b = 0.776955 + 1.167520I
−0.7851 − 19.7119I 0
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.33820 − 1.27595I
a = 0.812233 + 1.096010I
b = 0.776955 − 1.167520I
−0.7851 + 19.7119I 0
u = −1.84994 + 1.16767I
a = −0.268121 − 0.716754I
b = −0.161584 + 1.002220I
2.76309 + 0.92048I 0
u = −1.84994 − 1.16767I
a = −0.268121 + 0.716754I
b = −0.161584 − 1.002220I
2.76309 − 0.92048I 0
u = −3.09726 + 4.26344I
a = 0.245780 − 0.852545I
b = 0.354878 + 1.013590I
2.08506 − 0.96748I 0
u = −3.09726 − 4.26344I
a = 0.245780 + 0.852545I
b = 0.354878 − 1.013590I
2.08506 + 0.96748I 0
u = 1.50261 + 5.46217I
a = −0.986527 − 0.592195I
b = −0.733347 + 0.404998I
−1.87304 − 0.83221I 0
u = 1.50261 − 5.46217I
a = −0.986527 + 0.592195I
b = −0.733347 − 0.404998I
−1.87304 + 0.83221I 0
u = −6.26376 + 4.79909I
a = −0.372172 + 0.692722I
b = −0.582621 − 1.073900I
0.04635 − 5.79605I 0
u = −6.26376 − 4.79909I
a = −0.372172 − 0.692722I
b = −0.582621 + 1.073900I
0.04635 + 5.79605I 0
17
II.
I
u
2
= hb, u
7
−u
6
−u
5
+3u
4
+u
3
−3u
2
+a+3, u
8
−u
7
−u
6
+2u
5
+u
4
−2u
3
+2u−1i
(i) Arc colorings
a
8
=
1
0
a
12
=
0
u
a
4
=
−u
7
+ u
6
+ u
5
− 3u
4
− u
3
+ 3u
2
− 3
0
a
9
=
1
u
2
a
3
=
−u
7
+ u
6
+ u
5
− 3u
4
− u
3
+ 3u
2
− 3
0
a
7
=
1
0
a
6
=
−u
2
+ 1
−u
4
a
10
=
u
4
− u
2
+ 1
u
6
+ u
2
a
1
=
u
6
− u
4
+ 2u
2
− 1
u
6
+ u
2
a
11
=
u
u
a
5
=
−u
6
+ u
4
− 2u
2
+ 1
−u
6
− u
2
a
2
=
−u
7
+ 2u
6
+ u
5
− 4u
4
− u
3
+ 5u
2
− 4
u
6
+ u
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = u
7
− 4u
6
− 2u
5
+ 5u
4
+ 3u
3
− 5u
2
− 5u − 10
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
8
c
3
, c
7
u
8
c
4
(u + 1)
8
c
5
, c
10
u
8
+ u
7
− 3u
6
− 2u
5
+ 3u
4
+ 2u − 1
c
6
u
8
− 3u
7
+ 7u
6
− 10u
5
+ 11u
4
− 10u
3
+ 6u
2
− 4u + 1
c
8
u
8
− u
7
− u
6
+ 2u
5
+ u
4
− 2u
3
+ 2u − 1
c
9
u
8
+ 3u
7
+ 7u
6
+ 10u
5
+ 11u
4
+ 10u
3
+ 6u
2
+ 4u + 1
c
11
u
8
+ u
7
− u
6
− 2u
5
+ u
4
+ 2u
3
− 2u − 1
c
12
u
8
− u
7
− 3u
6
+ 2u
5
+ 3u
4
− 2u − 1
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
8
c
3
, c
7
y
8
c
5
, c
10
, c
12
y
8
− 7y
7
+ 19y
6
− 22y
5
+ 3y
4
+ 14y
3
− 6y
2
− 4y + 1
c
6
, c
9
y
8
+ 5y
7
+ 11y
6
+ 6y
5
− 17y
4
− 34y
3
− 22y
2
− 4y + 1
c
8
, c
11
y
8
− 3y
7
+ 7y
6
− 10y
5
+ 11y
4
− 10y
3
+ 6y
2
− 4y + 1
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.570868 + 0.730671I
a = −1.21928 + 2.03110I
b = 0
−2.68559 + 1.13123I −18.1377 − 5.3065I
u = 0.570868 − 0.730671I
a = −1.21928 − 2.03110I
b = 0
−2.68559 − 1.13123I −18.1377 + 5.3065I
u = −0.855237 + 0.665892I
a = 1.230330 + 0.083902I
b = 0
0.51448 + 2.57849I −10.11893 − 3.45077I
u = −0.855237 − 0.665892I
a = 1.230330 − 0.083902I
b = 0
0.51448 − 2.57849I −10.11893 + 3.45077I
u = −1.09818
a = −0.337834
b = 0
−8.14766 −12.9880
u = 1.031810 + 0.655470I
a = 0.370895 + 0.073482I
b = 0
−4.02461 − 6.44354I −10.82984 + 2.68172I
u = 1.031810 − 0.655470I
a = 0.370895 − 0.073482I
b = 0
−4.02461 + 6.44354I −10.82984 − 2.68172I
u = 0.603304
a = −2.42604
b = 0
−2.48997 −13.8390
21
III. I
u
3
= hb + 3u − 2, a + 3u − 1, 9u
2
− 9u + 1i
(i) Arc colorings
a
8
=
1
0
a
12
=
0
u
a
4
=
−3u + 1
−3u + 2
a
9
=
1
u −
1
9
a
3
=
−6u + 3
−3u + 2
a
7
=
0
3u − 3
a
6
=
3u − 3
8
3
u − 3
a
10
=
−9u + 9
−8u + 8
a
1
=
9u − 9
9u − 8
a
11
=
0
u
a
5
=
3u − 3
3u − 3
a
2
=
−2
3u − 3
(ii) Obstruction class = 1
(iii) Cusp Shapes = −560u +
4285
9
22
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
2
− 3u + 1
c
2
, c
3
u
2
+ u − 1
c
4
, c
7
u
2
− u − 1
c
5
(3u + 1)
2
c
8
9u
2
− 9u + 1
c
9
u
2
+ 3u + 1
c
10
(u − 1)
2
c
11
u
2
c
12
(u + 1)
2
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
, c
9
y
2
− 7y + 1
c
2
, c
3
, c
4
c
7
y
2
− 3y + 1
c
5
(9y −1)
2
c
8
81y
2
− 63y + 1
c
10
, c
12
(y −1)
2
c
11
y
2
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.872678
a = −1.61803
b = −0.618034
−2.63189 −12.5890
u = 0.127322
a = 0.618034
b = 1.61803
−10.5276 404.810
25
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
8
)(u
2
− 3u + 1)(u
129
+ 68u
128
+ ··· + 31u + 1)
c
2
((u − 1)
8
)(u
2
+ u − 1)(u
129
− 10u
128
+ ··· + 5u − 1)
c
3
u
8
(u
2
+ u − 1)(u
129
+ 2u
128
+ ··· + 896u + 256)
c
4
((u + 1)
8
)(u
2
− u − 1)(u
129
− 10u
128
+ ··· + 5u − 1)
c
5
(3u + 1)
2
(u
8
+ u
7
− 3u
6
− 2u
5
+ 3u
4
+ 2u − 1)
· (9u
129
− 72u
128
+ ··· − 1416882u + 58007)
c
6
(u
2
− 3u + 1)(u
8
− 3u
7
+ 7u
6
− 10u
5
+ 11u
4
− 10u
3
+ 6u
2
− 4u + 1)
· (u
129
− 3u
128
+ ··· + 3u − 1)
c
7
u
8
(u
2
− u − 1)(u
129
+ 2u
128
+ ··· + 896u + 256)
c
8
(9u
2
− 9u + 1)(u
8
− u
7
− u
6
+ 2u
5
+ u
4
− 2u
3
+ 2u − 1)
· (9u
129
− 111u
128
+ ··· + 5137u − 257)
c
9
(u
2
+ 3u + 1)(u
8
+ 3u
7
+ 7u
6
+ 10u
5
+ 11u
4
+ 10u
3
+ 6u
2
+ 4u + 1)
· (u
129
− 3u
128
+ ··· + 3u − 1)
c
10
(u − 1)
2
(u
8
+ u
7
− 3u
6
− 2u
5
+ 3u
4
+ 2u − 1)
· (u
129
− 4u
128
+ ··· + 810u − 81)
c
11
u
2
(u
8
+ u
7
− u
6
− 2u
5
+ u
4
+ 2u
3
− 2u − 1)
· (u
129
− 2u
128
+ ··· − 5940u + 324)
c
12
(u + 1)
2
(u
8
− u
7
− 3u
6
+ 2u
5
+ 3u
4
− 2u − 1)
· (u
129
− 4u
128
+ ··· + 810u − 81)
26
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y −1)
8
)(y
2
− 7y + 1)(y
129
− 4y
128
+ ··· + 1563y −1)
c
2
, c
4
((y −1)
8
)(y
2
− 3y + 1)(y
129
− 68y
128
+ ··· + 31y −1)
c
3
, c
7
y
8
(y
2
− 3y + 1)(y
129
+ 48y
128
+ ··· − 933888y −65536)
c
5
(9y −1)
2
(y
8
− 7y
7
+ 19y
6
− 22y
5
+ 3y
4
+ 14y
3
− 6y
2
− 4y + 1)
· (81y
129
− 1926y
128
+ ··· + 458235777734y −3364812049)
c
6
, c
9
(y
2
− 7y + 1)(y
8
+ 5y
7
+ ··· − 4y + 1)
· (y
129
+ 69y
128
+ ··· + 31y −1)
c
8
(81y
2
− 63y + 1)(y
8
− 3y
7
+ ··· − 4y + 1)
· (81y
129
+ 1953y
128
+ ··· − 1315317y −66049)
c
10
, c
12
(y −1)
2
(y
8
− 7y
7
+ 19y
6
− 22y
5
+ 3y
4
+ 14y
3
− 6y
2
− 4y + 1)
· (y
129
− 82y
128
+ ··· + 92178y −6561)
c
11
y
2
(y
8
− 3y
7
+ 7y
6
− 10y
5
+ 11y
4
− 10y
3
+ 6y
2
− 4y + 1)
· (y
129
+ 12y
128
+ ··· + 12906216y −104976)
27
