12a
0321
(K12a
0321
)
A knot diagram
1
Linearized knot diagam
3 6 8 11 2 10 5 12 1 7 4 9
Solving Sequence
6,10
7
3,11
2 1 5 8 4 9 12
c
6
c
10
c
2
c
1
c
5
c
7
c
4
c
9
c
12
c
3
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.99007 × 10
472
u
108
+ 6.02795 × 10
472
u
107
+ ··· + 7.29945 × 10
473
b + 1.94243 × 10
476
,
1.10968 × 10
476
u
108
− 2.92557 × 10
476
u
107
+ ··· + 7.29288 × 10
477
a − 1.87345 × 10
480
,
u
109
− 2u
108
+ ··· − 109940u − 9991i
I
u
2
= h−25716144203u
24
− 112935246648u
23
+ ··· + 50148875831b + 138327033199,
80137258579u
24
+ 357502315466u
23
+ ··· + 50148875831a − 608633590610,
u
25
+ 4u
24
+ ··· − 8u + 1i
I
u
3
= hb + 1, a + 2, u − 1i
* 3 irreducible components of dim
C
= 0, with total 135 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−1.99 × 10
472
u
108
+ 6.03 × 10
472
u
107
+ · · · + 7.30 × 10
473
b + 1.94 ×
10
476
, 1.11 × 10
476
u
108
− 2.93 × 10
476
u
107
+ · · · + 7.29 × 10
477
a − 1.87 ×
10
480
, u
109
− 2u
108
+ · · · − 109940u − 9991i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
u
a
7
=
1
u
2
a
3
=
−0.0152159u
108
+ 0.0401154u
107
+ ··· + 2397.87u + 256.887
0.0272632u
108
− 0.0825809u
107
+ ··· − 2662.37u − 266.107
a
11
=
−u
−u
3
+ u
a
2
=
0.0120473u
108
− 0.0424655u
107
+ ··· − 264.498u − 9.21983
0.0272632u
108
− 0.0825809u
107
+ ··· − 2662.37u − 266.107
a
1
=
−0.0309536u
108
+ 0.0971956u
107
+ ··· + 2759.58u + 267.809
0.0291866u
108
− 0.0948676u
107
+ ··· − 1781.19u − 152.041
a
5
=
−0.0360067u
108
+ 0.116129u
107
+ ··· + 2679.86u + 247.676
−0.0501905u
108
+ 0.151970u
107
+ ··· + 5267.74u + 535.227
a
8
=
−0.0121877u
108
+ 0.0321171u
107
+ ··· + 1791.13u + 187.009
−0.0198379u
108
+ 0.0648994u
107
+ ··· + 1260.31u + 108.071
a
4
=
0.00315228u
108
− 0.00784644u
107
+ ··· − 853.506u − 104.441
−0.0345567u
108
+ 0.100254u
107
+ ··· + 4172.79u + 431.183
a
9
=
0.0243292u
108
− 0.0776944u
107
+ ··· − 1908.35u − 190.269
−0.0436852u
108
+ 0.132054u
107
+ ··· + 4815.21u + 501.459
a
12
=
−0.0202956u
108
+ 0.0688861u
107
+ ··· + 1125.32u + 103.804
−0.0285451u
108
+ 0.0917335u
107
+ ··· + 2214.88u + 212.091
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.0628061u
108
− 0.159694u
107
+ ··· − 11604.2u − 1313.19
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
109
+ 53u
108
+ ··· + 114u + 1
c
2
, c
5
u
109
+ 5u
108
+ ··· + 18u + 1
c
3
u
109
+ 3u
108
+ ··· + 9062344u + 742717
c
4
, c
11
u
109
− 4u
108
+ ··· + 10u − 1
c
6
, c
10
u
109
− 2u
108
+ ··· − 109940u − 9991
c
7
u
109
− 7u
108
+ ··· − 1323756u + 105511
c
8
, c
9
, c
12
u
109
+ 3u
108
+ ··· + 95u − 7
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
109
+ 19y
108
+ ··· + 7262y −1
c
2
, c
5
y
109
− 53y
108
+ ··· + 114y −1
c
3
y
109
− 47y
108
+ ··· + 31084038325668y −551628542089
c
4
, c
11
y
109
+ 100y
108
+ ··· + 112y −1
c
6
, c
10
y
109
− 92y
108
+ ··· + 1884094310y −99820081
c
7
y
109
− 35y
108
+ ··· + 312381658400y −11132571121
c
8
, c
9
, c
12
y
109
− 117y
108
+ ··· − 537y −49
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.927360 + 0.368807I
a = −0.004486 + 0.281853I
b = 0.541893 + 0.407683I
−0.881908 − 0.499794I 0
u = −0.927360 − 0.368807I
a = −0.004486 − 0.281853I
b = 0.541893 − 0.407683I
−0.881908 + 0.499794I 0
u = −0.001942 + 0.975609I
a = 0.359346 + 1.195970I
b = −0.532276 − 0.624869I
−0.33225 + 2.57093I 0
u = −0.001942 − 0.975609I
a = 0.359346 − 1.195970I
b = −0.532276 + 0.624869I
−0.33225 − 2.57093I 0
u = 1.057370 + 0.207259I
a = 0.024452 + 0.732775I
b = −0.631857 − 0.932609I
−3.02837 − 3.95297I 0
u = 1.057370 − 0.207259I
a = 0.024452 − 0.732775I
b = −0.631857 + 0.932609I
−3.02837 + 3.95297I 0
u = −0.892897 + 0.611548I
a = −0.498464 − 0.905635I
b = 0.661982 + 0.108547I
−4.68433 + 2.02276I 0
u = −0.892897 − 0.611548I
a = −0.498464 + 0.905635I
b = 0.661982 − 0.108547I
−4.68433 − 2.02276I 0
u = 1.08678
a = −1.37532
b = −1.15010
−4.90949 0
u = −0.141033 + 1.081570I
a = −0.735304 − 0.856968I
b = 1.115130 + 0.539463I
−4.62116 − 6.15750I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.141033 − 1.081570I
a = −0.735304 + 0.856968I
b = 1.115130 − 0.539463I
−4.62116 + 6.15750I 0
u = 1.042030 + 0.340775I
a = −0.342757 + 0.367631I
b = 0.307587 − 0.839493I
0.59322 − 2.98567I 0
u = 1.042030 − 0.340775I
a = −0.342757 − 0.367631I
b = 0.307587 + 0.839493I
0.59322 + 2.98567I 0
u = 0.481404 + 0.728442I
a = 1.58446 − 0.53180I
b = −1.077880 + 0.314975I
−6.22931 + 1.23975I 0
u = 0.481404 − 0.728442I
a = 1.58446 + 0.53180I
b = −1.077880 − 0.314975I
−6.22931 − 1.23975I 0
u = −0.164225 + 1.134570I
a = 0.234584 − 1.329010I
b = −1.001660 + 0.578622I
−1.68142 + 7.31001I 0
u = −0.164225 − 1.134570I
a = 0.234584 + 1.329010I
b = −1.001660 − 0.578622I
−1.68142 − 7.31001I 0
u = −1.146230 + 0.151412I
a = −0.421695 − 1.097710I
b = −1.39389 + 0.83781I
−10.94360 + 3.34958I 0
u = −1.146230 − 0.151412I
a = −0.421695 + 1.097710I
b = −1.39389 − 0.83781I
−10.94360 − 3.34958I 0
u = −1.117690 + 0.324951I
a = −0.82076 − 1.63481I
b = −1.040340 + 0.440134I
−2.81887 + 3.16219I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.117690 − 0.324951I
a = −0.82076 + 1.63481I
b = −1.040340 − 0.440134I
−2.81887 − 3.16219I 0
u = −1.171050 + 0.062575I
a = 0.243573 − 0.861666I
b = −0.75611 + 1.19829I
−8.95265 + 4.63111I 0
u = −1.171050 − 0.062575I
a = 0.243573 + 0.861666I
b = −0.75611 − 1.19829I
−8.95265 − 4.63111I 0
u = 1.173030 + 0.041004I
a = −0.540423 + 0.900178I
b = −1.212730 − 0.663125I
−4.98444 − 2.41357I 0
u = 1.173030 − 0.041004I
a = −0.540423 − 0.900178I
b = −1.212730 + 0.663125I
−4.98444 + 2.41357I 0
u = −1.176150 + 0.036021I
a = 1.51938 − 1.46237I
b = 1.066390 + 0.426048I
−6.86041 − 0.88784I 0
u = −1.176150 − 0.036021I
a = 1.51938 + 1.46237I
b = 1.066390 − 0.426048I
−6.86041 + 0.88784I 0
u = 0.108220 + 1.194260I
a = −0.04457 − 1.44047I
b = −0.381359 + 0.662655I
−6.68074 − 5.67638I 0
u = 0.108220 − 1.194260I
a = −0.04457 + 1.44047I
b = −0.381359 − 0.662655I
−6.68074 + 5.67638I 0
u = −1.136990 + 0.387269I
a = −0.468289 − 0.722813I
b = 0.211741 + 1.127560I
−5.03193 + 5.61101I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.136990 − 0.387269I
a = −0.468289 + 0.722813I
b = 0.211741 − 1.127560I
−5.03193 − 5.61101I 0
u = 1.198400 + 0.113222I
a = 0.51876 − 1.94605I
b = 1.122610 + 0.582933I
−13.0830 − 7.0865I 0
u = 1.198400 − 0.113222I
a = 0.51876 + 1.94605I
b = 1.122610 − 0.582933I
−13.0830 + 7.0865I 0
u = 1.181720 + 0.307746I
a = 0.678893 − 0.995764I
b = −0.423479 + 0.760999I
−6.45027 − 1.36251I 0
u = 1.181720 − 0.307746I
a = 0.678893 + 0.995764I
b = −0.423479 − 0.760999I
−6.45027 + 1.36251I 0
u = −0.247531 + 0.733819I
a = 0.56761 + 1.55074I
b = 0.310446 − 0.709793I
−2.28524 − 1.40023I 0
u = −0.247531 − 0.733819I
a = 0.56761 − 1.55074I
b = 0.310446 + 0.709793I
−2.28524 + 1.40023I 0
u = 1.226970 + 0.097481I
a = −0.862780 − 0.648315I
b = 0.394183 + 0.774439I
−10.89780 + 1.94807I 0
u = 1.226970 − 0.097481I
a = −0.862780 + 0.648315I
b = 0.394183 − 0.774439I
−10.89780 − 1.94807I 0
u = 0.032475 + 0.748168I
a = −0.528278 + 1.089850I
b = 0.936740 − 0.608484I
1.92695 + 3.99796I −3.21801 − 6.20905I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.032475 − 0.748168I
a = −0.528278 − 1.089850I
b = 0.936740 + 0.608484I
1.92695 − 3.99796I −3.21801 + 6.20905I
u = 0.316631 + 0.673261I
a = −0.040172 − 1.317730I
b = 0.661258 + 0.648032I
2.74013 − 0.88698I 0
u = 0.316631 − 0.673261I
a = −0.040172 + 1.317730I
b = 0.661258 − 0.648032I
2.74013 + 0.88698I 0
u = −1.25835
a = −0.260141
b = −1.65764
−11.9769 0
u = −0.733035
a = 0.648851
b = −0.107199
−0.968982 −9.84640
u = 1.248920 + 0.255227I
a = 1.253130 + 0.044705I
b = 1.106620 − 0.157497I
−9.54974 − 5.10430I 0
u = 1.248920 − 0.255227I
a = 1.253130 − 0.044705I
b = 1.106620 + 0.157497I
−9.54974 + 5.10430I 0
u = −1.201150 + 0.436460I
a = −0.171617 − 0.684167I
b = −0.220383 + 0.206899I
−4.39780 + 2.11444I 0
u = −1.201150 − 0.436460I
a = −0.171617 + 0.684167I
b = −0.220383 − 0.206899I
−4.39780 − 2.11444I 0
u = −1.224520 + 0.378182I
a = 0.077221 − 0.365173I
b = −0.298317 − 0.328543I
−4.36955 + 2.20355I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.224520 − 0.378182I
a = 0.077221 + 0.365173I
b = −0.298317 + 0.328543I
−4.36955 − 2.20355I 0
u = 1.186760 + 0.526901I
a = 1.16922 − 1.11264I
b = 0.943150 + 0.121171I
−9.22014 − 5.07106I 0
u = 1.186760 − 0.526901I
a = 1.16922 + 1.11264I
b = 0.943150 − 0.121171I
−9.22014 + 5.07106I 0
u = −0.463740 + 0.510377I
a = 0.067072 − 1.240980I
b = 0.893561 − 0.026652I
−4.67096 + 1.93516I −15.9176 − 3.5896I
u = −0.463740 − 0.510377I
a = 0.067072 + 1.240980I
b = 0.893561 + 0.026652I
−4.67096 − 1.93516I −15.9176 + 3.5896I
u = −1.299780 + 0.179706I
a = 0.972081 + 0.717778I
b = 1.046880 − 0.479841I
−2.54445 + 3.37243I 0
u = −1.299780 − 0.179706I
a = 0.972081 − 0.717778I
b = 1.046880 + 0.479841I
−2.54445 − 3.37243I 0
u = 1.264240 + 0.390206I
a = 0.73496 − 1.23757I
b = 1.147500 + 0.584416I
−1.89007 − 8.23554I 0
u = 1.264240 − 0.390206I
a = 0.73496 + 1.23757I
b = 1.147500 − 0.584416I
−1.89007 + 8.23554I 0
u = 1.252170 + 0.558161I
a = −0.08507 + 1.67329I
b = −1.108000 − 0.585173I
−8.50772 − 6.47710I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.252170 − 0.558161I
a = −0.08507 − 1.67329I
b = −1.108000 + 0.585173I
−8.50772 + 6.47710I 0
u = −1.288050 + 0.518655I
a = 0.41587 + 1.40242I
b = 1.26484 − 0.63490I
−8.2774 + 11.7660I 0
u = −1.288050 − 0.518655I
a = 0.41587 − 1.40242I
b = 1.26484 + 0.63490I
−8.2774 − 11.7660I 0
u = 1.313920 + 0.456848I
a = 0.448450 − 0.453491I
b = −0.368355 + 0.821745I
−4.47485 − 7.63949I 0
u = 1.313920 − 0.456848I
a = 0.448450 + 0.453491I
b = −0.368355 − 0.821745I
−4.47485 + 7.63949I 0
u = −1.40284 + 0.26612I
a = −1.27343 − 0.81645I
b = −1.075530 + 0.475402I
−6.50588 + 6.06163I 0
u = −1.40284 − 0.26612I
a = −1.27343 + 0.81645I
b = −1.075530 − 0.475402I
−6.50588 − 6.06163I 0
u = −0.514954 + 0.241943I
a = 1.287940 + 0.250825I
b = −0.694966 − 0.159105I
−1.130220 − 0.058098I −6.31168 − 0.93824I
u = −0.514954 − 0.241943I
a = 1.287940 − 0.250825I
b = −0.694966 + 0.159105I
−1.130220 + 0.058098I −6.31168 + 0.93824I
u = −0.539163 + 0.088043I
a = −0.63521 + 1.61057I
b = 0.871250 − 0.779499I
1.25521 + 2.92708I −20.6191 − 7.0979I
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.539163 − 0.088043I
a = −0.63521 − 1.61057I
b = 0.871250 + 0.779499I
1.25521 − 2.92708I −20.6191 + 7.0979I
u = −0.136443 + 0.527344I
a = 1.68053 − 0.92025I
b = −0.723335 + 0.458886I
−0.79469 + 1.36894I −9.17150 − 4.18616I
u = −0.136443 − 0.527344I
a = 1.68053 + 0.92025I
b = −0.723335 − 0.458886I
−0.79469 − 1.36894I −9.17150 + 4.18616I
u = 0.85209 + 1.22980I
a = −0.664286 + 0.651414I
b = 1.051060 − 0.329189I
−10.33410 − 3.36596I 0
u = 0.85209 − 1.22980I
a = −0.664286 − 0.651414I
b = 1.051060 + 0.329189I
−10.33410 + 3.36596I 0
u = −0.374092 + 0.331035I
a = 1.032560 − 0.927902I
b = −1.142870 − 0.573781I
−8.60926 − 1.47993I −14.4229 + 2.1286I
u = −0.374092 − 0.331035I
a = 1.032560 + 0.927902I
b = −1.142870 + 0.573781I
−8.60926 + 1.47993I −14.4229 − 2.1286I
u = −1.48071 + 0.25387I
a = 0.319112 − 0.074073I
b = 1.404500 + 0.116946I
−18.0245 + 7.5939I 0
u = −1.48071 − 0.25387I
a = 0.319112 + 0.074073I
b = 1.404500 − 0.116946I
−18.0245 − 7.5939I 0
u = 0.480994 + 0.126570I
a = −1.96808 − 2.47848I
b = 1.076970 − 0.299233I
−10.61350 + 5.99402I −18.1018 − 3.7342I
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.480994 − 0.126570I
a = −1.96808 + 2.47848I
b = 1.076970 + 0.299233I
−10.61350 − 5.99402I −18.1018 + 3.7342I
u = 0.098496 + 0.483051I
a = 1.228410 + 0.028238I
b = −0.443278 + 0.446712I
−0.67889 + 1.28300I −6.58010 − 4.63125I
u = 0.098496 − 0.483051I
a = 1.228410 − 0.028238I
b = −0.443278 − 0.446712I
−0.67889 − 1.28300I −6.58010 + 4.63125I
u = 0.109455 + 0.479164I
a = −0.82993 + 1.99601I
b = −0.929731 − 0.602032I
−1.52384 − 3.08285I −9.69293 + 2.06484I
u = 0.109455 − 0.479164I
a = −0.82993 − 1.99601I
b = −0.929731 + 0.602032I
−1.52384 + 3.08285I −9.69293 − 2.06484I
u = −1.42468 + 0.49590I
a = 0.427632 + 0.788644I
b = −0.357295 − 1.022260I
−11.6087 + 11.5120I 0
u = −1.42468 − 0.49590I
a = 0.427632 − 0.788644I
b = −0.357295 + 1.022260I
−11.6087 − 11.5120I 0
u = −1.49024 + 0.24040I
a = −0.370784 + 0.651679I
b = −1.026120 − 0.440412I
−6.45908 − 1.19336I 0
u = −1.49024 − 0.24040I
a = −0.370784 − 0.651679I
b = −1.026120 + 0.440412I
−6.45908 + 1.19336I 0
u = 1.43521 + 0.47001I
a = −0.71708 + 1.34700I
b = −1.134240 − 0.591143I
−6.7727 − 12.9003I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.43521 − 0.47001I
a = −0.71708 − 1.34700I
b = −1.134240 + 0.591143I
−6.7727 + 12.9003I 0
u = 1.57342 + 0.01663I
a = −0.628685 + 0.255232I
b = −1.076440 + 0.245301I
−15.4353 + 0.3798I 0
u = 1.57342 − 0.01663I
a = −0.628685 − 0.255232I
b = −1.076440 − 0.245301I
−15.4353 − 0.3798I 0
u = 0.21277 + 1.56571I
a = 0.441834 + 1.098900I
b = −1.093730 − 0.544984I
−8.76583 − 10.38610I 0
u = 0.21277 − 1.56571I
a = 0.441834 − 1.098900I
b = −1.093730 + 0.544984I
−8.76583 + 10.38610I 0
u = −0.323820 + 0.250962I
a = −0.72155 − 1.63819I
b = −0.449755 − 0.739128I
−6.46389 − 3.71609I −11.41713 + 1.73666I
u = −0.323820 − 0.250962I
a = −0.72155 + 1.63819I
b = −0.449755 + 0.739128I
−6.46389 + 3.71609I −11.41713 − 1.73666I
u = 1.46267 + 0.69119I
a = −0.404631 + 1.074490I
b = 0.459672 − 0.742288I
−10.52840 − 0.73929I 0
u = 1.46267 − 0.69119I
a = −0.404631 − 1.074490I
b = 0.459672 + 0.742288I
−10.52840 + 0.73929I 0
u = −1.52696 + 0.58294I
a = −0.34024 − 1.38124I
b = −1.212060 + 0.653074I
−14.2664 + 17.5419I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.52696 − 0.58294I
a = −0.34024 + 1.38124I
b = −1.212060 − 0.653074I
−14.2664 − 17.5419I 0
u = −1.47302 + 0.79032I
a = 0.289378 + 1.321630I
b = 1.038930 − 0.449583I
−6.42133 + 5.28910I 0
u = −1.47302 − 0.79032I
a = 0.289378 − 1.321630I
b = 1.038930 + 0.449583I
−6.42133 − 5.28910I 0
u = 1.66666 + 0.21470I
a = 0.342970 + 0.113767I
b = 1.037410 − 0.252350I
−10.88430 + 0.64765I 0
u = 1.66666 − 0.21470I
a = 0.342970 − 0.113767I
b = 1.037410 + 0.252350I
−10.88430 − 0.64765I 0
u = 1.63703 + 0.96366I
a = −0.009749 − 1.382130I
b = 1.088920 + 0.588620I
−12.41950 − 5.82148I 0
u = 1.63703 − 0.96366I
a = −0.009749 + 1.382130I
b = 1.088920 − 0.588620I
−12.41950 + 5.82148I 0
u = 2.12651 + 0.36116I
a = −0.203081 − 0.490165I
b = −0.997778 + 0.268752I
−14.7882 + 0.8898I 0
u = 2.12651 − 0.36116I
a = −0.203081 + 0.490165I
b = −0.997778 − 0.268752I
−14.7882 − 0.8898I 0
15
II.
I
u
2
= h−2.57×10
10
u
24
−1.13×10
11
u
23
+· · ·+5.01×10
10
b+1.38×10
11
, 8.01×
10
10
u
24
+3.58×10
11
u
23
+· · ·+5.01×10
10
a−6.09×10
11
, u
25
+4u
24
+· · ·−8u+1i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
u
a
7
=
1
u
2
a
3
=
−1.59799u
24
− 7.12882u
23
+ ··· − 57.6221u + 12.1365
0.512796u
24
+ 2.25200u
23
+ ··· + 14.4684u − 2.75833
a
11
=
−u
−u
3
+ u
a
2
=
−1.08519u
24
− 4.87682u
23
+ ··· − 43.1537u + 9.37821
0.512796u
24
+ 2.25200u
23
+ ··· + 14.4684u − 2.75833
a
1
=
1.20923u
24
+ 4.70829u
23
+ ··· − 2.24711u − 7.01597
−0.0111263u
24
+ 0.0388091u
23
+ ··· − 3.53764u + 3.44465
a
5
=
2.57497u
24
+ 10.7378u
23
+ ··· + 34.2229u − 10.7623
−1.60455u
24
− 6.66333u
23
+ ··· − 17.7203u + 5.25580
a
8
=
−u
24
− 4u
23
+ ··· − 3u + 8
0.774803u
24
+ 3.01861u
23
+ ··· + 2.47448u − 3.60917
a
4
=
3.05016u
24
+ 12.6743u
23
+ ··· + 33.5807u − 10.5700
−1.44373u
24
− 5.96771u
23
+ ··· − 17.2669u + 5.02770
a
9
=
−u
24
− 4u
23
+ ··· − 2u + 7
−0.0159683u
24
+ 0.726898u
23
+ ··· + 7.22737u − 3.62514
a
12
=
−0.128625u
24
− 0.544109u
23
+ ··· + 2.65787u − 1.20923
0.112923u
24
+ 0.798958u
23
+ ··· + 5.59387u − 0.117499
(ii) Obstruction class = 1
(iii) Cusp Shapes
=
65044392892
50148875831
u
24
+
159543202607
50148875831
u
23
+ ··· −
1103313011400
50148875831
u +
372935725441
50148875831
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
25
− 13u
24
+ ··· + 16u − 1
c
2
u
25
− u
24
+ ··· + 8u
2
− 1
c
3
u
25
+ u
24
+ ··· + 4u − 1
c
4
u
25
+ 14u
23
+ ··· − 2u + 1
c
5
u
25
+ u
24
+ ··· − 8u
2
+ 1
c
6
u
25
+ 4u
24
+ ··· − 8u + 1
c
7
u
25
+ 3u
24
+ ··· − 2u + 1
c
8
, c
9
u
25
+ 3u
24
+ ··· − 3u − 1
c
10
u
25
− 4u
24
+ ··· − 8u − 1
c
11
u
25
+ 14u
23
+ ··· − 2u − 1
c
12
u
25
− 3u
24
+ ··· − 3u + 1
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
25
+ 11y
24
+ ··· + 12y −1
c
2
, c
5
y
25
− 13y
24
+ ··· + 16y −1
c
3
y
25
− 7y
24
+ ··· + 10y −1
c
4
, c
11
y
25
+ 28y
24
+ ··· − 42y −1
c
6
, c
10
y
25
− 28y
24
+ ··· + 60y −1
c
7
y
25
− 7y
24
+ ··· + 14y −1
c
8
, c
9
, c
12
y
25
− 29y
24
+ ··· + y −1
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.969986 + 0.204903I
a = 0.270688 + 0.668341I
b = −0.735305 − 0.749517I
−3.03260 − 3.38850I −13.63024 + 0.59156I
u = 0.969986 − 0.204903I
a = 0.270688 − 0.668341I
b = −0.735305 + 0.749517I
−3.03260 + 3.38850I −13.63024 − 0.59156I
u = −0.734968 + 0.662546I
a = −1.07522 − 1.93753I
b = 0.574709 + 0.388619I
−7.97737 + 4.24269I −13.01556 − 1.55556I
u = −0.734968 − 0.662546I
a = −1.07522 + 1.93753I
b = 0.574709 − 0.388619I
−7.97737 − 4.24269I −13.01556 + 1.55556I
u = −0.865758 + 0.332100I
a = −0.838267 − 0.386272I
b = −0.473807 + 0.858543I
−6.92118 + 4.94360I −13.8491 − 7.0409I
u = −0.865758 − 0.332100I
a = −0.838267 + 0.386272I
b = −0.473807 − 0.858543I
−6.92118 − 4.94360I −13.8491 + 7.0409I
u = 1.210180 + 0.021952I
a = −0.742841 + 0.943238I
b = −1.121790 − 0.533032I
−4.62324 − 1.98868I −12.48966 − 0.44574I
u = 1.210180 − 0.021952I
a = −0.742841 − 0.943238I
b = −1.121790 + 0.533032I
−4.62324 + 1.98868I −12.48966 + 0.44574I
u = −1.222280 + 0.207922I
a = −0.129640 − 1.220490I
b = −1.16333 + 0.84752I
−10.35600 + 3.71032I −14.8988 − 5.3062I
u = −1.222280 − 0.207922I
a = −0.129640 + 1.220490I
b = −1.16333 − 0.84752I
−10.35600 − 3.71032I −14.8988 + 5.3062I
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.138820 + 0.597465I
a = −0.790252 + 0.323436I
b = 0.743618 − 0.360851I
−4.71938 − 1.10605I −14.5407 − 4.1700I
u = 1.138820 − 0.597465I
a = −0.790252 − 0.323436I
b = 0.743618 + 0.360851I
−4.71938 + 1.10605I −14.5407 + 4.1700I
u = −1.011320 + 0.821968I
a = −0.13347 + 1.90974I
b = 1.090770 − 0.499634I
−9.85612 + 8.13985I −16.2664 − 7.3867I
u = −1.011320 − 0.821968I
a = −0.13347 − 1.90974I
b = 1.090770 + 0.499634I
−9.85612 − 8.13985I −16.2664 + 7.3867I
u = 0.627265 + 0.293480I
a = 0.643075 + 0.863662I
b = −0.772902 + 0.161877I
−1.92884 + 0.39340I −17.3153 − 1.2800I
u = 0.627265 − 0.293480I
a = 0.643075 − 0.863662I
b = −0.772902 − 0.161877I
−1.92884 − 0.39340I −17.3153 + 1.2800I
u = −0.527015
a = 3.67423
b = −0.480646
−3.95879 −8.21000
u = −1.46428 + 0.16139I
a = −0.275679 + 0.051058I
b = −1.193930 − 0.181729I
−10.94710 − 0.10199I −15.6139 − 2.1795I
u = −1.46428 − 0.16139I
a = −0.275679 − 0.051058I
b = −1.193930 + 0.181729I
−10.94710 + 0.10199I −15.6139 + 2.1795I
u = 1.39084 + 0.49425I
a = 0.85869 − 1.29735I
b = 0.999575 + 0.422001I
−5.69268 − 4.43024I −13.30448 + 2.77709I
20
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.39084 − 0.49425I
a = 0.85869 + 1.29735I
b = 0.999575 − 0.422001I
−5.69268 + 4.43024I −13.30448 − 2.77709I
u = 0.197277 + 0.044089I
a = −1.98047 − 2.86320I
b = 0.877863 + 0.729895I
1.57649 − 2.78288I 0.22422 − 1.94629I
u = 0.197277 − 0.044089I
a = −1.98047 + 2.86320I
b = 0.877863 − 0.729895I
1.57649 + 2.78288I 0.22422 + 1.94629I
u = −1.97226 + 0.14980I
a = 0.356263 − 0.242063I
b = 0.914851 + 0.304706I
−14.1444 − 1.2798I −12.69501 + 6.20324I
u = −1.97226 − 0.14980I
a = 0.356263 + 0.242063I
b = 0.914851 − 0.304706I
−14.1444 + 1.2798I −12.69501 − 6.20324I
21
III. I
u
3
= hb + 1, a + 2, u − 1i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
1
a
7
=
1
1
a
3
=
−2
−1
a
11
=
−1
0
a
2
=
−3
−1
a
1
=
−1
0
a
5
=
−2
−1
a
8
=
−1
0
a
4
=
−1
−1
a
9
=
1
1
a
12
=
0
1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −18
22
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
4
c
5
, c
8
, c
9
c
11
, c
12
u + 1
c
3
, c
6
, c
7
c
10
u − 1
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
6
c
7
, c
8
, c
9
c
10
, c
11
, c
12
y −1
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = −2.00000
b = −1.00000
−4.93480 −18.0000
25
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u + 1)(u
25
− 13u
24
+ ··· + 16u − 1)(u
109
+ 53u
108
+ ··· + 114u + 1)
c
2
(u + 1)(u
25
− u
24
+ ··· + 8u
2
− 1)(u
109
+ 5u
108
+ ··· + 18u + 1)
c
3
(u − 1)(u
25
+ u
24
+ ··· + 4u − 1)
· (u
109
+ 3u
108
+ ··· + 9062344u + 742717)
c
4
(u + 1)(u
25
+ 14u
23
+ ··· − 2u + 1)(u
109
− 4u
108
+ ··· + 10u − 1)
c
5
(u + 1)(u
25
+ u
24
+ ··· − 8u
2
+ 1)(u
109
+ 5u
108
+ ··· + 18u + 1)
c
6
(u − 1)(u
25
+ 4u
24
+ ··· − 8u + 1)(u
109
− 2u
108
+ ··· − 109940u − 9991)
c
7
(u − 1)(u
25
+ 3u
24
+ ··· − 2u + 1)
· (u
109
− 7u
108
+ ··· − 1323756u + 105511)
c
8
, c
9
(u + 1)(u
25
+ 3u
24
+ ··· − 3u − 1)(u
109
+ 3u
108
+ ··· + 95u − 7)
c
10
(u − 1)(u
25
− 4u
24
+ ··· − 8u − 1)(u
109
− 2u
108
+ ··· − 109940u − 9991)
c
11
(u + 1)(u
25
+ 14u
23
+ ··· − 2u − 1)(u
109
− 4u
108
+ ··· + 10u − 1)
c
12
(u + 1)(u
25
− 3u
24
+ ··· − 3u + 1)(u
109
+ 3u
108
+ ··· + 95u − 7)
26
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y −1)(y
25
+ 11y
24
+ ··· + 12y −1)(y
109
+ 19y
108
+ ··· + 7262y −1)
c
2
, c
5
(y −1)(y
25
− 13y
24
+ ··· + 16y −1)(y
109
− 53y
108
+ ··· + 114y −1)
c
3
(y −1)(y
25
− 7y
24
+ ··· + 10y −1)
· (y
109
− 47y
108
+ ··· + 31084038325668y −551628542089)
c
4
, c
11
(y −1)(y
25
+ 28y
24
+ ··· − 42y −1)(y
109
+ 100y
108
+ ··· + 112y −1)
c
6
, c
10
(y −1)(y
25
− 28y
24
+ ··· + 60y −1)
· (y
109
− 92y
108
+ ··· + 1884094310y −99820081)
c
7
(y −1)(y
25
− 7y
24
+ ··· + 14y −1)
· (y
109
− 35y
108
+ ··· + 312381658400y −11132571121)
c
8
, c
9
, c
12
(y −1)(y
25
− 29y
24
+ ··· + y −1)(y
109
− 117y
108
+ ··· − 537y −49)
27
