12a
0399
(K12a
0399
)
A knot diagram
1
Linearized knot diagam
3 6 9 11 2 1 10 12 5 8 4 7
Solving Sequence
2,6
3 1
7,10
8 11 5 4 9 12
c
2
c
1
c
6
c
7
c
10
c
5
c
4
c
9
c
12
c
3
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h8.68978 × 10
61
u
110
− 9.97257 × 10
61
u
109
+ ··· + 4.56538 × 10
61
b − 5.74038 × 10
61
,
1.13849 × 10
61
u
110
− 5.27519 × 10
61
u
109
+ ··· + 4.56538 × 10
61
a + 4.37740 × 10
61
, u
111
− 2u
110
+ ··· − 3u
2
+ 1i
I
u
2
= h14u
5
+ 12u
4
− 6u
3
− 15u
2
+ 17b − 10u − 4, 13u
5
+ 16u
4
− 8u
3
− 20u
2
+ 17a − 2u + 6,
u
6
+ u
5
− u
4
− 2u
3
+ u + 1i
* 2 irreducible components of dim
C
= 0, with total 117 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
= h8.69 × 10
61
u
110
− 9.97 × 10
61
u
109
+ · · · + 4.57 × 10
61
b − 5.74 ×
10
61
, 1.14 × 10
61
u
110
− 5.28 × 10
61
u
109
+ · · · + 4.57 × 10
61
a + 4.38 ×
10
61
, u
111
− 2u
110
+ · · · − 3u
2
+ 1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
u
2
a
1
=
−u
2
+ 1
−u
4
a
7
=
u
5
− 2u
3
+ u
u
7
− u
5
+ u
a
10
=
−0.249374u
110
+ 1.15548u
109
+ ··· + 1.33102u − 0.958826
−1.90341u
110
+ 2.18439u
109
+ ··· + 2.65883u + 1.25737
a
8
=
0.372838u
110
+ 0.358652u
109
+ ··· + 0.368291u − 1.43345
−1.46447u
110
+ 1.53387u
109
+ ··· + 3.34613u + 0.846984
a
11
=
−2.54332u
110
+ 3.45704u
109
+ ··· + 3.89125u + 2.46522
−1.84245u
110
+ 2.92307u
109
+ ··· + 1.27372u + 2.34650
a
5
=
u
u
a
4
=
−0.265304u
110
− 1.25314u
109
+ ··· − 2.83145u − 2.31909
−1.03887u
110
+ 0.341895u
109
+ ··· − 2.01617u − 0.317190
a
9
=
1.60670u
110
− 1.55222u
109
+ ··· − 0.323016u − 3.23798
−0.0473347u
110
− 0.523306u
109
+ ··· + 1.00479u − 1.02178
a
12
=
−u
8
+ 3u
6
− 3u
4
+ 1
−u
10
+ 2u
8
− u
6
− 2u
4
+ u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = 9.59749u
110
− 11.8018u
109
+ ··· − 18.8679u − 4.76652
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
111
+ 60u
110
+ ··· + 6u + 1
c
2
, c
5
u
111
+ 2u
110
+ ··· + 3u
2
− 1
c
3
u
111
− u
110
+ ··· − 44608u − 18496
c
4
, c
11
u
111
− 2u
110
+ ··· + 4u − 1
c
6
, c
12
u
111
+ 6u
110
+ ··· − 2040u − 117
c
7
, c
10
u
111
+ 7u
110
+ ··· − 4863u − 289
c
8
17(17u
111
+ 139u
110
+ ··· − 2325314u − 254971)
c
9
17(17u
111
+ 141u
110
+ ··· + 7037007u − 1137879)
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
111
− 16y
110
+ ··· − 6y −1
c
2
, c
5
y
111
− 60y
110
+ ··· + 6y −1
c
3
y
111
+ 39y
110
+ ··· − 3198476288y −342102016
c
4
, c
11
y
111
+ 60y
110
+ ··· + 6y −1
c
6
, c
12
y
111
+ 92y
110
+ ··· + 253098y −13689
c
7
, c
10
y
111
− 59y
110
+ ··· + 5219239y −83521
c
8
289(289y
111
+ 11857y
110
+ ··· − 7.53479 × 10
11
y −6.50102 × 10
10
)
c
9
289
· (289y
111
+ 5823y
110
+ ··· − 12739163227479y −1294768618641)
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.834615 + 0.535206I
a = 0.375202 − 0.459232I
b = 0.987509 + 0.500262I
−2.59566 − 2.01372I 0
u = 0.834615 − 0.535206I
a = 0.375202 + 0.459232I
b = 0.987509 − 0.500262I
−2.59566 + 2.01372I 0
u = −0.908007 + 0.440150I
a = 0.870965 − 0.756312I
b = 0.345171 − 1.298790I
−0.05778 + 3.59134I 0
u = −0.908007 − 0.440150I
a = 0.870965 + 0.756312I
b = 0.345171 + 1.298790I
−0.05778 − 3.59134I 0
u = 0.946570 + 0.255654I
a = −0.200806 + 0.059664I
b = 0.108262 + 0.411566I
−1.60448 − 0.97268I 0
u = 0.946570 − 0.255654I
a = −0.200806 − 0.059664I
b = 0.108262 − 0.411566I
−1.60448 + 0.97268I 0
u = −0.834031 + 0.470284I
a = 0.39107 − 1.63417I
b = −0.31447 − 2.37348I
1.48070 + 5.11628I 0
u = −0.834031 − 0.470284I
a = 0.39107 + 1.63417I
b = −0.31447 + 2.37348I
1.48070 − 5.11628I 0
u = 0.922985 + 0.492254I
a = −1.51818 − 0.60021I
b = −1.40133 − 1.55983I
−3.52013 − 7.01110I 0
u = 0.922985 − 0.492254I
a = −1.51818 + 0.60021I
b = −1.40133 + 1.55983I
−3.52013 + 7.01110I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.047250 + 0.044475I
a = 0.292931 + 0.818809I
b = −0.10216 + 1.96682I
−6.58005 − 2.08256I 0
u = −1.047250 − 0.044475I
a = 0.292931 − 0.818809I
b = −0.10216 − 1.96682I
−6.58005 + 2.08256I 0
u = −0.859614 + 0.351206I
a = 1.57761 − 3.31213I
b = −4.08024 − 4.07942I
−0.35301 + 1.43124I 0. − 47.2768I
u = −0.859614 − 0.351206I
a = 1.57761 + 3.31213I
b = −4.08024 + 4.07942I
−0.35301 − 1.43124I 0. + 47.2768I
u = 0.922542 + 0.577717I
a = 0.748820 + 0.420068I
b = 0.41068 + 1.81613I
−0.01792 − 12.83630I 0
u = 0.922542 − 0.577717I
a = 0.748820 − 0.420068I
b = 0.41068 − 1.81613I
−0.01792 + 12.83630I 0
u = −0.910545 + 0.597585I
a = −0.421795 + 0.262582I
b = −0.224428 + 1.279370I
3.46581 + 6.78260I 0
u = −0.910545 − 0.597585I
a = −0.421795 − 0.262582I
b = −0.224428 − 1.279370I
3.46581 − 6.78260I 0
u = 0.792090 + 0.442544I
a = 0.512881 − 0.924083I
b = 0.39332 − 1.55392I
2.67871 − 1.96737I 0
u = 0.792090 − 0.442544I
a = 0.512881 + 0.924083I
b = 0.39332 + 1.55392I
2.67871 + 1.96737I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.613109 + 0.665430I
a = 0.692454 − 0.212166I
b = −0.350298 − 0.262501I
4.33033 − 1.91604I 0
u = −0.613109 − 0.665430I
a = 0.692454 + 0.212166I
b = −0.350298 + 0.262501I
4.33033 + 1.91604I 0
u = 0.756067 + 0.438627I
a = 1.31896 − 0.63494I
b = 0.620894 − 0.741219I
2.78293 − 1.81354I 11.47406 + 5.81241I
u = 0.756067 − 0.438627I
a = 1.31896 + 0.63494I
b = 0.620894 + 0.741219I
2.78293 + 1.81354I 11.47406 − 5.81241I
u = −1.134190 + 0.049687I
a = 0.682870 + 0.550231I
b = 1.18470 + 1.53148I
−4.57094 + 7.52155I 0
u = −1.134190 − 0.049687I
a = 0.682870 − 0.550231I
b = 1.18470 − 1.53148I
−4.57094 − 7.52155I 0
u = 0.072095 + 0.859373I
a = −0.928042 − 0.252441I
b = −0.130706 − 0.452834I
−6.15310 − 1.82221I 1.55519 + 4.05739I
u = 0.072095 − 0.859373I
a = −0.928042 + 0.252441I
b = −0.130706 + 0.452834I
−6.15310 + 1.82221I 1.55519 − 4.05739I
u = 0.575345 + 0.641837I
a = −1.155040 − 0.439574I
b = 0.443919 − 0.568552I
0.97421 + 8.10105I 7.90130 − 5.08491I
u = 0.575345 − 0.641837I
a = −1.155040 + 0.439574I
b = 0.443919 + 0.568552I
0.97421 − 8.10105I 7.90130 + 5.08491I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.148173 + 0.848261I
a = −2.14461 − 0.47597I
b = −0.632480 + 0.223096I
−0.67070 − 7.63508I 7.39583 + 5.40933I
u = −0.148173 − 0.848261I
a = −2.14461 + 0.47597I
b = −0.632480 − 0.223096I
−0.67070 + 7.63508I 7.39583 − 5.40933I
u = 1.134030 + 0.110191I
a = −0.468579 + 0.465411I
b = −0.619619 + 1.146050I
−1.61397 − 1.69001I 0
u = 1.134030 − 0.110191I
a = −0.468579 − 0.465411I
b = −0.619619 − 1.146050I
−1.61397 + 1.69001I 0
u = 0.136956 + 0.849470I
a = 2.66559 − 0.79648I
b = 0.781787 + 0.266546I
−4.24399 + 13.44080I 4.60655 − 7.44035I
u = 0.136956 − 0.849470I
a = 2.66559 + 0.79648I
b = 0.781787 − 0.266546I
−4.24399 − 13.44080I 4.60655 + 7.44035I
u = 0.849419 + 0.110125I
a = 0.96130 − 1.04057I
b = 2.04338 − 0.43107I
−1.53260 − 2.25831I 0. + 3.30234I
u = 0.849419 − 0.110125I
a = 0.96130 + 1.04057I
b = 2.04338 + 0.43107I
−1.53260 + 2.25831I 0. − 3.30234I
u = 1.001650 + 0.562088I
a = −0.813131 + 0.346744I
b = −1.46484 + 0.18792I
−0.98280 + 1.31925I 0
u = 1.001650 − 0.562088I
a = −0.813131 − 0.346744I
b = −1.46484 − 0.18792I
−0.98280 − 1.31925I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.409158 + 0.743401I
a = −0.171239 + 0.839413I
b = 0.065651 + 0.169393I
3.36317 − 0.41806I 3.60069 − 8.61246I
u = −0.409158 − 0.743401I
a = −0.171239 − 0.839413I
b = 0.065651 − 0.169393I
3.36317 + 0.41806I 3.60069 + 8.61246I
u = 0.151823 + 0.816435I
a = 2.09192 + 0.59720I
b = 0.446118 + 0.412258I
−5.92471 + 2.62368I 1.84988 − 3.69517I
u = 0.151823 − 0.816435I
a = 2.09192 − 0.59720I
b = 0.446118 − 0.412258I
−5.92471 − 2.62368I 1.84988 + 3.69517I
u = 0.096912 + 0.821896I
a = −2.11840 + 0.22879I
b = −0.700414 − 0.643209I
−7.33687 + 6.64836I 1.77591 − 5.17753I
u = 0.096912 − 0.821896I
a = −2.11840 − 0.22879I
b = −0.700414 + 0.643209I
−7.33687 − 6.64836I 1.77591 + 5.17753I
u = 0.473451 + 0.670363I
a = −0.188811 + 1.380070I
b = −0.374975 + 0.164741I
0.53348 − 6.07102I 7.48092 + 6.72724I
u = 0.473451 − 0.670363I
a = −0.188811 − 1.380070I
b = −0.374975 − 0.164741I
0.53348 + 6.07102I 7.48092 − 6.72724I
u = −0.073132 + 0.817180I
a = 1.55186 + 0.54914I
b = 0.541244 − 0.302568I
−3.58815 − 2.70699I 4.59482 + 2.37332I
u = −0.073132 − 0.817180I
a = 1.55186 − 0.54914I
b = 0.541244 + 0.302568I
−3.58815 + 2.70699I 4.59482 − 2.37332I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.684067 + 0.439055I
a = −2.23694 − 0.06823I
b = −0.985617 + 0.441946I
1.91731 − 1.22530I 11.04588 + 1.99342I
u = −0.684067 − 0.439055I
a = −2.23694 + 0.06823I
b = −0.985617 − 0.441946I
1.91731 + 1.22530I 11.04588 − 1.99342I
u = −0.033204 + 0.769484I
a = 5.08904 + 3.02969I
b = 1.127060 + 0.656234I
−2.86008 − 0.10900I 9.84258 − 2.55547I
u = −0.033204 − 0.769484I
a = 5.08904 − 3.02969I
b = 1.127060 − 0.656234I
−2.86008 + 0.10900I 9.84258 + 2.55547I
u = −1.084640 + 0.583143I
a = 0.574630 − 0.107911I
b = 0.946178 − 0.226442I
1.38553 + 5.44700I 0
u = −1.084640 − 0.583143I
a = 0.574630 + 0.107911I
b = 0.946178 + 0.226442I
1.38553 − 5.44700I 0
u = 0.611298 + 0.456973I
a = 0.216368 − 1.032910I
b = 0.951362 + 0.081774I
−2.07546 − 2.11658I 4.00495 + 2.98042I
u = 0.611298 − 0.456973I
a = 0.216368 + 1.032910I
b = 0.951362 − 0.081774I
−2.07546 + 2.11658I 4.00495 − 2.98042I
u = −0.094700 + 0.755700I
a = 1.71110 + 0.94562I
b = 1.149410 + 0.270931I
−1.24302 − 4.87688I 6.15872 + 7.36426I
u = −0.094700 − 0.755700I
a = 1.71110 − 0.94562I
b = 1.149410 − 0.270931I
−1.24302 + 4.87688I 6.15872 − 7.36426I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.167110 + 0.447186I
a = 0.059015 − 1.247870I
b = −0.82878 − 1.64052I
−2.27607 + 2.52785I 0
u = −1.167110 − 0.447186I
a = 0.059015 + 1.247870I
b = −0.82878 + 1.64052I
−2.27607 − 2.52785I 0
u = 1.186580 + 0.414234I
a = −0.26976 − 1.91118I
b = −0.65215 − 2.05390I
−4.92588 + 0.84899I 0
u = 1.186580 − 0.414234I
a = −0.26976 + 1.91118I
b = −0.65215 + 2.05390I
−4.92588 − 0.84899I 0
u = −1.181480 + 0.432048I
a = 0.08317 − 2.05447I
b = −0.07886 − 2.71531I
−3.05777 + 2.55271I 0
u = −1.181480 − 0.432048I
a = 0.08317 + 2.05447I
b = −0.07886 + 2.71531I
−3.05777 − 2.55271I 0
u = 1.171300 + 0.465621I
a = −0.262232 + 0.143007I
b = 0.634808 + 0.005375I
−2.13515 − 5.82401I 0
u = 1.171300 − 0.465621I
a = −0.262232 − 0.143007I
b = 0.634808 − 0.005375I
−2.13515 + 5.82401I 0
u = 0.065295 + 0.728847I
a = −1.74544 − 0.09492I
b = −0.830463 + 0.399357I
0.45155 + 1.53825I 9.48415 − 0.44881I
u = 0.065295 − 0.728847I
a = −1.74544 + 0.09492I
b = −0.830463 − 0.399357I
0.45155 − 1.53825I 9.48415 + 0.44881I
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.182730 + 0.474899I
a = −0.39732 + 1.60339I
b = 0.06979 + 2.13006I
−2.74783 − 5.99194I 0
u = 1.182730 − 0.474899I
a = −0.39732 − 1.60339I
b = 0.06979 − 2.13006I
−2.74783 + 5.99194I 0
u = −1.219700 + 0.371465I
a = 0.50263 + 1.57686I
b = 0.15018 + 2.65967I
−10.07290 + 1.36463I 0
u = −1.219700 − 0.371465I
a = 0.50263 − 1.57686I
b = 0.15018 − 2.65967I
−10.07290 − 1.36463I 0
u = 1.199800 + 0.440822I
a = −2.19421 − 3.51627I
b = −3.96032 − 5.37523I
−6.43194 − 4.18755I 0
u = 1.199800 − 0.440822I
a = −2.19421 + 3.51627I
b = −3.96032 + 5.37523I
−6.43194 + 4.18755I 0
u = −1.186700 + 0.486566I
a = 0.98713 + 2.09189I
b = 1.23768 + 2.59947I
−4.41124 + 9.46317I 0
u = −1.186700 − 0.486566I
a = 0.98713 − 2.09189I
b = 1.23768 − 2.59947I
−4.41124 − 9.46317I 0
u = −1.198340 + 0.467259I
a = 1.54747 + 4.75010I
b = 1.94702 + 7.94556I
−6.24285 + 4.59853I 0
u = −1.198340 − 0.467259I
a = 1.54747 − 4.75010I
b = 1.94702 − 7.94556I
−6.24285 − 4.59853I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.225740 + 0.404164I
a = −0.310727 − 1.348810I
b = 0.59931 − 2.01057I
−11.31140 − 2.41858I 0
u = −1.225740 − 0.404164I
a = −0.310727 + 1.348810I
b = 0.59931 + 2.01057I
−11.31140 + 2.41858I 0
u = 1.240030 + 0.368039I
a = 0.16809 + 1.52440I
b = 0.96807 + 2.28237I
−4.95179 + 3.52392I 0
u = 1.240030 − 0.368039I
a = 0.16809 − 1.52440I
b = 0.96807 − 2.28237I
−4.95179 − 3.52392I 0
u = 1.225170 + 0.418267I
a = −0.035968 − 1.055780I
b = −0.77728 − 1.52376I
−7.46544 − 1.60252I 0
u = 1.225170 − 0.418267I
a = −0.035968 + 1.055780I
b = −0.77728 + 1.52376I
−7.46544 + 1.60252I 0
u = −1.242340 + 0.376296I
a = −0.39829 + 1.84552I
b = −1.52361 + 2.72383I
−8.48648 − 9.27237I 0
u = −1.242340 − 0.376296I
a = −0.39829 − 1.84552I
b = −1.52361 − 2.72383I
−8.48648 + 9.27237I 0
u = 0.487292 + 0.497011I
a = 1.31420 + 1.39855I
b = 0.097562 + 0.891708I
−2.35922 + 2.92531I 4.93460 − 2.97763I
u = 0.487292 − 0.497011I
a = 1.31420 − 1.39855I
b = 0.097562 − 0.891708I
−2.35922 − 2.92531I 4.93460 + 2.97763I
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.196470 + 0.520819I
a = −0.70602 − 1.78842I
b = −1.01996 − 2.82973I
−9.01307 − 7.53686I 0
u = 1.196470 − 0.520819I
a = −0.70602 + 1.78842I
b = −1.01996 + 2.82973I
−9.01307 + 7.53686I 0
u = −1.211100 + 0.489866I
a = 0.13518 + 1.72594I
b = 0.52771 + 2.53911I
−6.95115 + 7.44961I 0
u = −1.211100 − 0.489866I
a = 0.13518 − 1.72594I
b = 0.52771 − 2.53911I
−6.95115 − 7.44961I 0
u = 1.209200 + 0.499490I
a = 0.34195 + 2.22331I
b = −0.00360 + 3.25080I
−10.6314 − 11.4594I 0
u = 1.209200 − 0.499490I
a = 0.34195 − 2.22331I
b = −0.00360 − 3.25080I
−10.6314 + 11.4594I 0
u = −1.247010 + 0.417146I
a = −0.386749 − 0.568967I
b = −0.020014 − 1.127550I
−10.17840 + 6.27369I 0
u = −1.247010 − 0.417146I
a = −0.386749 + 0.568967I
b = −0.020014 + 1.127550I
−10.17840 − 6.27369I 0
u = −1.208710 + 0.525173I
a = −0.11494 − 2.07415I
b = −0.34802 − 3.19996I
−3.83617 + 12.64810I 0
u = −1.208710 − 0.525173I
a = −0.11494 + 2.07415I
b = −0.34802 + 3.19996I
−3.83617 − 12.64810I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.211700 + 0.521330I
a = 0.26134 − 2.56449I
b = 0.65968 − 3.97940I
−7.4521 − 18.4366I 0
u = 1.211700 − 0.521330I
a = 0.26134 + 2.56449I
b = 0.65968 + 3.97940I
−7.4521 + 18.4366I 0
u = 1.228900 + 0.494017I
a = 0.440809 + 0.916961I
b = 0.35173 + 1.46927I
−9.62629 − 3.05742I 0
u = 1.228900 − 0.494017I
a = 0.440809 − 0.916961I
b = 0.35173 − 1.46927I
−9.62629 + 3.05742I 0
u = 0.050741 + 0.672914I
a = −0.426694 − 0.829633I
b = −0.390008 + 0.690859I
1.00384 + 1.53449I 9.06398 − 3.66873I
u = 0.050741 − 0.672914I
a = −0.426694 + 0.829633I
b = −0.390008 − 0.690859I
1.00384 − 1.53449I 9.06398 + 3.66873I
u = −0.560641 + 0.291332I
a = −1.42054 + 0.18920I
b = −0.660713 + 0.576041I
0.930968 − 0.039487I 11.38983 + 0.48618I
u = −0.560641 − 0.291332I
a = −1.42054 − 0.18920I
b = −0.660713 − 0.576041I
0.930968 + 0.039487I 11.38983 − 0.48618I
u = −0.535332
a = −1.76526
b = −0.957282
0.895049 11.9250
u = −0.182707 + 0.342215I
a = −1.36709 − 2.30419I
b = −0.424404 + 0.710330I
1.02805 + 1.15491I 7.92536 − 0.29840I
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.182707 − 0.342215I
a = −1.36709 + 2.30419I
b = −0.424404 − 0.710330I
1.02805 − 1.15491I 7.92536 + 0.29840I
16
II. I
u
2
= h14u
5
+ 12u
4
− 6u
3
− 15u
2
+ 17b − 10u − 4, 13u
5
+ 16u
4
− 8u
3
−
20u
2
+ 17a − 2u + 6, u
6
+ u
5
− u
4
− 2u
3
+ u + 1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
u
2
a
1
=
−u
2
+ 1
−u
4
a
7
=
u
5
− 2u
3
+ u
u
5
+ u
4
− 2u
3
− u
2
+ u + 1
a
10
=
−0.764706u
5
− 0.941176u
4
+ ··· + 0.117647u − 0.352941
−0.823529u
5
− 0.705882u
4
+ ··· + 0.588235u + 0.235294
a
8
=
0.235294u
5
− 0.941176u
4
+ ··· + 1.11765u − 0.352941
0.176471u
5
+ 0.294118u
4
+ ··· + 1.58824u + 1.23529
a
11
=
−u
5
+ 2u
3
− u
−u
5
− u
4
+ 2u
3
+ u
2
− u − 1
a
5
=
u
u
a
4
=
1
u
2
a
9
=
−0.294118u
5
− 0.823529u
4
+ ··· + 0.352941u − 0.0588235
−0.352941u
5
− 0.588235u
4
+ ··· + 0.823529u + 0.529412
a
12
=
−2u
5
+ 3u
3
− 2u
−2u
5
− 2u
4
+ 3u
3
+ 2u
2
− u − 2
(ii) Obstruction class = 1
(iii) Cusp Shapes =
1033
289
u
5
+
1801
289
u
4
−
2269
289
u
3
−
1975
289
u
2
+
236
289
u +
4120
289
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1
c
2
, c
4
u
6
+ u
5
− u
4
− 2u
3
+ u + 1
c
3
u
6
c
5
, c
11
u
6
− u
5
− u
4
+ 2u
3
− u + 1
c
7
(u + 1)
6
c
8
17(17u
6
+ 58u
5
+ 89u
4
+ 74u
3
+ 35u
2
+ 9u + 1)
c
9
17(17u
6
+ 28u
5
+ 4u
4
− 15u
3
− 6u
2
+ 2u + 1)
c
10
(u − 1)
6
c
12
u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
, c
12
y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1
c
2
, c
4
, c
5
c
11
y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1
c
3
y
6
c
7
, c
10
(y −1)
6
c
8
289(289y
6
− 338y
5
+ 527y
4
− 256y
3
+ 71y
2
− 11y + 1)
c
9
289(289y
6
− 648y
5
+ 652y
4
− 351y
3
+ 104y
2
− 16y + 1)
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.002190 + 0.295542I
a = 0.602693 − 0.827374I
b = 1.41061 − 0.78118I
−0.245672 − 0.924305I 6.62801 + 0.58456I
u = 1.002190 − 0.295542I
a = 0.602693 + 0.827374I
b = 1.41061 + 0.78118I
−0.245672 + 0.924305I 6.62801 − 0.58456I
u = −0.428243 + 0.664531I
a = −0.169822 − 0.607111I
b = 0.179799 − 0.048858I
3.53554 − 0.92430I 9.92560 + 4.63647I
u = −0.428243 − 0.664531I
a = −0.169822 + 0.607111I
b = 0.179799 + 0.048858I
3.53554 + 0.92430I 9.92560 − 4.63647I
u = −1.073950 + 0.558752I
a = −0.374048 + 0.036748I
b = −0.796289 − 0.132787I
1.64493 + 5.69302I 11.7370 − 11.4468I
u = −1.073950 − 0.558752I
a = −0.374048 − 0.036748I
b = −0.796289 + 0.132787I
1.64493 − 5.69302I 11.7370 + 11.4468I
20
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1)(u
111
+ 60u
110
+ ··· + 6u + 1)
c
2
(u
6
+ u
5
− u
4
− 2u
3
+ u + 1)(u
111
+ 2u
110
+ ··· + 3u
2
− 1)
c
3
u
6
(u
111
− u
110
+ ··· − 44608u − 18496)
c
4
(u
6
+ u
5
− u
4
− 2u
3
+ u + 1)(u
111
− 2u
110
+ ··· + 4u − 1)
c
5
(u
6
− u
5
− u
4
+ 2u
3
− u + 1)(u
111
+ 2u
110
+ ··· + 3u
2
− 1)
c
6
(u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1)(u
111
+ 6u
110
+ ··· − 2040u − 117)
c
7
((u + 1)
6
)(u
111
+ 7u
110
+ ··· − 4863u − 289)
c
8
289(17u
6
+ 58u
5
+ 89u
4
+ 74u
3
+ 35u
2
+ 9u + 1)
· (17u
111
+ 139u
110
+ ··· − 2325314u − 254971)
c
9
289(17u
6
+ 28u
5
+ 4u
4
− 15u
3
− 6u
2
+ 2u + 1)
· (17u
111
+ 141u
110
+ ··· + 7037007u − 1137879)
c
10
((u − 1)
6
)(u
111
+ 7u
110
+ ··· − 4863u − 289)
c
11
(u
6
− u
5
− u
4
+ 2u
3
− u + 1)(u
111
− 2u
110
+ ··· + 4u − 1)
c
12
(u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1)(u
111
+ 6u
110
+ ··· − 2040u − 117)
21
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)(y
111
− 16y
110
+ ··· − 6y −1)
c
2
, c
5
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)(y
111
− 60y
110
+ ··· + 6y −1)
c
3
y
6
(y
111
+ 39y
110
+ ··· − 3.19848 × 10
9
y −3.42102 × 10
8
)
c
4
, c
11
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)(y
111
+ 60y
110
+ ··· + 6y −1)
c
6
, c
12
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)(y
111
+ 92y
110
+ ··· + 253098y −13689)
c
7
, c
10
((y −1)
6
)(y
111
− 59y
110
+ ··· + 5219239y −83521)
c
8
83521(289y
6
− 338y
5
+ 527y
4
− 256y
3
+ 71y
2
− 11y + 1)
· (289y
111
+ 11857y
110
+ ··· − 753479228508y −65010210841)
c
9
83521(289y
6
− 648y
5
+ 652y
4
− 351y
3
+ 104y
2
− 16y + 1)
· (289y
111
+ 5823y
110
+ ··· − 12739163227479y −1294768618641)
22
