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Label Polynomial Discriminant Galois group Class group Regulator
7.7.13841287201.1 $x^{7} - 21 x^{5} - 21 x^{4} + 91 x^{3} + 112 x^{2} - 84 x - 97$ $7^{12}$ $C_7$ (as 7T1) trivial $550.88577714$
7.3.3543369523456.3 $x^{7} - 21 x^{5} - 28 x^{4} - 7 x^{3} - 112 x^{2} + 259 x + 244$ $2^{8}\cdot 7^{12}$ $\GL(3,2)$ (as 7T5) $[7]$ $12405.1123243$
7.3.3543369523456.4 $x^{7} - 21 x^{5} - 70 x^{4} + 238 x^{3} + 1092 x^{2} - 2240 x + 736$ $2^{8}\cdot 7^{12}$ $\GL(3,2)$ (as 7T5) $[14]$ $6202.55616215$
7.3.645779095649856.3 $x^{7} - 21 x^{5} - 70 x^{4} - 105 x^{3} - 84 x^{2} - 35 x + 40818$ $2^{6}\cdot 3^{6}\cdot 7^{12}$ $A_7$ (as 7T6) $[7]$ $58386.9611144$
7.3.1148051725599744.1 $x^{7} - 42 x^{5} - 28 x^{4} + 609 x^{3} + 756 x^{2} - 3024 x + 864$ $2^{10}\cdot 3^{4}\cdot 7^{12}$ $A_7$ (as 7T6) $[7]$ $105789.61343$
7.3.13841287201000000.2 $x^{7} - 2744 x^{2} + 27440$ $2^{6}\cdot 5^{6}\cdot 7^{12}$ $A_7$ (as 7T6) $[7]$ $63284.5358524$
7.3.52308106747638336.4 $x^{7} - 84 x^{5} - 420 x^{4} + 5376 x^{3} - 3780 x^{2} - 16156 x + 27900$ $2^{6}\cdot 3^{10}\cdot 7^{12}$ $\GL(3,2)$ (as 7T5) $[7]$ $539181.587994$
7.3.52308106747638336.6 $x^{7} - 84 x^{5} - 364 x^{4} - 1680 x^{3} + 6720 x^{2} + 77728 x + 391638$ $2^{6}\cdot 3^{10}\cdot 7^{12}$ $\GL(3,2)$ (as 7T5) $[7]$ $539181.587994$
7.1.247979172729544704.1 $x^{7} - 882 x^{4} + 882 x^{3} - 15876$ $-\,2^{13}\cdot 3^{7}\cdot 7^{12}$ $S_7$ (as 7T7) $[7]$ $1346046.93683$
7.1.1313840933532421875.2 $x^{7} - 35 x^{5} - 70 x^{4} + 280 x^{3} + 1232 x^{2} + 1680 x - 117325$ $-\,3^{5}\cdot 5^{8}\cdot 7^{12}$ $S_7$ (as 7T7) $[7]$ $620527.310781$
7.7.874...849.1 $x^{7} - 903 x^{5} - 11739 x^{4} - 4515 x^{3} + 484008 x^{2} + 1555568 x - 609267$ $7^{12}\cdot 43^{6}$ $C_7$ (as 7T1) $[7]$ $80239711.6814$
7.7.874...849.2 $x^{7} - 903 x^{5} - 3311 x^{4} + 256753 x^{3} + 1655500 x^{2} - 20129676 x - 154845881$ $7^{12}\cdot 43^{6}$ $C_7$ (as 7T1) $[7]$ $3504328.2978067407$
7.7.874...849.3 $x^{7} - 903 x^{5} - 1204 x^{4} + 218827 x^{3} + 753704 x^{2} - 16141125 x - 86614900$ $7^{12}\cdot 43^{6}$ $C_7$ (as 7T1) $[7]$ $2429511482.583454$
7.7.874...849.4 $x^{7} - 903 x^{5} - 15953 x^{4} - 97223 x^{3} - 177590 x^{2} + 46956 x + 94471$ $7^{12}\cdot 43^{6}$ $C_7$ (as 7T1) $[7]$ $8351632.841147239$
7.7.874...849.5 $x^{7} - 903 x^{5} - 3311 x^{4} + 206185 x^{3} + 1491154 x^{2} - 1773492 x + 461089$ $7^{12}\cdot 43^{6}$ $C_7$ (as 7T1) $[7]$ $4703614.757954623$
7.7.874...849.6 $x^{7} - 903 x^{5} - 7525 x^{4} + 105049 x^{3} + 905408 x^{2} - 1520652 x + 545369$ $7^{12}\cdot 43^{6}$ $C_7$ (as 7T1) $[7]$ $12027627.652134134$
8.4.3543369523456.1 $x^{8} - 7 x^{6} - 14 x^{5} + 7 x^{4} + 28 x^{2} + 48 x + 14$ $2^{8}\cdot 7^{12}$ $C_2^3:\GL(3,2)$ (as 8T48) trivial $7262.24637552$
8.0.14173478093824.1 $x^{8} + 7 x^{6} + 21 x^{4} - 14 x^{3} + 42 x^{2} - 48 x + 28$ $2^{10}\cdot 7^{12}$ $C_2^3:\GL(3,2)$ (as 8T48) $[2]$ $1447.05229669$
8.0.226775649501184.4 $x^{8} - 2 x^{7} + 14 x^{6} - 14 x^{5} - 126 x^{4} + 630 x^{3} + 658 x^{2} - 5130 x + 10267$ $2^{14}\cdot 7^{12}$ $C_2^3:C_7$ (as 8T25) trivial $24239.5513308$
8.0.226775649501184.5 $x^{8} - 2 x^{7} + 14 x^{6} + 84 x^{4} - 112 x^{3} + 28 x^{2} + 188 x + 310$ $2^{14}\cdot 7^{12}$ $C_2^3:C_7$ (as 8T25) trivial $26620.3609911$
8.0.907102598004736.3 $x^{8} - 56 x^{5} + 7 x^{4} - 84 x^{3} + 770 x^{2} - 116 x + 2394$ $2^{16}\cdot 7^{12}$ $\PSL(2,7)$ (as 8T37) $[2, 6]$ $10627.578275$
8.0.907102598004736.6 $x^{8} - 56 x^{5} - 70 x^{4} + 224 x^{3} + 672 x^{2} + 264 x + 329$ $2^{16}\cdot 7^{12}$ $C_2^3:\GL(3,2)$ (as 8T48) $[2, 2]$ $25714.4903521$
8.4.907102598004736.7 $x^{8} - 28 x^{6} - 84 x^{5} + 133 x^{4} + 1204 x^{3} + 2310 x^{2} + 1224 x + 189$ $2^{16}\cdot 7^{12}$ $C_2^3:\GL(3,2)$ (as 8T48) $[2]$ $44501.4858602$
8.0.907102598004736.7 $x^{8} - 4 x^{7} + 14 x^{6} - 28 x^{5} + 70 x^{4} - 84 x^{3} + 378 x^{2} - 124 x + 517$ $2^{16}\cdot 7^{12}$ $C_2^3:\GL(3,2)$ (as 8T48) $[2, 2]$ $8070.98128542$
8.0.1803810389321521.1 $x^{8} - 2 x^{7} - 28 x^{6} + 154 x^{5} + 189 x^{4} - 2016 x^{3} + 5278 x^{2} + 2701 x + 2949$ $7^{12}\cdot 19^{4}$ $C_2^3:C_7$ (as 8T25) $[2, 4]$ $7631.3442133$
8.0.1803810389321521.2 $x^{8} - 4 x^{7} + 35 x^{6} - 42 x^{5} + 329 x^{4} - 14 x^{3} + 2611 x^{2} - 6607 x + 3692$ $7^{12}\cdot 19^{4}$ $C_2^3:C_7$ (as 8T25) $[2, 4]$ $7306.25989421$
8.0.2296103451199488.1 $x^{8} - 3 x^{7} + 28 x^{6} - 161 x^{5} + 392 x^{4} + 371 x^{3} + 672 x^{2} + 353 x + 187$ $2^{11}\cdot 3^{4}\cdot 7^{12}$ $\PGL(2,7)$ (as 8T43) $[2]$ $91728.6569631$
8.0.3628410392018944.1 $x^{8} - 4 x^{7} - 56 x^{5} + 196 x^{4} - 224 x^{3} + 1792 x^{2} + 1408 x + 1088$ $2^{18}\cdot 7^{12}$ $C_2^3:\GL(3,2)$ (as 8T48) $[2]$ $131688.580848$
8.4.3628410392018944.1 $x^{8} - 4 x^{7} + 28 x^{6} - 196 x^{4} - 784 x^{2} + 2016 x - 1008$ $2^{18}\cdot 7^{12}$ $C_2^3:\GL(3,2)$ (as 8T48) trivial $118573.087895$
8.0.3628410392018944.3 $x^{8} - 4 x^{7} + 28 x^{6} - 56 x^{5} + 301 x^{4} - 280 x^{3} + 2128 x^{2} + 320 x + 6672$ $2^{18}\cdot 7^{12}$ $C_2^3:\GL(3,2)$ (as 8T48) $[2]$ $181346.72701$
8.4.3628410392018944.3 $x^{8} - 4 x^{7} - 28 x^{6} - 28 x^{5} + 70 x^{4} + 588 x^{3} + 1764 x^{2} + 1940 x + 661$ $2^{18}\cdot 7^{12}$ $C_2^3:\GL(3,2)$ (as 8T48) trivial $146393.854072$
8.4.3628410392018944.4 $x^{8} - 4 x^{7} - 14 x^{6} + 56 x^{5} + 84 x^{4} - 28 x^{3} - 112 x^{2} - 16 x + 50$ $2^{18}\cdot 7^{12}$ $C_2^3:\GL(3,2)$ (as 8T48) $[2, 2]$ $51933.9162826$
8.0.12782719397154721.1 $x^{8} - 3 x^{7} - 56 x^{6} + 28 x^{5} + 1043 x^{4} - 567 x^{3} + 4704 x^{2} + 46853 x + 57555$ $7^{12}\cdot 31^{4}$ $C_2^3:C_7$ (as 8T25) $[2, 2, 2]$ $20731.5393723$
8.8.12782719397154721.1 $x^{8} - x^{7} - 42 x^{6} + 77 x^{5} + 420 x^{4} - 854 x^{3} - 987 x^{2} + 1577 x + 733$ $7^{12}\cdot 31^{4}$ $C_2^3:C_7$ (as 8T25) trivial $942691.948946$
8.4.14513641568075776.1 $x^{8} - 4 x^{7} + 14 x^{6} - 28 x^{5} - 273 x^{4} - 84 x^{3} + 2534 x^{2} + 4384 x - 9381$ $2^{20}\cdot 7^{12}$ $C_2^3:\GL(3,2)$ (as 8T48) $[2]$ $208750.585146$
8.0.14513641568075776.2 $x^{8} - 4 x^{7} + 28 x^{6} - 56 x^{5} + 252 x^{4} - 280 x^{3} + 952 x^{2} - 464 x + 1380$ $2^{20}\cdot 7^{12}$ $C_2^3:\GL(3,2)$ (as 8T48) $[2, 12]$ $15171.4047761$
8.0.14513641568075776.3 $x^{8} - 56 x^{5} + 126 x^{4} + 224 x^{3} - 112 x^{2} + 1048 x + 1505$ $2^{20}\cdot 7^{12}$ $C_2^3:\GL(3,2)$ (as 8T48) $[2, 2]$ $32642.9044999$
8.4.14513641568075776.5 $x^{8} - 28 x^{6} - 84 x^{5} + 210 x^{4} + 5096 x^{3} + 13552 x^{2} + 6008 x - 2002$ $2^{20}\cdot 7^{12}$ $C_2^3:\GL(3,2)$ (as 8T48) $[2]$ $144495.61499$
8.0.14513641568075776.7 $x^{8} - 4 x^{7} - 56 x^{5} + 490 x^{4} - 1008 x^{3} + 1400 x^{2} - 3296 x + 4616$ $2^{20}\cdot 7^{12}$ $C_2^3:\GL(3,2)$ (as 8T48) $[2, 2]$ $44578.5697838$
8.4.14513641568075776.11 $x^{8} - 4 x^{7} - 28 x^{6} + 56 x^{5} + 686 x^{4} - 4256 x^{3} + 14112 x^{2} - 16672 x + 4080$ $2^{20}\cdot 7^{12}$ $C_2^3:\GL(3,2)$ (as 8T48) $[2]$ $896141.00032$
8.0.470772960728745024.2 $x^{8} - 2 x^{7} + 28 x^{6} - 13608 x + 27216$ $2^{6}\cdot 3^{12}\cdot 7^{12}$ $\PSL(2,7)$ (as 8T37) $[4]$ $747394.855325$
8.0.928873060356849664.4 $x^{8} + 56 x^{6} + 952 x^{4} - 896 x^{3} + 7392 x^{2} + 2304 x + 15120$ $2^{26}\cdot 7^{12}$ $C_2^3:\GL(3,2)$ (as 8T48) $[2, 4]$ $258306.421026$
8.4.928873060356849664.7 $x^{8} - 56 x^{6} - 112 x^{5} + 350 x^{4} + 3528 x^{3} + 11592 x^{2} + 16120 x + 6727$ $2^{26}\cdot 7^{12}$ $C_2^3:\GL(3,2)$ (as 8T48) $[4]$ $719098.828771$
8.4.928873060356849664.8 $x^{8} - 28 x^{6} - 224 x^{5} - 1176 x^{4} - 1064 x^{3} - 6104 x^{2} - 7920 x + 8442$ $2^{26}\cdot 7^{12}$ $C_2^3:\GL(3,2)$ (as 8T48) $[2, 2]$ $1034710.48001$
8.0.928873060356849664.12 $x^{8} - 28 x^{6} - 112 x^{5} + 1386 x^{4} + 6272 x^{3} + 18060 x^{2} - 49520 x + 426209$ $2^{26}\cdot 7^{12}$ $C_2^3:\GL(3,2)$ (as 8T48) $[2, 4]$ $121607.01614$
8.0.3715492241427398656.1 $x^{8} - 896 x + 1568$ $2^{28}\cdot 7^{12}$ $A_8$ (as 8T49) $[2, 2]$ $468980.925517$
8.2.650...376.1 $x^{8} - 3528 x^{2} - 6048 x - 2646$ $-\,2^{31}\cdot 3^{7}\cdot 7^{12}$ $S_8$ (as 8T50) trivial $683277868.793$
8.2.131...864.1 $x^{8} - 56 x^{5} - 1050 x^{4} - 8400 x^{3} - 35000 x^{2} - 75000 x - 65625$ $-\,2^{29}\cdot 3^{11}\cdot 7^{12}$ $S_8$ (as 8T50) $[2]$ $1754817880.49$
8.2.186...216.1 $x^{8} - 5824 x - 5096$ $-\,2^{31}\cdot 7^{12}\cdot 13^{7}$ $S_8$ (as 8T50) $[2, 2]$ $16760064929.9$
9.3.203...368.1 $x^{9} - 3 x^{8} + 756 x^{2} - 2268 x + 1764$ $-\,2^{10}\cdot 3^{15}\cdot 7^{12}$ $S_9$ (as 9T34) trivial $38577167.6361$
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