Output of /home/aschiem/Pgm/Hn/hn --invar -t --herm_lll2 0.0001 --shells-4 -D6 --herm_lll3 0.8 &K=Q(sqrt(-2)) &Hdim=8 V=K^8 &HNeighbourhood at <3,-1+w> contains 26 classes: mass of the neighbourhood is 99161/275251200 Steinitz class <1,w>: &Hlattice (#1 <- #17) 4 1 4 -2+w 1 4 -2w -1-w -1+w 4 -1-w -w 1 2-w 4 2 0 -1 1+2w -1+2w 4 -1 -2+w 0 1-w 1-w -w 4 1 2w w 0 w 1-w 1 4 |Aut| = 2^14*3^2 #short vectors: 0 0 0 4320 &Hlattice (#2 <- #26) 4 2-2w 4 -2w 2-w 4 2+w w 0 4 w -1 -1-w 2 4 -1 -w -1 -1 1-w 4 -2w 2-w 2 -1-w -1-w 1 4 0 -1 -w 1-w 2-w 0 1 4 |Aut| = 2^14*3^4*5 #short vectors: 0 0 0 4320 &Hlattice (#3 <- #12) 2 1 2 -1 -1 2 1 0 0 2 0 1 -1 -1 2 1 1 0 0 0 2 0 0 -1 0 1 -1 2 -1 0 0 -1 1 -1 1 2 |Aut| = 2^14*3^5*5^2*7 #short vectors: 0 240 0 2400 &Hlattice (#4 <- #21) 2 0 2 0 1 2 0 0 0 2 0 -1 0 -1 2 0 w 0 0 -w 2 -1 -1 0 0 1 w 2 w 0 w -w w -1 0 4 |Aut| = 2^15*3^2*5*7 #short vectors: 0 128 0 3296 &Hlattice (#5 <- #24) 2 1 2 1 1 2 1 1 1 2 1 0 1 1 2 0 0 0 0 0 2 0 0 0 -1 0 1 2 1-w -w 1-w 1-w 1-w -1 -1 4 |Aut| = 2^14*3^2*5*7 #short vectors: 0 112 0 3424 &Hlattice (#6 <- #1) 2 1-w 2 0 0 2 0 0 1-w 2 0 0 0 0 2 0 0 0 0 1-w 2 0 0 0 0 0 0 2 0 0 0 0 0 0 1-w 2 |Aut| = 2^19*3^5 #short vectors: 0 96 0 3552 &Hlattice (#7 <- #2) 2 -w 2 0 1 2 -1 0 w 2 0 0 0 0 2 0 0 0 0 1-w 2 0 0 0 0 0 0 2 0 0 0 0 0 0 1-w 2 |Aut| = 2^17*3^4 #short vectors: 0 96 0 3552 &Hlattice (#8 <- #3) 2 -1 2 0 0 2 -1 1 0 2 -1 0 0 0 2 1 -1 0 -1 -1 2 0 0 1-w 0 0 0 2 -1 w 0 1+w 1-w -1 0 4 |Aut| = 2^12*3^5*5 #short vectors: 0 96 0 3552 &Hlattice (#9 <- #5) 2 0 2 0 1 2 0 w 0 2 -1 -1 0 w 2 0 0 0 0 0 2 0 0 0 0 0 1-w 2 -w -1 w -1+w 1+w 0 0 4 |Aut| = 2^14*3^3*5 #short vectors: 0 96 0 3552 &Hlattice (#10 <- #6) 2 -1 2 0 0 2 1 0 -1 2 0 -1 1 -1 2 0 0 0 0 0 2 0 0 0 0 0 1-w 2 -w w 1 -1 -w 0 0 4 |Aut| = 2^12*3^5*5 #short vectors: 0 96 0 3552 &Hlattice (#11 <- #7) 2 0 2 0 1 2 0 0 w 2 0 w 0 -1 2 -w 0 0 0 0 2 0 0 0 0 0 1 2 -1 0 0 0 0 0 w 2 |Aut| = 2^17*3^4 #short vectors: 0 96 0 3552 &Hlattice (#12 <- #11) 2 1 2 0 1 2 0 0 0 2 -1 0 0 0 2 0 0 -1 -1 0 2 1+w 1+w 1 -1 -1 0 4 -1+w -1 0 w -w -w w 4 |Aut| = 2^8*3^4*5*7 #short vectors: 0 72 0 3744 &Hlattice (#13 <- #22) 2 -1 2 0 -1 2 0 0 1 2 0 0 0 0 2 0 0 -1 -1 0 2 1 0 0 0 1+w -1 4 w -w -1 -1 -w 1 -2 4 |Aut| = 2^8*3^4*5*7 #short vectors: 0 72 0 3744 &Hlattice (#14 <- #18) 2 0 2 0 1 2 0 w 0 2 -1 0 0 0 2 0 0 0 0 -w 2 0 -1 w -1+w -1 -w 4 -w -1 0 w 1+w -1+w -w 4 |Aut| = 2^15*3^2 #short vectors: 0 64 0 3808 &Hlattice (#15 <- #8) 2 0 2 0 -w 2 0 1 0 2 0 0 0 0 2 -1 0 0 0 0 2 1-w -w 1 -w 0 -1+w 4 1-w 1 0 1 -1 w 2 4 |Aut| = 2^9*3^3*5 #short vectors: 0 48 0 3936 &Hlattice (#16 <- #10) 2 1 2 1 1 2 1 0 1 2 0 0 0 0 2 0 0 0 0 1 2 1-w 1 1-w 1-w 1 0 4 1-w -w 1-w 1-w -1 -1 1 4 |Aut| = 2^14*3^2 #short vectors: 0 48 0 3936 &Hlattice (#17 <- #19) 2 0 2 0 1 2 -1 0 0 2 0 0 0 -w 2 0 -w 1 -1 -w 4 -w -1 -1 1 1+w -2 4 -w -1 0 1+w -1+w -1-w 2+w 4 |Aut| = 2^9*3^3*5 #short vectors: 0 48 0 3936 &Hlattice (#18 <- #23) 2 0 2 0 0 2 0 1 0 2 0 0 0 1 2 1-w 0 1-w -1 -1 4 1 1-w 0 0 0 1 4 0 1-w -1 1 0 -1-w 2-w 4 |Aut| = 2^14*3^3 #short vectors: 0 48 0 3936 &Hlattice (#19 <- #20) 2 -1 2 0 1 2 0 0 0 2 0 0 0 0 2 1+w -1-w 0 0 -w 4 1 0 1 0 1+w -1 4 -1-w 1+w w 1 0 -2 -1 4 |Aut| = 2^7*3^2*5^2 #short vectors: 0 40 0 4000 &Hlattice (#20 <- #14) 2 0 2 0 -1 2 -1 0 0 2 -1 -1-w w 0 4 0 0 -1 -1+w 1 4 w w -1 0 -w 2-w 4 1 -1-w 1+w 0 1-w -1-w -1-w 4 |Aut| = 2^11*3^2 #short vectors: 0 32 0 4064 &Hlattice (#21 <- #16) 2 -w 2 0 0 2 0 0 0 2 -w 1 1 w 4 1-w 1 0 0 2+w 4 1-w 1 1+w 0 2+w 2 4 -w 1 1 1 2-w -w 2-w 4 |Aut| = 2^18*3 #short vectors: 0 32 0 4064 &Hlattice (#22 <- #25) 2 -w 2 0 0 2 0 0 -w 2 1-w 1 1 w 4 1-w 1 -w 1 2 4 -w 1 -w 1 2-w 2-w 4 1 0 -w 1 2 2 2 4 |Aut| = 2^17 #short vectors: 0 32 0 4064 &Hlattice (#23 <- #4) 2 1 2 0 0 2 0 0 0 2 1-w -w 1 -1 4 1-w 1 1 -1 2 4 -w 0 1 w 2-w 2-w 4 1-w 0 1-w 0 2-w 2 2 4 |Aut| = 2^8*3^5 #short vectors: 0 24 0 4128 &Hlattice (#24 <- #9) 2 1 2 0 0 2 0 0 1 2 0 0 0 0 2 -w 0 1-w 1-w -1 4 1-w -w -w -w 0 2 4 1-w 1 -w 0 0 2 2 4 |Aut| = 2^7*3^4 #short vectors: 0 24 0 4128 &Hlattice (#25 <- #15) 2 1 2 0 0 2 0 0 0 2 1-w 1-w 1 -1 4 1-w 0 1 -1 2 4 1-w -w 1-w 0 2-w 2 4 1-w -w 0 0 2-w 2 2 4 |Aut| = 2^8*3^5 #short vectors: 0 24 0 4128 &Hlattice (#26 <- #13) 2 0 2 0 0 2 1 0 -1+w 4 -1 -1+w 0 -2 4 -w 0 0 2-w -2+w 4 1-w -1 1 -1-w 1+w 0 4 0 1+w -1-w -1+w 1-w -1 -1-w 4 |Aut| = 2^12*3 #short vectors: 0 16 0 4192 classes of Z-lattices with respect to the trace form (scaled by 1/2) one representative of each class &Dim=16 V=Q^16 &Genus of the trace-forms: det= 256 = 2^8 2-adic symbol: 1^8_II 2^8_II -1-adic symbol: +^16 -^0 level=2, weight=8 a_0,..,a_4 determine modular form 16-classes of trace forms &Gram (#1 <- H1,H2) 4 2 4 2 0 4 2 0 0 4 2 0 2 0 4 2 0 0 2 0 4 2 2 0 0 0 2 4 2 0 0 2 0 2 2 4 2 0 1 1 1 1 1 2 4 2 2 1 1 0 0 1 1 0 4 2 1 2 0 1 1 2 1 0 2 4 1 2 0 0 1 -1 0 -1 1 1 -1 4 1 -1 2 0 2 0 0 0 0 0 2 -1 4 0 -1 -1 1 1 1 -1 0 -1 0 0 -1 1 4 0 -1 -1 1 -1 1 1 2 2 -1 -1 -1 0 0 4 1 -1 2 0 2 0 0 0 2 0 1 0 2 0 1 4 |Aut| = 2^21*3^5*5^2*7 #short vectors: 0 0 0 4320 &Gram (#2 <- H3) 2 1 2 -1 -1 2 1 0 0 2 0 1 -1 -1 2 1 1 0 0 0 2 0 0 -1 0 1 -1 2 -1 0 0 -1 1 -1 1 2 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 2 4 0 0 0 0 0 0 0 0 -2 -2 4 0 0 0 0 0 0 0 0 2 0 0 4 0 0 0 0 0 0 0 0 0 2 -2 -2 4 0 0 0 0 0 0 0 0 2 2 0 0 0 4 0 0 0 0 0 0 0 0 0 0 -2 0 2 -2 4 0 0 0 0 0 0 0 0 -2 0 0 -2 2 -2 2 4 |Aut| = 2^28*3^10*5^4*7^2 #short vectors: 0 240 0 2400 &Gram (#3 <- H4) 2 1 2 1 0 2 1 0 0 2 1 1 0 0 2 1 1 0 0 1 2 1 1 0 0 1 1 2 1 1 0 0 1 1 1 2 0 0 0 0 0 0 0 0 2 0 0 0 0 0 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 2 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 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 1 1 -1 1 -1 -1 1 4 |Aut| = 2^30*3^4*5^2*7^2 #short vectors: 0 128 0 3296 &Gram (#4 <- H5) 2 1 2 1 1 2 1 0 1 2 1 1 1 0 2 1 1 1 0 1 2 1 1 1 0 1 1 2 1 1 1 0 1 1 1 2 1 0 1 1 0 1 1 0 4 1 0 1 1 0 0 0 0 1 4 1 0 1 1 0 1 1 0 2 1 4 1 0 1 1 0 0 0 0 1 2 1 4 1 0 1 1 0 0 0 0 1 2 1 2 4 0 0 0 0 0 0 0 0 1 1 1 1 -1 4 0 0 0 0 0 0 0 0 1 -1 1 -1 -1 0 4 1 0 0 0 0 0 1 0 0 0 0 2 2 -1 -1 6 |Aut| = 2^28*3^4*5^2*7^2 #short vectors: 0 112 0 3424 &Gram (#5 <- H6,H7,H11) 2 1 2 1 0 2 1 0 0 2 0 0 0 0 2 0 0 0 0 1 2 0 0 0 0 1 0 2 0 0 0 0 1 0 0 2 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 1 2 0 0 0 0 0 0 0 0 1 0 2 0 0 0 0 0 0 0 0 1 0 0 2 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 1 2 0 0 0 0 0 0 0 0 0 0 0 0 -1 -1 2 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 2 |Aut| = 2^31*3^9 #short vectors: 0 96 0 3552 &Gram (#6 <- H8,H10) 2 1 2 1 0 2 1 0 0 2 1 1 0 0 2 1 0 1 0 0 2 0 0 0 0 0 0 2 0 0 0 0 0 0 -1 2 0 0 0 0 0 0 -1 0 2 0 0 0 0 0 0 1 0 0 2 1 0 1 0 0 1 0 0 0 0 4 1 0 1 0 0 1 0 0 0 0 0 4 1 0 0 1 0 1 0 0 0 0 0 0 4 1 0 1 0 0 1 0 0 0 0 2 0 2 4 1 0 1 0 0 1 0 0 0 0 2 0 2 2 4 1 0 1 0 0 1 0 0 0 0 2 0 0 2 2 4 |Aut| = 2^22*3^10*5^2 #short vectors: 0 96 0 3552 &Gram (#7 <- H9) 2 1 2 1 0 2 1 0 0 2 1 1 0 0 2 1 1 0 0 1 2 0 0 0 0 0 0 2 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 1 2 0 0 0 0 0 0 0 1 0 2 0 0 0 0 0 0 0 -1 0 0 2 0 0 0 0 0 0 0 0 0 0 0 2 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 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 1 0 0 1 1 -1 0 0 0 0 -1 -1 -1 -1 4 |Aut| = 2^27*3^6*5^2 #short vectors: 0 96 0 3552 &Gram (#8 <- H12,H13) 2 1 2 1 0 2 1 0 1 2 1 1 0 0 2 1 0 1 1 0 2 1 1 0 0 1 0 2 1 0 1 1 0 1 0 2 1 0 0 0 0 0 0 0 4 1 1 1 0 0 0 0 1 1 4 1 0 0 0 0 1 1 0 1 0 4 1 0 0 1 1 0 0 0 1 0 0 4 1 0 0 0 0 1 1 0 1 0 2 0 4 1 0 0 0 0 1 1 0 1 0 2 0 2 4 1 0 0 1 1 0 0 0 1 0 0 2 0 0 4 1 0 0 0 0 0 0 0 2 1 1 1 1 1 1 4 |Aut| = 2^15*3^8*5^2*7^2 #short vectors: 0 72 0 3744 &Gram (#9 <- H14) 2 1 2 1 1 2 1 1 0 2 0 0 0 0 2 0 0 0 0 -1 2 0 0 0 0 1 -1 2 0 0 0 0 -1 0 -1 2 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 2 1 1 0 1 -1 0 -1 1 -1 0 4 1 1 0 1 -1 0 -1 1 -1 0 2 4 1 1 0 1 -1 0 -1 1 -1 0 2 2 4 1 1 0 1 1 0 1 -1 0 1 0 0 0 4 1 0 1 0 1 -1 0 0 0 1 0 0 0 1 4 1 0 1 0 1 -1 0 0 0 -1 0 0 0 0 1 4 |Aut| = 2^30*3^4 #short vectors: 0 64 0 3808 &Gram (#10 <- H15,H17) 2 1 2 1 1 2 0 0 0 2 0 0 0 1 2 0 0 0 -1 -1 2 0 0 0 -1 -1 1 2 0 0 0 -1 -1 1 1 2 1 1 0 1 0 -1 -1 0 4 1 1 0 1 0 -1 0 -1 1 4 1 1 0 1 0 -1 -1 0 2 1 4 1 0 1 1 1 0 -1 -1 0 0 0 4 1 1 0 1 0 -1 0 0 2 2 2 0 4 1 0 1 1 1 0 -1 -1 0 0 0 2 0 4 1 0 1 1 1 0 -1 -1 0 0 0 2 0 2 4 1 0 1 -1 0 1 0 0 -1 -1 -1 1 -1 1 1 4 |Aut| = 2^17*3^6*5^2 #short vectors: 0 48 0 3936 &Gram (#11 <- H16,H18) 2 1 2 1 1 2 1 0 1 2 0 0 0 0 2 0 0 0 0 1 2 0 0 0 0 -1 0 2 0 0 0 0 1 0 0 2 1 0 0 0 -1 0 0 -1 4 1 0 0 1 -1 0 1 0 2 4 1 1 0 0 -1 0 1 -1 0 0 4 1 1 0 0 -1 0 1 -1 0 0 2 4 1 1 0 0 1 1 0 0 0 0 1 1 4 1 1 1 0 1 0 -1 0 0 -1 0 0 0 4 1 1 1 0 1 0 -1 0 0 -1 0 0 0 2 4 1 1 1 0 1 0 -1 0 0 -1 0 0 0 2 2 4 |Aut| = 2^27*3^5 #short vectors: 0 48 0 3936 &Gram (#12 <- H19) 2 1 2 1 0 2 1 0 1 2 0 0 0 0 2 0 0 0 0 1 2 0 0 0 0 1 0 2 0 0 0 0 1 0 1 2 1 0 0 1 -1 0 0 0 4 1 0 0 0 -1 0 0 -1 2 4 1 0 0 0 -1 0 0 -1 2 2 4 1 0 0 0 -1 0 0 -1 2 2 2 4 1 0 0 1 1 0 0 0 0 0 0 0 4 1 0 0 1 1 0 0 0 0 0 0 0 2 4 1 1 1 0 -1 0 0 0 1 1 1 1 -1 -1 4 1 1 1 0 -1 0 0 0 1 1 1 1 -1 -1 2 4 |Aut| = 2^15*3^4*5^4 #short vectors: 0 40 0 4000 &Gram (#13 <- H20) 2 1 2 1 0 2 0 0 0 2 0 0 0 -1 2 0 0 0 -1 0 2 0 0 0 0 0 0 2 0 0 0 0 0 0 0 2 1 0 0 -1 0 0 -1 1 4 1 0 0 -1 0 0 1 -1 1 4 1 0 1 -1 0 1 1 0 0 1 4 1 1 0 -1 1 0 0 -1 0 2 0 4 1 0 1 -1 0 1 1 0 0 1 2 0 4 1 1 0 -1 0 1 0 -1 0 2 1 2 1 4 1 1 0 -1 0 1 0 -1 0 2 1 2 1 2 4 1 1 0 -1 0 1 1 0 0 1 2 1 2 2 2 4 |Aut| = 2^22*3^4 #short vectors: 0 32 0 4064 &Gram (#14 <- H21,H22) 2 0 2 0 0 2 0 0 0 2 0 0 0 0 2 0 0 0 0 0 2 0 0 0 0 0 0 2 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 2 0 1 1 1 1 0 -1 0 1 0 0 4 0 1 0 1 -1 0 0 1 1 1 0 1 4 1 1 0 1 -1 1 0 0 1 0 -1 1 2 4 0 1 1 1 -1 0 1 0 1 0 0 1 2 2 4 1 1 1 0 -1 1 -1 -1 0 0 0 1 0 2 1 4 |Aut| = 2^30*3*7 #short vectors: 0 32 0 4064 &Gram (#15 <- H23,H24,H25) 2 1 2 0 0 2 0 0 1 2 0 0 0 0 2 0 0 0 0 -1 2 0 0 0 0 0 0 2 0 0 0 0 0 0 1 2 1 0 1 0 -1 1 -1 0 4 1 0 -1 -1 1 0 1 1 -1 4 1 0 1 1 -1 0 -1 0 2 -1 4 1 1 1 0 -1 1 -1 -1 2 -1 2 4 1 0 1 1 -1 1 1 0 1 0 1 1 4 1 0 1 1 1 0 1 0 0 1 0 0 1 4 1 1 1 1 -1 1 -1 0 2 -1 2 2 1 0 4 1 0 1 0 -1 0 1 0 1 0 1 1 2 1 1 4 |Aut| = 2^14*3^9 #short vectors: 0 24 0 4128 &Gram (#16 <- H26) 2 0 2 0 0 2 0 0 0 2 0 0 0 0 2 1 -1 -1 1 1 4 1 -1 -1 1 -1 1 4 1 -1 -1 1 1 2 1 4 1 0 -1 1 0 1 1 2 4 0 -1 -1 1 1 2 1 2 0 4 1 -1 0 0 1 1 0 2 0 2 4 0 -1 0 1 0 1 0 1 0 2 1 4 1 1 0 1 0 1 0 1 0 1 0 1 4 1 0 0 1 1 2 0 1 0 2 1 2 2 4 0 -1 0 1 0 1 0 1 2 1 0 2 0 1 4 1 -1 0 0 1 1 0 2 0 2 2 2 1 2 1 4 |Aut| = 2^25*3*7 #short vectors: 0 16 0 4192