12a
0778
(K12a
0778
)
A knot diagram
1
Linearized knot diagam
3 8 10 12 1 11 2 6 5 7 4 9
Solving Sequence
2,7
8 3
1,11
6 9 5 10 4 12
c
7
c
2
c
1
c
6
c
8
c
5
c
10
c
3
c
12
c
4
, c
9
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h2.83192 × 10
557
u
177
6.25443 × 10
556
u
176
+ ··· + 5.07791 × 10
558
b 2.49182 × 10
560
,
1.66942 × 10
562
u
177
+ 4.31753 × 10
560
u
176
+ ··· + 5.53848 × 10
562
a 9.73150 × 10
564
,
u
178
u
177
+ ··· 3043u + 839i
I
u
2
= h−8317077395u
45
6692694951u
44
+ ··· + 1782959561b 14602686346,
39738567974u
45
7168731592677u
44
+ ··· + 622252886789a + 2806256180785,
u
46
13u
44
+ ··· + 3u + 1i
* 2 irreducible components of dim
C
= 0, with total 224 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
= h2.83 × 10
557
u
177
6.25 × 10
556
u
176
+ · · · + 5.08 × 10
558
b 2.49 ×
10
560
, 1.67 × 10
562
u
177
+ 4.32 × 10
560
u
176
+ · · · + 5.54 × 10
562
a 9.73 ×
10
564
, u
178
u
177
+ · · · 3043u + 839i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
8
=
1
u
2
a
3
=
u
u
3
+ u
a
1
=
u
3
u
5
u
3
+ u
a
11
=
0.301422u
177
0.00779552u
176
+ ··· 467.541u + 175.707
0.0557695u
177
+ 0.0123169u
176
+ ··· 99.9826u + 49.0718
a
6
=
0.148718u
177
+ 0.164496u
176
+ ··· + 198.358u 54.6244
0.0620492u
177
+ 0.137246u
176
+ ··· + 315.427u 72.3130
a
9
=
0.343320u
177
0.0126359u
176
+ ··· 811.691u + 297.191
0.0116331u
177
0.0316594u
176
+ ··· 105.316u + 43.9533
a
5
=
0.117881u
177
+ 0.0434351u
176
+ ··· + 15.4920u 18.5703
0.0604457u
177
+ 0.0849581u
176
+ ··· + 172.096u 31.1648
a
10
=
0.245653u
177
0.0201125u
176
+ ··· 367.558u + 126.635
0.0557695u
177
+ 0.0123169u
176
+ ··· 99.9826u + 49.0718
a
4
=
0.0646156u
177
0.244183u
176
+ ··· + 260.057u 165.861
0.0305702u
177
0.0849381u
176
+ ··· 118.034u + 3.73802
a
12
=
0.120327u
177
+ 0.117052u
176
+ ··· + 179.284u 10.9664
0.113303u
177
+ 0.0278594u
176
+ ··· 245.370u + 99.0238
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0.0572173u
177
+ 0.0141848u
176
+ ··· 447.259u + 188.065
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
178
+ 85u
177
+ ··· + 12261791u + 703921
c
2
, c
7
u
178
+ u
177
+ ··· + 3043u + 839
c
3
u
178
+ u
177
+ ··· + 354196u + 339257
c
4
, c
11
u
178
+ u
177
+ ··· 563010u + 122123
c
5
u
178
+ 5u
177
+ ··· + 300u + 179
c
6
, c
10
u
178
+ 46u
176
+ ··· + 147913u + 12577
c
8
u
178
8u
177
+ ··· 193237632u + 17520832
c
9
u
178
3u
177
+ ··· 316u + 83
c
12
u
178
+ 6u
177
+ ··· 2444512u + 375469
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
178
+ 31y
177
+ ··· 583680219959y + 495504774241
c
2
, c
7
y
178
85y
177
+ ··· 12261791y + 703921
c
3
y
178
5y
177
+ ··· + 10288606046288y + 115095312049
c
4
, c
11
y
178
133y
177
+ ··· 108608624088y + 14914027129
c
5
y
178
19y
177
+ ··· + 637456y + 32041
c
6
, c
10
y
178
+ 92y
177
+ ··· + 9058774801y + 158180929
c
8
y
178
+ 8y
177
+ ··· + 24453354177839104y + 306979553972224
c
9
y
178
35y
177
+ ··· 612962y + 6889
c
12
y
178
+ 40y
177
+ ··· + 11873515289866y + 140976969961
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 1.002900 + 0.076332I
a = 0.410643 0.082087I
b = 0.579253 + 0.123214I
2.11950 0.08413I 0
u = 1.002900 0.076332I
a = 0.410643 + 0.082087I
b = 0.579253 0.123214I
2.11950 + 0.08413I 0
u = 0.226401 + 0.966400I
a = 0.409044 + 0.569674I
b = 0.439674 + 0.950963I
0.53209 2.15422I 0
u = 0.226401 0.966400I
a = 0.409044 0.569674I
b = 0.439674 0.950963I
0.53209 + 2.15422I 0
u = 0.335859 + 0.954059I
a = 0.159374 0.553582I
b = 0.536749 1.176660I
1.52044 8.62842I 0
u = 0.335859 0.954059I
a = 0.159374 + 0.553582I
b = 0.536749 + 1.176660I
1.52044 + 8.62842I 0
u = 0.919829 + 0.360834I
a = 3.14733 + 2.88557I
b = 0.080521 + 0.756472I
1.56137 + 3.49668I 0
u = 0.919829 0.360834I
a = 3.14733 2.88557I
b = 0.080521 0.756472I
1.56137 3.49668I 0
u = 0.374555 + 0.943169I
a = 0.356602 + 0.476093I
b = 0.677133 + 1.219760I
3.2314 + 14.8369I 0
u = 0.374555 0.943169I
a = 0.356602 0.476093I
b = 0.677133 1.219760I
3.2314 14.8369I 0
5
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.733219 + 0.657144I
a = 0.290021 0.279870I
b = 0.720709 0.133801I
2.84448 + 0.62683I 0
u = 0.733219 0.657144I
a = 0.290021 + 0.279870I
b = 0.720709 + 0.133801I
2.84448 0.62683I 0
u = 0.879338 + 0.433465I
a = 0.674827 0.733572I
b = 0.627845 0.975355I
2.79221 + 0.32953I 0
u = 0.879338 0.433465I
a = 0.674827 + 0.733572I
b = 0.627845 + 0.975355I
2.79221 0.32953I 0
u = 0.925580 + 0.310759I
a = 1.67998 1.78962I
b = 0.121356 + 0.308713I
1.66529 6.27208I 0
u = 0.925580 0.310759I
a = 1.67998 + 1.78962I
b = 0.121356 0.308713I
1.66529 + 6.27208I 0
u = 0.997517 + 0.261432I
a = 0.648349 + 0.344258I
b = 0.289800 0.362909I
3.41325 + 3.33568I 0
u = 0.997517 0.261432I
a = 0.648349 0.344258I
b = 0.289800 + 0.362909I
3.41325 3.33568I 0
u = 0.503693 + 0.823683I
a = 0.0536241 0.0652593I
b = 0.694699 1.139340I
4.22856 6.39408I 0
u = 0.503693 0.823683I
a = 0.0536241 + 0.0652593I
b = 0.694699 + 1.139340I
4.22856 + 6.39408I 0
6
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.863451 + 0.430814I
a = 1.35124 3.01221I
b = 0.421417 1.034660I
2.84586 3.91339I 0
u = 0.863451 0.430814I
a = 1.35124 + 3.01221I
b = 0.421417 + 1.034660I
2.84586 + 3.91339I 0
u = 0.932656 + 0.220528I
a = 0.026254 0.622186I
b = 0.752555 + 0.549421I
3.02952 2.41652I 0
u = 0.932656 0.220528I
a = 0.026254 + 0.622186I
b = 0.752555 0.549421I
3.02952 + 2.41652I 0
u = 0.961071 + 0.420548I
a = 0.69112 + 1.38885I
b = 1.43328 + 0.01277I
3.29043 + 3.04918I 0
u = 0.961071 0.420548I
a = 0.69112 1.38885I
b = 1.43328 0.01277I
3.29043 3.04918I 0
u = 0.791467 + 0.690929I
a = 0.642459 + 0.639450I
b = 0.357063 0.611371I
4.26263 + 0.47129I 0
u = 0.791467 0.690929I
a = 0.642459 0.639450I
b = 0.357063 + 0.611371I
4.26263 0.47129I 0
u = 0.860791 + 0.400076I
a = 0.033598 1.094830I
b = 1.348070 0.150928I
3.71483 + 0.26000I 0
u = 0.860791 0.400076I
a = 0.033598 + 1.094830I
b = 1.348070 + 0.150928I
3.71483 0.26000I 0
7
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.455344 + 0.832194I
a = 0.102653 + 0.514193I
b = 0.418681 + 0.944244I
0.802586 0.654897I 0
u = 0.455344 0.832194I
a = 0.102653 0.514193I
b = 0.418681 0.944244I
0.802586 + 0.654897I 0
u = 1.000000 + 0.351874I
a = 0.74966 + 2.66662I
b = 0.33424 + 1.39910I
3.13518 + 3.47455I 0
u = 1.000000 0.351874I
a = 0.74966 2.66662I
b = 0.33424 1.39910I
3.13518 3.47455I 0
u = 0.537889 + 0.769907I
a = 0.343867 0.772663I
b = 0.639669 0.652252I
6.38925 + 5.50798I 0
u = 0.537889 0.769907I
a = 0.343867 + 0.772663I
b = 0.639669 + 0.652252I
6.38925 5.50798I 0
u = 0.534702 + 0.760598I
a = 0.937376 0.313056I
b = 0.614535 0.327178I
2.93093 1.13494I 0
u = 0.534702 0.760598I
a = 0.937376 + 0.313056I
b = 0.614535 + 0.327178I
2.93093 + 1.13494I 0
u = 0.643610 + 0.668376I
a = 1.19281 + 1.30833I
b = 0.391945 + 0.888057I
4.34906 3.89150I 0
u = 0.643610 0.668376I
a = 1.19281 1.30833I
b = 0.391945 0.888057I
4.34906 + 3.89150I 0
8
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.988809 + 0.419771I
a = 0.88141 + 1.67174I
b = 0.40629 + 1.54254I
5.51999 + 2.80665I 0
u = 0.988809 0.419771I
a = 0.88141 1.67174I
b = 0.40629 1.54254I
5.51999 2.80665I 0
u = 1.030990 + 0.316344I
a = 0.19031 2.38027I
b = 0.124233 1.320040I
6.88304 + 0.74630I 0
u = 1.030990 0.316344I
a = 0.19031 + 2.38027I
b = 0.124233 + 1.320040I
6.88304 0.74630I 0
u = 0.491681 + 0.960663I
a = 0.515797 0.415645I
b = 0.520340 1.091510I
0.75536 + 5.62661I 0
u = 0.491681 0.960663I
a = 0.515797 + 0.415645I
b = 0.520340 + 1.091510I
0.75536 5.62661I 0
u = 1.046150 + 0.296906I
a = 1.38627 2.34666I
b = 0.089296 1.179670I
3.92608 1.74841I 0
u = 1.046150 0.296906I
a = 1.38627 + 2.34666I
b = 0.089296 + 1.179670I
3.92608 + 1.74841I 0
u = 0.429853 + 0.793813I
a = 0.614416 + 0.550696I
b = 1.082700 + 0.414154I
5.80834 8.54207I 0
u = 0.429853 0.793813I
a = 0.614416 0.550696I
b = 1.082700 0.414154I
5.80834 + 8.54207I 0
9
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.918420 + 0.608142I
a = 0.530491 0.020921I
b = 0.607930 0.613409I
3.86855 + 4.56902I 0
u = 0.918420 0.608142I
a = 0.530491 + 0.020921I
b = 0.607930 + 0.613409I
3.86855 4.56902I 0
u = 1.100700 + 0.116686I
a = 0.427374 + 1.031190I
b = 0.906577 + 0.038589I
0.64153 + 6.43482I 0
u = 1.100700 0.116686I
a = 0.427374 1.031190I
b = 0.906577 0.038589I
0.64153 6.43482I 0
u = 0.745874 + 0.823185I
a = 0.826267 0.189595I
b = 0.381633 + 0.815684I
4.59093 + 0.58252I 0
u = 0.745874 0.823185I
a = 0.826267 + 0.189595I
b = 0.381633 0.815684I
4.59093 0.58252I 0
u = 0.532615 + 0.978017I
a = 0.015242 + 0.382866I
b = 0.319357 + 0.756103I
4.00579 + 2.21397I 0
u = 0.532615 0.978017I
a = 0.015242 0.382866I
b = 0.319357 0.756103I
4.00579 2.21397I 0
u = 0.498374 + 0.728878I
a = 0.358226 0.756736I
b = 0.875651 0.219517I
1.36584 + 3.53840I 0
u = 0.498374 0.728878I
a = 0.358226 + 0.756736I
b = 0.875651 + 0.219517I
1.36584 3.53840I 0
10
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.976578 + 0.555103I
a = 0.573430 + 0.514163I
b = 1.31301 0.55907I
4.99134 4.59016I 0
u = 0.976578 0.555103I
a = 0.573430 0.514163I
b = 1.31301 + 0.55907I
4.99134 + 4.59016I 0
u = 0.065482 + 0.870039I
a = 0.324621 + 0.935946I
b = 0.382776 + 0.862810I
3.58038 + 1.00115I 0
u = 0.065482 0.870039I
a = 0.324621 0.935946I
b = 0.382776 0.862810I
3.58038 1.00115I 0
u = 0.638725 + 0.591019I
a = 0.82670 1.36318I
b = 1.084580 0.644673I
6.01799 + 0.02149I 0
u = 0.638725 0.591019I
a = 0.82670 + 1.36318I
b = 1.084580 + 0.644673I
6.01799 0.02149I 0
u = 1.065930 + 0.376474I
a = 1.10012 + 2.03588I
b = 0.597280 + 1.082100I
4.12211 + 4.42876I 0
u = 1.065930 0.376474I
a = 1.10012 2.03588I
b = 0.597280 1.082100I
4.12211 4.42876I 0
u = 0.892269 + 0.697624I
a = 0.118739 + 0.719472I
b = 0.567912 + 0.204651I
2.42353 + 4.54361I 0
u = 0.892269 0.697624I
a = 0.118739 0.719472I
b = 0.567912 0.204651I
2.42353 4.54361I 0
11
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 1.027730 + 0.484842I
a = 1.40720 + 1.43551I
b = 0.647611 + 1.193990I
4.98488 3.27724I 0
u = 1.027730 0.484842I
a = 1.40720 1.43551I
b = 0.647611 1.193990I
4.98488 + 3.27724I 0
u = 1.017850 + 0.506171I
a = 1.205170 + 0.070273I
b = 0.862311 0.588679I
2.95096 + 0.50612I 0
u = 1.017850 0.506171I
a = 1.205170 0.070273I
b = 0.862311 + 0.588679I
2.95096 0.50612I 0
u = 1.068610 + 0.390671I
a = 1.53381 1.90229I
b = 0.234645 1.316720I
4.22696 1.78557I 0
u = 1.068610 0.390671I
a = 1.53381 + 1.90229I
b = 0.234645 + 1.316720I
4.22696 + 1.78557I 0
u = 1.117730 + 0.232156I
a = 1.06354 + 1.97674I
b = 0.51053 + 1.31920I
1.55971 + 3.00952I 0
u = 1.117730 0.232156I
a = 1.06354 1.97674I
b = 0.51053 1.31920I
1.55971 3.00952I 0
u = 0.805641 + 0.294796I
a = 1.07909 + 2.44263I
b = 0.11023 + 1.53526I
4.63011 + 0.26293I 0
u = 0.805641 0.294796I
a = 1.07909 2.44263I
b = 0.11023 1.53526I
4.63011 0.26293I 0
12
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 1.030610 + 0.511647I
a = 0.857025 1.113470I
b = 1.46154 + 0.38377I
4.09351 2.85661I 0
u = 1.030610 0.511647I
a = 0.857025 + 1.113470I
b = 1.46154 0.38377I
4.09351 + 2.85661I 0
u = 1.056680 + 0.458003I
a = 1.02152 2.04281I
b = 0.03471 1.58391I
3.83664 8.67245I 0
u = 1.056680 0.458003I
a = 1.02152 + 2.04281I
b = 0.03471 + 1.58391I
3.83664 + 8.67245I 0
u = 0.078744 + 0.843924I
a = 0.951130 0.087666I
b = 0.634676 0.906333I
0.57601 + 2.49633I 0
u = 0.078744 0.843924I
a = 0.951130 + 0.087666I
b = 0.634676 + 0.906333I
0.57601 2.49633I 0
u = 0.504109 + 0.681189I
a = 0.623585 + 0.612398I
b = 0.493133 + 0.693577I
0.24404 1.65320I 0
u = 0.504109 0.681189I
a = 0.623585 0.612398I
b = 0.493133 0.693577I
0.24404 + 1.65320I 0
u = 1.020070 + 0.543373I
a = 2.28187 + 1.51956I
b = 0.446272 + 1.234780I
1.82010 + 9.54280I 0
u = 1.020070 0.543373I
a = 2.28187 1.51956I
b = 0.446272 1.234780I
1.82010 9.54280I 0
13
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 1.147040 + 0.152395I
a = 0.43103 + 1.93203I
b = 0.290755 + 1.183820I
1.91777 5.08765I 0
u = 1.147040 0.152395I
a = 0.43103 1.93203I
b = 0.290755 1.183820I
1.91777 + 5.08765I 0
u = 1.000260 + 0.586099I
a = 1.58088 + 2.70672I
b = 0.264832 + 0.991964I
3.23768 + 8.77205I 0
u = 1.000260 0.586099I
a = 1.58088 2.70672I
b = 0.264832 0.991964I
3.23768 8.77205I 0
u = 0.600479 + 0.586771I
a = 0.346395 0.270473I
b = 0.772809 0.878034I
4.19283 + 3.80808I 0
u = 0.600479 0.586771I
a = 0.346395 + 0.270473I
b = 0.772809 + 0.878034I
4.19283 3.80808I 0
u = 0.742136 + 0.900992I
a = 0.532909 0.520069I
b = 0.538981 0.923745I
5.58174 10.10730I 0
u = 0.742136 0.900992I
a = 0.532909 + 0.520069I
b = 0.538981 + 0.923745I
5.58174 + 10.10730I 0
u = 0.340027 + 0.744242I
a = 0.395591 + 0.358633I
b = 0.75158 + 1.27553I
2.91374 5.66390I 0
u = 0.340027 0.744242I
a = 0.395591 0.358633I
b = 0.75158 1.27553I
2.91374 + 5.66390I 0
14
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.414357 + 0.691815I
a = 0.303086 0.757140I
b = 0.483317 1.148190I
0.00039 + 3.83804I 0
u = 0.414357 0.691815I
a = 0.303086 + 0.757140I
b = 0.483317 + 1.148190I
0.00039 3.83804I 0
u = 1.068810 + 0.534728I
a = 1.81839 1.26370I
b = 0.301792 1.073170I
5.39193 5.98434I 0
u = 1.068810 0.534728I
a = 1.81839 + 1.26370I
b = 0.301792 + 1.073170I
5.39193 + 5.98434I 0
u = 1.056870 + 0.566007I
a = 0.268596 0.035077I
b = 0.698430 + 0.370411I
1.41651 3.15188I 0
u = 1.056870 0.566007I
a = 0.268596 + 0.035077I
b = 0.698430 0.370411I
1.41651 + 3.15188I 0
u = 0.145061 + 0.781986I
a = 0.730165 + 0.430423I
b = 0.339025 + 1.000820I
0.539309 1.235390I 0
u = 0.145061 0.781986I
a = 0.730165 0.430423I
b = 0.339025 1.000820I
0.539309 + 1.235390I 0
u = 1.129220 + 0.435354I
a = 0.65013 + 1.46535I
b = 0.228869 + 1.224050I
3.59973 3.05282I 0
u = 1.129220 0.435354I
a = 0.65013 1.46535I
b = 0.228869 1.224050I
3.59973 + 3.05282I 0
15
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 1.124380 + 0.454383I
a = 0.32000 2.13154I
b = 0.705214 0.694556I
2.68104 6.28248I 0
u = 1.124380 0.454383I
a = 0.32000 + 2.13154I
b = 0.705214 + 0.694556I
2.68104 + 6.28248I 0
u = 0.963197 + 0.740219I
a = 0.325782 0.495321I
b = 0.270728 + 0.793305I
3.92026 6.41702I 0
u = 0.963197 0.740219I
a = 0.325782 + 0.495321I
b = 0.270728 0.793305I
3.92026 + 6.41702I 0
u = 1.062000 + 0.598702I
a = 0.296376 + 0.570831I
b = 1.089920 0.070772I
0.31643 8.61700I 0
u = 1.062000 0.598702I
a = 0.296376 0.570831I
b = 1.089920 + 0.070772I
0.31643 + 8.61700I 0
u = 1.037710 + 0.643579I
a = 0.88980 1.74986I
b = 0.431012 0.819080I
4.90267 0.17583I 0
u = 1.037710 0.643579I
a = 0.88980 + 1.74986I
b = 0.431012 + 0.819080I
4.90267 + 0.17583I 0
u = 0.577315 + 0.520736I
a = 1.071830 0.743579I
b = 0.316760 + 1.167730I
0.45369 5.13953I 0
u = 0.577315 0.520736I
a = 1.071830 + 0.743579I
b = 0.316760 1.167730I
0.45369 + 5.13953I 0
16
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 1.088770 + 0.564897I
a = 1.25493 2.18049I
b = 0.470126 1.310230I
1.98689 8.69701I 0
u = 1.088770 0.564897I
a = 1.25493 + 2.18049I
b = 0.470126 + 1.310230I
1.98689 + 8.69701I 0
u = 1.190940 + 0.330945I
a = 0.447309 0.978475I
b = 0.585306 1.073920I
3.56178 + 1.46203I 0
u = 1.190940 0.330945I
a = 0.447309 + 0.978475I
b = 0.585306 + 1.073920I
3.56178 1.46203I 0
u = 1.067670 + 0.626280I
a = 0.032434 + 0.506548I
b = 0.836061 0.283749I
1.30935 + 6.42406I 0
u = 1.067670 0.626280I
a = 0.032434 0.506548I
b = 0.836061 + 0.283749I
1.30935 6.42406I 0
u = 0.745799 + 0.049882I
a = 0.93924 2.13980I
b = 0.26679 1.43329I
1.77412 + 5.58953I 0
u = 0.745799 0.049882I
a = 0.93924 + 2.13980I
b = 0.26679 + 1.43329I
1.77412 5.58953I 0
u = 1.117920 + 0.565724I
a = 1.21803 + 2.23264I
b = 0.77731 + 1.39873I
0.64025 + 10.62890I 0
u = 1.117920 0.565724I
a = 1.21803 2.23264I
b = 0.77731 1.39873I
0.64025 10.62890I 0
17
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 1.166080 + 0.459572I
a = 0.87354 1.48854I
b = 0.802358 0.888925I
2.74810 7.02865I 0
u = 1.166080 0.459572I
a = 0.87354 + 1.48854I
b = 0.802358 + 0.888925I
2.74810 + 7.02865I 0
u = 1.080380 + 0.639060I
a = 0.96725 + 1.59238I
b = 0.446377 + 1.224980I
1.03765 4.80800I 0
u = 1.080380 0.639060I
a = 0.96725 1.59238I
b = 0.446377 1.224980I
1.03765 + 4.80800I 0
u = 1.082490 + 0.638777I
a = 1.06846 1.64530I
b = 0.76154 1.26899I
2.47727 + 11.85550I 0
u = 1.082490 0.638777I
a = 1.06846 + 1.64530I
b = 0.76154 + 1.26899I
2.47727 11.85550I 0
u = 1.104130 + 0.609169I
a = 0.576034 0.615111I
b = 1.230980 + 0.361625I
3.7990 + 13.8139I 0
u = 1.104130 0.609169I
a = 0.576034 + 0.615111I
b = 1.230980 0.361625I
3.7990 13.8139I 0
u = 1.263260 + 0.021990I
a = 0.02390 1.98412I
b = 0.297847 1.149880I
5.89696 3.11148I 0
u = 1.263260 0.021990I
a = 0.02390 + 1.98412I
b = 0.297847 + 1.149880I
5.89696 + 3.11148I 0
18
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 1.163320 + 0.500177I
a = 1.36864 + 1.22472I
b = 0.056937 + 0.744575I
0.17746 + 3.58440I 0
u = 1.163320 0.500177I
a = 1.36864 1.22472I
b = 0.056937 0.744575I
0.17746 3.58440I 0
u = 0.956045 + 0.832685I
a = 0.376165 0.165442I
b = 0.427025 0.808821I
4.94992 + 3.81076I 0
u = 0.956045 0.832685I
a = 0.376165 + 0.165442I
b = 0.427025 + 0.808821I
4.94992 3.81076I 0
u = 0.489584 + 0.518546I
a = 0.935824 + 0.666432I
b = 1.249730 + 0.445727I
5.68299 1.39560I 11.11523 + 0.I
u = 0.489584 0.518546I
a = 0.935824 0.666432I
b = 1.249730 0.445727I
5.68299 + 1.39560I 11.11523 + 0.I
u = 0.634940 + 0.313078I
a = 2.12399 + 0.07983I
b = 0.203818 0.164584I
3.07344 0.45275I 0. 2.04570I
u = 0.634940 0.313078I
a = 2.12399 0.07983I
b = 0.203818 + 0.164584I
3.07344 + 0.45275I 0. + 2.04570I
u = 0.385920 + 0.576492I
a = 1.027280 + 0.319387I
b = 0.097709 1.018770I
3.45729 + 1.49634I 6.03648 0.76331I
u = 0.385920 0.576492I
a = 1.027280 0.319387I
b = 0.097709 + 1.018770I
3.45729 1.49634I 6.03648 + 0.76331I
19
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 1.026060 + 0.828448I
a = 0.376856 + 0.480730I
b = 0.003078 + 0.557286I
2.56853 + 4.27881I 0
u = 1.026060 0.828448I
a = 0.376856 0.480730I
b = 0.003078 0.557286I
2.56853 4.27881I 0
u = 1.326580 + 0.139331I
a = 0.50332 + 1.76180I
b = 0.518467 + 1.212420I
2.76141 11.41250I 0
u = 1.326580 0.139331I
a = 0.50332 1.76180I
b = 0.518467 1.212420I
2.76141 + 11.41250I 0
u = 1.150520 + 0.683850I
a = 1.29947 1.57463I
b = 0.574555 1.163460I
1.30612 11.63750I 0
u = 1.150520 0.683850I
a = 1.29947 + 1.57463I
b = 0.574555 + 1.163460I
1.30612 + 11.63750I 0
u = 1.176070 + 0.642500I
a = 1.11802 + 1.90279I
b = 0.70489 + 1.29500I
0.7855 20.6154I 0
u = 1.176070 0.642500I
a = 1.11802 1.90279I
b = 0.70489 1.29500I
0.7855 + 20.6154I 0
u = 1.187650 + 0.632861I
a = 0.98537 1.84503I
b = 0.56443 1.29825I
4.1124 + 14.3834I 0
u = 1.187650 0.632861I
a = 0.98537 + 1.84503I
b = 0.56443 + 1.29825I
4.1124 14.3834I 0
20
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 1.213860 + 0.602592I
a = 0.91914 + 1.69461I
b = 0.515726 + 1.085740I
3.50423 + 7.77458I 0
u = 1.213860 0.602592I
a = 0.91914 1.69461I
b = 0.515726 1.085740I
3.50423 7.77458I 0
u = 0.428021 + 0.440537I
a = 0.038516 1.158420I
b = 0.336616 + 1.033640I
3.28989 0.67593I 3.46240 + 2.11656I
u = 0.428021 0.440537I
a = 0.038516 + 1.158420I
b = 0.336616 1.033640I
3.28989 + 0.67593I 3.46240 2.11656I
u = 1.374950 + 0.178516I
a = 0.48025 1.67648I
b = 0.304567 1.136550I
7.42030 + 4.82870I 0
u = 1.374950 0.178516I
a = 0.48025 + 1.67648I
b = 0.304567 + 1.136550I
7.42030 4.82870I 0
u = 0.272573 + 0.531501I
a = 0.434699 0.897984I
b = 0.906164 0.554310I
5.13662 + 2.23226I 10.58231 4.44049I
u = 0.272573 0.531501I
a = 0.434699 + 0.897984I
b = 0.906164 + 0.554310I
5.13662 2.23226I 10.58231 + 4.44049I
u = 1.266350 + 0.612971I
a = 0.53210 + 1.77694I
b = 0.323250 + 1.145190I
0.06076 6.49031I 0
u = 1.266350 0.612971I
a = 0.53210 1.77694I
b = 0.323250 1.145190I
0.06076 + 6.49031I 0
21
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 1.41391 + 0.17970I
a = 0.29438 + 1.54211I
b = 0.026323 + 0.894160I
5.28549 + 3.79395I 0
u = 1.41391 0.17970I
a = 0.29438 1.54211I
b = 0.026323 0.894160I
5.28549 3.79395I 0
u = 1.40433 + 0.31068I
a = 0.25204 + 1.52788I
b = 0.249386 + 0.964809I
5.90557 2.36507I 0
u = 1.40433 0.31068I
a = 0.25204 1.52788I
b = 0.249386 0.964809I
5.90557 + 2.36507I 0
u = 0.145839 + 0.541331I
a = 0.568074 + 0.504752I
b = 0.177439 + 0.394688I
0.160507 1.160930I 2.09476 + 5.42026I
u = 0.145839 0.541331I
a = 0.568074 0.504752I
b = 0.177439 0.394688I
0.160507 + 1.160930I 2.09476 5.42026I
u = 0.013709 + 0.455046I
a = 1.062020 + 0.435805I
b = 0.037504 1.324710I
1.45705 + 5.11933I 0.27914 6.27378I
u = 0.013709 0.455046I
a = 1.062020 0.435805I
b = 0.037504 + 1.324710I
1.45705 5.11933I 0.27914 + 6.27378I
22
II. I
u
2
=
h−8.32×10
9
u
45
6.69×10
9
u
44
+· · ·+1.78×10
9
b1.46×10
10
, 3.97×10
10
u
45
7.17 × 10
12
u
44
+ · · · + 6.22 × 10
11
a + 2.81 × 10
12
, u
46
13u
44
+ · · · + 3u + 1i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
8
=
1
u
2
a
3
=
u
u
3
+ u
a
1
=
u
3
u
5
u
3
+ u
a
11
=
0.0638624u
45
+ 11.5206u
44
+ ··· 14.4748u 4.50983
4.66476u
45
+ 3.75370u
44
+ ··· + 22.8628u + 8.19014
a
6
=
12.5295u
45
+ 22.3749u
44
+ ··· 46.5577u 13.7090
5.65793u
45
+ 12.8490u
44
+ ··· 58.2644u 18.8836
a
9
=
0.770723u
45
5.51237u
44
+ ··· 39.5939u 10.8333
11.5357u
45
0.829968u
44
+ ··· 2.61246u + 3.05844
a
5
=
3.50039u
45
+ 13.0643u
44
+ ··· 10.8574u 4.45922
1.95735u
45
+ 4.90763u
44
+ ··· 32.4156u 12.7115
a
10
=
4.60090u
45
+ 7.76691u
44
+ ··· 37.3376u 12.7000
4.66476u
45
+ 3.75370u
44
+ ··· + 22.8628u + 8.19014
a
4
=
38.4502u
45
+ 20.6340u
44
+ ··· 156.788u 35.8446
10.3141u
45
+ 3.14360u
44
+ ··· 14.6467u 3.48782
a
12
=
20.7825u
45
4.86598u
44
+ ··· + 75.1849u + 13.0014
4.18709u
45
10.2509u
44
+ ··· + 19.7218u + 11.5511
(ii) Obstruction class = 1
(iii) Cusp Shapes
=
38029619317479
622252886789
u
45
+
25499483632642
622252886789
u
44
+ ···
86588044328609
622252886789
u
10648278393868
622252886789
23
(iv) u-Polynomials at the component
24
Crossings u-Polynomials at each crossing
c
1
u
46
26u
45
+ ··· 17u + 1
c
2
u
46
13u
44
+ ··· 3u + 1
c
3
u
46
7u
44
+ ··· 24u + 1
c
4
u
46
+ 2u
45
+ ··· 2u + 1
c
5
u
46
4u
44
+ ··· 2u + 1
c
6
u
46
u
45
+ ··· + 3u + 1
c
7
u
46
13u
44
+ ··· + 3u + 1
c
8
u
46
+ 3u
45
+ ··· 32u + 16
c
9
u
46
12u
44
+ ··· 4u + 1
c
10
u
46
+ u
45
+ ··· 3u + 1
c
11
u
46
2u
45
+ ··· + 2u + 1
c
12
u
46
u
45
+ ··· 4u + 1
25
26
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
46
+ 2y
45
+ ··· + 79y + 1
c
2
, c
7
y
46
26y
45
+ ··· 17y + 1
c
3
y
46
14y
45
+ ··· 126y + 1
c
4
, c
11
y
46
42y
45
+ ··· + 94y + 1
c
5
y
46
8y
45
+ ··· 6y + 1
c
6
, c
10
y
46
+ 23y
45
+ ··· + 39y + 1
c
8
y
46
17y
45
+ ··· + 6272y + 256
c
9
y
46
24y
45
+ ··· + 4y + 1
c
12
y
46
+ 11y
45
+ ··· + 20y + 1
27
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
1(vol +
1CS) Cusp shape
u = 0.983450 + 0.307125I
a = 1.27573 2.77840I
b = 0.29492 1.44654I
2.78091 4.08603I 1.94989 + 7.15790I
u = 0.983450 0.307125I
a = 1.27573 + 2.77840I
b = 0.29492 + 1.44654I
2.78091 + 4.08603I 1.94989 7.15790I
u = 0.508125 + 0.808557I
a = 0.485368 0.343164I
b = 0.514311 1.170440I
1.38404 + 5.17961I 4.31891 4.07830I
u = 0.508125 0.808557I
a = 0.485368 + 0.343164I
b = 0.514311 + 1.170440I
1.38404 5.17961I 4.31891 + 4.07830I
u = 0.486117 + 0.815840I
a = 0.290003 + 0.139054I
b = 0.317980 + 0.729688I
3.83350 1.89281I 3.03382 2.00944I
u = 0.486117 0.815840I
a = 0.290003 0.139054I
b = 0.317980 0.729688I
3.83350 + 1.89281I 3.03382 + 2.00944I
u = 1.016590 + 0.296435I
a = 0.44819 + 1.44608I
b = 0.299794 + 1.323860I
5.66471 1.82909I 6.27153 + 1.88473I
u = 1.016590 0.296435I
a = 0.44819 1.44608I
b = 0.299794 1.323860I
5.66471 + 1.82909I 6.27153 1.88473I
u = 1.017280 + 0.329546I
a = 1.84687 3.09272I
b = 0.210314 0.683314I
1.18852 6.75745I 5.85855 + 10.28788I
u = 1.017280 0.329546I
a = 1.84687 + 3.09272I
b = 0.210314 + 0.683314I
1.18852 + 6.75745I 5.85855 10.28788I
28
Solutions to I
u
2
1(vol +
1CS) Cusp shape
u = 0.889217 + 0.238247I
a = 1.11063 + 2.67494I
b = 0.12897 + 1.43140I
5.11527 0.32243I 10.16583 + 0.17691I
u = 0.889217 0.238247I
a = 1.11063 2.67494I
b = 0.12897 1.43140I
5.11527 + 0.32243I 10.16583 0.17691I
u = 0.884696 + 0.216141I
a = 0.37171 1.45187I
b = 0.146917 1.365460I
2.25285 + 6.28410I 4.60391 10.79728I
u = 0.884696 0.216141I
a = 0.37171 + 1.45187I
b = 0.146917 + 1.365460I
2.25285 6.28410I 4.60391 + 10.79728I
u = 0.988939 + 0.481946I
a = 0.390173 + 1.243250I
b = 1.331530 0.244460I
3.69812 + 3.98830I 2.47414 8.23564I
u = 0.988939 0.481946I
a = 0.390173 1.243250I
b = 1.331530 + 0.244460I
3.69812 3.98830I 2.47414 + 8.23564I
u = 0.988505 + 0.485066I
a = 0.853617 0.897578I
b = 1.343740 + 0.128159I
3.71797 1.68279I 3.63985 + 0.I
u = 0.988505 0.485066I
a = 0.853617 + 0.897578I
b = 1.343740 0.128159I
3.71797 + 1.68279I 3.63985 + 0.I
u = 0.009183 + 0.881297I
a = 0.721467 + 0.459682I
b = 0.374509 + 0.930811I
0.99961 1.53292I 10.15313 + 1.71263I
u = 0.009183 0.881297I
a = 0.721467 0.459682I
b = 0.374509 0.930811I
0.99961 + 1.53292I 10.15313 1.71263I
29
Solutions to I
u
2
1(vol +
1CS) Cusp shape
u = 0.892666 + 0.689566I
a = 0.669806 + 0.547107I
b = 0.010882 0.472603I
4.38829 + 7.42541I 4.35147 8.92139I
u = 0.892666 0.689566I
a = 0.669806 0.547107I
b = 0.010882 + 0.472603I
4.38829 7.42541I 4.35147 + 8.92139I
u = 0.838787 + 0.758510I
a = 1.286240 0.210947I
b = 0.093443 0.547401I
4.56776 1.93307I 0. + 4.28767I
u = 0.838787 0.758510I
a = 1.286240 + 0.210947I
b = 0.093443 + 0.547401I
4.56776 + 1.93307I 0. 4.28767I
u = 0.793997 + 0.311124I
a = 2.72418 + 1.51817I
b = 0.219312 0.546251I
2.02547 + 4.03936I 3.20903 6.00915I
u = 0.793997 0.311124I
a = 2.72418 1.51817I
b = 0.219312 + 0.546251I
2.02547 4.03936I 3.20903 + 6.00915I
u = 0.690355 + 0.473788I
a = 0.260469 + 0.713147I
b = 1.082070 + 0.192047I
4.72985 2.27614I 6.16486 + 3.97617I
u = 0.690355 0.473788I
a = 0.260469 0.713147I
b = 1.082070 0.192047I
4.72985 + 2.27614I 6.16486 3.97617I
u = 0.687149 + 0.469796I
a = 0.97857 1.17245I
b = 1.075890 0.291723I
4.72077 0.05313I 6.00851 + 0.58112I
u = 0.687149 0.469796I
a = 0.97857 + 1.17245I
b = 1.075890 + 0.291723I
4.72077 + 0.05313I 6.00851 0.58112I
30
Solutions to I
u
2
1(vol +
1CS) Cusp shape
u = 1.104990 + 0.484198I
a = 1.26286 + 1.49113I
b = 0.543770 + 0.938016I
4.14170 + 5.74758I 0
u = 1.104990 0.484198I
a = 1.26286 1.49113I
b = 0.543770 0.938016I
4.14170 5.74758I 0
u = 1.086570 + 0.602703I
a = 1.52060 1.91422I
b = 0.58461 1.31616I
0.42089 10.46380I 0
u = 1.086570 0.602703I
a = 1.52060 + 1.91422I
b = 0.58461 + 1.31616I
0.42089 + 10.46380I 0
u = 1.039100 + 0.794067I
a = 0.477616 + 0.305159I
b = 0.062581 + 0.655893I
2.33228 4.21371I 0
u = 1.039100 0.794067I
a = 0.477616 0.305159I
b = 0.062581 0.655893I
2.33228 + 4.21371I 0
u = 0.639983 + 0.249769I
a = 0.67363 1.32920I
b = 0.415246 + 0.716769I
2.01785 2.39313I 2.05637 + 2.65893I
u = 0.639983 0.249769I
a = 0.67363 + 1.32920I
b = 0.415246 0.716769I
2.01785 + 2.39313I 2.05637 2.65893I
u = 1.229560 + 0.569871I
a = 0.55297 + 1.90012I
b = 0.351530 + 1.133520I
0.14432 + 6.37560I 0
u = 1.229560 0.569871I
a = 0.55297 1.90012I
b = 0.351530 1.133520I
0.14432 6.37560I 0
31
Solutions to I
u
2
1(vol +
1CS) Cusp shape
u = 1.361530 + 0.103984I
a = 0.11044 + 1.88659I
b = 0.170996 + 0.980723I
5.68699 + 4.24746I 0
u = 1.361530 0.103984I
a = 0.11044 1.88659I
b = 0.170996 0.980723I
5.68699 4.24746I 0
u = 1.370330 + 0.276644I
a = 0.193597 + 1.398250I
b = 0.200358 + 0.968181I
5.69358 2.75745I 0
u = 1.370330 0.276644I
a = 0.193597 1.398250I
b = 0.200358 0.968181I
5.69358 + 2.75745I 0
u = 0.265250 + 0.299069I
a = 0.26672 + 3.18660I
b = 0.514614 + 0.864188I
3.26692 2.01340I 1.97380 + 3.73498I
u = 0.265250 0.299069I
a = 0.26672 3.18660I
b = 0.514614 0.864188I
3.26692 + 2.01340I 1.97380 3.73498I
32
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
46
26u
45
+ ··· 17u + 1)
· (u
178
+ 85u
177
+ ··· + 12261791u + 703921)
c
2
(u
46
13u
44
+ ··· 3u + 1)(u
178
+ u
177
+ ··· + 3043u + 839)
c
3
(u
46
7u
44
+ ··· 24u + 1)(u
178
+ u
177
+ ··· + 354196u + 339257)
c
4
(u
46
+ 2u
45
+ ··· 2u + 1)(u
178
+ u
177
+ ··· 563010u + 122123)
c
5
(u
46
4u
44
+ ··· 2u + 1)(u
178
+ 5u
177
+ ··· + 300u + 179)
c
6
(u
46
u
45
+ ··· + 3u + 1)(u
178
+ 46u
176
+ ··· + 147913u + 12577)
c
7
(u
46
13u
44
+ ··· + 3u + 1)(u
178
+ u
177
+ ··· + 3043u + 839)
c
8
(u
46
+ 3u
45
+ ··· 32u + 16)
· (u
178
8u
177
+ ··· 193237632u + 17520832)
c
9
(u
46
12u
44
+ ··· 4u + 1)(u
178
3u
177
+ ··· 316u + 83)
c
10
(u
46
+ u
45
+ ··· 3u + 1)(u
178
+ 46u
176
+ ··· + 147913u + 12577)
c
11
(u
46
2u
45
+ ··· + 2u + 1)(u
178
+ u
177
+ ··· 563010u + 122123)
c
12
(u
46
u
45
+ ··· 4u + 1)(u
178
+ 6u
177
+ ··· 2444512u + 375469)
33
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
46
+ 2y
45
+ ··· + 79y + 1)
· (y
178
+ 31y
177
+ ··· 583680219959y + 495504774241)
c
2
, c
7
(y
46
26y
45
+ ··· 17y + 1)
· (y
178
85y
177
+ ··· 12261791y + 703921)
c
3
(y
46
14y
45
+ ··· 126y + 1)
· (y
178
5y
177
+ ··· + 10288606046288y + 115095312049)
c
4
, c
11
(y
46
42y
45
+ ··· + 94y + 1)
· (y
178
133y
177
+ ··· 108608624088y + 14914027129)
c
5
(y
46
8y
45
+ ··· 6y + 1)(y
178
19y
177
+ ··· + 637456y + 32041)
c
6
, c
10
(y
46
+ 23y
45
+ ··· + 39y + 1)
· (y
178
+ 92y
177
+ ··· + 9058774801y + 158180929)
c
8
(y
46
17y
45
+ ··· + 6272y + 256)
· (y
178
+ 8y
177
+ ··· + 24453354177839104y + 306979553972224)
c
9
(y
46
24y
45
+ ··· + 4y + 1)(y
178
35y
177
+ ··· 612962y + 6889)
c
12
(y
46
+ 11y
45
+ ··· + 20y + 1)
· (y
178
+ 40y
177
+ ··· + 11873515289866y + 140976969961)
34