Output of /home/aschiem/Pgm/Hn/hn --invar -t --herm_lll2 0.0001 --shells-4 -D6 --herm_lll3 0.8 &K=Q(sqrt(-1)) &Hdim=9 V=K^9 &HNeighbourhood at <2,-1+w> contains 12 classes: mass of the neighbourhood is 16897/57076088832 Steinitz class <1,w>: &Hlattice (#1 <-- #8) 2 1+w 2 0 0 2 0 0 1 2 0 0 1 1 2 0 0 1 1 1 2 0 -1 0 0 0 0 2 1+w 1 1-w 1-w 1-w 1-w 0 3 1 0 0 0 0 0 1-w 0 3 |Aut| = 2^16*3^3*5 #short vectors: 0 180 4800 48420 &Hlattice (#2 <-- #11) 2 0 2 1 0 2 1 0 1 2 0 w 0 0 2 1 0 1 1 0 2 0 0 0 0 -w 0 2 w -w w w w w -1+w 3 0 -1 0 0 0 0 -w -1-w 3 |Aut| = 2^10*3^4*5^2*7 #short vectors: 0 180 4800 48420 &Hlattice (#3 <-- #12) 2 0 2 w 0 2 w 0 1 2 w 0 1 1 2 w 0 1 1 1 2 w 1 0 0 0 0 2 -w 0 0 0 0 0 -1 2 -1-w -1 0 0 0 0 -1+w -w 3 |Aut| = 2^10*3^4*5^2*7 #short vectors: 0 180 4800 48420 &Hlattice (#4 <-- #1) 1 0 1 0 0 1 0 0 0 1 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 |Aut| = 2^25*3^4*5*7 #short vectors: 36 612 6528 48996 &Hlattice (#5 <-- #2) 1 0 1 0 0 1 0 0 0 1 0 0 0 0 1 0 0 0 0 0 2 0 0 0 0 0 1 2 0 0 0 0 0 0 1+w 2 0 0 0 0 0 0 1+w 1 2 |Aut| = 2^23*3^3*5^2 #short vectors: 20 420 5760 48740 &Hlattice (#6 <-- #3) 1 0 1 0 0 1 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-w 1-w 1-w 1-w 2 0 0 0 0 0 0 0 1 3 |Aut| = 2^22*3^3*5 #short vectors: 12 324 5376 48612 &Hlattice (#7 <-- #7) 1 0 1 0 0 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 1 0 w w w 2 0 0 -1-w -1+w -1+w -1+w -1+w 0 3 |Aut| = 2^16*3^4*5*7 #short vectors: 8 276 5184 48548 &Hlattice (#8 <-- #4) 1 0 2 0 1+w 2 0 1+w 1 2 0 1+w 1 1 2 0 1+w 1 1 1 2 0 1+w 1 1 1 1 2 0 1+w 1 1 1 1 1 2 0 1 0 0 0 0 0 0 4 |Aut| = 2^24*3^2*5*7 #short vectors: 4 484 1920 63844 &Hlattice (#9 <-- #5) 1 0 2 0 1+w 2 0 1+w 1 2 0 1 0 0 2 0 0 0 0 0 2 0 0 0 0 0 1 2 0 0 0 0 0 0 1+w 2 0 0 0 0 0 0 1+w 1 2 |Aut| = 2^23*3^4*5^2 #short vectors: 4 484 1920 63844 &Hlattice (#10 <-- #6) 1 0 2 0 1+w 2 0 1+w 1 2 0 0 0 0 2 0 0 0 0 0 2 0 0 0 0 0 1 2 0 1 0 0 -1+w 0 0 3 0 1+w 1 1 1 1-w 1-w 0 3 |Aut| = 2^23*3^2 #short vectors: 4 228 4992 48484 &Hlattice (#11 <-- #9) 1 0 2 0 0 2 0 -w 1 2 0 -w 1 1 2 0 -w 1 1 1 2 0 -w 1 1 1 1 2 0 -w 1 1 1 1 1 2 0 1 0 0 0 0 0 0 2 |Aut| = 2^17*3^5*5^2*7 #short vectors: 4 484 1920 63844 &Hlattice (#12 <-- #10) 1 0 2 0 1 2 0 1 1 2 0 1 1 1 2 0 1 1 1 1 2 0 1 1 1 1 1 2 0 0 -w -w -w -w -w 2 0 -1+w -1+w -1+w -1+w -1+w -1+w -w 3 |Aut| = 2^17*3^2*5*7 #short vectors: 4 228 4992 48484 &Adjacence matrix (M_ij=#{neighbours of class i isometric to class j}): 217 128 128 0 0 1 6 0 0 30 0 0 210 45 210 0 0 0 0 0 0 0 0 45 210 210 45 0 0 0 0 0 0 0 0 45 0 0 0 72 252 168 0 18 0 0 0 0 0 0 0 15 35 300 0 0 10 150 0 0 64 0 0 1 30 37 192 6 0 180 0 0 126 0 0 0 0 63 65 0 0 0 4 252 0 0 0 1 0 56 0 57 70 70 128 128 0 0 0 0 30 0 0 225 30 225 0 0 256 0 0 0 2 24 0 1 1 98 0 128 0 0 0 0 0 0 120 135 0 0 120 135 0 128 128 0 0 0 56 1 0 70 1 126 classes of Z-lattices with respect to the trace form (scaled by 1/2) one representative of each class &Dim=18 V=Q^18 &Genus of the trace-forms: det= 1 = 1 2-adic symbol: 1^18_2 -1-adic symbol: +^18 -^0 level(of 2-scaled form)=4, weight=9 a_0,..,a_4 determine modular form 9-classes of trace forms &Gram (#1 <- H1) 2 1 2 1 1 2 1 1 0 2 1 0 0 0 2 1 0 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 0 2 0 0 0 0 0 0 0 0 1 2 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 -1 2 0 0 0 0 0 0 0 -1 0 0 0 0 2 1 1 1 0 0 0 1 0 0 0 0 0 -1 3 1 1 1 0 0 0 0 0 0 0 0 0 0 1 3 0 0 0 0 0 0 -1 -1 0 0 -1 1 0 0 0 3 1 0 0 0 1 1 -1 0 -1 -1 0 0 0 0 0 1 3 1 1 0 1 0 1 1 0 0 0 0 0 0 1 0 -1 0 3 |Aut| = 2^28*3^7*5^3 #short vectors: 0 180 4800 48420 &Gram (#2 <- H2,H3) 2 1 2 1 0 2 1 1 0 2 1 1 0 1 2 1 1 0 1 1 2 1 1 0 1 1 1 2 1 1 0 1 1 1 1 2 1 1 0 1 1 1 1 1 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 1 2 0 0 0 0 0 0 0 0 0 0 1 1 2 0 0 0 0 0 0 0 0 0 0 1 1 1 2 0 0 0 0 0 0 0 0 0 0 1 1 1 1 2 1 0 0 1 0 0 0 0 0 -1 0 0 0 0 0 3 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 3 1 0 0 0 1 1 1 1 1 0 1 1 1 1 1 0 1 3 |Aut| = 2^18*3^8*5^4*7^2 #short vectors: 0 180 4800 48420 &Gram (#3 <- H4) 1 0 1 0 0 1 0 0 0 1 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 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 1 0 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 1 0 0 0 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 1 |Aut| = 2^34*3^8*5^3*7^2*11*13*17 #short vectors: 36 612 6528 48996 &Gram (#4 <- H5) 1 0 1 0 0 1 0 0 0 1 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 -1 2 0 0 0 0 0 0 0 0 0 0 -1 0 2 0 0 0 0 0 0 0 0 0 0 1 0 0 2 0 0 0 0 0 0 0 0 0 0 -1 1 0 0 2 0 0 0 0 0 0 0 0 0 0 1 0 -1 0 0 2 0 0 0 0 0 0 0 0 0 0 -1 0 1 0 0 -1 2 0 0 0 0 0 0 0 0 0 0 -1 1 1 0 1 0 0 2 |Aut| = 2^32*3^9*5^4*7^2 #short vectors: 20 420 5760 48740 &Gram (#5 <- H6) 1 0 1 0 0 1 0 0 0 1 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 -1 2 0 0 0 0 0 0 -1 1 2 0 0 0 0 0 0 1 -1 0 2 0 0 0 0 0 0 1 0 0 1 2 0 0 0 0 0 0 -1 0 0 -1 -1 2 0 0 0 0 0 0 1 0 0 1 1 -1 2 0 0 0 0 0 0 -1 0 0 -1 -1 1 -1 2 0 0 0 0 0 0 1 0 0 1 1 -1 1 -1 2 0 0 0 0 0 0 1 0 0 1 1 -1 1 -1 1 2 0 0 0 0 0 0 -1 1 1 -1 0 0 0 0 0 0 3 0 0 0 0 0 0 1 -1 0 1 0 0 0 0 1 1 -1 3 |Aut| = 2^31*3^7*5^3*7*11 #short vectors: 12 324 5376 48612 &Gram (#6 <- H7) 1 0 1 0 0 1 0 0 0 1 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 0 0 0 0 0 0 -1 1 2 0 0 0 0 0 0 -1 1 0 2 0 0 0 0 0 0 1 0 0 -1 2 0 0 0 0 0 0 -1 1 0 1 0 2 0 0 0 0 0 0 1 -1 0 -1 0 -1 2 0 0 0 0 0 -1 0 0 0 0 0 0 0 2 0 0 0 0 0 1 0 0 0 0 0 0 0 -1 2 0 0 0 0 0 1 0 0 0 0 0 0 0 -1 1 2 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 1 1 2 0 0 0 0 -1 0 1 0 -1 0 0 0 0 -1 1 1 1 3 |Aut| = 2^28*3^9*5^2*7^2 #short vectors: 8 276 5184 48548 &Gram (#7 <- H8) 1 0 1 0 0 2 0 0 -1 2 0 0 -1 1 2 0 0 1 -1 0 2 0 0 1 0 0 1 2 0 0 -1 0 0 -1 -1 2 0 0 -1 0 0 -1 -1 1 2 0 0 -1 0 0 -1 -1 1 1 2 0 0 1 0 0 1 1 -1 -1 -1 2 0 0 1 0 0 1 1 -1 -1 -1 1 2 0 0 1 0 0 1 1 -1 -1 -1 1 1 2 0 0 -1 0 0 -1 -1 1 1 1 -1 -1 -1 2 0 0 1 0 0 1 1 -1 -1 -1 1 1 1 -1 2 0 0 1 0 0 1 1 -1 -1 -1 1 1 1 -1 1 2 0 0 -1 1 1 -1 0 0 0 0 -1 0 -1 0 0 0 4 0 0 1 -1 0 1 0 0 0 0 1 0 1 0 1 1 -2 4 |Aut| = 2^33*3^6*5^3*7^2*11*13 #short vectors: 4 484 1920 63844 &Gram (#8 <- H9,H11) 1 0 1 0 0 2 0 0 1 2 0 0 1 0 2 0 0 1 0 0 2 0 0 1 1 0 0 2 0 0 -1 0 0 -1 0 2 0 0 -1 0 0 -1 0 1 2 0 0 -1 0 0 -1 0 1 1 2 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 1 2 0 0 0 0 0 0 0 0 0 0 1 1 2 0 0 0 0 0 0 0 0 0 0 1 0 1 2 0 0 0 0 0 0 0 0 0 0 -1 -1 -1 0 2 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 2 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 2 |Aut| = 2^32*3^10*5^4*7^2 #short vectors: 4 484 1920 63844 &Gram (#9 <- H10,H12) 1 0 1 0 0 2 0 0 -1 2 0 0 -1 1 2 0 0 -1 1 0 2 0 0 -1 0 0 0 2 0 0 -1 0 0 0 1 2 0 0 -1 0 0 0 1 1 2 0 0 -1 0 0 0 1 1 1 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 -1 1 1 0 0 0 0 0 0 -1 0 3 0 0 1 -1 0 -1 0 0 0 -1 -1 0 0 -1 3 0 0 0 0 0 0 0 1 0 0 0 0 -1 0 0 3 0 0 1 -1 0 -1 0 -1 0 0 0 0 0 -1 1 -1 3 0 0 0 0 -1 1 0 0 0 0 1 -1 0 0 -1 0 -1 3 |Aut| = 2^32*3^4*5^2*7^2 #short vectors: 4 228 4992 48484