Table -4.  The norm -4 vectors of II_25,1.

There is a natural 1:1 correspondence between the elements of the following sets:

(1)

Orbits of norm -4 vectors u in II_25,1 under Aut(II_25,1).

(2)

Orbits of norm -4 vectors in the fundamental domain D of II_25,1 under Aut(D).

(3)

Orbits of norm -1 vectors v of I_25,1 under Aut(I_25,1).

(4)

25 dimensional unimodular positive definite lattices L.

(5)

Unimodular lattices L₁ of dimension at most 25 with no vectors of norm 1.

(6)

25 dimensional even lattices L₂ of determinant 4.

The height t is the height of the norm -4 vector u of D, in other words -(u,w) where w is the Weyl vector of D. The things in table -4 are listed in increasing order of their height.

Dim is the dimension of the lattice L₁. A capital E after the dimension means that L₁ is even.

The column ``roots'' gives the Dynkin diagram of the norm 2 vectors of L₂ arranged into orbits under Aut(L₂).

``Group'' gives the order of the subgroup of Aut(D) fixing u. The group Aut(L) @ Aut(L<sub>2</sub>) is of the form 2×R.G where R is the group generated by the reflections of norm 2 vectors of L, G is the group described in the column ``group'', and 2 is the group of order 2 generated by -1. If dim(L₁) £ 24 then Aut(L₁) is of the form R.G where R is the reflection group of L₁ and G is as above.

For any root r of u^{^} the vector u+r is a norm -2 vector of II_25,1. This vector u can be found as follows. Let X be the component of the Dynkin diagram of u^{^} to which u belongs and let h be the Coxeter number of X. Then r+u is conjugate to a norm -2 vector of II_25,1 in D of height t-h+1 (or t-h if the entry under ``Dim'' is 24E) whose letter is the letter corresponding to X in the column headed ``norm -2's''. For example let u be the vector of height 6 and root system a₂²a₁¹⁰. Then the norm -2 vectors corresponding to roots from the components a₂ or a₁ have heights 6-3+1 and 6-2+1 and letters a and b, so they are the vectors 4a and 5b of table -2.

If dim(L₁) £ 24 then the column ``neighbors'' gives the two even neighbors of L₁+I^24-dim(L₁). If dim(L₁) £ 23 then both neighbors are isomorphic so only one is listed, and if L₁ is a Niemeier lattice then the neighbor is preceded by 2 (to indicate that the corresponding norm 0 vector is twice a primitive vector). If the two neighbors are isomorphic then there is an automorphism of L exchanging them.

Height	Dim		Roots	Group	norm -2's	Neighbors
1	24	E		8315553613086720000		2L
2	23		a12	84610842624000	a	L
2	24			1002795171840		L	A124
3	25		a12	88704000	a
4	24		a18	20643840	a	A124	A124
4	25		a22	26127360	a
4	25		a16	138240	a
5	24		a112	190080	a	A124	A212
5	25		a2a17	5040	aa
5	25		a110	1920	a
6	23		a116a12	645120	ca	A124
6	24		a22a110	5760	ab	A212	A212
6	24		a116	43008	c	A124	A38
6	25		a3a18	21504	ac
6	25		a22a18	128	ab
6	25		a2a110a1	120	abc
6	25		a18a16	1152	bc
7	24		a24a18	384	bb	A212	A38
7	24	E	a124	244823040	a	2A124
7	25		a25a13	720	bb
7	25		a3a2a19	72	acb
7	25		a24a14a12	24	bba
7	25		a3a112	1440	ab
7	25		a23a16a13	12	bbb
7	25		a22a112	144	cb
8	22		a3a122	887040	ae	A124
8	23		a26a16a12	1440	bda	A212
8	24		a32a112	768	cc	A38	A38
8	24		a3a24a16	96	bbb	A38	A38
8	24		a28	672	a	A38	A38
8	24		a26a16	240	bd	A212	A46
8	24		a124	138240	e	A124	D46
8	25		a4a112	1440	ad
8	25		a3a24a14	16	bbb
8	25		a32a18a12	64	cbc
8	25		a3a23a16a1	12	bbbc
8	25		a3a23a13a13a1	6	bbbbd
8	25		a24a22a14	8	bab
8	25		a3a22a14a14a12	16	bbcbd
8	25		a24a2a14a12a1	8	bbbdb
8	25		a24a18a12	48	bdc
8	25		a3a115a1	720	cce
9	24		a32a24a14	16	bbb	A38	A46
9	24		a28a14	384	dc	A212	A54D4
9	25		a4a23a16a1	12	bdbb
9	25		a32a24a12	16	bba
9	25		a32a22a2a14a1	4	bbcba
9	25		a3a3a22a2a12a12a1	2	bbbbbbb
9	25		a3a26a12	6	abb
9	25		a32a22a14a14	8	bcbb
9	25		a3a24a2a14a1	8	bbbbc
9	25		a3a22a22a2a12a12a1	2	bbbdbbb
10	22		a3a210	2880	ac	A212
10	23		a34a18a12	384	cfa	A38
10	23		a33a24a12a12	48	bbea	A38
10	24		a34a22a12	32	bab	A46	A46
10	24		a4a3a24a14	16	bdbc	A46	A46
10	24		a32a3a24a12	16	bbbe	A38	A54D4
10	24		a34a14a14	48	cdf	A38	A54D4
10	24		a34a18	384	cd	A38	D46
10	24	E	a212	190080	a	2A212
10	25		a35	1920	c
10	25		d4a24a16	144	bcd
10	25		d4a3a112	576	ced
10	25		a5a115	720	cf
10	25		a4a3a24a12	8	bdbb
10	25		a33a3a2a13	6	bcbb
10	25		a4a3a22a2a12a12a1	2	bdbbbce
10	25		a33a3a14a12	24	bcce
10	25		a32a32a14a12	16	cbbd
10	25		a4a26a12	6	abe
10	25		a4a3a22a14a12a12	4	bdbccf
10	25		a32a3a22a2a12a1	2	bbbbbc
10	25		a32a3a22a2a1a1a1	2	bbbadbc
10	25		a4a25a15	10	bbc
10	25		a32a26	48	da
10	25		a32a24a22	8	bba
10	25		a33a22a13a12a1	12	bbdcf
10	25		a3a3a3a22a12a1a1a1a1	2	cbbbcebfd
10	25		a3a3a22a22a2a12a1	2	bbbbbee
10	25		a32a24a14a12	8	dbcf
10	25		a33a112	48	cf
10	25		a3a26a2a13	12	dbce
11	24		a4a32a3a22a12	4	bbbbb	A46	A54D4
11	24		a42a24a14	16	dca	A46	A54D4
11	24		a36	240	a	A46	D46
11	24		a34a24	24	be	A38	A64
11	25		a5a24a2a14	8	befb
11	25		d4a3a24a14	8	bcda
11	25		a4a32a3a2a12a1	2	bbbcba
11	25		a42a22a2a14a1	4	dcbbb
11	25		a4a32a24	4	bbb
11	25		a4a33a16	6	cbb
11	25		a4a32a22a2a12a1	2	bbbfab
11	25		a4a3a3a2a2a2a1a1a1	1	bbbbccbba
11	25		a4a3a3a2a2a2a1a1a1	1	bbbbecbbb
11	25		a34a3a14	8	bab
11	25		a32a32a22a2a1	2	bbbbb
11	25		a32a3a3a22a2a1	2	bbabda
11	25		a4a3a22a22a2a12a1	2	bbeccba
11	25		a32a32a22a14	4	bbdb
12	22		a36a3a12	96	dag	A38
12	23		a42a32a22a12a12	8	bcbha	A46
12	23		a4a35a12	40	aba	A46
12	24		d4a4a26	24	dca	A54D4	A54D4
12	24		d4a34a14	32	cde	A54D4	A54D4
12	24		a5a33a16a1	24	cfec	A54D4	A54D4
12	24		a42a32a3a12	8	bbbd	A54D4	A54D4
12	24		a5a32a24a1	16	bebf	A54D4	A54D4
12	24		d4a34a14	48	cdc	D46	A54D4
12	24		d42a116	1152	eb	D46	D46
12	24		a42a32a22a12	4	bcbh	A46	A64
12	24		a34a32a14	32	fdg	A38	A72D52
12	25		a5a32a3a14a1	8	cefdc
12	25		a5a32a22a2a1a1	2	bebbdh
12	25		d4a32a3a22a12	4	bddac
12	25		d4a4a24a14	8	dcae
12	25		a5a32a22a12a12a1	4	bfbdhf
12	25		a5a3a3a22a12a1a1a1	2	bfebhdee
12	25		a42a3a3a2a12a1	2	bbcade
12	25		a4a4a3a3a2a1a1a1	1	bbccbddd
12	25		a42a3a24	4	bbb
12	25		a42a32a14a12	4	bche
12	25		d4a32a24a1a1	8	bdaeg
12	25		d4a33a16a1a1	12	cdegb
12	25		a4a32a32a2a1	2	abcbc
12	25		a42a3a22a2a1a1a1	2	bcbbfdh
12	25		a4a4a3a2a2a2a1a1a1	1	bbcabbhhd
12	25		a4a34a14	8	ach
12	25		a4a32a3a3a12a12	2	bbcfde
12	25		a4a33a23a1	6	bbag
12	25		a4a3a3a3a2a2a2a1	1	bbbebbah
12	25		a34a3a3a12	8	bfdc
12	25		a4a32a3a22a12a1a1	2	bccbhge
12	25		a4a32a3a22a12a12	2	bcfbhh
12	25		a32a32a3a22a12	4	edbbh
13	24		a44a14	24	cc	A54D4	A64
13	24		a5a4a3a3a2a2a1	2	bebbddd	A54D4	A64
13	24		a42a34	16	bb	A46	A72D52
13	24		a42a4a3a22a12	4	ccahb	A46	A72D52
13	24	E	a38	2688	a	2A38
13	25		a6a26a13	12	dhd
13	25		a44a12	24	ca
13	25		a5a4a32a2a12	2	bfbdc
13	25		d4a4a33a12	6	bdac
13	25		d42a26	72	cc
13	25		a5a4a3a2a2a2a1a1	1	bebhdeda
13	25		a5a4a3a2a2a2a1a1	1	bebhdddd
13	25		d4a4a3a3a2a2a1a1	1	bdaaeccb
13	25		a42a4a3a22	2	bcbd
13	25		a4a4a4a3a2a1a1a1	1	bccbdbcd
13	25		a5a33a23	6	bbd
13	25		a5a32a3a22a2	2	abbhc
13	25		a5a4a22a22a2a12	2	behdfd
13	25		a5a32a3a22a12a1	2	bbbedd
13	25		a4a4a3a3a3a2a1	1	bcbbbdc
13	25		a4a4a3a3a3a2a1	1	bbbabdb
13	25		a43a23a13	6	cdb
13	25		d4a33a23a2	6	bacg
13	25		a42a3a3a22a2a1	2	ebaddd
13	25		a5a29	72	cf
14	21		d4a37	336	ag	A38
14	22		a44a3a22	16	aab	A46
14	23		a5a42a3a3a12a1	4	bbddaf	A54D4
14	23		d4a43a22a12	12	caca	A54D4
14	23		a5d4a33a13a12	12	dfega	A54D4
14	23		a52a3a24a12	16	efda	A54D4
14	23		d42a34a12	96	dcd	D46
14	24		a5a43a13	12	cbe	A64	A64
14	24		a52a32a22	8	eda	A64	A64
14	24		a6a33a23	12	bhd	A64	A64
14	24		d4a42a4a22	4	caac	A54D4	A72D52
14	24		a5d4a32a3a12a1	4	dfecbg	A54D4	A72D52
14	24		a52a32a12a12a12	8	febcg	A54D4	A72D52
14	24		a5a42a3a3a1	4	bbddf	A54D4	A72D52
14	24		d42a34	32	dc	D46	A72D52
14	24		a43a33	12	bh	A46	A83
14	24		a38	384	g	A38	D64
14	25		d5a32a24a12	8	bgbb
14	25		d5a33a18	48	cgc
14	25		a6a32a3a22a1	2	bhhcf
14	25		a52a3a3a14	8	efee
14	25		a6a32a3a2a12a12	2	bhhdeg
14	25		d4a43a13a1	6	cabc
14	25		a5d4a3a3a22a1	2	deeccb
14	25		a5a5a3a22a12a1a1	2	efddefg
14	25		a5a42a3a2a12	2	bbfdf
14	25		a5a4a4a3a2a1a1	1	cbbdabe
14	25		d4a42a32a12	4	baeb
14	25		d42a32a3a14	8	dcbb
14	25		a5a42a3a12a12a1	2	cbhcee
14	25		a5d4a32a14a12a1	4	dfegcg
14	25		a5a4a3a3a3a2	1	bbhddc
14	25		a5a4a3a3a3a2	1	bbeddc
14	25		a5a42a22a2a12	2	cbddf
14	25		a44a22	8	ba
14	25		d4a4a4a3a2a2a1a1	1	caaecbbg
14	25		a5a4a3a3a3a1a1a1	1	bbhedbfg
14	25		a5a32a32a3a1	4	dddcg
14	25		a5a32a3a3a3a1	2	bheddf
14	25		a5a4a32a22a12a1	2	cbhdge
14	25		a42a4a32a2a1	2	bbdbf
14	25		a4a4a4a3a3a2a1	1	abbdhcf
14	25		a42a4a3a22a2a1	2	bahbdf
14	25		d4a34a3a14	8	fegg
15	24		a52a42a12	4	bdc	A64	A72D52
15	24		a6a4a4a3a2a1a1	2	chhceaa	A64	A72D52
15	24		a52a4a3a22	4	bfdf	A54D4	A83
15	24		a44a32	16	hb	A46	A92D6
15	25		d5a35	20	ab
15	25		d5a4a32a22a12	2	bgbba
15	25		a6a42a3a12a1	2	chdcb
15	25		a6a4a4a2a2a1a1a1	1	chhefacc
15	25		a5d4a42a12a1	2	abeab
15	25		a5a5a4a3a2a1	1	bbddea
15	25		a6a4a3a3a2a2a1	1	bhdcfga
15	25		a6a4a32a22a1	2	bhdfc
15	25		d42a42a22	4	acb
15	25		a52a4a3a12a12	2	bedcc
15	25		a5d4a4a3a2a2a1	1	abecbba
15	25		a52a32a3a12	2	bdac
15	25		a5a42a4a2a12	2	adfec
15	25		a5a42a4a2a12	2	addca
15	25		a5a4a4a4a2a1a1	1	bhddeca
15	25		a45	5	d
15	25		a5a4a4a3a3a2	1	bhdcab
15	25		d4a42a32a3	2	bccb
16	21		d4a45	40	ab	A46
16	22		a52d4a32a3	8	ceba	A54D4
16	22		a53a3a3a13	12	ecad	A54D4
16	22		d44a3a16	144	bdc	D46
16	23		a6a5a4a3a2a12a1	2	bhdecah	A64
16	23		a53a4a12a1	6	daag	A64
16	24		d5d4a34	16	dgb	A72D52	A72D52
16	24		d5a5a32a3a12a1	4	fgbceb	A72D52	A72D52
16	24		a52d42a12	16	cef	A72D52	A72D52
16	24		a7a34a14	16	fge	A72D52	A72D52
16	24		d5a4a42a22	4	cbba	A72D52	A72D52
16	24		a6d4a42a2	4	ahcb	A72D52	A72D52
16	24		a6a5a4a3a2a1	2	bhdech	A64	A83
16	24		a52d4a32a12	4	eegd	A54D4	A92D6
16	24		a5a5a42a3	4	dddf	A54D4	A92D6
16	24		a52d4a32a12	8	eebd	A54D4	D64
16	24		d44a18	48	bc	D46	D64
16	24	E	a46	240	a	2A46
16	25		a7a34a12	8	fff
16	25		a7a3a3a3a22a12	2	efggch
16	25		a5d43a13	36	bcb
16	25		d5a42a3a3a1a1	2	bbcbdb
16	25		d5d4a33a13a1	6	dgbec
16	25		d5a5a3a24a1	4	egcad
16	25		a6a5a4a2a2a1a1	1	bhdcagh
16	25		d5a4a34	4	bbb
16	25		d5a42a3a22a12	2	cbcae
16	25		a6d4a4a3a2a1a1	1	ahcgafe
16	25		a52a5a3a2	2	deeb
16	25		a6a5a3a3a2a2	1	bhfebc
16	25		a6a5a3a3a2a1a1a1	1	bhegchhh
16	25		a6a42a32a1	2	bcee
16	25		a5a5a5a22a12a1	2	defchd
16	25		a52d4a3a22	4	cfcb
16	25		a5a5d4a3a22	2	ccdga
16	25		a6d4a32a22a2	2	ahgab
16	25		a5a5a4a4a2a1	1	ddddcg
16	25		a5a5a4a4a2a1	1	ddadad
16	25		a6a4a4a3a2a2a1	1	bddecah
16	25		a5d4a42a3a1	2	edccb
16	25		a5d42a32a1a1a1	2	cebecf
16	25		a52a4a32a12	2	haeh
16	25		a52a4a3a3a12	2	ddebd
16	25		a5a5a4a3a3a1a1	1	eddefdg
16	25		a52a34	8	cf
16	25		a52a4a3a22a12	2	hdcch
16	25		d4a42a4a32	2	hcbb
17	24		a7a42a32	4	bfc	A72D52	A83
17	24		a62a4a3a12	4	hebb	A72D52	A83
17	24		a6a5a5a3a2	2	dddcg	A64	A92D6
17	24		a62a32a22	4	hah	A64	A92D6
17	24		a54	24	a	A64	D64
17	25		a7a4a4a3a2a1	1	bfgcgb
17	25		a62a32a2a1	2	hcfa
17	25		a7a42a22a2a1	2	bfhea
17	25		d5d4a42a22	2	abbb
17	25		d5a5a4a3a3a1	1	bbbaab
17	25		d5a5a4a3a2a2a1	1	bbbaedb
17	25		a6a5d4a3a2a1	1	ecdafb
17	25		a6a5a42a12	2	ddeb
17	25		a6a5a4a3a3	1	dcgbc
17	25		a6a5a4a3a3	1	dcfcc
17	25		a6a5a4a3a3	1	dceac
17	25		a52d4a4a3	2	cdbb
17	25		a6a4a4a4a3a1	1	deffab
18	21		a53d4d4a1	12	bcab	A54D4
18	22		a62a42a3	4	caa	A64
18	23		a6d5a4a4a2a12	2	bhaaba	A72D52
18	23		a62d4a4a12	4	ceba	A72D52
18	23		d5a52d4a12a12	4	ebcfa	A72D52
18	23		a7a5a42a12a1	4	dfcag	A72D52
18	23		a7d42a32a12	8	cgfa	A72D52
18	23		d52a34a12	16	gea	A72D52
18	24		a7a52a22	8	ffa	A83	A83
18	24		a7a5a42a1	4	dfcg	A72D52	A92D6
18	24		a7a5d4a3a1a1a1	2	eggfdfc	A72D52	A92D6
18	24		a6d5a4a4a2	2	bhaab	A72D52	A92D6
18	24		d52a34	16	gb	A72D52	D64
18	24		d5a52d4a12	4	ebbc	A72D52	D64
18	24		a52a5d4a3a1	4	gbcdb	A54D4	A11D7E6
18	24		a54a14	48	cb	A54D4	E64
18	25		d6a34a3a12	8	ddcd
18	25		a7a52a14	8	fge
18	25		a7a5d4a22a1	2	egfbc
18	25		a7d42a3a14	4	cgef
18	25		a7a5a4a3a2	1	dfchb
18	25		a62a5a2a1a1	2	deaed
18	25		a7a5a4a3a1a1a1	1	dgchfeg
18	25		a6d5a4a3a2a1a1	1	bhaebfd
18	25		d5a5a5a4a1a1	1	dbcacc
18	25		a7a5a32a3a1	2	dggfd
18	25		a7a5a32a3a1	2	dfhfg
18	25		a6a6a4a3a2a1	1	cdchbg
18	25		a6a5a5a4a1	1	aeecc
18	25		d5a5d4a32a12a1	2	ebcefb
18	25		d5d42a32a3	4	cbbc
18	25		d5a5a42a3a1	2	dbadf
18	25		d5a5a42a3a1	2	dbabb
18	25		a6a5d4a4a2a1	1	cgeabf
18	25		a6a5a4a4a3	1	cfacg
18	25		a52d42a3a12	2	bgff
18	25		a6a42a42a1	2	bcag
19	24		a8a42a32	4	hhb	A83	A92D6
19	24		a7a6a5a2a1	2	dfceb	A83	A92D6
19	24		a6a6a5a4a1	2	eeaha	A64	A11D7E6
19	24	E	d46	2160	d	2D46
19	24	E	a54d4	48	aa	2A54D4
19	25		d6a42a4a22	2	addc
19	25		a8a4a4a3a2a1	1	hghbfb
19	25		a8a42a22a2a1	2	hhgeb
19	25		a7a6a4a2a2a1	1	dfheeb
19	25		d52a4a4a22	2	bbec
19	25		a6d5d4a4a2	1	bcaec
19	25		a6d5a5a3a2a1	1	bdabca
19	25		a7a52a3a12	2	dcab
19	25		d5a53a1	3	aaa
19	25		a7a52a22a12	2	dcdb
19	25		a7a5a4a4a2	1	achgc
19	25		a7d4a4a4a3	1	ccefb
19	25		a62a5a3a2	2	fbad
19	25		a6a53	6	cb
19	25		a6a52a5	2	ecb
19	25		a6a5a5d4a2	1	babcc
19	25		d5a52a4a22	2	dadc
20	20		d5a54	16	ad	A54D4
20	20		d5d45	120	dc	D46
20	21		a63d4a2	6	aaa	A64
20	22		a7d5a5a3a3a1	2	bgecad	A72D52
20	22		d52a52a3	8	bba	A72D52
20	22		a72a32a3a12	8	gdae	A72D52
20	23		a7a62a12a12	4	ecga	A83
20	23		a72a4a3a12	4	faea	A83
20	23		a8a52a22a12	4	dhba	A83
20	24		a72d4a14	8	gff	A92D6	A92D6
20	24		d6a52a32	8	edd	A92D6	A92D6
20	24		a8a52a3	4	dge	A92D6	A92D6
20	24		d6a52a32	4	edc	D64	A92D6
20	24		d6d43a16	12	bcb	D64	D64
20	24		a7d5a5a3a1a1a1	2	cgefecd	A72D52	A11D7E6
20	24		d5d5a52a12	4	bced	A72D52	A11D7E6
20	24		a7d5d4a3a3	2	bgecf	A72D52	A11D7E6
20	24		a6a6d5a4	2	aaeb	A72D52	A11D7E6
20	24		d52a52a12	8	cbc	A72D52	E64
20	24		a62a52	4	ch	A64	A122
20	24		d46	48	c	D46	D83
20	25		a8a52a12a12	2	dhfg
20	25		d6a52a3a12a1a1	2	eddfeb
20	25		d6a5d4a32a1	2	ccdcd
20	25		a7a7a3a22a12	2	fggbg
20	25		a8d4a4a3a3	1	chbff
20	25		d52a5d4a12a1	2	bbecb
20	25		a7d5a42a1a1	2	cfbcf
20	25		a7a6a5a3	1	ecfe
20	25		a62d5a3a12	2	aedd
20	25		a7d5a4a3a3	1	bfbfc
20	25		a7a6a5a2a1a1a1	1	echbgfe
20	25		a7a6a4a4a1	1	ecbad
20	25		a62a6a3a1	2	abee
20	25		a6a6a6a3a1	1	caceg
20	25		a6d5a5a4a2a1	1	aeebad
20	25		a6a6a5d4a1	1	abfhd
20	25		a7a52a4a12	2	ehag
20	25		d5a5a5a42	2	fbdb
21	24		a8a6a5a2a1	2	ehbga	A83	A11D7E6
21	24		a72a42	4	cg	A72D52	A122
21	25		d6a6a4a4a2	1	cdcdd
21	25		a8a6a4a3a1	1	eggbb
21	25		a7a6d5a2a1a1	1	aecfba
21	25		a6d5d5a4a2	1	baacc
21	25		a7d5a5a4a1	1	acbdb
21	25		a7a6a5a4	1	cgbe
22	21		a7d52d4a3	4	beac	A72D52
22	22		a8a62a3	4	bba	A83
22	23		a8a7a5a12a1	2	cgeac	A92D6
22	23		a8a6d5a2a12	2	abhba	A92D6
22	23		a7d6a5a3a12a1	2	dgdfab	A92D6
22	23		a9a5a42a12	4	fgba	A92D6
22	23		d6d5a52a12	4	bdcd	D64
22	23		d54a12	48	bd	D64
22	24		a9a5d4a3a1a1	2	gfffeb	A92D6	A11D7E6
22	24		a7d6a5a3a1	2	dgcfe	A92D6	A11D7E6
22	24		a8a6d5a2	2	abhb	A92D6	A11D7E6
22	24		d6d5a52	4	bdc	D64	A11D7E6
22	24		d54	48	b	D64	E64
22	24		a8a7a4a3	2	chbg	A83	A122
22	24		a7d52a32	4	eed	A72D52	D83
22	24		a72d42	8	fd	A72D52	D83
22	24	E	a64	24	a	2A64
22	25		e6d42a33	12	cbc
22	25		e6a5a42a3a1	2	dbace
22	25		e6a52a24	8	fba
22	25		d7a36	24	ge
22	25		a9a5d4a22	2	gfgb
22	25		a9a5a4a3a1a1	1	ffbgbc
22	25		a9a5a32a3	2	fggf
22	25		a8a7a4a2a1	1	chbbc
22	25		d6d5a5a3a3a1	1	bdcdbe
22	25		a7d6a32a3a12	2	dgfeb
22	25		a8d5a5a3a1	1	agffe
22	25		a8d5a5a2a2a1	1	ahfbab
22	25		a8a6a5a3	1	bbgg
22	25		a8a6a5a3	1	cbef
22	25		d6a52d4a3	2	bcdb
22	25		d6a53a13	6	cdb
22	25		a8a52d4	2	bfe
22	25		a8a6a4a4a1	1	cbbbc
22	25		a7a7a5a3a1	1	ghefc
22	25		d53a33	6	ec
22	25		a7d5d42a3	2	bffc
23	24		a82a32	4	hb	A92D6	A122
23	24		a9a6a5a2	2	cgbc	A92D6	A122
23	24		a73	12	a	A83	D83
23	25		d7a44	4	bd
23	25		a9a6a4a3	1	cfgb
23	25		a8d52a22	2	ebe
23	25		d6a6a6a4	1	accf
23	25		d6a62a4	2	bce
23	25		a8a7d4a3	1	fbbb
23	25		a72d5a3	2	baa
23	25		a62d52	2	cb
24	20		a72d5d5	4	cda	A72D52
24	21		a82d4a4	4	baa	A83
24	22		a9a7d4a3a1	2	fffad	A92D6
24	22		a72d6a3	4	cfa	A92D6
24	22		d62d42a3a12	4	cbdb	D64
24	24		d7a52a5a1	4	cdea	A11D7E6	A11D7E6
24	24		a9d52a12a1	4	efec	A11D7E6	A11D7E6
24	24		a7e6d4a32	4	bgce	A11D7E6	A11D7E6
24	24		e6a62a4	4	eaa	A11D7E6	A11D7E6
24	24		e6d5a52a12	4	cbca	E64	A11D7E6
24	24		d62d42a14	4	cbb	D64	D83
24	24		a72d6a12	4	dfd	A92D6	D83
24	24		a72d5d4	4	fde	A72D52	A15D9
24	25		d7a52d4a1a1	2	bdeeb
24	25		a9a7a32a1	2	fgcd
24	25		d6d52a5a1	2	bcba
24	25		a7d6d5a3a1a1	1	cedeeb
24	25		a8a7a6a1	1	aebd
24	25		a7d6a5d4a1	1	cfdfb
24	25		a72a7a12	2	edd
24	25		a8a7d4a4	1	bfgb
24	25		a7a7d5a4	1	ccgb
24	25		a72d5a4	2	cea
25	24		a10a6a5a1	2	hgbb	A11D7E6	A122
25	24		a8a72	4	eb	A83	A15D9
25	24	E	a72d52	8	aa	2A72D52
25	25		d7a6a6a2a2	1	adedc
25	25		a10a6a4a2a1	1	hgcea
25	25		e6a6d5a4a2	1	acaea
25	25		e6a62d4	2	bca
25	25		a7e6a5a4a1	1	acaeb
25	25		a10a5a4a4	1	gbcb
25	25		a8d6a6a2	1	dbfc
25	25		a9a6d5a2a1	1	bfbeb
25	25		a9a62a2	2	agc
25	25		a9d5a5a4	1	bbbe
26	19		a72d6d5	4	dae	A72D52
26	21		a9d6a5d4	2	cfea	A92D6
26	23		a9d6d5a12a1	2	cffab	A11D7E6
26	23		a10a6d5a12	2	bbga	A11D7E6
26	23		a8e6a6a2a12	2	ahaba	A11D7E6
26	23		d7a7d5a3a12	2	edeea	A11D7E6
26	23		e6d6a52a12	4	dbea	A11D7E6
26	23		e6d53a12	12	bce	E64
26	24		a92a22	8	ga	A122	A122
26	24		d7a7d5a3	2	eddc	A11D7E6	D83
26	24		a9d6a5a3	2	dfbd	A92D6	A15D9
26	24		a9a8a5	2	ebc	A92D6	A15D9
26	24		a72d52	8	ce	A72D52	D10E72
26	25		d7d52a3a3	2	bdba
26	25		a10d5a5a2a1	1	bgbbb
26	25		a7d62a3	2	bcc
26	25		a9d6d4a3a1	1	cfbeb
26	25		a9a7a6	1	egb
26	25		a9a7a6	1	efb
26	25		a7d6d5a5a1	1	dffeb
27	24		a82a7	4	ga	A83	A17E7
27	25		a8d7a4a4	1	dbde
27	25		a92a3a12	2	baa
27	25		a10a62a1	2	eca
28	20		a92d5a12	4	fac	A92D6
28	20		d63d5a12	6	bdb	D64
28	22		a9e6d5a3a1	2	cfead	A11D7E6
28	22		a9d7a5a3	2	dfca	A11D7E6
28	22		a11d5a5a3a1	2	fbeae	A11D7E6
28	22		e62a52a3	8	bae	E64
28	23		a10a9a2a12a1	2	bgaaf	A122
28	23		a11a7a4a12	2	gcaa	A122
28	24		d8d44	8	cb	D83	D83
28	24		a9d7a5a1a1	2	efede	A11D7E6	A15D9
28	24		a11d5d4a3	2	fbeb	A11D7E6	A15D9
28	24		a9a7d6a1	2	fefc	A92D6	A17E7
28	24		a9a7d6a1	2	fbfc	A92D6	D10E72
28	24		d62d6d4a12	2	bbbb	D64	D10E72
28	24	E	a83	12	a	2A83
28	25		d8a52a5a1	2	ddbe
28	25		a11a7a22a12	2	gbaf
28	25		a11d5a4a3	1	fcbb
28	25		e6d6d5a5a1	1	cceab
28	25		d7d6a5a5	1	cdcb
28	25		a8a7e6a1a1	1	aeedc
28	25		a9e6a42a1	2	cgbc
28	25		a10a8a4a1	1	bbae
28	25		a92a4a12	2	gaf
28	25		a9a8d5a1	1	fbcd
29	24		a11a8a3	2	bca	A122	A15D9
29	25		a10d6a6	1	fbe
30	21		d7a7e6d4	2	cada	A11D7E6
30	22		a102a3	4	ba	A122
30	23		d72a7a12	4	dcd	D83
30	23		d8a72a12	4	ddd	D83
30	24		d8a72	4	dd	D83	A15D9
30	24		a11d6a5a1	2	fbba	A11D7E6	A17E7
30	24		a10e6a6	2	agb	A11D7E6	A17E7
30	24		d7a7e6a3	2	caed	A11D7E6	D10E72
30	24		a9e6d6a1	2	efea	A11D7E6	D10E72
30	24		e62d52	8	ca	E64	D10E72
30	25		d8a7d5a3	1	cbdd
30	25		a10a9a4	1	bca
30	25		d7a7d52	2	cae
31	24		a12a7a4	2	gbf	A122	A17E7
31	24	E	d64	24	d	2D64
31	24	E	a92d6	4	aa	2A92D6
31	25		a12a6a5	1	gba
31	25		a8e62a22	2	aaa
31	25		a10e6d5a2	1	ebba
31	25		a11a8d4	1	bea
31	25		a11a7d5	1	bba
31	25		a8a8d7	1	dcb
31	25		a82d7	2	ca
32	18		a92d7	4	da	A92D6
32	18		d7d63	6	db	D64
32	20		a11e6d5a3	2	ebaa	A11D7E6
32	21		a12a8d4	2	bba	A122
32	22		d8d62a3a12	2	bbdb	D83
32	24		d8d62a12a12	2	bbba	D83	D10E72
32	24		d64	8	b	D64	D122
32	25		a9d8a5a1a1	1	dfecb
32	25		a12a7d4	1	bbf
32	25		a9d7d6a1	1	ceeb
34	19		a11d7d6	2	cea	A11D7E6
34	19		e63d6	12	ae	E64
34	23		a11d8a3a12	2	dbca	A15D9
34	23		a13a8a12a1	2	caac	A15D9
34	23		d9a72a12	4	eea	A15D9
34	24		a13d6a3a1	2	bbcb	A15D9	A17E7
34	24		d9a72	4	ed	A15D9	D10E72
34	24		a11d7d5	2	eee	A11D7E6	D122
34	25		e7a7d5a5	1	cbca
34	25		e7a72a3a1	2	dcab
34	25		d9a7d5a3	1	ddeb
34	25		a13a7a3a1	1	cfcc
34	25		d72e6a3	2	aca
34	25		d8a7e6a3	1	edda
34	25		a11d62	2	cb
35	24		a112	4	a	A122	D122
35	25		a12d7a4	1	ebc
36	20		d82d5d4	2	bda	D83
36	22		a13d7a3a1	2	ebab	A15D9
36	24		a9e7a7	2	cfa	D10E72	A17E7
36	24		e7d6d6d4a1	2	bbbaa	D10E72	D10E72
36	24		d82d42	2	bb	D83	D122
36	25		a12a10a1	1	aab
37	24	E	e64	48	e	2E64
37	24	E	a11d7e6	2	aaa	2A11D7E6
37	25		a13e6a4a1	1	baba
38	17		a11d8e6	2	dae	A11D7E6
38	21		a11d9d4	2	dea	A15D9
38	23		d9e62a12	4	add	D10E72
38	23		a9e7e6a12	2	aecd	D10E72
38	23		a14e6a2a12	2	bfaa	A17E7
38	23		a11e7a5a12	2	cbba	A17E7
38	24		a11d9a3	2	eeb	A15D9	D122
38	24		a12a11	2	af	A122	A24
38	25		d9d7a7	1	cdb
38	25		a11d8d5	1	dbc
40	20		a15d5d5	2	bba	A15D9
40	22		d8e7d6a3a1	1	bbada	D10E72
40	22		d10d62a3	2	bbd	D10E72
40	22		a15d6a3	2	bca	A17E7
40	24		d10d62a12	2	bba	D10E72	D122
40	24	E	a122	4	a	2A122
40	25		d10a9a5	1	dbb
40	25		a15d5a4	1	bca
40	25		e7e62a5	2	aaa
40	25		a9e7d7	1	aca
40	25		a11e7d5a1	1	aeba
40	25		a14a9	1	ac
41	24		a15a8	2	ac	A15D9	A24
42	21		a13e7d4	2	aba	A17E7
43	24		a16a7	2	fa	A17E7	A24
43	24	E	d83	6	d	2D83
44	16		d9d82	2	db	D83
44	20		e72d6d5	2	bad	D10E72
44	24		d82d8	2	ba	D83	D16E8
44	24		d83	6	a	D83	E83
46	23		d11a11a12	2	ebd	D122
46	24		a15d8	2	cb	A15D9	D16E8
46	25		d11a7e6	1	dab
47	25		a16d7	1	ca
48	18		d10e7d7a1	1	abda	D10E72
48	18		a17d7a1	2	cac	A17E7
48	22		d102a3a12	2	bdb	D122
48	24		a15e7a1	2	bcc	A17E7	D16E8
48	24		d10e7d6a1	1	abaa	D10E72	D16E8
48	24		d8e72a12	2	aaa	D10E72	D16E8
48	25		a13d10a1	1	bcb
49	24	E	a15d9	2	aa	2A15D9
50	15		a15d10	2	ba	A15D9
52	20		d12d8d5	1	bad	D122
52	23		a19a4a12	2	caa	A24
52	24		d12d8d4	1	bab	D122	D16E8
55	24	E	d10e72	2	dd	2D10E72
55	24	E	a17e7	2	aa	2A17E7
55	25		a19d5	1	aa
56	14		d11e72	2	da	D10E72
56	21		a20d4	2	aa	A24
58	25		e8a11e6	1	aac
58	25		a11d13	1	bb
60	24		e8d82	2	aa	E83	D16E8
62	23		a15e8a12	2	cbd	D16E8
64	22		e8e72a3	2	aae	E83
64	22		d14e7a3a1	1	abda	D16E8
67	24	E	d122	2	d	2D122
68	12		d13d12	1	db	D122
68	20		d12e8d5	1	aad	D16E8
68	24		d122	2	b	D122	D24
71	24		a23	2	a	A24	D24
76	16	E	d16d9	1	bd	D16E8
76	16	E	d9e82	2	ea	E83
76	24		d16d8	1	ba	D16E8	D24
76	24	E	a24	2	a	2A24
91	24	E	e83	6	e	2E83
91	24	E	d16e8	1	dd	2D16E8
92	8	E	d17e8	1	da	D16E8
100	20		d20d5	1	ad	D24
139	24	E	d24	1	d	2D24
140	0	E	d25	1	d	D24