This list is known to be complete for degree at most 44. There is only one known small Salem numbers with larger degree.
D Salem Number Coefficients of Minimal Polynomial 1.) 10 1.176280818259917506544070338474 1 1 0 -1 -1 -1 2.) 18 1.188368147508223588142960958629 1 -1 1 -1 0 0 -1 1 -1 1 3.) 14 1.200026523987391518902962100414 1 0 0 -1 -1 0 0 1 4.) 14 1.202616743688604261118295415948 1 0 -1 0 0 0 0 -1 5.) 10 1.216391661138265091626806311199 1 0 0 0 -1 -1 6.) 18 1.219720859040311844169606760414 1 -1 0 0 0 0 0 0 -1 1 7.) 10 1.230391434407224702790177938975 1 0 0 -1 0 -1 8.) 20 1.232613548593121003962731694807 1 -1 0 0 0 -1 1 0 0 -1 1 9.) 22 1.235664580389747308105169351531 1 0 -1 -1 0 0 0 1 1 0 -1 -1 10.) 16 1.236317931803230489899094869802 1 -1 0 0 0 0 0 0 -1 11.) 26 1.237504821217490608171021829989 1 0 -1 0 0 -1 0 0 -1 0 1 0 0 1 12.) 12 1.240726423652541392056148161575 1 -1 1 -1 0 0 -1 13.) 18 1.252775937410113900864582824053 1 0 0 0 0 0 -1 -1 -1 -1 14.) 20 1.253330650201489757028162788986 1 0 -1 0 0 -1 0 0 0 0 0 15.) 14 1.255093516763722879173091003232 1 0 -1 -1 0 1 0 -1 16.) 18 1.256221154391670233067434043309 1 -1 0 0 -1 1 0 0 0 -1 17.) 24 1.260103540354990920321649852331 1 -1 0 0 -1 1 0 -1 1 -1 0 1 -1 18.) 22 1.260284236896492963739228435283 1 -1 0 -1 1 0 0 0 -1 1 -1 1 19.) 10 1.261230961137138851946671503074 1 0 -1 0 0 -1 20.) 26 1.263038139930169261222022798085 1 -1 0 0 0 0 -1 0 0 0 0 0 0 1 21.) 14 1.267296442523068692734077407604 1 -1 0 0 0 0 -1 1 22.) 22 1.276779674019016861136497157605 1 -1 -1 1 0 0 0 0 0 -1 0 1 23.) 8 1.280638156267757596701902532710 1 0 0 -1 -1 24.) 26 1.281691371528106310055107748672 1 0 0 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 25.) 20 1.282495560639960169561207128806 1 -2 2 -2 2 -2 1 0 -1 1 -1 26.) 18 1.284616550925536736743131441485 1 0 0 0 -1 0 -1 -1 0 -1 27.) 26 1.284746821544843035729838140650 1 -2 1 1 -2 1 0 0 -1 1 0 -1 1 -1 28.) 30 1.285099363651876557117420034512 1 0 0 0 0 -1 -1 -1 -1 -1 -1 0 0 0 0 1 29.) 30 1.285121520153207532780681369174 1 -2 2 -2 1 0 -1 2 -2 1 0 -1 1 -1 1 -1 30.) 30 1.285185670752909791356387310393 1 -1 0 0 0 0 0 0 -1 0 0 0 -1 0 0 -1 31.) 26 1.285196726769853432068127270005 1 0 -1 -1 0 0 0 1 0 -1 -1 0 1 1 32.) 44 1.285199179205612167312192383918 1 -1 0 0 0 0 0 -1 0 0 0 -1 0 0 0 0 0 0 0 1 0 0 1 33.) 30 1.285235436228923770828415884707 1 0 -1 0 0 -1 -1 0 0 0 1 0 0 1 0 -1 34.) 34 1.285409064765363764030309848277 1 -1 0 0 -1 1 -1 0 1 -1 1 0 -1 1 -1 0 1 -1 35.) 18 1.286395966836277224044411092745 1 -2 2 -2 2 -2 2 -3 3 -3 36.) 26 1.286730182048201274368747282841 1 -1 0 0 -1 1 -1 0 1 -1 1 0 -1 1 37.) 24 1.291741425714500483635599066106 1 -1 0 0 0 0 -1 0 0 0 0 0 0 38.) 20 1.292039106017929461943480560567 1 0 -1 0 0 -1 0 0 -1 0 1 *39.) 40 1.292418657582426546281031229140 1 0 0 -1 0 -1 0 -1 0 -1 0 -1 0 0 1 0 1 0 1 0 1 *40.) 46 1.292900721780102794630870596243 1 0 0 0 -1 -1 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 41.) 10 1.293485953125454106519909883794 1 0 -1 -1 0 1 42.) 18 1.295675371944048235295741653561 1 -1 0 0 -1 1 -1 0 1 -1 *43.) 34 1.296210659593309216851783179125 1 -1 0 -1 0 1 0 1 -2 0 0 1 1 -1 -1 -1 1 1 44.) 22 1.296421365194547218873224266498 1 -1 0 0 0 -1 0 0 0 0 0 1 45.) 28 1.296821373714950077456125855369 1 0 0 0 -1 -1 -1 -1 -1 0 0 0 1 1 1 *46.) 36 1.298429835475111538327805425740 1 1 0 -1 -2 -2 -1 0 1 1 0 -1 -1 0 1 1 0 -1 -1 47.) 26 1.299744869472170731620096386139 1 -1 -1 0 2 0 -2 -1 2 2 -2 -2 0 3
Note: Salem numbers are truncated, not rounded.
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