Q(rt17) Disc=17 -------------------- n=4 Gram Matrix A= [ 2,-1,0,1/2*(rt17+3)] [-1,2,0,1/2*(-rt17-3)] [0,0,2,1] [1/2*(rt17+3),1/2*(-rt17-3),1,rt17+5] h=1 Automorphism group size: [144] Trivial case. -------------------- n=8 Gram Matrix A oplus A h=40 Automorphism group sizes: [ 696729600, 5160960, 221184, 80640, 2304, 43008, 2880, 384, 96, 864, 864, 40320, 1152, 768, 96, 336, 24, 96, 128, 216, 64, 64, 256, 512, 1024, 41472, 36864, 1024, 48, 1440, 64, 1152, 48, 128, 64, 672, 576, 384, 21504, 2580480] Neighbour Matrices: N(P)=2 [0 135 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [1 0 70 64 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [0 3 0 0 96 36 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [0 1 0 8 70 0 56 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [0 0 1 2 8 0 8 36 48 16 16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [0 0 7 0 0 0 0 112 0 0 0 16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [0 0 0 2 10 0 8 0 90 0 0 0 10 15 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [0 0 0 0 6 1 0 8 24 0 0 0 0 0 24 16 32 24 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [0 0 0 0 2 0 3 6 23 2 2 0 1 2 6 0 36 6 9 4 12 12 6 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [0 0 0 0 6 0 0 0 18 3 0 0 0 18 54 0 0 9 0 0 0 27 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [0 0 0 0 6 0 0 0 18 0 18 0 3 0 9 0 0 54 0 0 27 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [0 0 0 0 0 15 0 0 0 0 0 0 0 0 0 120 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [0 0 0 0 0 0 4 0 12 0 4 0 24 0 0 0 0 0 36 0 36 0 0 9 9 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [0 0 0 0 0 0 4 0 16 16 0 0 0 5 0 0 0 0 6 32 0 24 12 12 0 0 2 6 0 0 0 0 0 0 0 0 0 0 0 0] [0 0 0 0 0 0 0 6 6 6 1 0 0 0 6 0 28 0 0 12 3 12 12 3 0 0 0 0 24 4 12 0 0 0 0 0 0 0 0 0] [0 0 0 0 0 0 0 14 0 0 0 1 0 0 0 8 56 0 0 0 0 0 0 0 0 0 0 0 42 7 0 7 0 0 0 0 0 0 0 0] [0 0 0 0 0 0 0 2 9 0 0 0 0 0 7 4 35 6 3 3 6 6 3 0 0 0 0 0 12 0 12 0 12 6 9 0 0 0 0 0] [0 0 0 0 0 0 0 6 6 1 6 0 0 0 0 0 24 27 6 0 12 3 0 0 0 0 0 0 24 0 0 4 12 0 0 4 0 0 0 0] [0 0 0 0 0 0 0 0 12 0 0 0 4 1 0 0 16 8 26 0 16 4 0 0 2 0 0 2 0 0 0 0 16 8 16 4 0 0 0 0] [0 0 0 0 0 0 0 0 9 0 0 0 0 9 27 0 27 0 0 9 0 27 0 0 0 0 0 0 0 0 0 0 0 0 27 0 0 0 0 0] [0 0 0 0 0 0 0 0 8 0 2 0 2 0 2 0 16 8 8 0 34 0 1 2 4 0 0 0 8 0 16 0 4 8 8 0 4 0 0 0] [0 0 0 0 0 0 0 0 8 2 0 0 0 2 8 0 16 2 2 8 0 37 0 1 0 0 0 1 8 0 4 0 16 0 16 0 0 4 0 0] [0 0 0 0 0 0 0 0 16 0 0 0 0 4 32 0 32 0 0 0 4 0 5 0 0 0 0 2 0 0 16 0 0 16 8 0 0 0 0 0] [0 0 0 0 0 0 0 0 16 0 0 0 4 8 16 0 0 0 0 0 16 8 0 10 1 0 0 8 0 0 16 0 0 0 32 0 0 0 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 8 0 0 0 0 0 16 0 64 0 0 2 19 2 0 0 0 0 0 0 0 8 0 0 16 0 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 36 0 0 0 0 0 0 0 0 0 0 0 81 18 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 96 0 0 0 0 0 0 0 0 0 0 0 0 3 36 0 0 0 0 0 0 0 0 0 0 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 8 0 0 0 0 16 0 0 16 8 16 0 0 1 22 0 0 0 0 0 0 32 0 0 16 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 12 6 24 12 0 0 6 6 0 0 0 0 0 0 18 0 15 0 18 6 12 0 0 0 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 60 30 0 0 0 0 0 0 0 0 0 0 0 0 0 0 45 0 0 0 0 0 0 0 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 0 32 0 0 0 16 4 4 2 0 0 0 0 20 2 26 0 0 8 8 0 4 1 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 24 0 48 0 0 0 0 0 0 0 0 0 0 0 0 0 12 48 0 0 0 0 0 3 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 24 6 6 0 3 12 0 0 0 0 0 0 18 0 0 2 35 6 12 4 1 6 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 32 0 8 0 16 0 8 0 1 0 0 0 16 0 16 0 16 18 0 0 4 0 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 24 0 8 8 8 16 2 4 0 0 0 2 16 0 8 0 16 0 19 0 0 4 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 28 21 0 0 0 0 0 0 0 0 0 0 0 0 0 56 0 0 28 0 0 2 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 36 0 0 0 9 0 0 0 0 0 36 0 12 18 0 0 24 0 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 24 0 0 0 0 0 6 0 0 6 0 48 0 24 0 0 27 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 56 0 0 0 64 0 0 14 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 120 15] CharPoly = (x-135)(x-34)(x-22)(x-18)(x-14)^2(x-10)(x-1)(x+12)(x+17)(x^2-125x+3898)(x^2-81x+846)(x^2-61x+890)(x^2-31x-74)(x^2-11x-374)(x^2-11x-176)(x^2+15x-1800)(x^2+20x+72,)(x^2+22x-176)(x^2+27x-180)(x^3-105x^2+3060x-21708)(x^3-3x^2-34x+18)(x^4-37x^3+298x^2-72x-864) N(P)=9 [1120 7560 0 69120 302400 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 67200 151200 0 0 0 0 0 0 0 0 0 0 0 0 0] [56 1632 6160 12160 53760 0 46592 80640 107520 35840 35840 0 17920 107520 0 0 0 0 0 0 0 0 0 0 40320 8960 3360 40320 0 0 0 0 0 0 0 0 0 0 0 0] [0 264 1888 1536 26400 3744 11520 32256 96768 26112 10240 0 6144 13824 41472 18432 55296 41472 0 24576 41472 41472 13824 31104 19008 2240 96 19008 0 0 0 0 0 0 0 0 9216 9216 0 0] [8 190 560 3528 20580 630 23464 15120 119280 16800 16800 0 20720 27720 30240 0 40320 30240 55440 33600 40320 40320 20160 5040 5040 560 1680 5040 0 0 0 0 0 5040 20160 0 0 0 0 0] [1 24 275 588 9016 288 5448 16488 70704 10288 9344 144 7584 10056 38592 3456 88128 32688 25200 17280 48672 48672 12384 11448 4608 264 384 4608 26496 1728 20160 1728 22464 10512 30528 1728 3168 3456 0 0] [0 0 728 336 5376 2016 2688 34720 48384 5376 5376 1792 1344 10752 50176 15360 100352 24192 5376 10752 40320 40320 13440 8736 8736 896 0 8736 43008 3584 32256 3584 10752 5376 32256 0 10752 10752 0 0] [0 26 150 838 6810 180 8676 13140 75600 8280 7520 0 10180 13560 30240 2880 100800 27000 40860 20640 46080 46080 13680 8370 3690 160 390 3690 20160 0 15840 0 24480 12240 30240 3960 720 1440 0 0] [0 6 56 72 2748 310 1752 12576 38736 5304 4368 128 2856 5064 34736 9984 109408 28056 19488 13536 42768 42768 13200 6948 2856 92 24 2856 49344 2208 39648 1920 41376 16800 36096 1440 4176 4800 96 0] [0 2 42 142 2946 108 2520 9684 45156 5032 4144 48 4256 5642 30888 6048 111072 27528 25950 14912 43680 43680 12360 6642 2874 64 142 2874 43392 1440 33744 1344 42912 18528 37776 3420 3120 4464 24 0] [0 6 102 180 3858 108 2484 11934 45288 7544 4848 0 2994 8028 39960 6264 100656 28152 16200 16848 46656 46656 12528 9720 3780 146 204 3780 46944 2232 37476 1908 31248 14040 37152 1584 4356 2700 36 0] [0 6 40 180 3504 108 2256 9828 37296 4848 12736 0 5052 6984 24912 5904 87552 46224 23328 15840 50544 50544 7128 6156 4752 380 330 4752 40608 1296 30456 2664 44064 9072 38880 5184 4968 10008 216 0] [0 0 0 0 2520 1680 0 13440 20160 0 0 2080 0 0 33600 31200 120960 30240 0 26880 30240 30240 10080 0 5040 560 1680 5040 60480 7840 60480 3360 20160 15120 40320 0 11760 13440 0 0] [0 4 32 296 3792 36 4072 8568 51072 3992 6736 0 10896 6288 18864 3456 88416 35352 43128 13152 47376 47376 7056 9648 5904 640 216 5904 32256 288 17280 1872 52128 10440 44352 9216 1584 6624 288 0] [0 16 48 264 3352 192 3616 10128 45136 7136 6208 0 4192 11364 31488 8064 99744 29088 23148 21280 47472 47472 12720 8472 4296 216 448 4296 39168 1536 33024 1344 33600 12768 37344 2088 4224 3456 192 0] [0 0 18 36 1608 112 1008 8684 30888 4440 2768 80 1572 3936 37008 8976 116512 24120 14880 14688 41040 41040 13368 6156 2232 44 66 2232 57312 2800 48504 1544 41088 20016 39264 1440 4584 4536 0 0] [0 0 28 0 504 120 336 8736 21168 2436 2296 260 1008 3528 31416 13720 121968 24444 13944 12432 38304 38304 10416 4116 2100 56 84 2100 64008 3500 50316 3052 49056 21168 40320 1680 5376 6216 84 0] [0 0 6 12 918 56 840 6838 27768 2796 2432 72 1842 3117 29128 8712 119244 25164 19989 12660 40032 40032 11448 4518 1980 14 60 1980 57288 2096 44676 1884 53760 22728 40992 3222 4284 5964 48 0] [0 0 18 36 1362 54 900 7014 27528 3128 5136 72 2946 3636 24120 6984 100656 37816 22944 11568 44016 44016 7968 5382 3336 128 96 3336 55200 1320 34812 3564 60624 18072 41856 5568 4708 8436 240 4] [0 0 0 88 1400 16 1816 6496 34600 2400 3456 0 4792 3858 19840 5312 106608 30592 34794 11504 42952 42952 8848 5072 3352 132 76 3352 45312 512 28480 2176 65120 19984 43584 8092 3104 7680 248 0] [0 0 24 90 1620 54 1548 7614 33552 4212 3960 144 2466 5985 33048 7992 113940 26028 19413 17380 42336 42336 11664 5454 2646 72 210 2646 51336 2448 41364 1692 42336 19224 41256 2430 4212 5868 0 0] [0 0 12 32 1352 60 1024 7128 29120 3456 3744 48 2632 3956 27360 7296 106752 29344 21476 12544 47136 40944 9952 5816 3424 96 92 2740 53728 1664 40096 2368 55104 19464 42112 3960 4992 7456 120 0] [0 0 12 32 1352 60 1024 7128 29120 3456 3744 48 2632 3956 27360 7296 106752 29344 21476 12544 40944 47136 9952 5816 2740 96 92 3424 53728 1664 40096 2368 55104 19464 42112 3960 4992 7456 120 0] [0 0 16 64 1376 80 1216 8800 32960 3712 2112 64 1568 4240 35648 7936 122112 21248 17696 13824 39808 39808 15280 5280 1856 32 8 1856 54912 2304 48320 896 42368 22112 39360 1792 4352 3552 32 0] [0 0 72 32 2544 104 1488 9264 35424 5760 3648 0 4288 5648 32832 6272 96384 28704 20288 12928 46528 46528 10560 10172 4112 164 48 4112 51392 1600 36224 3040 47424 17160 41600 2304 4304 5504 144 0] [0 8 88 64 2048 208 1312 7616 30656 4480 5632 128 5248 5728 23808 6400 84480 35584 26816 12544 54784 43840 7424 8224 7304 384 224 5216 46080 1280 29696 4096 56576 15232 43264 4672 6272 10752 416 16] [4 72 420 288 4752 864 2304 9936 27648 7008 18240 576 23040 11664 19008 6912 24192 55296 42768 13824 62208 62208 5184 13284 15552 2796 864 15552 25920 576 0 8928 43200 5832 41472 3456 144 20736 1728 144] [8 24 16 768 6144 0 4992 2304 54528 8704 14080 1536 6912 21504 25344 9216 92160 36864 21888 35840 52992 52992 1152 3456 8064 768 3816 8064 21504 3072 18432 6144 4608 4608 46080 4608 9216 6144 0 48] [0 8 88 64 2048 208 1312 7616 30656 4480 5632 128 5248 5728 23808 6400 84480 35584 26816 12544 43840 54784 7424 8224 5216 384 224 7304 46080 1280 29696 4096 56576 15232 43264 4672 6272 10752 416 16] [0 0 0 0 552 48 336 6168 21696 2608 2256 72 1344 2448 28656 9144 114576 27600 16992 11408 40296 40296 10296 4818 2160 30 28 2160 63084 2188 46896 2608 58104 22236 42480 3216 4940 6776 84 0] [0 0 0 0 1080 120 0 8280 21600 3720 2160 280 360 2880 42000 15000 125760 19800 5760 16320 37440 37440 12960 4500 1800 20 120 1800 65640 5560 64260 1320 30960 20520 37440 0 6120 5580 0 0] [0 0 0 0 560 48 352 6608 22496 2776 2256 96 960 2752 32336 9584 119136 23208 14240 12256 40096 40096 12080 4528 1856 0 32 1856 62528 2856 53528 1728 49952 23536 40480 1984 5760 6008 32 0] [0 0 0 0 864 96 0 5760 16128 2544 3552 96 1872 2016 18528 10464 90432 42768 19584 9024 42624 42624 4032 6840 4608 248 192 4608 62592 1056 31104 7760 77568 17424 46080 7584 6768 10368 780 12] [0 0 0 0 468 12 408 5172 21456 1736 2448 24 2172 2100 20544 7008 107520 30312 24420 9408 41328 41328 7944 4446 2652 50 6 2652 58104 1032 37464 3232 74288 21876 45600 6888 4568 9624 308 2] [0 0 0 8 584 16 544 5600 24704 2080 1344 48 1160 2128 26688 8064 121216 24096 19984 11392 38928 38928 11056 4290 1904 18 16 1904 59296 1824 47072 1936 58336 26260 41920 4080 5320 5792 64 0] [0 0 0 16 848 48 672 6016 25184 2752 2880 64 2464 3112 26176 7680 109312 27904 21792 12224 42112 42112 9840 5200 2704 64 80 2704 56640 1664 40480 2560 60800 20960 44528 4256 4416 8208 128 0] [0 0 0 0 504 0 924 2520 23940 1232 4032 0 5376 1827 10080 3360 90216 38976 42483 7560 41580 41580 4704 3024 3066 56 84 3066 45024 0 20832 4424 96432 21420 44688 17290 3192 14112 966 30] [0 0 24 0 792 144 144 6264 18720 2904 3312 168 792 3168 27504 9216 102816 28248 13968 11232 44928 44928 9792 4842 3528 2 144 3528 59280 2448 51840 3384 54816 23940 39744 2736 10648 8448 204 4] [0 0 16 0 576 96 192 4800 17856 1200 4448 128 2208 1728 18144 7104 95424 33744 23040 10432 44736 44736 5328 4128 4032 192 64 4032 54208 1488 36048 3456 76992 17376 49248 8064 5632 17304 384 16] [0 0 0 0 0 0 0 5376 5376 896 5376 0 5376 5376 0 5376 43008 53760 41664 0 40320 40320 2688 6048 8736 896 0 8736 37632 0 10752 14560 137984 10752 43008 30912 7616 21504 4376 176] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 107520 0 0 0 0 0 0 40320 8960 3360 40320 0 0 0 26880 107520 0 0 115200 17920 107520 21120 1960] CharPoly = (x-598600)(x-8584)(x-8452)(x-7560)^2(x-5120)(x-720)^2(x-504)(x-288)(x+288)(x+3960)(x^2-132572x+4393490464)(x^2-27880x-5379200)(x^2-14508x+52218016)(x^2-4232x-89216)(x^2-4232x+3546064)(x^2-3044x-89216)(x^2-2664x+1447632)(x^2-208x-226176)(x^2+3720x+1849600)(x^3-32200x^2+345260800x-1232812800000)(x^3+32x^2-279840x-36191232)(x^4-6072x^3+11726208x^2-7484631552x+702841245696) -------------------- n=12 Gram Matrix A oplus A oplus A Mass = 774317689803.61