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Label Polynomial Discriminant Galois group Class group Regulator
8.2.15580341910480.1 $x^{8} - x^{7} + 3 x^{6} - 11 x^{5} + 44 x^{4} + 12 x^{3} + 112 x^{2} + 160 x - 64$ $-\,2^{4}\cdot 5\cdot 41^{7}$ $S_4\wr C_2$ (as 8T47) $[2]$ $43129.0788773$
8.6.99714188227072.1 $x^{8} - x^{7} + 3 x^{6} - 11 x^{5} - 284 x^{4} + 12 x^{3} + 276 x^{2} - 4 x - 64$ $-\,2^{9}\cdot 41^{7}$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[2]$ $168222.510269$
8.2.99714188227072.2 $x^{8} - 3 x^{7} - 14 x^{6} + 72 x^{5} - 3 x^{4} - 159 x^{3} - 24 x^{2} + 190 x + 100$ $-\,2^{9}\cdot 41^{7}$ $QD_{16}$ (as 8T8) $[2]$ $106238.57876$
8.4.99714188227072.1 $x^{8} - 3 x^{7} - 14 x^{6} + 72 x^{5} - 44 x^{4} - 1020 x^{3} - 1992 x^{2} - 2352 x - 1376$ $2^{9}\cdot 41^{7}$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[2]$ $108013.947264$
8.0.99714188227072.1 $x^{8} + 41 x^{6} + 410 x^{4} + 1312 x^{2} + 1312$ $2^{9}\cdot 41^{7}$ $QD_{16}$ (as 8T8) $[12]$ $928.504691932$
8.2.398856752908288.1 $x^{8} - 2 x^{7} + 12 x^{6} - 88 x^{5} + 7 x^{4} + 794 x^{3} - 1524 x^{2} + 964 x - 148$ $-\,2^{11}\cdot 41^{7}$ $Z_8 : Z_8^\times$ (as 8T15) $[2, 4]$ $29342.7550879$
8.6.398856752908288.2 $x^{8} - 2 x^{7} - 29 x^{6} - 88 x^{5} - 75 x^{4} + 1122 x^{3} + 2043 x^{2} - 1332 x - 640$ $-\,2^{11}\cdot 41^{7}$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[2]$ $494820.515651$
8.6.398856752908288.3 $x^{8} - 2 x^{7} - 29 x^{6} + 76 x^{5} - 321 x^{4} + 2926 x^{3} - 6731 x^{2} + 2440 x + 1000$ $-\,2^{11}\cdot 41^{7}$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[4]$ $182285.374261$
8.2.398856752908288.4 $x^{8} - 3 x^{7} - 14 x^{6} + 154 x^{5} - 700 x^{4} + 1932 x^{3} - 3304 x^{2} + 3224 x - 1376$ $-\,2^{11}\cdot 41^{7}$ $Z_8 : Z_8^\times$ (as 8T15) $[2, 4]$ $29342.7550879$
8.2.398856752908288.6 $x^{8} - 3 x^{7} + 27 x^{6} - 51 x^{5} + 202 x^{4} + 292 x^{3} + 714 x^{2} - 794 x + 100$ $-\,2^{11}\cdot 41^{7}$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[2, 12]$ $11885.8351584$
8.4.398856752908288.1 $x^{8} - 3 x^{7} - 14 x^{6} - 10 x^{5} + 161 x^{4} + 661 x^{3} - 1008 x^{2} - 3172 x - 64$ $2^{11}\cdot 41^{7}$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[2, 2]$ $117043.567897$
8.0.398856752908288.2 $x^{8} - 2 x^{7} + 12 x^{6} - 88 x^{5} + 253 x^{4} + 466 x^{3} + 4790 x^{2} + 6048 x + 14120$ $2^{11}\cdot 41^{7}$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[4, 12]$ $3815.88638149$
8.4.398856752908288.3 $x^{8} - 41 x^{6} - 82 x^{4} + 8774 x^{2} + 20992$ $2^{11}\cdot 41^{7}$ $C_4\wr C_2$ (as 8T17) $[2]$ $19212.410659$
8.0.398856752908288.4 $x^{8} - 2 x^{7} + 53 x^{6} - 170 x^{5} + 1278 x^{4} - 3798 x^{3} + 14015 x^{2} - 39462 x + 42615$ $2^{11}\cdot 41^{7}$ $C_4\wr C_2$ (as 8T17) $[68]$ $928.504691932$
8.4.398856752908288.5 $x^{8} + 41 x^{6} + 41 x^{4} - 205 x^{2} + 82$ $2^{11}\cdot 41^{7}$ $Z_8 : Z_8^\times$ (as 8T15) $[2]$ $74153.3338856$
8.4.398856752908288.6 $x^{8} - 41 x^{6} + 41 x^{4} + 205 x^{2} + 82$ $2^{11}\cdot 41^{7}$ $Z_8 : Z_8^\times$ (as 8T15) $[4]$ $37076.6669428$
8.4.398856752908288.10 $x^{8} - 3 x^{7} - 14 x^{6} + 72 x^{5} - 290 x^{4} + 702 x^{3} - 188 x^{2} - 1368 x + 592$ $2^{11}\cdot 41^{7}$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[2]$ $317719.174427$
8.2.1558034191048000.1 $x^{8} - 2 x^{7} + 12 x^{6} + 76 x^{5} - 362 x^{4} - 1174 x^{3} - 7 x^{2} - 430 x - 230$ $-\,2^{6}\cdot 5^{3}\cdot 41^{7}$ $D_{8}$ (as 8T6) $[4]$ $25689.8993353$
8.2.1558034191048000.3 $x^{8} - 2 x^{7} + 12 x^{6} - 6 x^{5} + 89 x^{4} - 600 x^{3} - 130 x^{2} - 3300 x + 1000$ $-\,2^{6}\cdot 5^{3}\cdot 41^{7}$ $Z_8 : Z_8^\times$ (as 8T15) $[4]$ $131241.109522$
8.2.1558034191048000.5 $x^{8} - 3 x^{7} + 27 x^{6} - 51 x^{5} - 290 x^{4} - 2988 x^{3} - 1336 x^{2} + 4864 x + 7808$ $-\,2^{6}\cdot 5^{3}\cdot 41^{7}$ $D_{8}$ (as 8T6) $[28]$ $20676.3376407$
8.2.1558034191048000.6 $x^{8} - x^{7} + 3 x^{6} + 71 x^{5} - 79 x^{4} + 135 x^{3} + 850 x^{2} - 250 x + 100$ $-\,2^{6}\cdot 5^{3}\cdot 41^{7}$ $Z_8 : Z_8^\times$ (as 8T15) $[4]$ $131241.109522$
8.6.1595427011633152.2 $x^{8} - 41 x^{6} + 82 x^{4} + 246 x^{2} - 328$ $-\,2^{13}\cdot 41^{7}$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[4]$ $270401.235499$
8.2.1595427011633152.2 $x^{8} + 41 x^{6} + 82 x^{4} - 246 x^{2} - 328$ $-\,2^{13}\cdot 41^{7}$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[28]$ $17060.0183684$
8.2.1595427011633152.3 $x^{8} - 697 x^{4} - 328$ $-\,2^{13}\cdot 41^{7}$ $(C_4^2 : C_2):C_2$ (as 8T26) $[2, 2]$ $64016.0444849$
8.6.1595427011633152.3 $x^{8} - 41 x^{6} + 3280 x^{2} - 5248$ $-\,2^{13}\cdot 41^{7}$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[4]$ $167891.869155$
8.6.1595427011633152.4 $x^{8} - 41 x^{6} + 123 x^{4} + 6847 x^{2} - 2050$ $-\,2^{13}\cdot 41^{7}$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[4]$ $379208.823211$
8.2.1595427011633152.5 $x^{8} - 328 x^{4} - 5248$ $-\,2^{13}\cdot 41^{7}$ $(C_4^2 : C_2):C_2$ (as 8T26) $[2, 4]$ $80719.1352164$
8.2.1595427011633152.6 $x^{8} + 41 x^{6} + 656 x^{4} + 3280 x^{2} - 5248$ $-\,2^{13}\cdot 41^{7}$ $QD_{16}$ (as 8T8) $[2, 2, 4]$ $11892.5085001$
8.2.1595427011633152.7 $x^{8} + 41 x^{6} + 205 x^{4} - 861 x^{2} - 2050$ $-\,2^{13}\cdot 41^{7}$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[4, 4]$ $9340.23602801$
8.4.1595427011633152.1 $x^{8} - 82 x^{4} + 1312$ $2^{13}\cdot 41^{7}$ $(C_4^2 : C_2):C_2$ (as 8T26) $[2]$ $91183.540845$
8.8.1595427011633152.2 $x^{8} - 41 x^{6} + 410 x^{4} - 1312 x^{2} + 1312$ $2^{13}\cdot 41^{7}$ $QD_{16}$ (as 8T8) $[2]$ $331529.208282$
8.0.1595427011633152.2 $x^{8} + 41 x^{6} + 533 x^{4} + 2911 x^{2} + 82$ $2^{13}\cdot 41^{7}$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[2, 4, 4]$ $2998.63484427$
8.4.1595427011633152.4 $x^{8} - 861 x^{4} + 8118 x^{2} + 20992$ $2^{13}\cdot 41^{7}$ $(C_4^2 : C_2):C_2$ (as 8T26) $[2]$ $100943.742643$
8.4.1595427011633152.5 $x^{8} - 533 x^{4} - 2214 x^{2} + 26568$ $2^{13}\cdot 41^{7}$ $(C_4^2 : C_2):C_2$ (as 8T26) $[2]$ $155951.358051$
8.4.1595427011633152.6 $x^{8} - 123 x^{4} + 82$ $2^{13}\cdot 41^{7}$ $(C_4^2 : C_2):C_2$ (as 8T26) $[2]$ $113584.123303$
8.0.1947542738810000.1 $x^{8} + 41 x^{4} - 1640 x^{2} + 11849$ $2^{4}\cdot 5^{4}\cdot 41^{7}$ $(C_4^2 : C_2):C_2$ (as 8T26) $[24]$ $6514.99792779$
8.0.1947542738810000.2 $x^{8} + 41 x^{4} + 1640 x^{2} + 11849$ $2^{4}\cdot 5^{4}\cdot 41^{7}$ $(C_4^2 : C_2):C_2$ (as 8T26) $[24]$ $2459.09470054$
8.0.2271613850547984.2 $x^{8} - x^{7} + 44 x^{6} - 52 x^{5} + 823 x^{4} + 1201 x^{3} + 11756 x^{2} + 25252 x + 55696$ $2^{4}\cdot 3^{6}\cdot 41^{7}$ $(C_8:C_2):C_2$ (as 8T16) $[68]$ $27414.4960779$
8.4.3043035529390625.1 $x^{8} - 3 x^{7} - 14 x^{6} + 31 x^{5} + 79 x^{4} + 128 x^{3} - 1951 x^{2} + 1174 x + 2396$ $5^{6}\cdot 41^{7}$ $S_4\wr C_2$ (as 8T47) $[2, 8]$ $8436.80077405$
8.2.6381708046532608.4 $x^{8} + 82 x^{4} - 328$ $-\,2^{15}\cdot 41^{7}$ $(C_4^2 : C_2):C_2$ (as 8T26) $[4, 4]$ $40320.8279462$
8.2.6381708046532608.5 $x^{8} + 41 x^{6} - 3280 x^{2} - 5248$ $-\,2^{15}\cdot 41^{7}$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[4, 4]$ $15529.4482415$
8.2.6381708046532608.6 $x^{8} - 82 x^{4} - 5248$ $-\,2^{15}\cdot 41^{7}$ $(C_4^2 : C_2):C_2$ (as 8T26) $[2, 2, 4]$ $15988.6494606$
8.2.6381708046532608.7 $x^{8} + 41 x^{6} + 123 x^{4} - 6847 x^{2} - 2050$ $-\,2^{15}\cdot 41^{7}$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[4, 4]$ $40907.8145293$
8.2.6381708046532608.8 $x^{8} + 82 x^{6} + 1927 x^{4} + 11316 x^{2} - 2050$ $-\,2^{15}\cdot 41^{7}$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[4, 16]$ $7396.5550451$
8.4.6381708046532608.1 $x^{8} - 2 x^{7} - 29 x^{6} + 76 x^{5} + 253 x^{4} - 1338 x^{3} + 1961 x^{2} - 512 x - 394$ $2^{15}\cdot 41^{7}$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[2, 4]$ $53849.0855851$
8.0.6381708046532608.1 $x^{8} + 492 x^{4} + 1312$ $2^{15}\cdot 41^{7}$ $(C_4^2 : C_2):C_2$ (as 8T26) $[4, 8]$ $4070.29335142$
8.8.6381708046532608.2 $x^{8} - 82 x^{6} + 1763 x^{4} - 4264 x^{2} + 82$ $2^{15}\cdot 41^{7}$ $C_4\wr C_2$ (as 8T17) $[2]$ $1473861.30732$
8.0.6381708046532608.2 $x^{8} - 2 x^{7} - 29 x^{6} - 6 x^{5} + 376 x^{4} - 354 x^{3} + 731 x^{2} + 5310 x + 4075$ $2^{15}\cdot 41^{7}$ $(C_4^2 : C_2):C_2$ (as 8T26) $[4, 8]$ $3617.32461018$
8.4.6381708046532608.3 $x^{8} - 2 x^{7} - 29 x^{6} - 88 x^{5} + 89 x^{4} + 958 x^{3} + 2945 x^{2} + 9164 x + 2066$ $2^{15}\cdot 41^{7}$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[2, 4]$ $121626.189991$
8.4.6381708046532608.4 $x^{8} - 2 x^{7} - 29 x^{6} + 76 x^{5} + 253 x^{4} - 190 x^{3} + 239 x^{2} - 2808 x + 2476$ $2^{15}\cdot 41^{7}$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[2, 4]$ $86727.6023905$
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