——————————

SALEM NUMBERS:

x^17 – 31*x^16 + 433*x^15 – 3608*x^14 + 20013*x^13 – 78079*x^12 +
220717*x^11 – 458940*x^10 + 705459*x^9 – 799257*x^8 + 660596*x^7 –
391294*x^6 + 161786*x^5 – 44982*x^4 + 7979*x^3 – 837*x^2 + 46*x – 1

x^18 – 33*x^17 + 494*x^16 – 4445*x^15 + 26854*x^14 – 115243*x^13 + 362498*x^12 – 850194*x^11 + 1498144*x^10 – 1983921*x^9 + 1962162*x^8 – 1431230*x^7 + 754969*x^6 – 280049*x^5 + 70262*x^4 – 11292*x^3 + 1074*x^2 – 53*x + 1

x^19 – 35*x^18 + 557*x^17 – 5344*x^16 + 34553*x^15 – 159439*x^14 + 542423*x^13 – 1386300*x^12 + 2687875*x^11 – 3966530*x^10 + 4445822*x^9 – 3758294*x^8 + 2367533*x^7 – 1091721*x^6 + 359274*x^5 – 81407*x^4 + 12063*x^3 – 1083*x^2 + 52*x – 1

x^19 – 35*x^18 + 558*x^17 – 5373*x^16 + 34930*x^15 – 162344*x^14 + 557208*x^13 – 1438734*x^12 + 2821126*x^11 – 4212363*x^10 + 4775880*x^9 – 4078746*x^8 + 2589161*x^7 – 1198202*x^6 + 393469*x^5 – 88329*x^4 + 12870*x^3 – 1130*x^2 + 53*x – 1

x^19 – 35*x^18 + 558*x^17 – 5374*x^16 + 34956*x^15 – 162647*x^14 + 559300*x^13 – 1448266*x^12 + 2851355*x^11 – 4280967*x^10 + 4888760*x^9 – 4213778*x^8 + 2705933*x^7 – 1270169*x^6 + 424300*x^5 – 97142*x^4 + 14439*x^3 – 1283*x^2 + 59*x – 1

x^19 – 35*x^18 + 560*x^17 – 5430*x^16 + 35664*x^15 – 167995*x^14 + 586218*x^13 – 1543608*x^12 + 3096048*x^11 – 4742710*x^10 + 5532312*x^9 – 4873839*x^8 + 3198484*x^7 – 1532318*x^6 + 520824*x^5 – 120639*x^4 + 17968*x^3 – 1574*x^2 + 69*x – 1

x^20 – 37*x^19 + 626*x^18 – 6429*x^17 + 44858*x^16 – 225492*x^15 + 844888*x^14 – 2408155*x^13 + 5282259*x^12 – 8963730*x^11 + 11769570*x^10 – 11904755*x^9 + 9193589*x^8 – 5345760*x^7 + 2294145*x^6 – 706514*x^5 + 150019*x^4 – 20708*x^3 + 1695*x^2 – 70*x + 1

x^20 – 37*x^19 + 627*x^18 – 6456*x^17 + 45185*x^16 – 227837*x^15 + 855952*x^14 – 2444204*x^13 + 5364880*x^12 – 9096041*x^11 + 11911051*x^10 – 11990136*x^9 + 9193950*x^8 – 5295224*x^7 + 2245421*x^6 – 681799*x^5 + 142556*x^4 – 19400*x^3 + 1577*x^2 – 66*x + 1

x^20 – 37*x^19 + 628*x^18 – 6486*x^17 + 45593*x^16 – 231168*x^15 + 874176*x^14 – 2514842*x^13 + 5564877*x^12 – 9516380*x^11 + 12570979*x^10 – 12762865*x^9 + 9862764*x^8 – 5715893*x^7 + 2432511*x^6 – 738161*x^5 + 153272*x^4 – 20528*x^3 + 1625*x^2 – 66*x + 1

——————————

41 MONIC INTEGER POLYNOMIALS OF SMALLEST POSSIBLE TRACE, IRREDUCIBLE, WITH DEGRE 17, AND HAVING ALL ROOTS REAL AND POSITIVE:

x^17 – 31*x^16 + 431*x^15 – 3555*x^14 + 19398*x^13 – 73951*x^12 +
202885*x^11 – 406759*x^10 + 599430*x^9 – 648390*x^8 + 510888*x^7 –
289314*x^6 + 115459*x^5 – 31585*x^4 + 5690*x^3 – 634*x^2 + 39*x – 1
x^17 – 31*x^16 + 431*x^15 – 3556*x^14 + 19419*x^13 – 74140*x^12 +
203844*x^11 – 409798*x^10 + 605728*x^9 – 657078*x^8 + 518850*x^7 –
294065*x^6 + 117231*x^5  31971*x^4 + 5734*x^3 – 636*x^2 + 39*x – 1

x^17 – 31*x^16 + 431*x^15 – 3557*x^14 + 19441*x^13 – 74353*x^12 +
205042*x^11 – 414146*x^10 + 616419*x^9 – 675267*x^8 + 540336*x^7 –
311494*x^6 + 126691*x^5 – 35256*x^4 + 6412*x^3 – 709*x^2 + 42*x – 1
x^17 – 31*x^16 + 432*x^15 – 3581*x^14 + 19694*x^13 – 75897*x^12 +
211095*x^11 – 430139*x^10 + 645490*x^9 – 711726*x^8 + 571511*x^7 –
329178*x^6 + 133040*x^5 – 36593*x^4 + 6557*x^3 – 715*x^2 + 42*x – 1
x^17 – 31*x^16 + 432*x^15 – 3581*x^14 + 19694*x^13 – 75898*x^12 +
211111*x^11 – 430247*x^10 + 645892*x^9 – 712631*x^8 + 572782*x^7 –
330284*x^6 + 133609*x^5 – 36747*x^4 + 6573*x^3 – 715*x^2 + 42*x – 1
x^17 – 31*x^16 + 432*x^15 – 3581*x^14 + 19694*x^13 – 75898*x^12 +
211112*x^11 – 430261*x^10 + 645973*x^9 – 712883*x^8 + 573242*x^7 –
330789*x^6 + 133937*x^5 – 36865*x^4 + 6593*x^3 – 716*x^2 + 42*x – 1
x^17 – 31*x^16 + 432*x^15 – 3581*x^14 + 19694*x^13 – 75898*x^12 +
211112*x^11 – 430262*x^10 + 645985*x^9 – 712942*x^8 + 573394*x^7 –
331008*x^6 + 134113*x^5 – 36940*x^4 + 6608*x^3 – 717*x^2 + 42*x – 1
x^17 – 31*x^16 + 432*x^15 – 3581*x^14 + 19694*x^13 – 75898*x^12 +
211112*x^11 – 430261*x^10 + 645973*x^9 – 712884*x^8 + 573249*x^7 –
330808*x^6 + 133963*x^5 – 36884*x^4 + 6600*x^3 – 717*x^2 + 42*x – 1
x^17 – 31*x^16 + 432*x^15 – 3581*x^14 + 19695*x^13 – 75916*x^12 +
211249*x^11 – 430838*x^10 + 647451*x^9 – 715268*x^8 + 575674*x^7 –
332324*x^6 + 134513*x^5 – 36988*x^4 + 6608*x^3 – 717*x^2 + 42*x – 1
x^17 – 31*x^16 + 432*x^15 – 3582*x^14 + 19716*x^13 – 76107*x^12 +
212239*x^11 – 434075*x^10 + 654430*x^9 – 725339*x^8 + 585346*x^7 –
338355*x^6 + 136842*x^5 – 37501*x^4 + 6663*x^3 – 719*x^2 + 42*x – 1

x^17 – 31*x^16 + 431*x^15 – 3557*x^14 + 19441*x^13 – 74354*x^12 +
205057*x^11 – 414242*x^10 + 616764*x^9 – 676039*x^8 + 541465*x^7 –
312597*x^6 + 127414*x^5 – 35570*x^4 + 6499*x^3 – 723*x^2 + 43*x – 1
x^17 – 31*x^16 + 432*x^15 – 3581*x^14 + 19695*x^13 – 75917*x^12 +
211267*x^11 – 430976*x^10 + 648041*x^9 – 716815*x^8 + 578255*x^7 –
335081*x^6 + 136368*x^5 – 37745*x^4 + 6784*x^3 – 738*x^2 + 43*x – 1
x^17 – 31*x^16 + 432*x^15 – 3582*x^14 + 19716*x^13 – 76109*x^12 +
212274*x^11 – 434336*x^10 + 655516*x^9 – 728113*x^8 + 589857*x^7 –
343046*x^6 + 139900*x^5 – 38696*x^4 + 6922*x^3 – 746*x^2 + 43*x – 1

x^17 – 31*x^16 + 432*x^15 – 3581*x^14 + 19695*x^13 – 75918*x^12 +
211284*x^11 – 431099*x^10 + 648540*x^9 – 718073*x^8 + 580315*x^7 –
337300*x^6 + 137922*x^5 – 38426*x^4 + 6957*x^3 – 760*x^2 + 44*x – 1
x^17 – 31*x^16 + 432*x^15 – 3582*x^14 + 19716*x^13 – 76109*x^12 +
212274*x^11 – 434336*x^10 + 655518*x^9 – 728134*x^8 + 589946*x^7 –
343243*x^6 + 140147*x^5 – 38874*x^4 + 6993*x^3 – 760*x^2 + 44*x – 1
x^17 – 31*x^16 + 432*x^15 – 3582*x^14 + 19716*x^13 – 76109*x^12 +
212275*x^11 – 434351*x^10 + 655612*x^9 – 728454*x^8 + 590591*x^7 –
344031*x^6 + 140722*x^5 – 39112*x^4 + 7043*x^3 – 764*x^2 + 44*x – 1
x^17 – 31*x^16 + 432*x^15 – 3582*x^14 + 19716*x^13 – 76110*x^12 +
212290*x^11 – 434446*x^10 + 655944*x^9 – 729157*x^8 + 591526*x^7 –
344819*x^6 + 141140*x^5 – 39248*x^4 + 7068*x^3 – 766*x^2 + 44*x – 1
x^17 – 31*x^16 + 432*x^15 – 3582*x^14 + 19716*x^13 – 76109*x^12 +
212276*x^11 – 434366*x^10 + 655705*x^9 – 728765*x^8 + 591203*x^7 –
344755*x^6 + 141226*x^5 – 39305*x^4 + 7078*x^3 – 766*x^2 + 44*x – 1
x^17 – 31*x^16 + 432*x^15 – 3582*x^14 + 19717*x^13 – 76128*x^12 +
212430*x^11 – 435065*x^10 + 657665*x^9 – 732298*x^8 + 595337*x^7 –
347862*x^6 + 142685*x^5 – 39713*x^4 + 7140*x^3 – 770*x^2 + 44*x – 1
x^17 – 31*x^16 + 433*x^15 – 3606*x^14 + 19970*x^13 – 77673*x^12 +
218500*x^11 – 451178*x^10 + 687197*x^9 – 769816*x^8 + 628013*x^7 –
366848*x^6 + 149691*x^5 – 41220*x^4 + 7301*x^3 – 776*x^2 + 44*x – 1

x^17 – 31*x^16 + 432*x^15 – 3581*x^14 + 19695*x^13 – 75918*x^12 +
211285*x^11 – 431113*x^10 + 648622*x^9 – 718337*x^8 + 580832*x^7 –
337945*x^6 + 138444*x^5 – 38698*x^4 + 7044*x^3 – 775*x^2 + 45*x – 1
x^17 – 31*x^16 + 432*x^15 – 3581*x^14 + 19694*x^13 – 75900*x^12 +
211147*x^11 – 430523*x^10 + 647073*x^9 – 715740*x^8 + 578023*x^7 –
336002*x^6 + 137604*x^5 – 38479*x^4 + 7012*x^3 – 773*x^2 + 45*x – 1
x^17 – 31*x^16 + 432*x^15 – 3582*x^14 + 19717*x^13 – 76129*x^12 +
212446*x^11 – 435173*x^10 + 658071*x^9 – 733244*x^8 + 596776*x^7 –
349326*x^6 + 143684*x^5 – 40160*x^4 + 7263*x^3 – 788*x^2 + 45*x – 1

x^17 – 31*x^16 + 432*x^15 – 3582*x^14 + 19717*x^13 – 76128*x^12 +
212431*x^11 – 435080*x^10 + 657761*x^9 – 732641*x^8 + 596090*x^7 –
348917*x^6 + 143634*x^5 – 40249*x^4 + 7319*x^3 – 801*x^2 + 46*x – 1
x^17 – 31*x^16 + 432*x^15 – 3583*x^14 + 19738*x^13 – 76322*x^12 +
213470*x^11 – 438659*x^10 + 666078*x^9 – 745945*x^8 + 610768*x^7 –
359929*x^6 + 149066*x^5 – 41901*x^4 + 7592*x^3 – 819*x^2 + 46*x – 1
x^17 – 31*x^16 + 433*x^15 – 3606*x^14 + 19971*x^13 – 77693*x^12 +
218673*x^11 – 452030*x^10 + 689844*x^9 – 775248*x^8 + 635508*x^7 –
373793*x^6 + 153935*x^5 – 42866*x^4 + 7679*x^3 – 821*x^2 + 46*x – 1
x^17 – 31*x^16 + 433*x^15 – 3607*x^14 + 19992*x^13 – 77885*x^12 +
219678*x^11 – 455362*x^10 + 697156*x^9 – 786032*x^8 + 646152*x^7 –
380677*x^6 + 156739*x^5 – 43539*x^4 + 7763*x^3 – 825*x^2 + 46*x – 1
x^17 – 31*x^16 + 433*x^15 – 3607*x^14 + 19992*x^13 – 77886*x^12 +
219696*x^11 – 455499*x^10 + 697733*x^9 – 787509*x^8 + 648526*x^7 –
383065*x^6 + 158190*x^5 – 44032*x^4 + 7843*x^3 – 829*x^2 + 46*x – 1
x^17 – 31*x^16 + 433*x^15 – 3607*x^14 + 19993*x^13 – 77904*x^12 +
219835*x^11 – 456103*x^10 + 699361*x^9 – 790339*x^8 + 651725*x^7 –
385384*x^6 + 159231*x^5 – 44304*x^4 + 7880*x^3 – 831*x^2 + 46*x – 1

x^17 – 31*x^16 + 432*x^15 – 3581*x^14 + 19695*x^13 – 75919*x^12 +
211302*x^11 – 431237*x^10 + 649132*x^9 – 719645*x^8 + 583017*x^7 –
340356*x^6 + 140188*x^5 – 39501*x^4 + 7266*x^3 – 808*x^2 + 47*x – 1
x^17 – 31*x^16 + 431*x^15 – 3559*x^14 + 19483*x^13 – 74741*x^12 +
207120*x^11 – 421307*x^10 + 633092*x^9 – 702088*x^8 + 570331*x^7 –
334672*x^6 + 138844*x^5 – 39437*x^4 + 7301*x^3 – 813*x^2 + 47*x – 1

x^17 – 31*x^16 + 432*x^15 – 3583*x^14 + 19738*x^13 – 76322*x^12 +
213471*x^11 – 438673*x^10 + 666162*x^9 – 746229*x^8 + 611366*x^7 –
360746*x^6 + 149796*x^5 – 42319*x^4 + 7737*x^3 – 846*x^2 + 48*x – 1
x^17 – 31*x^16 + 433*x^15 – 3607*x^14 + 19993*x^13 – 77905*x^12 +
219852*x^11 – 456228*x^10 + 699885*x^9 – 791726*x^8 + 654145*x^7 –
388198*x^6 + 161382*x^5 – 45342*x^4 + 8172*x^3 – 872*x^2 + 48*x – 1
x^17 – 31*x^16 + 433*x^15 – 3607*x^14 + 19993*x^13 – 77906*x^12 +
219870*x^11 – 456366*x^10 + 700475*x^9 – 793273*x^8 + 656722*x^7 –
390930*x^6 + 163177*x^5 – 46029*x^4 + 8307*x^3 – 882*x^2 + 48*x – 1

x^17 – 31*x^16 + 433*x^15 – 3607*x^14 + 19993*x^13 – 77905*x^12 +
219853*x^11 – 456244*x^10 + 699993*x^9 – 792129*x^8 + 655059*x^7 –
389502*x^6 + 162553*x^5 – 45986*x^4 + 8376*x^3 – 905*x^2 + 50*x – 1

x^17 – 31*x^16 + 433*x^15 – 3607*x^14 + 19993*x^13 – 77907*x^12 +
219888*x^11 – 456506*x^10 + 701093*x^9 – 794983*x^8 + 659813*x^7 –
394621*x^6 + 166059*x^5 – 47456*x^4 + 8729*x^3 – 948*x^2 + 52*x – 1
x^17 – 31*x^16 + 433*x^15 – 3607*x^14 + 19994*x^13 – 77925*x^12 +
220027*x^11 – 457110*x^10 + 702721*x^9 – 797812*x^8 + 663004*x^7 –
396915*x^6 + 167061*x^5 – 47696*x^4 + 8753*x^3 – 948*x^2 + 52*x – 1
x^17 – 31*x^16 + 433*x^15 – 3608*x^14 + 20015*x^13 – 78119*x^12 +
221066*x^11 – 460689*x^10 + 711038*x^9 – 811118*x^8 + 677700*x^7 –
407990*x^6 + 172601*x^5  49442*x^4 + 9065*x^3 – 972*x^2 + 52*x – 1

x^17 – 31*x^16 + 433*x^15 – 3607*x^14 + 19994*x^13 – 77926*x^12 +
220044*x^11 – 457234*x^10 + 703231*x^9 – 799120*x^8 + 665190*x^7 –
399333*x^6 + 168823*x^5 – 48520*x^4 + 8986*x^3 – 983*x^2 + 54*x – 1
x^17 – 31*x^16 + 434*x^15 – 3632*x^14 + 20270*x^13 – 79702*x^12 +
227450*x^11 – 478288*x^10 + 745032*x^9 – 857530*x^8 + 722335*x^7 –
437777*x^6 + 186010*x^5 – 53330*x^4 + 9739*x^3 – 1033*x^2 + 54*x – 1