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Label Polynomial $p$ $e$ $f$ $c$ Galois group Visible slopes Slope content Unram. Ext. Eisen. Poly.
3.15.0.1 $x^{15} + 2 x^{8} + x^{5} + 2 x^{2} + x + 1$ $3$ $1$ $15$ $0$ $C_{15}$ (as 15T1) $[\ ]$ $[\ ]^{15}$ $t^{15} + 2 t^{8} + t^{5} + 2 t^{2} + t + 1$ $x - 3$
3.15.12.1 $x^{15} + 10 x^{13} + 5 x^{12} + 40 x^{11} + 49 x^{10} + 90 x^{9} + 30 x^{8} - 130 x^{7} + 410 x^{6} + 269 x^{5} + 765 x^{4} - 515 x^{3} + 730 x^{2} + 205 x + 94$ $3$ $5$ $3$ $12$ $F_5\times C_3$ (as 15T8) $[\ ]$ $[\ ]_{5}^{12}$ $t^{3} + 2 t + 1$ $x^{5} + 3$
3.15.15.1 $x^{15} - 48 x^{14} + 906 x^{13} - 7365 x^{12} + 13968 x^{11} + 95301 x^{10} + 55413 x^{9} - 59940 x^{8} + 224694 x^{7} + 597321 x^{6} + 326997 x^{5} - 91206 x^{4} - 61803 x^{3} + 25758 x^{2} - 3888 x + 243$ $3$ $3$ $5$ $15$ $C_7^3:C_6$ (as 15T44) $[3/2]$ $[3/2, 3/2, 3/2, 3/2, 3/2]_{2}^{5}$ $t^{5} + 2 t + 1$ $x^{3} + \left(6 t^{4} + 3 t\right) x^{2} + \left(6 t^{4} + 6 t^{2} + 3 t\right) x + 3$
3.15.15.10 $x^{15} + 30 x^{14} + 519 x^{13} + 4605 x^{12} + 25533 x^{11} + 93573 x^{10} + 187578 x^{9} + 234171 x^{8} + 220158 x^{7} + 187947 x^{6} + 126198 x^{5} + 79137 x^{4} + 34425 x^{3} + 15066 x^{2} + 1215 x + 243$ $3$ $3$ $5$ $15$ $C_3^4:C_{10}$ (as 15T33) $[3/2]$ $[3/2, 3/2, 3/2, 3/2]_{2}^{5}$ $t^{5} + 2 t + 1$ $x^{3} + \left(6 t^{2} + 3 t + 6\right) x^{2} + \left(3 t^{3} + 6 t^{2} + 6 t + 3\right) x + 3$
3.15.15.11 $x^{15} - 33 x^{14} + 378 x^{13} - 966 x^{12} + 7461 x^{11} + 47682 x^{10} + 1575 x^{9} + 29160 x^{8} + 30780 x^{7} + 9423 x^{6} + 24138 x^{5} + 26244 x^{4} + 6966 x^{3} - 486 x^{2} + 243$ $3$ $3$ $5$ $15$ $C_3^4:C_{10}$ (as 15T33) $[3/2]$ $[3/2, 3/2, 3/2, 3/2]_{2}^{5}$ $t^{5} + 2 t + 1$ $x^{3} + \left(6 t^{4} + 3 t^{3} + 3\right) x^{2} + \left(3 t^{3} + 3 t^{2}\right) x + 3$
3.15.15.12 $x^{15} + 30 x^{14} + 567 x^{13} + 5343 x^{12} + 26946 x^{11} + 81891 x^{10} + 187308 x^{9} + 338094 x^{8} + 444204 x^{7} + 428112 x^{6} + 240165 x^{5} + 86994 x^{4} - 10773 x^{3} + 15309 x^{2} - 1458 x + 243$ $3$ $3$ $5$ $15$ $C_3^4:C_{10}$ (as 15T33) $[3/2]$ $[3/2, 3/2, 3/2, 3/2]_{2}^{5}$ $t^{5} + 2 t + 1$ $x^{3} + \left(3 t^{3} + 3 t^{2} + 6 t + 6\right) x^{2} + \left(6 t^{4} + 3 t^{3} + 3 t^{2} + 6 t + 6\right) x + 3$
3.15.15.13 $x^{15} - 33 x^{14} + 393 x^{13} - 1317 x^{12} + 12267 x^{11} + 29070 x^{10} + 19206 x^{9} + 4131 x^{8} + 7209 x^{7} + 104274 x^{6} + 116964 x^{5} + 74277 x^{4} + 22761 x^{3} + 6075 x^{2} + 1215 x + 243$ $3$ $3$ $5$ $15$ $C_7^3:C_6$ (as 15T44) $[3/2]$ $[3/2, 3/2, 3/2, 3/2, 3/2]_{2}^{5}$ $t^{5} + 2 t + 1$ $x^{3} + \left(6 t^{4} + 3 t^{3} + 3\right) x^{2} + \left(3 t^{3} + 6 t^{2} + 3\right) x + 3$
3.15.15.14 $x^{15} + 51 x^{13} + 60 x^{12} + 738 x^{11} + 1746 x^{10} + 3276 x^{9} + 8019 x^{8} + 11502 x^{7} + 13797 x^{6} + 20169 x^{5} + 16200 x^{4} + 5508 x^{3} + 2430 x^{2} + 1215 x + 243$ $3$ $3$ $5$ $15$ $C_7^3:C_6$ (as 15T44) $[3/2]$ $[3/2, 3/2, 3/2, 3/2, 3/2]_{2}^{5}$ $t^{5} + 2 t + 1$ $x^{3} + 3 t^{2} x^{2} + \left(3 t^{3} + 3\right) x + 3$
3.15.15.15 $x^{15} - 24 x^{14} + 597 x^{13} - 4503 x^{12} + 18945 x^{11} - 48726 x^{10} + 86652 x^{9} - 73467 x^{8} - 27135 x^{7} + 114804 x^{6} + 44550 x^{5} - 8667 x^{4} + 4293 x^{3} + 7776 x^{2} + 2430 x + 243$ $3$ $3$ $5$ $15$ $S_3 \times C_5$ (as 15T4) $[3/2]$ $[3/2]_{2}^{5}$ $t^{5} + 2 t + 1$ $x^{3} + \left(3 t^{4} + 3 t^{3} + 6 t^{2} + 3 t\right) x^{2} + 6 x + 3$
3.15.15.16 $x^{15} - 18 x^{14} + 174 x^{13} + 348 x^{12} - 9234 x^{11} + 11889 x^{10} + 136521 x^{9} + 196020 x^{8} + 62451 x^{7} - 5157 x^{6} + 3645 x^{5} - 32238 x^{4} - 16605 x^{3} + 13851 x^{2} - 1944 x + 243$ $3$ $3$ $5$ $15$ $C_7^3:C_6$ (as 15T44) $[3/2]$ $[3/2, 3/2, 3/2, 3/2, 3/2]_{2}^{5}$ $t^{5} + 2 t + 1$ $x^{3} + \left(6 t^{4} + 3 t^{2} + 3 t + 6\right) x^{2} + \left(3 t^{4} + 3 t^{3} + 6 t^{2} + 3 t\right) x + 3$
3.15.15.17 $x^{15} + 30 x^{14} + 480 x^{13} + 4686 x^{12} + 27108 x^{11} + 95319 x^{10} + 230805 x^{9} + 407268 x^{8} + 447120 x^{7} + 474282 x^{6} + 249642 x^{5} + 164592 x^{4} + 18144 x^{3} + 16038 x^{2} - 2673 x + 243$ $3$ $3$ $5$ $15$ $C_7^3:C_6$ (as 15T44) $[3/2]$ $[3/2, 3/2, 3/2, 3/2, 3/2]_{2}^{5}$ $t^{5} + 2 t + 1$ $x^{3} + \left(3 t^{3} + 3 t^{2} + 3 t + 6\right) x^{2} + \left(6 t^{4} + 6 t^{3} + 3 t^{2} + 3\right) x + 3$
3.15.15.18 $x^{15} - 9 x^{14} + 159 x^{13} - 876 x^{12} - 3105 x^{11} + 15786 x^{10} + 54090 x^{9} + 98253 x^{8} + 92259 x^{7} + 71307 x^{6} + 2430 x^{5} + 27621 x^{4} - 51597 x^{3} + 22599 x^{2} - 3888 x + 243$ $3$ $3$ $5$ $15$ $C_7^3:C_6$ (as 15T44) $[3/2]$ $[3/2, 3/2, 3/2, 3/2, 3/2]_{2}^{5}$ $t^{5} + 2 t + 1$ $x^{3} + \left(3 t^{4} + 6 t^{2} + 3 t + 3\right) x^{2} + 6 t^{4} x + 3$
3.15.15.19 $x^{15} - 48 x^{14} + 1026 x^{13} - 10398 x^{12} + 54189 x^{11} + 28296 x^{10} - 183645 x^{9} - 50301 x^{8} + 110889 x^{7} + 37044 x^{6} + 20817 x^{5} + 47385 x^{4} + 17901 x^{3} + 243$ $3$ $3$ $5$ $15$ $C_7^3:C_6$ (as 15T44) $[3/2]$ $[3/2, 3/2, 3/2, 3/2, 3/2]_{2}^{5}$ $t^{5} + 2 t + 1$ $x^{3} + \left(6 t^{4} + 3 t^{3} + 3 t\right) x^{2} + \left(6 t^{3} + 3 t\right) x + 3$
3.15.15.2 $x^{15} + 6 x^{14} + 201 x^{13} - 750 x^{12} - 5202 x^{11} + 13104 x^{10} + 50148 x^{9} + 206469 x^{8} + 249966 x^{7} + 370359 x^{6} + 133083 x^{5} + 169938 x^{4} - 14418 x^{3} + 17010 x^{2} - 2673 x + 243$ $3$ $3$ $5$ $15$ $C_7^3:C_6$ (as 15T44) $[3/2]$ $[3/2, 3/2, 3/2, 3/2, 3/2]_{2}^{5}$ $t^{5} + 2 t + 1$ $x^{3} + \left(3 t^{4} + 6 t^{2} + 6 t + 6\right) x^{2} + \left(6 t^{4} + 6 t^{3} + 3 t + 3\right) x + 3$
3.15.15.20 $x^{15} - 9 x^{14} + 174 x^{13} + 4479 x^{12} + 39375 x^{11} + 186093 x^{10} + 548082 x^{9} + 1077138 x^{8} + 1457352 x^{7} + 1359531 x^{6} + 855117 x^{5} + 350973 x^{4} + 91287 x^{3} + 16281 x^{2} + 2430 x + 243$ $3$ $3$ $5$ $15$ $C_3^4:C_{10}$ (as 15T33) $[3/2]$ $[3/2, 3/2, 3/2, 3/2]_{2}^{5}$ $t^{5} + 2 t + 1$ $x^{3} + \left(3 t^{4} + 6 t^{3} + 3 t^{2} + 3\right) x^{2} + \left(6 t^{3} + 3 t^{2} + 3 t + 6\right) x + 3$
3.15.15.21 $x^{15} + 6 x^{14} + 216 x^{13} + 4272 x^{12} + 32373 x^{11} + 101574 x^{10} + 55899 x^{9} - 94851 x^{8} - 2511 x^{7} + 76572 x^{6} + 21789 x^{5} + 41553 x^{4} - 7857 x^{3} + 17496 x^{2} - 1458 x + 243$ $3$ $3$ $5$ $15$ $C_7^3:C_6$ (as 15T44) $[3/2]$ $[3/2, 3/2, 3/2, 3/2, 3/2]_{2}^{5}$ $t^{5} + 2 t + 1$ $x^{3} + \left(3 t^{4} + 3 t^{3} + 6 t^{2} + 6\right) x^{2} + \left(6 t^{4} + 3 t^{3} + 6 t^{2} + 6 t + 6\right) x + 3$
3.15.15.22 $x^{15} + 30 x^{14} + 375 x^{13} + 2535 x^{12} + 10323 x^{11} + 28530 x^{10} + 63729 x^{9} + 116235 x^{8} + 143937 x^{7} + 149310 x^{6} + 107001 x^{5} + 66015 x^{4} + 25920 x^{3} + 8991 x^{2} + 1215 x + 243$ $3$ $3$ $5$ $15$ $C_3^4:C_{10}$ (as 15T33) $[3/2]$ $[3/2, 3/2, 3/2, 3/2]_{2}^{5}$ $t^{5} + 2 t + 1$ $x^{3} + 6 x^{2} + \left(3 t^{3} + 3 t^{2} + 3 t + 3\right) x + 3$
3.15.15.23 $x^{15} + 405 x^{13} + 1527 x^{12} + 5004 x^{11} - 28107 x^{10} + 36000 x^{9} + 23895 x^{8} - 37746 x^{7} + 81351 x^{6} + 62208 x^{5} - 36936 x^{4} - 10287 x^{3} + 6804 x^{2} - 729 x + 243$ $3$ $3$ $5$ $15$ $C_3^4:C_{10}$ (as 15T33) $[3/2]$ $[3/2, 3/2, 3/2, 3/2]_{2}^{5}$ $t^{5} + 2 t + 1$ $x^{3} + \left(6 t^{3} + 3 t^{2} + 6 t\right) x^{2} + \left(3 t^{4} + 6 t^{2} + 6 t + 3\right) x + 3$
3.15.15.24 $x^{15} + 150 x^{13} - 2235 x^{12} + 11961 x^{11} - 32922 x^{10} + 45342 x^{9} - 17577 x^{8} - 6723 x^{7} - 34884 x^{6} + 193671 x^{5} + 181197 x^{4} + 39285 x^{3} + 5103 x^{2} + 486 x + 243$ $3$ $3$ $5$ $15$ $C_7^3:C_6$ (as 15T44) $[3/2]$ $[3/2, 3/2, 3/2, 3/2, 3/2]_{2}^{5}$ $t^{5} + 2 t + 1$ $x^{3} + \left(6 t^{2} + 6 t\right) x^{2} + \left(3 t^{4} + 6 t^{3} + 3 t + 6\right) x + 3$
3.15.15.25 $x^{15} - 9 x^{14} + 228 x^{13} + 2040 x^{12} + 2547 x^{11} - 22914 x^{10} - 63036 x^{9} + 193752 x^{8} - 76950 x^{7} - 3051 x^{6} + 77517 x^{5} - 19116 x^{4} - 7857 x^{3} + 7533 x^{2} - 1944 x + 243$ $3$ $3$ $5$ $15$ $C_7^3:C_6$ (as 15T44) $[3/2]$ $[3/2, 3/2, 3/2, 3/2, 3/2]_{2}^{5}$ $t^{5} + 2 t + 1$ $x^{3} + \left(3 t^{4} + 3 t^{3} + 6 t^{2} + 3\right) x^{2} + \left(3 t^{4} + 6 t\right) x + 3$
3.15.15.26 $x^{15} + 6 x^{14} + 93 x^{13} + 843 x^{12} + 6003 x^{11} + 23661 x^{10} + 33300 x^{9} + 55404 x^{8} + 26487 x^{7} + 15336 x^{6} + 10125 x^{5} + 6885 x^{4} - 12231 x^{3} + 7533 x^{2} - 1944 x + 243$ $3$ $3$ $5$ $15$ $C_7^3:C_6$ (as 15T44) $[3/2]$ $[3/2, 3/2, 3/2, 3/2, 3/2]_{2}^{5}$ $t^{5} + 2 t + 1$ $x^{3} + \left(3 t^{4} + 3 t^{3} + 3 t + 6\right) x^{2} + \left(3 t^{4} + 3 t\right) x + 3$
3.15.15.27 $x^{15} + 15 x^{14} + 354 x^{13} + 3651 x^{12} + 33201 x^{11} + 81873 x^{10} + 4950 x^{9} - 129357 x^{8} + 55242 x^{7} + 237438 x^{6} + 144261 x^{5} + 113562 x^{4} - 38475 x^{3} + 26001 x^{2} - 1944 x + 243$ $3$ $3$ $5$ $15$ $C_7^3:C_6$ (as 15T44) $[3/2]$ $[3/2, 3/2, 3/2, 3/2, 3/2]_{2}^{5}$ $t^{5} + 2 t + 1$ $x^{3} + \left(6 t^{3} + 6 t + 3\right) x^{2} + \left(3 t^{4} + 6 t^{3} + 6 t^{2} + 6 t\right) x + 3$
3.15.15.28 $x^{15} + 381 x^{13} + 1383 x^{12} + 11340 x^{11} + 18261 x^{10} - 15192 x^{9} + 2916 x^{8} + 216837 x^{7} + 473310 x^{6} + 423549 x^{5} + 128871 x^{4} + 23733 x^{3} + 10206 x^{2} - 2673 x + 243$ $3$ $3$ $5$ $15$ $C_3^4:C_{10}$ (as 15T33) $[3/2]$ $[3/2, 3/2, 3/2, 3/2]_{2}^{5}$ $t^{5} + 2 t + 1$ $x^{3} + \left(6 t^{3} + 3 t^{2} + 6 t\right) x^{2} + \left(6 t^{4} + 6 t^{3} + 3\right) x + 3$
3.15.15.29 $x^{15} - 24 x^{14} + 387 x^{13} - 975 x^{12} + 29016 x^{11} + 513 x^{10} + 106173 x^{9} + 431487 x^{8} + 296460 x^{7} - 2322 x^{6} + 22437 x^{5} + 49086 x^{4} + 45603 x^{3} + 6318 x^{2} - 1458 x + 243$ $3$ $3$ $5$ $15$ $C_3^4:C_{10}$ (as 15T33) $[3/2]$ $[3/2, 3/2, 3/2, 3/2]_{2}^{5}$ $t^{5} + 2 t + 1$ $x^{3} + \left(3 t^{4} + 6 t^{3} + 3 t\right) x^{2} + \left(6 t^{4} + 3 t^{3} + 6 t^{2} + 6\right) x + 3$
3.15.15.3 $x^{15} + 30 x^{14} + 402 x^{13} + 2184 x^{12} + 8361 x^{11} + 25857 x^{10} + 61488 x^{9} + 110484 x^{8} + 150741 x^{7} + 157248 x^{6} + 125226 x^{5} + 74520 x^{4} + 31266 x^{3} + 7776 x^{2} + 486 x + 243$ $3$ $3$ $5$ $15$ $C_3^4:C_{10}$ (as 15T33) $[3/2]$ $[3/2, 3/2, 3/2, 3/2]_{2}^{5}$ $t^{5} + 2 t + 1$ $x^{3} + \left(3 t^{2} + 6 t + 6\right) x^{2} + \left(3 t^{4} + 3 t^{3} + 3 t^{2} + 3 t + 6\right) x + 3$
3.15.15.30 $x^{15} - 18 x^{14} + 540 x^{13} - 885 x^{12} + 67428 x^{11} + 364662 x^{10} + 236880 x^{9} + 45198 x^{8} + 204282 x^{7} + 233712 x^{6} + 65367 x^{5} + 13608 x^{4} + 13527 x^{3} + 2430 x^{2} + 243$ $3$ $3$ $5$ $15$ $C_7^3:C_6$ (as 15T44) $[3/2]$ $[3/2, 3/2, 3/2, 3/2, 3/2]_{2}^{5}$ $t^{5} + 2 t + 1$ $x^{3} + \left(6 t^{4} + 6 t^{3} + 6 t + 6\right) x^{2} + \left(3 t^{3} + 6 t\right) x + 3$
3.15.15.31 $x^{15} - 9 x^{14} + 111 x^{13} + 4596 x^{12} + 29925 x^{11} + 55764 x^{10} + 33786 x^{9} + 2916 x^{8} - 2025 x^{7} + 40851 x^{6} + 21384 x^{5} - 20331 x^{4} - 3483 x^{3} + 10449 x^{2} - 2673 x + 243$ $3$ $3$ $5$ $15$ $C_3^4:C_{10}$ (as 15T33) $[3/2]$ $[3/2, 3/2, 3/2, 3/2]_{2}^{5}$ $t^{5} + 2 t + 1$ $x^{3} + \left(3 t^{4} + 6 t^{3} + 3 t^{2} + 3\right) x^{2} + \left(6 t^{4} + 3 t^{2} + 3\right) x + 3$
3.15.15.32 $x^{15} + 30 x^{14} + 390 x^{13} + 4335 x^{12} + 42192 x^{11} + 175050 x^{10} + 290610 x^{9} + 398844 x^{8} + 395442 x^{7} + 336906 x^{6} + 217809 x^{5} + 112104 x^{4} + 43173 x^{3} + 12150 x^{2} + 2430 x + 243$ $3$ $3$ $5$ $15$ $C_3^4:C_{10}$ (as 15T33) $[3/2]$ $[3/2, 3/2, 3/2, 3/2]_{2}^{5}$ $t^{5} + 2 t + 1$ $x^{3} + \left(6 t^{3} + 6\right) x^{2} + \left(3 t + 6\right) x + 3$
3.15.15.33 $x^{15} - 18 x^{14} + 129 x^{13} + 303 x^{12} - 5427 x^{11} + 14859 x^{10} + 179100 x^{9} + 421929 x^{8} + 433917 x^{7} + 265626 x^{6} + 127089 x^{5} + 1296 x^{4} - 17334 x^{3} + 13122 x^{2} - 2673 x + 243$ $3$ $3$ $5$ $15$ $C_7^3:C_6$ (as 15T44) $[3/2]$ $[3/2, 3/2, 3/2, 3/2, 3/2]_{2}^{5}$ $t^{5} + 2 t + 1$ $x^{3} + \left(6 t^{4} + 3 t + 6\right) x^{2} + \left(6 t^{4} + 3 t^{3} + 3 t + 3\right) x + 3$
3.15.15.34 $x^{15} - 18 x^{14} + 462 x^{13} + 3948 x^{12} + 46782 x^{11} + 173079 x^{10} + 158742 x^{9} + 124092 x^{8} + 152685 x^{7} + 212733 x^{6} + 149931 x^{5} + 90234 x^{4} + 37827 x^{3} + 12150 x^{2} + 2430 x + 243$ $3$ $3$ $5$ $15$ $C_7^3:C_6$ (as 15T44) $[3/2]$ $[3/2, 3/2, 3/2, 3/2, 3/2]_{2}^{5}$ $t^{5} + 2 t + 1$ $x^{3} + \left(6 t^{4} + 6 t^{3} + 3 t^{2} + 3 t + 6\right) x^{2} + \left(6 t^{2} + 3 t + 6\right) x + 3$
3.15.15.35 $x^{15} + 51 x^{13} - 975 x^{12} + 2907 x^{11} + 2043 x^{10} - 9684 x^{9} + 9315 x^{8} + 34830 x^{7} + 11853 x^{6} - 13122 x^{5} - 3969 x^{4} + 9639 x^{3} + 6318 x^{2} + 1215 x + 243$ $3$ $3$ $5$ $15$ $C_7^3:C_6$ (as 15T44) $[3/2]$ $[3/2, 3/2, 3/2, 3/2, 3/2]_{2}^{5}$ $t^{5} + 2 t + 1$ $x^{3} + \left(3 t^{2} + 6 t\right) x^{2} + \left(6 t^{2} + 3 t + 3\right) x + 3$
3.15.15.36 $x^{15} - 33 x^{14} + 564 x^{13} + 645 x^{12} - 16551 x^{11} - 6462 x^{10} + 60327 x^{9} + 332586 x^{8} + 407025 x^{7} + 130842 x^{6} + 202257 x^{5} + 170505 x^{4} - 54999 x^{3} + 26973 x^{2} - 3888 x + 243$ $3$ $3$ $5$ $15$ $C_7^3:C_6$ (as 15T44) $[3/2]$ $[3/2, 3/2, 3/2, 3/2, 3/2]_{2}^{5}$ $t^{5} + 2 t + 1$ $x^{3} + \left(6 t^{4} + 3 t^{3} + 6 t^{2} + 3\right) x^{2} + \left(6 t^{4} + 6 t^{3} + 3 t\right) x + 3$
3.15.15.37 $x^{15} - 9 x^{14} + 213 x^{13} - 741 x^{12} - 2853 x^{11} + 11547 x^{10} + 55035 x^{9} + 80352 x^{8} + 23085 x^{7} - 75141 x^{6} - 83592 x^{5} - 5427 x^{4} + 29079 x^{3} + 11907 x^{2} + 486 x + 243$ $3$ $3$ $5$ $15$ $C_3^4:C_{10}$ (as 15T33) $[3/2]$ $[3/2, 3/2, 3/2, 3/2]_{2}^{5}$ $t^{5} + 2 t + 1$ $x^{3} + \left(3 t^{4} + 6 t^{2} + 3 t + 3\right) x^{2} + \left(3 t^{4} + 3 t^{3} + 6 t^{2} + 6 t + 6\right) x + 3$
3.15.15.38 $x^{15} + 30 x^{14} + 432 x^{13} + 4335 x^{12} + 32373 x^{11} + 162027 x^{10} + 501129 x^{9} + 945432 x^{8} + 1104921 x^{7} + 951939 x^{6} + 550233 x^{5} + 242271 x^{4} + 60669 x^{3} + 11664 x^{2} - 729 x + 243$ $3$ $3$ $5$ $15$ $C_3^4:C_{10}$ (as 15T33) $[3/2]$ $[3/2, 3/2, 3/2, 3/2]_{2}^{5}$ $t^{5} + 2 t + 1$ $x^{3} + \left(3 t^{3} + 3 t^{2} + 6\right) x^{2} + \left(3 t^{4} + 6 t^{3} + 6 t^{2} + 3\right) x + 3$
3.15.15.39 $x^{15} - 18 x^{14} + 636 x^{13} - 1623 x^{12} - 378 x^{11} + 83475 x^{10} + 197730 x^{9} + 142074 x^{8} + 49653 x^{7} + 194913 x^{6} + 392931 x^{5} + 317520 x^{4} + 107811 x^{3} + 12393 x^{2} + 486 x + 243$ $3$ $3$ $5$ $15$ $C_7^3:C_6$ (as 15T44) $[3/2]$ $[3/2, 3/2, 3/2, 3/2, 3/2]_{2}^{5}$ $t^{5} + 2 t + 1$ $x^{3} + \left(6 t^{4} + 3 t^{3} + 6 t^{2} + 6 t + 6\right) x^{2} + \left(3 t^{4} + 6 t^{3} + 6 t^{2} + 3 t + 6\right) x + 3$
3.15.15.4 $x^{15} + 30 x^{14} + 780 x^{13} + 11355 x^{12} + 93312 x^{11} + 395487 x^{10} + 1026306 x^{9} + 1765395 x^{8} + 2074653 x^{7} + 1673001 x^{6} + 913761 x^{5} + 331128 x^{4} + 77193 x^{3} + 10935 x^{2} + 486 x + 243$ $3$ $3$ $5$ $15$ $C_7^3:C_6$ (as 15T44) $[3/2]$ $[3/2, 3/2, 3/2, 3/2, 3/2]_{2}^{5}$ $t^{5} + 2 t + 1$ $x^{3} + \left(6 t^{3} + 3 t^{2} + 6 t + 6\right) x^{2} + \left(3 t^{4} + 6 t^{3} + 3 t^{2} + 3 t + 6\right) x + 3$
3.15.15.40 $x^{15} + 30 x^{14} + 366 x^{13} + 2409 x^{12} + 10854 x^{11} + 29988 x^{10} + 58950 x^{9} + 78894 x^{8} + 75168 x^{7} + 43848 x^{6} + 9801 x^{5} - 5184 x^{4} - 4455 x^{3} + 8748 x^{2} + 486 x + 243$ $3$ $3$ $5$ $15$ $C_7^3:C_6$ (as 15T44) $[3/2]$ $[3/2, 3/2, 3/2, 3/2, 3/2]_{2}^{5}$ $t^{5} + 2 t + 1$ $x^{3} + \left(6 t + 6\right) x^{2} + \left(3 t^{4} + 6 t^{2} + 6 t + 6\right) x + 3$
3.15.15.41 $x^{15} - 33 x^{14} + 741 x^{13} - 3054 x^{12} - 22212 x^{11} + 52065 x^{10} + 398718 x^{9} + 775089 x^{8} + 832599 x^{7} + 626886 x^{6} + 184761 x^{5} - 104409 x^{4} - 34101 x^{3} + 16281 x^{2} - 2673 x + 243$ $3$ $3$ $5$ $15$ $C_7^3:C_6$ (as 15T44) $[3/2]$ $[3/2, 3/2, 3/2, 3/2, 3/2]_{2}^{5}$ $t^{5} + 2 t + 1$ $x^{3} + \left(6 t^{4} + 3 t^{3} + 6 t^{2} + 3 t + 3\right) x^{2} + \left(6 t^{4} + 6 t^{2} + 6 t + 3\right) x + 3$
3.15.15.42 $x^{15} + 174 x^{13} + 1347 x^{12} + 15768 x^{11} + 10539 x^{10} + 60840 x^{9} + 191079 x^{8} + 317277 x^{7} + 343143 x^{6} + 264141 x^{5} + 143694 x^{4} + 53865 x^{3} + 13851 x^{2} + 2430 x + 243$ $3$ $3$ $5$ $15$ $C_7^3:C_6$ (as 15T44) $[3/2]$ $[3/2, 3/2, 3/2, 3/2, 3/2]_{2}^{5}$ $t^{5} + 2 t + 1$ $x^{3} + \left(6 t^{3} + 3 t\right) x^{2} + \left(3 t^{3} + 3 t^{2} + 3 t + 6\right) x + 3$
3.15.15.43 $x^{15} - 9 x^{14} + 33 x^{13} + 420 x^{12} + 3717 x^{11} + 8523 x^{10} + 9486 x^{9} + 17577 x^{8} + 9963 x^{7} + 17280 x^{6} + 8505 x^{5} + 9153 x^{4} + 4050 x^{3} + 2673 x^{2} + 1215 x + 243$ $3$ $3$ $5$ $15$ $C_7^3:C_6$ (as 15T44) $[3/2]$ $[3/2, 3/2, 3/2, 3/2, 3/2]_{2}^{5}$ $t^{5} + 2 t + 1$ $x^{3} + \left(3 t^{4} + 3 t^{3} + 3\right) x^{2} + \left(3 t^{2} + 3 t + 3\right) x + 3$
3.15.15.44 $x^{15} + 6 x^{14} + 27 x^{13} + 294 x^{12} + 819 x^{11} + 1080 x^{10} + 144 x^{9} + 1863 x^{8} + 1296 x^{7} + 2781 x^{6} + 648 x^{5} + 3402 x^{4} - 1053 x^{3} + 972 x^{2} - 729 x + 243$ $3$ $3$ $5$ $15$ $C_7^3:C_6$ (as 15T44) $[3/2]$ $[3/2, 3/2, 3/2, 3/2, 3/2]_{2}^{5}$ $t^{5} + 2 t + 1$ $x^{3} + \left(3 t^{4} + 3 t^{2} + 6\right) x^{2} + \left(3 t^{4} + 3\right) x + 3$
3.15.15.45 $x^{15} + 30 x^{14} + 537 x^{13} + 4506 x^{12} + 15993 x^{11} + 25695 x^{10} + 92187 x^{9} + 252639 x^{8} + 4455 x^{7} + 407295 x^{6} - 319707 x^{5} + 423711 x^{4} - 153900 x^{3} + 34506 x^{2} - 3888 x + 243$ $3$ $3$ $5$ $15$ $C_7^3:C_6$ (as 15T44) $[3/2]$ $[3/2, 3/2, 3/2, 3/2, 3/2]_{2}^{5}$ $t^{5} + 2 t + 1$ $x^{3} + \left(3 t^{3} + 3 t^{2} + 6 t + 6\right) x^{2} + \left(6 t^{4} + 3 t^{3} + 6 t\right) x + 3$
3.15.15.46 $x^{15} - 24 x^{14} + 534 x^{13} - 3027 x^{12} - 4050 x^{11} + 27846 x^{10} + 80712 x^{9} + 24867 x^{8} + 95823 x^{7} + 308799 x^{6} + 148554 x^{5} - 44388 x^{4} - 16605 x^{3} + 13122 x^{2} - 2673 x + 243$ $3$ $3$ $5$ $15$ $C_7^3:C_6$ (as 15T44) $[3/2]$ $[3/2, 3/2, 3/2, 3/2, 3/2]_{2}^{5}$ $t^{5} + 2 t + 1$ $x^{3} + \left(3 t^{4} + 3 t^{3} + 6 t^{2} + 3 t\right) x^{2} + \left(6 t^{4} + 6 t + 3\right) x + 3$
3.15.15.47 $x^{15} - 33 x^{14} + 558 x^{13} - 4287 x^{12} + 13527 x^{11} + 60021 x^{10} + 8136 x^{9} + 9477 x^{8} + 159408 x^{7} + 18414 x^{6} - 108297 x^{5} + 58806 x^{4} + 35397 x^{3} + 729 x^{2} + 243$ $3$ $3$ $5$ $15$ $C_7^3:C_6$ (as 15T44) $[3/2]$ $[3/2, 3/2, 3/2, 3/2, 3/2]_{2}^{5}$ $t^{5} + 2 t + 1$ $x^{3} + \left(6 t^{4} + 6 t + 3\right) x^{2} + \left(6 t^{3} + 3 t^{2}\right) x + 3$
3.15.15.48 $x^{15} - 24 x^{14} + 333 x^{13} - 2856 x^{12} + 9477 x^{11} + 27486 x^{10} - 38493 x^{9} + 24705 x^{8} + 256527 x^{7} + 115533 x^{6} - 123363 x^{5} - 63909 x^{4} + 18144 x^{3} + 8019 x^{2} - 729 x + 243$ $3$ $3$ $5$ $15$ $C_7^3:C_6$ (as 15T44) $[3/2]$ $[3/2, 3/2, 3/2, 3/2, 3/2]_{2}^{5}$ $t^{5} + 2 t + 1$ $x^{3} + \left(3 t^{4} + 3 t^{2} + 6 t\right) x^{2} + \left(3 t^{4} + 3 t^{3} + 6 t^{2} + 3 t + 3\right) x + 3$
3.15.15.49 $x^{15} - 18 x^{14} + 87 x^{13} + 663 x^{12} + 7002 x^{11} + 59229 x^{10} + 24984 x^{9} + 28998 x^{8} + 14823 x^{7} + 8208 x^{6} + 729 x^{5} - 3969 x^{4} - 2997 x^{3} + 972 x^{2} + 1215 x + 243$ $3$ $3$ $5$ $15$ $S_3 \times C_5$ (as 15T4) $[3/2]$ $[3/2]_{2}^{5}$ $t^{5} + 2 t + 1$ $x^{3} + \left(6 t^{4} + 3 t^{3} + 6\right) x^{2} + 3 x + 3$
3.15.15.5 $x^{15} - 48 x^{14} + 1098 x^{13} - 12297 x^{12} + 42660 x^{11} + 120393 x^{10} - 110880 x^{9} - 19116 x^{8} + 192699 x^{7} + 53244 x^{6} - 21951 x^{5} + 6075 x^{4} - 1053 x^{3} - 2916 x^{2} + 243$ $3$ $3$ $5$ $15$ $C_7^3:C_6$ (as 15T44) $[3/2]$ $[3/2, 3/2, 3/2, 3/2, 3/2]_{2}^{5}$ $t^{5} + 2 t + 1$ $x^{3} + \left(6 t^{4} + 6 t^{2} + 3 t\right) x^{2} + \left(3 t^{2} + 6 t\right) x + 3$
3.15.15.50 $x^{15} + 15 x^{14} + 414 x^{13} + 8511 x^{12} + 79749 x^{11} + 298971 x^{10} + 462087 x^{9} + 525123 x^{8} + 543672 x^{7} + 408591 x^{6} + 255312 x^{5} + 135351 x^{4} + 37098 x^{3} + 8505 x^{2} + 243$ $3$ $3$ $5$ $15$ $C_3^4:C_{10}$ (as 15T33) $[3/2]$ $[3/2, 3/2, 3/2, 3/2]_{2}^{5}$ $t^{5} + 2 t + 1$ $x^{3} + \left(6 t^{3} + 6 t^{2} + 3\right) x^{2} + \left(6 t^{3} + 3 t^{2} + 3 t\right) x + 3$
3.15.15.51 $x^{15} + 3 x + 3$ $3$ $15$ $1$ $15$ $C_3^4:(C_2\times F_5)$ (as 15T52) $[11/10]$ $[11/10, 11/10, 11/10, 11/10]_{10}^{4}$ $t + 1$ $x^{15} + 3 x + 3$
3.15.15.52 $x^{15} + 3 x^{2} + 6 x + 3$ $3$ $15$ $1$ $15$ $C_3^4:(C_2\times F_5)$ (as 15T52) $[11/10]$ $[11/10, 11/10, 11/10, 11/10]_{10}^{4}$ $t + 1$ $x^{15} + 3 x^{2} + 6 x + 3$
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