The following is a list of the known Salem numbers <1.3.
Click here
to plot the roots of the minimal polynomial and see
the beta-expansion for a given Salem number.
no. degree number half-polynomial
1 10 1.1762808183 1 1 0-1-1-1
2 18 1.1883681475 1-1 1-1 0 0-1 1-1 1
3 14 1.2000265240 1 0 0-1-1 0 0 1
4 14 1.2026167437 1 0-1 0 0 0 0-1
5 10 1.2163916611 1 0 0 0-1-1
6 18 1.2197208590 1-1 0 0 0 0 0 0-1 1
7 10 1.2303914344 1 0 0-1 0-1
8 20 1.2326135486 1-1 0 0 0-1 1 0 0-1 1
9 22 1.2356645804 1 0-1-1 0 0 0 1 1 0-1-1
10 16 1.2363179318 1-1 0 0 0 0 0 0-1
11 26 1.2375048212 1 0-1 0 0-1 0 0-1 0 1 0 0 1
12 12 1.2407264237 1-1 1-1 0 0-1
13 18 1.2527759374 1 0 0 0 0 0-1-1-1-1
14 20 1.2533306502 1 0-1 0 0-1 0 0 0 0 0
15 14 1.2550935168 1 0-1-1 0 1 0-1
16 18 1.2562211544 1-1 0 0-1 1 0 0 0-1
17 24 1.2601035404 1-1 0 0-1 1 0-1 1-1 0 1-1
18 22 1.2602842369 1-1 0-1 1 0 0 0-1 1-1 1
19 10 1.2612309611 1 0-1 0 0-1
20 26 1.2630381399 1-1 0 0 0 0-1 0 0 0 0 0 0 1
21 14 1.2672964425 1-1 0 0 0 0-1 1
21.5 22 1.2767796740 1-1-1 1 0 0 0 0 0-1 0 1
22 8 1.2806381563 1 0 0-1-1
23 26 1.2816913715 1 0 0 0 0 0-1-1-1-1-1-1-1-1
24 20 1.2824955606 1-2 2-2 2-2 1 0-1 1-1
25 18 1.2846165509 1 0 0 0-1 0-1-1 0-1
26 26 1.2847468215 1-2 1 1-2 1 0 0-1 1 0-1 1-1
27 30 1.2850993637 1 0 0 0 0-1-1-1-1-1-1 0 0 0 0 1
28 30 1.2851215202 1-2 2-2 1 0-1 2-2 1 0-1 1-1 1-1
29 30 1.2851856708 1-1 0 0 0 0 0 0-1 0 0 0-1 0 0-1
30 26 1.2851967268 1 0-1-1 0 0 0 1 0-1-1 0 1 1
31 44 1.2851991792 1-1 0 0 0 0 0-1 0 0 0-1 0 0 0 0 0 0 0 1 0 0 1
32 30 1.2852354362 1 0-1 0 0-1-1 0 0 0 1 0 0 1 0-1
33 34 1.2854090648 1-1 0 0-1 1-1 0 1-1 1 0-1 1-1 0 1-1
34 18 1.2863959668 1-2 2-2 2-2 2-3 3-3
35 26 1.2867301820 1-1 0 0-1 1-1 0 1-1 1 0-1 1
36 24 1.2917414257 1-1 0 0 0 0-1 0 0 0 0 0 0
37 20 1.2920391060 1 0-1 0 0-1 0 0-1 0 1
38 10 1.2934859531 1 0-1-1 0 1
39 18 1.2956753719 1-1 0 0-1 1-1 0 1-1
39.5 * 34 1.2962106596 1 1 0 1 0-1 0-1-2 0 0-1 1 1-1 1 1-1
40 22 1.2964213652 1-1 0 0 0-1 0 0 0 0 0 1
41 28 1.2968213737 1 0 0 0-1-1-1-1-1 0 0 0 1 1 1
41.5 * 36 1.2984298355 1 1 0-1-2-2-1 0 1 1 0-1-1 0 1 1 0-1-1
42 26 1.2997448695 1-1-1 0 2 0-2-1 2 2-2-2 0 3
See the paper [1] for the numbers 1-39, and the paper [2]
for 21.5 and 40,41 and 42. For 39.5 and 41.5 see [3].
[1] Small Salem numbers, Duke Math. Jour. 44 (1977), 315-328.
[2] Pisot and Salem numbers in intervals of the real line, Mathematics of
Computation 32 (1978), 1244-1260.
[3] two new Salem numbers marked * from Mike Mossinghoff's search of
height 1 up to degree 38, Feb 16, 1996.