ONE:=[ [ 6, [-20,28]], [ 9, [-24, 36]], [ 10, [-68, 364]], [ 13, [-104, 812]], [ 14, [-36, 260]], [ 15, [36, -288]], # [ 16, [196, 4108]], # [ 17, [-40, 364]], [ 18, [-276, 1908]], [ 19, [-332, 1792]], [ 20, [36, 28]], # [ 21, [-120, 2052]], [ 26, [-52, 812]], [ 29, [-376, 8060]], [ 30, [-84, 2052]], [ 31, [100, 2912]], # [ 35, [48, -260]], # [ 36, [84, 2556]], # [ 38, [-516, 15652]], [ 40, [2356, 148148]], # [ 44, [50036, 11406884]], # [ 47, [480, 24724]], # [ 51, [-972, 39168]], [ 53, [-712, 32500]], [ 54, [-164, 8036]], [ 57, [-2280, 70956]], [ 62, [53460/841, 12254284/24389]], # [ 63, [6564, 673632]], # [ 64, [49324/729, 27634708/19683]], # [ 66, [-2532, 108108]], [ 67, [-399020/121, 151476224/1331]], [ 70, [130612/729, 233048780/19683]], # [ 71, [68, -608]], # [ 72, [2257951620/1247689, 210768585826212/1393668613]], # [ 73, [-89717798504/158030041, 77265730632501572/1986595645411]], [ 74, [-4996, 109460]], [ 83, [-76, -1792]], [ 84, [636, 55404]], # [ 86, [-420, -34532]], [ 87, [100, -5824]], # [ 92, [6408640436/9579025, 1882920523965884/29647082375]], # [ 96, [6436, 805132]], # [ 98, [263636/2401, 881221748/117649]], # [ 99, [51614976/7921, 586752290676/704969]], # [101, [-8440, 354172]], [102, [-13927451079540/106215372649, 362520187661304361548/34616333453917643]], [103, [88, 3500]], # [107, [118811616/1311025, 5942682758636/1501123625]], # [108, [100, 6020]], # [109, [2723707216/3352561, 558871998491444/6138539191]], # [110, [-5428, 443324]], [112, [40155138290151330664945/32505331107937801, 8087337059337646625285073313321361/5860462500472878688184549]], # [113, [-122776/625, 310312132/15625]], [116, [780, 92492]], # [117, [-2600, 273644]], [119, [1284, 159200]], # [120, [3628, 486980]], # [122, [-2643647942807940/5099778876361, 705127723710168111397156/11516672543340879109]], [123, [112321830657456/67551961, 1195812539922182464332/555209567459]], # [124, [255562108/212521, 15127407257732/97972181]], # [127, [3460, 484096]], # [128, [2900724/49, 5582315404/343]], # [130, [-2210582868215531/138879202225, 25825080929380286738953/51755417897179625]], [132, [79780, 24873436]], # [133, [-1335218610915546200/105974403705769, -980583897458924448846603980/1090941523841420218603]], [142, [-121493651778952370463359660420/54727454720812833584888041, 120287786196999563903919614306662909447283156/404862801081772719402232087203316428661]], [143, [379071876/25, 7385416617824/125]], # [145, [-7927161573992/806162449, -23810049066526185932/22889370414457]], [147, [-20300, 734464]], [148, [474709952116/30591961, 507906129346525132/169204136291]], # [155, [35499683, 211584388550]], # [156, [7406052424260/77810041, 22584970661264526348/686362371661]], # [158, [-7594613659/1247689, 1165384138306081/1393668613]], [159, [144, -16380]], # [162, [-420, 65484]], [164, [30591819110788868/188224982079121, 53582461790475804906816572/2582354712109303429831]], # [166, [-243956/9, 15522164/27]], [167, [16564138200/93876721, 21783501340519436/909571549769]], # [172, [2039311243516/2044396225, 16035036167297770636/92437375313375]], # [175, [1109899012/22801, 47195777681536/3442951]], # [177, [-1600532606457895400719288872602056552863000/4216489864294939248323713357587084541129, 17551502920649953589434705332665169089975857243800664103187317772/273795679730722189468772898207282169644797335073220630314117]], [178, [-212, 32500]], [181, [-2371563109880/211208089, 5057290624209964364/3069487157437]], [185, [352, 62244]], # [187, [340591981745053002312053920/42088384723360325817769, 14498347780378019947728495917378963933252/8634623149897546519454398931640853]], # [189, [22742256/121, 118313265636/1331]], # [190, [1163487131205442830852071332/22564302942549058507089, 51746392711936829342039973496389355274180/3389478494326077097438129088948313]], # [191, [48356, 14084512]], # [192, [1860, 365364]], # [197, [-35320, 2086276]] ]: TWO:= [ [ 41, [[-1000, 26068], [4320, 334628]]], [ 69, [[-72, 1908], [-344, -22436]]], [ 76, [[1156, 96068], [4684, 478996]]], # [ 77, [[-4600, 167684], [-765, 54746]]], [ 94, [[-116, 8060], [-467, 42133]]], [105, [[-504, -51012], [-648, 65484]]], [106, [[-10724, 242668], [13393/16, 5857543/64]]], [126, [[-596, -72836], [-8052, 712188]]], [129, [[-14376, 684180], [-152, -15652]]], [136, [[121, 10507], [1444, 203476]]], # [149, [[-16072, 1258228], [-696, -101060]]], [151, [[100, -2752], [1024, 157324]]], # [154, [[-13451, 1362775], [-1652, 244948]]], [160, [[40084/9, 20841436/27], [316, -48188]]], # [161, [[-4041, 597556], [-23080, 1230188]]], [174, [[-6852, 1048572], [-804, 136836]]], [186, [[2916, 564372], [-18900, 2367828]]], [195, [[-13068, 2064384], [-27404, 2824192]]], [196, [[12340, 2779972], [5168884/9, 12138216724/27]]] ]: # WAS:=[ 3, 5, 6, 9, 10, 13, 14, 17, 18, 19, 21, 26, 29, 30, 38, 41, 51, 53, 54, 57, 66, 67, 69, 74, 77, 83, 86, 94, 101, 105, 106, 110, 117, 126, 129, 147, 149, 154, 161, 162, 166, 174, 178, 195, 197 ]: #All all-pos generator sets tested for HALFs; none found. NEGS:=[ [6, [-36, 36]], [9, [-56, 260]], [10, [-68, 364]], [13, [-104, 812]], [14, [-84, 836]], [17, [-40, 364]], [18, [-276, 1908]], [19, [-332, 1792]], [21, [-120, 2052]], [26, [-52, 812]], [29, [-376, 8060]], [30, [-84, 2052]], [38, [-516, 15652]], [51, [-972, 39168]], [53, [-712, 32500]], [54, [-164, 8036]], [57, [-2280, 70956]], [66, [-2532, 108108]], [67, [-399020/121, 151476224/1331]], [73, [-89717798504/158030041, 77265730632501572/1986595645411]], #*# [74, [-4996, 109460]], [83, [-76, -1792]], [86, [-420, -34532]], [101, [-8440, 354172]], [102, [-13927451079540/106215372649, 362520187661304361548/34616333453917643]], #*# [110, [-5428, 443324]], [113, [-122776/625, 310312132/15625]], #*# [117, [-2600, 273644]], [122, [-2643647942807940/5099778876361, 705127723710168111397156/11516672543340879109]], #*# [130, [-2210582868215531/138879202225, 25825080929380286738953/51755417897179625]], #*# [133, [-1335218610915546200/105974403705769, -980583897458924448846603980/1090941523841420218603]], #*# [142, [-121493651778952370463359660420/54727454720812833584888041, 120287786196999563903919614306662909447283156/404862801081772719402232087203316428661]], #*# [145, [-7927161573992/806162449, -23810049066526185932/22889370414457]], #*# [147, [-20300, 734464]], [158, [-7594613659/1247689, 1165384138306081/1393668613]], #*# [162, [-420, 65484]], [166, [-243956/9, 15522164/27]], [177, [-1600532606457895400719288872602056552863000/4216489864294939248323713357587084541129, 17551502920649953589434705332665169089975857243800664103187317772/273795679730722189468772898207282169644797335073220630314117]], #*# [178, [-212, 32500]], [181, [-2371563109880/211208089, 5057290624209964364/3069487157437]], #*# [197, [-35320, 2086276]], [41, [[-1000, 26068], [4320, 334628]]], [69, [[-72, 1908], [-344, -22436]]], [77, [[-4600, 167684], [-765, 54746]]], [94, [[-116, 8060], [-467, 42133]]], [105, [[-504, -51012], [-648, 65484]]], [106, [[-10724, 242668], [13393/16, 5857543/64]]], [126, [[-596, -72836], [-8052, 712188]]], [129, [[-14376, 684180], [-152, -15652]]], [149, [[-16072, 1258228], [-696, -101060]]], [154, [[-13451, 1362775], [-1652, 244948]]], [161, [[-4041, 597556], [-23080, 1230188]]], [174, [[-6852, 1048572], [-804, 136836]]], [186, [[2916, 564372], [-18900, 2367828]]], #*# [195, [[-13068, 2064384], [-27404, 2824192]]] ]: #Uses of Mest() recommended: MEST:=[ [6,30],[9,40],[11,200],[12,30],[15,50],[18,80],[21,50],[22,200],[24,1000], [27,80],[30,30],[33,1000],[34,2500],[36,3200],[39,400],[40,100],[42,150], [45,150],[46,4000],[48,1500],[51,300],[52,300],[54,50],[55,600],[57,50], [59,125],[60,475],[61,475],[63,400],[65,5000],[66,50],[67,100],[68,500], [69,175],[72,600],[75,3600],[78,3000],[79,4000],[80,1000],[81,1500],[82,350], [84,70],[87,150],[89,375],[90,200],[93,1500],[96,1200],[97,500],[99,200], [100,150],[102,150],[104,800],[105,300],[107,300],[108,2500],[111,300], [114,4000],[115,150],[117,200],[118,1000],[120,1500],[123,400],[125,850], [126,500],[128,1000],[129,175],[131,4000],[132,900],[135,1200],[137,850], [138,5000],[139,150],[141,4000],[144,1200],[146,4000],[147,100],[150,700], [152,500],[153,700],[156,800],[157,4000],[159,1600],[162,3500],[165,4000], [166,2000],[174,200],[177,250],[178,800],[180,500],[183,700],[185,1200], [186,1500],[187,500],[188,575],[189,1200],[192,100],[195,175],[198,2500], [199,200]]; PARITY:= #occasions when parity is necessary; alone: {43,91,155, #or in tandem with mest(): 42,55,59,60,61,68,80,81,82,89,90,93,97,100,104,114,115,125,135,137,139, 141,144,146,150,152,153,162,180,183,188,198,199}: #Note that there are also times when it could be used INSTEAD OF mest [11, 67, 107, 128, 187]: LSET:= #occasions when L-series calculations are needed. { 168, 170, 171, 173, 184, 193, 194}: