Cyclotomic Unit Calculator

Definitions

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              11-1
v(140,1)       1     1-11 1-1-1 -1-1  1  -1  1      -1    1 1 
v(105,1) 1 1 1 -1           1-11 -1     -1  -1      -1    1 -1
v(84,1)      1   11    -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     -11     -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) 111  -1-31 -1  -1  1 -11 2 -1 -111-1-2  -2-11  1   -11 2-1-1
v(210,11)             -1   1     -1   -1                   
v(420,23) 1     -2  -11 -1 1 1-111  -1  1 -1-1  -1-11      -1111-1 
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 -11-11  1-1  11   11111-1 1  -1-1-1 1
v(14,1)                     -1                         
v(420,31)   -1-1  1 1     1-11-1  -11 1 -1-1 1  1-1-1-1-1   1  1-1-11
v(105,8)             1      -1               -1          
v(140,11)                 1          -1   -1              
v(210,17)                             -1         1       
v(420,37)   1 1 -1      -1    1-11 -1    -1-1  -1    1 -1    11-2
v(210,19)   1   -1         -1  -11   -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   -11-2 -1-12-111  1  12-11 -111 1-1-1-211
v(10,1)                   -1                           
v(420,43) 1     -1   1 -1   1 11  -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 11  -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   -11    1        
v(70,9)       1     1     -1     1      1   1        1 
v(84,11)  1        -1   -11    2                     -11  
v(15,2)                                         1     
v(140,19) 11    -1  -1  -111   1 11  -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       -1-11
v(84,13)  -1-1  1         -1    -1             -1       1   
v(70,11)                 1              -1              
v(420,67) -1     1 -1   1-11 1-1-1 -1-1  21 -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       -11-1 -11 1 11 -1  11 -1 1    1    -1-1-11
v(35,6) -1     1           -1 -1   1      1            1 
v(210,37)   1 1 -1         -1 1-11 -1     -1         -1    11-2
v(105,19)   1   -1         -1   1   -1 1 -1  -1           1 -1
v(60,11)     -11     -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 1-11  -11    -1 -11-11-1-11-1 11  -1  21 1-111  -1  11
v(5,1)                                               
v(84,17)           1    -1                           -1  
v(210,43) 1     -1   1 -1   1 11  -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)      -1-11    -1-1 11  1 -1-1  1 -1-1  -1 1 11   -11 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   -1-1-1-11 1    1 1 -1   -11    -11 
v(30,7)     1             2                     -1     
v(21,5)               1     -1                      -1  
v(420,101) 1 -1     111 -11-1-1 11  1-11-1-1-111 -11  -1  1-11    -1 
v(70,17)                         1          -1          
v(420,103) -1 -1 -1 1           -11-1 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 -1111-1-1 1-1 11  -1 -1   11-1
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 -11  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  12-1     11-1    -111  -1-112  1 -1 -1-1   1-1 -2-11
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  11 -1    1    1      1 
v(105,31) -1     1   -1 1   -1 -1   1        1 -1    1    -11 
v(10,3)                   1                           
v(420,127) 11 -1 -1-1 1-1       -11 11 1-1-1   1  -2   1-1  -11  -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 -11          -11 -1   11 -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           -11-1 1     1         1    -1 1
v(420,137)   1   -1 -1     -1 -1   1     1 -1    1 1       11-1
v(70,23) 1     -1           1 1   -1                   -1 
v(420,139)-1      1     1-11 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           -11-1 1     1              -1 1
v(420,143)   -1   1 1   -11-1  11  1  -1-1-111 -11 -1   1    -1-1-11
v(35,12)                                1              
v(84,29)  1   -1    -1   -11    1             1       -1   
v(210,73)   1   -1       -1 -1   1     1 -1    1 1       11-1
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) 11 -1             -11 11 1 -1 11   -1  -1 -1-1     -1 
v(210,79)     -1 -1           -11      1 -1    1 1  1 -1    1
v(21,8)   -1           -1                               
v(60,23)    -11      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)-111 -11   1     1 1-11-1 1-11 -1-1     -2-1-1-11-1-1  111-1-1
v(42,17)           1                                -1  
v(140,57)    1  -1     -11  -111     -11    -1-11    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              -1-11
v(420,179) -1 11    -1 -1 1 -11-11-1 1-11-1 11 -1   1 11  1-1  -1 1 
v(420,181)-11   1 -2 1 1 -1-1  1-11   -21   -1-1  -1-11-1 1 -1 -1112 -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   11  1     -1-1 1 
v(105,47)                           1                   
v(20,9)    -1              -1                           
v(42,19)   -1                                        1  
v(420,191) -1-1   12-1 1  1  -1-11-1-1-1 1  -1 11  11-1  -1   1-1 -11 
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  -11  -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)    -11-1     1      -1                           
v(35,17)                         1                     
v(84,41)   1  -1   -1     1                  1       -1   
v(210,103) -1 -1 -1 1           -11-1 1     1  1      1    -1 2
v(140,69) 1     -1     -11-1 -111 11  -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              11-1
v(2,1)                                               
v(420,211)-1  1 1              -1  -1     -1              11-1
v(105,53) 1     -1           1 1          -1      -1     -1 
v(140,71) 1     -1     -11-1 -111 11  -2  1  -1      1    -1 -1 
v(210,107) -1 -1 -1 1           -11-1 1     1  1      1    -1 2
v(84,43)   1  -1   -1     1                  1       -1   
v(60,31)    -11-1     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  -11  -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   12-1 1  1  -1-11-1-1-1 1  -1 11  11-1  -1   1-1 -11 
v(42,23)   -1                                        1  
v(20,11)    -1              -1                           
v(420,233)       1  1    -1  1       -1 1   11  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)-11   1 -2 1 1 -1-1  1-11   -21   -1-1  -1-11-1 1 -1 -1112 -1
v(7,4)                     1                         
v(420,241) -1 11    -1 -1 1 -11-11-1 1-11-1 11 -1   1 11  1-1  -1 1 
v(210,121)   -1   1     -1 1 1  1-1     -1 1              -1-11
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     -11  -111     -11    -1-11    1      -1 
v(42,25)           1                                -1  
v(420,251)-111 -11   1     1 1-11-1 1-11 -1-1     -2-1-1-11-1-1  111-1-1
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)    -11      1      1           -1         -1     
v(21,13)   -1           -1                               
v(140,87)                  1                            
v(210,131)     -1 -1           -11      1 -1    1 1  1 -1    1
v(420,263) 11 -1             -11 11 1 -1 11   -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       11-1
v(84,55)  1   -1    -1   -11    1             1       -1   
v(420,277)   -1   1 1   -11-1  11  1  -1-1-111 -11 -1   1    -1-1-11
v(210,139)   -1 -1 1           -11-1 1     1              -1 1
v(3,2)                                               
v(420,281)-1      1     1-11 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       11-1
v(105,71)   -1 -1 1           -11-1 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 -11          -11 -1   11 -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) 11 -1 -1-1 1-1       -11 11 1-1-1   1  -2   1-1  -11  -1 
v(10,7)                   1                           
v(84,59)                1                              
v(105,74) -1     1   -1 1   -1 -1   1        1 -1    1    -11 
v(140,99) -1-1 1              -1 -1-1  11 -1    1    1      1 
v(210,149)     1 1     1 1    -1    1 -1 1    -1 -1  -1 1    -1
v(420,299)   -1  12-1     11-1    -111  -1-112  1 -1 -1-1   1-1 -2-11
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 -11  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 -1111-1-1 1-1 11  -1 -1   11-1
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           -11-1 1     1  1    -1 1    -1 2
v(70,53)                         1          -1          
v(420,319) 1 -1     111 -11-1-1 11  1-11-1-1-111 -11  -1  1-11    -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   -1-1-1-11 1    1 1 -1   -11    -11 
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)      -1-11    -1-1 11  1 -1-1  1 -1-1  -1 1 11   -11 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 11  -1        -1 1    -1    1-1 
v(84,67)           1    -1                           -1  
v(5,4)                                               
v(420,337) -1-1 1-11  -11    -1 -11-11-1-11-1 11  -1  21 1-111  -1  11
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)     -11     -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 1-11 -1     -1         -1    11-2
v(420,347)         1                                     
v(35,29) -1     1           -1 -1   1      1            1 
v(420,349)1  -1 -1       -11-1 -11 1 11 -1  11 -1 1    1    -1-1-11
v(6,5)                                               
v(140,117) 1     -1           1 1   -1       -1           -1 
v(420,353) -1     1 -1   1-11 1-1-1 -1-1  21 -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       -1-11
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) 11    -1  -1  -111   1 11  -1      -1-1  -1        -2 
v(84,73)  1        -1   -11    2                     -11  
v(70,61)       1     1     -1     1      1   1        1 
v(420,367)  -1 1             1   -1 -1 1 -1   -11    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 11  -1     -1    1 1    -1  1  
v(105,94)             -1   1     -1                       
v(420,377) 1     -1   1 -1   1 11  -1      -1 -1 1    -1    1-1 
v(10,9)                   -1                           
v(420,379)1-2-1 1-1 2 -1 -1 1   -11-2 -1-12-111  1  12-11 -111 1-1-1-211
v(140,127)    -1         -1   -1       -1    1 -1    -1        
v(210,191)   1   -1         -1  -11   -1 1 -1  -1           1 -1
v(420,383)   1 1 -1      -1    1-11 -1    -1-1  -1    1 -1    11-2
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     1-11-1  -11 1 -1-1 1  1-1-1-1-1   1  1-1-11
v(14,13)                     -1                         
v(420,391)1    -1   -1    1-1 -11-11  1-1  11   11111-1 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  -11 -1 1 1-111  -1  1 -1-1  -1-11      -1111-1 
v(210,199)             -1   1     -1   -1                   
v(20,19)    1                                          
v(21,20)   1                                           
v(420,401) 111  -1-31 -1  -1  1 -11 2 -1 -111-1-2  -2-11  1   -11 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     -11     -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   11    -1    -1             -1       1   
v(105,104) 1 1 1 -1           1-11 -1     -1  -1      -1    1 -1
v(140,139)       1     1-11 1-1-1 -1-1  1  -1  1      -1    1 1 
v(210,209)   1 1              -1  -1     -1              11-1
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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