Editing Quadratic residue (section)

==Table of quadratic residues==

The following table {{OEIS|id=A096008}} lists the quadratic residues mod 1 to 75 (a {{color|crimson|red number}} means it is not coprime to ''n''). (For the quadratic residues coprime to ''n'', see {{oeis|id=A096103}}, and for nonzero quadratic residues, see {{oeis|id=A046071}}.)

{| class="wikitable"
!''n''
!quadratic residues mod ''n''
!''n''
!quadratic residues mod ''n''
!''n''
!quadratic residues mod ''n''
|-
|1
|0
|26
|{{color|crimson|0}}, 1, 3, {{color|crimson|4}}, 9, {{color|crimson|10}}, {{color|crimson|12}}, {{color|crimson|13}}, {{color|crimson|14}}, {{color|crimson|16}}, 17, {{color|crimson|22}}, 23, 25
|51
|{{color|crimson|0}}, 1, 4, {{color|crimson|9}}, 13, {{color|crimson|15}}, 16, {{color|crimson|18}}, 19, {{color|crimson|21}}, 25, {{color|crimson|30}}, {{color|crimson|33}}, {{color|crimson|34}}, {{color|crimson|36}}, {{color|crimson|42}}, 43, 49
|-
|2
|{{color|crimson|0}}, 1
|27
|{{color|crimson|0}}, 1, 4, 7, {{color|crimson|9}}, 10, 13, 16, 19, 22, 25
|52
|{{color|crimson|0}}, 1, {{color|crimson|4}}, 9, {{color|crimson|12}}, {{color|crimson|13}}, {{color|crimson|16}}, 17, 25, 29, {{color|crimson|36}}, {{color|crimson|40}}, {{color|crimson|48}}, 49
|-
|3
|{{color|crimson|0}}, 1
|28
|{{color|crimson|0}}, 1, {{color|crimson|4}}, {{color|crimson|8}}, 9, {{color|crimson|16}}, {{color|crimson|21}}, 25
|53
|{{color|crimson|0}}, 1, 4, 6, 7, 9, 10, 11, 13, 15, 16, 17, 24, 25, 28, 29, 36, 37, 38, 40, 42, 43, 44, 46, 47, 49, 52
|-
|4
|{{color|crimson|0}}, 1
|29
|{{color|crimson|0}}, 1, 4, 5, 6, 7, 9, 13, 16, 20, 22, 23, 24, 25, 28
|54
|{{color|crimson|0}}, 1, {{color|crimson|4}}, 7, {{color|crimson|9}}, {{color|crimson|10}}, 13, {{color|crimson|16}}, 19, {{color|crimson|22}}, 25, {{color|crimson|27}}, {{color|crimson|28}}, 31, {{color|crimson|34}}, {{color|crimson|36}}, 37, {{color|crimson|40}}, 43, {{color|crimson|46}}, 49, {{color|crimson|52}}
|-
|5
|{{color|crimson|0}}, 1, 4
|30
|{{color|crimson|0}}, 1, {{color|crimson|4}}, {{color|crimson|6}}, {{color|crimson|9}}, {{color|crimson|10}}, {{color|crimson|15}}, {{color|crimson|16}}, 19, {{color|crimson|21}}, {{color|crimson|24}}, {{color|crimson|25}}
|55
|{{color|crimson|0}}, 1, 4, {{color|crimson|5}}, 9, {{color|crimson|11}}, 14, {{color|crimson|15}}, 16, {{color|crimson|20}}, {{color|crimson|25}}, 26, 31, 34, 36, {{color|crimson|44}}, {{color|crimson|45}}, 49
|-
|6
|{{color|crimson|0}}, 1, {{color|crimson|3}}, {{color|crimson|4}}
|31
|{{color|crimson|0}}, 1, 2, 4, 5, 7, 8, 9, 10, 14, 16, 18, 19, 20, 25, 28
|56
|{{color|crimson|0}}, 1, {{color|crimson|4}}, {{color|crimson|8}}, 9, {{color|crimson|16}}, 25, {{color|crimson|28}}, {{color|crimson|32}}, {{color|crimson|36}}, {{color|crimson|44}}, {{color|crimson|49}}
|-
|7
|{{color|crimson|0}}, 1, 2, 4
|32
|{{color|crimson|0}}, 1, {{color|crimson|4}}, 9, {{color|crimson|16}}, 17, 25
|57
|{{color|crimson|0}}, 1, 4, {{color|crimson|6}}, 7, {{color|crimson|9}}, 16, {{color|crimson|19}}, {{color|crimson|24}}, 25, 28, {{color|crimson|30}}, {{color|crimson|36}}, {{color|crimson|39}}, {{color|crimson|42}}, 43, {{color|crimson|45}}, 49, {{color|crimson|54}}, 55
|-
|8
|{{color|crimson|0}}, 1, {{color|crimson|4}}
|33
|{{color|crimson|0}}, 1, {{color|crimson|3}}, 4, {{color|crimson|9}}, {{color|crimson|12}}, {{color|crimson|15}}, 16, {{color|crimson|22}}, 25, {{color|crimson|27}}, 31
|58
|{{color|crimson|0}}, 1, {{color|crimson|4}}, 5, {{color|crimson|6}}, 7, 9, 13, {{color|crimson|16}}, {{color|crimson|20}}, {{color|crimson|22}}, 23, {{color|crimson|24}}, 25, {{color|crimson|28}}, {{color|crimson|29}}, {{color|crimson|30}}, 33, {{color|crimson|34}}, 35, {{color|crimson|36}}, {{color|crimson|38}}, {{color|crimson|42}}, 45, 49, 51, {{color|crimson|52}}, 53, {{color|crimson|54}}, 57
|-
|9
|{{color|crimson|0}}, 1, 4, 7
|34
|{{color|crimson|0}}, 1, {{color|crimson|2}}, {{color|crimson|4}}, {{color|crimson|8}}, 9, 13, 15, {{color|crimson|16}}, {{color|crimson|17}}, {{color|crimson|18}}, 19, 21, 25, {{color|crimson|26}}, {{color|crimson|30}}, {{color|crimson|32}}, 33
|59
|{{color|crimson|0}}, 1, 3, 4, 5, 7, 9, 12, 15, 16, 17, 19, 20, 21, 22, 25, 26, 27, 28, 29, 35, 36, 41, 45, 46, 48, 49, 51, 53, 57
|-
|10
|{{color|crimson|0}}, 1, {{color|crimson|4}}, {{color|crimson|5}}, {{color|crimson|6}}, 9
|35
|{{color|crimson|0}}, 1, 4, 9, 11, {{color|crimson|14}}, {{color|crimson|15}}, 16, {{color|crimson|21}}, {{color|crimson|25}}, 29, {{color|crimson|30}}
|60
|{{color|crimson|0}}, 1, {{color|crimson|4}}, {{color|crimson|9}}, {{color|crimson|16}}, {{color|crimson|21}}, {{color|crimson|24}}, {{color|crimson|25}}, {{color|crimson|36}}, {{color|crimson|40}}, {{color|crimson|45}}, 49
|-
|11
|{{color|crimson|0}}, 1, 3, 4, 5, 9
|36
|{{color|crimson|0}}, 1, {{color|crimson|4}}, {{color|crimson|9}}, 13, {{color|crimson|16}}, 25, {{color|crimson|28}}
|61
|{{color|crimson|0}}, 1, 3, 4, 5, 9, 12, 13, 14, 15, 16, 19, 20, 22, 25, 27, 34, 36, 39, 41, 42, 45, 46, 47, 48, 49, 52, 56, 57, 58, 60
|-
|12
|{{color|crimson|0}}, 1, {{color|crimson|4}}, {{color|crimson|9}}
|37
|{{color|crimson|0}}, 1, 3, 4, 7, 9, 10, 11, 12, 16, 21, 25, 26, 27, 28, 30, 33, 34, 36
|62
|{{color|crimson|0}}, 1, {{color|crimson|2}}, {{color|crimson|4}}, 5, 7, {{color|crimson|8}}, 9, {{color|crimson|10}}, {{color|crimson|14}}, {{color|crimson|16}}, {{color|crimson|18}}, 19, {{color|crimson|20}}, 25, {{color|crimson|28}}, {{color|crimson|31}}, {{color|crimson|32}}, 33, 35, {{color|crimson|36}}, {{color|crimson|38}}, 39, {{color|crimson|40}}, 41, 45, 47, 49, {{color|crimson|50}}, 51, {{color|crimson|56}}, 59
|-
|13
|{{color|crimson|0}}, 1, 3, 4, 9, 10, 12
|38
|{{color|crimson|0}}, 1, {{color|crimson|4}}, 5, {{color|crimson|6}}, 7, 9, 11, {{color|crimson|16}}, 17, {{color|crimson|19}}, {{color|crimson|20}}, 23, {{color|crimson|24}}, 25, {{color|crimson|26}}, {{color|crimson|28}}, {{color|crimson|30}}, 35, {{color|crimson|36}}
|63
|{{color|crimson|0}}, 1, 4, {{color|crimson|7}}, {{color|crimson|9}}, 16, {{color|crimson|18}}, 22, 25, {{color|crimson|28}}, {{color|crimson|36}}, 37, 43, 46, {{color|crimson|49}}, 58
|-
|14
|{{color|crimson|0}}, 1, {{color|crimson|2}}, {{color|crimson|4}}, {{color|crimson|7}}, {{color|crimson|8}}, 9, 11
|39
|{{color|crimson|0}}, 1, {{color|crimson|3}}, 4, {{color|crimson|9}}, 10, {{color|crimson|12}}, {{color|crimson|13}}, 16, 22, 25, {{color|crimson|27}}, {{color|crimson|30}}, {{color|crimson|36}}
|64
|{{color|crimson|0}}, 1, {{color|crimson|4}}, 9, {{color|crimson|16}}, 17, 25, 33, {{color|crimson|36}}, 41, 49, 57
|-
|15
|{{color|crimson|0}}, 1, 4, {{color|crimson|6}}, {{color|crimson|9}}, {{color|crimson|10}}
|40
|{{color|crimson|0}}, 1, {{color|crimson|4}}, 9, {{color|crimson|16}}, {{color|crimson|20}}, {{color|crimson|24}}, {{color|crimson|25}}, {{color|crimson|36}}
|65
|{{color|crimson|0}}, 1, 4, 9, {{color|crimson|10}}, 14, 16, {{color|crimson|25}}, {{color|crimson|26}}, 29, {{color|crimson|30}}, {{color|crimson|35}}, 36, {{color|crimson|39}}, {{color|crimson|40}}, 49, 51, {{color|crimson|55}}, 56, 61, 64
|-
|16
|{{color|crimson|0}}, 1, {{color|crimson|4}}, 9
|41
|{{color|crimson|0}}, 1, 2, 4, 5, 8, 9, 10, 16, 18, 20, 21, 23, 25, 31, 32, 33, 36, 37, 39, 40
|66
|{{color|crimson|0}}, 1, {{color|crimson|3}}, {{color|crimson|4}}, {{color|crimson|9}}, {{color|crimson|12}}, {{color|crimson|15}}, {{color|crimson|16}}, {{color|crimson|22}}, 25, {{color|crimson|27}}, 31, {{color|crimson|33}}, {{color|crimson|34}}, {{color|crimson|36}}, 37, {{color|crimson|42}}, {{color|crimson|45}}, {{color|crimson|48}}, 49, {{color|crimson|55}}, {{color|crimson|58}}, {{color|crimson|60}}, {{color|crimson|64}}
|-
|17
|{{color|crimson|0}}, 1, 2, 4, 8, 9, 13, 15, 16
|42
|{{color|crimson|0}}, 1, {{color|crimson|4}}, {{color|crimson|7}}, {{color|crimson|9}}, {{color|crimson|15}}, {{color|crimson|16}}, {{color|crimson|18}}, {{color|crimson|21}}, {{color|crimson|22}}, 25, {{color|crimson|28}}, {{color|crimson|30}}, {{color|crimson|36}}, 37, {{color|crimson|39}}
|67
|{{color|crimson|0}}, 1, 4, 6, 9, 10, 14, 15, 16, 17, 19, 21, 22, 23, 24, 25, 26, 29, 33, 35, 36, 37, 39, 40, 47, 49, 54, 55, 56, 59, 60, 62, 64, 65
|-
|18
|{{color|crimson|0}}, 1, {{color|crimson|4}}, 7, {{color|crimson|9}}, {{color|crimson|10}}, 13, {{color|crimson|16}}
|43
|{{color|crimson|0}}, 1, 4, 6, 9, 10, 11, 13, 14, 15, 16, 17, 21, 23, 24, 25, 31, 35, 36, 38, 40, 41
|68
|{{color|crimson|0}}, 1, {{color|crimson|4}}, {{color|crimson|8}}, 9, 13, {{color|crimson|16}}, {{color|crimson|17}}, 21, 25, {{color|crimson|32}}, 33, {{color|crimson|36}}, 49, {{color|crimson|52}}, 53, {{color|crimson|60}}, {{color|crimson|64}}
|-
|19
|{{color|crimson|0}}, 1, 4, 5, 6, 7, 9, 11, 16, 17
|44
|{{color|crimson|0}}, 1, {{color|crimson|4}}, 5, 9, {{color|crimson|12}}, {{color|crimson|16}}, {{color|crimson|20}}, 25, {{color|crimson|33}}, {{color|crimson|36}}, 37
|69
|{{color|crimson|0}}, 1, {{color|crimson|3}}, 4, {{color|crimson|6}}, {{color|crimson|9}}, {{color|crimson|12}}, 13, 16, {{color|crimson|18}}, {{color|crimson|24}}, 25, {{color|crimson|27}}, 31, {{color|crimson|36}}, {{color|crimson|39}}, {{color|crimson|46}}, {{color|crimson|48}}, 49, 52, {{color|crimson|54}}, 55, 58, 64
|-
|20
|{{color|crimson|0}}, 1, {{color|crimson|4}}, {{color|crimson|5}}, 9, {{color|crimson|16}}
|45
|{{color|crimson|0}}, 1, 4, {{color|crimson|9}}, {{color|crimson|10}}, 16, 19, {{color|crimson|25}}, 31, 34, {{color|crimson|36}}, {{color|crimson|40}}
|70
|{{color|crimson|0}}, 1, {{color|crimson|4}}, 9, 11, {{color|crimson|14}}, {{color|crimson|15}}, {{color|crimson|16}}, {{color|crimson|21}}, {{color|crimson|25}}, 29, {{color|crimson|30}}, {{color|crimson|35}}, {{color|crimson|36}}, 39, {{color|crimson|44}}, {{color|crimson|46}}, {{color|crimson|49}}, {{color|crimson|50}}, 51, {{color|crimson|56}}, {{color|crimson|60}}, {{color|crimson|64}}, {{color|crimson|65}}
|-
|21
|{{color|crimson|0}}, 1, 4, {{color|crimson|7}}, {{color|crimson|9}}, {{color|crimson|15}}, 16, {{color|crimson|18}}
|46
|{{color|crimson|0}}, 1, {{color|crimson|2}}, 3, {{color|crimson|4}}, {{color|crimson|6}}, {{color|crimson|8}}, 9, {{color|crimson|12}}, 13, {{color|crimson|16}}, {{color|crimson|18}}, {{color|crimson|23}}, {{color|crimson|24}}, 25, {{color|crimson|26}}, 27, 29, 31, {{color|crimson|32}}, 35, {{color|crimson|36}}, 39, 41
|71
|{{color|crimson|0}}, 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 19, 20, 24, 25, 27, 29, 30, 32, 36, 37, 38, 40, 43, 45, 48, 49, 50, 54, 57, 58, 60, 64
|-
|22
|{{color|crimson|0}}, 1, 3, {{color|crimson|4}}, 5, 9, {{color|crimson|11}}, {{color|crimson|12}}, {{color|crimson|14}}, 15, {{color|crimson|16}}, {{color|crimson|20}}
|47
|{{color|crimson|0}}, 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 17, 18, 21, 24, 25, 27, 28, 32, 34, 36, 37, 42
|72
|{{color|crimson|0}}, 1, {{color|crimson|4}}, {{color|crimson|9}}, {{color|crimson|16}}, 25, {{color|crimson|28}}, {{color|crimson|36}}, {{color|crimson|40}}, 49, {{color|crimson|52}}, {{color|crimson|64}}
|-
|23
|{{color|crimson|0}}, 1, 2, 3, 4, 6, 8, 9, 12, 13, 16, 18
|48
|{{color|crimson|0}}, 1, {{color|crimson|4}}, {{color|crimson|9}}, {{color|crimson|16}}, 25, {{color|crimson|33}}, {{color|crimson|36}}
|73
|{{color|crimson|0}}, 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 19, 23, 24, 25, 27, 32, 35, 36, 37, 38, 41, 46, 48, 49, 50, 54, 55, 57, 61, 64, 65, 67, 69, 70, 71, 72
|-
|24
|{{color|crimson|0}}, 1, {{color|crimson|4}}, {{color|crimson|9}}, {{color|crimson|12}}, {{color|crimson|16}}
|49
|{{color|crimson|0}}, 1, 2, 4, 8, 9, 11, 15, 16, 18, 22, 23, 25, 29, 30, 32, 36, 37, 39, 43, 44, 46
|74
|{{color|crimson|0}}, 1, 3, {{color|crimson|4}}, 7, 9, {{color|crimson|10}}, 11, {{color|crimson|12}}, {{color|crimson|16}}, 21, 25, {{color|crimson|26}}, 27, {{color|crimson|28}}, {{color|crimson|30}}, 33, {{color|crimson|34}}, {{color|crimson|36}}, {{color|crimson|37}}, {{color|crimson|38}}, {{color|crimson|40}}, 41, {{color|crimson|44}}, {{color|crimson|46}}, 47, {{color|crimson|48}}, 49, 53, {{color|crimson|58}}, {{color|crimson|62}}, 63, {{color|crimson|64}}, 65, 67, {{color|crimson|70}}, 71, 73
|-
|25
|{{color|crimson|0}}, 1, 4, 6, 9, 11, 14, 16, 19, 21, 24
|50
|{{color|crimson|0}}, 1, {{color|crimson|4}}, {{color|crimson|6}}, 9, 11, {{color|crimson|14}}, {{color|crimson|16}}, 19, 21, {{color|crimson|24}}, {{color|crimson|25}}, {{color|crimson|26}}, 29, 31, {{color|crimson|34}}, {{color|crimson|36}}, 39, 41, {{color|crimson|44}}, {{color|crimson|46}}, 49
|75
|{{color|crimson|0}}, 1, 4, {{color|crimson|6}}, {{color|crimson|9}}, 16, 19, {{color|crimson|21}}, {{color|crimson|24}}, {{color|crimson|25}}, 31, 34, {{color|crimson|36}}, {{color|crimson|39}}, 46, 49, {{color|crimson|51}}, {{color|crimson|54}}, 61, 64, {{color|crimson|66}}, {{color|crimson|69}}
|}

{| class="wikitable" style="text-align:right;"
|+ Quadratic Residues (see also {{OEIS link|A048152}}, {{OEIS link|A343720}})
|-style="text-align:right;"
! ''x'' || 1||2|| 3|| 4||5|| 6|| 7|| 8 ||9 ||10|| 11|| 12|| 13|| 14 ||15|| 16|| 17|| 18 ||19|| 20|| 21|| 22|| 23|| 24 ||25
|-style="text-align:right;"
! ''x''<sup>2</sup>
! style="width:25px;"|1
! style="width:25px;"|4
! style="width:25px;"|9
! style="width:25px;"|16
! style="width:25px;"|25
! style="width:25px;"|36
! style="width:25px;"|49
! style="width:25px;"|64
! style="width:25px;"|81
!100|| 121|| 144|| 169|| 196 ||225|| 256|| 289|| 324 ||361 || 400|| 441|| 484|| 529|| 576 ||625
|-
! mod 1
| 0 || 0 || 0 || 0 || 0
| 0 || 0 || 0 || 0 || 0
| 0 || 0 || 0 || 0 || 0
| 0 || 0 || 0 || 0 || 0
| 0 || 0 || 0 || 0 || 0
|-
! mod 2
| 1 || 0
| 1 || 0
| 1 || 0
| 1 || 0
| 1 || 0
| 1 || 0
| 1 || 0
| 1 || 0
| 1 || 0
| 1 || 0
| 1 || 0
| 1 || 0
| 1
|-
! mod 3
| 1 || 1 || 0
| 1 || 1 || 0
| 1 || 1 || 0
| 1 || 1 || 0
| 1 || 1 || 0
| 1 || 1 || 0
| 1 || 1 || 0
| 1 || 1 || 0
| 1
|-
! mod 4
| 1 || 0
| 1 || 0
| 1 || 0
| 1 || 0
| 1 || 0
| 1 || 0
| 1 || 0
| 1 || 0
| 1 || 0
| 1 || 0
| 1 || 0
| 1 || 0
| 1
|-
! mod 5
| 1 || 4 || 4 || 1 || 0
| 1 || 4 || 4 || 1 || 0
| 1 || 4 || 4 || 1 || 0
| 1 || 4 || 4 || 1 || 0
| 1 || 4 || 4 || 1 || 0
|-

! mod 6
| 1 || 4 || 3 || 4 || 1 || 0
| 1 || 4 || 3 || 4 || 1 || 0
| 1 || 4 || 3 || 4 || 1 || 0
| 1 || 4 || 3 || 4 || 1 || 0
| 1
|-
! mod 7
| 1 || 4 || 2 || 2 || 4 || 1 || 0
| 1 || 4 || 2 || 2 || 4 || 1 || 0
| 1 || 4 || 2 || 2 || 4 || 1 || 0
| 1 || 4 || 2 || 2
|-

! mod 8
| 1 || 4 || 1 || 0
| 1 || 4 || 1 || 0
| 1 || 4 || 1 || 0
| 1 || 4 || 1 || 0
| 1 || 4 || 1 || 0
| 1 || 4 || 1 || 0
| 1
|-

! mod 9
| 1 || 4 || 0 || 7 || 7 || 0 || 4 || 1 || 0
| 1 || 4 || 0 || 7 || 7 || 0 || 4 || 1 || 0
| 1 || 4 || 0 || 7 || 7 || 0 || 4
|-

! mod 10
| 1 || 4 || 9 || 6 || 5 || 6 || 9 || 4 || 1 || 0
| 1 || 4 || 9 || 6 || 5 || 6 || 9 || 4 || 1 || 0
| 1 || 4 || 9 || 6 || 5
|-

! mod 11
| 1 || 4 || 9 || 5 || 3 || 3 || 5 || 9 || 4 || 1 || 0
| 1 || 4 || 9 || 5 || 3 || 3 || 5 || 9 || 4 || 1 || 0
| 1 || 4 || 9
|-

! mod 12
| 1 || 4 || 9 || 4 || 1 || 0
| 1 || 4 || 9 || 4 || 1 || 0
| 1 || 4 || 9 || 4 || 1 || 0
| 1 || 4 || 9 || 4 || 1 || 0
| 1
|-

! mod 13
| 1 || 4 || 9 || 3 || 12 || 10 || 10 || 12 || 3 || 9 || 4 || 1 || 0
| 1 || 4 || 9 || 3 || 12 || 10 || 10 || 12 || 3 || 9 || 4 || 1
|-

! mod 14
| 1 || 4 || 9 || 2 || 11 || 8 || 7 || 8 || 11 || 2 || 9 || 4 || 1 || 0
| 1 || 4 || 9 || 2 || 11 || 8 || 7 || 8 || 11 || 2 || 9
|-

! mod 15
| 1 || 4 || 9 || 1 || 10 || 6 || 4 || 4 || 6 || 10 || 1 || 9 || 4 || 1 || 0
| 1 || 4 || 9 || 1 || 10 || 6 || 4 || 4 || 6 || 10
|-

! mod 16
| 1 || 4 || 9 || 0 || 9 || 4 || 1 || 0
| 1 || 4 || 9 || 0 || 9 || 4 || 1 || 0
| 1 || 4 || 9 || 0 || 9 || 4 || 1 || 0
| 1
|-

! mod 17
| 1 || 4 || 9 || 16 || 8 || 2 || 15 || 13 || 13 || 15 || 2 || 8 || 16 || 9 || 4 || 1 || 0
| 1 || 4 || 9 || 16 || 8 || 2 || 15 || 13
|-

! mod 18
| 1 || 4 || 9 || 16 || 7 || 0 || 13 || 10 || 9 || 10 || 13 || 0 || 7 || 16 || 9 || 4 || 1 || 0
| 1 || 4 || 9 || 16 || 7 || 0 || 13
|-

! mod 19
| 1 || 4 || 9 || 16 || 6 || 17 || 11 || 7 || 5 || 5 || 7 || 11 || 17 || 6 || 16 || 9 || 4 || 1 || 0
| 1 || 4 || 9 || 16 || 6 || 17
|-

! mod 20
| 1 || 4 || 9 || 16 || 5 || 16 || 9 || 4 || 1 || 0
| 1 || 4 || 9 || 16 || 5 || 16 || 9 || 4 || 1 || 0
| 1 || 4 || 9 || 16 || 5
|-

! mod 21
| 1 || 4 || 9 || 16 || 4 || 15 || 7 || 1 || 18 || 16 || 16 || 18 || 1 || 7 || 15 || 4 || 16 || 9 || 4 || 1 || 0
| 1 || 4 || 9 || 16
|-

! mod 22
| 1 || 4 || 9 || 16 || 3 || 14 || 5 || 20 || 15 || 12 || 11 || 12 || 15 ||  20 || 5 || 14 || 3 || 16 ||  9 || 4 || 1 || 0
| 1 || 4 || 9
|-

! mod 23
| 1 || 4 || 9 || 16 || 2 || 13 || 3 || 18 || 12 || 8 || 6 || 6 || 8 || 12 ||18 || 3 || 13 || 2 || 16 || 9 || 4 || 1 || 0
| 1 || 4
|-

! mod 24
| 1 || 4 || 9 || 16 || 1 || 12 || 1 || 16 || 9 || 4 || 1 || 0
| 1 || 4 || 9 || 16 || 1 || 12 || 1 || 16 || 9 || 4 || 1 || 0
| 1
|-

! mod 25
| 1 || 4 || 9 || 16 || 0 || 11 || 24 || 14 || 6 || 0 || 21 || 19  || 19 || 21 || 0 || 6 || 14 || 24 || 11 || 0 || 16 || 9 || 4 || 1 || 0
|}