12a
1272
(K12a
1272
)
A knot diagram
1
Linearized knot diagam
5 8 7 1 10 11 12 2 4 6 3 9
Solving Sequence
2,5
1
4,9
10 6 8 3 12 7 11
c
1
c
4
c
9
c
5
c
8
c
2
c
12
c
7
c
11
c
3
, c
6
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−5.27398 × 10
429
u
131
− 9.58434 × 10
429
u
130
+ ··· + 9.61277 × 10
428
b − 5.45766 × 10
432
,
1.80780 × 10
432
u
131
+ 3.29725 × 10
432
u
130
+ ··· + 2.02829 × 10
431
a + 1.86013 × 10
435
,
u
132
+ u
131
+ ··· − 1451u − 844i
I
u
2
= h2318651091u
29
+ 8025321455u
28
+ ··· + 9372903b + 4797253946,
− 1257579720u
29
− 4274580356u
28
+ ··· + 9372903a − 2710745983, u
30
+ 4u
29
+ ··· + 7u + 1i
I
u
3
= hb + a − 1, a
2
− 3a + 3, u − 1i
* 3 irreducible components of dim
C
= 0, with total 164 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−5.27 × 10
429
u
131
− 9.58 × 10
429
u
130
+ · · · + 9.61 × 10
428
b − 5.46 ×
10
432
, 1.81 × 10
432
u
131
+ 3.30 × 10
432
u
130
+ · · · + 2.03 × 10
431
a + 1.86 ×
10
435
, u
132
+ u
131
+ · · · − 1451u − 844i
(i) Arc colorings
a
2
=
1
0
a
5
=
0
u
a
1
=
1
−u
2
a
4
=
u
−u
3
+ u
a
9
=
−8.91293u
131
− 16.2563u
130
+ ··· − 26935.2u − 9170.89
5.48643u
131
+ 9.97042u
130
+ ··· + 16692.0u + 5677.51
a
10
=
−3.34622u
131
− 6.13050u
130
+ ··· − 9951.53u − 3393.85
7.33783u
131
+ 13.3479u
130
+ ··· + 22362.1u + 7606.69
a
6
=
−4.96312u
131
− 9.02635u
130
+ ··· − 15167.5u − 5149.06
12.2350u
131
+ 22.1179u
130
+ ··· + 37446.3u + 12681.3
a
8
=
−3.42650u
131
− 6.28584u
130
+ ··· − 10243.3u − 3493.38
5.48643u
131
+ 9.97042u
130
+ ··· + 16692.0u + 5677.51
a
3
=
11.5848u
131
+ 21.0113u
130
+ ··· + 35412.9u + 12022.8
−19.5383u
131
− 35.3500u
130
+ ··· − 60023.3u − 20340.8
a
12
=
0.967020u
131
+ 1.73517u
130
+ ··· + 3148.59u + 1041.78
−0.912310u
131
− 1.60702u
130
+ ··· − 2865.28u − 960.299
a
7
=
−4.07589u
131
− 7.57566u
130
+ ··· − 11810.1u − 4058.04
6.06028u
131
+ 10.9765u
130
+ ··· + 18294.1u + 6226.53
a
11
=
5.61423u
131
+ 10.2551u
130
+ ··· + 16930.8u + 5749.34
−11.4857u
131
− 20.7801u
130
+ ··· − 35554.7u − 12041.1
(ii) Obstruction class = −1
(iii) Cusp Shapes = 769.616u
131
+ 1391.64u
130
+ ··· + 2.37325 × 10
6
u + 803188.
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
132
− u
131
+ ··· + 1451u − 844
c
2
, c
8
u
132
+ 44u
130
+ ··· − 21827u − 1189
c
3
u
132
− 4u
131
+ ··· + 9472u − 2239
c
5
, c
6
, c
10
u
132
+ 2u
131
+ ··· + 130u + 19
c
7
u
132
+ u
130
+ ··· − 28u + 8
c
9
u
132
− 4u
130
+ ··· − 37881u + 2437
c
11
u
132
+ 6u
131
+ ··· + 89459u + 56393
c
12
u
132
− 5u
131
+ ··· + 4452u + 103
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
132
− 63y
131
+ ··· − 11311753y + 712336
c
2
, c
8
y
132
+ 88y
131
+ ··· − 71456419y + 1413721
c
3
y
132
− 36y
131
+ ··· − 304367236y + 5013121
c
5
, c
6
, c
10
y
132
− 144y
131
+ ··· − 14848y + 361
c
7
y
132
+ 2y
131
+ ··· − 4464y + 64
c
9
y
132
− 8y
131
+ ··· − 75967363y + 5938969
c
11
y
132
+ 62y
131
+ ··· + 237776842153y + 3180170449
c
12
y
132
− 27y
131
+ ··· − 6883504y + 10609
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.888433 + 0.459649I
a = −0.192013 + 1.130340I
b = 0.135369 + 1.366530I
10.08520 − 8.84662I 0
u = 0.888433 − 0.459649I
a = −0.192013 − 1.130340I
b = 0.135369 − 1.366530I
10.08520 + 8.84662I 0
u = −0.860001 + 0.505931I
a = −0.524831 − 0.211304I
b = 0.00912 − 1.53664I
10.41720 + 2.03214I 0
u = −0.860001 − 0.505931I
a = −0.524831 + 0.211304I
b = 0.00912 + 1.53664I
10.41720 − 2.03214I 0
u = −0.128893 + 0.987034I
a = −0.107867 + 0.455133I
b = −1.064690 − 0.044525I
6.25496 − 6.63131I 0
u = −0.128893 − 0.987034I
a = −0.107867 − 0.455133I
b = −1.064690 + 0.044525I
6.25496 + 6.63131I 0
u = −0.817665 + 0.595071I
a = −1.375280 − 0.085348I
b = −0.01154 − 1.61726I
10.91990 + 2.34128I 0
u = −0.817665 − 0.595071I
a = −1.375280 + 0.085348I
b = −0.01154 + 1.61726I
10.91990 − 2.34128I 0
u = −0.887029 + 0.426126I
a = −0.238037 − 0.107971I
b = 0.44793 + 1.51254I
9.85464 − 4.57208I 0
u = −0.887029 − 0.426126I
a = −0.238037 + 0.107971I
b = 0.44793 − 1.51254I
9.85464 + 4.57208I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.299028 + 0.934814I
a = −0.339354 + 0.092362I
b = 0.388248 + 1.036060I
6.49844 − 4.55251I 0
u = −0.299028 − 0.934814I
a = −0.339354 − 0.092362I
b = 0.388248 − 1.036060I
6.49844 + 4.55251I 0
u = 0.259667 + 1.010660I
a = −0.136638 − 0.521034I
b = 0.403078 − 1.345030I
3.78458 + 8.55429I 0
u = 0.259667 − 1.010660I
a = −0.136638 + 0.521034I
b = 0.403078 + 1.345030I
3.78458 − 8.55429I 0
u = 0.881749 + 0.328399I
a = 2.48900 + 0.26366I
b = −0.17445 − 1.63310I
9.18224 − 1.20024I 0
u = 0.881749 − 0.328399I
a = 2.48900 − 0.26366I
b = −0.17445 + 1.63310I
9.18224 + 1.20024I 0
u = −0.971761 + 0.434578I
a = 1.40070 + 0.56574I
b = −0.282247 + 0.929840I
1.49064 + 1.85110I 0
u = −0.971761 − 0.434578I
a = 1.40070 − 0.56574I
b = −0.282247 − 0.929840I
1.49064 − 1.85110I 0
u = −0.917872 + 0.166230I
a = 1.326400 + 0.401788I
b = −0.149482 + 0.636067I
1.40547 + 1.62272I 0
u = −0.917872 − 0.166230I
a = 1.326400 − 0.401788I
b = −0.149482 − 0.636067I
1.40547 − 1.62272I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.902863 + 0.202398I
a = 1.93367 − 1.39062I
b = −0.181766 + 0.639474I
−0.956671 − 0.870714I 0
u = 0.902863 − 0.202398I
a = 1.93367 + 1.39062I
b = −0.181766 − 0.639474I
−0.956671 + 0.870714I 0
u = 0.924821
a = −3.20484
b = 2.41225
−0.379463 0
u = 0.919150 + 0.062875I
a = −1.22487 − 1.47381I
b = 0.43120 + 1.81191I
−0.312377 − 0.392334I 0
u = 0.919150 − 0.062875I
a = −1.22487 + 1.47381I
b = 0.43120 − 1.81191I
−0.312377 + 0.392334I 0
u = 0.854419 + 0.330939I
a = 1.40388 − 0.54442I
b = 0.05937 − 1.64090I
9.26391 − 1.67107I 0
u = 0.854419 − 0.330939I
a = 1.40388 + 0.54442I
b = 0.05937 + 1.64090I
9.26391 + 1.67107I 0
u = −0.747724 + 0.524870I
a = −2.12221 − 0.04445I
b = −0.080811 − 1.350620I
10.74310 + 2.15226I 0
u = −0.747724 − 0.524870I
a = −2.12221 + 0.04445I
b = −0.080811 + 1.350620I
10.74310 − 2.15226I 0
u = −0.989013 + 0.458677I
a = 2.20619 + 0.31109I
b = −0.232381 + 1.160650I
1.20534 + 2.58602I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.989013 − 0.458677I
a = 2.20619 − 0.31109I
b = −0.232381 − 1.160650I
1.20534 − 2.58602I 0
u = 1.017390 + 0.399155I
a = 2.00809 + 0.70527I
b = −0.011529 − 1.090260I
2.53408 + 1.30747I 0
u = 1.017390 − 0.399155I
a = 2.00809 − 0.70527I
b = −0.011529 + 1.090260I
2.53408 − 1.30747I 0
u = 1.025520 + 0.398648I
a = −1.23586 + 0.83864I
b = 0.657096 − 0.430489I
−3.47015 − 2.63906I 0
u = 1.025520 − 0.398648I
a = −1.23586 − 0.83864I
b = 0.657096 + 0.430489I
−3.47015 + 2.63906I 0
u = 0.777156 + 0.445739I
a = −2.98626 − 0.24164I
b = −0.139684 + 1.116770I
10.45930 + 5.07607I 0
u = 0.777156 − 0.445739I
a = −2.98626 + 0.24164I
b = −0.139684 − 1.116770I
10.45930 − 5.07607I 0
u = 1.086330 + 0.215183I
a = 1.114480 − 0.586549I
b = −1.144630 + 0.562319I
−1.66184 − 0.75099I 0
u = 1.086330 − 0.215183I
a = 1.114480 + 0.586549I
b = −1.144630 − 0.562319I
−1.66184 + 0.75099I 0
u = −0.798505 + 0.397196I
a = 2.86222 − 0.71894I
b = −0.63968 + 1.32038I
10.17010 + 8.06121I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.798505 − 0.397196I
a = 2.86222 + 0.71894I
b = −0.63968 − 1.32038I
10.17010 − 8.06121I 0
u = −1.065870 + 0.319329I
a = −0.671097 + 0.337438I
b = 0.065196 + 0.246846I
−1.06962 + 3.70198I 0
u = −1.065870 − 0.319329I
a = −0.671097 − 0.337438I
b = 0.065196 − 0.246846I
−1.06962 − 3.70198I 0
u = −1.045210 + 0.408453I
a = −1.81053 + 0.50219I
b = 0.63280 − 1.27162I
2.58381 + 7.13715I 0
u = −1.045210 − 0.408453I
a = −1.81053 − 0.50219I
b = 0.63280 + 1.27162I
2.58381 − 7.13715I 0
u = −0.159394 + 0.861713I
a = −0.568599 − 0.640734I
b = −0.457630 + 0.026165I
7.95380 − 2.88865I 0
u = −0.159394 − 0.861713I
a = −0.568599 + 0.640734I
b = −0.457630 − 0.026165I
7.95380 + 2.88865I 0
u = 0.218566 + 1.107950I
a = 0.175980 + 0.419203I
b = 0.113053 + 1.137110I
4.87895 − 0.96047I 0
u = 0.218566 − 1.107950I
a = 0.175980 − 0.419203I
b = 0.113053 − 1.137110I
4.87895 + 0.96047I 0
u = 1.089370 + 0.342018I
a = −0.336039 + 0.778881I
b = 0.288735 − 0.667558I
−2.55378 − 0.72472I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.089370 − 0.342018I
a = −0.336039 − 0.778881I
b = 0.288735 + 0.667558I
−2.55378 + 0.72472I 0
u = 0.954127 + 0.635674I
a = 0.038859 − 0.760829I
b = −0.138686 + 0.697586I
2.05134 − 2.56323I 0
u = 0.954127 − 0.635674I
a = 0.038859 + 0.760829I
b = −0.138686 − 0.697586I
2.05134 + 2.56323I 0
u = −1.114630 + 0.308899I
a = −1.60111 − 0.32041I
b = 0.781702 − 0.119471I
−4.68421 + 3.54811I 0
u = −1.114630 − 0.308899I
a = −1.60111 + 0.32041I
b = 0.781702 + 0.119471I
−4.68421 − 3.54811I 0
u = −0.962547 + 0.685515I
a = −1.13022 − 0.93033I
b = 0.155733 − 0.969552I
−2.01475 + 2.72647I 0
u = −0.962547 − 0.685515I
a = −1.13022 + 0.93033I
b = 0.155733 + 0.969552I
−2.01475 − 2.72647I 0
u = 1.072570 + 0.500941I
a = 1.029600 − 0.741523I
b = −0.903930 + 0.587094I
2.25264 − 4.65575I 0
u = 1.072570 − 0.500941I
a = 1.029600 + 0.741523I
b = −0.903930 − 0.587094I
2.25264 + 4.65575I 0
u = 0.813276
a = 5.52679
b = −3.46759
7.70114 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.356229 + 1.148630I
a = 0.168781 + 0.343370I
b = 0.433166 + 1.136880I
4.67103 − 1.62587I 0
u = −0.356229 − 1.148630I
a = 0.168781 − 0.343370I
b = 0.433166 − 1.136880I
4.67103 + 1.62587I 0
u = 0.022902 + 0.792156I
a = −0.047072 − 0.341718I
b = 0.798408 + 0.086019I
−0.69629 − 4.11755I 0
u = 0.022902 − 0.792156I
a = −0.047072 + 0.341718I
b = 0.798408 − 0.086019I
−0.69629 + 4.11755I 0
u = 0.437509 + 1.134300I
a = 0.033613 + 0.440353I
b = −0.51268 + 1.38631I
10.7695 + 12.2620I 0
u = 0.437509 − 1.134300I
a = 0.033613 − 0.440353I
b = −0.51268 − 1.38631I
10.7695 − 12.2620I 0
u = 0.783115
a = 0.911346
b = −0.608263
−1.26571 0
u = −0.598940 + 0.479604I
a = 0.448566 + 1.299910I
b = 0.052445 + 1.214290I
2.37714 + 1.31479I 0
u = −0.598940 − 0.479604I
a = 0.448566 − 1.299910I
b = 0.052445 − 1.214290I
2.37714 − 1.31479I 0
u = −1.120900 + 0.520454I
a = −1.92871 + 0.05999I
b = 0.404571 − 1.109500I
−1.30487 + 6.80594I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.120900 − 0.520454I
a = −1.92871 − 0.05999I
b = 0.404571 + 1.109500I
−1.30487 − 6.80594I 0
u = 1.164660 + 0.451459I
a = −1.95379 − 0.33001I
b = 0.35644 + 1.40839I
0.23382 − 7.72074I 0
u = 1.164660 − 0.451459I
a = −1.95379 + 0.33001I
b = 0.35644 − 1.40839I
0.23382 + 7.72074I 0
u = −0.736825
a = 3.08179
b = −0.0914915
3.02836 0
u = 1.203490 + 0.441169I
a = −0.969440 + 0.454908I
b = 1.325330 − 0.289045I
4.00324 − 1.47776I 0
u = 1.203490 − 0.441169I
a = −0.969440 − 0.454908I
b = 1.325330 + 0.289045I
4.00324 + 1.47776I 0
u = −0.261769 + 0.668003I
a = 0.590878 − 0.537091I
b = −0.209541 − 1.078610I
1.14713 − 2.21877I 0
u = −0.261769 − 0.668003I
a = 0.590878 + 0.537091I
b = −0.209541 + 1.078610I
1.14713 + 2.21877I 0
u = −1.205320 + 0.443525I
a = 1.37582 + 0.46499I
b = −1.145380 + 0.183326I
−4.29889 + 8.50488I 0
u = −1.205320 − 0.443525I
a = 1.37582 − 0.46499I
b = −1.145380 − 0.183326I
−4.29889 − 8.50488I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.171030 + 0.567634I
a = 0.574993 − 0.152351I
b = −0.110535 − 0.133405I
5.04933 + 8.10612I 0
u = −1.171030 − 0.567634I
a = 0.574993 + 0.152351I
b = −0.110535 + 0.133405I
5.04933 − 8.10612I 0
u = −0.982808 + 0.857356I
a = 0.894536 + 0.951800I
b = −0.061059 + 1.106970I
3.38915 + 3.27485I 0
u = −0.982808 − 0.857356I
a = 0.894536 − 0.951800I
b = −0.061059 − 1.106970I
3.38915 − 3.27485I 0
u = 1.228330 + 0.450570I
a = 1.077480 − 0.460181I
b = −0.888292 − 0.412295I
−4.23965 − 0.44921I 0
u = 1.228330 − 0.450570I
a = 1.077480 + 0.460181I
b = −0.888292 + 0.412295I
−4.23965 + 0.44921I 0
u = −1.230990 + 0.456388I
a = 0.181491 − 0.569155I
b = 0.262429 + 1.124450I
0.303412 + 0.871916I 0
u = −1.230990 − 0.456388I
a = 0.181491 + 0.569155I
b = 0.262429 − 1.124450I
0.303412 − 0.871916I 0
u = −0.088702 + 0.669160I
a = 0.589046 + 0.615861I
b = −0.232592 + 1.350320I
3.53727 + 3.67602I 0
u = −0.088702 − 0.669160I
a = 0.589046 − 0.615861I
b = −0.232592 − 1.350320I
3.53727 − 3.67602I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.320950 + 0.133082I
a = 0.478618 − 0.725833I
b = −0.277492 + 0.675710I
0.737823 + 0.896249I 0
u = 1.320950 − 0.133082I
a = 0.478618 + 0.725833I
b = −0.277492 − 0.675710I
0.737823 − 0.896249I 0
u = −1.185620 + 0.603238I
a = 1.68091 − 0.06456I
b = −0.567314 + 1.056540I
3.80200 + 10.11980I 0
u = −1.185620 − 0.603238I
a = 1.68091 + 0.06456I
b = −0.567314 − 1.056540I
3.80200 − 10.11980I 0
u = −1.328520 + 0.130575I
a = 0.398662 + 0.634277I
b = −0.472934 − 1.050020I
−2.16348 − 4.52737I 0
u = −1.328520 − 0.130575I
a = 0.398662 − 0.634277I
b = −0.472934 + 1.050020I
−2.16348 + 4.52737I 0
u = 1.081850 + 0.785669I
a = −0.640885 + 0.556637I
b = 0.254533 + 0.510690I
−2.02817 − 3.19514I 0
u = 1.081850 − 0.785669I
a = −0.640885 − 0.556637I
b = 0.254533 − 0.510690I
−2.02817 + 3.19514I 0
u = 1.231000 + 0.562678I
a = −1.340210 − 0.312386I
b = 0.111927 + 1.159600I
1.61202 − 4.74931I 0
u = 1.231000 − 0.562678I
a = −1.340210 + 0.312386I
b = 0.111927 − 1.159600I
1.61202 + 4.74931I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.237580 + 0.550508I
a = −1.254670 − 0.578778I
b = 1.40334 − 0.22807I
2.86994 + 12.04640I 0
u = −1.237580 − 0.550508I
a = −1.254670 + 0.578778I
b = 1.40334 + 0.22807I
2.86994 − 12.04640I 0
u = 0.598628 + 0.240960I
a = −0.41746 − 1.52277I
b = −0.128247 − 1.357570I
4.03807 − 4.46460I 0
u = 0.598628 − 0.240960I
a = −0.41746 + 1.52277I
b = −0.128247 + 1.357570I
4.03807 + 4.46460I 0
u = 0.364776 + 0.524785I
a = −1.53447 + 0.83795I
b = 0.754945 + 0.279104I
4.27359 + 0.41818I 0
u = 0.364776 − 0.524785I
a = −1.53447 − 0.83795I
b = 0.754945 − 0.279104I
4.27359 − 0.41818I 0
u = 1.225200 + 0.596736I
a = 1.70251 + 0.01514I
b = −0.50100 − 1.43795I
0.7781 − 14.2874I 0
u = 1.225200 − 0.596736I
a = 1.70251 − 0.01514I
b = −0.50100 + 1.43795I
0.7781 + 14.2874I 0
u = −0.209142 + 1.347150I
a = −0.218609 − 0.341615I
b = −0.294285 − 0.745193I
8.42783 − 2.79167I 0
u = −0.209142 − 1.347150I
a = −0.218609 + 0.341615I
b = −0.294285 + 0.745193I
8.42783 + 2.79167I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.219590 + 0.614211I
a = 1.46312 + 0.04774I
b = −0.61836 + 1.36761I
1.77093 + 7.69029I 0
u = −1.219590 − 0.614211I
a = 1.46312 − 0.04774I
b = −0.61836 − 1.36761I
1.77093 − 7.69029I 0
u = 0.607449 + 1.225470I
a = −0.008727 − 0.481828I
b = 0.061565 − 1.176820I
10.82320 + 2.58085I 0
u = 0.607449 − 1.225470I
a = −0.008727 + 0.481828I
b = 0.061565 + 1.176820I
10.82320 − 2.58085I 0
u = −0.559620 + 1.277610I
a = −0.167666 − 0.342309I
b = −0.603837 − 1.262080I
10.67920 − 1.72002I 0
u = −0.559620 − 1.277610I
a = −0.167666 + 0.342309I
b = −0.603837 + 1.262080I
10.67920 + 1.72002I 0
u = −0.492501 + 0.320631I
a = 0.129165 + 0.362271I
b = −0.32006 − 1.40564I
4.32601 − 3.70375I 0
u = −0.492501 − 0.320631I
a = 0.129165 − 0.362271I
b = −0.32006 + 1.40564I
4.32601 + 3.70375I 0
u = 1.23135 + 0.70339I
a = −1.61586 + 0.17680I
b = 0.57319 + 1.49506I
8.2076 − 18.7958I 0
u = 1.23135 − 0.70339I
a = −1.61586 − 0.17680I
b = 0.57319 − 1.49506I
8.2076 + 18.7958I 0
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.42213 + 0.13324I
a = −0.831170 + 0.429200I
b = 0.685492 − 1.091570I
2.81720 + 8.47909I 0
u = −1.42213 − 0.13324I
a = −0.831170 − 0.429200I
b = 0.685492 + 1.091570I
2.81720 − 8.47909I 0
u = 1.41683 + 0.26438I
a = −1.109950 + 0.168625I
b = 1.212520 + 0.615511I
0.99534 + 1.82942I 0
u = 1.41683 − 0.26438I
a = −1.109950 − 0.168625I
b = 1.212520 − 0.615511I
0.99534 − 1.82942I 0
u = 1.22825 + 0.75949I
a = 1.235980 − 0.105262I
b = −0.174476 − 1.243520I
8.61807 − 9.62658I 0
u = 1.22825 − 0.75949I
a = 1.235980 + 0.105262I
b = −0.174476 + 1.243520I
8.61807 + 9.62658I 0
u = −1.26281 + 0.76234I
a = −1.335770 − 0.250024I
b = 0.62952 − 1.50563I
8.22324 + 8.90731I 0
u = −1.26281 − 0.76234I
a = −1.335770 + 0.250024I
b = 0.62952 + 1.50563I
8.22324 − 8.90731I 0
u = 0.147938 + 0.455430I
a = 0.803767 − 0.078291I
b = −0.587379 − 0.193361I
−1.35324 − 0.77267I −5.30506 + 0.81512I
u = 0.147938 − 0.455430I
a = 0.803767 + 0.078291I
b = −0.587379 + 0.193361I
−1.35324 + 0.77267I −5.30506 − 0.81512I
17
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.151254 + 0.297937I
a = 1.78806 + 0.81849I
b = 0.307687 − 0.326506I
1.15096 − 0.92104I 4.55484 + 2.14940I
u = −0.151254 − 0.297937I
a = 1.78806 − 0.81849I
b = 0.307687 + 0.326506I
1.15096 + 0.92104I 4.55484 − 2.14940I
18
II.
I
u
2
= h2.32 × 10
9
u
29
+ 8.03 × 10
9
u
28
+ · · · + 9.37 × 10
6
b + 4.80 × 10
9
, −1.26 ×
10
9
u
29
−4.27×10
9
u
28
+· · · +9.37×10
6
a−2.71×10
9
, u
30
+4u
29
+· · · +7u +1i
(i) Arc colorings
a
2
=
1
0
a
5
=
0
u
a
1
=
1
−u
2
a
4
=
u
−u
3
+ u
a
9
=
134.172u
29
+ 456.057u
28
+ ··· + 1557.17u + 289.211
−247.378u
29
− 856.226u
28
+ ··· − 2556.65u − 511.822
a
10
=
45.0125u
29
+ 152.845u
28
+ ··· + 560.461u + 96.1842
−315.172u
29
− 1089.94u
28
+ ··· − 3268.54u − 651.423
a
6
=
141.162u
29
+ 473.575u
28
+ ··· + 1137.50u + 179.919
−267.159u
29
− 964.190u
28
+ ··· − 2740.63u − 585.096
a
8
=
−113.206u
29
− 400.169u
28
+ ··· − 999.486u − 222.611
−247.378u
29
− 856.226u
28
+ ··· − 2556.65u − 511.822
a
3
=
455.829u
29
+ 1623.13u
28
+ ··· + 5161.07u + 1090.23
−74.5440u
29
− 255.803u
28
+ ··· − 1160.53u − 242.557
a
12
=
−366.303u
29
− 1332.00u
28
+ ··· − 4413.63u − 979.914
−u
29
− 3u
28
+ ··· − 7u
2
− 7u
a
7
=
427.626u
29
+ 1511.62u
28
+ ··· + 4483.79u + 933.241
174.722u
29
+ 617.886u
28
+ ··· + 1617.71u + 318.379
a
11
=
72.2048u
29
+ 292.216u
28
+ ··· + 913.748u + 248.119
120.311u
29
+ 434.477u
28
+ ··· + 1633.83u + 355.868
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
2124368078
9372903
u
29
−
1389203474
9372903
u
28
+ ··· −
42689783696
3124301
u −
22166136335
9372903
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
30
+ 4u
29
+ ··· + 7u + 1
c
2
u
30
− 2u
29
+ ··· − 4u − 1
c
3
u
30
− 4u
29
+ ··· − 5u + 1
c
4
u
30
− 4u
29
+ ··· − 7u + 1
c
5
, c
6
u
30
− u
29
+ ··· − 16u
2
− 1
c
7
u
30
− u
29
+ ··· − 12u − 3
c
8
u
30
+ 2u
29
+ ··· + 4u − 1
c
9
u
30
+ 2u
29
+ ··· + 20u + 1
c
10
u
30
+ u
29
+ ··· − 16u
2
− 1
c
11
u
30
+ 12u
28
+ ··· + 8u − 1
c
12
u
30
− 6u
29
+ ··· − 2u − 1
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
30
− 10y
29
+ ··· − 23y + 1
c
2
, c
8
y
30
+ 14y
29
+ ··· − 10y + 1
c
3
y
30
− 18y
29
+ ··· + y + 1
c
5
, c
6
, c
10
y
30
− 39y
29
+ ··· + 32y + 1
c
7
y
30
− 7y
29
+ ··· − 1020y + 9
c
9
y
30
− 14y
29
+ ··· − 214y + 1
c
11
y
30
+ 24y
29
+ ··· − 14y + 1
c
12
y
30
− 14y
29
+ ··· − 40y + 1
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.914247 + 0.478404I
a = 1.93608 + 1.23966I
b = −0.161051 + 0.967060I
−0.08292 + 1.96806I −3.02444 − 3.31718I
u = −0.914247 − 0.478404I
a = 1.93608 − 1.23966I
b = −0.161051 − 0.967060I
−0.08292 − 1.96806I −3.02444 + 3.31718I
u = 0.966933 + 0.421943I
a = −1.066120 + 0.925837I
b = 0.344795 − 0.186269I
−3.48026 − 1.82580I −8.91337 − 0.41811I
u = 0.966933 − 0.421943I
a = −1.066120 − 0.925837I
b = 0.344795 + 0.186269I
−3.48026 + 1.82580I −8.91337 + 0.41811I
u = −0.843224 + 0.323111I
a = 2.18551 + 0.44187I
b = −0.02670 + 1.63927I
9.58575 + 1.48104I 15.8659 − 1.4053I
u = −0.843224 − 0.323111I
a = 2.18551 − 0.44187I
b = −0.02670 − 1.63927I
9.58575 − 1.48104I 15.8659 + 1.4053I
u = 0.892802
a = 2.51005
b = −1.68772
−0.327469 31.3600
u = 1.092830 + 0.410784I
a = −0.040120 + 0.596864I
b = 0.344289 − 0.968431I
−0.49604 − 1.69025I −3.00353 + 2.31093I
u = 1.092830 − 0.410784I
a = −0.040120 − 0.596864I
b = 0.344289 + 0.968431I
−0.49604 + 1.69025I −3.00353 − 2.31093I
u = 0.982431 + 0.678623I
a = 0.481945 − 0.966192I
b = −0.301537 + 0.216828I
1.13399 − 2.76492I −4.71775 + 2.69778I
22
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.982431 − 0.678623I
a = 0.481945 + 0.966192I
b = −0.301537 − 0.216828I
1.13399 + 2.76492I −4.71775 − 2.69778I
u = −0.001235 + 0.805919I
a = 0.013308 + 1.372580I
b = 0.266019 + 1.380800I
10.77260 + 0.39997I 4.81859 + 0.26297I
u = −0.001235 − 0.805919I
a = 0.013308 − 1.372580I
b = 0.266019 − 1.380800I
10.77260 − 0.39997I 4.81859 − 0.26297I
u = 0.803639
a = −5.39360
b = 3.31619
7.71010 406.100
u = −0.188499 + 1.199910I
a = −0.100781 − 0.411198I
b = −0.334755 − 1.093000I
4.36107 − 1.46727I −9.10722 + 0.91856I
u = −0.188499 − 1.199910I
a = −0.100781 + 0.411198I
b = −0.334755 + 1.093000I
4.36107 + 1.46727I −9.10722 − 0.91856I
u = 0.769194
a = 3.09657
b = −0.392673
2.83265 −18.2700
u = 1.24130
a = 0.934361
b = −0.451498
0.517848 −1.73050
u = −1.188050 + 0.465930I
a = −1.63669 + 0.35983I
b = 0.437433 − 1.269120I
0.55049 + 6.62323I −2.00000 − 4.98434I
u = −1.188050 − 0.465930I
a = −1.63669 − 0.35983I
b = 0.437433 + 1.269120I
0.55049 − 6.62323I −2.00000 + 4.98434I
23
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.058040 + 0.817556I
a = −0.844520 − 0.579922I
b = 0.124690 − 0.940651I
−0.89236 + 3.28717I 0. − 4.27413I
u = −1.058040 − 0.817556I
a = −0.844520 + 0.579922I
b = 0.124690 + 0.940651I
−0.89236 − 3.28717I 0. + 4.27413I
u = −0.590403 + 0.063266I
a = 0.881544 − 0.820988I
b = −0.226195 − 1.378450I
3.71119 − 3.90958I −5.50347 + 2.08979I
u = −0.590403 − 0.063266I
a = 0.881544 + 0.820988I
b = −0.226195 + 1.378450I
3.71119 + 3.90958I −5.50347 − 2.08979I
u = −1.277630 + 0.597190I
a = 1.231240 − 0.157559I
b = −0.603405 + 0.987716I
5.09603 + 9.97190I 0. − 8.63860I
u = −1.277630 − 0.597190I
a = 1.231240 + 0.157559I
b = −0.603405 − 0.987716I
5.09603 − 9.97190I 0. + 8.63860I
u = −0.38968 + 1.35980I
a = 0.032493 + 0.174740I
b = 0.361338 + 0.858086I
8.57240 − 3.34121I 0. + 9.69583I
u = −0.38968 − 1.35980I
a = 0.032493 − 0.174740I
b = 0.361338 − 0.858086I
8.57240 + 3.34121I 0. − 9.69583I
u = −0.444659 + 0.029162I
a = −4.14758 − 0.30591I
b = 0.382925 − 1.299300I
10.08430 + 6.63124I 1.74300 − 4.80854I
u = −0.444659 − 0.029162I
a = −4.14758 + 0.30591I
b = 0.382925 + 1.299300I
10.08430 − 6.63124I 1.74300 + 4.80854I
24
III. I
u
3
= hb + a − 1, a
2
− 3a + 3, u − 1i
(i) Arc colorings
a
2
=
1
0
a
5
=
0
1
a
1
=
1
−1
a
4
=
1
0
a
9
=
a
−a + 1
a
10
=
1
−a + 1
a
6
=
1
−a + 2
a
8
=
1
−a + 1
a
3
=
−a + 2
a − 2
a
12
=
−a + 1
a − 2
a
7
=
1
−a + 1
a
11
=
0
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −3
25
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
10
, c
12
(u − 1)
2
c
2
, c
3
u
2
+ u + 1
c
4
, c
5
, c
6
(u + 1)
2
c
7
u
2
c
8
, c
9
, c
11
u
2
− u + 1
26
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
5
c
6
, c
10
, c
12
(y −1)
2
c
2
, c
3
, c
8
c
9
, c
11
y
2
+ y + 1
c
7
y
2
27
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = 1.50000 + 0.86603I
b = −0.500000 − 0.866025I
0 −3.00000
u = 1.00000
a = 1.50000 − 0.86603I
b = −0.500000 + 0.866025I
0 −3.00000
28
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
2
)(u
30
+ 4u
29
+ ··· + 7u + 1)(u
132
− u
131
+ ··· + 1451u − 844)
c
2
(u
2
+ u + 1)(u
30
− 2u
29
+ ··· − 4u − 1)
· (u
132
+ 44u
130
+ ··· − 21827u − 1189)
c
3
(u
2
+ u + 1)(u
30
− 4u
29
+ ··· − 5u + 1)
· (u
132
− 4u
131
+ ··· + 9472u − 2239)
c
4
((u + 1)
2
)(u
30
− 4u
29
+ ··· − 7u + 1)(u
132
− u
131
+ ··· + 1451u − 844)
c
5
, c
6
((u + 1)
2
)(u
30
− u
29
+ ··· − 16u
2
− 1)(u
132
+ 2u
131
+ ··· + 130u + 19)
c
7
u
2
(u
30
− u
29
+ ··· − 12u − 3)(u
132
+ u
130
+ ··· − 28u + 8)
c
8
(u
2
− u + 1)(u
30
+ 2u
29
+ ··· + 4u − 1)
· (u
132
+ 44u
130
+ ··· − 21827u − 1189)
c
9
(u
2
− u + 1)(u
30
+ 2u
29
+ ··· + 20u + 1)
· (u
132
− 4u
130
+ ··· − 37881u + 2437)
c
10
((u − 1)
2
)(u
30
+ u
29
+ ··· − 16u
2
− 1)(u
132
+ 2u
131
+ ··· + 130u + 19)
c
11
(u
2
− u + 1)(u
30
+ 12u
28
+ ··· + 8u − 1)
· (u
132
+ 6u
131
+ ··· + 89459u + 56393)
c
12
((u − 1)
2
)(u
30
− 6u
29
+ ··· − 2u − 1)(u
132
− 5u
131
+ ··· + 4452u + 103)
29
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
((y −1)
2
)(y
30
− 10y
29
+ ··· − 23y + 1)
· (y
132
− 63y
131
+ ··· − 11311753y + 712336)
c
2
, c
8
(y
2
+ y + 1)(y
30
+ 14y
29
+ ··· − 10y + 1)
· (y
132
+ 88y
131
+ ··· − 71456419y + 1413721)
c
3
(y
2
+ y + 1)(y
30
− 18y
29
+ ··· + y + 1)
· (y
132
− 36y
131
+ ··· − 304367236y + 5013121)
c
5
, c
6
, c
10
((y −1)
2
)(y
30
− 39y
29
+ ··· + 32y + 1)
· (y
132
− 144y
131
+ ··· − 14848y + 361)
c
7
y
2
(y
30
− 7y
29
+ ··· − 1020y + 9)(y
132
+ 2y
131
+ ··· − 4464y + 64)
c
9
(y
2
+ y + 1)(y
30
− 14y
29
+ ··· − 214y + 1)
· (y
132
− 8y
131
+ ··· − 75967363y + 5938969)
c
11
(y
2
+ y + 1)(y
30
+ 24y
29
+ ··· − 14y + 1)
· (y
132
+ 62y
131
+ ··· + 237776842153y + 3180170449)
c
12
((y −1)
2
)(y
30
− 14y
29
+ ··· − 40y + 1)
· (y
132
− 27y
131
+ ··· − 6883504y + 10609)
30
