12n
0255
(K12n
0255
)
A knot diagram
1
Linearized knot diagam
3 5 8 2 11 10 12 3 7 1 8 6
Solving Sequence
7,12 3,8
4 9 10 6 1 2 11 5
c
7
c
3
c
8
c
9
c
6
c
12
c
1
c
11
c
5
c
2
, c
4
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h1.59660 × 10
327
u
87
− 4.52798 × 10
327
u
86
+ ··· + 9.40594 × 10
329
b + 8.06817 × 10
330
,
− 1.52962 × 10
329
u
87
+ 3.20986 × 10
329
u
86
+ ··· + 4.75941 × 10
331
a − 3.66335 × 10
331
,
u
88
− 2u
87
+ ··· − 4968u − 1771i
I
u
2
= h4u
8
+ u
6
− 4u
5
+ 2u
4
− 5u
3
− u
2
+ 7b + u + 3, 4u
8
+ 7u
7
+ 15u
6
+ 10u
5
+ 16u
4
+ 9u
3
+ 13u
2
+ 7a + u + 3,
u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1i
I
u
3
= h−4u
15
− 30u
13
+ ··· + b + 8, 2u
15
+ 14u
13
+ ··· + a − 7, u
16
+ 8u
14
+ ··· − 3u + 1i
* 3 irreducible components of dim
C
= 0, with total 113 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
= h1.60 × 10
327
u
87
− 4.53 × 10
327
u
86
+ · · · + 9.41 × 10
329
b + 8.07 ×
10
330
, −1.53 × 10
329
u
87
+ 3.21 × 10
329
u
86
+ · · · + 4.76 × 10
331
a − 3.66 ×
10
331
, u
88
− 2u
87
+ · · · − 4968u − 1771i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
u
a
3
=
0.00321388u
87
− 0.00674424u
86
+ ··· − 11.3051u + 0.769708
−0.00169744u
87
+ 0.00481396u
86
+ ··· − 12.5593u − 8.57774
a
8
=
1
u
2
a
4
=
0.00233250u
87
− 0.00315963u
86
+ ··· − 27.9840u − 7.24757
−0.00137179u
87
+ 0.00300797u
86
+ ··· − 5.06937u − 5.35127
a
9
=
0.00153178u
87
− 0.00266896u
86
+ ··· − 23.2890u − 2.25667
−0.00185920u
87
+ 0.00347861u
86
+ ··· + 19.0323u + 2.82726
a
10
=
−0.000327420u
87
+ 0.000809657u
86
+ ··· − 4.25669u + 0.570591
−0.00185920u
87
+ 0.00347861u
86
+ ··· + 19.0323u + 2.82726
a
6
=
0.000561869u
87
− 0.00155079u
86
+ ··· − 8.50672u − 1.66797
−0.000861961u
87
+ 0.00450290u
86
+ ··· − 41.5986u − 14.7883
a
1
=
−0.000151726u
87
+ 0.00147337u
86
+ ··· + 0.554564u − 2.10313
−0.00150768u
87
+ 0.00204381u
86
+ ··· + 20.3844u + 3.14401
a
2
=
−0.00467421u
87
+ 0.0109893u
86
+ ··· + 15.1651u − 4.16426
0.00197314u
87
− 0.00700781u
86
+ ··· + 30.3390u + 12.6165
a
11
=
u
u
3
+ u
a
5
=
0.000632418u
87
− 0.00298532u
86
+ ··· + 1.50043u + 2.65355
−1.09936 × 10
−6
u
87
+ 0.00267945u
86
+ ··· − 37.8923u − 12.7574
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.0135860u
87
− 0.0234158u
86
+ ··· − 148.906u − 31.3158
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
88
+ 36u
87
+ ··· + 9016u + 2401
c
2
, c
4
u
88
− 16u
87
+ ··· + 504u − 49
c
3
, c
8
u
88
+ u
87
+ ··· + 14336u + 25088
c
5
u
88
− u
87
+ ··· + 8558243u − 2435537
c
6
, c
9
u
88
+ 3u
87
+ ··· − 1497u − 181
c
7
, c
11
u
88
+ 2u
87
+ ··· + 4968u − 1771
c
10
u
88
− 14u
87
+ ··· − 5848u + 1043
c
12
u
88
− 4u
87
+ ··· + 2u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
88
+ 48y
87
+ ··· − 1539089020y + 5764801
c
2
, c
4
y
88
− 36y
87
+ ··· − 9016y + 2401
c
3
, c
8
y
88
− 63y
87
+ ··· − 10096214016y + 629407744
c
5
y
88
+ 33y
87
+ ··· + 85934090519941y + 5931840478369
c
6
, c
9
y
88
+ 49y
87
+ ··· − 883509y + 32761
c
7
, c
11
y
88
+ 70y
87
+ ··· + 39623986y + 3136441
c
10
y
88
+ 2y
87
+ ··· + 12594048y + 1087849
c
12
y
88
− 16y
87
+ ··· + 6y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.805310 + 0.589984I
a = 0.054018 − 0.595613I
b = −0.564062 + 0.307745I
−0.95191 − 5.34222I 0
u = 0.805310 − 0.589984I
a = 0.054018 + 0.595613I
b = −0.564062 − 0.307745I
−0.95191 + 5.34222I 0
u = −0.992163 + 0.083390I
a = 0.98711 + 1.32599I
b = 1.43776 + 0.20661I
−3.57000 + 4.86222I 0
u = −0.992163 − 0.083390I
a = 0.98711 − 1.32599I
b = 1.43776 − 0.20661I
−3.57000 − 4.86222I 0
u = −0.948677 + 0.240901I
a = 0.003868 − 0.312365I
b = 1.265110 − 0.356204I
4.48132 − 0.68778I 0
u = −0.948677 − 0.240901I
a = 0.003868 + 0.312365I
b = 1.265110 + 0.356204I
4.48132 + 0.68778I 0
u = −0.139706 + 0.952235I
a = −0.096405 + 1.302030I
b = 0.428123 + 0.474722I
−8.88186 + 0.52240I 0
u = −0.139706 − 0.952235I
a = −0.096405 − 1.302030I
b = 0.428123 − 0.474722I
−8.88186 − 0.52240I 0
u = −0.517483 + 0.776305I
a = 2.48790 − 5.29655I
b = −4.92316 + 0.17599I
−2.86090 + 2.57918I 0
u = −0.517483 − 0.776305I
a = 2.48790 + 5.29655I
b = −4.92316 − 0.17599I
−2.86090 − 2.57918I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.919116 + 0.059965I
a = 0.276517 − 0.504859I
b = −1.240560 − 0.144966I
4.06052 − 5.39830I 0
u = −0.919116 − 0.059965I
a = 0.276517 + 0.504859I
b = −1.240560 + 0.144966I
4.06052 + 5.39830I 0
u = 0.740792 + 0.830928I
a = 0.330688 + 0.146176I
b = −0.648519 + 0.066233I
−0.52740 − 2.78156I 0
u = 0.740792 − 0.830928I
a = 0.330688 − 0.146176I
b = −0.648519 − 0.066233I
−0.52740 + 2.78156I 0
u = 0.248018 + 0.848575I
a = 0.59296 + 1.67847I
b = −1.039260 − 0.222833I
−2.35191 − 3.21223I −7.96555 + 6.35540I
u = 0.248018 − 0.848575I
a = 0.59296 − 1.67847I
b = −1.039260 + 0.222833I
−2.35191 + 3.21223I −7.96555 − 6.35540I
u = 0.079212 + 1.132010I
a = −2.23389 − 0.84898I
b = 1.65660 + 0.78050I
2.28913 + 1.10084I 0
u = 0.079212 − 1.132010I
a = −2.23389 + 0.84898I
b = 1.65660 − 0.78050I
2.28913 − 1.10084I 0
u = −0.319029 + 1.102470I
a = −1.74887 + 0.76112I
b = 0.788989 − 0.262436I
6.66068 + 5.31014I 0
u = −0.319029 − 1.102470I
a = −1.74887 − 0.76112I
b = 0.788989 + 0.262436I
6.66068 − 5.31014I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.174859 + 0.815548I
a = −0.149816 + 0.368917I
b = 0.641340 − 0.280050I
1.08551 − 1.92358I 4.64840 + 3.23156I
u = 0.174859 − 0.815548I
a = −0.149816 − 0.368917I
b = 0.641340 + 0.280050I
1.08551 + 1.92358I 4.64840 − 3.23156I
u = 0.767240 + 0.896651I
a = −0.055340 + 0.668537I
b = 0.212608 − 0.126711I
−0.156171 − 0.447897I 0
u = 0.767240 − 0.896651I
a = −0.055340 − 0.668537I
b = 0.212608 + 0.126711I
−0.156171 + 0.447897I 0
u = −0.237078 + 0.779145I
a = −0.81168 − 1.26283I
b = −0.67193 + 1.62533I
−2.63864 + 1.15581I −8.11133 + 0.I
u = −0.237078 − 0.779145I
a = −0.81168 + 1.26283I
b = −0.67193 − 1.62533I
−2.63864 − 1.15581I −8.11133 + 0.I
u = 0.451795 + 1.101000I
a = 0.358681 + 0.343345I
b = −0.360929 − 0.818141I
0.22772 − 2.36626I 0
u = 0.451795 − 1.101000I
a = 0.358681 − 0.343345I
b = −0.360929 + 0.818141I
0.22772 + 2.36626I 0
u = −0.938892 + 0.789370I
a = 0.273538 − 0.331883I
b = 0.201529 − 0.414522I
−5.45148 − 0.98119I 0
u = −0.938892 − 0.789370I
a = 0.273538 + 0.331883I
b = 0.201529 + 0.414522I
−5.45148 + 0.98119I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.785869 + 0.950757I
a = −0.138404 + 0.139505I
b = −0.271984 + 0.082732I
−4.90136 + 7.25149I 0
u = −0.785869 − 0.950757I
a = −0.138404 − 0.139505I
b = −0.271984 − 0.082732I
−4.90136 − 7.25149I 0
u = −0.135066 + 1.254400I
a = 2.22121 + 0.15503I
b = −2.05694 − 0.67244I
1.84545 + 6.92325I 0
u = −0.135066 − 1.254400I
a = 2.22121 − 0.15503I
b = −2.05694 + 0.67244I
1.84545 − 6.92325I 0
u = −0.166697 + 1.254150I
a = −0.034446 − 0.623225I
b = −0.319789 − 0.663059I
1.34449 + 3.11057I 0
u = −0.166697 − 1.254150I
a = −0.034446 + 0.623225I
b = −0.319789 + 0.663059I
1.34449 − 3.11057I 0
u = −0.128440 + 1.272930I
a = 1.93796 − 0.20251I
b = −2.15691 − 0.51379I
1.74481 + 1.77274I 0
u = −0.128440 − 1.272930I
a = 1.93796 + 0.20251I
b = −2.15691 + 0.51379I
1.74481 − 1.77274I 0
u = 0.696650 + 0.064826I
a = 1.51721 + 1.08264I
b = 1.40952 + 0.93931I
−4.59376 + 2.75184I −8.12364 − 4.75878I
u = 0.696650 − 0.064826I
a = 1.51721 − 1.08264I
b = 1.40952 − 0.93931I
−4.59376 − 2.75184I −8.12364 + 4.75878I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.112427 + 1.300630I
a = 1.68962 − 0.37026I
b = −1.092740 + 0.486491I
8.28391 − 2.17535I 0
u = −0.112427 − 1.300630I
a = 1.68962 + 0.37026I
b = −1.092740 − 0.486491I
8.28391 + 2.17535I 0
u = 0.313929 + 1.278860I
a = −1.83698 − 0.13210I
b = 1.40992 − 1.21165I
−0.73301 − 6.46230I 0
u = 0.313929 − 1.278860I
a = −1.83698 + 0.13210I
b = 1.40992 + 1.21165I
−0.73301 + 6.46230I 0
u = 0.266726 + 1.305550I
a = −0.493116 + 0.134447I
b = 0.801100 + 0.630667I
3.68905 − 4.17717I 0
u = 0.266726 − 1.305550I
a = −0.493116 − 0.134447I
b = 0.801100 − 0.630667I
3.68905 + 4.17717I 0
u = 0.021756 + 1.350550I
a = 0.747687 − 0.219765I
b = −0.820694 − 0.756021I
2.82569 + 0.98099I 0
u = 0.021756 − 1.350550I
a = 0.747687 + 0.219765I
b = −0.820694 + 0.756021I
2.82569 − 0.98099I 0
u = −0.018865 + 0.638570I
a = 0.079600 + 0.747971I
b = 0.756230 − 0.701359I
0.93570 − 1.73737I 2.01048 + 1.71572I
u = −0.018865 − 0.638570I
a = 0.079600 − 0.747971I
b = 0.756230 + 0.701359I
0.93570 + 1.73737I 2.01048 − 1.71572I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.588985
a = 0.818540
b = −0.302376
−1.64409 −5.83610
u = 0.094002 + 0.577464I
a = −0.249160 − 1.294160I
b = −0.365512 + 1.099090I
−2.55730 + 1.15360I −7.35870 + 0.72400I
u = 0.094002 − 0.577464I
a = −0.249160 + 1.294160I
b = −0.365512 − 1.099090I
−2.55730 − 1.15360I −7.35870 − 0.72400I
u = −0.54155 + 1.31866I
a = 1.35023 − 0.95631I
b = −1.88027 + 0.08346I
7.90999 + 10.78390I 0
u = −0.54155 − 1.31866I
a = 1.35023 + 0.95631I
b = −1.88027 − 0.08346I
7.90999 − 10.78390I 0
u = −0.41333 + 1.36783I
a = 0.044748 + 0.458558I
b = 0.159156 + 0.689302I
1.05954 + 9.78750I 0
u = −0.41333 − 1.36783I
a = 0.044748 − 0.458558I
b = 0.159156 − 0.689302I
1.05954 − 9.78750I 0
u = 1.40756 + 0.26250I
a = −0.226308 + 0.033161I
b = −1.81552 + 0.07911I
1.45716 − 4.42701I 0
u = 1.40756 − 0.26250I
a = −0.226308 − 0.033161I
b = −1.81552 − 0.07911I
1.45716 + 4.42701I 0
u = −0.42686 + 1.41707I
a = −1.42953 + 0.73379I
b = 1.96059 + 0.05533I
9.65161 + 4.27098I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.42686 − 1.41707I
a = −1.42953 − 0.73379I
b = 1.96059 − 0.05533I
9.65161 − 4.27098I 0
u = 0.26866 + 1.45831I
a = 1.54716 + 0.09889I
b = −1.83374 + 0.14991I
5.43825 − 8.83857I 0
u = 0.26866 − 1.45831I
a = 1.54716 − 0.09889I
b = −1.83374 − 0.14991I
5.43825 + 8.83857I 0
u = 0.478957 + 0.175114I
a = 0.62555 + 1.48896I
b = −0.128706 − 0.360441I
−0.78467 − 1.23926I −5.32242 + 5.47295I
u = 0.478957 − 0.175114I
a = 0.62555 − 1.48896I
b = −0.128706 + 0.360441I
−0.78467 + 1.23926I −5.32242 − 5.47295I
u = 0.07800 + 1.49272I
a = −1.50386 + 0.09747I
b = 1.82804 + 0.09407I
8.16387 − 2.18472I 0
u = 0.07800 − 1.49272I
a = −1.50386 − 0.09747I
b = 1.82804 − 0.09407I
8.16387 + 2.18472I 0
u = 1.51183 + 0.01086I
a = 0.317761 − 0.182920I
b = 2.09380 + 0.13018I
0.06365 + 10.42840I 0
u = 1.51183 − 0.01086I
a = 0.317761 + 0.182920I
b = 2.09380 − 0.13018I
0.06365 − 10.42840I 0
u = −0.13980 + 1.52059I
a = −0.39445 + 1.40951I
b = 1.54870 − 3.66586I
1.66607 + 0.20314I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.13980 − 1.52059I
a = −0.39445 − 1.40951I
b = 1.54870 + 3.66586I
1.66607 − 0.20314I 0
u = 0.030492 + 0.449001I
a = 0.296509 − 1.156240I
b = −1.046570 + 0.812879I
−1.21942 − 6.06914I −0.76059 − 2.63784I
u = 0.030492 − 0.449001I
a = 0.296509 + 1.156240I
b = −1.046570 − 0.812879I
−1.21942 + 6.06914I −0.76059 + 2.63784I
u = 0.50465 + 1.51967I
a = 1.50482 + 0.37400I
b = −2.01643 + 0.96407I
7.20481 − 10.90700I 0
u = 0.50465 − 1.51967I
a = 1.50482 − 0.37400I
b = −2.01643 − 0.96407I
7.20481 + 10.90700I 0
u = −0.378884
a = −2.36935
b = −0.867969
−2.22317 −0.252670
u = 0.64911 + 1.49897I
a = −1.44538 − 0.56337I
b = 2.26266 − 0.99181I
4.8344 − 17.8080I 0
u = 0.64911 − 1.49897I
a = −1.44538 + 0.56337I
b = 2.26266 + 0.99181I
4.8344 + 17.8080I 0
u = −0.71431 + 1.53469I
a = 1.114620 − 0.373137I
b = −1.21769 − 1.82144I
7.13913 + 0.48203I 0
u = −0.71431 − 1.53469I
a = 1.114620 + 0.373137I
b = −1.21769 + 1.82144I
7.13913 − 0.48203I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.92191 + 1.43934I
a = −1.111690 + 0.636225I
b = 1.44949 + 1.78433I
6.56818 + 7.36505I 0
u = −0.92191 − 1.43934I
a = −1.111690 − 0.636225I
b = 1.44949 − 1.78433I
6.56818 − 7.36505I 0
u = −0.237720 + 0.158364I
a = −3.64518 − 2.93335I
b = −0.681565 − 0.621880I
−2.23495 − 1.29247I −6.68617 − 1.38636I
u = −0.237720 − 0.158364I
a = −3.64518 + 2.93335I
b = −0.681565 + 0.621880I
−2.23495 + 1.29247I −6.68617 + 1.38636I
u = 0.62041 + 1.63980I
a = 0.998177 + 0.582876I
b = −2.10790 + 0.42331I
6.07321 − 3.61773I 0
u = 0.62041 − 1.63980I
a = 0.998177 − 0.582876I
b = −2.10790 − 0.42331I
6.07321 + 3.61773I 0
u = 0.43998 + 1.83287I
a = −1.036670 − 0.340691I
b = 2.46384 − 0.76211I
6.26435 + 2.30308I 0
u = 0.43998 − 1.83287I
a = −1.036670 + 0.340691I
b = 2.46384 + 0.76211I
6.26435 − 2.30308I 0
13
II. I
u
2
= h4u
8
+ u
6
− 4u
5
+ 2u
4
− 5u
3
− u
2
+ 7b + u + 3, 4u
8
+ 7u
7
+ · · · +
7a + 3, u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
u
a
3
=
−
4
7
u
8
− u
7
+ ··· −
1
7
u −
3
7
−
4
7
u
8
−
1
7
u
6
+ ··· −
1
7
u −
3
7
a
8
=
1
u
2
a
4
=
−
4
7
u
8
− u
7
+ ··· −
1
7
u −
3
7
−
4
7
u
8
−
1
7
u
6
+ ··· −
1
7
u −
3
7
a
9
=
1
u
2
a
10
=
u
2
+ 1
u
2
a
6
=
u
4
+ u
2
+ 1
u
4
a
1
=
u
8
+ u
6
+ u
4
− 1
u
8
+ u
7
+ u
6
+ 2u
5
+ u
4
+ 2u
3
+ 2u − 1
a
2
=
3
7
u
8
− u
7
+ ··· −
1
7
u −
10
7
3
7
u
8
+ u
7
+ ··· +
13
7
u −
10
7
a
11
=
u
u
3
+ u
a
5
=
−u
8
− u
6
− u
4
+ 1
−u
8
− u
7
− u
6
− 2u
5
− u
4
− 2u
3
− 2u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −
5
49
u
8
−
16
7
u
7
−
241
49
u
6
−
184
49
u
5
−
307
49
u
4
−
342
49
u
3
−
361
49
u
2
+
95
49
u −
618
49
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
9
c
3
, c
8
u
9
c
4
(u + 1)
9
c
5
, c
10
u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1
c
6
u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1
c
7
u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1
c
9
u
9
− 3u
8
+ 8u
7
− 13u
6
+ 17u
5
− 17u
4
+ 12u
3
− 6u
2
+ u + 1
c
11
u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1
c
12
u
9
+ 5u
8
+ 12u
7
+ 15u
6
+ 9u
5
− u
4
− 4u
3
− 2u
2
+ u + 1
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
9
c
3
, c
8
y
9
c
5
, c
10
y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1
c
6
, c
9
y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y −1
c
7
, c
11
y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y −1
c
12
y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y −1
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.140343 + 0.966856I
a = 0.903964 + 0.094390I
b = −0.852846 + 0.158943I
0.13850 − 2.09337I −5.47770 + 4.24226I
u = 0.140343 − 0.966856I
a = 0.903964 − 0.094390I
b = −0.852846 − 0.158943I
0.13850 + 2.09337I −5.47770 − 4.24226I
u = 0.628449 + 0.875112I
a = −0.53175 + 1.59553I
b = −1.55776 − 1.17662I
−2.26187 − 2.45442I −3.78210 + 4.39771I
u = 0.628449 − 0.875112I
a = −0.53175 − 1.59553I
b = −1.55776 + 1.17662I
−2.26187 + 2.45442I −3.78210 − 4.39771I
u = −0.796005 + 0.733148I
a = 0.476406 + 0.294981I
b = 0.390088 − 0.527698I
−6.01628 − 1.33617I −12.84367 + 3.27176I
u = −0.796005 − 0.733148I
a = 0.476406 − 0.294981I
b = 0.390088 + 0.527698I
−6.01628 + 1.33617I −12.84367 − 3.27176I
u = −0.728966 + 0.986295I
a = −0.352455 − 0.113243I
b = −0.007269 + 0.556797I
−5.24306 + 7.08493I −15.6193 − 1.7431I
u = −0.728966 − 0.986295I
a = −0.352455 + 0.113243I
b = −0.007269 − 0.556797I
−5.24306 − 7.08493I −15.6193 + 1.7431I
u = 0.512358
a = −1.42091
b = −0.373004
−2.84338 −15.1670
17
III. I
u
3
=
h−4u
15
−30u
13
+· · ·+b+8, 2u
15
+14u
13
+· · ·+a−7, u
16
+8u
14
+· · ·−3u+1i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
u
a
3
=
−2u
15
− 14u
13
+ ··· − 13u + 7
4u
15
+ 30u
13
+ ··· + 18u − 8
a
8
=
1
u
2
a
4
=
−2u
14
− 14u
12
+ ··· + 3u − 1
2u
15
+ 15u
13
+ ··· + 10u − 6
a
9
=
−u
15
− u
14
+ ··· − 5u + 2
u
15
+ 8u
13
+ ··· + 10u − 3
a
10
=
−u
14
− 7u
12
+ ··· + 5u − 1
u
15
+ 8u
13
+ ··· + 10u − 3
a
6
=
−u
15
− 7u
13
+ ··· − u − 1
−3u
15
− u
14
+ ··· − 14u − 1
a
1
=
−3u
15
+ 2u
14
+ ··· − 13u + 3
−u
15
+ u
14
+ ··· − 13u + 4
a
2
=
−u
15
+ u
14
+ ··· − 8u + 4
−2u
15
− u
14
+ ··· − 11u − 1
a
11
=
u
u
3
+ u
a
5
=
−u
15
− 7u
13
+ ··· + 5u
2
− u
−3u
15
− u
14
+ ··· + 17u
2
− 14u
(ii) Obstruction class = 1
(iii) Cusp Shapes = 35u
15
+ 12u
14
+ 275u
13
− 18u
12
+ 898u
11
− 348u
10
+ 1661u
9
−
964u
8
+ 1955u
7
− 1160u
6
+ 1383u
5
− 706u
4
+ 579u
3
− 256u
2
+ 146u − 39
18
(iv) u-Polynomials at the component
19
Crossings u-Polynomials at each crossing
c
1
u
16
− 10u
15
+ ··· − 7u + 1
c
2
u
16
+ 6u
15
+ ··· − u + 1
c
3
u
16
− 3u
14
+ ··· − u + 1
c
4
u
16
− 6u
15
+ ··· + u + 1
c
5
u
16
+ 3u
15
+ ··· + 6u + 1
c
6
u
16
+ 3u
15
+ ··· + 8u
2
+ 1
c
7
u
16
+ 8u
14
+ ··· − 3u + 1
c
8
u
16
− 3u
14
+ ··· + u + 1
c
9
u
16
− 3u
15
+ ··· + 8u
2
+ 1
c
10
u
16
− 5u
13
+ ··· − 5u + 1
c
11
u
16
+ 8u
14
+ ··· + 3u + 1
c
12
u
16
− 6u
15
+ ··· − 3u + 1
20
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
16
− 2y
15
+ ··· + 61y + 1
c
2
, c
4
y
16
− 10y
15
+ ··· − 7y + 1
c
3
, c
8
y
16
− 6y
15
+ ··· + 9y + 1
c
5
y
16
− 5y
15
+ ··· − 14y + 1
c
6
, c
9
y
16
+ 11y
15
+ ··· + 16y + 1
c
7
, c
11
y
16
+ 16y
15
+ ··· + 11y + 1
c
10
y
16
+ 10y
14
+ ··· + 9y + 1
c
12
y
16
− 14y
15
+ ··· − 5y + 1
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.192282 + 1.004160I
a = −0.054945 − 1.233160I
b = 0.391316 − 0.450641I
−8.83850 − 0.76161I −4.2680 + 18.7238I
u = 0.192282 − 1.004160I
a = −0.054945 + 1.233160I
b = 0.391316 + 0.450641I
−8.83850 + 0.76161I −4.2680 − 18.7238I
u = 0.405160 + 0.782797I
a = −0.41658 + 1.39011I
b = −0.522604 − 0.259087I
−1.72004 − 2.39298I −3.94028 + 2.30129I
u = 0.405160 − 0.782797I
a = −0.41658 − 1.39011I
b = −0.522604 + 0.259087I
−1.72004 + 2.39298I −3.94028 − 2.30129I
u = −0.380479 + 0.681918I
a = −3.58192 − 6.22555I
b = −2.28948 + 4.19034I
−2.96721 + 2.98693I −21.6572 + 12.8409I
u = −0.380479 − 0.681918I
a = −3.58192 + 6.22555I
b = −2.28948 − 4.19034I
−2.96721 − 2.98693I −21.6572 − 12.8409I
u = 0.445295 + 0.521652I
a = −1.043710 + 0.252877I
b = 0.938529 − 0.582515I
0.00207 − 2.08322I −6.76763 + 3.46484I
u = 0.445295 − 0.521652I
a = −1.043710 − 0.252877I
b = 0.938529 + 0.582515I
0.00207 + 2.08322I −6.76763 − 3.46484I
u = 0.279505 + 0.496867I
a = 0.739008 − 0.233492I
b = −1.056140 + 0.735456I
−1.36164 − 6.43556I −8.1558 + 16.1878I
u = 0.279505 − 0.496867I
a = 0.739008 + 0.233492I
b = −1.056140 − 0.735456I
−1.36164 + 6.43556I −8.1558 − 16.1878I
23
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.08961 + 1.47734I
a = 0.703553 − 0.688380I
b = −1.15108 + 2.45886I
1.50817 − 0.70603I −8.36846 + 5.87842I
u = 0.08961 − 1.47734I
a = 0.703553 + 0.688380I
b = −1.15108 − 2.45886I
1.50817 + 0.70603I −8.36846 − 5.87842I
u = −0.60082 + 1.36455I
a = 1.40109 − 0.55373I
b = −1.40464 − 0.96198I
6.18219 + 6.62853I −4.79477 − 3.23115I
u = −0.60082 − 1.36455I
a = 1.40109 + 0.55373I
b = −1.40464 + 0.96198I
6.18219 − 6.62853I −4.79477 + 3.23115I
u = −0.43055 + 1.58967I
a = −1.246490 + 0.210919I
b = 1.59410 + 1.15005I
7.19496 − 0.24679I −1.04785 + 3.22477I
u = −0.43055 − 1.58967I
a = −1.246490 − 0.210919I
b = 1.59410 − 1.15005I
7.19496 + 0.24679I −1.04785 − 3.22477I
24
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
9
)(u
16
− 10u
15
+ ··· − 7u + 1)
· (u
88
+ 36u
87
+ ··· + 9016u + 2401)
c
2
((u − 1)
9
)(u
16
+ 6u
15
+ ··· − u + 1)(u
88
− 16u
87
+ ··· + 504u − 49)
c
3
u
9
(u
16
− 3u
14
+ ··· − u + 1)(u
88
+ u
87
+ ··· + 14336u + 25088)
c
4
((u + 1)
9
)(u
16
− 6u
15
+ ··· + u + 1)(u
88
− 16u
87
+ ··· + 504u − 49)
c
5
(u
9
+ u
8
+ ··· − u − 1)(u
16
+ 3u
15
+ ··· + 6u + 1)
· (u
88
− u
87
+ ··· + 8558243u − 2435537)
c
6
(u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1)
· (u
16
+ 3u
15
+ ··· + 8u
2
+ 1)(u
88
+ 3u
87
+ ··· − 1497u − 181)
c
7
(u
9
+ u
8
+ ··· + u − 1)(u
16
+ 8u
14
+ ··· − 3u + 1)
· (u
88
+ 2u
87
+ ··· + 4968u − 1771)
c
8
u
9
(u
16
− 3u
14
+ ··· + u + 1)(u
88
+ u
87
+ ··· + 14336u + 25088)
c
9
(u
9
− 3u
8
+ 8u
7
− 13u
6
+ 17u
5
− 17u
4
+ 12u
3
− 6u
2
+ u + 1)
· (u
16
− 3u
15
+ ··· + 8u
2
+ 1)(u
88
+ 3u
87
+ ··· − 1497u − 181)
c
10
(u
9
+ u
8
+ ··· − u − 1)(u
16
− 5u
13
+ ··· − 5u + 1)
· (u
88
− 14u
87
+ ··· − 5848u + 1043)
c
11
(u
9
− u
8
+ ··· + u + 1)(u
16
+ 8u
14
+ ··· + 3u + 1)
· (u
88
+ 2u
87
+ ··· + 4968u − 1771)
c
12
(u
9
+ 5u
8
+ 12u
7
+ 15u
6
+ 9u
5
− u
4
− 4u
3
− 2u
2
+ u + 1)
· (u
16
− 6u
15
+ ··· − 3u + 1)(u
88
− 4u
87
+ ··· + 2u − 1)
25
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y −1)
9
)(y
16
− 2y
15
+ ··· + 61y + 1)
· (y
88
+ 48y
87
+ ··· − 1539089020y + 5764801)
c
2
, c
4
((y −1)
9
)(y
16
− 10y
15
+ ··· − 7y + 1)
· (y
88
− 36y
87
+ ··· − 9016y + 2401)
c
3
, c
8
y
9
(y
16
− 6y
15
+ ··· + 9y + 1)
· (y
88
− 63y
87
+ ··· − 10096214016y + 629407744)
c
5
(y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1)
· (y
16
− 5y
15
+ ··· − 14y + 1)
· (y
88
+ 33y
87
+ ··· + 85934090519941y + 5931840478369)
c
6
, c
9
(y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y −1)
· (y
16
+ 11y
15
+ ··· + 16y + 1)(y
88
+ 49y
87
+ ··· − 883509y + 32761)
c
7
, c
11
(y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y −1)
· (y
16
+ 16y
15
+ ··· + 11y + 1)
· (y
88
+ 70y
87
+ ··· + 39623986y + 3136441)
c
10
(y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1)
· (y
16
+ 10y
14
+ ··· + 9y + 1)
· (y
88
+ 2y
87
+ ··· + 12594048y + 1087849)
c
12
(y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y −1)
· (y
16
− 14y
15
+ ··· − 5y + 1)(y
88
− 16y
87
+ ··· + 6y + 1)
26
