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Table A.8: Coefficients for d = 8, normalized by (1/6561) = (1/3 8 )4ˆ 8 4ˆ 7 4ˆ 6 4ˆ 5 4ˆ 4 4ˆ 3 4ˆ 2 4ˆ 1 4ˆ 0(7, 0, 0, 0, 0, 0, 0, 0) −1/2520 (7, 0, 0, 0, 0, 0, 0) 1/2520 (7, 0, 0, 0, 0, 0) −1/2520 (7, 0, 0, 0, 0) 1/2520 (7, 0, 0, 0) −1/2520 (7, 0, 0) 1/2520 (7, 0) −1/2520 (7, ) 1/2520(6, 1, 0, 0, 0, 0, 0, 0) −1/360 (6, 1, 0, 0, 0, 0, 0) 1/360 (6, 1, 0, 0, 0, 0) −1/360 (6, 1, 0, 0, 0) 1/360 (6, 1, 0, 0) −1/360 (6, 1, 0) 1/360 (6, 1) −1/360(5, 2, 0, 0, 0, 0, 0, 0) −1/120 (5, 2, 0, 0, 0, 0, 0) 1/120 (5, 2, 0, 0, 0, 0) −1/120 (5, 2, 0, 0, 0) 1/120 (5, 2, 0, 0) −1/120 (5, 2, 0) 1/120 (5, 2) −1/120(4, 3, 0, 0, 0, 0, 0, 0) −1/72 (4, 3, 0, 0, 0, 0, 0) 1/72 (4, 3, 0, 0, 0, 0) −1/72 (4, 3, 0, 0, 0) 1/72 (4, 3, 0, 0) −1/72 (4, 3, 0) 1/72 (4, 3) −1/72(4, 2, 1, 0, 0, 0, 0, 0) −1/24 (4, 2, 1, 0, 0, 0, 0) 1/24 (4, 2, 1, 0, 0, 0) −1/24 (4, 2, 1, 0, 0) 1/24 (4, 2, 1, 0) −1/24 (4, 2, 1) 1/24(3, 3, 1, 0, 0, 0, 0, 0) −1/18 (3, 3, 1, 0, 0, 0, 0) 1/18 (3, 3, 1, 0, 0, 0) −1/18 (3, 3, 1, 0, 0) 1/18 (3, 3, 1, 0) −1/18 (3, 3, 1) 1/18(3, 2, 2, 0, 0, 0, 0, 0) −1/12 (3, 2, 2, 0, 0, 0, 0) 1/12 (3, 2, 2, 0, 0, 0) −1/12 (3, 2, 2, 0, 0) 1/12 (3, 2, 2, 0) −1/12 (3, 2, 2) 1/12(3, 2, 1, 1, 0, 0, 0, 0) −1/6 (3, 2, 1, 1, 0, 0, 0) 1/6 (3, 2, 1, 1, 0, 0) −1/6 (3, 2, 1, 1, 0) 1/6 (3, 2, 1, 1) −1/6(2, 2, 2, 1, 0, 0, 0, 0) −1/4 (2, 2, 2, 1, 0, 0, 0) 1/4 (2, 2, 2, 1, 0, 0) −1/4 (2, 2, 2, 1, 0) 1/4 (2, 2, 2, 1) −1/4(2, 2, 1, 1, 1, 0, 0, 0) −1/2 (2, 2, 1, 1, 1, 0, 0) 1/2 (2, 2, 1, 1, 1, 0) −1/2 (2, 2, 1, 1, 1) 1/2(2, 1, 1, 1, 1, 1, 0, 0) −1 (2, 1, 1, 1, 1, 1, 0) 1 (2, 1, 1, 1, 1, 1) −1(1, 1, 1, 1, 1, 1, 1, 0) −2 (1, 1, 1, 1, 1, 1, 1) 2(6, 0, 0, 0, 0, 0, 0, 0) 49/1080 (6, 0, 0, 0, 0, 0, 0) −1/27 (6, 0, 0, 0, 0, 0) 31/1080 (6, 0, 0, 0, 0) −11/540 (6, 0, 0, 0) 13/1080 (6, 0, 0) −1/270 (6, 0) −1/216 (6, ) 7/540(5, 1, 0, 0, 0, 0, 0, 0) 49/180 (5, 1, 0, 0, 0, 0, 0) −2/9 (5, 1, 0, 0, 0, 0) 31/180 (5, 1, 0, 0, 0) −11/90 (5, 1, 0, 0) 13/180 (5, 1, 0) −1/45 (5, 1) −1/36(4, 2, 0, 0, 0, 0, 0, 0) 49/72 (4, 2, 0, 0, 0, 0, 0) −5/9 (4, 2, 0, 0, 0, 0) 31/72 (4, 2, 0, 0, 0) −11/36 (4, 2, 0, 0) 13/72 (4, 2, 0) −1/18 (4, 2) −5/72(4, 1, 1, 0, 0, 0, 0, 0) 49/36 (4, 1, 1, 0, 0, 0, 0) −10/9 (4, 1, 1, 0, 0, 0) 31/36 (4, 1, 1, 0, 0) −11/18 (4, 1, 1, 0) 13/36 (4, 1, 1) −1/9 (3, 3) −5/54(3, 3, 0, 0, 0, 0, 0, 0) 49/54 (3, 3, 0, 0, 0, 0, 0) −20/27 (3, 3, 0, 0, 0, 0) 31/54 (3, 3, 0, 0, 0) −11/27 (3, 3, 0, 0) 13/54 (3, 3, 0) −2/27(3, 2, 1, 0, 0, 0, 0, 0) 49/18 (3, 2, 1, 0, 0, 0, 0) −20/9 (3, 2, 1, 0, 0, 0) 31/18 (3, 2, 1, 0, 0) −11/9 (3, 2, 1, 0) 13/18 (3, 2, 1) −2/9(3, 1, 1, 1, 0, 0, 0, 0) 49/9 (3, 1, 1, 1, 0, 0, 0) −40/9 (3, 1, 1, 1, 0, 0) 31/9 (3, 1, 1, 1, 0) −22/9 (3, 1, 1, 1) 13/9 (2, 2, 2) −1/3(2, 2, 2, 0, 0, 0, 0, 0) 49/12 (2, 2, 2, 0, 0, 0, 0) −10/3 (2, 2, 2, 0, 0, 0) 31/12 (2, 2, 2, 0, 0) −11/6 (2, 2, 2, 0) 13/12(2, 2, 1, 1, 0, 0, 0, 0) 49/6 (2, 2, 1, 1, 0, 0, 0) −20/3 (2, 2, 1, 1, 0, 0) 31/6 (2, 2, 1, 1, 0) −11/3 (2, 2, 1, 1) 13/6(2, 1, 1, 1, 1, 0, 0, 0) 49/3 (2, 1, 1, 1, 1, 0, 0) −40/3 (2, 1, 1, 1, 1, 0) 31/3 (2, 1, 1, 1, 1) −22/3(1, 1, 1, 1, 1, 1, 0, 0) 98/3 (1, 1, 1, 1, 1, 1, 0) −80/3 (1, 1, 1, 1, 1, 1) 62/3(5, 0, 0, 0, 0, 0, 0, 0) −719/360 (5, 0, 0, 0, 0, 0, 0) 58/45 (5, 0, 0, 0, 0, 0) −263/360 (5, 0, 0, 0, 0) 29/90 (5, 0, 0, 0) −23/360 (5, 0, 0) −2/45 (5, 0) 1/360 (5, ) 17/90(4, 1, 0, 0, 0, 0, 0, 0) −719/72 (4, 1, 0, 0, 0, 0, 0) 58/9 (4, 1, 0, 0, 0, 0) −263/72 (4, 1, 0, 0, 0) 29/18 (4, 1, 0, 0) −23/72 (4, 1, 0) −2/9 (4, 1) 1/72(3, 2, 0, 0, 0, 0, 0, 0) −719/36 (3, 2, 0, 0, 0, 0, 0) 116/9 (3, 2, 0, 0, 0, 0) −263/36 (3, 2, 0, 0, 0) 29/9 (3, 2, 0, 0) −23/36 (3, 2, 0) −4/9 (3, 2) 1/36(3, 1, 1, 0, 0, 0, 0, 0) −719/18 (3, 1, 1, 0, 0, 0, 0) 232/9 (3, 1, 1, 0, 0, 0) −263/18 (3, 1, 1, 0, 0) 58/9 (3, 1, 1, 0) −23/18 (3, 1, 1) −8/9(2, 2, 1, 0, 0, 0, 0, 0) −719/12 (2, 2, 1, 0, 0, 0, 0) 116/3 (2, 2, 1, 0, 0, 0) −263/12 (2, 2, 1, 0, 0) 29/3 (2, 2, 1, 0) −23/12 (2, 2, 1) −4/3(2, 1, 1, 1, 0, 0, 0, 0) −719/6 (2, 1, 1, 1, 0, 0, 0) 232/3 (2, 1, 1, 1, 0, 0) −263/6 (2, 1, 1, 1, 0) 58/3 (2, 1, 1, 1) −23/6(1, 1, 1, 1, 1, 0, 0, 0) −719/3 (1, 1, 1, 1, 1, 0, 0) 464/3 (1, 1, 1, 1, 1, 0) −263/3 (1, 1, 1, 1, 1) 116/3(4, 0, 0, 0, 0, 0, 0, 0) 3113/72 (4, 0, 0, 0, 0, 0, 0) −253/12 (4, 0, 0, 0, 0, 0) 571/72 (4, 0, 0, 0, 0) −55/36 (4, 0, 0, 0) −3/8 (4, 0, 0) 1/36 (4, 0) 23/72 (4, ) 19/12(3, 1, 0, 0, 0, 0, 0, 0) 3113/18 (3, 1, 0, 0, 0, 0, 0) −253/3 (3, 1, 0, 0, 0, 0) 571/18 (3, 1, 0, 0, 0) −55/9 (3, 1, 0, 0) −3/2 (3, 1, 0) 1/9 (3, 1) 23/18(2, 2, 0, 0, 0, 0, 0, 0) 3113/12 (2, 2, 0, 0, 0, 0, 0) −253/2 (2, 2, 0, 0, 0, 0) 571/12 (2, 2, 0, 0, 0) −55/6 (2, 2, 0, 0) −9/4 (2, 2, 0) 1/6 (2, 2) 23/12(2, 1, 1, 0, 0, 0, 0, 0) 3113/6 (2, 1, 1, 0, 0, 0, 0) −253 (2, 1, 1, 0, 0, 0) 571/6 (2, 1, 1, 0, 0) −55/3 (2, 1, 1, 0) −9/2 (2, 1, 1) 1/3(1, 1, 1, 1, 0, 0, 0, 0) 3113/3 (1, 1, 1, 1, 0, 0, 0) −506 (1, 1, 1, 1, 0, 0) 571/3 (1, 1, 1, 1, 0) −110/3 (1, 1, 1, 1) −9(3, 0, 0, 0, 0, 0, 0, 0) −789649/1620 (3, 0, 0, 0, 0, 0, 0) 543353/3240 (3, 0, 0, 0, 0, 0) −55429/1620 (3, 0, 0, 0, 0) −4927/3240 (3, 0, 0, 0) 1631/1620 (3, 0, 0) 4073/3240 (3, 0) 3611/1620 (3, ) 26033/3240(2, 1, 0, 0, 0, 0, 0, 0) −789649/540 (2, 1, 0, 0, 0, 0, 0) 543353/1080 (2, 1, 0, 0, 0, 0) −55429/540 (2, 1, 0, 0, 0) −4927/1080 (2, 1, 0, 0) 1631/540 (2, 1, 0) 4073/1080 (2, 1) 3611/540(1, 1, 1, 0, 0, 0, 0, 0) −789649/270 (1, 1, 1, 0, 0, 0, 0) 543353/540 (1, 1, 1, 0, 0, 0) −55429/270 (1, 1, 1, 0, 0) −4927/540 (1, 1, 1, 0) 1631/270 (1, 1, 1) 4073/540(2, 0, 0, 0, 0, 0, 0, 0) 375892/135 (2, 0, 0, 0, 0, 0, 0) −64919/108 (2, 0, 0, 0, 0, 0) 8411/270 (2, 0, 0, 0, 0) 1649/135 (2, 0, 0, 0) 709/135 (2, 0, 0) 2267/540 (2, 0) 361/54 (2, ) 6169/270(1, 1, 0, 0, 0, 0, 0, 0) 751784/135 (1, 1, 0, 0, 0, 0, 0) −64919/54 (1, 1, 0, 0, 0, 0) 8411/135 (1, 1, 0, 0, 0) 3298/135 (1, 1, 0, 0) 1418/135 (1, 1, 0) 2267/270 (1, 1) 361/27(1, 0, 0, 0, 0, 0, 0, 0) −60917648/8505 (1, 0, 0, 0, 0, 0, 0) 6417293/8505 (1, 0, 0, 0, 0, 0) 506659/8505 (1, 0, 0, 0, 0) 165979/17010 (1, 0, 0, 0) 33844/8505 (1, 0, 0) 31613/8505 (1, 0) 56587/8505 (1, ) 415207/17010(0, 0, 0, 0, 0, 0, 0, 0) 4360960/729 (0, 0, 0, 0, 0, 0, 0) −73216/729 (0, 0, 0, 0, 0, 0) −15488/729 (0, 0, 0, 0, 0) −4672/729 (0, 0, 0, 0) −2384/729 (0, 0, 0) −2224/729 (0, 0) −3860/729 (0, ) −13870/729 () 2213497/729