The 54 admissible genera (Lemma 3.3; SM Tables S6-S8). One block per genus; complement classes K with |Aut| and root count. n det discriminant_group genus_symbol length ternary_witness #tern mass_rank19 min_classes_rank19 E2 level closed_by #K mass(C) 1 24 2x2x6 2^-3_3 3^1 3 [1 1 3 0 0 0] 1 6058752757810589/11619303595714805760000 1917772 2063076375508/31513745731 12 both 1 1/192 2 24 2x2x6 2^-3_7 3^-1 3 [1 2 2 -2 0 0] 1 5626556391995831/32368060016634101760000 5752731 54290658386/829393369 12 both 2 5/2304 3 24 24 8^-1_3 3^1 1 [1 2 2 1 1 1] 1 82996613120693/158857666347663360000 1914026 28205907968/431695147 48 both 1 1/144 4 24 24 8^1_7 3^1 1 [1 1 4 0 0 -1] 1 6058752757810589/11641997548050186240000 1921518 2067090112512/31513745731 48 both 1 1/240 5 26 26 2^-1_5 13^1 1 [1 2 2 -1 0 -1] 1 10765418216602033841/5022443979247724789760000 466535 4440784059922/70611350023 52 both 2 7/480 6 28 28 4^-1_3 7^1 1 [1 1 5 1 1 1] 1 40371950752577187377/19372283919955509903360000 479846 13437445937490/221273965267 56 both 2 5/768 7 28 28 4^1_7 7^-1 1 [1 1 4 -1 -1 0] 2 81931910201254361/39161356563335086080000 477975 5948914770680/98343979689 56 both 1 1/96 8 30 30 2^1_7 3^-1 5^1 1 [1 1 4 0 -1 0] 1 428843499994620731/110383384159290654720000 257398 130609342140736/2230568824549 60 both 2 13/1440 9 30 30 2^1_7 3^1 5^-1 1 [1 1 5 0 0 -1] 2 1980779078327409053/509796945261987102720000 257372 46400687339472/792518637199 60 Niemeier 1 1/96 10 32 2x2x8 2^-2 8^-1_5 3 [2 2 2 2 2 2] 1 2056934555822089/3540256564319354880000 1721133 180825600/3202291 16 both 1 1/768 11 32 2x4x4 2^1_7 4^2_6 3 [1 2 2 0 0 0] 1 8003636403977/2304854534062080000 287976 181534720/3202291 8 both 1 1/192 12 32 2x2x8 2^2_6 8^1_7 3 [1 1 4 0 0 0] 1 8003636403977/2304854534062080000 287976 181537490/3202291 16 both 1 1/192 13 34 34 2^1_1 17^-1 1 [1 1 6 1 1 1] 2 42769207164460798451/1784289308416954859520000 41720 941198287607613/17112152560033 68 both 2 1/40 14 36 3x12 4^-1_5 3^-2 2 [1 1 6 0 0 -1] 1 224173852038991793/22408656934592839680000 99962 44424077238/829393369 24 both 1 1/192 15 36 36 4^-1_5 9^-1 1 [1 1 5 -1 -1 0] 1 6058752757810589/302835073139343360000 49984 171504108/3202291 72 both 2 3/320 16 36 36 4^-1_5 9^1 1 [1 2 3 -2 -1 0] 1 296134546947149/14800210341396480000 49978 44415050706/829393369 72 both 2 3/256 17 36 3x12 4^1_1 3^2 2 [2 2 2 1 2 2] 1 58346619023847179/11619303595714805760000 199143 1644834720/30838501 24 both 2 5/1152 18 38 38 2^-1_3 19^1 1 [1 1 5 0 -1 0] 2 218389565791605690281/3348295986165149859840000 15332 13636733435945620/262135948859769 76 both 2 1/32 19 40 2x2x10 2^-3_1 5^-1 3 [1 1 5 0 0 0] 1 41354789299349159/2397634075306229760000 57978 17620144613348/347470989537 20 both 2 13/2304 20 40 2x2x10 2^-3_5 5^1 3 [1 2 3 -2 0 0] 1 3908023586970293537/75525473372146237440000 19326 79289440889982/1563617851771 20 both 2 1/64 21 40 40 8^-1_5 5^1 1 [1 2 3 -1 0 -1] 1 53534569684524569/1032574831259811840000 19289 1084043595264/21419422627 80 Niemeier 1 1/48 22 40 40 8^1_1 5^1 1 [1 1 7 1 1 1] 1 205685451945804923/3982788634859274240000 19364 4181311010304/82295676409 80 Niemeier 2 1/80 23 42 42 2^-1_5 3^-1 7^1 1 [1 2 3 -1 -1 0] 1 3031480677446411357/37762736686073118720000 12457 60017218235330/1212909082831 84 Niemeier 2 1/48 24 42 42 2^-1_5 3^1 7^-1 1 [1 1 7 0 0 -1] 2 418651598900012751293/5215614901526483435520000 12459 107760915341535015/2177557092192547 84 Niemeier 2 5/288 25 44 44 4^-1_3 11^-1 1 [1 1 6 -1 -1 0] 2 3693181207506354983/30210189348858494976000 8180 356485702069508/7388292236945 88 Niemeier 2 5/192 26 44 44 4^1_7 11^1 1 [1 2 3 0 -1 0] 1 174742185058932840473/1434983994070778511360000 8213 3386614169660326/69915135857059 88 Niemeier 3 61/3840 27 46 46 2^1_7 23^-1 1 [1 1 6 0 -1 0] 3 67490196586097831213/185380707367995310080000 2747 14045821591402368/297034450377269 92 Niemeier 2 11/240 28 48 48 16^-1_3 3^-1 1 [1 2 4 2 1 1] 1 82996613120693/310268879585280000 3739 1534200710/33207319 96 Niemeier 2 1/36 29 48 48 16^1_7 3^1 1 [1 1 8 0 0 -1] 2 296134546947149/1111269150351360000 3753 38464603515/829393369 96 Niemeier 1 1/48 30 48 2x2x12 2^-2_2 4^1_1 3^1 3 [1 2 3 0 0 0] 1 5626556391995831/42145911479992320000 7491 729402851840/15758474011 24 both 2 5/384 31 48 2x2x12 2^2 4^-1_3 3^-1 3 [2 2 2 0 0 -2] 1 1557099458757321373/34857910787144417280000 22387 111777480300/2424134287 24 both 1 1/192 32 48 2x2x12 2^2_6 4^-1_5 3^-1 3 [1 1 6 0 0 0] 1 6058752757810589/45387904670760960000 7492 112215823360/2424134287 24 both 2 1/96 33 50 5x10 2^1_1 5^-2 2 [2 2 2 -1 -1 -1] 1 14558585345259918317/113288210058219356160000 7782 10279270560/226660789 20 both 2 13/1440 34 52 52 4^-1_5 13^-1 1 [1 2 4 -2 -1 0] 2 10765418216602033841/19580678281667543040000 1819 1720735708230350/38765631162627 104 Niemeier 2 7/192 35 52 52 4^1_1 13^1 1 [1 1 7 -1 -1 0] 2 319077282840968825603/582625080299413831680000 1826 39822740676188100/893649813285943 104 Niemeier 3 17/768 36 54 54 2^-1_3 27^1 1 [1 1 7 0 -1 0] 2 20168176988328399/13085466123304960000 649 56522425652/1295085441 108 Niemeier 3 9/160 37 54 3x18 2^-1_3 3^1 9^-1 2 [2 2 2 1 1 1] 1 3070874685465641/11954016044974080000 3893 696968256160/15972720439 36 both 1 1/96 38 54 3x18 2^-1_3 3^1 9^1 2 [1 1 9 0 0 -1] 2 3070874685465641/11954016044974080000 3893 697180746482/15972720439 36 both 1 1/96 39 56 2x2x14 2^3_3 7^1 3 [2 2 3 2 2 2] 1 40371950752577187377/113288210058219356160000 2807 9482141421600/221273965267 28 both 3 25/2304 40 56 2x2x14 2^3_7 7^-1 3 [1 1 7 0 0 0] 2 5981029444691568353/5594479509047869440000 936 37929146695552/885095817201 28 both 2 1/32 41 56 56 8^-1_3 7^-1 1 [1 3 3 2 1 1] 1 314791023404819387/295021380359946240000 938 74079797248/1725332977 112 Niemeier 2 1/40 42 56 56 8^1_7 7^-1 1 [1 2 4 0 0 -1] 2 81931910201254361/76487024537763840000 934 37854776393728/885095817201 112 Niemeier 1 1/24 43 58 58 2^-1_5 29^1 1 [1 1 10 1 1 1] 3 4369634263520456342813/1490175686150423838720000 342 957115290147996870/22728034732978627 116 Niemeier 3 7/96 44 60 60 4^-1_3 3^-1 5^-1 1 [1 3 3 1 1 1] 1 1530127204075918883/1541336191268290560000 1008 1244349246314402/29998328763361 120 Niemeier 3 13/768 45 60 60 4^-1_3 3^1 5^1 1 [1 1 10 0 0 -1] 1 155703887122974326711/156860598542149877760000 1008 33597429650488854/809871751540969 120 Niemeier 3 1/80 46 60 60 4^1_7 3^-1 5^1 1 [1 2 4 0 -1 0] 2 37634802488220772007/37762736686073118720000 1004 622174623157201/15057854106781 120 Niemeier 2 5/192 47 60 60 4^1_7 3^1 5^-1 1 [1 1 8 -1 -1 0] 2 428843499994620731/430344577619066880000 1004 2488698492628804/60225358262823 120 Niemeier 2 13/576 48 62 62 2^1_7 31^-1 1 [1 1 8 0 -1 0] 3 10736332949392969950329/2008977591699089915904000 188 174948067244702976/4295655204896707 124 Niemeier 3 1/12 49 64 2x2x16 2^-2_4 16^-1_5 3 [1 3 3 -2 0 0] 1 8003636403977/4501669011840000 563 128377344/3202291 32 both 1 1/48 50 64 2x2x16 2^-2_6 16^-1_3 3 [2 2 3 -2 -2 0] 1 8003636403977/9003338023680000 1125 16432049295/409893248 32 both 1 1/96 51 64 2x4x8 2^1_7 4^1_7 8^1_7 3 [1 2 4 0 0 0] 1 8003636403977/4501669011840000 563 128377344/3202291 16 both 2 1/48 52 64 2x2x16 2^2_6 16^1_7 3 [1 1 8 0 0 0] 1 8003636403977/9003338023680000 1125 16432550769/409893248 32 both 1 1/96 53 64 4x4x4 4^3_5 3 [2 2 2 0 0 0] 1 2056934555822089/13829127204372480000 6724 127875870/3202291 8 both 1 1/384 54 64 64 64^-1_5 1 [1 1 11 1 1 1] 2 16007272807954/2255230667064375 141 128628081/3202291 128 Niemeier 3 1/15 genus 1 (det 24) class K1: |Aut| = 192, roots = 14, dual shells = 66; Gram rows: 2 -1 -1 0 -1 ; -1 2 0 0 0 ; -1 0 2 0 0 ; 0 0 0 2 0 ; -1 0 0 0 4 genus 2 (det 24) class K1: |Aut| = 2304, roots = 24, dual shells = 63; Gram rows: 2 -1 -1 -1 0 ; -1 2 0 0 0 ; -1 0 2 0 0 ; -1 0 0 2 0 ; 0 0 0 0 6 genus 2 (det 24) class K2: |Aut| = 576, roots = 12, dual shells = 70; Gram rows: 2 -1 0 0 0 ; -1 2 0 0 0 ; 0 0 2 0 0 ; 0 0 0 2 0 ; 0 0 0 0 2 genus 3 (det 24) class K1: |Aut| = 144, roots = 12, dual shells = 71; Gram rows: 2 -1 0 0 -1 ; -1 2 0 0 0 ; 0 0 2 -1 -1 ; 0 0 -1 2 0 ; -1 0 -1 0 4 genus 4 (det 24) class K1: |Aut| = 240, roots = 20, dual shells = 63; Gram rows: 2 -1 -1 -1 -1 ; -1 2 0 0 0 ; -1 0 2 1 0 ; -1 0 1 2 0 ; -1 0 0 0 6 genus 5 (det 26) class K1: |Aut| = 240, roots = 20, dual shells = 68; Gram rows: 2 -1 -1 -1 -1 ; -1 2 0 0 0 ; -1 0 2 1 1 ; -1 0 1 2 1 ; -1 0 1 1 6 genus 5 (det 26) class K2: |Aut| = 96, roots = 14, dual shells = 71; Gram rows: 2 -1 -1 0 -1 ; -1 2 0 0 0 ; -1 0 2 0 1 ; 0 0 0 2 0 ; -1 0 1 0 4 genus 6 (det 28) class K1: |Aut| = 768, roots = 24, dual shells = 71; Gram rows: 2 -1 -1 -1 -1 ; -1 2 0 0 0 ; -1 0 2 0 0 ; -1 0 0 2 1 ; -1 0 0 1 8 genus 6 (det 28) class K2: |Aut| = 192, roots = 14, dual shells = 79; Gram rows: 2 -1 -1 0 0 ; -1 2 0 0 0 ; -1 0 2 0 0 ; 0 0 0 2 -1 ; 0 0 0 -1 4 genus 7 (det 28) class K1: |Aut| = 96, roots = 10, dual shells = 88; Gram rows: 2 -1 0 0 -1 ; -1 2 0 0 0 ; 0 0 2 0 -1 ; 0 0 0 2 -1 ; -1 0 -1 -1 4 genus 8 (det 30) class K1: |Aut| = 480, roots = 20, dual shells = 78; Gram rows: 2 -1 -1 -1 0 ; -1 2 0 0 0 ; -1 0 2 1 0 ; -1 0 1 2 0 ; 0 0 0 0 6 genus 8 (det 30) class K2: |Aut| = 144, roots = 12, dual shells = 83; Gram rows: 2 -1 0 0 -1 ; -1 2 0 0 0 ; 0 0 2 -1 0 ; 0 0 -1 2 0 ; -1 0 0 0 4 genus 9 (det 30) class K1: |Aut| = 96, roots = 12, dual shells = 87; Gram rows: 2 -1 -1 -1 -1 ; -1 2 0 0 0 ; -1 0 2 0 1 ; -1 0 0 4 -1 ; -1 0 1 -1 4 genus 10 (det 32) class K1: |Aut| = 768, roots = 8, dual shells = 85; Gram rows: 2 0 0 0 -1 ; 0 2 0 0 -1 ; 0 0 2 0 -1 ; 0 0 0 2 -1 ; -1 -1 -1 -1 4 genus 11 (det 32) class K1: |Aut| = 192, roots = 14, dual shells = 78; Gram rows: 2 -1 -1 0 0 ; -1 2 0 0 0 ; -1 0 2 0 0 ; 0 0 0 2 0 ; 0 0 0 0 4 genus 12 (det 32) class K1: |Aut| = 192, roots = 12, dual shells = 85; Gram rows: 2 -1 -1 -1 -1 ; -1 2 0 0 0 ; -1 0 2 0 0 ; -1 0 0 4 0 ; -1 0 0 0 4 genus 13 (det 34) class K1: |Aut| = 240, roots = 20, dual shells = 83; Gram rows: 2 -1 -1 -1 -1 ; -1 2 0 0 0 ; -1 0 2 1 0 ; -1 0 1 2 0 ; -1 0 0 0 8 genus 13 (det 34) class K2: |Aut| = 48, roots = 10, dual shells = 91; Gram rows: 2 -1 0 0 -1 ; -1 2 0 0 0 ; 0 0 2 0 -1 ; 0 0 0 2 0 ; -1 0 -1 0 4 genus 14 (det 36) class K1: |Aut| = 192, roots = 10, dual shells = 85; Gram rows: 2 -1 0 0 0 ; -1 2 0 0 0 ; 0 0 2 0 -1 ; 0 0 0 2 -1 ; 0 0 -1 -1 4 genus 15 (det 36) class K1: |Aut| = 240, roots = 20, dual shells = 73; Gram rows: 2 -1 -1 -1 -1 ; -1 2 0 0 0 ; -1 0 2 1 1 ; -1 0 1 2 1 ; -1 0 1 1 8 genus 15 (det 36) class K2: |Aut| = 192, roots = 14, dual shells = 75; Gram rows: 2 -1 -1 0 -1 ; -1 2 0 0 0 ; -1 0 2 0 0 ; 0 0 0 2 -1 ; -1 0 0 -1 6 genus 16 (det 36) class K1: |Aut| = 768, roots = 24, dual shells = 72; Gram rows: 2 -1 -1 -1 -1 ; -1 2 0 0 0 ; -1 0 2 0 0 ; -1 0 0 2 1 ; -1 0 0 1 10 genus 16 (det 36) class K2: |Aut| = 96, roots = 12, dual shells = 77; Gram rows: 2 -1 -1 -1 -1 ; -1 2 0 0 0 ; -1 0 2 1 1 ; -1 0 1 4 2 ; -1 0 1 2 4 genus 17 (det 36) class K1: |Aut| = 384, roots = 12, dual shells = 85; Gram rows: 2 -1 -1 -1 -1 ; -1 2 0 0 0 ; -1 0 2 0 0 ; -1 0 0 4 1 ; -1 0 0 1 4 genus 17 (det 36) class K2: |Aut| = 576, roots = 12, dual shells = 86; Gram rows: 2 -1 0 0 0 ; -1 2 0 0 0 ; 0 0 2 -1 0 ; 0 0 -1 2 0 ; 0 0 0 0 4 genus 18 (det 38) class K1: |Aut| = 48, roots = 12, dual shells = 92; Gram rows: 2 -1 -1 -1 -1 ; -1 2 0 0 0 ; -1 0 2 0 1 ; -1 0 0 4 0 ; -1 0 1 0 4 genus 18 (det 38) class K2: |Aut| = 96, roots = 14, dual shells = 91; Gram rows: 2 -1 -1 0 -1 ; -1 2 0 0 0 ; -1 0 2 0 1 ; 0 0 0 2 -1 ; -1 0 1 -1 6 genus 19 (det 40) class K1: |Aut| = 2304, roots = 24, dual shells = 88; Gram rows: 2 -1 -1 -1 0 ; -1 2 0 0 0 ; -1 0 2 0 0 ; -1 0 0 2 0 ; 0 0 0 0 10 genus 19 (det 40) class K2: |Aut| = 192, roots = 8, dual shells = 103; Gram rows: 2 0 0 0 -1 ; 0 2 0 0 -1 ; 0 0 2 0 -1 ; 0 0 0 2 0 ; -1 -1 -1 0 4 genus 20 (det 40) class K1: |Aut| = 192, roots = 14, dual shells = 89; Gram rows: 2 -1 -1 0 -1 ; -1 2 0 0 0 ; -1 0 2 0 0 ; 0 0 0 2 0 ; -1 0 0 0 6 genus 20 (det 40) class K2: |Aut| = 96, roots = 10, dual shells = 90; Gram rows: 2 -1 0 0 -1 ; -1 2 0 0 0 ; 0 0 2 0 0 ; 0 0 0 2 0 ; -1 0 0 0 4 genus 21 (det 40) class K1: |Aut| = 48, roots = 8, dual shells = 100; Gram rows: 2 -1 0 -1 -1 ; -1 2 0 0 0 ; 0 0 2 -1 -1 ; -1 0 -1 4 0 ; -1 0 -1 0 4 genus 22 (det 40) class K1: |Aut| = 96, roots = 12, dual shells = 94; Gram rows: 2 -1 -1 -1 -1 ; -1 2 0 0 0 ; -1 0 2 1 1 ; -1 0 1 4 0 ; -1 0 1 0 4 genus 22 (det 40) class K2: |Aut| = 480, roots = 20, dual shells = 88; Gram rows: 2 -1 -1 -1 0 ; -1 2 0 0 0 ; -1 0 2 1 0 ; -1 0 1 2 0 ; 0 0 0 0 8 genus 23 (det 42) class K1: |Aut| = 96, roots = 12, dual shells = 98; Gram rows: 2 -1 -1 -1 -1 ; -1 2 0 0 0 ; -1 0 2 1 1 ; -1 0 1 4 1 ; -1 0 1 1 4 genus 23 (det 42) class K2: |Aut| = 96, roots = 10, dual shells = 100; Gram rows: 2 -1 0 0 0 ; -1 2 0 0 0 ; 0 0 2 0 -1 ; 0 0 0 2 0 ; 0 0 -1 0 4 genus 24 (det 42) class K1: |Aut| = 96, roots = 14, dual shells = 96; Gram rows: 2 -1 -1 0 -1 ; -1 2 0 0 0 ; -1 0 2 0 1 ; 0 0 0 2 0 ; -1 0 1 0 6 genus 24 (det 42) class K2: |Aut| = 144, roots = 12, dual shells = 96; Gram rows: 2 -1 0 0 -1 ; -1 2 0 0 0 ; 0 0 2 -1 -1 ; 0 0 -1 2 0 ; -1 0 -1 0 6 genus 25 (det 44) class K1: |Aut| = 192, roots = 14, dual shells = 100; Gram rows: 2 -1 -1 0 0 ; -1 2 0 0 0 ; -1 0 2 0 0 ; 0 0 0 2 -1 ; 0 0 0 -1 6 genus 25 (det 44) class K2: |Aut| = 48, roots = 8, dual shells = 103; Gram rows: 2 -1 0 -1 -1 ; -1 2 0 0 0 ; 0 0 2 -1 -1 ; -1 0 -1 4 2 ; -1 0 -1 2 4 genus 26 (det 44) class K1: |Aut| = 768, roots = 24, dual shells = 80; Gram rows: 2 -1 -1 -1 -1 ; -1 2 0 0 0 ; -1 0 2 0 0 ; -1 0 0 2 1 ; -1 0 0 1 12 genus 26 (det 44) class K2: |Aut| = 240, roots = 20, dual shells = 84; Gram rows: 2 -1 -1 -1 -1 ; -1 2 0 0 0 ; -1 0 2 1 0 ; -1 0 1 2 0 ; -1 0 0 0 10 genus 26 (det 44) class K3: |Aut| = 96, roots = 12, dual shells = 85; Gram rows: 2 -1 -1 -1 0 ; -1 2 0 0 0 ; -1 0 2 0 0 ; -1 0 0 4 -1 ; 0 0 0 -1 4 genus 27 (det 46) class K1: |Aut| = 240, roots = 20, dual shells = 99; Gram rows: 2 -1 -1 -1 -1 ; -1 2 0 0 0 ; -1 0 2 1 1 ; -1 0 1 2 1 ; -1 0 1 1 10 genus 27 (det 46) class K2: |Aut| = 24, roots = 8, dual shells = 110; Gram rows: 2 -1 0 -1 -1 ; -1 2 0 0 0 ; 0 0 2 -1 0 ; -1 0 -1 4 2 ; -1 0 0 2 4 genus 28 (det 48) class K1: |Aut| = 48, roots = 8, dual shells = 106; Gram rows: 2 -1 0 -1 -1 ; -1 2 0 0 0 ; 0 0 2 -1 -1 ; -1 0 -1 4 1 ; -1 0 -1 1 4 genus 28 (det 48) class K2: |Aut| = 144, roots = 12, dual shells = 105; Gram rows: 2 -1 0 0 -1 ; -1 2 0 0 0 ; 0 0 2 -1 0 ; 0 0 -1 2 0 ; -1 0 0 0 6 genus 29 (det 48) class K1: |Aut| = 48, roots = 12, dual shells = 101; Gram rows: 2 -1 -1 -1 0 ; -1 2 0 0 0 ; -1 0 2 1 0 ; -1 0 1 4 -1 ; 0 0 0 -1 4 genus 30 (det 48) class K1: |Aut| = 192, roots = 12, dual shells = 101; Gram rows: 2 -1 -1 -1 0 ; -1 2 0 0 0 ; -1 0 2 0 0 ; -1 0 0 4 0 ; 0 0 0 0 4 genus 30 (det 48) class K2: |Aut| = 128, roots = 8, dual shells = 104; Gram rows: 2 0 0 0 -1 ; 0 2 0 0 -1 ; 0 0 2 0 0 ; 0 0 0 2 0 ; -1 -1 0 0 4 genus 31 (det 48) class K1: |Aut| = 192, roots = 6, dual shells = 102; Gram rows: 2 0 0 -1 -1 ; 0 2 0 -1 -1 ; 0 0 2 -1 -1 ; -1 -1 -1 4 1 ; -1 -1 -1 1 4 genus 32 (det 48) class K1: |Aut| = 192, roots = 14, dual shells = 101; Gram rows: 2 -1 -1 0 0 ; -1 2 0 0 0 ; -1 0 2 0 0 ; 0 0 0 2 0 ; 0 0 0 0 6 genus 32 (det 48) class K2: |Aut| = 192, roots = 10, dual shells = 105; Gram rows: 2 -1 0 0 0 ; -1 2 0 0 0 ; 0 0 2 0 0 ; 0 0 0 2 0 ; 0 0 0 0 4 genus 33 (det 50) class K1: |Aut| = 480, roots = 20, dual shells = 89; Gram rows: 2 -1 -1 -1 0 ; -1 2 0 0 0 ; -1 0 2 1 0 ; -1 0 1 2 0 ; 0 0 0 0 10 genus 33 (det 50) class K2: |Aut| = 144, roots = 8, dual shells = 94; Gram rows: 2 -1 0 -1 -1 ; -1 2 0 0 0 ; 0 0 2 0 0 ; -1 0 0 4 -1 ; -1 0 0 -1 4 genus 34 (det 52) class K1: |Aut| = 192, roots = 14, dual shells = 112; Gram rows: 2 -1 -1 0 -1 ; -1 2 0 0 0 ; -1 0 2 0 0 ; 0 0 0 2 -1 ; -1 0 0 -1 8 genus 34 (det 52) class K2: |Aut| = 32, roots = 6, dual shells = 118; Gram rows: 2 0 0 -1 -1 ; 0 2 0 -1 -1 ; 0 0 2 -1 0 ; -1 -1 -1 4 0 ; -1 -1 0 0 4 genus 35 (det 52) class K1: |Aut| = 768, roots = 24, dual shells = 97; Gram rows: 2 -1 -1 -1 -1 ; -1 2 0 0 0 ; -1 0 2 0 0 ; -1 0 0 2 1 ; -1 0 0 1 14 genus 35 (det 52) class K2: |Aut| = 96, roots = 12, dual shells = 110; Gram rows: 2 -1 -1 -1 0 ; -1 2 0 0 0 ; -1 0 2 1 0 ; -1 0 1 4 0 ; 0 0 0 0 4 genus 35 (det 52) class K3: |Aut| = 96, roots = 10, dual shells = 111; Gram rows: 2 -1 0 0 -1 ; -1 2 0 0 0 ; 0 0 2 0 -1 ; 0 0 0 2 -1 ; -1 0 -1 -1 6 genus 36 (det 54) class K1: |Aut| = 240, roots = 20, dual shells = 99; Gram rows: 2 -1 -1 -1 -1 ; -1 2 0 0 0 ; -1 0 2 1 0 ; -1 0 1 2 0 ; -1 0 0 0 12 genus 36 (det 54) class K2: |Aut| = 96, roots = 14, dual shells = 101; Gram rows: 2 -1 -1 0 -1 ; -1 2 0 0 0 ; -1 0 2 0 1 ; 0 0 0 2 -1 ; -1 0 1 -1 8 genus 36 (det 54) class K3: |Aut| = 24, roots = 8, dual shells = 104; Gram rows: 2 -1 0 -1 -1 ; -1 2 0 0 0 ; 0 0 2 -1 0 ; -1 0 -1 4 0 ; -1 0 0 0 4 genus 37 (det 54) class K1: |Aut| = 96, roots = 12, dual shells = 97; Gram rows: 2 -1 -1 -1 -1 ; -1 2 0 0 0 ; -1 0 2 0 1 ; -1 0 0 4 -1 ; -1 0 1 -1 6 genus 38 (det 54) class K1: |Aut| = 96, roots = 6, dual shells = 127; Gram rows: 2 0 0 -1 -1 ; 0 2 0 -1 0 ; 0 0 2 0 -1 ; -1 -1 0 4 -1 ; -1 0 -1 -1 4 genus 39 (det 56) class K1: |Aut| = 2304, roots = 24, dual shells = 89; Gram rows: 2 -1 -1 -1 0 ; -1 2 0 0 0 ; -1 0 2 0 0 ; -1 0 0 2 0 ; 0 0 0 0 14 genus 39 (det 56) class K2: |Aut| = 192, roots = 14, dual shells = 99; Gram rows: 2 -1 -1 0 -1 ; -1 2 0 0 0 ; -1 0 2 0 0 ; 0 0 0 2 0 ; -1 0 0 0 8 genus 39 (det 56) class K3: |Aut| = 192, roots = 8, dual shells = 99; Gram rows: 2 0 0 0 -1 ; 0 2 0 0 0 ; 0 0 2 0 0 ; 0 0 0 2 0 ; -1 0 0 0 4 genus 40 (det 56) class K1: |Aut| = 96, roots = 12, dual shells = 108; Gram rows: 2 -1 -1 -1 -1 ; -1 2 0 0 0 ; -1 0 2 0 0 ; -1 0 0 4 0 ; -1 0 0 0 6 genus 40 (det 56) class K2: |Aut| = 48, roots = 8, dual shells = 110; Gram rows: 2 -1 0 -1 -1 ; -1 2 0 0 0 ; 0 0 2 0 0 ; -1 0 0 4 2 ; -1 0 0 2 4 genus 41 (det 56) class K1: |Aut| = 48, roots = 12, dual shells = 99; Gram rows: 2 -1 -1 -1 -1 ; -1 2 0 0 0 ; -1 0 2 1 0 ; -1 0 1 4 -1 ; -1 0 0 -1 6 genus 41 (det 56) class K2: |Aut| = 240, roots = 20, dual shells = 99; Gram rows: 2 -1 -1 -1 -1 ; -1 2 0 0 0 ; -1 0 2 1 1 ; -1 0 1 2 1 ; -1 0 1 1 12 genus 42 (det 56) class K1: |Aut| = 24, roots = 8, dual shells = 113; Gram rows: 2 -1 0 -1 -1 ; -1 2 0 0 0 ; 0 0 2 -1 0 ; -1 0 -1 4 1 ; -1 0 0 1 4 genus 43 (det 58) class K1: |Aut| = 96, roots = 14, dual shells = 116; Gram rows: 2 -1 -1 0 -1 ; -1 2 0 0 0 ; -1 0 2 0 1 ; 0 0 0 2 0 ; -1 0 1 0 8 genus 43 (det 58) class K2: |Aut| = 24, roots = 8, dual shells = 120; Gram rows: 2 -1 0 -1 0 ; -1 2 0 0 0 ; 0 0 2 -1 -1 ; -1 0 -1 4 0 ; 0 0 -1 0 4 genus 43 (det 58) class K3: |Aut| = 48, roots = 10, dual shells = 121; Gram rows: 2 -1 0 0 -1 ; -1 2 0 0 0 ; 0 0 2 0 -1 ; 0 0 0 2 0 ; -1 0 -1 0 6 genus 44 (det 60) class K1: |Aut| = 768, roots = 24, dual shells = 97; Gram rows: 2 -1 -1 -1 -1 ; -1 2 0 0 0 ; -1 0 2 0 0 ; -1 0 0 2 1 ; -1 0 0 1 16 genus 44 (det 60) class K2: |Aut| = 192, roots = 12, dual shells = 106; Gram rows: 2 -1 -1 0 0 ; -1 2 0 0 0 ; -1 0 2 0 0 ; 0 0 0 4 -1 ; 0 0 0 -1 4 genus 44 (det 60) class K3: |Aut| = 96, roots = 8, dual shells = 110; Gram rows: 2 -1 0 0 0 ; -1 2 0 0 0 ; 0 0 2 -1 -1 ; 0 0 -1 4 -1 ; 0 0 -1 -1 4 genus 45 (det 60) class K1: |Aut| = 192, roots = 12, dual shells = 108; Gram rows: 2 -1 -1 -1 -1 ; -1 2 0 0 0 ; -1 0 2 0 0 ; -1 0 0 4 1 ; -1 0 0 1 6 genus 45 (det 60) class K2: |Aut| = 480, roots = 20, dual shells = 109; Gram rows: 2 -1 -1 -1 0 ; -1 2 0 0 0 ; -1 0 2 1 0 ; -1 0 1 2 0 ; 0 0 0 0 12 genus 45 (det 60) class K3: |Aut| = 192, roots = 14, dual shells = 108; Gram rows: 2 -1 -1 0 0 ; -1 2 0 0 0 ; -1 0 2 0 0 ; 0 0 0 2 -1 ; 0 0 0 -1 8 genus 46 (det 60) class K1: |Aut| = 48, roots = 6, dual shells = 125; Gram rows: 2 -1 -1 -1 -1 ; -1 2 0 0 0 ; -1 0 4 -1 -1 ; -1 0 -1 4 1 ; -1 0 -1 1 4 genus 46 (det 60) class K2: |Aut| = 192, roots = 10, dual shells = 124; Gram rows: 2 -1 0 0 0 ; -1 2 0 0 0 ; 0 0 2 0 -1 ; 0 0 0 2 -1 ; 0 0 -1 -1 6 genus 47 (det 60) class K1: |Aut| = 144, roots = 12, dual shells = 120; Gram rows: 2 -1 0 0 -1 ; -1 2 0 0 0 ; 0 0 2 -1 -1 ; 0 0 -1 2 0 ; -1 0 -1 0 8 genus 47 (det 60) class K2: |Aut| = 64, roots = 6, dual shells = 124; Gram rows: 2 0 0 -1 -1 ; 0 2 0 -1 -1 ; 0 0 2 -1 0 ; -1 -1 -1 4 1 ; -1 -1 0 1 4 genus 48 (det 62) class K1: |Aut| = 48, roots = 12, dual shells = 117; Gram rows: 2 -1 -1 -1 -1 ; -1 2 0 0 0 ; -1 0 2 0 1 ; -1 0 0 4 0 ; -1 0 1 0 6 genus 48 (det 62) class K2: |Aut| = 48, roots = 12, dual shells = 119; Gram rows: 2 -1 -1 -1 -1 ; -1 2 0 0 0 ; -1 0 2 1 1 ; -1 0 1 4 2 ; -1 0 1 2 6 genus 48 (det 62) class K3: |Aut| = 24, roots = 8, dual shells = 121; Gram rows: 2 -1 0 -1 0 ; -1 2 0 0 0 ; 0 0 2 -1 0 ; -1 0 -1 4 -1 ; 0 0 0 -1 4 genus 49 (det 64) class K1: |Aut| = 48, roots = 8, dual shells = 117; Gram rows: 2 -1 0 -1 -1 ; -1 2 0 0 0 ; 0 0 2 0 0 ; -1 0 0 4 0 ; -1 0 0 0 4 genus 50 (det 64) class K1: |Aut| = 96, roots = 10, dual shells = 110; Gram rows: 2 -1 0 0 -1 ; -1 2 0 0 0 ; 0 0 2 0 0 ; 0 0 0 2 0 ; -1 0 0 0 6 genus 51 (det 64) class K1: |Aut| = 192, roots = 14, dual shells = 111; Gram rows: 2 -1 -1 0 0 ; -1 2 0 0 0 ; -1 0 2 0 0 ; 0 0 0 2 0 ; 0 0 0 0 8 genus 51 (det 64) class K2: |Aut| = 64, roots = 6, dual shells = 115; Gram rows: 2 0 0 -1 -1 ; 0 2 0 -1 -1 ; 0 0 2 0 0 ; -1 -1 0 4 0 ; -1 -1 0 0 4 genus 52 (det 64) class K1: |Aut| = 96, roots = 6, dual shells = 131; Gram rows: 2 -1 -1 -1 -1 ; -1 2 0 0 0 ; -1 0 4 2 2 ; -1 0 2 4 0 ; -1 0 2 0 4 genus 53 (det 64) class K1: |Aut| = 384, roots = 4, dual shells = 123; Gram rows: 2 0 -1 -1 -1 ; 0 2 -1 -1 -1 ; -1 -1 4 0 0 ; -1 -1 0 4 0 ; -1 -1 0 0 4 genus 54 (det 64) class K1: |Aut| = 240, roots = 20, dual shells = 105; Gram rows: 2 -1 -1 -1 -1 ; -1 2 0 0 0 ; -1 0 2 1 0 ; -1 0 1 2 0 ; -1 0 0 0 14 genus 54 (det 64) class K2: |Aut| = 48, roots = 12, dual shells = 111; Gram rows: 2 -1 -1 -1 -1 ; -1 2 0 0 0 ; -1 0 2 1 0 ; -1 0 1 4 0 ; -1 0 0 0 6 genus 54 (det 64) class K3: |Aut| = 24, roots = 8, dual shells = 113; Gram rows: 2 -1 0 -1 0 ; -1 2 0 0 0 ; 0 0 2 0 -1 ; -1 0 0 4 -1 ; 0 0 -1 -1 4