p^3、p^4阶有限环序列Rpppp、Rpppp3

 

C:\soft\MathTool\gaptool>FiniteRing
R4_1×R4_1=R16_107,R9_1×R9_1=R81_107
R4_1×R4_2=R16_96,R9_1×R9_3=R81_96
R4_1×R4_3=R16_112,R9_1×R9_2=R81_112
R4_1×R4_4=R16_206,R9_1×R9_4=R81_206
R4_1×R4_5=R16_207,R9_1×R9_5=R81_232
R4_1×R4_6=R16_208,R9_1×R9_6=R81_228
R4_1×R4_7=R16_209,R9_1×R9_7=R81_226
R4_1×R4_8=R16_255,R9_1×R9_8=R81_229
R4_1×R4_9=R16_210,R9_1×R9_9=R81_230
R4_1×R4_10=R16_224,R9_1×R9_10=R81_210
R4_1×R4_11=R16_211,R9_1×R9_11=R81_211
R4_2×R4_2=R16_103,R9_3×R9_3=R81_98
R4_2×R4_3=R16_113,R9_3×R9_2=R81_113
R4_2×R4_4=R16_212,R9_3×R9_4=R81_212
R4_2×R4_5=R16_213,R9_3×R9_5=R81_508
R4_2×R4_6=R16_214,R9_3×R9_6=R81_214
R4_2×R4_7=R16_215,R9_3×R9_7=R81_225
R4_2×R4_8=R16_256,R9_3×R9_8=R81_235
R4_2×R4_9=R16_216,R9_3×R9_9=R81_236
R4_2×R4_10=R16_217,R9_3×R9_10=R81_217
R4_2×R4_11=R16_218,R9_3×R9_11=R81_218
R4_3×R4_3=R16_104,R9_2×R9_2=R81_104
R4_3×R4_4=R16_219,R9_2×R9_4=R81_219
R4_3×R4_5=R16_220,R9_2×R9_5=R81_220
R4_3×R4_6=R16_221,R9_2×R9_6=R81_221
R4_3×R4_7=R16_222,R9_2×R9_7=R81_222
R4_3×R4_8=R16_223,R9_2×R9_8=R81_223
R4_3×R4_9=R16_225,R9_2×R9_9=R81_216
R4_3×R4_10=R16_226,R9_2×R9_10=R81_244
R4_3×R4_11=R16_227,R9_2×R9_11=R81_227
R4_4×R4_4=R16_301,R9_4×R9_4=R81_301
R4_4×R4_5=R16_303,R9_4×R9_5=R81_303
R4_4×R4_6=R16_305,R9_4×R9_6=R81_305
R4_4×R4_7=R16_308,R9_4×R9_7=R81_308
R4_4×R4_8=R16_354,R9_4×R9_8=R81_354
R4_4×R4_9=R16_314,R9_4×R9_9=R81_377
R4_4×R4_10=R16_307,R9_4×R9_10=R81_314
R4_4×R4_11=R16_324,R9_4×R9_11=R81_324
R4_5×R4_5=R16_304,R9_5×R9_5=R81_387
R4_5×R4_6=R16_306,R9_5×R9_6=R81_306
R4_5×R4_7=R16_309,R9_5×R9_7=R81_309
R4_5×R4_8=R16_355,R9_5×R9_8=R81_355
R4_5×R4_9=R16_315,R9_5×R9_9=R81_333
R4_5×R4_10=R16_319,R9_5×R9_10=R81_334
R4_5×R4_11=R16_325,R9_5×R9_11=R81_399
R4_6×R4_6=R16_307,R9_6×R9_6=R81_314
R4_6×R4_7=R16_310,R9_6×R9_7=R81_310
R4_6×R4_8=R16_356,R9_6×R9_8=R81_352
R4_6×R4_9=R16_316,R9_6×R9_9=R81_339
R4_6×R4_10=R16_320,R9_6×R9_10=R81_340
R4_6×R4_11=R16_326,R9_6×R9_11=R81_326
R4_7×R4_7=R16_311,R9_7×R9_7=R81_373
R4_7×R4_8=R16_312,R9_7×R9_8=R81_312
R4_7×R4_9=R16_317,R9_7×R9_9=R81_304
R4_7×R4_10=R16_321,R9_7×R9_10=R81_341
R4_7×R4_11=R16_327,R9_7×R9_11=R81_327
R4_8×R4_8=R16_313,R9_8×R9_8=R81_370
R4_8×R4_9=R16_318,R9_8×R9_9=R81_318
R4_8×R4_10=R16_322,R9_8×R9_10=R81_322
R4_8×R4_11=R16_328,R9_8×R9_11=R81_328
R4_9×R4_9=R16_384,R9_9×R9_9=R81_385
R4_9×R4_10=R16_323,R9_9×R9_10=R81_332
R4_9×R4_11=R16_302,R9_9×R9_11=R81_369
R4_10×R4_10=R16_386,R9_10×R9_10=R81_412
R4_10×R4_11=R16_387,R9_10×R9_11=R81_388
R4_11×R4_11=R16_389,R9_11×R9_11=R81_321
R8_1×R2_1=R16_12,R27_1×R3_1=R81_12
R8_1×R2_2=R16_13,R27_1×R3_2=R81_16
R8_2×R2_1=R16_10,R27_2×R3_1=R81_10
R8_2×R2_2=R16_14,R27_2×R3_2=R81_27
R8_3×R2_1=R16_11,R27_3×R3_1=R81_11
R8_3×R2_2=R16_6,R27_3×R3_2=R81_6
R8_4×R2_1=R16_9,R27_4×R3_1=R81_9
R8_4×R2_2=R16_15,R27_4×R3_2=R81_30
R8_5×R2_1=R16_206,R27_5×R3_1=R81_206
R8_5×R2_2=R16_208,R27_5×R3_2=R81_228
R8_6×R2_1=R16_230,R27_6×R3_1=R81_248
R8_6×R2_2=R16_239,R27_6×R3_2=R81_169
R8_7×R2_1=R16_208,R27_7×R3_1=R81_228
R8_7×R2_2=R16_224,R27_7×R3_2=R81_210
R8_8×R2_1=R16_231,R27_8×R3_1=R81_231
R8_8×R2_2=R16_240,R27_8×R3_2=R81_240
R8_9×R2_1=R16_152,R27_9×R3_1=R81_246
R8_9×R2_2=R16_241,R27_9×R3_2=R81_208
R8_10×R2_1=R16_233,R27_10×R3_1=R81_233
R8_10×R2_2=R16_242,R27_10×R3_2=R81_242
R8_11×R2_1=R16_180,R27_11×R3_1=R81_180
R8_11×R2_2=R16_243,R27_11×R3_2=R81_243
R8_12×R2_1=R16_235,R27_12×R3_1=R81_254
R8_12×R2_2=R16_244,R27_12×R3_2=R81_160
R8_13×R2_1=R16_219,R27_13×R3_1=R81_219
R8_13×R2_2=R16_221,R27_13×R3_2=R81_221
R8_14×R2_1=R16_221,R27_14×R3_1=R81_221
R8_14×R2_2=R16_226,R27_14×R3_2=R81_244
R8_15×R2_1=R16_204,R27_15×R3_1=R81_204
R8_15×R2_2=R16_245,R27_15×R3_2=R81_245
R8_16×R2_1=R16_212,R27_16×R3_1=R81_212
R8_16×R2_2=R16_214,R27_16×R3_2=R81_214
R8_17×R2_1=R16_214,R27_17×R3_1=R81_214
R8_17×R2_2=R16_217,R27_17×R3_2=R81_217
R8_18×R2_1=R16_236,R27_18×R3_1=R81_460
R8_18×R2_2=R16_246,R27_18×R3_2=R81_267
R8_19×R2_1=R16_252,R27_19×R3_1=R81_252
R8_19×R2_2=R16_253,R27_19×R3_2=R81_181
R8_20×R2_1=R16_203,R27_20×R3_1=R81_203
R8_20×R2_2=R16_247,R27_20×R3_2=R81_247
R8_21×R2_1=R16_251,R27_21×R3_1=R81_251
R8_21×R2_2=R16_254,R27_21×R3_2=R81_166
R8_22×R2_1=R16_237,R27_22×R3_1=R81_255
R8_22×R2_2=R16_248,R27_22×R3_2=R81_270
R8_23×R2_1=R16_200,R27_23×R3_1=R81_200
R8_23×R2_2=R16_249,R27_23×R3_2=R81_249
R8_24×R2_1=R16_238,R27_24×R3_1=R81_238
R8_24×R2_2=R16_250,R27_24×R3_2=R81_250
R8_25×R2_1=R16_301,R27_25×R3_1=R81_301
R8_25×R2_2=R16_305,R27_25×R3_2=R81_305
R8_26×R2_1=R16_303,R27_26×R3_1=R81_308
R8_26×R2_2=R16_306,R27_26×R3_2=R81_310
R8_27×R2_1=R16_305,R27_27×R3_1=R81_305
R8_27×R2_2=R16_307,R27_27×R3_2=R81_314
R8_28×R2_1=R16_343,R27_28×R3_1=R81_354
R8_28×R2_2=R16_344,R27_28×R3_2=R81_352
R8_29×R2_1=R16_308,R27_29×R3_1=R81_323
R8_29×R2_2=R16_310,R27_29×R3_2=R81_403
R8_30×R2_1=R16_349,R27_30×R3_1=R81_349
R8_30×R2_2=R16_350,R27_30×R3_2=R81_350
R8_31×R2_1=R16_333,R27_31×R3_1=R81_325
R8_31×R2_2=R16_338,R27_31×R3_2=R81_338
R8_32×R2_1=R16_334,R27_32×R3_1=R81_509
R8_32×R2_2=R16_339,R27_32×R3_2=R81_510
R8_33×R2_1=R16_345,R27_33×R3_1=R81_306
R8_33×R2_2=R16_346,R27_33×R3_2=R81_334
R8_34×R2_1=R16_354,R27_34×R3_1=R81_348
R8_34×R2_2=R16_356,R27_34×R3_2=R81_396
R8_35×R2_1=R16_314,R27_35×R3_1=R81_377
R8_35×R2_2=R16_316,R27_35×R3_2=R81_339
R8_36×R2_1=R16_335,R27_36×R3_1=R81_335
R8_36×R2_2=R16_340,R27_36×R3_2=R81_371
R8_37×R2_1=R16_336,R27_37×R3_1=R81_336
R8_37×R2_2=R16_341,R27_37×R3_2=R81_384
R8_38×R2_1=R16_306,R27_38×R3_1=R81_314
R8_38×R2_2=R16_319,R27_38×R3_2=R81_340
R8_39×R2_1=R16_337,R27_39×R3_1=R81_337
R8_39×R2_2=R16_342,R27_39×R3_2=R81_342
R8_40×R2_1=R16_307,
R8_40×R2_2=R16_320,
R8_41×R2_1=R16_310,R27_41×R3_1=R81_310
R8_41×R2_2=R16_321,R27_41×R3_2=R81_341
R8_42×R2_1=R16_324,R27_42×R3_1=R81_324
R8_42×R2_2=R16_326,R27_42×R3_2=R81_326
R8_43×R2_1=R16_353,R27_43×R3_1=R81_404
R8_43×R2_2=R16_351,R27_43×R3_2=R81_351
R8_44×R2_1=R16_352,R27_44×R3_1=R81_401
R8_44×R2_2=R16_347,R27_44×R3_2=R81_367
R8_45×R2_1=R16_329,R27_45×R3_1=R81_329
R8_45×R2_2=R16_332,R27_45×R3_2=R81_402
R8_46×R2_1=R16_348,R27_46×R3_1=R81_339
R8_46×R2_2=R16_382,R27_46×R3_2=R81_332
R8_47×R2_1=R16_356,R27_47×R3_1=R81_352
R8_47×R2_2=R16_322,R27_47×R3_2=R81_322
R8_48×R2_1=R16_316,R27_48×R3_1=R81_362
R8_48×R2_2=R16_323,R27_48×R3_2=R81_344
R8_49×R2_1=R16_330,R27_49×R3_1=R81_330
R8_49×R2_2=R16_380,R27_49×R3_2=R81_380
R8_50×R2_1=R16_320,R27_50×R3_1=R81_340
R8_50×R2_2=R16_386,R27_50×R3_2=R81_412
R8_51×R2_1=R16_326,R27_51×R3_1=R81_326
R8_51×R2_2=R16_387,R27_51×R3_2=R81_388
R8_52×R2_1=R16_331,R27_52×R3_1=R81_364
R8_52×R2_2=R16_388,R27_52×R3_2=R81_394
R27_53×R3_1=R81_458
R27_53×R3_2=R81_273
R27_54×R3_1=R81_161
R27_54×R3_2=R81_274
R27_55×R3_1=R81_489
R27_55×R3_2=R81_275
R8_56×R2_1=R16_303,R27_56×R3_1=R81_303
R8_56×R2_2=R16_306,R27_56×R3_2=R81_306
R8_57×R2_1=R16_345,R27_57×R3_1=R81_345
R8_57×R2_2=R16_346,R27_57×R3_2=R81_311
R27_58×R3_1=R81_366
R27_58×R3_2=R81_320
R8_59×R2_1=R16_331,R27_59×R3_1=R81_331
R8_59×R2_2=R16_388,R27_59×R3_2=R81_315
129种16阶可分解环
6,9,10,11,12,13,14,15,96,103,104,107,112,113,152,180,200,203,204,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,230,231,233,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,380,382,384,386,387,388,389,
141种81阶可分解环
6,9,10,11,12,16,27,30,96,98,104,107,112,113,160,161,166,169,180,181,200,203,204,206,208,210,211,212,214,216,217,218,219,220,221,222,223,225,226,227,228,229,230,231,232,233,235,236,238,240,242,243,244,245,246,247,248,249,250,251,252,254,255,267,270,273,274,275,301,303,304,305,306,308,309,310,311,312,314,315,318,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,344,345,348,349,350,351,352,354,355,362,364,366,367,369,370,371,373,377,380,384,385,387,388,394,396,399,401,402,403,404,412,458,460,489,508,509,510,

D:\MathTool\gaptool>Rpppp3 1 59 27
ret=0,环表示数据表中的记录条数=862
ret2=0,环表示数据表中的记录条数=902
Rpppp3(1,3)=R27_1,Rpppp3(1,2)=R8_1
Rpppp3(2,3)=R27_2,Rpppp3(2,2)=R8_2
Rpppp3(3,3)=R27_3,Rpppp3(3,2)=R8_3
Rpppp3(4,3)=R27_4,Rpppp3(4,2)=R8_4
Rpppp3(5,3)=R27_5,Rpppp3(5,2)=R8_5
Rpppp3(7,3)=R27_7,Rpppp3(7,2)=R8_7
Rpppp3(8,3)=R27_8,Rpppp3(8,2)=R8_8
Rpppp3(10,3)=R27_10,Rpppp3(10,2)=R8_10
Rpppp3(11,3)=R27_11,Rpppp3(11,2)=R8_11
Rpppp3(13,3)=R27_13,Rpppp3(13,2)=R8_13
Rpppp3(15,3)=R27_15,Rpppp3(15,2)=R8_15
Rpppp3(16,3)=R27_16,Rpppp3(16,2)=R8_16
Rpppp3(17,3)=R27_17,Rpppp3(17,2)=R8_7
Rpppp3(18,3)=R243_207,Rpppp3(18,2)=R32_3005
Rpppp3(19,3)=R27_19,Rpppp3(19,2)=R8_19
Rpppp3(20,3)=R27_20,Rpppp3(20,2)=R8_20
Rpppp3(21,3)=R27_21,Rpppp3(21,2)=R8_21
Rpppp3(23,3)=R27_23,Rpppp3(23,2)=R8_23
Rpppp3(24,3)=R27_24,Rpppp3(24,2)=R8_24
Rpppp3(25,3)=R27_25,Rpppp3(25,2)=R8_25
Rpppp3(26,3)=R27_26,Rpppp3(26,2)=R8_29
Rpppp3(27,3)=R27_27,Rpppp3(27,2)=R8_27
Rpppp3(28,3)=R27_28,Rpppp3(28,2)=R8_28
Rpppp3(29,3)=R27_29,Rpppp3(29,2)=R8_32
Rpppp3(30,3)=R27_30,Rpppp3(30,2)=R8_30
Rpppp3(31,3)=R27_31,Rpppp3(31,2)=R8_31
Rpppp3(32,3)=R27_29,Rpppp3(32,2)=R8_32
Rpppp3(33,3)=R27_33,Rpppp3(33,2)=R8_33
Rpppp3(34,3)=R27_34,Rpppp3(34,2)=R8_39
Rpppp3(35,3)=R27_35,Rpppp3(35,2)=R8_35
Rpppp3(36,3)=R27_36,Rpppp3(36,2)=R8_36
Rpppp3(37,3)=R27_37,Rpppp3(37,2)=R8_37
Rpppp3(38,3)=R27_38,Rpppp3(38,2)=R8_38
Rpppp3(39,3)=R27_39,Rpppp3(39,2)=R8_39
Rpppp3(41,3)=R27_41,Rpppp3(41,2)=R8_41
Rpppp3(42,3)=R27_42,Rpppp3(42,2)=R8_42
Rpppp3(43,3)=R27_43,Rpppp3(43,2)=R8_43
Rpppp3(44,3)=R27_44,Rpppp3(44,2)=R8_44
Rpppp3(45,3)=R27_45,Rpppp3(45,2)=R8_45
Rpppp3(46,3)=R27_46,Rpppp3(46,2)=R8_46
Rpppp3(47,3)=R27_47,Rpppp3(47,2)=R8_47
Rpppp3(48,3)=R27_48,Rpppp3(48,2)=R8_28
Rpppp3(49,3)=R27_49,Rpppp3(49,2)=R8_49
Rpppp3(50,3)=R27_50,Rpppp3(50,2)=R8_50
Rpppp3(51,3)=R27_51,Rpppp3(51,2)=R8_51
Rpppp3(52,3)=R27_52,Rpppp3(52,2)=R8_51
Rpppp3(56,3)=R27_56,Rpppp3(56,2)=R8_26
Rpppp3(57,3)=R27_57,Rpppp3(57,2)=R8_33
Rpppp3(58,3)=R27_58,Rpppp3(58,2)=R8_31
Rpppp3(59,3)=R27_59,Rpppp3(59,2)=R8_52

D:\MathTool\gaptool>Rpppp3 1 499
ret=0,环表示数据表中的记录条数=862
ret2=0,环表示数据表中的记录条数=902
Rpppp3(1,3)=R81_1,Rpppp3(1,2)=R16_1
Rpppp3(2,3)=R81_2,Rpppp3(2,2)=R16_2
Rpppp3(3,3)=R81_3,Rpppp3(3,2)=R16_3
Rpppp3(4,3)=R81_4,Rpppp3(4,2)=R16_4
Rpppp3(5,3)=R81_5,Rpppp3(5,2)=R16_5
Rpppp3(7,3)=R81_7,Rpppp3(7,2)=R16_7
Rpppp3(9,3)=R81_9,Rpppp3(9,2)=R16_9
Rpppp3(10,3)=R81_10,Rpppp3(10,2)=R16_10
Rpppp3(11,3)=R81_11,Rpppp3(11,2)=R16_11
Rpppp3(12,3)=R81_12,Rpppp3(12,2)=R16_12
Rpppp3(13,3)=R81_13,Rpppp3(13,2)=R16_17
Rpppp3(17,3)=R243_401,Rpppp3(17,2)=R32_1007
Rpppp3(18,3)=R81_18,Rpppp3(18,2)=R16_18
Rpppp3(19,3)=R81_19,Rpppp3(19,2)=R16_19
Rpppp3(20,3)=R81_20,Rpppp3(20,2)=R16_20
Rpppp3(21,3)=R81_21,Rpppp3(21,2)=R16_21
Rpppp3(23,3)=R81_23,Rpppp3(23,2)=R16_23
Rpppp3(24,3)=R81_24,Rpppp3(24,2)=R16_24
Rpppp3(25,3)=R81_25,Rpppp3(25,2)=R16_25
Rpppp3(26,3)=R81_26,Rpppp3(26,2)=R16_16
Rpppp3(32,3)=R81_32,Rpppp3(32,2)=R16_24
Rpppp3(34,3)=R81_34,Rpppp3(34,2)=R16_87
Rpppp3(35,3)=R81_35,Rpppp3(35,2)=R16_88
Rpppp3(36,3)=R81_36,Rpppp3(36,2)=R16_60
Rpppp3(37,3)=R81_37,Rpppp3(37,2)=R16_55
Rpppp3(38,3)=R81_38,Rpppp3(38,2)=R16_62
Rpppp3(39,3)=R81_39,Rpppp3(39,2)=R16_72
Rpppp3(40,3)=R81_40,Rpppp3(40,2)=R16_63

Rpppp3(42,3)=R81_42,Rpppp3(42,2)=R16_75
Rpppp3(43,3)=R81_43,Rpppp3(43,2)=R16_58
Rpppp3(44,3)=R81_44,Rpppp3(44,2)=R16_58

Rpppp3(45,3)=R81_45,Rpppp3(45,2)=R16_75
Rpppp3(46,3)=R81_46,Rpppp3(46,2)=R16_63
Rpppp3(47,3)=R81_47,Rpppp3(47,2)=R16_72
Rpppp3(48,3)=R81_48,Rpppp3(48,2)=R16_58
Rpppp3(49,3)=R81_49,Rpppp3(49,2)=R16_88
Rpppp3(50,3)=R81_50,Rpppp3(50,2)=R16_71
Rpppp3(51,3)=R81_51,Rpppp3(51,2)=R16_90
Rpppp3(52,3)=R81_52,Rpppp3(52,2)=R16_103
Rpppp3(53,3)=R81_53,Rpppp3(53,2)=R16_98
Rpppp3(54,3)=R81_54,Rpppp3(54,2)=R16_69
Rpppp3(55,3)=R81_55,Rpppp3(55,2)=R16_90
Rpppp3(56,3)=R81_56,Rpppp3(56,2)=R16_56
Rpppp3(57,3)=R81_57,Rpppp3(57,2)=R16_85
Rpppp3(58,3)=R81_58,Rpppp3(58,2)=R16_85
Rpppp3(59,3)=R81_59,Rpppp3(59,2)=R16_88
Rpppp3(60,3)=R81_60,Rpppp3(60,2)=R16_84
Rpppp3(61,3)=R81_61,Rpppp3(61,2)=R16_68
Rpppp3(62,3)=R81_62,Rpppp3(62,2)=R16_60
Rpppp3(63,3)=R81_63,Rpppp3(63,2)=R16_61
Rpppp3(64,3)=R81_64,Rpppp3(64,2)=R16_81

Rpppp3(65,3)=R81_65,Rpppp3(65,2)=R16_60
Rpppp3(66,3)=R81_66,Rpppp3(66,2)=R16_64

Rpppp3(67,3)=R81_67,Rpppp3(67,2)=R16_67
Rpppp3(68,3)=R81_68,Rpppp3(68,2)=R16_68
Rpppp3(69,3)=R729_0,Rpppp3(69,2)=R64_-1
Rpppp3(70,3)=R81_70,Rpppp3(70,2)=R16_53

Rpppp3(71,3)=R81_71,Rpppp3(71,2)=R16_84
Rpppp3(72,3)=R81_72,Rpppp3(72,2)=R16_83

Rpppp3(73,3)=R81_73,Rpppp3(73,2)=R16_73
Rpppp3(74,3)=R81_74,Rpppp3(74,2)=R16_65
Rpppp3(75,3)=R81_75,Rpppp3(75,2)=R16_75
Rpppp3(76,3)=R81_76,Rpppp3(76,2)=R16_76
Rpppp3(77,3)=R81_77,Rpppp3(77,2)=R16_55
Rpppp3(78,3)=R81_78,Rpppp3(78,2)=R16_78
Rpppp3(79,3)=R81_79,Rpppp3(79,2)=R16_79

Rpppp3(80,3)=R81_80,Rpppp3(80,2)=R16_57
Rpppp3(81,3)=R81_81,Rpppp3(81,2)=R16_58

Rpppp3(82,3)=R81_82,Rpppp3(82,2)=R16_82
Rpppp3(83,3)=R81_83,Rpppp3(83,2)=R16_83
Rpppp3(84,3)=R81_84,Rpppp3(84,2)=R16_84
Rpppp3(85,3)=R81_85,Rpppp3(85,2)=R16_85

Rpppp3(86,3)=R81_86,Rpppp3(86,2)=R16_86
Rpppp3(87,3)=R81_87,Rpppp3(87,2)=R16_57

Rpppp3(88,3)=R81_88,Rpppp3(88,2)=R16_87
Rpppp3(89,3)=R81_89,Rpppp3(89,2)=R16_89
Rpppp3(90,3)=R81_90,Rpppp3(90,2)=R16_94
Rpppp3(91,3)=R81_91,Rpppp3(91,2)=R16_91
Rpppp3(92,3)=R81_92,Rpppp3(92,2)=R16_88
Rpppp3(93,3)=R81_93,Rpppp3(93,2)=R16_93
Rpppp3(94,3)=R81_94,Rpppp3(94,2)=R16_94
Rpppp3(95,3)=R81_95,Rpppp3(95,2)=R16_95
Rpppp3(96,3)=R81_96,Rpppp3(96,2)=R16_96
Rpppp3(97,3)=R81_97,Rpppp3(97,2)=R16_97
Rpppp3(98,3)=R81_98,Rpppp3(98,2)=R16_103
Rpppp3(99,3)=R81_99,Rpppp3(99,2)=R16_99
Rpppp3(100,3)=R81_100,Rpppp3(100,2)=R16_70
Rpppp3(101,3)=R81_101,Rpppp3(101,2)=R16_101
Rpppp3(102,3)=R81_102,Rpppp3(102,2)=R16_102
Rpppp3(103,3)=R81_103,Rpppp3(103,2)=R16_70
Rpppp3(104,3)=R81_104,Rpppp3(104,2)=R16_92
Rpppp3(105,3)=R81_106,Rpppp3(105,2)=R16_106
Rpppp3(106,3)=R81_106,Rpppp3(106,2)=R16_106
Rpppp3(107,3)=R81_107,Rpppp3(107,2)=R16_107
Rpppp3(108,3)=R81_108,Rpppp3(108,2)=R16_108
Rpppp3(109,3)=R81_109,Rpppp3(109,2)=R16_109
Rpppp3(110,3)=R81_106,Rpppp3(110,2)=R16_106
Rpppp3(111,3)=R81_111,Rpppp3(111,2)=R16_111
Rpppp3(112,3)=R81_112,Rpppp3(112,2)=R16_112
Rpppp3(113,3)=R81_113,Rpppp3(113,2)=R16_113
Rpppp3(115,3)=R81_115,Rpppp3(115,2)=R16_64
Rpppp3(116,3)=R81_116,Rpppp3(116,2)=R16_59
Rpppp3(117,3)=R81_117,Rpppp3(117,2)=R16_73

Rpppp3(118,3)=R81_118,Rpppp3(118,2)=R16_94
Rpppp3(119,3)=R81_119,Rpppp3(119,2)=R16_85

Rpppp3(120,3)=R81_120,Rpppp3(120,2)=R16_81

Rpppp3(121,3)=R81_121,Rpppp3(121,2)=R16_71
Rpppp3(122,3)=R81_122,Rpppp3(122,2)=R16_100

Rpppp3(124,3)=R81_268,Rpppp3(124,2)=R16_268
Rpppp3(125,3)=R81_125,Rpppp3(125,2)=R16_67
Rpppp3(126,3)=R81_126,Rpppp3(126,2)=R16_60
Rpppp3(127,3)=R81_127,Rpppp3(127,2)=R16_74
Rpppp3(128,3)=R81_128,Rpppp3(128,2)=R16_78
Rpppp3(129,3)=R81_47,Rpppp3(129,2)=R16_72
Rpppp3(130,3)=R81_130,Rpppp3(130,2)=R16_64
Rpppp3(131,3)=R81_131,Rpppp3(131,2)=R16_80
Rpppp3(132,3)=R81_132,Rpppp3(132,2)=R16_62
Rpppp3(133,3)=R81_133,Rpppp3(133,2)=R16_63
Rpppp3(134,3)=R81_134,Rpppp3(134,2)=R16_58
Rpppp3(135,3)=R81_135,Rpppp3(135,2)=R16_54

Rpppp3(136,3)=R81_136,Rpppp3(136,2)=R16_76
Rpppp3(137,3)=R81_137,Rpppp3(137,2)=R16_64
Rpppp3(138,3)=R81_138,Rpppp3(138,2)=R16_54
Rpppp3(139,3)=R81_139,Rpppp3(139,2)=R16_63
Rpppp3(140,3)=R81_140,Rpppp3(140,2)=R16_94
Rpppp3(141,3)=R81_141,Rpppp3(141,2)=R16_80
Rpppp3(142,3)=R81_142,Rpppp3(142,2)=R16_65
Rpppp3(143,3)=R81_143,Rpppp3(143,2)=R16_80
Rpppp3(144,3)=R81_144,Rpppp3(144,2)=R16_76
Rpppp3(145,3)=R81_145,Rpppp3(145,2)=R16_71
Rpppp3(149,3)=R81_149,Rpppp3(149,2)=R16_170
Rpppp3(156,3)=R81_156,Rpppp3(156,2)=R16_234
Rpppp3(157,3)=R81_157,Rpppp3(157,2)=R16_154

Rpppp3(166,3)=R81_166,Rpppp3(166,2)=R16_254
Rpppp3(172,3)=R81_172,Rpppp3(172,2)=R16_155

Rpppp3(180,3)=R81_180,Rpppp3(180,2)=R16_180
Rpppp3(198,3)=R81_198,Rpppp3(198,2)=R16_198
Rpppp3(199,3)=R81_199,Rpppp3(199,2)=R16_199
Rpppp3(200,3)=R81_200,Rpppp3(200,2)=R16_200
Rpppp3(201,3)=R81_201,Rpppp3(201,2)=R16_201
Rpppp3(202,3)=R81_202,Rpppp3(202,2)=R16_202
Rpppp3(203,3)=R81_203,Rpppp3(203,2)=R16_203
Rpppp3(204,3)=R81_204,Rpppp3(204,2)=R16_204
Rpppp3(205,3)=R81_205,Rpppp3(205,2)=R16_205
Rpppp3(206,3)=R81_206,Rpppp3(206,2)=R16_206
Rpppp3(207,3)=R81_207,Rpppp3(207,2)=R16_177
Rpppp3(210,3)=R81_210,Rpppp3(210,2)=R2_1
Rpppp3(211,3)=R81_211,Rpppp3(211,2)=R4_6
Rpppp3(212,3)=R81_212,Rpppp3(212,2)=R16_212
Rpppp3(214,3)=R81_214,Rpppp3(214,2)=R16_214
Rpppp3(216,3)=R81_243,Rpppp3(216,2)=R16_243
Rpppp3(217,3)=R81_217,Rpppp3(217,2)=R8_35
Rpppp3(218,3)=R81_218,Rpppp3(218,2)=R4_6
Rpppp3(219,3)=R81_219,Rpppp3(219,2)=R16_219
Rpppp3(220,3)=R81_220,Rpppp3(220,2)=R16_220
Rpppp3(221,3)=R81_221,Rpppp3(221,2)=R16_251
Rpppp3(222,3)=R81_222,Rpppp3(222,2)=R16_222
Rpppp3(223,3)=R81_223,Rpppp3(223,2)=R16_223
Rpppp3(225,3)=R81_225,Rpppp3(225,2)=R16_215
Rpppp3(226,3)=R81_226,Rpppp3(226,2)=R16_209
Rpppp3(227,3)=R81_227,Rpppp3(227,2)=R16_227
Rpppp3(229,3)=R81_229,Rpppp3(229,2)=R16_255
Rpppp3(230,3)=R81_230,Rpppp3(230,2)=R4_9
Rpppp3(231,3)=R81_231,Rpppp3(231,2)=R16_231

Rpppp3(233,3)=R81_233,Rpppp3(233,2)=R16_233
Rpppp3(235,3)=R81_235,Rpppp3(235,2)=R16_256

Rpppp3(238,3)=R81_238,Rpppp3(238,2)=R16_238
Rpppp3(240,3)=R81_240,Rpppp3(240,2)=R16_240
Rpppp3(242,3)=R81_242,Rpppp3(242,2)=R16_242
Rpppp3(243,3)=R81_243,Rpppp3(243,2)=R16_243
Rpppp3(244,3)=R81_244,Rpppp3(244,2)=R16_226
Rpppp3(245,3)=R81_245,Rpppp3(245,2)=R16_245
Rpppp3(247,3)=R81_247,Rpppp3(247,2)=R4_6
Rpppp3(250,3)=R81_250,Rpppp3(250,2)=R16_250
Rpppp3(251,3)=R81_251,Rpppp3(251,2)=R16_251
Rpppp3(255,3)=R81_255,Rpppp3(255,2)=R16_237
Rpppp3(256,3)=R81_256,Rpppp3(256,2)=R16_192
Rpppp3(257,3)=R81_257,Rpppp3(257,2)=R16_257
Rpppp3(258,3)=R81_258,Rpppp3(258,2)=R16_258
Rpppp3(259,3)=R81_259,Rpppp3(259,2)=R16_259
Rpppp3(260,3)=R81_260,Rpppp3(260,2)=R16_260
Rpppp3(261,3)=R81_439,Rpppp3(261,2)=R16_261
Rpppp3(262,3)=R81_436,Rpppp3(262,2)=R16_262
Rpppp3(263,3)=R81_263,Rpppp3(263,2)=R16_263
Rpppp3(264,3)=R81_264,Rpppp3(264,2)=R16_264
Rpppp3(265,3)=R81_265,Rpppp3(265,2)=R16_265

Rpppp3(266,3)=R81_266,Rpppp3(266,2)=R16_266
Rpppp3(267,3)=R81_267,Rpppp3(267,2)=R32_0

Rpppp3(268,3)=R81_268,Rpppp3(268,2)=R16_268
Rpppp3(269,3)=R81_269,Rpppp3(269,2)=R16_269
Rpppp3(300,3)=R81_300,Rpppp3(300,2)=R16_300
Rpppp3(301,3)=R81_301,Rpppp3(301,2)=R16_301
Rpppp3(302,3)=R81_302,Rpppp3(302,2)=R16_366
Rpppp3(303,3)=R81_303,Rpppp3(303,2)=R16_303
Rpppp3(304,3)=R81_304,Rpppp3(304,2)=R16_317
Rpppp3(305,3)=R81_305,Rpppp3(305,2)=R16_305
Rpppp3(306,3)=R81_306,Rpppp3(306,2)=R16_306
Rpppp3(307,3)=R81_307,Rpppp3(307,2)=R16_385
Rpppp3(308,3)=R81_308,Rpppp3(308,2)=R16_308
Rpppp3(309,3)=R81_309,Rpppp3(309,2)=R16_309
Rpppp3(310,3)=R81_310,Rpppp3(310,2)=R16_310
Rpppp3(312,3)=R81_312,Rpppp3(312,2)=R16_312
Rpppp3(313,3)=R81_313,Rpppp3(313,2)=R16_381
Rpppp3(314,3)=R81_314,Rpppp3(314,2)=R16_314

Rpppp3(315,3)=R81_315,Rpppp3(315,2)=R16_388
Rpppp3(316,3)=R81_316,Rpppp3(316,2)=R16_275
Rpppp3(317,3)=R81_317,Rpppp3(317,2)=R16_274
Rpppp3(318,3)=R81_318,Rpppp3(318,2)=R16_318
Rpppp3(319,3)=R81_319,Rpppp3(319,2)=R16_361

Rpppp3(320,3)=R81_320,Rpppp3(320,2)=R16_338
Rpppp3(321,3)=R81_321,Rpppp3(321,2)=R16_385

Rpppp3(322,3)=R81_322,Rpppp3(322,2)=R16_296
Rpppp3(323,3)=R81_323,Rpppp3(323,2)=R16_334

Rpppp3(324,3)=R81_324,Rpppp3(324,2)=R16_324
Rpppp3(325,3)=R81_325,Rpppp3(325,2)=R16_333
Rpppp3(326,3)=R81_326,Rpppp3(326,2)=R16_326
Rpppp3(327,3)=R81_327,Rpppp3(327,2)=R16_327
Rpppp3(328,3)=R81_328,Rpppp3(328,2)=R16_328
Rpppp3(329,3)=R81_329,Rpppp3(329,2)=R16_329
Rpppp3(330,3)=R81_330,Rpppp3(330,2)=R16_330
Rpppp3(331,3)=R81_331,Rpppp3(331,2)=R16_348

Rpppp3(332,3)=R81_332,Rpppp3(332,2)=R16_382
Rpppp3(333,3)=R81_333,Rpppp3(333,2)=R16_315

Rpppp3(334,3)=R81_334,Rpppp3(334,2)=R16_319
Rpppp3(335,3)=R81_335,Rpppp3(335,2)=R16_335
Rpppp3(336,3)=R81_336,Rpppp3(336,2)=R16_336
Rpppp3(337,3)=R81_337,Rpppp3(337,2)=R16_337
Rpppp3(338,3)=R81_338,Rpppp3(338,2)=R16_338
Rpppp3(339,3)=R81_339,Rpppp3(339,2)=R16_325
Rpppp3(340,3)=R81_340,Rpppp3(340,2)=R16_320
Rpppp3(341,3)=R81_341,Rpppp3(341,2)=R16_341
Rpppp3(342,3)=R81_342,Rpppp3(342,2)=R16_342
Rpppp3(343,3)=R81_343,Rpppp3(343,2)=R16_285
Rpppp3(344,3)=R81_344,Rpppp3(344,2)=R16_344

Rpppp3(345,3)=R81_345,Rpppp3(345,2)=R16_345
Rpppp3(346,3)=R81_346,Rpppp3(346,2)=R16_357
Rpppp3(348,3)=R81_348,Rpppp3(348,2)=R16_343

Rpppp3(349,3)=R81_349,Rpppp3(349,2)=R16_349
Rpppp3(350,3)=R81_350,Rpppp3(350,2)=R16_350
Rpppp3(351,3)=R81_351,Rpppp3(351,2)=R16_351
Rpppp3(352,3)=R81_352,Rpppp3(352,2)=R16_352
Rpppp3(353,3)=R81_353,Rpppp3(353,2)=R16_369
Rpppp3(354,3)=R81_354,Rpppp3(354,2)=R16_354
Rpppp3(355,3)=R81_355,Rpppp3(355,2)=R16_355
Rpppp3(356,3)=R81_356,Rpppp3(356,2)=R16_284
Rpppp3(357,3)=R81_357,Rpppp3(357,2)=R16_370
Rpppp3(358,3)=R81_358,Rpppp3(358,2)=R16_312
Rpppp3(359,3)=R81_359,Rpppp3(359,2)=R16_359
Rpppp3(360,3)=R81_360,Rpppp3(360,2)=R16_360
Rpppp3(361,3)=R81_361,Rpppp3(361,2)=R16_361
Rpppp3(362,3)=R81_362,Rpppp3(362,2)=R16_343
Rpppp3(363,3)=R81_363,Rpppp3(363,2)=R16_292
Rpppp3(364,3)=R81_364,Rpppp3(364,2)=R16_348
Rpppp3(365,3)=R81_365,Rpppp3(365,2)=R16_365
Rpppp3(367,3)=R81_367,Rpppp3(367,2)=R16_347
Rpppp3(368,3)=R81_368,Rpppp3(368,2)=R16_368
Rpppp3(369,3)=R81_369,Rpppp3(369,2)=R16_302
Rpppp3(370,3)=R81_370,Rpppp3(370,2)=R16_370
Rpppp3(371,3)=R81_371,Rpppp3(371,2)=R16_340
Rpppp3(372,3)=R81_372,Rpppp3(372,2)=R16_375
Rpppp3(373,3)=R81_373,Rpppp3(373,2)=R16_311
Rpppp3(374,3)=R81_374,Rpppp3(374,2)=R16_374
Rpppp3(375,3)=R81_375,Rpppp3(375,2)=R16_375
Rpppp3(376,3)=R81_376,Rpppp3(376,2)=R16_376
Rpppp3(377,3)=R81_377,Rpppp3(377,2)=R16_314
Rpppp3(378,3)=R81_378,Rpppp3(378,2)=R16_378
Rpppp3(379,3)=R81_379,Rpppp3(379,2)=R8_31
Rpppp3(380,3)=R81_380,Rpppp3(380,2)=R16_380
Rpppp3(381,3)=R81_381,Rpppp3(381,2)=R16_381
Rpppp3(383,3)=R81_383,Rpppp3(383,2)=R16_383
Rpppp3(384,3)=R81_384,Rpppp3(384,2)=R16_341
Rpppp3(385,3)=R81_385,Rpppp3(385,2)=R16_385
Rpppp3(386,3)=R81_386,Rpppp3(386,2)=R16_288
Rpppp3(387,3)=R81_387,Rpppp3(387,2)=R16_304
Rpppp3(388,3)=R81_388,Rpppp3(388,2)=R16_388
Rpppp3(389,3)=R81_389,Rpppp3(389,2)=R16_287

Rpppp3(390,3)=R81_390,Rpppp3(390,2)=R16_390
Rpppp3(391,3)=R81_391,Rpppp3(391,2)=R16_276
Rpppp3(392,3)=R81_392,Rpppp3(392,2)=R16_282

Rpppp3(393,3)=R81_393,Rpppp3(393,2)=R16_293
Rpppp3(394,3)=R81_394,Rpppp3(394,2)=R16_390
Rpppp3(395,3)=R81_395,Rpppp3(395,2)=R16_295
Rpppp3(396,3)=R81_396,Rpppp3(396,2)=R16_342
Rpppp3(397,3)=R81_397,Rpppp3(397,2)=R16_297
Rpppp3(398,3)=R81_398,Rpppp3(398,2)=R16_298
Rpppp3(399,3)=R81_399,Rpppp3(399,2)=R16_325
Rpppp3(400,3)=R81_400,Rpppp3(400,2)=R16_357
Rpppp3(401,3)=R81_401,Rpppp3(401,2)=R16_352
Rpppp3(402,3)=R81_402,Rpppp3(402,2)=R16_332
Rpppp3(403,3)=R81_403,Rpppp3(403,2)=R16_339
Rpppp3(404,3)=R81_404,Rpppp3(404,2)=R16_353
Rpppp3(405,3)=R81_405,Rpppp3(405,2)=R16_374
Rpppp3(406,3)=R81_406,Rpppp3(406,2)=R16_363
Rpppp3(407,3)=R81_407,Rpppp3(407,2)=R16_283
Rpppp3(408,3)=R81_408,Rpppp3(408,2)=R16_294
Rpppp3(409,3)=R81_409,Rpppp3(409,2)=R16_278
Rpppp3(410,3)=R81_410,Rpppp3(410,2)=R16_281
Rpppp3(411,3)=R81_411,Rpppp3(411,2)=R16_279
Rpppp3(412,3)=R81_412,Rpppp3(412,2)=R16_323

Rpppp3(413,3)=R81_413,Rpppp3(413,2)=R16_277
Rpppp3(414,3)=R81_414,Rpppp3(414,2)=R16_286
Rpppp3(415,3)=R81_415,Rpppp3(415,2)=R16_291
Rpppp3(416,3)=R81_416,Rpppp3(416,2)=R16_288

Rpppp3(417,3)=R81_417,Rpppp3(417,2)=R16_273
Rpppp3(418,3)=R81_418,Rpppp3(418,2)=R16_289
Rpppp3(419,3)=R81_419,Rpppp3(419,2)=R16_39
Rpppp3(420,3)=R81_420,Rpppp3(420,2)=R16_377
Rpppp3(421,3)=R81_421,Rpppp3(421,2)=R16_299

Rpppp3(422,3)=R81_422,Rpppp3(422,2)=R16_296
Rpppp3(423,3)=R81_423,Rpppp3(423,2)=R16_290
Rpppp3(424,3)=R81_424,Rpppp3(424,2)=R16_280
Rpppp3(425,3)=R81_425,Rpppp3(425,2)=R16_367

Rpppp3(436,3)=R81_436,Rpppp3(436,2)=R16_262
Rpppp3(439,3)=R81_439,Rpppp3(439,2)=R16_261
Rpppp3(455,3)=R81_455,Rpppp3(455,2)=R16_174
Rpppp3(456,3)=R81_456,Rpppp3(456,2)=R16_193
Rpppp3(457,3)=R81_457,Rpppp3(457,2)=R16_178

Rpppp3(462,3)=R81_462,Rpppp3(462,2)=R8_10
Rpppp3(492,3)=R81_492,Rpppp3(492,2)=R16_191
Rpppp3(502,3)=R81_502,Rpppp3(502,2)=R16_38
Rpppp3(503,3)=R81_503,Rpppp3(503,2)=R16_299
Rpppp3(507,3)=R81_507,Rpppp3(507,2)=R16_26