Cyclotomic Unit Calculator
Definitions
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εn := e2πi/n is an nth root of unity.
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For n=pα a prime power:
v(n,a) := (1 - εna)/ (1 - εn)
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For all other n:
v(n,a) := 1 - εna
Cyclotomic Unit Calculation
Basis for Cyclotomic Units for n = 420 = 2^2*3*5*7
Note that this basis extends to a universal basis, i.e the basis for d is a subset of the basis for n iff d|n.
v(420,1), v(35,1), v(28,1), v(21,1), v(20,1), v(15,1), v(12,1), v(35,3), v(420,61), v(420,73), v(28,5), v(21,4), v(60,13), v(35,8), v(140,33), v(7,2), v(84,25), v(35,11), v(140,53), v(5,2), v(105,43), v(7,3), v(140,61), v(105,46), v(420,193), v(35,18), v(140,73), v(105,58), v(140,81), v(105,61), v(420,253), v(20,13), v(35,23), v(140,93), v(105,73), v(84,61), v(35,26), v(420,313), v(140,113), v(105,88), v(420,361), v(15,13), v(420,373), v(28,25), v(21,19), v(35,33), v(105,103)
The rank (number of elements in basis) is 47
Cyclotomic Units Base Representations for n = 420 = 2^2*3*5*7
| v(420,1) | v(35,1) | v(28,1) | v(21,1) | v(20,1) | v(15,1) | v(12,1) | v(35,3) | v(420,61) | v(420,73) | v(28,5) | v(21,4) | v(60,13) | v(35,8) | v(140,33) | v(7,2) | v(84,25) | v(35,11) | v(140,53) | v(5,2) | v(105,43) | v(7,3) | v(140,61) | v(105,46) | v(420,193) | v(35,18) | v(140,73) | v(105,58) | v(140,81) | v(105,61) | v(420,253) | v(20,13) | v(35,23) | v(140,93) | v(105,73) | v(84,61) | v(35,26) | v(420,313) | v(140,113) | v(105,88) | v(420,361) | v(15,13) | v(420,373) | v(28,25) | v(21,19) | v(35,33) | v(105,103) |
v(210,1) | | | | 1 | | 1 | | | | | | | | | | | | | | | -1 | | | -1 | | | | | | -1 | | | | | | | | | | | | | | | 1 | 1 | -1 |
v(140,1) | | | | | | | | 1 | | | | | | 1 | -1 | 1 | | 1 | -1 | -1 | | -1 | -1 | | | 1 | | | -1 | | | 1 | | | | | | | -1 | | | | | 1 | | 1 | |
v(105,1) | | 1 | | 1 | | 1 | | -1 | | | | | | | | | | | | 1 | -1 | 1 | | -1 | | | | | | -1 | | | -1 | | | | | | | -1 | | | | | 1 | | -1 |
v(84,1) | | | | | | | 1 | | | | 1 | 1 | | | | | -1 | | | | | -1 | | | | | | | | | | | | | | -1 | | | | | | | | 1 | | | |
v(70,1) | | 1 | | | | | | | | | | | | | | | | | | | | | | | | -1 | | | | | | | | | | | | | | | | | | | | | |
v(60,1) | | | | | 1 | | 1 | | | | | | -1 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 1 | | | | | |
v(105,2) | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 1 |
v(140,3) | | | | | | | | 1 | | | | | | | | -1 | | | | | | | | | | | -1 | | | | | | 1 | | | | 1 | | | | | | | | | 1 | |
v(42,1) | | | | 1 | | | | | | | | 1 | | | | | | | | | | -1 | | | | | | | | | | | | | | | | | | | | | | | | | |
v(420,11) | | | | | | | | | | | | | | -1 | | | | 1 | | | | | | -1 | | | | -1 | -1 | | | | | | | | | | 1 | | 1 | | | | | | |
v(420,13) | | | | | | | 1 | | | -1 | | | | | | | | | | | | | | | -1 | | | | | | -1 | 1 | | | | | | -1 | | | | 1 | -1 | | | | |
v(30,1) | | | | | | 1 | | | | | | | | | | | | | | -1 | | | | | | | | | | | | | | | | | | | | | | 1 | | | | | |
v(105,4) | | 1 | | | | | | -1 | | | | 1 | | | | -1 | | | | | | 1 | | -1 | | | | | | | | | | | 1 | | | | | -1 | | | | | 1 | | |
v(420,17) | | | | | | | | | | | | | | | | | | | | | | | | | -1 | | | | | -1 | | | | | | | | | | 1 | | | | | | | |
v(70,3) | | | | | | | | 1 | | | | | | | | -1 | | | | | | | | | | | | | | | | | 1 | | | | 1 | | | | | | | | | 1 | |
v(420,19) | | 1 | 1 | 1 | | | -1 | -3 | 1 | | -1 | | | -1 | | | 1 | | -1 | 1 | | 2 | | -1 | | -1 | 1 | 1 | -1 | -2 | | | -2 | -1 | 1 | | | 1 | | | | -1 | 1 | | 2 | -1 | -1 |
v(210,11) | | | | | | | | | | | | | | -1 | | | | 1 | | | | | | -1 | | | | -1 | | | | | | | | | | | | | | | | | | | |
v(420,23) | | 1 | | | | | | -2 | | | -1 | 1 | | -1 | | 1 | | 1 | -1 | 1 | 1 | | | -1 | | | 1 | | -1 | -1 | | | -1 | -1 | 1 | | | | | | | -1 | 1 | 1 | 1 | -1 | |
v(35,2) | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 1 | |
v(84,5) | | | | | | | | | | | 1 | | | | | 1 | | | | | | -1 | | | | | | | | | | | | | | -1 | | | | | | | | 1 | | | |
v(210,13) | | | | | | 1 | | | | | | | | | | | | | | 1 | -1 | | | -1 | | | | -1 | | | | | | | -1 | | | | | -1 | | 1 | | | | | -1 |
v(140,9) | | | | | | | | 1 | | | | | | 1 | | | | | | -1 | | | -1 | | | 1 | | | | | | | 1 | | | | 1 | | | | | | | | | 1 | |
v(420,29) | 1 | | | | | -1 | | | | -1 | | | | | 1 | -1 | | -1 | 1 | -1 | 1 | | | 1 | -1 | | | 1 | 1 | | | | 1 | 1 | 1 | 1 | 1 | -1 | | 1 | | | -1 | -1 | -1 | | 1 |
v(14,1) | | | | | | | | | | | | | | | | | | | | | | -1 | | | | | | | | | | | | | | | | | | | | | | | | | |
v(420,31) | | | | -1 | -1 | | | 1 | | 1 | | | | | | 1 | -1 | 1 | -1 | | | -1 | 1 | | 1 | | -1 | -1 | | 1 | | | 1 | -1 | -1 | -1 | -1 | | | | 1 | | | 1 | -1 | -1 | 1 |
v(105,8) | | | | | | | | | | | | | | 1 | | | | | | | -1 | | | | | | | | | | | | | | | | -1 | | | | | | | | | | |
v(140,11) | | | | | | | | | | | | | | | | | | 1 | | | | | | | | | | | -1 | | | | -1 | | | | | | | | | | | | | | |
v(210,17) | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | -1 | | | | | | | | | | 1 | | | | | | | |
v(420,37) | | | | 1 | | 1 | | -1 | | | | | | | -1 | | | | | 1 | -1 | 1 | | -1 | | | | | -1 | -1 | | | -1 | | | | | 1 | | -1 | | | | | 1 | 1 | -2 |
v(210,19) | | | | 1 | | | | -1 | | | | | | | | | | -1 | | | -1 | 1 | | | | -1 | | 1 | | -1 | | | -1 | | | | | | | | | | | | 1 | | -1 |
v(140,13) | | | | | -1 | | | | | | | | | | -1 | | | | -1 | | | | | | | | -1 | | | | | 1 | | -1 | | | | | -1 | | | | | | | | |
v(21,2) | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 1 | | |
v(420,41) | 1 | -2 | -1 | | 1 | -1 | | 2 | | -1 | | -1 | | 1 | | | | -1 | 1 | -2 | | -1 | -1 | 2 | -1 | 1 | 1 | | | 1 | | | 1 | 2 | -1 | 1 | | -1 | 1 | 1 | | 1 | -1 | -1 | -2 | 1 | 1 |
v(10,1) | | | | | | | | | | | | | | | | | | | | -1 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
v(420,43) | | 1 | | | | | | -1 | | | | 1 | | -1 | | | | 1 | | 1 | 1 | | | -1 | | | | | | | -1 | | -1 | | 1 | | | | | -1 | | | | | 1 | -1 | |
v(105,11) | | | | | | | | | | | | | | -1 | | | | 1 | | | | | | -1 | | | | | | | | | | | | | | | | | | | | | | | |
v(28,3) | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 1 | | | |
v(210,23) | | 1 | | | | | | -1 | | | | 1 | | -1 | | | | 1 | | 1 | 1 | | | -1 | | | | | | -1 | | | | | 1 | | 1 | | | | | -1 | | | 1 | | |
v(420,47) | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 1 | | | | |
v(35,4) | | | | | | | | -1 | | | | | | | | -1 | | -1 | | | | 1 | | | | -1 | | | | | | | | | | | | | | | | | | | | | |
v(60,7) | | | | | 1 | | | | | | | | -1 | | | | | | | 1 | | | | | | | | | | | | 1 | | | | | | | | | | | | | | | |
v(42,5) | | | | 1 | | | | | | | | | | | | 2 | | | | | | -1 | | | | | | | | | | | | | | | | | | | | | | | -1 | | |
v(140,17) | | | | | | | | | | | | | | | | | | | -1 | | | | | | | 1 | | | | | | | | | | | -1 | | | | | | | | | | |
v(105,13) | | | | | | 1 | | | | | | | | | | | | | | 1 | -1 | | | | | | | -1 | | | | | | | -1 | | | | | -1 | | 1 | | | | | -1 |
v(420,53) | | | -1 | | 1 | | | | | | | | | | | | | | 1 | | | | -1 | | -1 | | 1 | | -1 | | | | -1 | 1 | | | | | 1 | | | | | | | | |
v(70,9) | | | | | | | | 1 | | | | | | 1 | | | | | | -1 | | | | | | 1 | | | | | | | 1 | | | | 1 | | | | | | | | | 1 | |
v(84,11) | | | 1 | | | | | | | | | -1 | | | | -1 | 1 | | | | | 2 | | | | | | | | | | | | | | | | | | | | | | -1 | 1 | | |
v(15,2) | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 1 | | | | | |
v(140,19) | | 1 | 1 | | | | | -1 | | | -1 | | | -1 | 1 | 1 | | | | 1 | | 1 | 1 | | | -1 | | | | | | | -1 | -1 | | | -1 | | | | | | | | | -2 | |
v(210,29) | | 1 | | | | | | -2 | | | | 1 | | -1 | | -1 | | | | | 1 | | | -1 | | | | 1 | | -1 | | | | | 2 | | 1 | | | | | -1 | | | 1 | | |
v(420,59) | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 1 | | | | | | |
v(7,1) | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
v(210,31) | | -1 | | | | | | 1 | | | | -1 | | 1 | | | | | | -1 | | | | 1 | | | | | | | | | 1 | | -1 | | | | | 1 | | | | | -1 | | 1 |
v(20,3) | | | | | | | | | | | | | | | | | | | | 1 | | | | | | | | | | | | -1 | | | | | | | | | | | | | | | |
v(105,16) | | | | -1 | | | | 1 | | | | | | | | 1 | | 1 | | | | -1 | | | | | | -1 | | 1 | | | | | | | -1 | | | | | | | | -1 | -1 | 1 |
v(84,13) | | | -1 | -1 | | | 1 | | | | | | | | | | -1 | | | | | -1 | | | | | | | | | | | | | | -1 | | | | | | | | 1 | | | |
v(70,11) | | | | | | | | | | | | | | | | | | 1 | | | | | | | | | | | | | | | -1 | | | | | | | | | | | | | | |
v(420,67) | | -1 | | | | | | 1 | | -1 | | | | 1 | -1 | 1 | | 1 | -1 | -1 | | -1 | -1 | | | 2 | 1 | | -1 | | | 1 | | | | | | | -1 | | | | | 1 | | 1 | |
v(105,17) | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 1 | | | | | | | |
v(140,23) | | 1 | | | | | | -1 | | | | | | | | | | | | 1 | | 1 | | | | -1 | | | | | | | | -1 | | | | | | | | | | | | -1 | |
v(6,1) | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
v(420,71) | 1 | | | -1 | | -1 | | | | | | | | -1 | 1 | -1 | | -1 | 1 | | 1 | | 1 | 1 | | -1 | | | 1 | 1 | | -1 | | 1 | | | | | 1 | | | | | -1 | -1 | -1 | 1 |
v(35,6) | | -1 | | | | | | 1 | | | | | | | | | | | | -1 | | -1 | | | | 1 | | | | | | | 1 | | | | | | | | | | | | | 1 | |
v(210,37) | | | | 1 | | 1 | | -1 | | | | | | | | | | -1 | | 1 | -1 | 1 | | -1 | | | | | | -1 | | | | | | | | | | -1 | | | | | 1 | 1 | -2 |
v(105,19) | | | | 1 | | | | -1 | | | | | | | | | | -1 | | | | 1 | | | | -1 | | 1 | | -1 | | | -1 | | | | | | | | | | | | 1 | | -1 |
v(60,11) | | | | | | -1 | 1 | | | | | | -1 | | | | | | | -1 | | | | | | | | | | | | 1 | | | | | | | | | | | | | | | |
v(70,13) | | | | | | | | -1 | | | | | | -1 | | | | -1 | | 1 | | | | | | -1 | | | | | | | -1 | | | | | | | | | | | | | -1 | |
v(420,79) | | | | | | | | | -1 | | | | | | | | | | | | | | 1 | | | | -1 | | | | | | | | | | | | | | | | | | | | |
v(140,27) | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 1 | | | | | | | | |
v(210,41) | | -1 | | | | | | 2 | | | | -1 | | 1 | | 1 | | | | -1 | -1 | -1 | | 1 | | 1 | | -1 | | 1 | | | 1 | | -2 | | -1 | | | | | 1 | | | -1 | | |
v(420,83) | | -1 | -1 | | 1 | -1 | 1 | | | -1 | 1 | | | | | -1 | | -1 | 1 | -1 | 1 | -1 | -1 | 1 | -1 | | 1 | 1 | | | -1 | | | 2 | 1 | | 1 | -1 | 1 | 1 | | | -1 | | | 1 | 1 |
v(5,1) | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
v(84,17) | | | | | | | | | | | | 1 | | | | | -1 | | | | | | | | | | | | | | | | | | | | | | | | | | | | -1 | | |
v(210,43) | | 1 | | | | | | -1 | | | | 1 | | -1 | | | | 1 | | 1 | 1 | | | -1 | | | | | | | | | -1 | | 1 | | | | | -1 | | | | | 1 | -1 | |
v(140,29) | | | 1 | | -1 | | | | | | | | | | | | | | | | | | 1 | | | | -1 | | 1 | | | | 1 | -1 | | | | | -1 | | | | | | | | |
v(105,22) | | | | | | -1 | | -1 | | | | | | -1 | | -1 | | | | | 1 | | | | | -1 | | 1 | | | | | | | 1 | | 1 | | | 1 | | -1 | | | | | 1 |
v(420,89) | | | | | | | -1 | -1 | 1 | | | | | -1 | -1 | | 1 | 1 | | | 1 | | -1 | -1 | | | 1 | | -1 | -1 | | | -1 | | 1 | | 1 | 1 | | | | -1 | 1 | | 1 | | |
v(14,3) | | | | | | | | | | | | | | | | -1 | | | | | | 1 | | | | | | | | | | | | | | | | | | | | | | | | | |
v(105,23) | | | | | | | | 1 | | | | | | | | 1 | | 1 | | | | -1 | | | | 1 | | -1 | | | | | 1 | | | | | | | | | | | | | | |
v(140,31) | | | | | | | | -1 | | | -1 | | | | | 1 | | | -1 | | | | | | | | 1 | | -1 | | | | -1 | | | | -1 | | | | | | | 1 | | -1 | |
v(210,47) | | | | | | | | 1 | | | | -1 | | 1 | | 1 | | | | | -1 | | | 1 | | | | | | 1 | | | | | -1 | | -1 | | | | | 1 | | | -1 | | |
v(84,19) | | | | -1 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | -1 | | | | | | | | | 1 | | |
v(420,97) | | -1 | | | | | | 2 | | | | -1 | | 2 | | 1 | | | | -1 | -1 | -1 | -1 | 1 | | 1 | | | | | 1 | | 1 | | -1 | | | | -1 | 1 | | | | | -1 | 1 | |
v(30,7) | | | | | | 1 | | | | | | | | | | | | | | 2 | | | | | | | | | | | | | | | | | | | | | | -1 | | | | | |
v(21,5) | | | | | | | | | | | | | | | | 1 | | | | | | -1 | | | | | | | | | | | | | | | | | | | | | | | -1 | | |
v(420,101) | | 1 | | -1 | | | | | | 1 | 1 | 1 | | -1 | 1 | -1 | -1 | | 1 | 1 | | | 1 | -1 | 1 | -1 | -1 | -1 | 1 | 1 | | -1 | 1 | | | -1 | | | 1 | -1 | 1 | | | | | -1 | |
v(70,17) | | | | | | | | | | | | | | | | | | | | | | | | | | 1 | | | | | | | | | | | -1 | | | | | | | | | | |
v(420,103) | | -1 | | -1 | | -1 | | 1 | | | | | | | | | | | | -1 | 1 | -1 | | 1 | | | | | | 1 | | | 1 | | | | | -1 | | 1 | | | | | -1 | | 2 |
v(105,26) | | | | | | | | -1 | | | | | | | | | | | | | | | | | | | | | | -1 | | | | | | | 1 | | | | | | | | | | |
v(4,1) | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
v(210,53) | | 1 | | | | | | | | | | | | | | | | | | 1 | | 1 | | | | | | | | 1 | | | -1 | | | | -1 | | | -1 | | | | | | -1 | |
v(420,107) | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 1 | | | | | | | | | |
v(35,9) | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 1 | | | | | | | | | | |
v(420,109) | | | | 1 | | | | -1 | | -1 | -1 | | | 1 | -1 | | 1 | | -1 | -1 | | 1 | -1 | | -1 | 1 | 1 | 1 | -1 | -1 | | 1 | -1 | | 1 | 1 | | | -1 | | -1 | | | | 1 | 1 | -1 |
v(42,11) | | | | | | | | | | | | -1 | | | | -1 | | | | | | 2 | | | | | | | | | | | | | | | | | | | | | | | 1 | | |
v(140,37) | | -1 | | | | | | | | | | | | | -1 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 1 | |
v(15,4) | | | | | | -1 | | | | | | | | | | | | | | -1 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
v(420,113) | | | | | | | | -1 | | | | | | -1 | | | | | | 1 | | | 1 | | | -1 | | | | | -1 | | -1 | | | | -1 | | 1 | | | | | | | -1 | |
v(70,19) | | | | | | | | | | | | | | -1 | | 1 | | | | | | | | | | | | | | | | | -1 | | | | -1 | | | | | | | | | -1 | |
v(84,23) | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 1 | | | | | | | | | | | |
v(105,29) | | | | | | | | -1 | | | | 1 | | -1 | | -1 | | | | | 1 | | | -1 | | | | 1 | | -1 | | | | | 1 | | 1 | | | | | -1 | | | 1 | | |
v(140,39) | | | | | | | | | | | 1 | | | | | -2 | | -1 | 1 | | | 1 | | | | -1 | -1 | | 1 | | | | 1 | | | | 1 | | | | | | | -1 | | | |
v(210,59) | | | | | | | | -1 | | | | | | | | -1 | | -1 | | | | 1 | | 1 | | -1 | | 1 | | | | | -1 | | | | | | | | | | | | | | |
v(60,17) | | | | | | -1 | | | | | | | -1 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 1 | | | | | |
v(420,121) | | | | -1 | | | 1 | 2 | -1 | | | | | | 1 | 1 | -1 | | | | | -1 | 1 | 1 | | | -1 | -1 | 1 | 2 | | | 1 | | -1 | | -1 | -1 | | | | 1 | -1 | | -2 | -1 | 1 |
v(210,61) | | | | | | 1 | | 1 | | | | | | 1 | | 1 | | | | | -1 | | | | | 1 | | -1 | | 1 | | | | | -1 | | -1 | | | -1 | | 1 | | | | | -1 |
v(140,41) | | -1 | -1 | | 1 | | | | | | | | | | | | | | | -1 | | -1 | -1 | | | 1 | 1 | | -1 | | | | | 1 | | | | | 1 | | | | | | | 1 | |
v(105,31) | | -1 | | | | | | 1 | | | | -1 | | 1 | | | | -1 | | -1 | | | | 1 | | | | | | | | | 1 | | -1 | | | | | 1 | | | | | -1 | 1 | |
v(10,3) | | | | | | | | | | | | | | | | | | | | 1 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
v(420,127) | | 1 | 1 | | -1 | | -1 | -1 | | 1 | -1 | | | | | | | | -1 | 1 | | 1 | 1 | | 1 | -1 | -1 | | | | 1 | | | -2 | | | | 1 | -1 | | | -1 | 1 | | | -1 | |
v(105,32) | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 1 | | | | | | | | | | | | |
v(140,43) | | | | | | | | 1 | | | | | | 1 | | 1 | | 1 | | | | -1 | | | | 1 | | | | | | | | | | | | | -1 | | | | | | | | |
v(42,13) | | | | -1 | | | | | | | | -1 | | | | -1 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
v(420,131) | | | | | | -1 | | -1 | 1 | | | | | | | | | | | -1 | 1 | | -1 | | | | 1 | 1 | | -1 | | | | | 1 | | 1 | | | 1 | | -1 | | | | | 1 |
v(60,19) | | | | | | | -1 | | | | | | 1 | | | | | | | | | | | | | | | | | | | -1 | | | | | | | | | | -1 | | | | | |
v(210,67) | | -1 | | -1 | | | | 2 | | | | | | | | | | 1 | | | | -1 | | | | 1 | | -1 | | 1 | | | 1 | | -1 | | | | | | | | | | -1 | | 1 |
v(28,9) | | | | | | | | | | | -1 | | | | | 1 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
v(105,34) | | | | -1 | | -1 | | 1 | | | | | | | | | | | | -1 | 1 | -1 | | 1 | | | | | | 1 | | | | | | | | | | 1 | | | | | -1 | | 1 |
v(420,137) | | | | 1 | | | | -1 | | -1 | | | | | | -1 | | -1 | | | | 1 | | | | | | 1 | | -1 | | | | | 1 | | 1 | | | | | | | | 1 | 1 | -1 |
v(70,23) | | 1 | | | | | | -1 | | | | | | | | | | | | 1 | | 1 | | | | -1 | | | | | | | | | | | | | | | | | | | | -1 | |
v(420,139) | -1 | | | | | | | 1 | | | | | | 1 | -1 | 1 | | 1 | -1 | -1 | | -1 | -1 | | | 1 | | | -1 | | | 1 | | -1 | | | | | -1 | | | | | 1 | | 1 | |
v(3,1) | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
v(140,47) | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 1 | | | | | | | | | | | | | |
v(210,71) | | | | -1 | | -1 | | 1 | | | | | | | | | | | | -1 | 1 | -1 | | 1 | | | | | | 1 | | | | | | | | | | | | | | | -1 | | 1 |
v(420,143) | | | | -1 | | | | 1 | | 1 | | | | -1 | 1 | -1 | | | 1 | 1 | | | 1 | | | -1 | -1 | -1 | 1 | 1 | | -1 | 1 | | -1 | | | | 1 | | | | | -1 | -1 | -1 | 1 |
v(35,12) | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 1 | | | | | | | | | | | | | | |
v(84,29) | | | 1 | | | | -1 | | | | | -1 | | | | -1 | 1 | | | | | 1 | | | | | | | | | | | | | | 1 | | | | | | | | -1 | | | |
v(210,73) | | | | 1 | | | | -1 | | | | | | | | -1 | | -1 | | | | 1 | | | | | | 1 | | -1 | | | | | 1 | | 1 | | | | | | | | 1 | 1 | -1 |
v(20,7) | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 1 | | | | | | | | | | | | | | | |
v(105,37) | | | | | | | | | | | | | | | | | | -1 | | | | | | | | | | | | | | | | | | | | | | | | | | | | 1 | -1 |
v(420,149) | | | | | | 1 | | 1 | -1 | | | | | 1 | | 1 | | | | | -1 | | | | | 1 | | -1 | | 1 | | | | | -1 | | -1 | | | -1 | | 1 | | | | | -1 |
v(14,5) | | | | | | | | | | | | | | | | 1 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
v(420,151) | | | | | | | | -1 | | | | | | | | -1 | | -1 | | | | 1 | | 1 | | -1 | | 1 | | | | | -1 | | | | | | | | -1 | | | | | | |
v(105,38) | | -1 | | | | | | 1 | | | | | | | | | | | | | | | | | | | | | | | | | | | -1 | | | | | | | | | | | | |
v(140,51) | | -1 | -1 | | | | | 1 | | | 1 | | | | -1 | | | | | -1 | | -1 | -1 | | | 1 | | | | | | | | 1 | | | | | | | | | | | | 1 | |
v(30,11) | | | | | | -1 | | | | | | | | | | | | | | -1 | | | | | | | | | | | | | | | | | | | | | | -1 | | | | | |
v(84,31) | | | -1 | | | | | | | | | | | | | | -1 | | | | | | | | | | | | | | | | | | | | | | | | | | | 1 | | | |
v(35,13) | | | | | | | | -1 | | | | | | -1 | | | | | | 1 | | | | | | -1 | | | | | | | -1 | | | | | | | | | | | | | -1 | |
v(420,157) | | 1 | 1 | | -1 | | | | | | | | | | | | | | -1 | 1 | | 1 | 1 | | 1 | | -1 | | 1 | 1 | | | | -1 | | | -1 | | -1 | -1 | | | | | | -1 | |
v(210,79) | | | | | | -1 | | -1 | | | | | | | | | | | | -1 | 1 | | | | | | | 1 | | -1 | | | | | 1 | | 1 | | | 1 | | -1 | | | | | 1 |
v(21,8) | | | | -1 | | | | | | | | | | | | -1 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
v(60,23) | | | | | -1 | 1 | | | | | | | 1 | | | | | | | 1 | | | | | | | | | | | | -1 | | | | | | | | | | -1 | | | | | |
v(70,27) | | | | | | | | 1 | | | | | | 1 | | 1 | | 1 | | | | -1 | | | | 1 | | | | | | | | | | | | | | | | | | | | | |
v(420,163) | | | | | | | | 1 | | | | -1 | | 1 | | 1 | | | | | -1 | | | 1 | | | | | | 1 | | | | | -1 | | -1 | | | | | 1 | -1 | | -1 | | |
v(105,41) | | -1 | | | | | | 2 | | | | -1 | | 1 | | 1 | | | | -1 | -1 | -1 | | 1 | | 1 | | -1 | | 1 | | | 1 | | -1 | | -1 | | | | | 1 | | | -1 | | |
v(28,11) | | | | | | | | | | | | | | | | -1 | | | | | | 1 | | | | | | | | | | | | | | | | | | | | | | -1 | | | |
v(210,83) | | | | | | -1 | | -1 | | | | | | | | -1 | | -1 | | | 1 | | | 1 | | -1 | | 1 | | | | | | | 1 | | 1 | | | 1 | | -1 | | | | | 1 |
v(420,167) | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 1 | | | | | | | | | | | | | | | | |
v(420,169) | -1 | 1 | 1 | | -1 | 1 | | | | 1 | | | | | | 1 | | 1 | -1 | 1 | -1 | | 1 | -1 | 1 | | -1 | -1 | | | | | | -2 | -1 | -1 | -1 | 1 | -1 | -1 | | | 1 | 1 | 1 | -1 | -1 |
v(42,17) | | | | | | | | | | | | 1 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | -1 | | |
v(140,57) | | | | | 1 | | | -1 | | | | | | -1 | 1 | | | -1 | 1 | 1 | | | | | | -1 | 1 | | | | | -1 | -1 | 1 | | | | | 1 | | | | | | | -1 | |
v(420,173) | | | | | | | | | | | | | | | 1 | | | -1 | | | | | | | | | | | 1 | | | | 1 | | | | | -1 | | | | | | | | | |
v(70,29) | | -1 | | | | | | | | | | | | | | | | | | -1 | | -1 | | | | 1 | | | | | | | 1 | | | | | | | | | | | | | 1 | |
v(12,5) | | | | | | | -1 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
v(105,44) | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 1 | | | | | | | | | | | | | | | | | |
v(140,59) | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 1 | | | | | | | | | | | | | | | | | | |
v(210,89) | | | | -1 | | | | 1 | | | | | | -1 | | 1 | | 1 | | | 1 | -1 | | | | | | -1 | | 1 | | | | | | | | | | | | | | | -1 | -1 | 1 |
v(420,179) | | -1 | | 1 | 1 | | | | | -1 | | -1 | | 1 | | -1 | 1 | -1 | 1 | -1 | | 1 | -1 | 1 | -1 | | 1 | 1 | | -1 | | | | 1 | | 1 | 1 | | | 1 | -1 | | | -1 | | 1 | |
v(420,181) | -1 | 1 | | | | 1 | | -2 | | 1 | | 1 | | -1 | -1 | | | 1 | -1 | 1 | | | | -2 | 1 | | | | -1 | -1 | | | -1 | -1 | 1 | -1 | | 1 | | -1 | | -1 | 1 | 1 | 2 | | -1 |
v(30,13) | | | | | | -1 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 1 | | | | | |
v(84,37) | | | | 1 | | | | | | | -1 | | | | | 1 | | | | | | | | | | | | | | | | | | | | 1 | | | | | | | | -1 | -1 | | |
v(70,31) | | | | | | | | -1 | | | | | | | | -1 | | -1 | | | | 1 | | | | -1 | | | | | | | | | | | | | | | | | | | | -1 | |
v(420,187) | | | | | | | | 1 | | | 1 | | | | | -1 | | | 1 | | | | | | | | -1 | | 1 | | | | 1 | 1 | | | 1 | | | | | | -1 | -1 | | 1 | |
v(105,47) | | | | | | | | | | | | | | | | | | | | | | | | | | | | 1 | | | | | | | | | | | | | | | | | | | |
v(20,9) | | | | | -1 | | | | | | | | | | | | | | | -1 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
v(42,19) | | | | -1 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 1 | | |
v(420,191) | | -1 | -1 | | | | 1 | 2 | -1 | | 1 | | | 1 | | | -1 | -1 | 1 | -1 | -1 | -1 | | 1 | | | -1 | | 1 | 1 | | | 1 | 1 | -1 | | | -1 | | | | 1 | -1 | | -1 | 1 | |
v(35,16) | | | | | | | | | | | | | | | | 1 | | | | | | | | | | | | | | | | | -1 | | | | -1 | | | | | | | | | -1 | |
v(210,97) | | -1 | | | | | | 1 | | | | -1 | | 1 | | 1 | | | | | -1 | -1 | | 1 | | | | | | | | | | | -1 | | -1 | | | 1 | | | | | -1 | | |
v(28,13) | | | -1 | | | | | | | | | | | | | | | | | | | -1 | | | | | | | | | | | | | | | | | | | | | | | | | |
v(15,7) | | | | | | | | | | | | | | | | | | | | 1 | | | | | | | | | | | | | | | | | | | | | | -1 | | | | | |
v(420,197) | | | | | | 1 | -1 | | | 1 | | | | | | | | | | 1 | -1 | | | -1 | 1 | | | -1 | | | 1 | -1 | | | -1 | | | 1 | | -1 | | | 1 | | | | -1 |
v(70,33) | | -1 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 1 | |
v(420,199) | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 1 | | | | | | | | | | -1 | | -1 | | | | | | |
v(21,10) | | | | | | | | | | | | -1 | | | | | | | | | | 1 | | | | | | | | | | | | | | | | | | | | | | | | | |
v(140,67) | | | | | | | | | | | | | | | | | | | | | | | | | | | 1 | | | | | | | | | | | | | | | | | | | | |
v(210,101) | | 1 | | | | | | -1 | | | | 1 | | | | -1 | | | | | | 1 | | -1 | | | | | | | | | | | 1 | | | | | -1 | | | | | 1 | | -1 |
v(60,29) | | | | | -1 | 1 | -1 | | | | | | 1 | | | | | | | -1 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
v(35,17) | | | | | | | | | | | | | | | | | | | | | | | | | | 1 | | | | | | | | | | | | | | | | | | | | | |
v(84,41) | | | | 1 | | | -1 | | | | -1 | | | | | | 1 | | | | | | | | | | | | | | | | | | | 1 | | | | | | | | -1 | | | |
v(210,103) | | -1 | | -1 | | -1 | | 1 | | | | | | | | | | | | -1 | 1 | -1 | | 1 | | | | | | 1 | | | 1 | | | | | | | 1 | | | | | -1 | | 2 |
v(140,69) | | 1 | | | | | | -1 | | | | | | -1 | 1 | -1 | | -1 | 1 | 1 | | 1 | 1 | | | -2 | | | 1 | | | -1 | | | | | | | 1 | | | | | -1 | | -1 | |
v(105,52) | | 1 | | | | | | -1 | | | | | | | | | | | | 1 | | 1 | | | | | | | | | | | -1 | | | | | | | -1 | | | | | | -1 | |
v(420,209) | -1 | | | 1 | | 1 | | | | | | | | | | | | | | | -1 | | | -1 | | | | | | -1 | | | | | | | | | | | | | | | 1 | 1 | -1 |
v(2,1) | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
v(420,211) | -1 | | | 1 | | 1 | | | | | | | | | | | | | | | -1 | | | -1 | | | | | | -1 | | | | | | | | | | | | | | | 1 | 1 | -1 |
v(105,53) | | 1 | | | | | | -1 | | | | | | | | | | | | 1 | | 1 | | | | | | | | | | | -1 | | | | | | | -1 | | | | | | -1 | |
v(140,71) | | 1 | | | | | | -1 | | | | | | -1 | 1 | -1 | | -1 | 1 | 1 | | 1 | 1 | | | -2 | | | 1 | | | -1 | | | | | | | 1 | | | | | -1 | | -1 | |
v(210,107) | | -1 | | -1 | | -1 | | 1 | | | | | | | | | | | | -1 | 1 | -1 | | 1 | | | | | | 1 | | | 1 | | | | | | | 1 | | | | | -1 | | 2 |
v(84,43) | | | | 1 | | | -1 | | | | -1 | | | | | | 1 | | | | | | | | | | | | | | | | | | | 1 | | | | | | | | -1 | | | |
v(60,31) | | | | | -1 | 1 | -1 | | | | | | 1 | | | | | | | -1 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
v(210,109) | | 1 | | | | | | -1 | | | | 1 | | | | -1 | | | | | | 1 | | -1 | | | | | | | | | | | 1 | | | | | -1 | | | | | 1 | | -1 |
v(21,11) | | | | | | | | | | | | -1 | | | | | | | | | | 1 | | | | | | | | | | | | | | | | | | | | | | | | | |
v(420,221) | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 1 | | | | | | | | | | -1 | | -1 | | | | | | |
v(70,37) | | -1 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 1 | |
v(420,223) | | | | | | 1 | -1 | | | 1 | | | | | | | | | | 1 | -1 | | | -1 | 1 | | | -1 | | | 1 | -1 | | | -1 | | | 1 | | -1 | | | 1 | | | | -1 |
v(15,8) | | | | | | | | | | | | | | | | | | | | 1 | | | | | | | | | | | | | | | | | | | | | | -1 | | | | | |
v(28,15) | | | -1 | | | | | | | | | | | | | | | | | | | -1 | | | | | | | | | | | | | | | | | | | | | | | | | |
v(210,113) | | -1 | | | | | | 1 | | | | -1 | | 1 | | 1 | | | | | -1 | -1 | | 1 | | | | | | | | | | | -1 | | -1 | | | 1 | | | | | -1 | | |
v(420,227) | | | | | | | | | | | | | | | | | | | | | | | | | 1 | | | | | | | | | | | | | | | | | | | | | | |
v(35,19) | | | | | | | | | | | | | | | | 1 | | | | | | | | | | | | | | | | | -1 | | | | -1 | | | | | | | | | -1 | |
v(420,229) | | -1 | -1 | | | | 1 | 2 | -1 | | 1 | | | 1 | | | -1 | -1 | 1 | -1 | -1 | -1 | | 1 | | | -1 | | 1 | 1 | | | 1 | 1 | -1 | | | -1 | | | | 1 | -1 | | -1 | 1 | |
v(42,23) | | | | -1 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 1 | | |
v(20,11) | | | | | -1 | | | | | | | | | | | | | | | -1 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
v(420,233) | | | | | | | | 1 | | | 1 | | | | | -1 | | | 1 | | | | | | | | -1 | | 1 | | | | 1 | 1 | | | 1 | | | | | | -1 | -1 | | 1 | |
v(70,39) | | | | | | | | -1 | | | | | | | | -1 | | -1 | | | | 1 | | | | -1 | | | | | | | | | | | | | | | | | | | | -1 | |
v(84,47) | | | | 1 | | | | | | | -1 | | | | | 1 | | | | | | | | | | | | | | | | | | | | 1 | | | | | | | | -1 | -1 | | |
v(105,59) | | | | | | | | | | | | | | | | | | | | | | | | 1 | | | | | | | | | | | | | | | | | | | | | | | |
v(140,79) | | | | | | | | | | | | | | | | | | | | | | | 1 | | | | | | | | | | | | | | | | | | | | | | | | |
v(30,17) | | | | | | -1 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 1 | | | | | |
v(420,239) | -1 | 1 | | | | 1 | | -2 | | 1 | | 1 | | -1 | -1 | | | 1 | -1 | 1 | | | | -2 | 1 | | | | -1 | -1 | | | -1 | -1 | 1 | -1 | | 1 | | -1 | | -1 | 1 | 1 | 2 | | -1 |
v(7,4) | | | | | | | | | | | | | | | | | | | | | | 1 | | | | | | | | | | | | | | | | | | | | | | | | | |
v(420,241) | | -1 | | 1 | 1 | | | | | -1 | | -1 | | 1 | | -1 | 1 | -1 | 1 | -1 | | 1 | -1 | 1 | -1 | | 1 | 1 | | -1 | | | | 1 | | 1 | 1 | | | 1 | -1 | | | -1 | | 1 | |
v(210,121) | | | | -1 | | | | 1 | | | | | | -1 | | 1 | | 1 | | | 1 | -1 | | | | | | -1 | | 1 | | | | | | | | | | | | | | | -1 | -1 | 1 |
v(12,7) | | | | | | | -1 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
v(70,41) | | -1 | | | | | | | | | | | | | | | | | | -1 | | -1 | | | | 1 | | | | | | | 1 | | | | | | | | | | | | | 1 | |
v(420,247) | | | | | | | | | | | | | | | 1 | | | -1 | | | | | | | | | | | 1 | | | | 1 | | | | | -1 | | | | | | | | | |
v(105,62) | | | | | | | | | | | | | | | | | | | | | 1 | | | | | | | | | | | | | | | | | | | | | | | | | | |
v(140,83) | | | | | 1 | | | -1 | | | | | | -1 | 1 | | | -1 | 1 | 1 | | | | | | -1 | 1 | | | | | -1 | -1 | 1 | | | | | 1 | | | | | | | -1 | |
v(42,25) | | | | | | | | | | | | 1 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | -1 | | |
v(420,251) | -1 | 1 | 1 | | -1 | 1 | | | | 1 | | | | | | 1 | | 1 | -1 | 1 | -1 | | 1 | -1 | 1 | | -1 | -1 | | | | | | -2 | -1 | -1 | -1 | 1 | -1 | -1 | | | 1 | 1 | 1 | -1 | -1 |
v(5,3) | | | | | | | | | | | | | | | | | | | | 1 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
v(210,127) | | | | | | -1 | | -1 | | | | | | | | -1 | | -1 | | | 1 | | | 1 | | -1 | | 1 | | | | | | | 1 | | 1 | | | 1 | | -1 | | | | | 1 |
v(28,17) | | | | | | | | | | | | | | | | -1 | | | | | | 1 | | | | | | | | | | | | | | | | | | | | | | -1 | | | |
v(105,64) | | -1 | | | | | | 2 | | | | -1 | | 1 | | 1 | | | | -1 | -1 | -1 | | 1 | | 1 | | -1 | | 1 | | | 1 | | -1 | | -1 | | | | | 1 | | | -1 | | |
v(420,257) | | | | | | | | 1 | | | | -1 | | 1 | | 1 | | | | | -1 | | | 1 | | | | | | 1 | | | | | -1 | | -1 | | | | | 1 | -1 | | -1 | | |
v(70,43) | | | | | | | | 1 | | | | | | 1 | | 1 | | 1 | | | | -1 | | | | 1 | | | | | | | | | | | | | | | | | | | | | |
v(60,37) | | | | | -1 | 1 | | | | | | | 1 | | | | | | | 1 | | | | | | | | | | | | -1 | | | | | | | | | | -1 | | | | | |
v(21,13) | | | | -1 | | | | | | | | | | | | -1 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
v(140,87) | | | | | | | | | | | | | | | | | | | 1 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
v(210,131) | | | | | | -1 | | -1 | | | | | | | | | | | | -1 | 1 | | | | | | | 1 | | -1 | | | | | 1 | | 1 | | | 1 | | -1 | | | | | 1 |
v(420,263) | | 1 | 1 | | -1 | | | | | | | | | | | | | | -1 | 1 | | 1 | 1 | | 1 | | -1 | | 1 | 1 | | | | -1 | | | -1 | | -1 | -1 | | | | | | -1 | |
v(35,22) | | | | | | | | -1 | | | | | | -1 | | | | | | 1 | | | | | | -1 | | | | | | | -1 | | | | | | | | | | | | | -1 | |
v(84,53) | | | -1 | | | | | | | | | | | | | | -1 | | | | | | | | | | | | | | | | | | | | | | | | | | | 1 | | | |
v(30,19) | | | | | | -1 | | | | | | | | | | | | | | -1 | | | | | | | | | | | | | | | | | | | | | | -1 | | | | | |
v(140,89) | | -1 | -1 | | | | | 1 | | | 1 | | | | -1 | | | | | -1 | | -1 | -1 | | | 1 | | | | | | | | 1 | | | | | | | | | | | | 1 | |
v(105,67) | | -1 | | | | | | 1 | | | | | | | | | | | | | | | | | | | | | | | | | | | -1 | | | | | | | | | | | | |
v(420,269) | | | | | | | | -1 | | | | | | | | -1 | | -1 | | | | 1 | | 1 | | -1 | | 1 | | | | | -1 | | | | | | | | -1 | | | | | | |
v(14,9) | | | | | | | | | | | | | | | | 1 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
v(420,271) | | | | | | 1 | | 1 | -1 | | | | | 1 | | 1 | | | | | -1 | | | | | 1 | | -1 | | 1 | | | | | -1 | | -1 | | | -1 | | 1 | | | | | -1 |
v(105,68) | | | | | | | | | | | | | | | | | | -1 | | | | | | | | | | | | | | | | | | | | | | | | | | | | 1 | -1 |
v(210,137) | | | | 1 | | | | -1 | | | | | | | | -1 | | -1 | | | | 1 | | | | | | 1 | | -1 | | | | | 1 | | 1 | | | | | | | | 1 | 1 | -1 |
v(84,55) | | | 1 | | | | -1 | | | | | -1 | | | | -1 | 1 | | | | | 1 | | | | | | | | | | | | | | 1 | | | | | | | | -1 | | | |
v(420,277) | | | | -1 | | | | 1 | | 1 | | | | -1 | 1 | -1 | | | 1 | 1 | | | 1 | | | -1 | -1 | -1 | 1 | 1 | | -1 | 1 | | -1 | | | | 1 | | | | | -1 | -1 | -1 | 1 |
v(210,139) | | | | -1 | | -1 | | 1 | | | | | | | | | | | | -1 | 1 | -1 | | 1 | | | | | | 1 | | | | | | | | | | | | | | | -1 | | 1 |
v(3,2) | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
v(420,281) | -1 | | | | | | | 1 | | | | | | 1 | -1 | 1 | | 1 | -1 | -1 | | -1 | -1 | | | 1 | | | -1 | | | 1 | | -1 | | | | | -1 | | | | | 1 | | 1 | |
v(70,47) | | 1 | | | | | | -1 | | | | | | | | | | | | 1 | | 1 | | | | -1 | | | | | | | | | | | | | | | | | | | | -1 | |
v(420,283) | | | | 1 | | | | -1 | | -1 | | | | | | -1 | | -1 | | | | 1 | | | | | | 1 | | -1 | | | | | 1 | | 1 | | | | | | | | 1 | 1 | -1 |
v(105,71) | | | | -1 | | -1 | | 1 | | | | | | | | | | | | -1 | 1 | -1 | | 1 | | | | | | 1 | | | | | | | | | | 1 | | | | | -1 | | 1 |
v(28,19) | | | | | | | | | | | -1 | | | | | 1 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
v(210,143) | | -1 | | -1 | | | | 2 | | | | | | | | | | 1 | | | | -1 | | | | 1 | | -1 | | 1 | | | 1 | | -1 | | | | | | | | | | -1 | | 1 |
v(60,41) | | | | | | | -1 | | | | | | 1 | | | | | | | | | | | | | | | | | | | -1 | | | | | | | | | | -1 | | | | | |
v(35,24) | | | | | | | | | | | | | | | | | | 1 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
v(420,289) | | | | | | -1 | | -1 | 1 | | | | | | | | | | | -1 | 1 | | -1 | | | | 1 | 1 | | -1 | | | | | 1 | | 1 | | | 1 | | -1 | | | | | 1 |
v(42,29) | | | | -1 | | | | | | | | -1 | | | | -1 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
v(140,97) | | | | | | | | 1 | | | | | | 1 | | 1 | | 1 | | | | -1 | | | | 1 | | | | | | | | | | | | | -1 | | | | | | | | |
v(420,293) | | 1 | 1 | | -1 | | -1 | -1 | | 1 | -1 | | | | | | | | -1 | 1 | | 1 | 1 | | 1 | -1 | -1 | | | | 1 | | | -2 | | | | 1 | -1 | | | -1 | 1 | | | -1 | |
v(10,7) | | | | | | | | | | | | | | | | | | | | 1 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
v(84,59) | | | | | | | | | | | | | | | | | 1 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
v(105,74) | | -1 | | | | | | 1 | | | | -1 | | 1 | | | | -1 | | -1 | | | | 1 | | | | | | | | | 1 | | -1 | | | | | 1 | | | | | -1 | 1 | |
v(140,99) | | -1 | -1 | | 1 | | | | | | | | | | | | | | | -1 | | -1 | -1 | | | 1 | 1 | | -1 | | | | | 1 | | | | | 1 | | | | | | | 1 | |
v(210,149) | | | | | | 1 | | 1 | | | | | | 1 | | 1 | | | | | -1 | | | | | 1 | | -1 | | 1 | | | | | -1 | | -1 | | | -1 | | 1 | | | | | -1 |
v(420,299) | | | | -1 | | | 1 | 2 | -1 | | | | | | 1 | 1 | -1 | | | | | -1 | 1 | 1 | | | -1 | -1 | 1 | 2 | | | 1 | | -1 | | -1 | -1 | | | | 1 | -1 | | -2 | -1 | 1 |
v(7,5) | | | | | | | | | | | | | | | | 1 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
v(60,43) | | | | | | -1 | | | | | | | -1 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 1 | | | | | |
v(210,151) | | | | | | | | -1 | | | | | | | | -1 | | -1 | | | | 1 | | 1 | | -1 | | 1 | | | | | -1 | | | | | | | | | | | | | | |
v(140,101) | | | | | | | | | | | 1 | | | | | -2 | | -1 | 1 | | | 1 | | | | -1 | -1 | | 1 | | | | 1 | | | | 1 | | | | | | | -1 | | | |
v(105,76) | | | | | | | | -1 | | | | 1 | | -1 | | -1 | | | | | 1 | | | -1 | | | | 1 | | -1 | | | | | 1 | | 1 | | | | | -1 | | | 1 | | |
v(70,51) | | | | | | | | | | | | | | -1 | | 1 | | | | | | | | | | | | | | | | | -1 | | | | -1 | | | | | | | | | -1 | |
v(420,307) | | | | | | | | -1 | | | | | | -1 | | | | | | 1 | | | 1 | | | -1 | | | | | -1 | | -1 | | | | -1 | | 1 | | | | | | | -1 | |
v(15,11) | | | | | | -1 | | | | | | | | | | | | | | -1 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
v(140,103) | | -1 | | | | | | | | | | | | | -1 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 1 | |
v(42,31) | | | | | | | | | | | | -1 | | | | -1 | | | | | | 2 | | | | | | | | | | | | | | | | | | | | | | | 1 | | |
v(420,311) | | | | 1 | | | | -1 | | -1 | -1 | | | 1 | -1 | | 1 | | -1 | -1 | | 1 | -1 | | -1 | 1 | 1 | 1 | -1 | -1 | | 1 | -1 | | 1 | 1 | | | -1 | | -1 | | | | 1 | 1 | -1 |
v(210,157) | | 1 | | | | | | | | | | | | | | | | | | 1 | | 1 | | | | | | | | 1 | | | -1 | | | | -1 | | | -1 | | | | | | -1 | |
v(4,3) | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
v(105,79) | | | | | | | | -1 | | | | | | | | | | | | | | | | | | | | | | -1 | | | | | | | 1 | | | | | | | | | | |
v(420,317) | | -1 | | -1 | | -1 | | 1 | | | | | | | | | | | | -1 | 1 | -1 | | 1 | | | | | | 1 | | | 1 | | | | | -1 | | 1 | | | | | -1 | | 2 |
v(70,53) | | | | | | | | | | | | | | | | | | | | | | | | | | 1 | | | | | | | | | | | -1 | | | | | | | | | | |
v(420,319) | | 1 | | -1 | | | | | | 1 | 1 | 1 | | -1 | 1 | -1 | -1 | | 1 | 1 | | | 1 | -1 | 1 | -1 | -1 | -1 | 1 | 1 | | -1 | 1 | | | -1 | | | 1 | -1 | 1 | | | | | -1 | |
v(21,16) | | | | | | | | | | | | | | | | 1 | | | | | | -1 | | | | | | | | | | | | | | | | | | | | | | | -1 | | |
v(140,107) | | | | | | | | | | | | | | | 1 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
v(30,23) | | | | | | 1 | | | | | | | | | | | | | | 2 | | | | | | | | | | | | | | | | | | | | | | -1 | | | | | |
v(420,323) | | -1 | | | | | | 2 | | | | -1 | | 2 | | 1 | | | | -1 | -1 | -1 | -1 | 1 | | 1 | | | | | 1 | | 1 | | -1 | | | | -1 | 1 | | | | | -1 | 1 | |
v(35,27) | | | | | | | | | | | | | | 1 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
v(84,65) | | | | -1 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | -1 | | | | | | | | | 1 | | |
v(210,163) | | | | | | | | 1 | | | | -1 | | 1 | | 1 | | | | | -1 | | | 1 | | | | | | 1 | | | | | -1 | | -1 | | | | | 1 | | | -1 | | |
v(140,109) | | | | | | | | -1 | | | -1 | | | | | 1 | | | -1 | | | | | | | | 1 | | -1 | | | | -1 | | | | -1 | | | | | | | 1 | | -1 | |
v(105,82) | | | | | | | | 1 | | | | | | | | 1 | | 1 | | | | -1 | | | | 1 | | -1 | | | | | 1 | | | | | | | | | | | | | | |
v(60,47) | | | | | | | | | | | | | 1 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
v(14,11) | | | | | | | | | | | | | | | | -1 | | | | | | 1 | | | | | | | | | | | | | | | | | | | | | | | | | |
v(420,331) | | | | | | | -1 | -1 | 1 | | | | | -1 | -1 | | 1 | 1 | | | 1 | | -1 | -1 | | | 1 | | -1 | -1 | | | -1 | | 1 | | 1 | 1 | | | | -1 | 1 | | 1 | | |
v(105,83) | | | | | | -1 | | -1 | | | | | | -1 | | -1 | | | | | 1 | | | | | -1 | | 1 | | | | | | | 1 | | 1 | | | 1 | | -1 | | | | | 1 |
v(140,111) | | | 1 | | -1 | | | | | | | | | | | | | | | | | | 1 | | | | -1 | | 1 | | | | 1 | -1 | | | | | -1 | | | | | | | | |
v(210,167) | | 1 | | | | | | -1 | | | | 1 | | -1 | | | | 1 | | 1 | 1 | | | -1 | | | | | | | | | -1 | | 1 | | | | | -1 | | | | | 1 | -1 | |
v(84,67) | | | | | | | | | | | | 1 | | | | | -1 | | | | | | | | | | | | | | | | | | | | | | | | | | | | -1 | | |
v(5,4) | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
v(420,337) | | -1 | -1 | | 1 | -1 | 1 | | | -1 | 1 | | | | | -1 | | -1 | 1 | -1 | 1 | -1 | -1 | 1 | -1 | | 1 | 1 | | | -1 | | | 2 | 1 | | 1 | -1 | 1 | 1 | | | -1 | | | 1 | 1 |
v(210,169) | | -1 | | | | | | 2 | | | | -1 | | 1 | | 1 | | | | -1 | -1 | -1 | | 1 | | 1 | | -1 | | 1 | | | 1 | | -2 | | -1 | | | | | 1 | | | -1 | | |
v(21,17) | | | | | | | | | | | | 1 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
v(420,341) | | | | | | | | | -1 | | | | | | | | | | | | | | 1 | | | | -1 | | | | | | | | | | | | | | | | | | | | |
v(70,57) | | | | | | | | -1 | | | | | | -1 | | | | -1 | | 1 | | | | | | -1 | | | | | | | -1 | | | | | | | | | | | | | -1 | |
v(60,49) | | | | | | -1 | 1 | | | | | | -1 | | | | | | | -1 | | | | | | | | | | | | 1 | | | | | | | | | | | | | | | |
v(105,86) | | | | 1 | | | | -1 | | | | | | | | | | -1 | | | | 1 | | | | -1 | | 1 | | -1 | | | -1 | | | | | | | | | | | | 1 | | -1 |
v(28,23) | | | | | | | | | | | 1 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
v(210,173) | | | | 1 | | 1 | | -1 | | | | | | | | | | -1 | | 1 | -1 | 1 | | -1 | | | | | | -1 | | | | | | | | | | -1 | | | | | 1 | 1 | -2 |
v(420,347) | | | | | | | | | | 1 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
v(35,29) | | -1 | | | | | | 1 | | | | | | | | | | | | -1 | | -1 | | | | 1 | | | | | | | 1 | | | | | | | | | | | | | 1 | |
v(420,349) | 1 | | | -1 | | -1 | | | | | | | | -1 | 1 | -1 | | -1 | 1 | | 1 | | 1 | 1 | | -1 | | | 1 | 1 | | -1 | | 1 | | | | | 1 | | | | | -1 | -1 | -1 | 1 |
v(6,5) | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
v(140,117) | | 1 | | | | | | -1 | | | | | | | | | | | | 1 | | 1 | | | | -1 | | | | | | | | -1 | | | | | | | | | | | | -1 | |
v(420,353) | | -1 | | | | | | 1 | | -1 | | | | 1 | -1 | 1 | | 1 | -1 | -1 | | -1 | -1 | | | 2 | 1 | | -1 | | | 1 | | | | | | | -1 | | | | | 1 | | 1 | |
v(70,59) | | | | | | | | | | | | | | | | | | 1 | | | | | | | | | | | | | | | -1 | | | | | | | | | | | | | | |
v(84,71) | | | -1 | -1 | | | 1 | | | | | | | | | | -1 | | | | | -1 | | | | | | | | | | | | | | -1 | | | | | | | | 1 | | | |
v(105,89) | | | | -1 | | | | 1 | | | | | | | | 1 | | 1 | | | | -1 | | | | | | -1 | | 1 | | | | | | | -1 | | | | | | | | -1 | -1 | 1 |
v(20,17) | | | | | | | | | | | | | | | | | | | | 1 | | | | | | | | | | | | -1 | | | | | | | | | | | | | | | |
v(210,179) | | -1 | | | | | | 1 | | | | -1 | | 1 | | | | | | -1 | | | | 1 | | | | | | | | | 1 | | -1 | | | | | 1 | | | | | -1 | | 1 |
v(420,359) | | | | | | | | | 1 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
v(7,6) | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
v(210,181) | | 1 | | | | | | -2 | | | | 1 | | -1 | | -1 | | | | | 1 | | | -1 | | | | 1 | | -1 | | | | | 2 | | 1 | | | | | -1 | | | 1 | | |
v(140,121) | | 1 | 1 | | | | | -1 | | | -1 | | | -1 | 1 | 1 | | | | 1 | | 1 | 1 | | | -1 | | | | | | | -1 | -1 | | | -1 | | | | | | | | | -2 | |
v(84,73) | | | 1 | | | | | | | | | -1 | | | | -1 | 1 | | | | | 2 | | | | | | | | | | | | | | | | | | | | | | -1 | 1 | | |
v(70,61) | | | | | | | | 1 | | | | | | 1 | | | | | | -1 | | | | | | 1 | | | | | | | 1 | | | | 1 | | | | | | | | | 1 | |
v(420,367) | | | -1 | | 1 | | | | | | | | | | | | | | 1 | | | | -1 | | -1 | | 1 | | -1 | | | | -1 | 1 | | | | | 1 | | | | | | | | |
v(105,92) | | | | | | 1 | | | | | | | | | | | | | | 1 | -1 | | | | | | | -1 | | | | | | | -1 | | | | | -1 | | 1 | | | | | -1 |
v(140,123) | | | | | | | | | | | | | | | | | | | -1 | | | | | | | 1 | | | | | | | | | | | -1 | | | | | | | | | | |
v(42,37) | | | | 1 | | | | | | | | | | | | 2 | | | | | | -1 | | | | | | | | | | | | | | | | | | | | | | | -1 | | |
v(60,53) | | | | | 1 | | | | | | | | -1 | | | | | | | 1 | | | | | | | | | | | | 1 | | | | | | | | | | | | | | | |
v(35,31) | | | | | | | | -1 | | | | | | | | -1 | | -1 | | | | 1 | | | | -1 | | | | | | | | | | | | | | | | | | | | | |
v(210,187) | | 1 | | | | | | -1 | | | | 1 | | -1 | | | | 1 | | 1 | 1 | | | -1 | | | | | | -1 | | | | | 1 | | 1 | | | | | -1 | | | 1 | | |
v(105,94) | | | | | | | | | | | | | | -1 | | | | 1 | | | | | | -1 | | | | | | | | | | | | | | | | | | | | | | | |
v(420,377) | | 1 | | | | | | -1 | | | | 1 | | -1 | | | | 1 | | 1 | 1 | | | -1 | | | | | | | -1 | | -1 | | 1 | | | | | -1 | | | | | 1 | -1 | |
v(10,9) | | | | | | | | | | | | | | | | | | | | -1 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
v(420,379) | 1 | -2 | -1 | | 1 | -1 | | 2 | | -1 | | -1 | | 1 | | | | -1 | 1 | -2 | | -1 | -1 | 2 | -1 | 1 | 1 | | | 1 | | | 1 | 2 | -1 | 1 | | -1 | 1 | 1 | | 1 | -1 | -1 | -2 | 1 | 1 |
v(140,127) | | | | | -1 | | | | | | | | | | -1 | | | | -1 | | | | | | | | -1 | | | | | 1 | | -1 | | | | | -1 | | | | | | | | |
v(210,191) | | | | 1 | | | | -1 | | | | | | | | | | -1 | | | -1 | 1 | | | | -1 | | 1 | | -1 | | | -1 | | | | | | | | | | | | 1 | | -1 |
v(420,383) | | | | 1 | | 1 | | -1 | | | | | | | -1 | | | | | 1 | -1 | 1 | | -1 | | | | | -1 | -1 | | | -1 | | | | | 1 | | -1 | | | | | 1 | 1 | -2 |
v(35,32) | | | | | | | | 1 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
v(12,11) | | | | | | | 1 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
v(210,193) | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | -1 | | | | | | | | | | 1 | | | | | | | |
v(140,129) | | | | | | | | | | | | | | | | | | 1 | | | | | | | | | | | -1 | | | | -1 | | | | | | | | | | | | | | |
v(105,97) | | | | | | | | | | | | | | 1 | | | | | | | -1 | | | | | | | | | | | | | | | | -1 | | | | | | | | | | |
v(420,389) | | | | -1 | -1 | | | 1 | | 1 | | | | | | 1 | -1 | 1 | -1 | | | -1 | 1 | | 1 | | -1 | -1 | | 1 | | | 1 | -1 | -1 | -1 | -1 | | | | 1 | | | 1 | -1 | -1 | 1 |
v(14,13) | | | | | | | | | | | | | | | | | | | | | | -1 | | | | | | | | | | | | | | | | | | | | | | | | | |
v(420,391) | 1 | | | | | -1 | | | | -1 | | | | | 1 | -1 | | -1 | 1 | -1 | 1 | | | 1 | -1 | | | 1 | 1 | | | | 1 | 1 | 1 | 1 | 1 | -1 | | 1 | | | -1 | -1 | -1 | | 1 |
v(15,14) | | | | | | 1 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
v(140,131) | | | | | | | | 1 | | | | | | 1 | | | | | | -1 | | | -1 | | | 1 | | | | | | | 1 | | | | 1 | | | | | | | | | 1 | |
v(210,197) | | | | | | 1 | | | | | | | | | | | | | | 1 | -1 | | | -1 | | | | -1 | | | | | | | -1 | | | | | -1 | | 1 | | | | | -1 |
v(84,79) | | | | | | | | | | | 1 | | | | | 1 | | | | | | -1 | | | | | | | | | | | | | | -1 | | | | | | | | 1 | | | |
v(420,397) | | 1 | | | | | | -2 | | | -1 | 1 | | -1 | | 1 | | 1 | -1 | 1 | 1 | | | -1 | | | 1 | | -1 | -1 | | | -1 | -1 | 1 | | | | | | | -1 | 1 | 1 | 1 | -1 | |
v(210,199) | | | | | | | | | | | | | | -1 | | | | 1 | | | | | | -1 | | | | -1 | | | | | | | | | | | | | | | | | | | |
v(20,19) | | | | | 1 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
v(21,20) | | | | 1 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
v(420,401) | | 1 | 1 | 1 | | | -1 | -3 | 1 | | -1 | | | -1 | | | 1 | | -1 | 1 | | 2 | | -1 | | -1 | 1 | 1 | -1 | -2 | | | -2 | -1 | 1 | | | 1 | | | | -1 | 1 | | 2 | -1 | -1 |
v(70,67) | | | | | | | | 1 | | | | | | | | -1 | | | | | | | | | | | | | | | | | 1 | | | | 1 | | | | | | | | | 1 | |
v(420,403) | | | | | | | | | | | | | | | | | | | | | | | | | -1 | | | | | -1 | | | | | | | | | | 1 | | | | | | | |
v(105,101) | | 1 | | | | | | -1 | | | | 1 | | | | -1 | | | | | | 1 | | -1 | | | | | | | | | | | 1 | | | | | -1 | | | | | 1 | | |
v(28,27) | | | 1 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
v(30,29) | | | | | | 1 | | | | | | | | | | | | | | -1 | | | | | | | | | | | | | | | | | | | | | | 1 | | | | | |
v(420,407) | | | | | | | 1 | | | -1 | | | | | | | | | | | | | | | -1 | | | | | | -1 | 1 | | | | | | -1 | | | | 1 | -1 | | | | |
v(35,34) | | 1 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
v(420,409) | | | | | | | | | | | | | | -1 | | | | 1 | | | | | | -1 | | | | -1 | -1 | | | | | | | | | | 1 | | 1 | | | | | | |
v(42,41) | | | | 1 | | | | | | | | 1 | | | | | | | | | | -1 | | | | | | | | | | | | | | | | | | | | | | | | | |
v(140,137) | | | | | | | | 1 | | | | | | | | -1 | | | | | | | | | | | -1 | | | | | | 1 | | | | 1 | | | | | | | | | 1 | |
v(60,59) | | | | | 1 | | 1 | | | | | | -1 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 1 | | | | | |
v(70,69) | | 1 | | | | | | | | | | | | | | | | | | | | | | | | -1 | | | | | | | | | | | | | | | | | | | | | |
v(84,83) | | | | | | | 1 | | | | 1 | 1 | | | | | -1 | | | | | -1 | | | | | | | | | | | | | | -1 | | | | | | | | 1 | | | |
v(105,104) | | 1 | | 1 | | 1 | | -1 | | | | | | | | | | | | 1 | -1 | 1 | | -1 | | | | | | -1 | | | -1 | | | | | | | -1 | | | | | 1 | | -1 |
v(140,139) | | | | | | | | 1 | | | | | | 1 | -1 | 1 | | 1 | -1 | -1 | | -1 | -1 | | | 1 | | | -1 | | | 1 | | | | | | | -1 | | | | | 1 | | 1 | |
v(210,209) | | | | 1 | | 1 | | | | | | | | | | | | | | | -1 | | | -1 | | | | | | -1 | | | | | | | | | | | | | | | 1 | 1 | -1 |
v(420,419) | 1 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
Cyclotomic Units Base Representations for n = 420 = 2^2*3*5*7
See Algorithm 2.4 for details
Note that equality is modulo multiplication by an nth unit root.
1: v(420,1) is in basis
2: v(210,1) = v(105,43)^-1 v(105,46)^-1 v(105,61)^-1 v(105,103)^-1 v(35,33) v(21,1) v(21,19) v(15,1)
3: v(140,1) = v(140,33)^-1 v(140,53)^-1 v(140,61)^-1 v(140,81)^-1 v(140,113)^-1 v(35,3) v(35,8) v(35,11) v(35,18) v(35,33) v(28,25) v(20,13) v(7,2) v(7,3)^-1 v(5,2)^-1
4: v(105,1) = v(105,43)^-1 v(105,46)^-1 v(105,61)^-1 v(105,88)^-1 v(105,103)^-1 v(35,1) v(35,3)^-1 v(35,23)^-1 v(21,1) v(21,19) v(15,1) v(7,3) v(5,2)
5: v(84,1) = v(84,25)^-1 v(84,61)^-1 v(28,5) v(28,25) v(21,4) v(12,1) v(7,3)^-1
6: v(70,1) = v(35,1) v(35,18)^-1
7: v(60,1) = v(60,13)^-1 v(20,1) v(15,13) v(12,1)
8: v(105,2) = v(105,103)
9: v(140,3) = v(140,73)^-1 v(35,3) v(35,23) v(35,26) v(35,33) v(7,2)^-1
10: v(42,1) = v(21,1) v(21,4) v(7,3)^-1
11: v(420,11) = v(420,361) v(140,81)^-1 v(140,113) v(105,46)^-1 v(105,58)^-1 v(35,8)^-1 v(35,11)
12: v(35,1) is in basis
13: v(420,13) = v(420,73)^-1 v(420,193)^-1 v(420,253)^-1 v(420,313)^-1 v(420,373)^-1 v(20,13) v(15,13) v(12,1)
14: v(30,1) = v(15,1) v(15,13) v(5,2)^-1
15: v(28,1) is in basis
16: v(105,4) = v(105,46)^-1 v(105,73) v(105,88)^-1 v(35,1) v(35,3)^-1 v(21,4) v(21,19) v(7,2)^-1 v(7,3)
17: v(420,17) = v(420,193)^-1 v(105,61)^-1 v(105,88)
18: v(70,3) = v(35,3) v(35,23) v(35,26) v(35,33) v(7,2)^-1
19: v(420,19) = v(420,61) v(420,313) v(420,373) v(140,53)^-1 v(140,73) v(140,81)^-1 v(140,93)^-1 v(105,46)^-1 v(105,58) v(105,61)^-2 v(105,73) v(105,103)^-1 v(84,25) v(35,1) v(35,3)^-3 v(35,8)^-1 v(35,18)^-1 v(35,23)^-2 v(35,33)^-1 v(28,1) v(28,5)^-1 v(21,1) v(21,19)^2 v(15,13)^-1 v(12,1)^-1 v(7,3)^2 v(5,2)
20: v(21,1) is in basis
21: v(20,1) is in basis
22: v(210,11) = v(105,46)^-1 v(105,58)^-1 v(35,8)^-1 v(35,11)
23: v(420,23) = v(420,373) v(140,53)^-1 v(140,73) v(140,81)^-1 v(140,93)^-1 v(105,43) v(105,46)^-1 v(105,61)^-1 v(105,73) v(35,1) v(35,3)^-2 v(35,8)^-1 v(35,11) v(35,23)^-1 v(35,33)^-1 v(28,5)^-1 v(28,25) v(21,4) v(21,19) v(15,13)^-1 v(7,2) v(5,2)
24: v(35,2) = v(35,33)
25: v(84,5) = v(84,61)^-1 v(28,5) v(28,25) v(7,2) v(7,3)^-1
26: v(210,13) = v(105,43)^-1 v(105,46)^-1 v(105,58)^-1 v(105,73)^-1 v(105,88)^-1 v(105,103)^-1 v(15,1) v(15,13) v(5,2)
27: v(140,9) = v(140,61)^-1 v(35,3) v(35,8) v(35,18) v(35,23) v(35,26) v(35,33) v(5,2)^-1
28: v(15,1) is in basis
29: v(420,29) = v(420,1) v(420,73)^-1 v(420,193)^-1 v(420,313)^-1 v(420,373)^-1 v(140,33) v(140,53) v(140,81) v(140,93) v(105,43) v(105,46) v(105,58) v(105,73) v(105,88) v(105,103) v(84,61) v(35,11)^-1 v(35,23) v(35,26) v(28,25)^-1 v(21,19)^-1 v(15,1)^-1 v(7,2)^-1 v(5,2)^-1
30: v(14,1) = v(7,3)^-1
31: v(420,31) = v(420,73) v(420,193) v(420,361) v(140,53)^-1 v(140,61) v(140,73)^-1 v(140,93)^-1 v(105,58)^-1 v(105,61) v(105,73)^-1 v(105,103) v(84,25)^-1 v(84,61)^-1 v(35,3) v(35,11) v(35,23) v(35,26)^-1 v(35,33)^-1 v(28,25) v(21,1)^-1 v(21,19)^-1 v(20,1)^-1 v(7,2) v(7,3)^-1
32: v(105,8) = v(105,43)^-1 v(35,8) v(35,26)^-1
33: v(140,11) = v(140,81)^-1 v(35,11) v(35,23)^-1
34: v(210,17) = v(105,61)^-1 v(105,88)
35: v(12,1) is in basis
36: v(35,3) is in basis
37: v(420,37) = v(420,313) v(140,33)^-1 v(140,81)^-1 v(105,43)^-1 v(105,46)^-1 v(105,61)^-1 v(105,88)^-1 v(105,103)^-2 v(35,3)^-1 v(35,23)^-1 v(35,33) v(21,1) v(21,19) v(15,1) v(7,3) v(5,2)
38: v(210,19) = v(105,43)^-1 v(105,58) v(105,61)^-1 v(105,103)^-1 v(35,3)^-1 v(35,11)^-1 v(35,18)^-1 v(35,23)^-1 v(21,1) v(21,19) v(7,3)
39: v(140,13) = v(140,33)^-1 v(140,53)^-1 v(140,73)^-1 v(140,93)^-1 v(140,113)^-1 v(20,1)^-1 v(20,13)
40: v(21,2) = v(21,19)
41: v(420,41) = v(420,1) v(420,73)^-1 v(420,193)^-1 v(420,313)^-1 v(420,373)^-1 v(140,53) v(140,61)^-1 v(140,73) v(140,93)^2 v(140,113) v(105,46)^2 v(105,61) v(105,73)^-1 v(105,88) v(105,103) v(84,61) v(35,1)^-2 v(35,3)^2 v(35,8) v(35,11)^-1 v(35,18) v(35,23) v(35,33) v(28,1)^-1 v(28,25)^-1 v(21,4)^-1 v(21,19)^-2 v(20,1) v(15,1)^-1 v(15,13) v(7,3)^-1 v(5,2)^-2
42: v(10,1) = v(5,2)^-1
43: v(420,43) = v(420,253)^-1 v(105,43) v(105,46)^-1 v(105,73) v(105,88)^-1 v(35,1) v(35,3)^-1 v(35,8)^-1 v(35,11) v(35,23)^-1 v(35,33)^-1 v(21,4) v(21,19) v(5,2)
44: v(105,11) = v(105,46)^-1 v(35,8)^-1 v(35,11)
45: v(28,3) = v(28,25)
46: v(210,23) = v(105,43) v(105,46)^-1 v(105,61)^-1 v(105,73) v(35,1) v(35,3)^-1 v(35,8)^-1 v(35,11) v(35,26) v(21,4) v(21,19) v(15,13)^-1 v(5,2)
47: v(420,47) = v(420,373)
48: v(35,4) = v(35,3)^-1 v(35,11)^-1 v(35,18)^-1 v(7,2)^-1 v(7,3)
49: v(60,7) = v(60,13)^-1 v(20,1) v(20,13) v(5,2)
50: v(42,5) = v(21,1) v(21,19)^-1 v(7,2)^2 v(7,3)^-1
51: v(140,17) = v(140,53)^-1 v(35,18) v(35,26)^-1
52: v(105,13) = v(105,43)^-1 v(105,58)^-1 v(105,73)^-1 v(105,88)^-1 v(105,103)^-1 v(15,1) v(15,13) v(5,2)
53: v(420,53) = v(420,193)^-1 v(140,53) v(140,61)^-1 v(140,73) v(140,81)^-1 v(140,93) v(140,113) v(35,23)^-1 v(28,1)^-1 v(20,1)
54: v(70,9) = v(35,3) v(35,8) v(35,18) v(35,23) v(35,26) v(35,33) v(5,2)^-1
55: v(84,11) = v(84,25) v(28,1) v(28,25)^-1 v(21,4)^-1 v(21,19) v(7,2)^-1 v(7,3)^2
56: v(15,2) = v(15,13)
57: v(140,19) = v(140,33) v(140,61) v(140,93)^-1 v(35,1) v(35,3)^-1 v(35,8)^-1 v(35,18)^-1 v(35,23)^-1 v(35,26)^-1 v(35,33)^-2 v(28,1) v(28,5)^-1 v(7,2) v(7,3) v(5,2)
58: v(210,29) = v(105,43) v(105,46)^-1 v(105,58) v(105,61)^-1 v(105,73)^2 v(35,1) v(35,3)^-2 v(35,8)^-1 v(35,26) v(21,4) v(21,19) v(15,13)^-1 v(7,2)^-1
59: v(420,59) = v(420,361)
60: v(7,1) = 1
61: v(420,61) is in basis
62: v(210,31) = v(105,46) v(105,73)^-1 v(105,88) v(105,103) v(35,1)^-1 v(35,3) v(35,8) v(35,23) v(21,4)^-1 v(21,19)^-1 v(5,2)^-1
63: v(20,3) = v(20,13)^-1 v(5,2)
64: v(105,16) = v(105,58)^-1 v(105,61) v(105,103) v(35,3) v(35,11) v(35,26)^-1 v(35,33)^-1 v(21,1)^-1 v(21,19)^-1 v(7,2) v(7,3)^-1
65: v(84,13) = v(84,25)^-1 v(84,61)^-1 v(28,1)^-1 v(28,25) v(21,1)^-1 v(12,1) v(7,3)^-1
66: v(70,11) = v(35,11) v(35,23)^-1
67: v(420,67) = v(420,73)^-1 v(140,33)^-1 v(140,53)^-1 v(140,61)^-1 v(140,73) v(140,81)^-1 v(140,113)^-1 v(35,1)^-1 v(35,3) v(35,8) v(35,11) v(35,18)^2 v(35,33) v(28,25) v(20,13) v(7,2) v(7,3)^-1 v(5,2)^-1
68: v(105,17) = v(105,88)
69: v(140,23) = v(140,93)^-1 v(35,1) v(35,3)^-1 v(35,18)^-1 v(35,33)^-1 v(7,3) v(5,2)
70: v(6,1) = 1
71: v(420,71) = v(420,1) v(140,33) v(140,53) v(140,61) v(140,81) v(140,93) v(140,113) v(105,43) v(105,46) v(105,61) v(105,103) v(35,8)^-1 v(35,11)^-1 v(35,18)^-1 v(35,33)^-1 v(28,25)^-1 v(21,1)^-1 v(21,19)^-1 v(20,13)^-1 v(15,1)^-1 v(7,2)^-1
72: v(35,6) = v(35,1)^-1 v(35,3) v(35,18) v(35,23) v(35,33) v(7,3)^-1 v(5,2)^-1
73: v(420,73) is in basis
74: v(210,37) = v(105,43)^-1 v(105,46)^-1 v(105,61)^-1 v(105,88)^-1 v(105,103)^-2 v(35,3)^-1 v(35,11)^-1 v(35,33) v(21,1) v(21,19) v(15,1) v(7,3) v(5,2)
75: v(28,5) is in basis
76: v(105,19) = v(105,58) v(105,61)^-1 v(105,103)^-1 v(35,3)^-1 v(35,11)^-1 v(35,18)^-1 v(35,23)^-1 v(21,1) v(21,19) v(7,3)
77: v(60,11) = v(60,13)^-1 v(20,13) v(15,1)^-1 v(12,1) v(5,2)^-1
78: v(70,13) = v(35,3)^-1 v(35,8)^-1 v(35,11)^-1 v(35,18)^-1 v(35,23)^-1 v(35,33)^-1 v(5,2)
79: v(420,79) = v(420,61)^-1 v(140,61) v(140,73)^-1
80: v(21,4) is in basis
81: v(140,27) = v(140,113)
82: v(210,41) = v(105,43)^-1 v(105,46) v(105,58)^-1 v(105,61) v(105,73)^-2 v(35,1)^-1 v(35,3)^2 v(35,8) v(35,18) v(35,23) v(35,26)^-1 v(21,4)^-1 v(21,19)^-1 v(15,13) v(7,2) v(7,3)^-1 v(5,2)^-1
83: v(420,83) = v(420,73)^-1 v(420,193)^-1 v(420,253)^-1 v(420,313)^-1 v(420,373)^-1 v(140,53) v(140,61)^-1 v(140,73) v(140,93)^2 v(140,113) v(105,43) v(105,46) v(105,58) v(105,73) v(105,88) v(105,103) v(35,1)^-1 v(35,11)^-1 v(35,26) v(35,33) v(28,1)^-1 v(28,5) v(20,1) v(15,1)^-1 v(12,1) v(7,2)^-1 v(7,3)^-1 v(5,2)^-1
84: v(5,1) = 1
85: v(84,17) = v(84,25)^-1 v(21,4) v(21,19)^-1
86: v(210,43) = v(105,43) v(105,46)^-1 v(105,73) v(105,88)^-1 v(35,1) v(35,3)^-1 v(35,8)^-1 v(35,11) v(35,23)^-1 v(35,33)^-1 v(21,4) v(21,19) v(5,2)
87: v(140,29) = v(140,61) v(140,73)^-1 v(140,81) v(140,93)^-1 v(140,113)^-1 v(35,23) v(28,1) v(20,1)^-1
88: v(105,22) = v(105,43) v(105,58) v(105,73) v(105,88) v(105,103) v(35,3)^-1 v(35,8)^-1 v(35,18)^-1 v(35,26) v(15,1)^-1 v(15,13)^-1 v(7,2)^-1
89: v(420,89) = v(420,61) v(420,313) v(420,373) v(140,33)^-1 v(140,61)^-1 v(140,73) v(140,81)^-1 v(105,43) v(105,46)^-1 v(105,61)^-1 v(105,73) v(84,25) v(35,3)^-1 v(35,8)^-1 v(35,11) v(35,23)^-1 v(35,26) v(21,19) v(15,13)^-1 v(12,1)^-1
90: v(14,3) = v(7,2)^-1 v(7,3)
91: v(60,13) is in basis
92: v(105,23) = v(105,58)^-1 v(35,3) v(35,11) v(35,18) v(35,23) v(7,2) v(7,3)^-1
93: v(140,31) = v(140,53)^-1 v(140,73) v(140,81)^-1 v(35,3)^-1 v(35,23)^-1 v(35,26)^-1 v(35,33)^-1 v(28,5)^-1 v(28,25) v(7,2)
94: v(210,47) = v(105,43)^-1 v(105,46) v(105,61) v(105,73)^-1 v(35,3) v(35,8) v(35,26)^-1 v(21,4)^-1 v(21,19)^-1 v(15,13) v(7,2)
95: v(84,19) = v(84,61)^-1 v(21,1)^-1 v(21,19)
96: v(35,8) is in basis
97: v(420,97) = v(420,253) v(140,61)^-1 v(140,113)^-1 v(105,43)^-1 v(105,46) v(105,73)^-1 v(105,88) v(35,1)^-1 v(35,3)^2 v(35,8)^2 v(35,18) v(35,23) v(35,33) v(21,4)^-1 v(21,19)^-1 v(7,2) v(7,3)^-1 v(5,2)^-1
98: v(30,7) = v(15,1) v(15,13)^-1 v(5,2)^2
99: v(140,33) is in basis
100: v(21,5) = v(21,19)^-1 v(7,2) v(7,3)^-1
101: v(420,101) = v(420,73) v(420,193) v(420,361) v(140,33) v(140,53) v(140,61) v(140,73)^-1 v(140,81) v(140,113) v(105,46)^-1 v(105,58)^-1 v(105,61) v(105,88)^-1 v(84,25)^-1 v(84,61)^-1 v(35,1) v(35,8)^-1 v(35,18)^-1 v(35,23) v(35,33)^-1 v(28,5) v(21,1)^-1 v(21,4) v(20,13)^-1 v(7,2)^-1 v(5,2)
102: v(70,17) = v(35,18) v(35,26)^-1
103: v(420,103) = v(420,313)^-1 v(105,43) v(105,46) v(105,61) v(105,88) v(105,103)^2 v(35,1)^-1 v(35,3) v(35,23) v(21,1)^-1 v(21,19)^-1 v(15,1)^-1 v(7,3)^-1 v(5,2)^-1
104: v(105,26) = v(105,61)^-1 v(35,3)^-1 v(35,26)
105: v(4,1) = 1
106: v(210,53) = v(105,61) v(105,88)^-1 v(35,1) v(35,23)^-1 v(35,26)^-1 v(35,33)^-1 v(7,3) v(5,2)
107: v(420,107) = v(420,313)
108: v(35,9) = v(35,26)
109: v(420,109) = v(420,73)^-1 v(420,193)^-1 v(420,361)^-1 v(140,33)^-1 v(140,53)^-1 v(140,61)^-1 v(140,73) v(140,81)^-1 v(140,113)^-1 v(105,58) v(105,61)^-1 v(105,73) v(105,103)^-1 v(84,25) v(84,61) v(35,3)^-1 v(35,8) v(35,18) v(35,23)^-1 v(35,33) v(28,5)^-1 v(21,1) v(21,19) v(20,13) v(7,3) v(5,2)^-1
110: v(42,11) = v(21,4)^-1 v(21,19) v(7,2)^-1 v(7,3)^2
111: v(140,37) = v(140,33)^-1 v(35,1)^-1 v(35,33)
112: v(15,4) = v(15,1)^-1 v(5,2)^-1
113: v(420,113) = v(420,253)^-1 v(140,61) v(140,113) v(35,3)^-1 v(35,8)^-1 v(35,18)^-1 v(35,23)^-1 v(35,26)^-1 v(35,33)^-1 v(5,2)
114: v(70,19) = v(35,8)^-1 v(35,23)^-1 v(35,26)^-1 v(35,33)^-1 v(7,2)
115: v(84,23) = v(84,61)
116: v(105,29) = v(105,43) v(105,46)^-1 v(105,58) v(105,61)^-1 v(105,73) v(35,3)^-1 v(35,8)^-1 v(35,26) v(21,4) v(21,19) v(15,13)^-1 v(7,2)^-1
117: v(140,39) = v(140,53) v(140,73)^-1 v(140,81) v(35,11)^-1 v(35,18)^-1 v(35,23) v(35,26) v(28,5) v(28,25)^-1 v(7,2)^-2 v(7,3)
118: v(210,59) = v(105,46) v(105,58) v(35,3)^-1 v(35,11)^-1 v(35,18)^-1 v(35,23)^-1 v(7,2)^-1 v(7,3)
119: v(60,17) = v(60,13)^-1 v(15,1)^-1 v(15,13)
120: v(7,2) is in basis
121: v(420,121) = v(420,61)^-1 v(420,313)^-1 v(420,373)^-1 v(140,33) v(140,61) v(140,73)^-1 v(140,81) v(105,46) v(105,58)^-1 v(105,61)^2 v(105,73)^-1 v(105,103) v(84,25)^-1 v(35,3)^2 v(35,23) v(35,26)^-1 v(35,33)^-1 v(21,1)^-1 v(21,19)^-2 v(15,13) v(12,1) v(7,2) v(7,3)^-1
122: v(210,61) = v(105,43)^-1 v(105,58)^-1 v(105,61) v(105,73)^-1 v(105,88)^-1 v(105,103)^-1 v(35,3) v(35,8) v(35,18) v(35,26)^-1 v(15,1) v(15,13) v(7,2)
123: v(140,41) = v(140,61)^-1 v(140,73) v(140,81)^-1 v(140,93) v(140,113) v(35,1)^-1 v(35,18) v(35,33) v(28,1)^-1 v(20,1) v(7,3)^-1 v(5,2)^-1
124: v(105,31) = v(105,46) v(105,73)^-1 v(105,88) v(35,1)^-1 v(35,3) v(35,8) v(35,11)^-1 v(35,23) v(35,33) v(21,4)^-1 v(21,19)^-1 v(5,2)^-1
125: v(84,25) is in basis
126: v(10,3) = v(5,2)
127: v(420,127) = v(420,73) v(420,193) v(420,253) v(420,313) v(420,373) v(140,53)^-1 v(140,61) v(140,73)^-1 v(140,93)^-2 v(140,113)^-1 v(35,1) v(35,3)^-1 v(35,18)^-1 v(35,33)^-1 v(28,1) v(28,5)^-1 v(20,1)^-1 v(15,13)^-1 v(12,1)^-1 v(7,3) v(5,2)
128: v(105,32) = v(105,73)
129: v(140,43) = v(140,113)^-1 v(35,3) v(35,8) v(35,11) v(35,18) v(7,2) v(7,3)^-1
130: v(42,13) = v(21,1)^-1 v(21,4)^-1 v(7,2)^-1
131: v(420,131) = v(420,61) v(140,61)^-1 v(140,73) v(105,43) v(105,58) v(105,61)^-1 v(105,73) v(105,88) v(105,103) v(35,3)^-1 v(35,26) v(15,1)^-1 v(15,13)^-1 v(5,2)^-1
132: v(35,11) is in basis
133: v(60,19) = v(60,13) v(20,13)^-1 v(15,13)^-1 v(12,1)^-1
134: v(210,67) = v(105,58)^-1 v(105,61) v(105,73)^-1 v(105,103) v(35,1)^-1 v(35,3)^2 v(35,11) v(35,18) v(35,23) v(21,1)^-1 v(21,19)^-1 v(7,3)^-1
135: v(28,9) = v(28,5)^-1 v(7,2)
136: v(105,34) = v(105,43) v(105,46) v(105,61) v(105,88) v(105,103) v(35,3) v(21,1)^-1 v(21,19)^-1 v(15,1)^-1 v(7,3)^-1 v(5,2)^-1
137: v(420,137) = v(420,73)^-1 v(105,58) v(105,61)^-1 v(105,73) v(105,103)^-1 v(35,3)^-1 v(35,11)^-1 v(35,26) v(35,33) v(21,1) v(21,19) v(7,2)^-1 v(7,3)
138: v(70,23) = v(35,1) v(35,3)^-1 v(35,18)^-1 v(35,33)^-1 v(7,3) v(5,2)
139: v(420,139) = v(420,1)^-1 v(140,33)^-1 v(140,53)^-1 v(140,61)^-1 v(140,81)^-1 v(140,93)^-1 v(140,113)^-1 v(35,3) v(35,8) v(35,11) v(35,18) v(35,33) v(28,25) v(20,13) v(7,2) v(7,3)^-1 v(5,2)^-1
140: v(3,1) = 1
141: v(140,47) = v(140,93)
142: v(210,71) = v(105,43) v(105,46) v(105,61) v(105,103) v(35,3) v(21,1)^-1 v(21,19)^-1 v(15,1)^-1 v(7,3)^-1 v(5,2)^-1
143: v(420,143) = v(420,73) v(140,33) v(140,53) v(140,61) v(140,73)^-1 v(140,81) v(140,113) v(105,58)^-1 v(105,61) v(105,73)^-1 v(105,103) v(35,3) v(35,8)^-1 v(35,18)^-1 v(35,23) v(35,33)^-1 v(28,25)^-1 v(21,1)^-1 v(21,19)^-1 v(20,13)^-1 v(7,2)^-1 v(5,2)
144: v(35,12) = v(35,23)
145: v(84,29) = v(84,25) v(84,61) v(28,1) v(28,25)^-1 v(21,4)^-1 v(12,1)^-1 v(7,2)^-1 v(7,3)
146: v(210,73) = v(105,58) v(105,61)^-1 v(105,73) v(105,103)^-1 v(35,3)^-1 v(35,11)^-1 v(35,26) v(35,33) v(21,1) v(21,19) v(7,2)^-1 v(7,3)
147: v(20,7) = v(20,13)
148: v(105,37) = v(105,103)^-1 v(35,11)^-1 v(35,33)
149: v(420,149) = v(420,61)^-1 v(105,43)^-1 v(105,58)^-1 v(105,61) v(105,73)^-1 v(105,88)^-1 v(105,103)^-1 v(35,3) v(35,8) v(35,18) v(35,26)^-1 v(15,1) v(15,13) v(7,2)
150: v(14,5) = v(7,2)
151: v(420,151) = v(420,361)^-1 v(105,46) v(105,58) v(35,3)^-1 v(35,11)^-1 v(35,18)^-1 v(35,23)^-1 v(7,2)^-1 v(7,3)
152: v(105,38) = v(105,73)^-1 v(35,1)^-1 v(35,3)
153: v(140,51) = v(140,33)^-1 v(140,61)^-1 v(140,93) v(35,1)^-1 v(35,3) v(35,18) v(35,33) v(28,1)^-1 v(28,5) v(7,3)^-1 v(5,2)^-1
154: v(30,11) = v(15,1)^-1 v(15,13)^-1 v(5,2)^-1
155: v(84,31) = v(84,25)^-1 v(28,1)^-1 v(28,25)
156: v(35,13) = v(35,3)^-1 v(35,8)^-1 v(35,18)^-1 v(35,23)^-1 v(35,33)^-1 v(5,2)
157: v(420,157) = v(420,193) v(140,53)^-1 v(140,61) v(140,73)^-1 v(140,81) v(140,93)^-1 v(140,113)^-1 v(105,61) v(105,88)^-1 v(35,1) v(35,26)^-1 v(35,33)^-1 v(28,1) v(20,1)^-1 v(7,3) v(5,2)
158: v(210,79) = v(105,43) v(105,58) v(105,61)^-1 v(105,73) v(105,88) v(105,103) v(35,3)^-1 v(35,26) v(15,1)^-1 v(15,13)^-1 v(5,2)^-1
159: v(140,53) is in basis
160: v(21,8) = v(21,1)^-1 v(7,2)^-1
161: v(60,23) = v(60,13) v(20,1)^-1 v(20,13)^-1 v(15,1) v(15,13)^-1 v(5,2)
162: v(70,27) = v(35,3) v(35,8) v(35,11) v(35,18) v(7,2) v(7,3)^-1
163: v(420,163) = v(420,373)^-1 v(105,43)^-1 v(105,46) v(105,61) v(105,73)^-1 v(35,3) v(35,8) v(35,26)^-1 v(21,4)^-1 v(21,19)^-1 v(15,13) v(7,2)
164: v(105,41) = v(105,43)^-1 v(105,46) v(105,58)^-1 v(105,61) v(105,73)^-1 v(35,1)^-1 v(35,3)^2 v(35,8) v(35,18) v(35,23) v(35,26)^-1 v(21,4)^-1 v(21,19)^-1 v(15,13) v(7,2) v(7,3)^-1 v(5,2)^-1
165: v(28,11) = v(28,25)^-1 v(7,2)^-1 v(7,3)
166: v(210,83) = v(105,43) v(105,46) v(105,58) v(105,73) v(105,88) v(105,103) v(35,3)^-1 v(35,11)^-1 v(35,18)^-1 v(35,26) v(15,1)^-1 v(15,13)^-1 v(7,2)^-1
167: v(420,167) = v(420,253)
168: v(5,2) is in basis
169: v(420,169) = v(420,1)^-1 v(420,73) v(420,193) v(420,313) v(420,373) v(140,53)^-1 v(140,61) v(140,73)^-1 v(140,93)^-2 v(140,113)^-1 v(105,43)^-1 v(105,46)^-1 v(105,58)^-1 v(105,73)^-1 v(105,88)^-1 v(105,103)^-1 v(84,61)^-1 v(35,1) v(35,11) v(35,26)^-1 v(35,33)^-1 v(28,1) v(28,25) v(21,19) v(20,1)^-1 v(15,1) v(7,2) v(5,2)
170: v(42,17) = v(21,4) v(21,19)^-1
171: v(140,57) = v(140,33) v(140,53) v(140,73) v(140,93) v(140,113) v(35,3)^-1 v(35,8)^-1 v(35,11)^-1 v(35,18)^-1 v(35,23)^-1 v(35,33)^-1 v(20,1) v(20,13)^-1 v(5,2)
172: v(105,43) is in basis
173: v(420,173) = v(420,313)^-1 v(140,33) v(140,81) v(35,11)^-1 v(35,23)
174: v(70,29) = v(35,1)^-1 v(35,18) v(35,23) v(35,33) v(7,3)^-1 v(5,2)^-1
175: v(12,5) = v(12,1)^-1
176: v(105,44) = v(105,61)
177: v(140,59) = v(140,81)
178: v(210,89) = v(105,43) v(105,58)^-1 v(105,61) v(105,103) v(35,3) v(35,8)^-1 v(35,11) v(35,33)^-1 v(21,1)^-1 v(21,19)^-1 v(7,2) v(7,3)^-1
179: v(420,179) = v(420,73)^-1 v(420,193)^-1 v(420,361)^-1 v(140,53) v(140,61)^-1 v(140,73) v(140,93) v(105,46) v(105,58) v(105,61)^-1 v(105,88) v(84,25) v(84,61) v(35,1)^-1 v(35,8) v(35,11)^-1 v(35,26) v(35,33) v(28,25)^-1 v(21,1) v(21,4)^-1 v(20,1) v(7,2)^-1 v(7,3) v(5,2)^-1
180: v(7,3) is in basis
181: v(420,181) = v(420,1)^-1 v(420,73) v(420,193) v(420,313) v(420,373) v(140,33)^-1 v(140,53)^-1 v(140,81)^-1 v(140,93)^-1 v(105,46)^-2 v(105,61)^-1 v(105,73) v(105,88)^-1 v(105,103)^-1 v(84,61)^-1 v(35,1) v(35,3)^-2 v(35,8)^-1 v(35,11) v(35,23)^-1 v(28,25) v(21,4) v(21,19)^2 v(15,1) v(15,13)^-1 v(5,2)
182: v(30,13) = v(15,1)^-1 v(15,13)
183: v(140,61) is in basis
184: v(105,46) is in basis
185: v(84,37) = v(84,61) v(28,5)^-1 v(28,25)^-1 v(21,1) v(21,19)^-1 v(7,2)
186: v(70,31) = v(35,3)^-1 v(35,11)^-1 v(35,18)^-1 v(35,33)^-1 v(7,2)^-1 v(7,3)
187: v(420,187) = v(420,373)^-1 v(140,53) v(140,73)^-1 v(140,81) v(140,93) v(35,3) v(35,23) v(35,26) v(35,33) v(28,5) v(28,25)^-1 v(7,2)^-1
188: v(105,47) = v(105,58)
189: v(20,9) = v(20,1)^-1 v(5,2)^-1
190: v(42,19) = v(21,1)^-1 v(21,19)
191: v(420,191) = v(420,61)^-1 v(420,313)^-1 v(420,373)^-1 v(140,53) v(140,73)^-1 v(140,81) v(140,93) v(105,43)^-1 v(105,46) v(105,61) v(105,73)^-1 v(84,25)^-1 v(35,1)^-1 v(35,3)^2 v(35,8) v(35,11)^-1 v(35,23) v(35,33) v(28,1)^-1 v(28,5) v(21,19)^-1 v(15,13) v(12,1) v(7,3)^-1 v(5,2)^-1
192: v(35,16) = v(35,23)^-1 v(35,26)^-1 v(35,33)^-1 v(7,2)
193: v(420,193) is in basis
194: v(210,97) = v(105,43)^-1 v(105,46) v(105,73)^-1 v(105,88) v(35,1)^-1 v(35,3) v(35,8) v(35,26)^-1 v(21,4)^-1 v(21,19)^-1 v(7,2) v(7,3)^-1
195: v(28,13) = v(28,1)^-1 v(7,3)^-1
196: v(15,7) = v(15,13)^-1 v(5,2)
197: v(420,197) = v(420,73) v(420,193) v(420,253) v(420,313) v(420,373) v(105,43)^-1 v(105,46)^-1 v(105,58)^-1 v(105,73)^-1 v(105,88)^-1 v(105,103)^-1 v(20,13)^-1 v(15,1) v(12,1)^-1 v(5,2)
198: v(70,33) = v(35,1)^-1 v(35,33)
199: v(420,199) = v(420,361)^-1 v(140,81) v(140,113)^-1
200: v(21,10) = v(21,4)^-1 v(7,3)
201: v(140,67) = v(140,73)
202: v(210,101) = v(105,46)^-1 v(105,73) v(105,88)^-1 v(105,103)^-1 v(35,1) v(35,3)^-1 v(21,4) v(21,19) v(7,2)^-1 v(7,3)
203: v(60,29) = v(60,13) v(20,1)^-1 v(15,1) v(12,1)^-1 v(5,2)^-1
204: v(35,17) = v(35,18)
205: v(84,41) = v(84,25) v(84,61) v(28,5)^-1 v(28,25)^-1 v(21,1) v(12,1)^-1
206: v(210,103) = v(105,43) v(105,46) v(105,61) v(105,88) v(105,103)^2 v(35,1)^-1 v(35,3) v(35,23) v(21,1)^-1 v(21,19)^-1 v(15,1)^-1 v(7,3)^-1 v(5,2)^-1
207: v(140,69) = v(140,33) v(140,53) v(140,61) v(140,81) v(140,113) v(35,1) v(35,3)^-1 v(35,8)^-1 v(35,11)^-1 v(35,18)^-2 v(35,33)^-1 v(28,25)^-1 v(20,13)^-1 v(7,2)^-1 v(7,3) v(5,2)
208: v(105,52) = v(105,88)^-1 v(35,1) v(35,3)^-1 v(35,23)^-1 v(35,33)^-1 v(7,3) v(5,2)
209: v(420,209) = v(420,1)^-1 v(105,43)^-1 v(105,46)^-1 v(105,61)^-1 v(105,103)^-1 v(35,33) v(21,1) v(21,19) v(15,1)
210: v(2,1) = 1
211: v(420,211) = v(420,1)^-1 v(105,43)^-1 v(105,46)^-1 v(105,61)^-1 v(105,103)^-1 v(35,33) v(21,1) v(21,19) v(15,1)
212: v(105,53) = v(105,88)^-1 v(35,1) v(35,3)^-1 v(35,23)^-1 v(35,33)^-1 v(7,3) v(5,2)
213: v(140,71) = v(140,33) v(140,53) v(140,61) v(140,81) v(140,113) v(35,1) v(35,3)^-1 v(35,8)^-1 v(35,11)^-1 v(35,18)^-2 v(35,33)^-1 v(28,25)^-1 v(20,13)^-1 v(7,2)^-1 v(7,3) v(5,2)
214: v(210,107) = v(105,43) v(105,46) v(105,61) v(105,88) v(105,103)^2 v(35,1)^-1 v(35,3) v(35,23) v(21,1)^-1 v(21,19)^-1 v(15,1)^-1 v(7,3)^-1 v(5,2)^-1
215: v(84,43) = v(84,25) v(84,61) v(28,5)^-1 v(28,25)^-1 v(21,1) v(12,1)^-1
216: v(35,18) is in basis
217: v(60,31) = v(60,13) v(20,1)^-1 v(15,1) v(12,1)^-1 v(5,2)^-1
218: v(210,109) = v(105,46)^-1 v(105,73) v(105,88)^-1 v(105,103)^-1 v(35,1) v(35,3)^-1 v(21,4) v(21,19) v(7,2)^-1 v(7,3)
219: v(140,73) is in basis
220: v(21,11) = v(21,4)^-1 v(7,3)
221: v(420,221) = v(420,361)^-1 v(140,81) v(140,113)^-1
222: v(70,37) = v(35,1)^-1 v(35,33)
223: v(420,223) = v(420,73) v(420,193) v(420,253) v(420,313) v(420,373) v(105,43)^-1 v(105,46)^-1 v(105,58)^-1 v(105,73)^-1 v(105,88)^-1 v(105,103)^-1 v(20,13)^-1 v(15,1) v(12,1)^-1 v(5,2)
224: v(15,8) = v(15,13)^-1 v(5,2)
225: v(28,15) = v(28,1)^-1 v(7,3)^-1
226: v(210,113) = v(105,43)^-1 v(105,46) v(105,73)^-1 v(105,88) v(35,1)^-1 v(35,3) v(35,8) v(35,26)^-1 v(21,4)^-1 v(21,19)^-1 v(7,2) v(7,3)^-1
227: v(420,227) = v(420,193)
228: v(35,19) = v(35,23)^-1 v(35,26)^-1 v(35,33)^-1 v(7,2)
229: v(420,229) = v(420,61)^-1 v(420,313)^-1 v(420,373)^-1 v(140,53) v(140,73)^-1 v(140,81) v(140,93) v(105,43)^-1 v(105,46) v(105,61) v(105,73)^-1 v(84,25)^-1 v(35,1)^-1 v(35,3)^2 v(35,8) v(35,11)^-1 v(35,23) v(35,33) v(28,1)^-1 v(28,5) v(21,19)^-1 v(15,13) v(12,1) v(7,3)^-1 v(5,2)^-1
230: v(42,23) = v(21,1)^-1 v(21,19)
231: v(20,11) = v(20,1)^-1 v(5,2)^-1
232: v(105,58) is in basis
233: v(420,233) = v(420,373)^-1 v(140,53) v(140,73)^-1 v(140,81) v(140,93) v(35,3) v(35,23) v(35,26) v(35,33) v(28,5) v(28,25)^-1 v(7,2)^-1
234: v(70,39) = v(35,3)^-1 v(35,11)^-1 v(35,18)^-1 v(35,33)^-1 v(7,2)^-1 v(7,3)
235: v(84,47) = v(84,61) v(28,5)^-1 v(28,25)^-1 v(21,1) v(21,19)^-1 v(7,2)
236: v(105,59) = v(105,46)
237: v(140,79) = v(140,61)
238: v(30,17) = v(15,1)^-1 v(15,13)
239: v(420,239) = v(420,1)^-1 v(420,73) v(420,193) v(420,313) v(420,373) v(140,33)^-1 v(140,53)^-1 v(140,81)^-1 v(140,93)^-1 v(105,46)^-2 v(105,61)^-1 v(105,73) v(105,88)^-1 v(105,103)^-1 v(84,61)^-1 v(35,1) v(35,3)^-2 v(35,8)^-1 v(35,11) v(35,23)^-1 v(28,25) v(21,4) v(21,19)^2 v(15,1) v(15,13)^-1 v(5,2)
240: v(7,4) = v(7,3)
241: v(420,241) = v(420,73)^-1 v(420,193)^-1 v(420,361)^-1 v(140,53) v(140,61)^-1 v(140,73) v(140,93) v(105,46) v(105,58) v(105,61)^-1 v(105,88) v(84,25) v(84,61) v(35,1)^-1 v(35,8) v(35,11)^-1 v(35,26) v(35,33) v(28,25)^-1 v(21,1) v(21,4)^-1 v(20,1) v(7,2)^-1 v(7,3) v(5,2)^-1
242: v(210,121) = v(105,43) v(105,58)^-1 v(105,61) v(105,103) v(35,3) v(35,8)^-1 v(35,11) v(35,33)^-1 v(21,1)^-1 v(21,19)^-1 v(7,2) v(7,3)^-1
243: v(140,81) is in basis
244: v(105,61) is in basis
245: v(12,7) = v(12,1)^-1
246: v(70,41) = v(35,1)^-1 v(35,18) v(35,23) v(35,33) v(7,3)^-1 v(5,2)^-1
247: v(420,247) = v(420,313)^-1 v(140,33) v(140,81) v(35,11)^-1 v(35,23)
248: v(105,62) = v(105,43)
249: v(140,83) = v(140,33) v(140,53) v(140,73) v(140,93) v(140,113) v(35,3)^-1 v(35,8)^-1 v(35,11)^-1 v(35,18)^-1 v(35,23)^-1 v(35,33)^-1 v(20,1) v(20,13)^-1 v(5,2)
250: v(42,25) = v(21,4) v(21,19)^-1
251: v(420,251) = v(420,1)^-1 v(420,73) v(420,193) v(420,313) v(420,373) v(140,53)^-1 v(140,61) v(140,73)^-1 v(140,93)^-2 v(140,113)^-1 v(105,43)^-1 v(105,46)^-1 v(105,58)^-1 v(105,73)^-1 v(105,88)^-1 v(105,103)^-1 v(84,61)^-1 v(35,1) v(35,11) v(35,26)^-1 v(35,33)^-1 v(28,1) v(28,25) v(21,19) v(20,1)^-1 v(15,1) v(7,2) v(5,2)
252: v(5,3) = v(5,2)
253: v(420,253) is in basis
254: v(210,127) = v(105,43) v(105,46) v(105,58) v(105,73) v(105,88) v(105,103) v(35,3)^-1 v(35,11)^-1 v(35,18)^-1 v(35,26) v(15,1)^-1 v(15,13)^-1 v(7,2)^-1
255: v(28,17) = v(28,25)^-1 v(7,2)^-1 v(7,3)
256: v(105,64) = v(105,43)^-1 v(105,46) v(105,58)^-1 v(105,61) v(105,73)^-1 v(35,1)^-1 v(35,3)^2 v(35,8) v(35,18) v(35,23) v(35,26)^-1 v(21,4)^-1 v(21,19)^-1 v(15,13) v(7,2) v(7,3)^-1 v(5,2)^-1
257: v(420,257) = v(420,373)^-1 v(105,43)^-1 v(105,46) v(105,61) v(105,73)^-1 v(35,3) v(35,8) v(35,26)^-1 v(21,4)^-1 v(21,19)^-1 v(15,13) v(7,2)
258: v(70,43) = v(35,3) v(35,8) v(35,11) v(35,18) v(7,2) v(7,3)^-1
259: v(60,37) = v(60,13) v(20,1)^-1 v(20,13)^-1 v(15,1) v(15,13)^-1 v(5,2)
260: v(21,13) = v(21,1)^-1 v(7,2)^-1
261: v(140,87) = v(140,53)
262: v(210,131) = v(105,43) v(105,58) v(105,61)^-1 v(105,73) v(105,88) v(105,103) v(35,3)^-1 v(35,26) v(15,1)^-1 v(15,13)^-1 v(5,2)^-1
263: v(420,263) = v(420,193) v(140,53)^-1 v(140,61) v(140,73)^-1 v(140,81) v(140,93)^-1 v(140,113)^-1 v(105,61) v(105,88)^-1 v(35,1) v(35,26)^-1 v(35,33)^-1 v(28,1) v(20,1)^-1 v(7,3) v(5,2)
264: v(35,22) = v(35,3)^-1 v(35,8)^-1 v(35,18)^-1 v(35,23)^-1 v(35,33)^-1 v(5,2)
265: v(84,53) = v(84,25)^-1 v(28,1)^-1 v(28,25)
266: v(30,19) = v(15,1)^-1 v(15,13)^-1 v(5,2)^-1
267: v(140,89) = v(140,33)^-1 v(140,61)^-1 v(140,93) v(35,1)^-1 v(35,3) v(35,18) v(35,33) v(28,1)^-1 v(28,5) v(7,3)^-1 v(5,2)^-1
268: v(105,67) = v(105,73)^-1 v(35,1)^-1 v(35,3)
269: v(420,269) = v(420,361)^-1 v(105,46) v(105,58) v(35,3)^-1 v(35,11)^-1 v(35,18)^-1 v(35,23)^-1 v(7,2)^-1 v(7,3)
270: v(14,9) = v(7,2)
271: v(420,271) = v(420,61)^-1 v(105,43)^-1 v(105,58)^-1 v(105,61) v(105,73)^-1 v(105,88)^-1 v(105,103)^-1 v(35,3) v(35,8) v(35,18) v(35,26)^-1 v(15,1) v(15,13) v(7,2)
272: v(105,68) = v(105,103)^-1 v(35,11)^-1 v(35,33)
273: v(20,13) is in basis
274: v(210,137) = v(105,58) v(105,61)^-1 v(105,73) v(105,103)^-1 v(35,3)^-1 v(35,11)^-1 v(35,26) v(35,33) v(21,1) v(21,19) v(7,2)^-1 v(7,3)
275: v(84,55) = v(84,25) v(84,61) v(28,1) v(28,25)^-1 v(21,4)^-1 v(12,1)^-1 v(7,2)^-1 v(7,3)
276: v(35,23) is in basis
277: v(420,277) = v(420,73) v(140,33) v(140,53) v(140,61) v(140,73)^-1 v(140,81) v(140,113) v(105,58)^-1 v(105,61) v(105,73)^-1 v(105,103) v(35,3) v(35,8)^-1 v(35,18)^-1 v(35,23) v(35,33)^-1 v(28,25)^-1 v(21,1)^-1 v(21,19)^-1 v(20,13)^-1 v(7,2)^-1 v(5,2)
278: v(210,139) = v(105,43) v(105,46) v(105,61) v(105,103) v(35,3) v(21,1)^-1 v(21,19)^-1 v(15,1)^-1 v(7,3)^-1 v(5,2)^-1
279: v(140,93) is in basis
280: v(3,2) = 1
281: v(420,281) = v(420,1)^-1 v(140,33)^-1 v(140,53)^-1 v(140,61)^-1 v(140,81)^-1 v(140,93)^-1 v(140,113)^-1 v(35,3) v(35,8) v(35,11) v(35,18) v(35,33) v(28,25) v(20,13) v(7,2) v(7,3)^-1 v(5,2)^-1
282: v(70,47) = v(35,1) v(35,3)^-1 v(35,18)^-1 v(35,33)^-1 v(7,3) v(5,2)
283: v(420,283) = v(420,73)^-1 v(105,58) v(105,61)^-1 v(105,73) v(105,103)^-1 v(35,3)^-1 v(35,11)^-1 v(35,26) v(35,33) v(21,1) v(21,19) v(7,2)^-1 v(7,3)
284: v(105,71) = v(105,43) v(105,46) v(105,61) v(105,88) v(105,103) v(35,3) v(21,1)^-1 v(21,19)^-1 v(15,1)^-1 v(7,3)^-1 v(5,2)^-1
285: v(28,19) = v(28,5)^-1 v(7,2)
286: v(210,143) = v(105,58)^-1 v(105,61) v(105,73)^-1 v(105,103) v(35,1)^-1 v(35,3)^2 v(35,11) v(35,18) v(35,23) v(21,1)^-1 v(21,19)^-1 v(7,3)^-1
287: v(60,41) = v(60,13) v(20,13)^-1 v(15,13)^-1 v(12,1)^-1
288: v(35,24) = v(35,11)
289: v(420,289) = v(420,61) v(140,61)^-1 v(140,73) v(105,43) v(105,58) v(105,61)^-1 v(105,73) v(105,88) v(105,103) v(35,3)^-1 v(35,26) v(15,1)^-1 v(15,13)^-1 v(5,2)^-1
290: v(42,29) = v(21,1)^-1 v(21,4)^-1 v(7,2)^-1
291: v(140,97) = v(140,113)^-1 v(35,3) v(35,8) v(35,11) v(35,18) v(7,2) v(7,3)^-1
292: v(105,73) is in basis
293: v(420,293) = v(420,73) v(420,193) v(420,253) v(420,313) v(420,373) v(140,53)^-1 v(140,61) v(140,73)^-1 v(140,93)^-2 v(140,113)^-1 v(35,1) v(35,3)^-1 v(35,18)^-1 v(35,33)^-1 v(28,1) v(28,5)^-1 v(20,1)^-1 v(15,13)^-1 v(12,1)^-1 v(7,3) v(5,2)
294: v(10,7) = v(5,2)
295: v(84,59) = v(84,25)
296: v(105,74) = v(105,46) v(105,73)^-1 v(105,88) v(35,1)^-1 v(35,3) v(35,8) v(35,11)^-1 v(35,23) v(35,33) v(21,4)^-1 v(21,19)^-1 v(5,2)^-1
297: v(140,99) = v(140,61)^-1 v(140,73) v(140,81)^-1 v(140,93) v(140,113) v(35,1)^-1 v(35,18) v(35,33) v(28,1)^-1 v(20,1) v(7,3)^-1 v(5,2)^-1
298: v(210,149) = v(105,43)^-1 v(105,58)^-1 v(105,61) v(105,73)^-1 v(105,88)^-1 v(105,103)^-1 v(35,3) v(35,8) v(35,18) v(35,26)^-1 v(15,1) v(15,13) v(7,2)
299: v(420,299) = v(420,61)^-1 v(420,313)^-1 v(420,373)^-1 v(140,33) v(140,61) v(140,73)^-1 v(140,81) v(105,46) v(105,58)^-1 v(105,61)^2 v(105,73)^-1 v(105,103) v(84,25)^-1 v(35,3)^2 v(35,23) v(35,26)^-1 v(35,33)^-1 v(21,1)^-1 v(21,19)^-2 v(15,13) v(12,1) v(7,2) v(7,3)^-1
300: v(7,5) = v(7,2)
301: v(60,43) = v(60,13)^-1 v(15,1)^-1 v(15,13)
302: v(210,151) = v(105,46) v(105,58) v(35,3)^-1 v(35,11)^-1 v(35,18)^-1 v(35,23)^-1 v(7,2)^-1 v(7,3)
303: v(140,101) = v(140,53) v(140,73)^-1 v(140,81) v(35,11)^-1 v(35,18)^-1 v(35,23) v(35,26) v(28,5) v(28,25)^-1 v(7,2)^-2 v(7,3)
304: v(105,76) = v(105,43) v(105,46)^-1 v(105,58) v(105,61)^-1 v(105,73) v(35,3)^-1 v(35,8)^-1 v(35,26) v(21,4) v(21,19) v(15,13)^-1 v(7,2)^-1
305: v(84,61) is in basis
306: v(70,51) = v(35,8)^-1 v(35,23)^-1 v(35,26)^-1 v(35,33)^-1 v(7,2)
307: v(420,307) = v(420,253)^-1 v(140,61) v(140,113) v(35,3)^-1 v(35,8)^-1 v(35,18)^-1 v(35,23)^-1 v(35,26)^-1 v(35,33)^-1 v(5,2)
308: v(15,11) = v(15,1)^-1 v(5,2)^-1
309: v(140,103) = v(140,33)^-1 v(35,1)^-1 v(35,33)
310: v(42,31) = v(21,4)^-1 v(21,19) v(7,2)^-1 v(7,3)^2
311: v(420,311) = v(420,73)^-1 v(420,193)^-1 v(420,361)^-1 v(140,33)^-1 v(140,53)^-1 v(140,61)^-1 v(140,73) v(140,81)^-1 v(140,113)^-1 v(105,58) v(105,61)^-1 v(105,73) v(105,103)^-1 v(84,25) v(84,61) v(35,3)^-1 v(35,8) v(35,18) v(35,23)^-1 v(35,33) v(28,5)^-1 v(21,1) v(21,19) v(20,13) v(7,3) v(5,2)^-1
312: v(35,26) is in basis
313: v(420,313) is in basis
314: v(210,157) = v(105,61) v(105,88)^-1 v(35,1) v(35,23)^-1 v(35,26)^-1 v(35,33)^-1 v(7,3) v(5,2)
315: v(4,3) = 1
316: v(105,79) = v(105,61)^-1 v(35,3)^-1 v(35,26)
317: v(420,317) = v(420,313)^-1 v(105,43) v(105,46) v(105,61) v(105,88) v(105,103)^2 v(35,1)^-1 v(35,3) v(35,23) v(21,1)^-1 v(21,19)^-1 v(15,1)^-1 v(7,3)^-1 v(5,2)^-1
318: v(70,53) = v(35,18) v(35,26)^-1
319: v(420,319) = v(420,73) v(420,193) v(420,361) v(140,33) v(140,53) v(140,61) v(140,73)^-1 v(140,81) v(140,113) v(105,46)^-1 v(105,58)^-1 v(105,61) v(105,88)^-1 v(84,25)^-1 v(84,61)^-1 v(35,1) v(35,8)^-1 v(35,18)^-1 v(35,23) v(35,33)^-1 v(28,5) v(21,1)^-1 v(21,4) v(20,13)^-1 v(7,2)^-1 v(5,2)
320: v(21,16) = v(21,19)^-1 v(7,2) v(7,3)^-1
321: v(140,107) = v(140,33)
322: v(30,23) = v(15,1) v(15,13)^-1 v(5,2)^2
323: v(420,323) = v(420,253) v(140,61)^-1 v(140,113)^-1 v(105,43)^-1 v(105,46) v(105,73)^-1 v(105,88) v(35,1)^-1 v(35,3)^2 v(35,8)^2 v(35,18) v(35,23) v(35,33) v(21,4)^-1 v(21,19)^-1 v(7,2) v(7,3)^-1 v(5,2)^-1
324: v(35,27) = v(35,8)
325: v(84,65) = v(84,61)^-1 v(21,1)^-1 v(21,19)
326: v(210,163) = v(105,43)^-1 v(105,46) v(105,61) v(105,73)^-1 v(35,3) v(35,8) v(35,26)^-1 v(21,4)^-1 v(21,19)^-1 v(15,13) v(7,2)
327: v(140,109) = v(140,53)^-1 v(140,73) v(140,81)^-1 v(35,3)^-1 v(35,23)^-1 v(35,26)^-1 v(35,33)^-1 v(28,5)^-1 v(28,25) v(7,2)
328: v(105,82) = v(105,58)^-1 v(35,3) v(35,11) v(35,18) v(35,23) v(7,2) v(7,3)^-1
329: v(60,47) = v(60,13)
330: v(14,11) = v(7,2)^-1 v(7,3)
331: v(420,331) = v(420,61) v(420,313) v(420,373) v(140,33)^-1 v(140,61)^-1 v(140,73) v(140,81)^-1 v(105,43) v(105,46)^-1 v(105,61)^-1 v(105,73) v(84,25) v(35,3)^-1 v(35,8)^-1 v(35,11) v(35,23)^-1 v(35,26) v(21,19) v(15,13)^-1 v(12,1)^-1
332: v(105,83) = v(105,43) v(105,58) v(105,73) v(105,88) v(105,103) v(35,3)^-1 v(35,8)^-1 v(35,18)^-1 v(35,26) v(15,1)^-1 v(15,13)^-1 v(7,2)^-1
333: v(140,111) = v(140,61) v(140,73)^-1 v(140,81) v(140,93)^-1 v(140,113)^-1 v(35,23) v(28,1) v(20,1)^-1
334: v(210,167) = v(105,43) v(105,46)^-1 v(105,73) v(105,88)^-1 v(35,1) v(35,3)^-1 v(35,8)^-1 v(35,11) v(35,23)^-1 v(35,33)^-1 v(21,4) v(21,19) v(5,2)
335: v(84,67) = v(84,25)^-1 v(21,4) v(21,19)^-1
336: v(5,4) = 1
337: v(420,337) = v(420,73)^-1 v(420,193)^-1 v(420,253)^-1 v(420,313)^-1 v(420,373)^-1 v(140,53) v(140,61)^-1 v(140,73) v(140,93)^2 v(140,113) v(105,43) v(105,46) v(105,58) v(105,73) v(105,88) v(105,103) v(35,1)^-1 v(35,11)^-1 v(35,26) v(35,33) v(28,1)^-1 v(28,5) v(20,1) v(15,1)^-1 v(12,1) v(7,2)^-1 v(7,3)^-1 v(5,2)^-1
338: v(210,169) = v(105,43)^-1 v(105,46) v(105,58)^-1 v(105,61) v(105,73)^-2 v(35,1)^-1 v(35,3)^2 v(35,8) v(35,18) v(35,23) v(35,26)^-1 v(21,4)^-1 v(21,19)^-1 v(15,13) v(7,2) v(7,3)^-1 v(5,2)^-1
339: v(140,113) is in basis
340: v(21,17) = v(21,4)
341: v(420,341) = v(420,61)^-1 v(140,61) v(140,73)^-1
342: v(70,57) = v(35,3)^-1 v(35,8)^-1 v(35,11)^-1 v(35,18)^-1 v(35,23)^-1 v(35,33)^-1 v(5,2)
343: v(60,49) = v(60,13)^-1 v(20,13) v(15,1)^-1 v(12,1) v(5,2)^-1
344: v(105,86) = v(105,58) v(105,61)^-1 v(105,103)^-1 v(35,3)^-1 v(35,11)^-1 v(35,18)^-1 v(35,23)^-1 v(21,1) v(21,19) v(7,3)
345: v(28,23) = v(28,5)
346: v(210,173) = v(105,43)^-1 v(105,46)^-1 v(105,61)^-1 v(105,88)^-1 v(105,103)^-2 v(35,3)^-1 v(35,11)^-1 v(35,33) v(21,1) v(21,19) v(15,1) v(7,3) v(5,2)
347: v(420,347) = v(420,73)
348: v(35,29) = v(35,1)^-1 v(35,3) v(35,18) v(35,23) v(35,33) v(7,3)^-1 v(5,2)^-1
349: v(420,349) = v(420,1) v(140,33) v(140,53) v(140,61) v(140,81) v(140,93) v(140,113) v(105,43) v(105,46) v(105,61) v(105,103) v(35,8)^-1 v(35,11)^-1 v(35,18)^-1 v(35,33)^-1 v(28,25)^-1 v(21,1)^-1 v(21,19)^-1 v(20,13)^-1 v(15,1)^-1 v(7,2)^-1
350: v(6,5) = 1
351: v(140,117) = v(140,93)^-1 v(35,1) v(35,3)^-1 v(35,18)^-1 v(35,33)^-1 v(7,3) v(5,2)
352: v(105,88) is in basis
353: v(420,353) = v(420,73)^-1 v(140,33)^-1 v(140,53)^-1 v(140,61)^-1 v(140,73) v(140,81)^-1 v(140,113)^-1 v(35,1)^-1 v(35,3) v(35,8) v(35,11) v(35,18)^2 v(35,33) v(28,25) v(20,13) v(7,2) v(7,3)^-1 v(5,2)^-1
354: v(70,59) = v(35,11) v(35,23)^-1
355: v(84,71) = v(84,25)^-1 v(84,61)^-1 v(28,1)^-1 v(28,25) v(21,1)^-1 v(12,1) v(7,3)^-1
356: v(105,89) = v(105,58)^-1 v(105,61) v(105,103) v(35,3) v(35,11) v(35,26)^-1 v(35,33)^-1 v(21,1)^-1 v(21,19)^-1 v(7,2) v(7,3)^-1
357: v(20,17) = v(20,13)^-1 v(5,2)
358: v(210,179) = v(105,46) v(105,73)^-1 v(105,88) v(105,103) v(35,1)^-1 v(35,3) v(35,8) v(35,23) v(21,4)^-1 v(21,19)^-1 v(5,2)^-1
359: v(420,359) = v(420,61)
360: v(7,6) = 1
361: v(420,361) is in basis
362: v(210,181) = v(105,43) v(105,46)^-1 v(105,58) v(105,61)^-1 v(105,73)^2 v(35,1) v(35,3)^-2 v(35,8)^-1 v(35,26) v(21,4) v(21,19) v(15,13)^-1 v(7,2)^-1
363: v(140,121) = v(140,33) v(140,61) v(140,93)^-1 v(35,1) v(35,3)^-1 v(35,8)^-1 v(35,18)^-1 v(35,23)^-1 v(35,26)^-1 v(35,33)^-2 v(28,1) v(28,5)^-1 v(7,2) v(7,3) v(5,2)
364: v(15,13) is in basis
365: v(84,73) = v(84,25) v(28,1) v(28,25)^-1 v(21,4)^-1 v(21,19) v(7,2)^-1 v(7,3)^2
366: v(70,61) = v(35,3) v(35,8) v(35,18) v(35,23) v(35,26) v(35,33) v(5,2)^-1
367: v(420,367) = v(420,193)^-1 v(140,53) v(140,61)^-1 v(140,73) v(140,81)^-1 v(140,93) v(140,113) v(35,23)^-1 v(28,1)^-1 v(20,1)
368: v(105,92) = v(105,43)^-1 v(105,58)^-1 v(105,73)^-1 v(105,88)^-1 v(105,103)^-1 v(15,1) v(15,13) v(5,2)
369: v(140,123) = v(140,53)^-1 v(35,18) v(35,26)^-1
370: v(42,37) = v(21,1) v(21,19)^-1 v(7,2)^2 v(7,3)^-1
371: v(60,53) = v(60,13)^-1 v(20,1) v(20,13) v(5,2)
372: v(35,31) = v(35,3)^-1 v(35,11)^-1 v(35,18)^-1 v(7,2)^-1 v(7,3)
373: v(420,373) is in basis
374: v(210,187) = v(105,43) v(105,46)^-1 v(105,61)^-1 v(105,73) v(35,1) v(35,3)^-1 v(35,8)^-1 v(35,11) v(35,26) v(21,4) v(21,19) v(15,13)^-1 v(5,2)
375: v(28,25) is in basis
376: v(105,94) = v(105,46)^-1 v(35,8)^-1 v(35,11)
377: v(420,377) = v(420,253)^-1 v(105,43) v(105,46)^-1 v(105,73) v(105,88)^-1 v(35,1) v(35,3)^-1 v(35,8)^-1 v(35,11) v(35,23)^-1 v(35,33)^-1 v(21,4) v(21,19) v(5,2)
378: v(10,9) = v(5,2)^-1
379: v(420,379) = v(420,1) v(420,73)^-1 v(420,193)^-1 v(420,313)^-1 v(420,373)^-1 v(140,53) v(140,61)^-1 v(140,73) v(140,93)^2 v(140,113) v(105,46)^2 v(105,61) v(105,73)^-1 v(105,88) v(105,103) v(84,61) v(35,1)^-2 v(35,3)^2 v(35,8) v(35,11)^-1 v(35,18) v(35,23) v(35,33) v(28,1)^-1 v(28,25)^-1 v(21,4)^-1 v(21,19)^-2 v(20,1) v(15,1)^-1 v(15,13) v(7,3)^-1 v(5,2)^-2
380: v(21,19) is in basis
381: v(140,127) = v(140,33)^-1 v(140,53)^-1 v(140,73)^-1 v(140,93)^-1 v(140,113)^-1 v(20,1)^-1 v(20,13)
382: v(210,191) = v(105,43)^-1 v(105,58) v(105,61)^-1 v(105,103)^-1 v(35,3)^-1 v(35,11)^-1 v(35,18)^-1 v(35,23)^-1 v(21,1) v(21,19) v(7,3)
383: v(420,383) = v(420,313) v(140,33)^-1 v(140,81)^-1 v(105,43)^-1 v(105,46)^-1 v(105,61)^-1 v(105,88)^-1 v(105,103)^-2 v(35,3)^-1 v(35,23)^-1 v(35,33) v(21,1) v(21,19) v(15,1) v(7,3) v(5,2)
384: v(35,32) = v(35,3)
385: v(12,11) = v(12,1)
386: v(210,193) = v(105,61)^-1 v(105,88)
387: v(140,129) = v(140,81)^-1 v(35,11) v(35,23)^-1
388: v(105,97) = v(105,43)^-1 v(35,8) v(35,26)^-1
389: v(420,389) = v(420,73) v(420,193) v(420,361) v(140,53)^-1 v(140,61) v(140,73)^-1 v(140,93)^-1 v(105,58)^-1 v(105,61) v(105,73)^-1 v(105,103) v(84,25)^-1 v(84,61)^-1 v(35,3) v(35,11) v(35,23) v(35,26)^-1 v(35,33)^-1 v(28,25) v(21,1)^-1 v(21,19)^-1 v(20,1)^-1 v(7,2) v(7,3)^-1
390: v(14,13) = v(7,3)^-1
391: v(420,391) = v(420,1) v(420,73)^-1 v(420,193)^-1 v(420,313)^-1 v(420,373)^-1 v(140,33) v(140,53) v(140,81) v(140,93) v(105,43) v(105,46) v(105,58) v(105,73) v(105,88) v(105,103) v(84,61) v(35,11)^-1 v(35,23) v(35,26) v(28,25)^-1 v(21,19)^-1 v(15,1)^-1 v(7,2)^-1 v(5,2)^-1
392: v(15,14) = v(15,1)
393: v(140,131) = v(140,61)^-1 v(35,3) v(35,8) v(35,18) v(35,23) v(35,26) v(35,33) v(5,2)^-1
394: v(210,197) = v(105,43)^-1 v(105,46)^-1 v(105,58)^-1 v(105,73)^-1 v(105,88)^-1 v(105,103)^-1 v(15,1) v(15,13) v(5,2)
395: v(84,79) = v(84,61)^-1 v(28,5) v(28,25) v(7,2) v(7,3)^-1
396: v(35,33) is in basis
397: v(420,397) = v(420,373) v(140,53)^-1 v(140,73) v(140,81)^-1 v(140,93)^-1 v(105,43) v(105,46)^-1 v(105,61)^-1 v(105,73) v(35,1) v(35,3)^-2 v(35,8)^-1 v(35,11) v(35,23)^-1 v(35,33)^-1 v(28,5)^-1 v(28,25) v(21,4) v(21,19) v(15,13)^-1 v(7,2) v(5,2)
398: v(210,199) = v(105,46)^-1 v(105,58)^-1 v(35,8)^-1 v(35,11)
399: v(20,19) = v(20,1)
400: v(21,20) = v(21,1)
401: v(420,401) = v(420,61) v(420,313) v(420,373) v(140,53)^-1 v(140,73) v(140,81)^-1 v(140,93)^-1 v(105,46)^-1 v(105,58) v(105,61)^-2 v(105,73) v(105,103)^-1 v(84,25) v(35,1) v(35,3)^-3 v(35,8)^-1 v(35,18)^-1 v(35,23)^-2 v(35,33)^-1 v(28,1) v(28,5)^-1 v(21,1) v(21,19)^2 v(15,13)^-1 v(12,1)^-1 v(7,3)^2 v(5,2)
402: v(70,67) = v(35,3) v(35,23) v(35,26) v(35,33) v(7,2)^-1
403: v(420,403) = v(420,193)^-1 v(105,61)^-1 v(105,88)
404: v(105,101) = v(105,46)^-1 v(105,73) v(105,88)^-1 v(35,1) v(35,3)^-1 v(21,4) v(21,19) v(7,2)^-1 v(7,3)
405: v(28,27) = v(28,1)
406: v(30,29) = v(15,1) v(15,13) v(5,2)^-1
407: v(420,407) = v(420,73)^-1 v(420,193)^-1 v(420,253)^-1 v(420,313)^-1 v(420,373)^-1 v(20,13) v(15,13) v(12,1)
408: v(35,34) = v(35,1)
409: v(420,409) = v(420,361) v(140,81)^-1 v(140,113) v(105,46)^-1 v(105,58)^-1 v(35,8)^-1 v(35,11)
410: v(42,41) = v(21,1) v(21,4) v(7,3)^-1
411: v(140,137) = v(140,73)^-1 v(35,3) v(35,23) v(35,26) v(35,33) v(7,2)^-1
412: v(105,103) is in basis
413: v(60,59) = v(60,13)^-1 v(20,1) v(15,13) v(12,1)
414: v(70,69) = v(35,1) v(35,18)^-1
415: v(84,83) = v(84,25)^-1 v(84,61)^-1 v(28,5) v(28,25) v(21,4) v(12,1) v(7,3)^-1
416: v(105,104) = v(105,43)^-1 v(105,46)^-1 v(105,61)^-1 v(105,88)^-1 v(105,103)^-1 v(35,1) v(35,3)^-1 v(35,23)^-1 v(21,1) v(21,19) v(15,1) v(7,3) v(5,2)
417: v(140,139) = v(140,33)^-1 v(140,53)^-1 v(140,61)^-1 v(140,81)^-1 v(140,113)^-1 v(35,3) v(35,8) v(35,11) v(35,18) v(35,33) v(28,25) v(20,13) v(7,2) v(7,3)^-1 v(5,2)^-1
418: v(210,209) = v(105,43)^-1 v(105,46)^-1 v(105,61)^-1 v(105,103)^-1 v(35,33) v(21,1) v(21,19) v(15,1)
419: v(420,419) = v(420,1)
The rank is: 47
Cyclotomic Units - Methods for First Development for n = 420 = 2^2*3*5*7
Compare with Algorithm 1.2 and 2.2
1: v(420,1) - method B (Case V,i - A12)
2: v(210,1) - method Z-2 (Case IV - A12)
3: v(140,1) - method E (Case V,i - A12)
4: v(105,1) - method E (Case V,i - A12)
5: v(84,1) - method E (Case V,i - A12)
6: v(70,1) - method Z-2 (Case IV - A12)
7: v(60,1) - method E (Case V,i - A12)
8: v(105,2) - method Z-3 (Case V,iv - A12)
9: v(140,3) - method Z-2 (Case V,iv - A12)
10: v(42,1) - method Z-2 (Case IV - A12)
11: v(420,11) - method Z-2 (Case V,iv - A12)
12: v(35,1) - method B (Case V,i - A12)
13: v(420,13) - method Z-7 (Case V,iv - A12)
14: v(30,1) - method Z-2 (Case IV - A12)
15: v(28,1) - method B (Case V,i - A12)
16: v(105,4) - method Z-5 (Case V,iv - A12)
17: v(420,17) - method Z-3 (Case V,iv - A12)
18: v(70,3) - method Z-2 (Case IV - A12)
19: v(420,19) - method Z-2 (Case V,iv - A12)
20: v(21,1) - method B (Case V,i - A12)
21: v(20,1) - method B (Case V,i - A12)
22: v(210,11) - method Z-2 (Case IV - A12)
23: v(420,23) - method Z-2 (Case V,iv - A12)
24: v(35,2) - method S (Case V,ii - A12 for p=5)
25: v(84,5) - method Z-3 (Case V,iv - A12)
26: v(210,13) - method Z-2 (Case IV - A12)
27: v(140,9) - method Z-5 (Case V,iv - A12)
28: v(15,1) - method B (Case V,i - A12)
29: v(420,29) - method Z-3 (Case V,iv - A12)
30: v(14,1) - method Z-2 (Case IV - A12)
31: v(420,31) - method Z-2 (Case V,iv - A12)
32: v(105,8) - method Z-3 (Case V,iv - A12)
33: v(140,11) - method Z-2 (Case V,iv - A12)
34: v(210,17) - method Z-2 (Case IV - A12)
35: v(12,1) - method B (Case V,i - A12)
36: v(35,3) - method B (Case V,iii - A12)
37: v(420,37) - method S (Case V,ii - A12 for p=5)
38: v(210,19) - method Z-2 (Case IV - A12)
39: v(140,13) - method Z-7 (Case V,iv - A12)
40: v(21,2) - method Z-3 (Case V,iv - A12)
41: v(420,41) - method Z-3 (Case V,iv - A12)
42: v(10,1) - method Z-2 (Case IV - A12)
43: v(420,43) - method Z-2 (Case V,iv - A12)
44: v(105,11) - method Z-3 (Case V,iv - A12)
45: v(28,3) - method Z-2 (Case V,iv - A12)
46: v(210,23) - method Z-2 (Case IV - A12)
47: v(420,47) - method Z-2 (Case V,iv - A12)
48: v(35,4) - method Z-5 (Case V,iv - A12)
49: v(60,7) - method Z-2 (Case V,iv - A12)
50: v(42,5) - method Z-2 (Case IV - A12)
51: v(140,17) - method S (Case V,ii - A12 for p=5)
52: v(105,13) - method Z-7 (Case V,iv - A12)
53: v(420,53) - method Z-3 (Case V,iv - A12)
54: v(70,9) - method Z-2 (Case IV - A12)
55: v(84,11) - method Z-2 (Case V,iv - A12)
56: v(15,2) - method Z-3 (Case V,iv - A12)
57: v(140,19) - method Z-2 (Case V,iv - A12)
58: v(210,29) - method Z-2 (Case IV - A12)
59: v(420,59) - method Z-2 (Case V,iv - A12)
60: v(7,1) - method T (Case III, A22)
61: v(420,61) - method B (Case V,iii - A12)
62: v(210,31) - method Z-2 (Case IV - A12)
63: v(20,3) - method Z-2 (Case V,iv - A12)
64: v(105,16) - method S (Case V,ii - A12 for p=7)
65: v(84,13) - method Z-7 (Case V,iv - A12)
66: v(70,11) - method Z-2 (Case IV - A12)
67: v(420,67) - method Z-2 (Case V,iv - A12)
68: v(105,17) - method Z-3 (Case V,iv - A12)
69: v(140,23) - method Z-2 (Case V,iv - A12)
70: v(6,1) - method Z-2 (Case IV - A12)
71: v(420,71) - method Z-2 (Case V,iv - A12)
72: v(35,6) - method Z-7 (Case V,iv - A12)
73: v(420,73) - method B (Case V,iii - A12)
74: v(210,37) - method Z-2 (Case IV - A12)
75: v(28,5) - method B (Case V,iii - A12)
76: v(105,19) - method Z-5 (Case V,iv - A12)
77: v(60,11) - method Z-2 (Case V,iv - A12)
78: v(70,13) - method Z-2 (Case IV - A12)
79: v(420,79) - method Z-2 (Case V,iv - A12)
80: v(21,4) - method B (Case V,iii - A12)
81: v(140,27) - method Z-2 (Case V,iv - A12)
82: v(210,41) - method Z-2 (Case IV - A12)
83: v(420,83) - method Z-2 (Case V,iv - A12)
84: v(5,1) - method T (Case III, A22)
85: v(84,17) - method Z-3 (Case V,iv - A12)
86: v(210,43) - method Z-2 (Case IV - A12)
87: v(140,29) - method Z-5 (Case V,iv - A12)
88: v(105,22) - method S (Case V,ii - A12 for p=5)
89: v(420,89) - method Z-3 (Case V,iv - A12)
90: v(14,3) - method Z-2 (Case IV - A12)
91: v(60,13) - method B (Case V,iii - A12)
92: v(105,23) - method Z-3 (Case V,iv - A12)
93: v(140,31) - method Z-2 (Case V,iv - A12)
94: v(210,47) - method Z-2 (Case IV - A12)
95: v(84,19) - method Z-2 (Case V,iv - A12)
96: v(35,8) - method B (Case V,iii - A12)
97: v(420,97) - method S (Case V,ii - A12 for p=5)
98: v(30,7) - method Z-2 (Case IV - A12)
99: v(140,33) - method B (Case V,iii - A12)
100: v(21,5) - method Z-3 (Case V,iv - A12)
101: v(420,101) - method Z-3 (Case V,iv - A12)
102: v(70,17) - method Z-2 (Case IV - A12)
103: v(420,103) - method Z-2 (Case V,iv - A12)
104: v(105,26) - method Z-3 (Case V,iv - A12)
105: v(4,1) - method T (Case II - A22)
106: v(210,53) - method Z-2 (Case IV - A12)
107: v(420,107) - method Z-2 (Case V,iv - A12)
108: v(35,9) - method Z-5 (Case V,iv - A12)
109: v(420,109) - method Z-5 (Case V,iv - A12)
110: v(42,11) - method Z-2 (Case IV - A12)
111: v(140,37) - method S (Case V,ii - A12 for p=5)
112: v(15,4) - method Z-5 (Case V,iv - A12)
113: v(420,113) - method Z-3 (Case V,iv - A12)
114: v(70,19) - method Z-2 (Case IV - A12)
115: v(84,23) - method Z-2 (Case V,iv - A12)
116: v(105,29) - method Z-3 (Case V,iv - A12)
117: v(140,39) - method Z-2 (Case V,iv - A12)
118: v(210,59) - method Z-2 (Case IV - A12)
119: v(60,17) - method Z-3 (Case V,iv - A12)
120: v(7,2) - method B (Case III, A22)
121: v(420,121) - method S (Case V,ii - A12 for p=7)
122: v(210,61) - method Z-2 (Case IV - A12)
123: v(140,41) - method Z-7 (Case V,iv - A12)
124: v(105,31) - method S (Case V,ii - A12 for p=7)
125: v(84,25) - method B (Case V,iii - A12)
126: v(10,3) - method Z-2 (Case IV - A12)
127: v(420,127) - method Z-2 (Case V,iv - A12)
128: v(105,32) - method Z-3 (Case V,iv - A12)
129: v(140,43) - method Z-2 (Case V,iv - A12)
130: v(42,13) - method Z-2 (Case IV - A12)
131: v(420,131) - method Z-2 (Case V,iv - A12)
132: v(35,11) - method B (Case V,iii - A12)
133: v(60,19) - method Z-2 (Case V,iv - A12)
134: v(210,67) - method Z-2 (Case IV - A12)
135: v(28,9) - method S (Case V,ii - A12 for p=7)
136: v(105,34) - method Z-5 (Case V,iv - A12)
137: v(420,137) - method Z-3 (Case V,iv - A12)
138: v(70,23) - method Z-2 (Case IV - A12)
139: v(420,139) - method Z-2 (Case V,iv - A12)
140: v(3,1) - method T (Case III, A22)
141: v(140,47) - method Z-2 (Case V,iv - A12)
142: v(210,71) - method Z-2 (Case IV - A12)
143: v(420,143) - method Z-2 (Case V,iv - A12)
144: v(35,12) - method S (Case V,ii - A12 for p=5)
145: v(84,29) - method Z-3 (Case V,iv - A12)
146: v(210,73) - method Z-2 (Case IV - A12)
147: v(20,7) - method Z-2 (Case V,iv - A12)
148: v(105,37) - method S (Case V,ii - A12 for p=5)
149: v(420,149) - method Z-3 (Case V,iv - A12)
150: v(14,5) - method Z-2 (Case IV - A12)
151: v(420,151) - method Z-2 (Case V,iv - A12)
152: v(105,38) - method Z-3 (Case V,iv - A12)
153: v(140,51) - method Z-2 (Case V,iv - A12)
154: v(30,11) - method Z-2 (Case IV - A12)
155: v(84,31) - method Z-2 (Case V,iv - A12)
156: v(35,13) - method Z-7 (Case V,iv - A12)
157: v(420,157) - method S (Case V,ii - A12 for p=5)
158: v(210,79) - method Z-2 (Case IV - A12)
159: v(140,53) - method B (Case V,iii - A12)
160: v(21,8) - method Z-3 (Case V,iv - A12)
161: v(60,23) - method Z-2 (Case V,iv - A12)
162: v(70,27) - method Z-2 (Case IV - A12)
163: v(420,163) - method Z-2 (Case V,iv - A12)
164: v(105,41) - method Z-3 (Case V,iv - A12)
165: v(28,11) - method Z-2 (Case V,iv - A12)
166: v(210,83) - method Z-2 (Case IV - A12)
167: v(420,167) - method Z-2 (Case V,iv - A12)
168: v(5,2) - method B (Case III, A22)
169: v(420,169) - method Z-5 (Case V,iv - A12)
170: v(42,17) - method Z-2 (Case IV - A12)
171: v(140,57) - method S (Case V,ii - A12 for p=5)
172: v(105,43) - method B (Case V,iii - A12)
173: v(420,173) - method Z-3 (Case V,iv - A12)
174: v(70,29) - method Z-2 (Case IV - A12)
175: v(12,5) - method Z-3 (Case V,iv - A12)
176: v(105,44) - method Z-3 (Case V,iv - A12)
177: v(140,59) - method Z-2 (Case V,iv - A12)
178: v(210,89) - method Z-2 (Case IV - A12)
179: v(420,179) - method Z-2 (Case V,iv - A12)
180: v(7,3) - method B (Case III, A22)
181: v(420,181) - method Z-7 (Case V,iv - A12)
182: v(30,13) - method Z-2 (Case IV - A12)
183: v(140,61) - method B (Case V,iii - A12)
184: v(105,46) - method B (Case V,iii - A12)
185: v(84,37) - method S (Case V,ii - A12 for p=7)
186: v(70,31) - method Z-2 (Case IV - A12)
187: v(420,187) - method Z-2 (Case V,iv - A12)
188: v(105,47) - method Z-3 (Case V,iv - A12)
189: v(20,9) - method Z-5 (Case V,iv - A12)
190: v(42,19) - method Z-2 (Case IV - A12)
191: v(420,191) - method Z-2 (Case V,iv - A12)
192: v(35,16) - method S (Case V,ii - A12 for p=7)
193: v(420,193) - method B (Case V,iii - A12)
194: v(210,97) - method Z-2 (Case IV - A12)
195: v(28,13) - method Z-7 (Case V,iv - A12)
196: v(15,7) - method S (Case V,ii - A12 for p=5)
197: v(420,197) - method Z-3 (Case V,iv - A12)
198: v(70,33) - method Z-2 (Case IV - A12)
199: v(420,199) - method Z-2 (Case V,iv - A12)
200: v(21,10) - method S (Case V,ii - A12 for p=7)
201: v(140,67) - method Z-2 (Case V,iv - A12)
202: v(210,101) - method Z-2 (Case IV - A12)
203: v(60,29) - method Z-3 (Case V,iv - A12)
204: v(35,17) - method S (Case V,ii - A12 for p=5)
205: v(84,41) - method Z-3 (Case V,iv - A12)
206: v(210,103) - method Z-2 (Case IV - A12)
207: v(140,69) - method Z-5 (Case V,iv - A12)
208: v(105,52) - method S (Case V,ii - A12 for p=5)
209: v(420,209) - method Z-3 (Case V,iv - A12)
210: v(2,1) - method T (Case II - A22)
211: v(420,211) - method Z-2 (Case V,iv - A12)
212: v(105,53) - method Z-3 (Case V,iv - A12)
213: v(140,71) - method Z-2 (Case V,iv - A12)
214: v(210,107) - method Z-2 (Case IV - A12)
215: v(84,43) - method Z-2 (Case V,iv - A12)
216: v(35,18) - method B (Case V,iii - A12)
217: v(60,31) - method Z-2 (Case V,iv - A12)
218: v(210,109) - method Z-2 (Case IV - A12)
219: v(140,73) - method B (Case V,iii - A12)
220: v(21,11) - method Z-3 (Case V,iv - A12)
221: v(420,221) - method Z-3 (Case V,iv - A12)
222: v(70,37) - method Z-2 (Case IV - A12)
223: v(420,223) - method Z-2 (Case V,iv - A12)
224: v(15,8) - method Z-3 (Case V,iv - A12)
225: v(28,15) - method Z-2 (Case V,iv - A12)
226: v(210,113) - method Z-2 (Case IV - A12)
227: v(420,227) - method Z-2 (Case V,iv - A12)
228: v(35,19) - method Z-5 (Case V,iv - A12)
229: v(420,229) - method Z-5 (Case V,iv - A12)
230: v(42,23) - method Z-2 (Case IV - A12)
231: v(20,11) - method Z-2 (Case V,iv - A12)
232: v(105,58) - method B (Case V,iii - A12)
233: v(420,233) - method Z-3 (Case V,iv - A12)
234: v(70,39) - method Z-2 (Case IV - A12)
235: v(84,47) - method Z-2 (Case V,iv - A12)
236: v(105,59) - method Z-3 (Case V,iv - A12)
237: v(140,79) - method Z-2 (Case V,iv - A12)
238: v(30,17) - method Z-2 (Case IV - A12)
239: v(420,239) - method Z-2 (Case V,iv - A12)
240: v(7,4) - method S (Case III, A22)
241: v(420,241) - method S (Case V,ii - A12 for p=7)
242: v(210,121) - method Z-2 (Case IV - A12)
243: v(140,81) - method B (Case V,iii - A12)
244: v(105,61) - method B (Case V,iii - A12)
245: v(12,7) - method Z-2 (Case V,iv - A12)
246: v(70,41) - method Z-2 (Case IV - A12)
247: v(420,247) - method Z-2 (Case V,iv - A12)
248: v(105,62) - method Z-3 (Case V,iv - A12)
249: v(140,83) - method Z-2 (Case V,iv - A12)
250: v(42,25) - method Z-2 (Case IV - A12)
251: v(420,251) - method Z-2 (Case V,iv - A12)
252: v(5,3) - method S (Case III, A22)
253: v(420,253) - method B (Case V,iii - A12)
254: v(210,127) - method Z-2 (Case IV - A12)
255: v(28,17) - method S (Case V,ii - A12 for p=7)
256: v(105,64) - method Z-5 (Case V,iv - A12)
257: v(420,257) - method Z-3 (Case V,iv - A12)
258: v(70,43) - method Z-2 (Case IV - A12)
259: v(60,37) - method S (Case V,ii - A12 for p=5)
260: v(21,13) - method Z-7 (Case V,iv - A12)
261: v(140,87) - method Z-2 (Case V,iv - A12)
262: v(210,131) - method Z-2 (Case IV - A12)
263: v(420,263) - method Z-2 (Case V,iv - A12)
264: v(35,22) - method S (Case V,ii - A12 for p=5)
265: v(84,53) - method Z-3 (Case V,iv - A12)
266: v(30,19) - method Z-2 (Case IV - A12)
267: v(140,89) - method Z-5 (Case V,iv - A12)
268: v(105,67) - method S (Case V,ii - A12 for p=5)
269: v(420,269) - method Z-3 (Case V,iv - A12)
270: v(14,9) - method Z-2 (Case IV - A12)
271: v(420,271) - method Z-2 (Case V,iv - A12)
272: v(105,68) - method Z-3 (Case V,iv - A12)
273: v(20,13) - method B (Case V,iii - A12)
274: v(210,137) - method Z-2 (Case IV - A12)
275: v(84,55) - method Z-2 (Case V,iv - A12)
276: v(35,23) - method B (Case V,iii - A12)
277: v(420,277) - method S (Case V,ii - A12 for p=5)
278: v(210,139) - method Z-2 (Case IV - A12)
279: v(140,93) - method B (Case V,iii - A12)
280: v(3,2) - method S (Case III, A22)
281: v(420,281) - method Z-3 (Case V,iv - A12)
282: v(70,47) - method Z-2 (Case IV - A12)
283: v(420,283) - method Z-2 (Case V,iv - A12)
284: v(105,71) - method Z-3 (Case V,iv - A12)
285: v(28,19) - method Z-2 (Case V,iv - A12)
286: v(210,143) - method Z-2 (Case IV - A12)
287: v(60,41) - method Z-3 (Case V,iv - A12)
288: v(35,24) - method Z-5 (Case V,iv - A12)
289: v(420,289) - method Z-5 (Case V,iv - A12)
290: v(42,29) - method Z-2 (Case IV - A12)
291: v(140,97) - method S (Case V,ii - A12 for p=5)
292: v(105,73) - method B (Case V,iii - A12)
293: v(420,293) - method Z-3 (Case V,iv - A12)
294: v(10,7) - method Z-2 (Case IV - A12)
295: v(84,59) - method Z-2 (Case V,iv - A12)
296: v(105,74) - method Z-3 (Case V,iv - A12)
297: v(140,99) - method Z-2 (Case V,iv - A12)
298: v(210,149) - method Z-2 (Case IV - A12)
299: v(420,299) - method Z-2 (Case V,iv - A12)
300: v(7,5) - method S (Case III, A22)
301: v(60,43) - method Z-2 (Case V,iv - A12)
302: v(210,151) - method Z-2 (Case IV - A12)
303: v(140,101) - method S (Case V,ii - A12 for p=7)
304: v(105,76) - method Z-7 (Case V,iv - A12)
305: v(84,61) - method B (Case V,iii - A12)
306: v(70,51) - method Z-2 (Case IV - A12)
307: v(420,307) - method Z-2 (Case V,iv - A12)
308: v(15,11) - method Z-3 (Case V,iv - A12)
309: v(140,103) - method Z-2 (Case V,iv - A12)
310: v(42,31) - method Z-2 (Case IV - A12)
311: v(420,311) - method Z-2 (Case V,iv - A12)
312: v(35,26) - method B (Case V,iii - A12)
313: v(420,313) - method B (Case V,iii - A12)
314: v(210,157) - method Z-2 (Case IV - A12)
315: v(4,3) - method T (Case II - A22)
316: v(105,79) - method Z-5 (Case V,iv - A12)
317: v(420,317) - method Z-3 (Case V,iv - A12)
318: v(70,53) - method Z-2 (Case IV - A12)
319: v(420,319) - method Z-2 (Case V,iv - A12)
320: v(21,16) - method S (Case V,ii - A12 for p=7)
321: v(140,107) - method Z-2 (Case V,iv - A12)
322: v(30,23) - method Z-2 (Case IV - A12)
323: v(420,323) - method Z-2 (Case V,iv - A12)
324: v(35,27) - method S (Case V,ii - A12 for p=5)
325: v(84,65) - method Z-3 (Case V,iv - A12)
326: v(210,163) - method Z-2 (Case IV - A12)
327: v(140,109) - method Z-5 (Case V,iv - A12)
328: v(105,82) - method S (Case V,ii - A12 for p=5)
329: v(60,47) - method Z-2 (Case V,iv - A12)
330: v(14,11) - method Z-2 (Case IV - A12)
331: v(420,331) - method Z-2 (Case V,iv - A12)
332: v(105,83) - method Z-3 (Case V,iv - A12)
333: v(140,111) - method Z-2 (Case V,iv - A12)
334: v(210,167) - method Z-2 (Case IV - A12)
335: v(84,67) - method Z-2 (Case V,iv - A12)
336: v(5,4) - method S (Case III, A22)
337: v(420,337) - method S (Case V,ii - A12 for p=5)
338: v(210,169) - method Z-2 (Case IV - A12)
339: v(140,113) - method B (Case V,iii - A12)
340: v(21,17) - method Z-3 (Case V,iv - A12)
341: v(420,341) - method Z-3 (Case V,iv - A12)
342: v(70,57) - method Z-2 (Case IV - A12)
343: v(60,49) - method Z-5 (Case V,iv - A12)
344: v(105,86) - method Z-3 (Case V,iv - A12)
345: v(28,23) - method Z-2 (Case V,iv - A12)
346: v(210,173) - method Z-2 (Case IV - A12)
347: v(420,347) - method Z-2 (Case V,iv - A12)
348: v(35,29) - method Z-5 (Case V,iv - A12)
349: v(420,349) - method Z-5 (Case V,iv - A12)
350: v(6,5) - method Z-2 (Case IV - A12)
351: v(140,117) - method S (Case V,ii - A12 for p=5)
352: v(105,88) - method B (Case V,iii - A12)
353: v(420,353) - method Z-3 (Case V,iv - A12)
354: v(70,59) - method Z-2 (Case IV - A12)
355: v(84,71) - method Z-2 (Case V,iv - A12)
356: v(105,89) - method Z-3 (Case V,iv - A12)
357: v(20,17) - method S (Case V,ii - A12 for p=5)
358: v(210,179) - method Z-2 (Case IV - A12)
359: v(420,359) - method Z-2 (Case V,iv - A12)
360: v(7,6) - method S (Case III, A22)
361: v(420,361) - method B (Case V,iii - A12)
362: v(210,181) - method Z-2 (Case IV - A12)
363: v(140,121) - method S (Case V,ii - A12 for p=7)
364: v(15,13) - method B (Case V,iii - A12)
365: v(84,73) - method S (Case V,ii - A12 for p=7)
366: v(70,61) - method Z-2 (Case IV - A12)
367: v(420,367) - method Z-2 (Case V,iv - A12)
368: v(105,92) - method Z-3 (Case V,iv - A12)
369: v(140,123) - method Z-2 (Case V,iv - A12)
370: v(42,37) - method Z-2 (Case IV - A12)
371: v(60,53) - method Z-3 (Case V,iv - A12)
372: v(35,31) - method S (Case V,ii - A12 for p=7)
373: v(420,373) - method B (Case V,iii - A12)
374: v(210,187) - method Z-2 (Case IV - A12)
375: v(28,25) - method B (Case V,iii - A12)
376: v(105,94) - method Z-5 (Case V,iv - A12)
377: v(420,377) - method Z-3 (Case V,iv - A12)
378: v(10,9) - method Z-2 (Case IV - A12)
379: v(420,379) - method Z-2 (Case V,iv - A12)
380: v(21,19) - method B (Case V,iii - A12)
381: v(140,127) - method Z-2 (Case V,iv - A12)
382: v(210,191) - method Z-2 (Case IV - A12)
383: v(420,383) - method Z-2 (Case V,iv - A12)
384: v(35,32) - method S (Case V,ii - A12 for p=5)
385: v(12,11) - method Z-2 (Case V,iv - A12)
386: v(210,193) - method Z-2 (Case IV - A12)
387: v(140,129) - method Z-5 (Case V,iv - A12)
388: v(105,97) - method S (Case V,ii - A12 for p=5)
389: v(420,389) - method Z-3 (Case V,iv - A12)
390: v(14,13) - method Z-2 (Case IV - A12)
391: v(420,391) - method Z-2 (Case V,iv - A12)
392: v(15,14) - method Z-3 (Case V,iv - A12)
393: v(140,131) - method Z-2 (Case V,iv - A12)
394: v(210,197) - method Z-2 (Case IV - A12)
395: v(84,79) - method Z-2 (Case V,iv - A12)
396: v(35,33) - method B (Case V,iii - A12)
397: v(420,397) - method S (Case V,ii - A12 for p=5)
398: v(210,199) - method Z-2 (Case IV - A12)
399: v(20,19) - method Z-2 (Case V,iv - A12)
400: v(21,20) - method Z-3 (Case V,iv - A12)
401: v(420,401) - method Z-3 (Case V,iv - A12)
402: v(70,67) - method Z-2 (Case IV - A12)
403: v(420,403) - method Z-2 (Case V,iv - A12)
404: v(105,101) - method Z-3 (Case V,iv - A12)
405: v(28,27) - method Z-2 (Case V,iv - A12)
406: v(30,29) - method Z-2 (Case IV - A12)
407: v(420,407) - method Z-2 (Case V,iv - A12)
408: v(35,34) - method Z-5 (Case V,iv - A12)
409: v(420,409) - method Z-5 (Case V,iv - A12)
410: v(42,41) - method Z-2 (Case IV - A12)
411: v(140,137) - method S (Case V,ii - A12 for p=5)
412: v(105,103) - method B (Case V,iii - A12)
413: v(60,59) - method Z-2 (Case V,iv - A12)
414: v(70,69) - method Z-2 (Case IV - A12)
415: v(84,83) - method Z-2 (Case V,iv - A12)
416: v(105,104) - method Z-3 (Case V,iv - A12)
417: v(140,139) - method Z-2 (Case V,iv - A12)
418: v(210,209) - method Z-2 (Case IV - A12)
419: v(420,419) - method Z-2 (Case V,iv - A12)
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© by: Marc Conrad, 2016. If you want me
to come to your organisation and talk about cyclotomic units please contact me.
The material on this page is presented "as is". There is no warranty implied by presenting this stuff.
Feel free to use and modify the material for your own teaching.
When doing so please link to this web site (http://perisic.com/cyclotomic).
In acadmic publications cite this page as: Conrad, Marc (2016)
Cyclotomic Units - Relations and Computations (online),
available at: http://perisic.com/cyclotomic.
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