Output of hn -T10 -A100000 --graph_max2500 --herm_lll3 0.8 -t --shells-10 &K=Q(sqrt(-14)) &Hdim=3 V=K^3 &HNeighbourhood at <3,-1+w> contains 62 classes: mass of the neighbourhood is 33/4 Steinitz class <3,1+w>: &Hlattice (#1 <- #34) <1> <1> <3,1+w> 4 w 5 1 -2/3-1/3w 2/3 |Aut| = 2^2 #short vectors: 0 0 0 6 12 6 12 18 32 42 &Hlattice (#2 <- #45) <1> <1> <3,1+w> 4 2+w 5 1 1/3-1/3w 2/3 |Aut| = 2^2*3 #short vectors: 0 0 0 6 12 6 12 18 32 42 &Hlattice (#3 <- #37) <1> <3,1+w> <1> 5 2 4/3 2-2w 1/3-2/3w 13 |Aut| = 2^2 #short vectors: 0 0 0 4 10 16 12 24 24 20 &Hlattice (#4 <- #38) <1> <1> <3,1+w> 4 -1-w 8 -1/3+1/3w 1/3-1/3w 1 |Aut| = 2^2 #short vectors: 0 0 0 4 14 8 12 24 24 36 &Hlattice (#5 <- #26) <1> <1> <3,1+w> 3 w 6 -1/3+1/3w 1 1 |Aut| = 2^2 #short vectors: 0 0 6 6 0 4 16 22 24 28 &Hlattice (#6 <- #27) <3,1+w> <3,1+w> <3,-1+w> 1/3 0 1/3 0 0 1/3 |Aut| = 2^4 #short vectors: 0 0 6 0 6 18 0 24 32 18 &Hlattice (#7 <- #28) <3,-1+w> <3,-1+w> <3,-1+w> 1/3 0 1/3 0 0 1/3 |Aut| = 2^4*3 #short vectors: 0 0 6 0 6 18 0 24 32 18 &Hlattice (#8 <- #29) <3,1+w> <1> <1> 1/3 0 3 0 w 5 |Aut| = 2^3 #short vectors: 0 0 6 0 6 18 0 24 32 18 &Hlattice (#9 <- #30) <1> <1> <3,1+w> 3 -1 3 2/3+1/3w -1 1 |Aut| = 2^2 #short vectors: 0 0 6 4 2 10 8 20 32 26 &Hlattice (#10 <- #40) <1> <2,w> <3,-1+w> 3 1 1 4/3+1/3w 2/3+1/6w 4/3 |Aut| = 2^2*3 #short vectors: 0 0 6 6 0 0 24 30 8 24 &Hlattice (#11 <- #33) <1> <2,w> <3,-1+w> 3 -1/2w 3/2 -2/3+1/3w -2/3-1/6w 1 |Aut| = 2^2 #short vectors: 0 0 2 4 6 18 8 20 32 18 &Hlattice (#12 <- #35) <3,1+w> <1> <1> 1/3 0 4 0 -1+w 4 |Aut| = 2^3 #short vectors: 0 0 2 8 2 10 16 16 32 26 &Hlattice (#13 <- #47) <3,-1+w> <1> <2,w> 1/3 0 4 0 2-1/2w 2 |Aut| = 2^4 #short vectors: 0 0 2 8 2 10 16 16 32 26 &Hlattice (#14 <- #43) <1> <2,w> <3,-1+w> 2 0 1/2 1 0 2/3 |Aut| = 2^3*3 #short vectors: 0 8 0 12 0 6 2 20 16 42 &Hlattice (#15 <- #44) <1> <1> <3,1+w> 2 1 2 -2/3-1/3w -1 5/3 |Aut| = 2^2*3 #short vectors: 0 6 0 6 6 12 12 18 20 0 &Hlattice (#16 <- #24) <2,w> <2,w> <3,1+w> 1/2 0 1/2 0 0 1/3 |Aut| = 2^4 #short vectors: 0 4 2 4 10 2 20 12 24 26 &Hlattice (#17 <- #25) <2,w> <1> <3,-1+w> 1/2 0 2 0 -1/3-1/3w 1 |Aut| = 2^3 #short vectors: 0 4 4 4 8 2 10 12 32 30 &Hlattice (#18 <- #42) <1> <3,1+w> <1> 2 0 1/3 1-w 0 8 |Aut| = 2^4 #short vectors: 0 4 2 4 10 2 16 28 8 18 &Hlattice (#19 <- #3) <1> <3,-1+w> <2,w> 2 0 1/3 1-1/2w 0 5/2 |Aut| = 2^3 #short vectors: 0 2 2 2 14 6 8 26 20 30 &Hlattice (#20 <- #6) <1> <1> <3,1+w> 2 1 4 1 1/3-1/3w 1 |Aut| = 2^2 #short vectors: 0 2 2 4 12 4 8 20 28 36 &Hlattice (#21 <- #31) <2,w> <2,w> <3,1+w> 1/2 0 1 0 2/3-1/6w 1 |Aut| = 2^3 #short vectors: 0 2 0 6 4 18 18 14 28 6 &Hlattice (#22 <- #36) <1> <1> <3,1+w> 2 -1 4 -2/3-1/3w -1 5/3 |Aut| = 2^2 #short vectors: 0 2 0 6 6 16 12 18 28 12 &Hlattice (#23 <- #39) <1> <1> <3,1+w> 2 1 3 1/3-1/3w 1 4/3 |Aut| = 2^2 #short vectors: 0 2 6 4 4 4 8 20 28 28 &Hlattice (#24 <- #46) <1> <3,-1+w> <2,w> 2 0 1/3 -1/2w 0 2 |Aut| = 2^3 #short vectors: 0 2 2 6 6 6 16 22 20 22 &Hlattice (#25 <- #49) <2,w> <2,w> <3,1+w> 1/2 0 1 0 -1/3-1/6w 2/3 |Aut| = 2^3*3 #short vectors: 0 2 0 6 0 30 2 38 4 18 &Hlattice (#26 <- #4) <1> <1> <3,1+w> 1 0 1 0 0 1/3 |Aut| = 2^4 #short vectors: 4 4 2 12 18 10 24 28 12 34 &Hlattice (#27 <- #2) <1> <2,w> <3,-1+w> 1 0 1/2 0 0 1/3 |Aut| = 2^3 #short vectors: 2 2 6 6 6 18 14 18 30 18 &Hlattice (#28 <- #5) <1> <1> <3,1+w> 1 0 2 0 1/3-1/3w 1 |Aut| = 2^3 #short vectors: 2 2 8 10 0 6 20 22 22 26 &Hlattice (#29 <- #32) <1> <2,w> <3,-1+w> 1 0 1 0 -2/3-1/6w 1 |Aut| = 2^3 #short vectors: 2 0 0 8 16 14 20 28 18 34 &Hlattice (#30 <- #41) <1> <1> <3,1+w> 1 0 2 0 1 2/3 |Aut| = 2^3*3 #short vectors: 2 6 12 2 0 18 12 6 14 30 &Hlattice (#31 <- #48) <1> <2,w> <3,-1+w> 1 0 1 0 1/3-1/6w 2/3 |Aut| = 2^3*3 #short vectors: 2 0 0 8 12 18 36 12 2 54 Steinitz class <3,-1+w>: &Hlattice (#32 <- #21) <1> <1> <3,-1+w> 4 w 5 -1 -2/3+1/3w 2/3 |Aut| = 2^2 #short vectors: 0 0 0 6 12 6 12 18 32 42 &Hlattice (#33 <- #51) <1> <1> <3,-1+w> 4 2+w 5 1 2/3-1/3w 2/3 |Aut| = 2^2*3 #short vectors: 0 0 0 6 12 6 12 18 32 42 &Hlattice (#34 <- #22) <1> <1> <3,-1+w> 4 1-w 8 -1/3-1/3w -1/3-1/3w 1 |Aut| = 2^2 #short vectors: 0 0 0 4 14 8 12 24 24 36 &Hlattice (#35 <- #23) <1> <3,-1+w> <1> 5 2 4/3 2+2w 1/3+2/3w 13 |Aut| = 2^2 #short vectors: 0 0 0 4 10 16 12 24 24 20 &Hlattice (#36 <- #8) <3,-1+w> <3,1+w> <3,-1+w> 1/3 0 1/3 0 0 1/3 |Aut| = 2^4 #short vectors: 0 0 6 0 6 18 0 24 32 18 &Hlattice (#37 <- #12) <1> <1> <3,-1+w> 3 1 3 2/3-1/3w 1 1 |Aut| = 2^2 #short vectors: 0 0 6 4 2 10 8 20 32 26 &Hlattice (#38 <- #14) <1> <1> <3,-1+w> 3 w 6 1/3+1/3w 1 1 |Aut| = 2^2 #short vectors: 0 0 6 6 0 4 16 22 24 28 &Hlattice (#39 <- #15) <3,-1+w> <1> <1> 1/3 0 3 0 w 5 |Aut| = 2^3 #short vectors: 0 0 6 0 6 18 0 24 32 18 &Hlattice (#40 <- #53) <3,1+w> <3,1+w> <3,1+w> 1/3 0 1/3 0 0 1/3 |Aut| = 2^4*3 #short vectors: 0 0 6 0 6 18 0 24 32 18 &Hlattice (#41 <- #62) <1> <2,w> <3,1+w> 3 1 1 -4/3+1/3w -2/3+1/6w 4/3 |Aut| = 2^2*3 #short vectors: 0 0 6 6 0 0 24 30 8 24 &Hlattice (#42 <- #20) <3,1+w> <1> <2,w> 1/3 0 4 0 2-1/2w 2 |Aut| = 2^4 #short vectors: 0 0 2 8 2 10 16 16 32 26 &Hlattice (#43 <- #54) <1> <2,w> <3,1+w> 3 -1/2w 3/2 -2/3-1/3w 2/3-1/6w 1 |Aut| = 2^2 #short vectors: 0 0 2 4 6 18 8 20 32 18 &Hlattice (#44 <- #57) <3,-1+w> <1> <1> 1/3 0 4 0 1+w 4 |Aut| = 2^3 #short vectors: 0 0 2 8 2 10 16 16 32 26 &Hlattice (#45 <- #58) <1> <2,w> <3,1+w> 2 0 1/2 1 0 2/3 |Aut| = 2^3*3 #short vectors: 0 8 0 12 0 6 2 20 16 42 &Hlattice (#46 <- #59) <1> <1> <3,-1+w> 2 1 2 2/3-1/3w 1 5/3 |Aut| = 2^2*3 #short vectors: 0 6 0 6 6 12 12 18 20 0 &Hlattice (#47 <- #7) <2,w> <2,w> <3,-1+w> 1/2 0 1/2 0 0 1/3 |Aut| = 2^4 #short vectors: 0 4 2 4 10 2 20 12 24 26 &Hlattice (#48 <- #10) <1> <2,w> <3,1+w> 2 0 1/2 1/3-1/3w 0 1 |Aut| = 2^3 #short vectors: 0 4 4 4 8 2 10 12 32 30 &Hlattice (#49 <- #60) <1> <3,-1+w> <1> 2 0 1/3 1-w 0 8 |Aut| = 2^4 #short vectors: 0 4 2 4 10 2 16 28 8 18 &Hlattice (#50 <- #13) <1> <3,1+w> <2,w> 2 0 1/3 1-1/2w 0 5/2 |Aut| = 2^3 #short vectors: 0 2 2 2 14 6 8 26 20 30 &Hlattice (#51 <- #16) <1> <1> <3,-1+w> 2 1 3 -1/3-1/3w -1 4/3 |Aut| = 2^2 #short vectors: 0 2 6 4 4 4 8 20 28 28 &Hlattice (#52 <- #17) <1> <1> <3,-1+w> 2 -1 4 1 -1/3-1/3w 1 |Aut| = 2^2 #short vectors: 0 2 2 4 12 4 8 20 28 36 &Hlattice (#53 <- #19) <1> <1> <3,-1+w> 2 -1 4 2/3-1/3w -5/3+1/3w 5/3 |Aut| = 2^2 #short vectors: 0 2 0 6 6 16 12 18 28 12 &Hlattice (#54 <- #50) <2,w> <2,w> <3,-1+w> 1/2 0 1 0 -2/3-1/6w 1 |Aut| = 2^3 #short vectors: 0 2 0 6 4 18 18 14 28 6 &Hlattice (#55 <- #52) <1> <3,1+w> <2,w> 2 0 1/3 -1/2w 0 2 |Aut| = 2^3 #short vectors: 0 2 2 6 6 6 16 22 20 22 &Hlattice (#56 <- #56) <2,w> <2,w> <3,-1+w> 1/2 0 1 0 1/3-1/6w 2/3 |Aut| = 2^3*3 #short vectors: 0 2 0 6 0 30 2 38 4 18 &Hlattice (#57 <- #1) <1> <1> <3,-1+w> 1 0 1 0 0 1/3 |Aut| = 2^4 #short vectors: 4 4 2 12 18 10 24 28 12 34 &Hlattice (#58 <- #9) <1> <2,w> <3,1+w> 1 0 1/2 0 0 1/3 |Aut| = 2^3 #short vectors: 2 2 6 6 6 18 14 18 30 18 &Hlattice (#59 <- #11) <1> <1> <3,-1+w> 1 0 2 0 -1/3-1/3w 1 |Aut| = 2^3 #short vectors: 2 2 8 10 0 6 20 22 22 26 &Hlattice (#60 <- #18) <1> <2,w> <3,1+w> 1 0 1 0 2/3-1/6w 1 |Aut| = 2^3 #short vectors: 2 0 0 8 16 14 20 28 18 34 &Hlattice (#61 <- #55) <1> <1> <3,-1+w> 1 0 2 0 1 2/3 |Aut| = 2^3*3 #short vectors: 2 6 12 2 0 18 12 6 14 30 &Hlattice (#62 <- #61) <1> <2,w> <3,1+w> 1 0 1 0 -1/3-1/6w 2/3 |Aut| = 2^3*3 #short vectors: 2 0 0 8 12 18 36 12 2 54 &Adjacence matrix (M_ij=#{neighbours of class i isometric to class j}): 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 0 0 0 0 0 0 0 1 2 0 0 0 2 0 0 0 0 2 0 1 0 0 0 0 0 2 2 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 3 0 0 0 0 6 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 2 1 0 0 1 2 0 0 0 0 0 0 1 0 0 1 0 0 2 2 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 2 0 1 2 0 2 0 0 0 1 0 0 0 0 0 1 0 0 0 0 2 1 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 2 0 0 1 0 2 1 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 2 0 0 0 2 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 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 2 1 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 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 0 0 0 0 0 0 0 0 0 0 4 1 2 0 1 1 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 2 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 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 0 0 1 2 1 0 0 1 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 2 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 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 3 0 0 0 3 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 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 1 0 0 0 0 0 0 3 1 0 0 0 0 0 0 2 0 0 2 0 0 0 0 0 2 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 1 0 0 0 0 0 0 0 0 4 2 2 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 1 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 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 0 0 0 0 0 0 0 0 0 6 0 0 0 0 0 0 0 0 0 0 0 0 1 2 0 0 0 0 0 0 0 0 0 3 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 1 0 0 0 3 0 3 0 3 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 2 0 0 0 4 0 0 0 2 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 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 4 2 1 0 0 0 2 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 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 4 0 0 1 0 0 0 0 0 4 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 0 0 0 0 0 0 0 1 0 0 1 4 2 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 2 0 2 2 0 0 1 0 0 0 0 0 0 0 0 0 2 0 1 1 0 1 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 4 2 0 0 2 1 0 0 0 0 0 1 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 1 2 0 2 0 0 0 0 0 0 2 0 1 0 1 0 0 0 1 2 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 1 0 2 0 0 1 0 0 0 2 2 1 0 0 1 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 2 0 0 2 0 0 0 0 2 0 2 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 0 2 0 0 0 3 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 4 0 0 0 1 2 0 4 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 0 0 0 0 0 0 0 0 0 0 0 0 2 4 0 0 0 0 0 0 0 0 0 1 2 0 0 0 0 0 0 0 0 1 1 2 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 2 0 0 0 0 0 1 0 0 0 2 0 0 0 0 0 2 1 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 0 0 0 0 0 0 0 0 2 0 2 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 1 0 0 2 0 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 1 0 0 0 0 0 6 0 0 0 0 0 0 0 0 0 3 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 0 0 0 0 0 0 0 2 0 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 3 0 1 2 2 0 0 0 0 2 0 0 0 0 0 0 0 1 0 0 2 0 2 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 6 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 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 0 0 0 0 0 0 0 0 2 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2 1 1 2 0 0 0 0 0 2 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 0 0 0 0 0 0 0 0 2 0 2 1 0 0 0 0 2 1 0 0 0 0 1 0 0 0 2 0 0 0 0 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 2 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 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 0 0 0 0 0 0 0 0 0 0 2 0 2 0 0 1 0 0 3 0 0 1 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 2 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 0 0 0 0 0 0 0 0 0 0 0 0 1 2 0 0 0 0 1 2 2 0 0 0 1 0 0 0 1 0 0 2 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 2 0 0 0 0 0 0 0 2 0 0 0 4 0 0 0 0 0 0 2 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 0 0 0 0 0 0 0 0 0 0 0 0 3 0 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 3 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 3 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 4 1 0 0 0 0 0 0 0 4 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 2 0 0 1 0 0 1 0 1 0 0 0 0 0 0 2 0 2 0 0 0 0 2 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 2 0 0 1 2 0 0 0 0 0 0 0 0 0 0 2 0 0 0 2 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 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 6 0 1 0 0 0 0 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 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 3 0 0 0 3 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 1 4 0 2 0 0 0 0 0 0 0 2 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 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 4 0 0 0 0 0 0 2 1 0 0 2 1 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 1 0 0 0 0 4 4 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 2 0 0 0 2 0 0 0 0 0 0 0 1 0 0 1 0 0 2 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 0 0 2 0 1 0 0 0 1 0 0 0 1 0 2 0 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 2 1 0 0 0 0 0 2 0 0 0 1 0 1 0 0 1 0 0 2 0 0 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 0 0 0 0 0 0 0 0 0 0 0 2 0 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 0 1 0 2 1 1 2 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 2 0 0 0 1 0 0 0 1 4 0 0 0 0 2 0 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 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 2 0 0 2 0 0 2 0 0 0 4 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 0 0 0 2 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 4 0 0 0 0 0 1 2 4 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 4 0 0 0 0 1 0 0 0 0 2 0 0 0 0 1 1 0 2 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 2 0 0 0 0 1 0 0 0 0 2 0 0 0 2 0 1 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 0 0 0 0 0 0 0 0 0 2 0 4 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 2 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 0 0 0 0 0 1 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 3 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 0 0 0 0 0 0 6 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 3 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 0 0 0 0 0 0 classes of Z-lattices with respect to the trace form (scaled by 1/2) one representative of each class &Dim=6 V=Q^6 &Genus of the trace-forms: det= 2744 = 2^3 *7^3 2-adic symbol: [1^3 2^3]_4 7-adic symbol: 1^-3 7^-3 -1-adic symbol: +^6 -^0 level(of 2-scaled form)=56, weight=3 a_0,..,a_24 determine modular form 27 classes of trace forms &begin_block &Gram (#1 <- H1,H2,H32,H33) 4 1 4 1 1 4 1 2 1 5 2 0 0 1 5 1 1 2 0 1 5 |Aut| = 2^2*3 #short vectors: 0 0 0 6 12 6 12 18 32 42 48 30 24 48 68 90 60 116 108 126 168 156 144 138 &Gram (#2 <- H3,H35) 4 0 4 2 2 5 0 0 1 5 2 -1 1 -1 6 0 -2 0 -2 3 6 |Aut| = 2^3 #short vectors: 0 0 0 4 10 16 12 24 24 20 44 30 54 50 80 80 56 120 112 106 142 160 140 182 &Gram (#3 <- H4,H34) 4 0 4 2 -2 5 1 0 0 5 1 0 0 -2 5 0 2 0 1 1 6 |Aut| = 2^3 #short vectors: 0 0 0 4 14 8 12 24 24 36 44 30 34 50 80 80 56 120 104 122 170 160 140 150 &Gram (#4 <- H5,H38) 3 1 3 1 1 3 0 -1 0 6 0 -1 0 -1 6 1 -1 -1 -1 -1 7 |Aut| = 2^3 #short vectors: 0 0 6 6 0 4 16 22 24 28 44 58 56 50 76 78 60 116 66 70 176 164 140 150 &Gram (#5 <- H6,H7,H8,H36,H39,H40) 3 0 3 0 0 3 0 0 -1 5 1 0 0 0 5 0 1 0 0 0 5 |Aut| = 2^4*3 #short vectors: 0 0 6 0 6 18 0 24 32 18 48 42 54 48 80 96 48 128 102 90 150 144 144 138 &Gram (#6 <- H9,H37) 3 1 3 0 1 3 1 0 -1 6 0 0 0 2 6 1 0 -1 0 -2 6 |Aut| = 2^3 #short vectors: 0 0 6 4 2 10 8 20 32 26 48 50 50 48 72 92 56 120 86 82 162 152 144 138 &Gram (#7 <- H10,H41) 3 1 3 1 1 3 1 -1 1 7 1 -1 -1 2 7 1 -1 1 0 2 7 |Aut| = 2^3*3^2 #short vectors: 0 0 6 6 0 0 24 30 8 24 36 66 72 54 92 54 60 116 42 54 192 180 132 174 &Gram (#8 <- H11,H43) 3 1 4 1 -1 4 1 2 1 6 1 2 1 0 6 0 0 0 2 -2 6 |Aut| = 2^3 #short vectors: 0 0 2 4 6 18 8 20 32 18 48 34 54 48 72 92 56 120 114 98 134 152 144 170 &Gram (#9 <- H12,H13,H42,H44) 3 0 4 0 -1 4 0 0 -1 4 0 -1 0 1 4 1 0 0 0 0 5 |Aut| = 2^5 #short vectors: 0 0 2 8 2 10 16 16 32 26 48 42 50 48 64 88 64 112 98 90 146 160 144 170 &Gram (#10 <- H14,H45) 2 1 2 0 0 2 0 0 0 7 1 0 0 0 10 1 0 0 0 -4 10 |Aut| = 2^5*3^2 #short vectors: 0 8 0 12 0 6 2 20 16 42 24 54 12 96 40 108 84 80 108 150 192 168 216 90 &Gram (#11 <- H15,H46) 2 1 2 1 0 4 1 1 1 5 1 1 -1 -1 11 1 1 -1 -1 -3 11 |Aut| = 2^3*3^2 #short vectors: 0 6 0 6 6 12 12 18 20 0 48 30 66 60 68 78 96 122 120 114 102 168 168 222 &Gram (#12 <- H16,H47) 2 0 2 0 0 3 0 0 -1 5 0 0 0 0 7 0 0 0 0 0 7 |Aut| = 2^7 #short vectors: 0 4 2 4 10 2 20 12 24 26 24 50 34 92 72 76 88 60 90 146 194 176 200 122 &Gram (#13 <- H17,H48) 2 0 2 0 1 3 0 0 -1 6 0 0 0 0 7 0 -1 -1 3 0 9 |Aut| = 2^5 #short vectors: 0 4 4 4 8 2 10 12 32 30 40 46 28 72 64 92 84 92 96 134 176 160 184 114 &Gram (#14 <- H18,H49) 2 0 2 0 0 3 0 0 -1 5 1 -1 0 0 8 1 -1 0 0 1 8 |Aut| = 2^7 #short vectors: 0 4 2 4 10 2 16 28 8 18 40 42 58 60 88 60 80 124 82 106 162 176 152 186 &Gram (#15 <- H19,H50) 2 0 3 0 0 4 1 0 2 5 0 -1 0 0 5 0 0 2 1 0 8 |Aut| = 2^5 #short vectors: 0 2 2 2 14 6 8 26 20 30 44 34 38 54 84 78 64 126 98 122 170 160 148 146 &Gram (#16 <- H20,H52) 2 0 3 1 1 4 1 0 0 5 1 -1 0 2 6 0 -1 1 2 1 9 |Aut| = 2^3 #short vectors: 0 2 2 4 12 4 8 20 28 36 48 34 28 52 72 88 68 122 102 126 168 156 152 134 &Gram (#17 <- H21,H54) 2 0 4 0 2 4 0 0 -1 5 0 0 -1 -2 5 0 0 0 0 0 7 |Aut| = 2^5 #short vectors: 0 2 0 6 4 18 18 14 28 6 36 38 64 70 68 82 76 86 116 110 128 168 172 194 &Gram (#18 <- H22,H53) 2 1 4 0 -1 4 1 -1 1 5 1 2 1 -1 6 1 0 -1 0 2 9 |Aut| = 2^3 #short vectors: 0 2 0 6 6 16 12 18 28 12 48 30 58 52 68 86 72 118 120 106 118 160 152 198 &Gram (#19 <- H23,H51) 2 1 3 0 1 3 1 1 0 6 0 -1 -1 2 7 0 0 1 1 3 9 |Aut| = 2^3 #short vectors: 0 2 6 4 4 4 8 20 28 28 48 50 44 52 72 88 68 122 82 94 168 156 152 134 &Gram (#20 <- H24,H55) 2 0 3 1 0 4 0 0 0 4 0 -1 0 0 5 0 0 0 2 0 8 |Aut| = 2^5 #short vectors: 0 2 2 6 6 6 16 22 20 22 44 42 54 54 76 74 72 118 90 98 154 168 148 178 &Gram (#21 <- H25,H56) 2 0 4 0 2 4 0 -2 0 6 0 2 0 1 6 0 0 0 0 0 7 |Aut| = 2^5*3^2 #short vectors: 0 2 0 6 0 30 2 38 4 18 12 54 60 90 76 90 36 86 108 102 180 168 180 138 &Gram (#22 <- H26,H57) 1 0 1 0 0 3 0 0 -1 5 0 0 0 0 14 0 0 0 0 0 14 |Aut| = 2^7 #short vectors: 4 4 2 12 18 10 24 28 12 34 32 18 42 44 64 60 40 92 106 98 146 176 136 170 &Gram (#23 <- H27,H58) 1 0 2 0 0 3 0 0 -1 5 0 0 0 0 7 0 0 0 0 0 14 |Aut| = 2^5 #short vectors: 2 2 6 6 6 18 14 18 30 18 32 42 54 62 64 86 48 78 102 90 150 160 164 138 &Gram (#24 <- H28,H59) 1 0 2 0 1 3 0 0 -1 6 0 -1 -1 3 9 0 0 0 0 0 14 |Aut| = 2^5 #short vectors: 2 2 8 10 0 6 20 22 22 26 40 54 60 46 64 74 52 102 68 54 160 168 140 154 &Gram (#25 <- H29,H60) 1 0 4 0 2 4 0 0 -1 5 0 0 -1 -2 5 0 0 0 0 0 14 |Aut| = 2^5 #short vectors: 2 0 0 8 16 14 20 28 18 34 36 22 44 44 76 68 36 104 108 102 156 168 128 170 &Gram (#26 <- H30,H61) 1 0 2 0 1 2 0 -1 -1 10 0 1 0 -5 10 0 0 0 0 0 14 |Aut| = 2^5*3^2 #short vectors: 2 6 12 2 0 18 12 6 14 30 48 30 36 86 112 50 36 154 120 54 96 144 196 114 &Gram (#27 <- H31,H62) 1 0 4 0 2 4 0 2 0 6 0 -2 0 1 6 0 0 0 0 0 14 |Aut| = 2^5*3^2 #short vectors: 2 0 0 8 12 18 36 12 2 54 36 6 24 80 124 20 12 136 132 78 120 168 160 162 &end_block