Output of hn-2.8.6 --invar &K=Q(sqrt(-3)) &Hdim=14 V=K^14 Family contains 58 classes: mass of the family is 902121810728123/70284505321046016000 Steinitz class <1,w>: &Hlattice (#1 <- 0) 3 -1+w 3 w 0 3 -1+w -1+w w 3 -1 1-w -2+w 0 3 1-w 0 -1 0 w 3 2-w -w 1-2w -1 -1+w w 3 -1+w -1+w 1-w 0 -1 0 0 3 0 -w 1 -1 -w -1+w w -1+2w 3 1 -1 2-w 0 -1-w -2+w w 0 1 3 -1 1-w -w -1+w w w 1-w w 1-w -w 3 1-2w -1 -1 0 1 1-w 1-w -1 -1+w 0 -1 3 1 -1 1-w 1-w 0 -1 w 0 0 1 -1 w 3 -1+w w -w -w 0 -1 0 2-w 0 0 0 -w 1-w 3 |Aut| = 2^8*3^7*7*13 #short vectors: 0 0 17472 &Hlattice (#2 <- d14) 2 0 2 0 0 2 0 0 0 2 1 0 0 0 2 0 -w 0 0 0 2 1-w 0 0 0 1-w 0 2 -w 0 0 1 0 0 1-w 2 0 0 -w 0 0 0 0 0 2 1-w 1 0 0 0 -1+w 1 w 0 2 1 0 -w 0 1 0 0 0 1 0 2 1-w 0 0 0 0 0 1 w 0 1 0 2 1 1 1 -w 1-w 0 w -1 -1+w w 0 w 4 1 -w -w 1-w 1-w 0 1 0 0 0 1 0 1-w 4 |Aut| = 2^24*3^6*5^2*7^2*11*13 #short vectors: 0 1092 17472 682668 &Hlattice (#3 <- e7e7) 2 0 2 0 0 2 0 0 0 2 0 0 -w 0 2 0 0 0 0 0 2 1 0 0 1 0 1-w 2 0 -w 0 0 0 0 0 2 0 -w -w 0 1 0 0 1 2 0 1-w 1-w 0 w 0 0 w w 2 0 1 1 0 0 0 0 -1+w -1+w w 2 0 0 0 w 0 1 w 0 0 0 0 2 -1+w 0 0 0 0 -w 0 0 0 0 0 0 2 1-w 1-w 1-w 1-w w 0 1-w 0 w 1 1-w -w -1 3 |Aut| = 2^21*3^9*5^2*7^2 #short vectors: 0 756 17472 &Hlattice (#4 <- k8e6) 2 1-w 2 0 0 2 1 0 0 2 0 0 0 0 2 0 0 1 0 1 2 0 0 -w 0 -w -w 2 1 w 0 0 0 0 0 2 -w 0 0 -w 0 0 0 0 2 0 0 0 0 -w -w 1 0 0 2 1-w 1 0 0 0 0 0 1-w 0 0 2 1 w -w 0 1 1-w 0 1 0 0 w 3 -w 0 1-w -w 1 1-w w 0 1 0 0 1 3 1-w 1-w 0 1-w 1 1 0 -w 0 0 1-w 1 w 4 |Aut| = 2^15*3^14*5^2*7 #short vectors: 0 720 17472 702756 &Hlattice (#5 <- d8u5a1) 2 0 2 1-w 0 2 w 0 -1+w 2 0 0 0 0 2 0 1 0 0 1 2 0 0 0 0 0 w 2 0 0 0 0 1-w 1-w -w 2 1-w 0 1 1-w 0 0 0 0 2 -1+w 0 -1 w 1 1 1-w w -1 3 1-w 0 0 1-w -w 0 1 0 1 -w 3 0 0 0 0 -w -w -1 1-w 0 -w 0 3 0 1-w 0 0 0 1-w -w 0 0 0 -w 1+w 3 1 1 -1+w 1 -w 1-w -w 1 w 1-2w 1 0 0 4 |Aut| = 2^22*3^7*5^2*7 #short vectors: 0 612 17472 708588 &Hlattice (#6 <- u5u5d4) 2 1 2 1 1 2 1 1 1 2 0 0 0 0 2 0 0 0 0 1 2 0 0 0 0 1 1 2 0 0 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 1 1 2 0 0 0 0 0 0 0 0 1 1 1 2 1 1-w 1-w 1-w 0 0 0 0 -w 1-w 1-w 1-w 3 0 0 0 0 1 1-w 1-w 1-w 1-w -w 1-w 1-w 1 3 |Aut| = 2^21*3^11*5^2 #short vectors: 0 612 17472 &Hlattice (#7 <- a13a1+) 2 0 2 0 0 2 1 -w 0 2 0 -w 0 1 2 1 0 0 1 0 2 0 0 -w 0 0 0 2 1 0 -w 1 0 1 1 2 1 0 1-w 1 0 1 0 1 3 1-w -w 1 1-w 0 1-w -1+w 0 0 3 1-w 1-w 1-w 1 w 1-w w 1 1-w 1 3 0 1-w 1 0 0 0 0 0 0 w 1 3 0 -w 0 0 1-w 0 0 0 -1+w 1 -w 1-w 3 0 -w 1 1 1 0 0 0 1 0 1 1 0 3 |Aut| = 2^13*3^6*5^2*7^2*11*13 #short vectors: 0 552 17472 &Hlattice (#8 <- a13a1-) 2 0 2 0 0 2 0 -w 0 2 1-w 0 0 0 2 -w 0 1 0 1-w 2 0 0 0 0 0 0 2 1-w 0 0 0 0 0 0 2 1 1 0 0 w -1+w 0 0 2 -w 0 0 0 1-w 1 1 0 -w 2 0 0 0 0 0 0 0 0 0 0 2 1-w 1 1-w -1+w 1 1 0 0 1-w w 0 3 1-w 1 -w -1+w 1-w 0 1-w 0 1-w 1 -1 2-w 4 1-w 1-w 1-w 1 1-w 1 1-w 0 1-w 1 0 2-w 2 4 |Aut| = 2^13*3^6*5^2*7^2*11*13 #short vectors: 0 552 17472 711828 &Hlattice (#9 <- d8d6) 2 0 2 -w 0 2 -w 0 0 2 0 0 0 0 2 1-w 0 0 0 0 2 0 0 0 0 0 0 2 0 1 0 0 1 0 1-w 2 1-w 0 0 w 0 1 0 0 2 0 0 0 0 1 0 1-w 1 0 2 0 0 0 0 0 0 0 0 0 0 2 1 0 -1+w 0 0 0 0 0 0 0 -w 2 -w 0 1 0 1-w 1-w -w 1-w 1-w 1-w 1-w 0 3 -w 1-w 0 1 -w 1-w 1-w 1-w 1-w 1-w 0 0 1 3 |Aut| = 2^23*3^5*5^2*7 #short vectors: 0 516 17472 713772 &Hlattice (#10 <- k6e6a2) 2 0 2 0 0 2 0 0 0 2 0 0 0 0 2 1 0 -1 0 1-w 2 0 w 0 0 0 0 2 0 w 0 -1 0 0 0 2 0 -w 0 1-w 0 0 -1 -1+w 2 0 0 0 -1+w 0 0 0 0 0 2 0 0 -1 1-w 1-w 1 0 0 0 -1 3 -w 1 w 0 0 -w 1-w 1-w -1 -w 0 4 0 -w 0 w 0 0 -1 -w 0 0 -1+2w 1-w 4 1-w 1 -w 0 1-w 1 1-w 1-w -1 0 1+w 1+w 1 4 |Aut| = 2^13*3^13*5^2 #short vectors: 0 504 17472 714420 &Hlattice (#11 <- a8e6) 2 0 2 0 0 2 0 0 0 2 1 1 0 0 2 0 0 -w 0 0 2 0 0 0 0 0 0 2 0 0 -w 0 0 1 -w 2 0 0 1 1-w 0 0 0 0 2 -1+w 1-w 0 0 0 0 0 0 0 2 1 1 -w 0 1 0 1 0 -w 0 3 0 0 1-w 1 0 1 1-w w 1 0 0 3 1-w 0 1-w 0 1-w w 1 w 0 -1 1 w 3 1-w 0 1 0 1-w 0 1-w w 1 0 0 1 1 3 |Aut| = 2^15*3^9*5^2*7 #short vectors: 0 432 17472 718308 &Hlattice (#12 <- a11a3) 2 0 2 0 0 2 1 1-w 0 2 1-w 0 0 1-w 2 0 1 0 0 0 2 0 0 -w 0 0 0 2 0 -w -w 1-w 0 0 1 2 1-w 0 0 1-w 1 0 0 0 2 1-w -w -w 1-w 0 0 0 1 0 3 1 1-w 1-w 1 w 1-w w w w w 3 1 1 0 1 w 1 0 0 w 0 1+w 3 -w 1 1 0 1-w 0 0 -1+w 1-w -1+w 0 0 3 1 1 1-w 1 0 w 1 w 1 -1+2w 1 1 1 4 |Aut| = 2^14*3^7*5^2*7*11 #short vectors: 0 432 17472 718308 &Hlattice (#13 <- a8k5) 2 0 2 0 1 2 1 0 0 2 0 0 0 0 2 1 0 0 0 0 2 0 0 0 w 0 0 2 0 0 0 0 1 0 0 2 0 -1+w 0 -1+w 0 w w 0 3 0 -w 0 0 1 0 0 0 -1+w 3 0 0 1-w 0 1-w 1-w 0 1-w -w -w 3 1-w 0 1-w 0 0 1-w 0 0 1 -w 1 3 0 1-w 1-w w 0 0 1 0 1-w w 0 1-w 3 0 0 -w 1 0 0 0 0 1-2w -1 1 1-2w 1-w 3 |Aut| = 2^11*3^10*5^2*7 #short vectors: 0 396 17472 &Hlattice (#14 <- k5k5a2a2) 2 -1 2 -w 1 2 -w 1 1 2 -w 1 1 1 2 0 0 0 0 0 2 0 0 0 0 0 -1 2 0 0 0 0 0 -w 1 2 0 0 0 0 0 -w 1 1 2 0 0 0 0 0 -w 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 1 -1 -1 -1 -1 -1 1 3 0 1 1 1 1 0 1 1 1 1 1 0 -2+w 4 |Aut| = 2^11*3^13*5^2 #short vectors: 0 396 17472 720252 &Hlattice (#15 <- d6d6a1a1) 2 0 2 -1 0 2 1 0 0 2 0 0 0 -1 2 0 0 0 0 0 2 -w 0 0 -w 0 0 2 0 0 0 0 0 -w 0 2 0 w 0 0 0 0 0 w 2 0 -1 0 0 0 0 0 1 0 2 -w 0 w 0 0 0 1 0 0 0 2 0 -1 1-w 0 0 0 0 0 -1+w 1 0 3 -1 -1+w 0 -1 1 0 1-w 0 w 1-w 1-w 1-2w 3 -1+w 1-w 1-w 0 0 -1 0 0 0 -1+w -w 0 0 3 |Aut| = 2^21*3^5*5^2 #short vectors: 0 372 17472 &Hlattice (#16 <- a8d5+) 2 0 2 0 0 2 0 0 0 2 0 1 0 1-w 2 0 0 0 0 0 2 0 0 0 -w 0 0 2 0 0 -w 0 0 0 0 2 w 0 0 0 0 1 0 0 2 -1+w -1+w -1+w 0 -1+w 0 1 -w w 3 1-w 0 -w -1 -w 0 0 1 -w -2+w 3 0 0 0 -w 1-w w 0 0 w 0 w 3 1 0 -w 0 0 1-w 0 w 1-w -1 w -1 3 0 -w 1 0 -w 0 -1 0 0 -1 w 1 -1 3 |Aut| = 2^15*3^6*5^2*7 #short vectors: 0 336 17472 &Hlattice (#17 <- a8d5-) 2 0 2 0 0 2 1 0 -1 2 0 0 0 0 2 0 0 0 0 0 2 0 0 0 0 0 0 2 0 1 0 0 1 0 1-w 2 1 0 1 0 0 w 0 0 3 0 0 1 -1 1 w 1-w 1 1 3 1-w 0 -w 1 -w 0 1 0 1-w -w 3 1 1 0 0 -w 0 -w 1-w 0 1-w 0 3 0 1-w -1 1 1-w -1 0 1-w -1+w -1 1 0 3 -1 0 0 0 1-w 0 -w 1-w -1+w 1-w 0 0 1 3 |Aut| = 2^15*3^6*5^2*7 #short vectors: 0 336 17472 723492 &Hlattice (#18 <- a9a4a1) 2 0 2 0 1 2 -w -w 0 2 0 -w -w 0 2 0 0 0 0 0 2 0 1-w 1-w 0 w 1-w 2 0 0 0 0 0 0 0 2 -w -w 0 1 0 0 0 -1+w 3 1-w 1 1 w -1+w 0 w 0 w 3 0 1 1 0 -1+w 1-w w 0 w 1 3 1-w 1-w 1-w w 0 1-w 1 0 w 1-w 1 3 0 1-w 1-w 0 w 1-w 1 0 -1+w 0 1 1 3 1-w w 0 -1+w 0 0 0 1 -1 1 -1+w w 0 3 |Aut| = 2^13*3^6*5^3*7 #short vectors: 0 336 17472 723492 &Hlattice (#19 <- a7a7) 2 0 2 1 0 2 0 0 0 2 -w 0 -w 0 2 0 1 0 1 0 2 0 0 0 0 0 0 2 0 0 -1+w 0 0 -w 1 3 0 0 0 0 0 1 1-w -1+w 3 1-w 1-w -w 0 w 1-w 0 w 0 3 0 0 1-w w 0 w 1 -1 w -1+w 3 1-w 1-w 0 0 0 1-w 1-w 1 1-w 1 1-w 3 0 1-w 0 1 0 1-w -1 0 -w 1 -w 1-w 3 1-w 0 1 -w w 0 0 -w w 0 -1+w 0 -1 3 |Aut| = 2^15*3^5*5^2*7^2 #short vectors: 0 336 17472 &Hlattice (#20 <- d6d4d4) 2 0 2 0 1-w 2 1-w 0 0 2 1-w 0 0 1 2 0 1-w 0 0 0 2 0 1 w 0 0 w 2 0 0 0 0 0 0 0 2 -w -w 1-w 0 0 0 0 -1+w 3 1 -w 0 w w 1 1-w 0 0 3 1 -w 0 0 0 1-w 0 0 w 1 3 1-w -w 1-w 0 0 1-w -w 0 1+w 1-w 2-w 3 1-w 1 w 0 1 1 1-w 0 -1+w 1-w 0 w 3 0 0 0 0 0 -1 w 1-w 0 -1+w 1-w -w -1 3 |Aut| = 2^22*3^6*5 #short vectors: 0 324 17472 724140 &Hlattice (#21 <- k4k4d4) 2 1 2 1-w 1-w 2 -w 1-w 1 2 0 0 0 0 2 1 1-w w 0 0 3 1-w 1-w 1 1 -w 0 3 1-w 1-w 1 1 0 0 1 3 1 1-w 1 0 0 2-w 0 0 3 1 1-w w 0 1 1 w w 1 3 -w 1-w 1 1 0 1 1-w 0 w 0 3 1 1-w 0 0 -w 1 1 0 1 0 0 3 -w 1-w 0 1 0 1 0 1 0 0 1 0 3 -w 1-w 1 1 1 -w w w 0 1 1 -1 1 4 |Aut| = 2^14*3^11 #short vectors: 0 288 17472 &Hlattice (#22 <- a7k4a1a1) 2 w 2 1-w 1-w 2 0 0 0 2 0 0 0 1-w 2 0 -w 1-w 0 0 2 1 1-w w 0 0 -1+w 3 0 0 0 0 1-w 0 0 3 0 0 0 -1 0 0 -1 -1+w 3 1 1 w 0 0 0 0 0 1 3 -1+w 0 0 w -1+w w 0 0 -w -1 3 -1+w 0 0 0 0 w 0 0 1-w 0 1+w 3 -1+w 0 -w w -1+w 1 -1 -w 0 -1+w 2-w 1-w 3 1 1-w w 1 -1+w 0 w -w -1+w 0 1-w -1 1-w 4 |Aut| = 2^13*3^7*5*7 #short vectors: 0 288 17472 &Hlattice (#23 <- a5a5k4) 2 0 2 0 1-w 2 -w 0 0 2 1-w 0 0 1 2 1-w 0 0 w 1 2 0 1 0 0 0 0 2 1-w -w 0 0 1-w 1-w -w 3 -w 1 1 1 1-w 1-w w 0 3 1 0 0 0 1 1 0 w 0 3 1-w 1 0 1 1 1-w 1 w 1 1-w 3 1 1 w -1+w 0 1 0 w w 1 w 3 1-w 1 w w 1 1 1 w 1+w 0 1 1 3 1 0 0 -1+w 0 1 1 w 0 1 w 1 1 3 |Aut| = 2^13*3^9*5^2 #short vectors: 0 288 17472 &Hlattice (#24 <- d5a4k4) 2 0 2 0 0 2 0 0 0 2 0 0 -w 0 2 0 0 0 0 0 2 1 0 0 1 0 1-w 2 0 -w 0 0 0 0 0 2 0 0 -w 0 0 0 0 0 2 1-w 0 1-w 1-w 1 0 1-w 0 -1+w 3 0 -w 1 1 0 1-w 1 1 -1+w w 3 1-w 1 0 1 0 1 1 0 0 1 w 3 1-w -w 0 0 0 -w 1-w 1-w 0 1 1-w 1-w 3 0 1-w 1-w -w 0 1 0 w w 1-w 1 1-w -1+w 3 |Aut| = 2^14*3^7*5^2 #short vectors: 0 288 17472 &Hlattice (#25 <- a6d5a2) 2 0 2 0 0 2 1-w 0 0 2 0 0 0 0 2 0 1-w 0 0 -1 2 0 0 0 0 0 -1+w 2 0 0 w 0 0 0 0 2 0 0 -1 0 0 0 0 -1+w 2 1 0 0 w 0 0 0 0 w 2 0 0 0 1-w -w w 1-w 1 0 0 3 1 -w -w w -1+w 1-w 0 -1 w 1 -1 3 -1 0 -1 -w 0 0 0 -1 w 0 -w 0 3 1-w 0 1-w w 0 0 0 0 -1+w 1 -1+w 1 -1+w 3 |Aut| = 2^13*3^5*5^2*7 #short vectors: 0 264 17472 &Hlattice (#26 <- a7a5a1+) 2 -1+w 2 1-w -1 2 -1+w 1 -1 2 0 0 0 0 2 0 0 0 0 0 2 0 1 0 0 0 0 2 1 -w w -w 0 -1+w 0 3 -1 0 -w 0 w 0 -w 0 3 0 1 -1 1 0 w 0 0 0 3 w 1-w -1+w 1-w 1 -1+w 0 w 1-w 1 3 w 0 0 0 0 -1+w 0 0 -w -1+2w 1 3 1-w 0 0 0 -w w 0 0 -2+w 1 -w 1-2w 3 1 0 0 0 -1 -1+w 0 1 -1+w w 0 1-w 1 3 |Aut| = 2^13*3^5*5^2*7 #short vectors: 0 264 17472 727380 &Hlattice (#27 <- a7a5a1-) 2 1 2 0 0 2 0 0 -w 2 -w -w 0 0 2 -w 0 -w 0 0 2 0 0 0 0 0 0 2 0 0 0 0 0 0 0 2 1 0 0 0 0 -1+w 0 1-w 3 1-w 1-w 0 -w 0 w 0 0 1 3 1 1-w 1 -1+w 0 -1+w 1 0 1 1 3 1 1 1 0 -1+w -1+w 1-w 0 0 w 1 3 1 0 1 -1+w 0 -1+w 1-w -1 1-w 0 2-w 1 3 -w 0 1-w w 0 1 1-w 0 -w -w 1-2w 1-w 1-w 3 |Aut| = 2^13*3^5*5^2*7 #short vectors: 0 264 17472 &Hlattice (#28 <- a6a6) 2 0 2 0 1-w 2 -w 0 0 2 1-w 0 0 w 2 -1 0 0 1-w -w 2 -w 0 0 1 1-w w 3 1-w -w 0 0 1 -1+w w 3 1-w 0 0 0 1 -1 1 1 3 -w -w 0 1-w 1-w w 1 2-w 1-w 3 -w 0 0 1-w -w 1 0 1-w 0 1 3 -w 1-w 1 1 1-w w 1+w 0 0 1 0 3 0 1 0 0 -1 0 0 -1 -1 0 1-w w 3 1 0 0 -1+w w -1 -1+w -1+w 0 0 -1 w 1-w 3 |Aut| = 2^10*3^5*5^2*7^2 #short vectors: 0 252 17472 &Hlattice (#29 <- d4d4d4a1a1) 2 0 2 0 -1 2 1 0 0 2 0 0 0 0 2 0 -w 0 0 0 2 0 0 0 0 0 0 2 0 1-w w -w -w -1+w 0 3 0 0 0 0 1-w 0 -w w 3 1 0 0 1 w 0 0 -1 -2+w 3 1-w w -w 1 0 0 0 -2+w w 1-w 3 0 0 0 0 1-w -1 -1+w w 0 -w 0 3 0 -1+w 1-w 0 1-w 0 w 0 1-w -1 0 1-w 3 0 -w 1 -1+w 1-w 0 0 1-w 1 -1 -1+w 1 w 3 |Aut| = 2^21*3^5 #short vectors: 0 228 17472 &Hlattice (#30 <- a6a2d4) 2 0 2 0 1-w 2 -w 0 0 2 0 -w 0 0 2 1-w 0 0 w 0 2 0 1-w 0 0 0 0 2 -w 1-w 0 0 w 1-w 0 3 1 1-w 0 0 0 0 1 w 3 1-w -w 1-w 0 0 0 0 0 1-w 3 1-w 1 w w 0 1 0 w 0 -1+w 3 1-w -w 1-w 0 1 1 0 1 1-w 1 0 3 0 1-w 1 0 0 0 1-w 0 0 -1+2w 2-w 0 3 1 1 0 -1+w -1+w w w w 1 0 w w -1+w 3 |Aut| = 2^12*3^6*5*7 #short vectors: 0 216 17472 &Hlattice (#31 <- a5a5a3+) 2 -w 2 0 0 2 0 0 1-w 2 1-w 0 0 0 2 1-w w 0 0 0 2 -w 0 0 0 1-w 0 2 1 0 1-w 1 0 0 -1+w 3 -w 1-w 1-w 1-w 1-w 0 1 1-w 3 1-w 1 1 w w 1-w -1+w 1 -1+2w 3 -w 1-w 0 0 1-w 1-w 0 0 1 1-w 3 1-w w -w 0 1 1 0 0 0 0 w 3 1-w w 1 0 0 1 0 0 w 1 w w 3 1 0 1-w 0 0 w 0 1 1 0 w w 1 3 |Aut| = 2^13*3^6*5^2 #short vectors: 0 216 17472 729972 &Hlattice (#32 <- a5a5a3-) 2 0 2 0 0 2 1-w 0 0 2 0 0 -w 0 2 0 0 -w 0 1 2 0 0 0 0 0 0 2 1 0 0 0 0 0 0 2 -w 0 -w 1-w 1 1 1-w -1 3 1-w 1 1 1 0 0 0 0 w 3 1-w 1-w 1-w 0 w 0 0 1-w w 1-w 3 -w 0 1-w 1-w 1 w 0 0 1 1-w 1-w 3 1-w 1 -w 1 1 1 1 0 1+w 1 1 1 3 1-w 0 1-w 0 w w 1-w 0 1+w 1 1 w 1 3 |Aut| = 2^13*3^6*5^2 #short vectors: 0 216 17472 729972 &Hlattice (#33 <- a5a5a2a2) 2 0 2 w 0 2 0 1 0 2 0 0 0 0 2 -1 w -1+w 0 1 3 -1+w 0 w -1+w 1 1-w 3 1 -w 0 -w 0 -1 0 3 0 1 0 1 0 0 0 -1+w 3 w 0 0 0 -w -w -w w w 3 0 1-w 0 0 0 -w 1 w -w -1 3 0 0 0 0 w -1+w w 0 1-w -1-w w 3 -1 0 -1 0 1 1 w -1+w 0 w -1+w 0 3 1-w -1+w -w 0 -w 0 -1-w 1-w -1 1 -1 -2+w 0 4 |Aut| = 2^12*3^7*5^2 #short vectors: 0 216 17472 &Hlattice (#34 <- a4a4d4) 2 0 2 1 0 2 -w 0 -w 2 0 0 0 0 2 0 1-w 0 0 0 2 0 0 0 0 0 0 3 1-w w -w 1 0 -1+w 0 3 0 w 0 0 -1 -1+w -1+w 0 3 -w 0 -w w -1 0 w 0 1 3 0 -1 0 0 -w 0 -w -1+w w 0 3 0 0 0 -w w -w 1-w 0 -1 -1 -1 3 -w -1 1-w w 0 0 0 -1+w 0 1 1 -1 3 1-w 1 1 w 0 w 0 1-w 1-w 0 -1 -1 w 3 |Aut| = 2^14*3^4*5^2 #short vectors: 0 192 17472 &Hlattice (#35 <- a5a4a3a1+) 2 0 2 1 0 2 0 0 0 2 0 -w 0 0 2 0 0 0 w 0 2 -w 0 1-w w 0 1 3 -1 -w -1 w 1 1-w 1-w 3 0 -w 0 w 0 1 1-w 1 3 1 1-w 0 1-w w -w -w 0 0 3 0 1-w 0 1 1 1-w 1-w 1 0 1 3 -w 0 1-w 0 0 0 1+w w -1+w -1 0 3 0 1 0 0 -1+w 0 1 -1+w -1+w w w 1-w 3 -w 0 -1 1 0 1-w 0 1 -w 0 1 w -1+w 3 |Aut| = 2^12*3^5*5^2 #short vectors: 0 192 17472 731268 &Hlattice (#36 <- a5a4a3a1-) 2 0 2 1 0 2 0 0 0 2 0 1 0 0 2 0 0 0 0 0 2 0 w -1+w -1+w w -1+w 3 0 0 0 -1 0 1-w -1+w 3 0 w w -1 w 0 1 1 3 0 0 w 0 0 -1+w 1-w -1 1 3 0 1-w 0 1-w 1-w 0 -1-w -1+w 0 1 3 0 -1+w 0 0 -1+w -w -1+w w w 0 0 3 1-w w 1 0 w 0 1-w -1+w 1 1-w -1+w 1 3 -w 0 -1 -1+w 0 0 1 1-w w w -1+w 0 0 3 |Aut| = 2^12*3^5*5^2 #short vectors: 0 192 17472 731268 &Hlattice (#37 <- a4a4d4) 2 0 2 1 0 2 0 0 0 2 0 0 0 1 2 0 0 0 1 1 2 1-w 1-w 1-w 0 0 0 2 0 0 0 -w -w -w 0 2 -w 0 0 1-w 0 0 0 0 3 1 1 0 1-w 0 0 w 0 w 3 1 1 1 1 1 1 w -1+w 0 1 3 1-w 1-w 0 1-w 0 0 1 0 1 2-w 1-w 3 1-w -w 0 -w 0 0 1-w 0 1 1-2w -w 2-w 3 1 0 0 1 0 1 0 -1+w w 1 1 w w 3 |Aut| = 2^12*3^5*5^2 #short vectors: 0 192 17472 &Hlattice (#38 <- a4a4k3a1) 2 0 2 1 -1 2 0 0 0 2 0 w -w 0 2 0 0 0 -w 0 3 1-w 1 -w 0 1-w -1 3 0 0 0 0 -w w 1-w 3 -1+w -w w 0 -1+w 0 -1 0 3 0 0 0 1-w 0 0 w -1+w 0 3 1 0 1 0 0 -1+w w w 1-w 0 3 0 0 0 1-w 0 -w w -1 -w 1 0 3 1 -1 1 0 0 1 -1+w w 1-w w 1 -1+w 3 1-w 1 -w -w 1-w 1 1 0 -2+w 0 -w -w 0 3 |Aut| = 2^10*3^6*5^2 #short vectors: 0 180 17472 &Hlattice (#39 <- a5k3a2a2) 2 0 2 0 1-w 2 1 0 0 2 1 0 0 0 3 0 -w 1-w 0 w 3 1-w 0 0 -w 1-w -1 3 0 1-w 0 0 w w 1 3 0 -1 0 0 0 1-w 0 -w 3 0 -1+w -1 0 -1 -1 0 -1+w -1+w 3 0 -1 1-w 0 -1 0 0 -1 1-w 0 3 1-w w -1+w 1-w 0 -1 w -1+w 0 1-w -w 3 0 -w 1-w 0 -w w 1-w 1-w -1+w w w -1 3 -w 1 -1+w 1-w -w -1 w w -1 0 -1 2-w -1+w 3 |Aut| = 2^9*3^9*5 #short vectors: 0 180 17472 &Hlattice (#40 <- d4k3k3) 2 0 2 0 1-w 2 1 0 0 2 0 1-w 1-w 0 2 0 1 w 0 0 3 0 -w 1-w 0 1-w 1-w 3 1 1-w 0 1 1-w 0 0 3 0 1 1 0 w 1-w 0 -1+w 3 1 -w 0 0 1-w 0 w 1-w -1 3 -w 1-w 1-w 1-w 1 -w 0 1 1-2w -1+w 3 1-w 1-w 1 0 1 1-w w 1 1 1 w 3 0 0 0 0 0 1 1 0 1 -1 -1+w 0 3 1 1-w 0 0 1-w 1-w 1-w 1 0 1 0 w -w 4 |Aut| = 2^13*3^10 #short vectors: 0 180 17472 731916 &Hlattice (#41 <- k3k3a2a2a2a2) 2 0 2 0 1-w 2 1 0 0 2 0 0 0 0 2 1 -1 -w w 0 3 0 0 0 0 0 0 3 0 1-w 1-w 1 -w 0 0 3 -w -w 0 -w 0 -1 w -w 3 -w 1-w 1 -w 0 -1 w 0 1+w 3 1 w -1+w w 0 1 0 -1+w -1 -2+w 3 -w 1 0 1-w 0 -w 1-w 1 -1+w w 1-2w 3 0 0 0 0 w 0 2-w -1 0 1-w 0 1 3 -w 0 0 0 -w 1-w -w w 0 0 1-w 1 -w 3 |Aut| = 2^10*3^12 #short vectors: 0 180 17472 &Hlattice (#42 <- d4d4a1a1a1a1a1a1) 2 1 2 0 0 2 -w 0 0 2 1-w 0 0 0 2 0 0 0 0 0 2 1 0 -w 0 w 0 3 1-w 0 1-w 0 1 0 1 3 -w -w 1 0 1-w 0 0 1 3 -w -w -w 0 1-w -w 1-w 1-w 1-w 3 1 1-w 1-w 0 w 1 1+w w w -1+2w 3 -w 0 0 1 1-w -w -w -w 0 1 -w 3 1 1 0 0 0 1 1 1 0 -1+w 1 -1+w 3 0 1-w 0 0 0 1-w -1+w -1+w w w 1 0 0 3 |Aut| = 2^20*3^5 #short vectors: 0 180 17472 &Hlattice (#43 <- a4a4a3) 2 0 2 -1 0 2 0 0 0 2 0 -1 0 0 2 w 0 1-w 0 0 3 0 0 0 1-w 0 -w 3 0 w 0 1 -w 0 -1+w 3 1-w 1 -1+w 0 -1 0 w 1-w 3 1-w -1 -1+w 0 1-w -w 0 w 0 3 0 0 0 0 w 1-w 0 -1 -w -1+w 3 1 w -w 0 0 1-w 0 0 w -1 w 3 1-w w -1 0 -w -w 0 1 1+w 0 -1+w 2-w 3 -w 0 1 -1 0 w 0 -w 1-w -w -1+w 0 0 3 |Aut| = 2^11*3^4*5^2 #short vectors: 0 156 17472 733212 &Hlattice (#44 <- a4a4a2a2) 2 0 2 -1 0 2 -w 0 w 3 0 0 0 0 3 0 1-w 0 0 -1 3 0 0 0 -w 0 -w 3 0 1-w 0 2-w 0 0 -1+w 3 0 -w 1 1-w -w 1 0 1-w 3 w -1+w 1-w -w 0 -w w 0 1-w 3 -1+w 0 1 1-2w -1 0 0 1-w 1 w 3 1 0 -1 -2+w -1+w 1-w 1 -1 -1 1-w -w 3 w 0 -w -1-w w -w 1 -w -w 1 1-2w w 3 0 1 0 0 w 1-w 0 w 0 1-w 0 1-w 0 3 |Aut| = 2^10*3^5*5^2 #short vectors: 0 156 17472 733212 &Hlattice (#45 <- a4a3a3a1a1) 2 0 2 1 0 2 0 0 0 2 -w -w -w 0 2 0 0 0 0 0 2 -w 1-w -w 1 1 0 3 1 1 1 0 -1+w 0 -1+w 3 1 0 0 1 0 -w 1 w 3 0 0 0 1-w 0 0 1-w 1 1-w 3 1 1-w 1-w 0 w 1-w w 1-w w -1 3 0 0 0 -w 0 -1+w -w 0 -w 1-w -1 3 1-w 1-w 1-w 1 w 0 1+w 1-w 1 0 1 0 3 1 1 1-w 0 -1+w 1 w 1 w 0 1+w 0 1+w 3 |Aut| = 2^13*3^4*5 #short vectors: 0 144 17472 &Hlattice (#46 <- a3a3a3a3) 2 1-w 2 0 0 2 0 0 1 2 0 0 1-w 1-w 2 -w 1-w 1-w 0 1 3 1 1 -w -w 1-w 1 3 1-w 0 1 0 0 w 0 3 1-w 0 1-w 1-w w w 0 1-w 3 1-w 1-w 1-w 0 0 1 1-w 0 1 3 1 1 0 0 -1+w -1+w 1 0 w w 3 -w 0 1 0 0 0 -1 2-w 0 0 0 3 1-w 1 0 0 0 0 1-w 1 0 0 1 w 3 1-w 0 -w -w 0 0 1-w 0 2-w 2-w 1-w 0 w 3 |Aut| = 2^15*3^5 #short vectors: 0 144 17472 &Hlattice (#47 <- a3a3a2a2a1a1) 2 0 2 0 0 2 0 1 0 2 1-w 0 0 0 2 0 0 0 0 0 2 0 0 0 0 w 0 3 0 1-w w 1 0 -1 0 3 1-w 0 -w 0 0 -1 -1+w 0 3 1-w 1-w 0 1-w 0 -1 w 1 1 3 0 -w 0 1-w 1 0 1-2w 1-w 0 -w 3 -w 1 -1 0 0 -w 0 -1+2w 1 1 -1+w 3 -w 0 1-w 0 0 1-w 0 0 0 0 0 w 3 0 0 1-w 0 0 w 0 1-w 0 -w 0 -1 w 3 |Aut| = 2^12*3^5 #short vectors: 0 120 17472 &Hlattice (#48 <- a3a3a3a1a1+) 2 1-w 2 0 0 2 0 0 0 2 0 0 0 -1 3 0 0 -1 -1+w 1 3 0 0 0 w -w -1 3 0 0 0 -1 1+w 1 -2+w 3 -1 0 0 1 0 -w 0 0 3 w 0 -1 0 0 1 -1 1 -w 3 0 0 w 0 0 1-2w -1+2w 1-w 0 1-2w 3 -1 -w 0 -1+w 1-w 0 1+w -w w -1 1-w 3 w 0 -w 0 0 1 0 0 -1 1 0 0 3 w -1+w 1-w -w 0 -1+w -1 1 -w 1 0 -1 w 3 |Aut| = 2^13*3^5 #short vectors: 0 120 17472 735156 &Hlattice (#49 <- a3a3a3a1a1-) 2 0 2 0 1 2 -w 0 0 2 0 0 0 0 2 1-w 0 0 0 0 3 0 0 0 1 0 -1 3 0 1 1-w 0 0 0 -1+w 3 0 0 0 0 1-w w 1 1-w 3 -w -w 0 1 0 0 1 -1-w 0 3 1 -w 1-w -1+w 0 0 -1+w 0 0 0 3 1 0 0 0 w w -w 0 0 -1 1 3 -w 0 0 0 -1 -w 0 -1 -1 1 0 -1 3 0 -1+w 0 -1 -w 0 -w -1+w 1-w -w 0 -1 1 3 |Aut| = 2^13*3^5 #short vectors: 0 120 17472 735156 &Hlattice (#50 <- a3a3a2a2) 2 1 2 0 0 2 0 0 1-w 2 -w 0 0 0 2 0 0 -w 1-w 0 3 0 0 0 0 0 -w 3 0 0 -w 1-w -w 0 1-w 3 0 0 0 -w 0 1-w -1+w -w 3 0 -w w 0 0 0 w -1 0 3 -w 1-w 0 0 1-w -1 1-2w 1 0 -1 3 w -1+w 0 1 -1 0 0 0 -1+w 1-w -1 3 0 0 -w -w w 0 0 0 1-w -1 0 -1-w 3 0 0 -w 1-w -1 w -w 2-w -1+w -1 1-w 1-w w 3 |Aut| = 2^11*3^6 #short vectors: 0 108 17472 &Hlattice (#51 <- a3a2a2a2a2) 2 0 2 -w -w 3 0 0 w 3 -w 1 w 0 3 -w -w 1 w 0 3 1 0 w 1-w -1+w -1+w 3 1 0 -1+w 0 -1+w w 1-w 3 0 w -1 0 1+w -w -w 1-w 3 0 w -w 1-w 0 -1 0 -1 1-w 3 1-w 0 1 1-2w 0 -1 0 -w -w 1 3 -w 0 0 -1 1 1 -w 0 0 -w -w 3 1-w 0 w -1 0 -1+w 1 0 -1 -1 1-w 1 3 1-w 1-w -1+w -1+w 1-w -1+w -1 0 1-2w -w 1 0 w 4 |Aut| = 2^10*3^7 #short vectors: 0 108 17472 &Hlattice (#52 <- a2a2a2a2a2a2) 2 0 2 0 1-w 2 1-w 0 0 2 0 0 0 0 2 0 0 0 0 0 2 1 1 0 0 w 0 3 1 1-w 1-w w -1 0 1 3 1 0 0 w 0 1 0 0 3 1 1-w 1-w 0 0 0 1 1 0 3 1-w 1 w 1-w 0 -1 1 0 -1 1 3 1 1-w 1 0 1-w 0 1-w w 1 1 1-w 3 0 0 1-w 0 0 1 0 1 0 w -1 1-w 3 1 1-w 0 1 0 -1+w 1-w 1-w w 1 1 w -1 4 |Aut| = 2^9*3^9 #short vectors: 0 108 17472 &Hlattice (#53 <- a2a2a2a2a1a1) 2 1-w 2 0 0 2 0 0 0 2 0 0 -1+w 0 3 -1 -w 1-w -1+w -1 3 0 0 0 1 -1+w -1 3 1-w 1 0 -1 -1+w -1+w w 3 -1 0 1-w 0 -1 1 0 0 3 -1+w -1 -w 1 -1+w 1-2w 1 -1 1 3 0 0 1-w -1 -w 1 -2+w w 1 -1+w 3 w 0 w 0 1-w -1 0 0 -1 0 0 3 w 0 0 0 0 -w -1+w -1+w -w 0 1 1 3 0 0 0 -1 0 0 -2+w w 0 -1 1+w 0 1+w 3 |Aut| = 2^10*3^5 #short vectors: 0 84 17472 &Hlattice (#54 <- a1a1a1a1a1a1a1a1a1a1a1a1a1a1) 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 -w 1-w 0 1 0 1-w -w 3 w 0 0 1-w -w 0 1-w 0 3 1-w 1-w -w 0 1 -w 0 1 -1 3 0 1-w 1-w -w 0 1 -w 1 1-w w 3 -w 1 0 -w 1-w 1-w 0 1 0 1 1 3 0 -w 1 0 -w 1-w 1-w 1 1 0 1 1-w 3 1-w 0 -w 1-w 0 0 w 0 0 1 0 w -1 3 |Aut| = 2^16*3^2*7*13 #short vectors: 0 84 17472 &Hlattice (#55 <- a2a2a1a1a1a1a1a1) 2 1 2 0 0 2 0 0 0 2 1 1-w 0 0 3 0 0 -1+w w 0 3 0 0 0 1-w w 1-w 3 0 0 -1 0 -w 1 0 3 0 0 w 0 0 1 w 1-w 3 -w 0 -1 0 -1-w w -1 1 -1+w 3 -w 1-w -1+w -w 0 0 1-w 1-w 1 1-w 3 0 1 -1+w 1-w w 1-w 1-w 1-w w 1-w 1+w 3 1 1-w -1 -1+w 1 w -1 1 -1+w 0 0 0 3 1 1-w -w 0 2-w 0 1-2w w -1-w -1+2w 0 0 1+w 4 |Aut| = 2^11*3^5 #short vectors: 0 72 17472 737748 &Hlattice (#56 <- a2a2a2a2) 2 1 2 0 0 2 0 0 w 3 0 1-w -w -w 3 0 0 -1+w -1+w -w 3 1-w 1 0 1 -1+w -1 3 0 0 0 1 -1+w -1 0 3 0 0 0 -w 0 0 0 -w 3 1-w 0 0 0 -1 0 0 w 0 3 0 0 -1 -1+w 0 w 0 1-w -1 0 3 0 0 0 0 w 1 -w -w -w -1+w 1 3 -w -w -1 w 1 -1+w 1-w 0 0 0 1-w 0 3 1 1 -1 -1 2-w -1+2w 0 -w w w 1-w -w 1 4 |Aut| = 2^8*3^9 #short vectors: 0 72 17472 &Hlattice (#57 <- a1a1a1a1a1a1a1a1) 2 1 3 0 -w 3 -w 0 -1 3 0 0 0 -1+w 3 -w -1 0 0 1-w 3 0 -1+w 0 -1 -1+2w -w 3 0 0 -1+w -w -1+2w 0 1 3 -w -1+w -1 w 1 1 1-w 1-w 3 0 -1+w -1 1-w -1+w -1 1 1 w 3 0 1 1 w 1-w 0 -1-w -1-w 1-2w -1-w 3 -1 -w 1-w 0 1-w 1-w -1 -w -w -1+w 1-w 3 -w 1 w 1-w w 0 1-w 1-w 1-w 1-w w -1+2w 3 0 1-w 1 1 1-w -1+w -1-w -1 -w -1 2-w w 1-w 3 |Aut| = 2^13*3^2*7 #short vectors: 0 48 17472 &Hlattice (#58 <- a1a1a1a1a1a1) 2 1-w 3 1 0 3 0 0 0 3 w 0 1+w -1+w 3 -w 0 -1 1 -1 3 0 0 0 -w 0 -1+w 3 0 2-w 0 0 1 0 0 3 0 0 1+w 1 1 0 0 0 3 1 1-w w -1 1 -1 0 1-w -1+w 3 1-w 1+w 0 -w 0 0 1+w w 0 0 3 1 0 1-w -1+w 1-w -1 -2+w 1-w -1 1 -1+w 3 0 0 1-w 1-w 1-w -1 1+w 0 1-w 0 1 -w 3 w -2+w 1+w w 2-w 0 0 -1 1 1-w -1+w 0 w 4 |Aut| = 2^13*3^4*5 #short vectors: 0 36 17472 739692