alfa = {1, 2, 0, 1, 2, 4, 8, 0, 1, 2, 4, 6, 11, 20, 0, 1, 2, 4, 2, 6, 11, 8, 
      14, 24, 40, 0, 1, 2, 4, 2, 6, 11, 6, 8, 14, 24, 17, 28, 45, 70, 0, 1, 2,
       4, 2, 6, 11, 2, 6, 8, 14, 24, 8, 14, 17, 28, 45, 20, 32, 50, 76, 112, 
      1, 2, 4, 2, 6, 11, 2, 6, 8, 14, 24, 6, 8, 14, 17, 28, 45, 8, 17, 28, 20,
       32, 50, 76, 36, 55, 82, 119, 168, 2, 6, 11, 2, 6, 8, 14, 24, 2, 6, 8, 
      14, 17, 28, 45, 8, 14, 8, 17, 28, 20, 32, 50, 76, 17, 20, 32, 50, 36, 
      55, 82, 119, 40, 60, 88, 126, 176, 240, 2, 6, 8, 14, 17, 28, 45, 6, 8, 
      14, 8, 17, 28, 20, 32, 50, 76, 8, 17, 28, 17, 20, 32, 50, 36, 55, 82, 
      119, 20, 32, 36, 55, 82, 40, 60, 88, 126, 176, 65, 94, 133, 184, 249, 
      330, 8, 14, 8, 17, 28, 17, 20, 32, 50, 36, 55, 82, 119, 8, 17, 20, 32, 
      50, 20, 32, 36, 55, 82, 40, 60, 88, 126, 176, 20, 36, 55, 40, 60, 88, 
      126, 65, 94, 133, 184, 249, 70, 100, 140, 192, 258, 340, 440, 17, 20, 
      32, 36, 55, 82, 20, 36, 55, 40, 60, 88, 126, 65, 94, 133, 184, 249, 36, 
      40, 60, 88, 65, 94, 133, 184, 70, 100, 140, 192, 258, 340, 106, 147, 
      200, 267, 350, 451, 572, 40, 60, 65, 94, 133, 70, 100, 140, 192, 258, 
      106, 147, 200, 267, 350, 451, 112, 154, 208, 276, 360, 462, 584, 728, 
      161, 216, 285, 370, 473, 596, 741, 910, 1105};


Length[alfa]
292


beta = {3360, 7280, 0, 3360, 1680, 21840, 21840, 0, 3360, 3360, 21840, 21840, 
      87360, 48048, 0, 3360, 3360, 21840, 1680, 43680, 87360, 7280, 131040, 
      240240, 80080, 0, 3360, 3360, 21840, 3360, 43680, 87360, 21840, 21840, 
      262080, 240240, 87360, 480480, 480480, 102960, 0, 3360, 3360, 21840, 
      3360, 43680, 87360, 1680, 43680, 21840, 262080, 240240, 21840, 131040, 
      262080, 960960, 480480, 21840, 480480, 1201200, 720720, 102960, 1680, 
      3360, 21840, 3360, 43680, 87360, 3360, 43680, 21840, 262080, 240240, 
      21840, 43680, 262080, 262080, 960960, 480480, 7280, 262080, 480480, 
      87360, 1441440, 2402400, 720720, 240240, 1601600, 2162160, 823680, 
      80080, 1680, 21840, 43680, 3360, 43680, 21840, 262080, 240240, 1680, 
      43680, 43680, 262080, 262080, 960960, 480480, 21840, 131040, 21840, 
      524160, 960960, 87360, 1441440, 2402400, 720720, 87360, 131040, 1441440,
       1201200, 960960, 4804800, 4324320, 823680, 48048, 1201200, 3603600, 
      2882880, 720720, 48048, 1680, 21840, 21840, 131040, 131040, 480480, 
      240240, 21840, 43680, 262080, 21840, 524160, 960960, 87360, 1441440, 
      2402400, 720720, 21840, 262080, 480480, 262080, 262080, 2882880, 
      2402400, 960960, 4804800, 4324320, 823680, 87360, 480480, 1441440, 
      4804800, 2162160, 240240, 4804800, 10810800, 5765760, 720720, 480480, 
      3603600, 5765760, 2882880, 480480, 21840, 7280, 43680, 21840, 262080, 
      480480, 131040, 131040, 1441440, 1201200, 480480, 2402400, 2162160, 
      411840, 7280, 262080, 131040, 1441440, 1201200, 262080, 1441440, 
      2882880, 9609600, 4324320, 240240, 4804800, 10810800, 5765760, 720720, 
      21840, 960960, 1601600, 480480, 7207200, 10810800, 2882880, 2402400, 
      14414400, 17297280, 5765760, 480480, 80080, 2162160, 7207200, 6726720, 
      2162160, 240240, 7280, 21840, 87360, 480480, 480480, 1601600, 720720, 
      43680, 1441440, 2402400, 480480, 7207200, 10810800, 2882880, 1201200, 
      7207200, 8648640, 2882880, 240240, 240240, 480480, 4804800, 3603600, 
      4804800, 21621600, 17297280, 2882880, 480480, 10810800, 28828800, 
      20180160, 4324320, 240240, 720720, 5765760, 10090080, 5765760, 1201200, 
      87360, 1680, 48048, 240240, 1201200, 3603600, 1441440, 400400, 7207200, 
      14414400, 6726720, 720720, 2162160, 14414400, 20180160, 8648640, 
      1201200, 43680, 102960, 2882880, 10090080, 10090080, 3603600, 480480, 
      21840, 240, 102960, 960960, 2018016, 1441440, 400400, 43680, 1680, 16, 
      0};


Length[beta]
292


Tr[ alfa beta ]
233677032034817280


alfa . beta
70578471600

(* this is ok as a work around: *)
MapThread[Times[#1,#2]&, {alfa, beta}]

(* the error occurs for a list longer than 249 elements  *)

waw=249; Tr[ Take[ alfa,waw] Take[ beta,waw] ] ==   Take[ alfa,waw] . Take[ beta,waw] 
True

waw=250; Tr[ Take[ alfa,waw] Take[ beta,waw] ] ==   Take[ alfa,waw] . Take[ beta,waw] 
False