12a
0010
(K12a
0010
)
A knot diagram
1
Linearized knot diagam
3 5 6 8 2 11 9 4 12 7 1 10
Solving Sequence
9,12
10
1,4
8 5 7 11 6 3 2
c
9
c
12
c
8
c
4
c
7
c
11
c
6
c
3
c
2
c
1
, c
5
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h1.53494 × 10
76
u
118
+ 2.11404 × 10
77
u
117
+ ··· + 6.29838 × 10
74
b − 4.20588 × 10
76
,
− 3.27734 × 10
76
u
118
− 1.76333 × 10
77
u
117
+ ··· + 3.14919 × 10
74
a − 2.34713 × 10
77
,
u
119
+ 13u
118
+ ··· − 20u − 1i
I
u
2
= h−a
3
− a
2
+ b − a, a
4
+ a
3
+ a
2
+ 1, u − 1i
I
u
3
= hb, u
2
a + a
2
+ 2au + 3u
2
+ a + 5u + 4, u
3
+ u
2
− 1i
I
u
4
= h−a
5
+ 2a
4
− 2a
3
+ 2a
2
+ b − 2a + 1, a
6
− 2a
5
+ 2a
4
− 2a
3
+ 2a
2
− a + 1, u − 1i
* 4 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
= h1.53 × 10
76
u
118
+ 2.11 × 10
77
u
117
+ · · · + 6.30 × 10
74
b − 4.21 ×
10
76
, −3.28 × 10
76
u
118
− 1.76 × 10
77
u
117
+ · · · + 3.15 × 10
74
a − 2.35 ×
10
77
, u
119
+ 13u
118
+ · · · − 20u − 1i
(i) Arc colorings
a
9
=
1
0
a
12
=
0
u
a
10
=
1
u
2
a
1
=
−u
−u
3
+ u
a
4
=
104.069u
118
+ 559.930u
117
+ ··· + 12845.3u + 745.312
−24.3704u
118
− 335.648u
117
+ ··· + 1158.29u + 66.7771
a
8
=
148.115u
118
+ 1786.08u
117
+ ··· − 3799.29u − 227.176
27.5034u
118
+ 486.129u
117
+ ··· − 4211.15u − 238.606
a
5
=
509.194u
118
+ 5592.67u
117
+ ··· + 4807.30u + 342.681
332.399u
118
+ 4415.95u
117
+ ··· − 11668.3u − 608.640
a
7
=
175.618u
118
+ 2272.21u
117
+ ··· − 8010.44u − 465.782
27.5034u
118
+ 486.129u
117
+ ··· − 4211.15u − 238.606
a
11
=
u
3
u
5
− u
3
+ u
a
6
=
99.1977u
118
+ 1386.25u
117
+ ··· − 7021.64u − 412.862
−67.9945u
118
− 781.463u
117
+ ··· − 702.392u − 51.4383
a
3
=
928.371u
118
+ 10559.2u
117
+ ··· − 672.763u + 54.6534
660.964u
118
+ 8651.81u
117
+ ··· − 22541.4u − 1190.83
a
2
=
466.460u
118
+ 5235.90u
117
+ ··· + 1169.98u + 102.276
557.127u
118
+ 7140.14u
117
+ ··· − 16297.2u − 860.184
(ii) Obstruction class = −1
(iii) Cusp Shapes = 413.566u
118
+ 3160.04u
117
+ ··· + 29822.9u + 1714.64
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
119
+ 55u
118
+ ··· + 208u − 1
c
2
, c
5
u
119
+ 5u
118
+ ··· + 8u − 1
c
3
u
119
− 5u
118
+ ··· + 5788u − 292
c
4
, c
8
u
119
− 2u
118
+ ··· + 32u + 64
c
6
, c
10
u
119
− 3u
118
+ ··· − 5120u + 1024
c
7
u
119
+ 40u
118
+ ··· − 80896u − 4096
c
9
, c
12
u
119
− 13u
118
+ ··· − 20u + 1
c
11
u
119
+ 53u
118
+ ··· − 14u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
119
+ 23y
118
+ ··· + 45340y −1
c
2
, c
5
y
119
+ 55y
118
+ ··· + 208y −1
c
3
y
119
− 9y
118
+ ··· + 26282120y −85264
c
4
, c
8
y
119
+ 40y
118
+ ··· − 80896y −4096
c
6
, c
10
y
119
+ 69y
118
+ ··· − 31981568y −1048576
c
7
y
119
+ 68y
118
+ ··· + 5134876672y −16777216
c
9
, c
12
y
119
− 53y
118
+ ··· − 14y −1
c
11
y
119
+ 39y
118
+ ··· + 5618y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.839718 + 0.548941I
a = 1.03007 + 1.37383I
b = −0.794811 − 0.704672I
1.89954 − 0.71334I 0
u = 0.839718 − 0.548941I
a = 1.03007 − 1.37383I
b = −0.794811 + 0.704672I
1.89954 + 0.71334I 0
u = −0.414192 + 0.897221I
a = 1.060200 − 0.496479I
b = −0.687708 + 1.025140I
0.91210 − 4.63467I 0
u = −0.414192 − 0.897221I
a = 1.060200 + 0.496479I
b = −0.687708 − 1.025140I
0.91210 + 4.63467I 0
u = −0.835785 + 0.571845I
a = 0.665117 − 0.447173I
b = −0.834943 − 0.140628I
1.84382 + 2.29296I 0
u = −0.835785 − 0.571845I
a = 0.665117 + 0.447173I
b = −0.834943 + 0.140628I
1.84382 − 2.29296I 0
u = −0.479737 + 0.894115I
a = 1.68069 + 0.21651I
b = −0.948305 − 0.723106I
5.19353 − 5.82530I 0
u = −0.479737 − 0.894115I
a = 1.68069 − 0.21651I
b = −0.948305 + 0.723106I
5.19353 + 5.82530I 0
u = 0.859164 + 0.551104I
a = 2.56167 + 0.36793I
b = −0.692210 + 0.826381I
1.83580 − 3.70893I 0
u = 0.859164 − 0.551104I
a = 2.56167 − 0.36793I
b = −0.692210 − 0.826381I
1.83580 + 3.70893I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.920082 + 0.330594I
a = −1.05886 − 1.09117I
b = 0.701252 + 0.313348I
−2.14764 + 0.46525I 0
u = 0.920082 − 0.330594I
a = −1.05886 + 1.09117I
b = 0.701252 − 0.313348I
−2.14764 − 0.46525I 0
u = −0.535990 + 0.870642I
a = 1.351430 − 0.147219I
b = −0.718212 + 0.865805I
5.58089 + 1.54128I 0
u = −0.535990 − 0.870642I
a = 1.351430 + 0.147219I
b = −0.718212 − 0.865805I
5.58089 − 1.54128I 0
u = −0.811525 + 0.533856I
a = −0.006008 + 1.406260I
b = −0.202031 + 0.895750I
1.40789 − 0.40488I 0
u = −0.811525 − 0.533856I
a = −0.006008 − 1.406260I
b = −0.202031 − 0.895750I
1.40789 + 0.40488I 0
u = −0.506849 + 0.899088I
a = −1.324780 + 0.302703I
b = 0.743370 − 0.916592I
6.96695 − 3.78303I 0
u = −0.506849 − 0.899088I
a = −1.324780 − 0.302703I
b = 0.743370 + 0.916592I
6.96695 + 3.78303I 0
u = −0.520633 + 0.894920I
a = −1.58006 − 0.26157I
b = 0.896350 + 0.744474I
7.05859 − 0.70677I 0
u = −0.520633 − 0.894920I
a = −1.58006 + 0.26157I
b = 0.896350 − 0.744474I
7.05859 + 0.70677I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.700245 + 0.663386I
a = −0.88509 − 1.53838I
b = 0.659039 + 0.972129I
−0.29156 + 6.55308I 0
u = 0.700245 − 0.663386I
a = −0.88509 + 1.53838I
b = 0.659039 − 0.972129I
−0.29156 − 6.55308I 0
u = −0.880230 + 0.554713I
a = 0.36352 − 1.59110I
b = 0.057310 − 0.897606I
1.17161 + 4.80695I 0
u = −0.880230 − 0.554713I
a = 0.36352 + 1.59110I
b = 0.057310 + 0.897606I
1.17161 − 4.80695I 0
u = −0.563327 + 0.775350I
a = 1.353100 − 0.003460I
b = −0.815150 − 0.602192I
2.15561 + 0.96157I 0
u = −0.563327 − 0.775350I
a = 1.353100 + 0.003460I
b = −0.815150 + 0.602192I
2.15561 − 0.96157I 0
u = 0.729173 + 0.618822I
a = 0.91485 + 1.48291I
b = −0.677218 − 0.888176I
1.64414 + 1.56779I 0
u = 0.729173 − 0.618822I
a = 0.91485 − 1.48291I
b = −0.677218 + 0.888176I
1.64414 − 1.56779I 0
u = 0.806433 + 0.513028I
a = −2.73489 − 0.49333I
b = 0.677943 − 0.716615I
0.49484 + 1.35815I 0
u = 0.806433 − 0.513028I
a = −2.73489 + 0.49333I
b = 0.677943 + 0.716615I
0.49484 − 1.35815I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.896751 + 0.539049I
a = −1.09612 − 1.34285I
b = 0.874636 + 0.641589I
0.17888 − 5.63399I 0
u = 0.896751 − 0.539049I
a = −1.09612 + 1.34285I
b = 0.874636 − 0.641589I
0.17888 + 5.63399I 0
u = −0.449457 + 0.951285I
a = −1.264510 + 0.571043I
b = 0.774340 − 1.021660I
6.17714 − 6.89104I 0
u = −0.449457 − 0.951285I
a = −1.264510 − 0.571043I
b = 0.774340 + 1.021660I
6.17714 + 6.89104I 0
u = −0.432123 + 0.970962I
a = 1.25415 − 0.65761I
b = −0.785309 + 1.057920I
4.11704 − 12.19560I 0
u = −0.432123 − 0.970962I
a = 1.25415 + 0.65761I
b = −0.785309 − 1.057920I
4.11704 + 12.19560I 0
u = −0.935084 + 0.512602I
a = −0.632458 + 0.577496I
b = 1.039780 − 0.012368I
−1.16555 + 5.57300I 0
u = −0.935084 − 0.512602I
a = −0.632458 − 0.577496I
b = 1.039780 + 0.012368I
−1.16555 − 5.57300I 0
u = −0.810344 + 0.451943I
a = −0.728244 + 0.571667I
b = 1.018150 + 0.257504I
−0.64746 − 1.61824I 0
u = −0.810344 − 0.451943I
a = −0.728244 − 0.571667I
b = 1.018150 − 0.257504I
−0.64746 + 1.61824I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.857581 + 0.325966I
a = 0.188149 − 0.845340I
b = 0.348024 − 1.228190I
−5.56356 + 0.94413I 0
u = −0.857581 − 0.325966I
a = 0.188149 + 0.845340I
b = 0.348024 + 1.228190I
−5.56356 − 0.94413I 0
u = 1.073860 + 0.172674I
a = 1.16829 + 1.04677I
b = −0.698025 + 0.105091I
−2.63266 − 2.23010I 0
u = 1.073860 − 0.172674I
a = 1.16829 − 1.04677I
b = −0.698025 − 0.105091I
−2.63266 + 2.23010I 0
u = −0.612148 + 0.916355I
a = −1.36804 − 0.41960I
b = 0.767030 + 0.815475I
7.27557 + 1.92163I 0
u = −0.612148 − 0.916355I
a = −1.36804 + 0.41960I
b = 0.767030 − 0.815475I
7.27557 − 1.92163I 0
u = 0.895015 + 0.056762I
a = −0.97632 − 4.21446I
b = 0.037868 − 0.362547I
−1.30782 − 2.14757I 0
u = 0.895015 − 0.056762I
a = −0.97632 + 4.21446I
b = 0.037868 + 0.362547I
−1.30782 + 2.14757I 0
u = 0.938429 + 0.604225I
a = 2.35579 + 0.15592I
b = −0.711352 + 0.998662I
0.99788 − 6.39299I 0
u = 0.938429 − 0.604225I
a = 2.35579 − 0.15592I
b = −0.711352 − 0.998662I
0.99788 + 6.39299I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.978707 + 0.546639I
a = −2.16911 − 0.28799I
b = 0.578860 − 1.013760I
−3.94184 − 4.12095I 0
u = 0.978707 − 0.546639I
a = −2.16911 + 0.28799I
b = 0.578860 + 1.013760I
−3.94184 + 4.12095I 0
u = −1.029680 + 0.451076I
a = −0.759282 + 0.856662I
b = 0.104751 + 1.287900I
−6.58231 + 2.05524I 0
u = −1.029680 − 0.451076I
a = −0.759282 − 0.856662I
b = 0.104751 − 1.287900I
−6.58231 − 2.05524I 0
u = −0.649950 + 0.933230I
a = 1.287340 + 0.511260I
b = −0.706439 − 0.861121I
5.59145 + 6.98652I 0
u = −0.649950 − 0.933230I
a = 1.287340 − 0.511260I
b = −0.706439 + 0.861121I
5.59145 − 6.98652I 0
u = 0.960992 + 0.623339I
a = −2.31214 − 0.07898I
b = 0.724478 − 1.053400I
−1.08963 − 11.56600I 0
u = 0.960992 − 0.623339I
a = −2.31214 + 0.07898I
b = 0.724478 + 1.053400I
−1.08963 + 11.56600I 0
u = −0.817590 + 0.805347I
a = 0.587598 + 0.323895I
b = −0.296511 − 0.547479I
2.77173 + 1.39379I 0
u = −0.817590 − 0.805347I
a = 0.587598 − 0.323895I
b = −0.296511 + 0.547479I
2.77173 − 1.39379I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.111590 + 0.323733I
a = −1.17299 − 0.82930I
b = 0.066112 − 0.973792I
−3.92676 − 1.15806I 0
u = 1.111590 − 0.323733I
a = −1.17299 + 0.82930I
b = 0.066112 + 0.973792I
−3.92676 + 1.15806I 0
u = −1.039170 + 0.511622I
a = 0.966640 − 0.982366I
b = −0.216751 − 1.189260I
−2.70805 + 5.79660I 0
u = −1.039170 − 0.511622I
a = 0.966640 + 0.982366I
b = −0.216751 + 1.189260I
−2.70805 − 5.79660I 0
u = 0.825868
a = −0.825487
b = 0.262404
−1.19842 0
u = −0.789158 + 0.234058I
a = 0.046847 − 0.787410I
b = 0.556048 − 1.191030I
−3.70047 − 7.10733I 0
u = −0.789158 − 0.234058I
a = 0.046847 + 0.787410I
b = 0.556048 + 1.191030I
−3.70047 + 7.10733I 0
u = −0.757598 + 0.296110I
a = −0.051753 + 0.850977I
b = −0.477016 + 1.110170I
−1.16003 − 2.19769I 0
u = −0.757598 − 0.296110I
a = −0.051753 − 0.850977I
b = −0.477016 − 1.110170I
−1.16003 + 2.19769I 0
u = −1.086580 + 0.507173I
a = −1.060610 + 0.806288I
b = 0.299743 + 1.275690I
−5.76467 + 10.31460I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.086580 − 0.507173I
a = −1.060610 − 0.806288I
b = 0.299743 − 1.275690I
−5.76467 − 10.31460I 0
u = 1.137620 + 0.399746I
a = 1.317670 + 0.471398I
b = −0.156909 + 1.115740I
−6.84406 − 5.05649I 0
u = 1.137620 − 0.399746I
a = 1.317670 − 0.471398I
b = −0.156909 − 1.115740I
−6.84406 + 5.05649I 0
u = 0.566725 + 0.544339I
a = −0.74644 − 1.42376I
b = 0.411940 + 0.873848I
−2.76173 − 0.28929I 0
u = 0.566725 − 0.544339I
a = −0.74644 + 1.42376I
b = 0.411940 − 0.873848I
−2.76173 + 0.28929I 0
u = −0.918520 + 0.804272I
a = −0.183100 − 0.583283I
b = −0.138746 + 0.590858I
2.48569 + 4.61487I 0
u = −0.918520 − 0.804272I
a = −0.183100 + 0.583283I
b = −0.138746 − 0.590858I
2.48569 − 4.61487I 0
u = −1.059890 + 0.640593I
a = 0.480179 − 0.776739I
b = −0.955852 + 0.487819I
0.63997 + 4.40174I 0
u = −1.059890 − 0.640593I
a = 0.480179 + 0.776739I
b = −0.955852 − 0.487819I
0.63997 − 4.40174I 0
u = 1.197300 + 0.316904I
a = 0.855329 + 0.548247I
b = 0.063583 + 1.105510I
−7.04263 + 2.47483I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.197300 − 0.316904I
a = 0.855329 − 0.548247I
b = 0.063583 − 1.105510I
−7.04263 − 2.47483I 0
u = 1.251080 + 0.049890I
a = 0.757436 + 0.867886I
b = −0.772334 + 0.600594I
−1.06625 + 3.37112I 0
u = 1.251080 − 0.049890I
a = 0.757436 − 0.867886I
b = −0.772334 − 0.600594I
−1.06625 − 3.37112I 0
u = 1.269350 + 0.008920I
a = −0.555567 + 0.802077I
b = 0.702631 + 0.733404I
0.42376 + 1.47707I 0
u = 1.269350 − 0.008920I
a = −0.555567 − 0.802077I
b = 0.702631 − 0.733404I
0.42376 − 1.47707I 0
u = −1.087090 + 0.679594I
a = 1.86636 − 1.04154I
b = −0.629300 − 0.928389I
3.90770 + 4.19903I 0
u = −1.087090 − 0.679594I
a = 1.86636 + 1.04154I
b = −0.629300 + 0.928389I
3.90770 − 4.19903I 0
u = 1.284030 + 0.143247I
a = 0.036853 − 0.615614I
b = −0.495015 − 0.986392I
−4.93724 + 1.60165I 0
u = 1.284030 − 0.143247I
a = 0.036853 + 0.615614I
b = −0.495015 + 0.986392I
−4.93724 − 1.60165I 0
u = −1.064710 + 0.741240I
a = −0.277342 + 0.897515I
b = 0.742689 − 0.725590I
5.89617 + 4.15536I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.064710 − 0.741240I
a = −0.277342 − 0.897515I
b = 0.742689 + 0.725590I
5.89617 − 4.15536I 0
u = −1.102950 + 0.686493I
a = −0.440580 + 0.903893I
b = 0.949091 − 0.677833I
5.28838 + 6.53580I 0
u = −1.102950 − 0.686493I
a = −0.440580 − 0.903893I
b = 0.949091 + 0.677833I
5.28838 − 6.53580I 0
u = −1.111110 + 0.682830I
a = −1.88014 + 0.91406I
b = 0.686421 + 0.974756I
5.12997 + 9.61003I 0
u = −1.111110 − 0.682830I
a = −1.88014 − 0.91406I
b = 0.686421 − 0.974756I
5.12997 − 9.61003I 0
u = −1.050750 + 0.774843I
a = 0.177397 − 0.916450I
b = −0.634242 + 0.782662I
4.37242 − 0.75282I 0
u = −1.050750 − 0.774843I
a = 0.177397 + 0.916450I
b = −0.634242 − 0.782662I
4.37242 + 0.75282I 0
u = −1.121590 + 0.670685I
a = 0.492218 − 0.917395I
b = −1.022270 + 0.680881I
3.24675 + 11.59470I 0
u = −1.121590 − 0.670685I
a = 0.492218 + 0.917395I
b = −1.022270 − 0.680881I
3.24675 − 11.59470I 0
u = −0.075409 + 0.682425I
a = 0.086947 + 0.787821I
b = 0.292630 − 1.071980I
−3.15480 − 6.11083I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.075409 − 0.682425I
a = 0.086947 − 0.787821I
b = 0.292630 + 1.071980I
−3.15480 + 6.11083I 0
u = −1.147180 + 0.650115I
a = 1.73131 − 0.74067I
b = −0.686674 − 1.117410I
−1.29805 + 10.32960I 0
u = −1.147180 − 0.650115I
a = 1.73131 + 0.74067I
b = −0.686674 + 1.117410I
−1.29805 − 10.32960I 0
u = 1.326620 + 0.083300I
a = −0.325119 + 0.532619I
b = 0.671338 + 0.960557I
−0.26952 + 3.81757I 0
u = 1.326620 − 0.083300I
a = −0.325119 − 0.532619I
b = 0.671338 − 0.960557I
−0.26952 − 3.81757I 0
u = −1.155800 + 0.680181I
a = −1.86342 + 0.70790I
b = 0.768201 + 1.078860I
4.01736 + 12.84630I 0
u = −1.155800 − 0.680181I
a = −1.86342 − 0.70790I
b = 0.768201 − 1.078860I
4.01736 − 12.84630I 0
u = −1.170030 + 0.679801I
a = 1.86153 − 0.64817I
b = −0.794031 − 1.111020I
1.8548 + 18.2010I 0
u = −1.170030 − 0.679801I
a = 1.86153 + 0.64817I
b = −0.794031 + 1.111020I
1.8548 − 18.2010I 0
u = 1.350500 + 0.100867I
a = 0.291784 − 0.425025I
b = −0.680751 − 1.032630I
−2.33665 + 8.88021I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.350500 − 0.100867I
a = 0.291784 + 0.425025I
b = −0.680751 + 1.032630I
−2.33665 − 8.88021I 0
u = 0.150755 + 0.591114I
a = 0.504351 + 1.143880I
b = 0.056505 − 1.015650I
−3.91792 + 1.14684I −8.51521 + 0.I
u = 0.150755 − 0.591114I
a = 0.504351 − 1.143880I
b = 0.056505 + 1.015650I
−3.91792 − 1.14684I −8.51521 + 0.I
u = −0.093073 + 0.502065I
a = −0.508653 − 0.490205I
b = −0.275501 + 0.917380I
−0.62717 − 1.91102I −1.98255 + 3.82961I
u = −0.093073 − 0.502065I
a = −0.508653 + 0.490205I
b = −0.275501 − 0.917380I
−0.62717 + 1.91102I −1.98255 − 3.82961I
u = −0.184995 + 0.007775I
a = −0.96664 + 2.79178I
b = −0.495391 + 0.508906I
0.72033 − 1.37466I 2.82252 + 4.33533I
u = −0.184995 − 0.007775I
a = −0.96664 − 2.79178I
b = −0.495391 − 0.508906I
0.72033 + 1.37466I 2.82252 − 4.33533I
u = 0.000756 + 0.150219I
a = −3.95378 + 3.90980I
b = 0.597693 + 0.197031I
−0.27659 − 2.59654I 1.38730 + 3.76116I
u = 0.000756 − 0.150219I
a = −3.95378 − 3.90980I
b = 0.597693 − 0.197031I
−0.27659 + 2.59654I 1.38730 − 3.76116I
16
II. I
u
2
= h−a
3
− a
2
+ b − a, a
4
+ a
3
+ a
2
+ 1, u − 1i
(i) Arc colorings
a
9
=
1
0
a
12
=
0
1
a
10
=
1
1
a
1
=
−1
0
a
4
=
a
a
3
+ a
2
+ a
a
8
=
0
−a
2
− a − 1
a
5
=
a
a + 1
a
7
=
−a
2
− a − 1
−a
2
− a − 1
a
11
=
1
1
a
6
=
−a
2
− a − 1
−a
2
− a − 1
a
3
=
−a
3
− 2a
2
− a − 1
−a
2
− a − 1
a
2
=
−a
3
− 2a
2
− a
−a
3
− 2a
2
− 2a
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4a
3
+ 9a
2
+ 6a − 7
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
u
4
− 2u
3
+ 3u
2
− u + 1
c
2
, c
4
u
4
+ u
2
+ u + 1
c
3
u
4
+ 3u
3
+ 4u
2
+ 3u + 2
c
5
, c
8
u
4
+ u
2
− u + 1
c
6
, c
10
u
4
c
9
, c
11
(u − 1)
4
c
12
(u + 1)
4
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
4
+ 2y
3
+ 7y
2
+ 5y + 1
c
2
, c
4
, c
5
c
8
y
4
+ 2y
3
+ 3y
2
+ y + 1
c
3
y
4
− y
3
+ 2y
2
+ 7y + 4
c
6
, c
10
y
4
c
9
, c
11
, c
12
(y −1)
4
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = 0.351808 + 0.720342I
b = −0.547424 + 1.120870I
−4.26996 − 7.64338I −10.46170 + 8.45840I
u = 1.00000
a = 0.351808 − 0.720342I
b = −0.547424 − 1.120870I
−4.26996 + 7.64338I −10.46170 − 8.45840I
u = 1.00000
a = −0.851808 + 0.911292I
b = 0.547424 + 0.585652I
−0.66484 + 1.39709I −7.03830 − 3.59727I
u = 1.00000
a = −0.851808 − 0.911292I
b = 0.547424 − 0.585652I
−0.66484 − 1.39709I −7.03830 + 3.59727I
20
III. I
u
3
= hb, u
2
a + a
2
+ 2au + 3u
2
+ a + 5u + 4, u
3
+ u
2
− 1i
(i) Arc colorings
a
9
=
1
0
a
12
=
0
u
a
10
=
1
u
2
a
1
=
−u
u
2
+ u − 1
a
4
=
a
0
a
8
=
1
0
a
5
=
a
0
a
7
=
1
0
a
11
=
−u
2
+ 1
u
2
a
6
=
u
−u
2
− u + 1
a
3
=
−au + 2a
2u
2
a + au − 2a
a
2
=
−au + u
2
+ 2a + 2u + 1
2u
2
a + au − 2a
(ii) Obstruction class = 1
(iii) Cusp Shapes = −7u
2
a − 3au + 3u
2
+ 8a + u − 2
21
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
5
(u
2
− u + 1)
3
c
2
(u
2
+ u + 1)
3
c
4
, c
7
, c
8
u
6
c
6
, c
11
(u
3
− u
2
+ 2u − 1)
2
c
9
(u
3
+ u
2
− 1)
2
c
10
(u
3
+ u
2
+ 2u + 1)
2
c
12
(u
3
− u
2
+ 1)
2
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
5
(y
2
+ y + 1)
3
c
4
, c
7
, c
8
y
6
c
6
, c
10
, c
11
(y
3
+ 3y
2
+ 2y −1)
2
c
9
, c
12
(y
3
− y
2
+ 2y −1)
2
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.877439 + 0.744862I
a = 0.111778 − 0.558770I
b = 0
3.02413 + 0.79824I −0.92725 + 3.21674I
u = −0.877439 + 0.744862I
a = 0.428020 + 0.376187I
b = 0
3.02413 + 4.85801I 2.65209 − 7.50333I
u = −0.877439 − 0.744862I
a = 0.111778 + 0.558770I
b = 0
3.02413 − 0.79824I −0.92725 − 3.21674I
u = −0.877439 − 0.744862I
a = 0.428020 − 0.376187I
b = 0
3.02413 − 4.85801I 2.65209 + 7.50333I
u = 0.754878
a = −1.53980 + 2.66701I
b = 0
−1.11345 + 2.02988I −2.22484 + 4.65789I
u = 0.754878
a = −1.53980 − 2.66701I
b = 0
−1.11345 − 2.02988I −2.22484 − 4.65789I
24
IV.
I
u
4
= h−a
5
+2a
4
−2a
3
+2a
2
+b−2a+1, a
6
−2a
5
+2a
4
−2a
3
+2a
2
−a+1, u−1i
(i) Arc colorings
a
9
=
1
0
a
12
=
0
1
a
10
=
1
1
a
1
=
−1
0
a
4
=
a
a
5
− 2a
4
+ 2a
3
− 2a
2
+ 2a − 1
a
8
=
0
−a
5
+ a
4
− 1
a
5
=
a
a
4
− a
3
a
7
=
−a
5
+ a
4
− 1
−a
5
+ a
4
− 1
a
11
=
1
1
a
6
=
−a
5
+ a
4
− 1
−a
5
+ a
4
− 1
a
3
=
a
2
a
5
− 2a
4
+ 2a
3
− a
2
+ a − 1
a
2
=
−a
4
+ a
3
+ a − 1
a
5
− 2a
4
+ 2a
3
− a
2
+ 2a − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = a
5
− 4a
4
+ 3a
3
+ a
2
− 9
25
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
u
6
− 3u
5
+ 4u
4
− 2u
3
+ 1
c
2
, c
4
u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1
c
3
(u
3
− u
2
+ 1)
2
c
5
, c
8
u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1
c
6
, c
10
u
6
c
9
, c
11
(u − 1)
6
c
12
(u + 1)
6
26
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
6
− y
5
+ 4y
4
− 2y
3
+ 8y
2
+ 1
c
2
, c
4
, c
5
c
8
y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1
c
3
(y
3
− y
2
+ 2y −1)
2
c
6
, c
10
y
6
c
9
, c
11
, c
12
(y −1)
6
27
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = −0.398606 + 0.800120I
b = 0.498832 + 1.001300I
−1.91067 + 2.82812I −7.09522 − 3.87141I
u = 1.00000
a = −0.398606 − 0.800120I
b = 0.498832 − 1.001300I
−1.91067 − 2.82812I −7.09522 + 3.87141I
u = 1.00000
a = 0.215080 + 0.841795I
b = −0.284920 + 1.115140I
−6.04826 −11.76463 + 0.99756I
u = 1.00000
a = 0.215080 − 0.841795I
b = −0.284920 − 1.115140I
−6.04826 −11.76463 − 0.99756I
u = 1.00000
a = 1.183530 + 0.507021I
b = −0.713912 + 0.305839I
−1.91067 + 2.82812I −6.64015 − 0.59776I
u = 1.00000
a = 1.183530 − 0.507021I
b = −0.713912 − 0.305839I
−1.91067 − 2.82812I −6.64015 + 0.59776I
28
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
2
− u + 1)
3
(u
4
− 2u
3
+ 3u
2
− u + 1)(u
6
− 3u
5
+ 4u
4
− 2u
3
+ 1)
· (u
119
+ 55u
118
+ ··· + 208u − 1)
c
2
(u
2
+ u + 1)
3
(u
4
+ u
2
+ u + 1)(u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1)
· (u
119
+ 5u
118
+ ··· + 8u − 1)
c
3
(u
2
− u + 1)
3
(u
3
− u
2
+ 1)
2
(u
4
+ 3u
3
+ 4u
2
+ 3u + 2)
· (u
119
− 5u
118
+ ··· + 5788u − 292)
c
4
u
6
(u
4
+ u
2
+ u + 1)(u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1)
· (u
119
− 2u
118
+ ··· + 32u + 64)
c
5
(u
2
− u + 1)
3
(u
4
+ u
2
− u + 1)(u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1)
· (u
119
+ 5u
118
+ ··· + 8u − 1)
c
6
u
10
(u
3
− u
2
+ 2u − 1)
2
(u
119
− 3u
118
+ ··· − 5120u + 1024)
c
7
u
6
(u
4
− 2u
3
+ 3u
2
− u + 1)(u
6
− 3u
5
+ 4u
4
− 2u
3
+ 1)
· (u
119
+ 40u
118
+ ··· − 80896u − 4096)
c
8
u
6
(u
4
+ u
2
− u + 1)(u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1)
· (u
119
− 2u
118
+ ··· + 32u + 64)
c
9
((u − 1)
10
)(u
3
+ u
2
− 1)
2
(u
119
− 13u
118
+ ··· − 20u + 1)
c
10
u
10
(u
3
+ u
2
+ 2u + 1)
2
(u
119
− 3u
118
+ ··· − 5120u + 1024)
c
11
((u − 1)
10
)(u
3
− u
2
+ 2u − 1)
2
(u
119
+ 53u
118
+ ··· − 14u + 1)
c
12
((u + 1)
10
)(u
3
− u
2
+ 1)
2
(u
119
− 13u
118
+ ··· − 20u + 1)
29
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
2
+ y + 1)
3
)(y
4
+ 2y
3
+ ··· + 5y + 1)(y
6
− y
5
+ ··· + 8y
2
+ 1)
· (y
119
+ 23y
118
+ ··· + 45340y −1)
c
2
, c
5
(y
2
+ y + 1)
3
(y
4
+ 2y
3
+ 3y
2
+ y + 1)(y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1)
· (y
119
+ 55y
118
+ ··· + 208y −1)
c
3
(y
2
+ y + 1)
3
(y
3
− y
2
+ 2y −1)
2
(y
4
− y
3
+ 2y
2
+ 7y + 4)
· (y
119
− 9y
118
+ ··· + 26282120y −85264)
c
4
, c
8
y
6
(y
4
+ 2y
3
+ 3y
2
+ y + 1)(y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1)
· (y
119
+ 40y
118
+ ··· − 80896y −4096)
c
6
, c
10
y
10
(y
3
+ 3y
2
+ 2y −1)
2
(y
119
+ 69y
118
+ ··· − 3.19816 × 10
7
y −1048576)
c
7
y
6
(y
4
+ 2y
3
+ 7y
2
+ 5y + 1)(y
6
− y
5
+ 4y
4
− 2y
3
+ 8y
2
+ 1)
· (y
119
+ 68y
118
+ ··· + 5134876672y −16777216)
c
9
, c
12
((y −1)
10
)(y
3
− y
2
+ 2y −1)
2
(y
119
− 53y
118
+ ··· − 14y −1)
c
11
((y −1)
10
)(y
3
+ 3y
2
+ 2y −1)
2
(y
119
+ 39y
118
+ ··· + 5618y −1)
30
