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Label Polynomial $p$ $e$ $f$ $c$ Galois group Visible slopes Slope content Unram. Ext. Eisen. Poly.
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) $[3/2]$ $[3/2, 3/2, 3/2, 3/2, 3/2]_{2}^{5}$ $t^{5} + 2 t + 1$ $x^{3} + \left(6 t^{4} + 3 t\right) x^{2} + \left(6 t^{4} + 6 t^{2} + 3 t\right) x + 3$
3.15.15.13 $x^{15} - 33 x^{14} + 393 x^{13} - 1317 x^{12} + 12267 x^{11} + 29070 x^{10} + 19206 x^{9} + 4131 x^{8} + 7209 x^{7} + 104274 x^{6} + 116964 x^{5} + 74277 x^{4} + 22761 x^{3} + 6075 x^{2} + 1215 x + 243$ $3$ $3$ $5$ $15$ $C_7^3:C_6$ (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) $[3/2]$ $[3/2, 3/2, 3/2, 3/2, 3/2]_{2}^{5}$ $t^{5} + 2 t + 1$ $x^{3} + 3 t^{2} x^{2} + \left(3 t^{3} + 3\right) x + 3$
3.15.15.16 $x^{15} - 18 x^{14} + 174 x^{13} + 348 x^{12} - 9234 x^{11} + 11889 x^{10} + 136521 x^{9} + 196020 x^{8} + 62451 x^{7} - 5157 x^{6} + 3645 x^{5} - 32238 x^{4} - 16605 x^{3} + 13851 x^{2} - 1944 x + 243$ $3$ $3$ $5$ $15$ $C_7^3:C_6$ (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) $[3/2]$ $[3/2, 3/2, 3/2, 3/2, 3/2]_{2}^{5}$ $t^{5} + 2 t + 1$ $x^{3} + \left(3 t^{4} + 6 t^{2} + 6 t + 6\right) x^{2} + \left(6 t^{4} + 6 t^{3} + 3 t + 3\right) x + 3$
3.15.15.21 $x^{15} + 6 x^{14} + 216 x^{13} + 4272 x^{12} + 32373 x^{11} + 101574 x^{10} + 55899 x^{9} - 94851 x^{8} - 2511 x^{7} + 76572 x^{6} + 21789 x^{5} + 41553 x^{4} - 7857 x^{3} + 17496 x^{2} - 1458 x + 243$ $3$ $3$ $5$ $15$ $C_7^3:C_6$ (as 15T44) $[3/2]$ $[3/2, 3/2, 3/2, 3/2, 3/2]_{2}^{5}$ $t^{5} + 2 t + 1$ $x^{3} + \left(3 t^{4} + 3 t^{3} + 6 t^{2} + 6\right) x^{2} + \left(6 t^{4} + 3 t^{3} + 6 t^{2} + 6 t + 6\right) x + 3$
3.15.15.24 $x^{15} + 150 x^{13} - 2235 x^{12} + 11961 x^{11} - 32922 x^{10} + 45342 x^{9} - 17577 x^{8} - 6723 x^{7} - 34884 x^{6} + 193671 x^{5} + 181197 x^{4} + 39285 x^{3} + 5103 x^{2} + 486 x + 243$ $3$ $3$ $5$ $15$ $C_7^3:C_6$ (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) $[3/2]$ $[3/2, 3/2, 3/2, 3/2, 3/2]_{2}^{5}$ $t^{5} + 2 t + 1$ $x^{3} + \left(6 t^{3} + 6 t + 3\right) x^{2} + \left(3 t^{4} + 6 t^{3} + 6 t^{2} + 6 t\right) x + 3$
3.15.15.30 $x^{15} - 18 x^{14} + 540 x^{13} - 885 x^{12} + 67428 x^{11} + 364662 x^{10} + 236880 x^{9} + 45198 x^{8} + 204282 x^{7} + 233712 x^{6} + 65367 x^{5} + 13608 x^{4} + 13527 x^{3} + 2430 x^{2} + 243$ $3$ $3$ $5$ $15$ $C_7^3:C_6$ (as 15T44) $[3/2]$ $[3/2, 3/2, 3/2, 3/2, 3/2]_{2}^{5}$ $t^{5} + 2 t + 1$ $x^{3} + \left(6 t^{4} + 6 t^{3} + 6 t + 6\right) x^{2} + \left(3 t^{3} + 6 t\right) x + 3$
3.15.15.33 $x^{15} - 18 x^{14} + 129 x^{13} + 303 x^{12} - 5427 x^{11} + 14859 x^{10} + 179100 x^{9} + 421929 x^{8} + 433917 x^{7} + 265626 x^{6} + 127089 x^{5} + 1296 x^{4} - 17334 x^{3} + 13122 x^{2} - 2673 x + 243$ $3$ $3$ $5$ $15$ $C_7^3:C_6$ (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) $[3/2]$ $[3/2, 3/2, 3/2, 3/2, 3/2]_{2}^{5}$ $t^{5} + 2 t + 1$ $x^{3} + \left(6 t^{4} + 3 t^{3} + 6 t^{2} + 3\right) x^{2} + \left(6 t^{4} + 6 t^{3} + 3 t\right) x + 3$
3.15.15.39 $x^{15} - 18 x^{14} + 636 x^{13} - 1623 x^{12} - 378 x^{11} + 83475 x^{10} + 197730 x^{9} + 142074 x^{8} + 49653 x^{7} + 194913 x^{6} + 392931 x^{5} + 317520 x^{4} + 107811 x^{3} + 12393 x^{2} + 486 x + 243$ $3$ $3$ $5$ $15$ $C_7^3:C_6$ (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) $[3/2]$ $[3/2, 3/2, 3/2, 3/2, 3/2]_{2}^{5}$ $t^{5} + 2 t + 1$ $x^{3} + \left(3 t^{4} + 3 t^{2} + 6 t\right) x^{2} + \left(3 t^{4} + 3 t^{3} + 6 t^{2} + 3 t + 3\right) x + 3$
3.15.15.5 $x^{15} - 48 x^{14} + 1098 x^{13} - 12297 x^{12} + 42660 x^{11} + 120393 x^{10} - 110880 x^{9} - 19116 x^{8} + 192699 x^{7} + 53244 x^{6} - 21951 x^{5} + 6075 x^{4} - 1053 x^{3} - 2916 x^{2} + 243$ $3$ $3$ $5$ $15$ $C_7^3:C_6$ (as 15T44) $[3/2]$ $[3/2, 3/2, 3/2, 3/2, 3/2]_{2}^{5}$ $t^{5} + 2 t + 1$ $x^{3} + \left(6 t^{4} + 6 t^{2} + 3 t\right) x^{2} + \left(3 t^{2} + 6 t\right) x + 3$
3.15.15.7 $x^{15} - 9 x^{14} + 84 x^{13} + 42 x^{12} - 279 x^{11} + 1440 x^{10} - 180 x^{9} + 2754 x^{8} - 648 x^{7} - 2079 x^{6} + 243 x^{5} + 8586 x^{4} + 14013 x^{3} + 9963 x^{2} + 2430 x + 243$ $3$ $3$ $5$ $15$ $C_7^3:C_6$ (as 15T44) $[3/2]$ $[3/2, 3/2, 3/2, 3/2, 3/2]_{2}^{5}$ $t^{5} + 2 t + 1$ $x^{3} + \left(3 t^{4} + 3 t^{2} + 3\right) x^{2} + \left(3 t^{2} + 6 t + 6\right) x + 3$
3.15.15.8 $x^{15} + 6 x^{14} + 63 x^{13} + 1815 x^{12} + 15750 x^{11} + 55431 x^{10} + 102339 x^{9} + 205983 x^{8} + 352188 x^{7} + 333585 x^{6} + 167103 x^{5} + 57348 x^{4} - 3240 x^{3} + 6804 x^{2} - 1458 x + 243$ $3$ $3$ $5$ $15$ $C_7^3:C_6$ (as 15T44) $[3/2]$ $[3/2, 3/2, 3/2, 3/2, 3/2]_{2}^{5}$ $t^{5} + 2 t + 1$ $x^{3} + \left(3 t^{4} + 3 t^{3} + 3 t^{2} + 6\right) x^{2} + \left(6 t^{4} + 3 t^{3} + 3 t + 6\right) x + 3$
3.15.20.11 $x^{15} - 48 x^{14} + 990 x^{13} - 3603 x^{12} + 17568 x^{11} - 9072 x^{10} + 122886 x^{9} + 357534 x^{8} + 133164 x^{7} + 3850848 x^{6} - 281475 x^{5} + 13592691 x^{4} - 241623 x^{3} + 15534747 x^{2} + 5605524$ $3$ $3$ $5$ $20$ $C_7^3:C_6$ (as 15T44) $[2]$ $[2, 2, 2, 2, 2]^{10}$ $t^{5} + 2 t + 1$ $x^{3} + \left(6 t^{4} + 6 t^{3} + 3 t^{2}\right) x^{2} + 18 t^{4} + 9 t + 21$
3.15.20.14 $x^{15} - 24 x^{14} + 216 x^{13} + 960 x^{12} + 16992 x^{11} - 20817 x^{10} + 83844 x^{9} + 4293 x^{8} + 277506 x^{7} + 108162 x^{6} + 182574 x^{5} + 1027890 x^{4} + 279612 x^{3} + 851715 x^{2} + 1106865$ $3$ $3$ $5$ $20$ $C_7^3:C_6$ (as 15T44) $[2]$ $[2, 2, 2, 2, 2]^{10}$ $t^{5} + 2 t + 1$ $x^{3} + \left(3 t^{4} + 6 t^{3}\right) x^{2} + 9 t^{4} + 18 t + 12$
3.15.20.17 $x^{15} - 33 x^{14} + 558 x^{13} - 4485 x^{12} + 17181 x^{11} + 36045 x^{10} - 126162 x^{9} + 355185 x^{8} + 441774 x^{7} - 668952 x^{6} - 526986 x^{5} + 2487834 x^{4} + 1208601 x^{3} - 886221 x^{2} + 7056234$ $3$ $3$ $5$ $20$ $C_7^3:C_6$ (as 15T44) $[2]$ $[2, 2, 2, 2, 2]^{10}$ $t^{5} + 2 t + 1$ $x^{3} + \left(6 t^{4} + 6 t + 3\right) x^{2} + 9 t^{3} + 21$
3.15.20.2 $x^{15} + 6 x^{14} + 189 x^{13} + 321 x^{12} - 1980 x^{11} + 9072 x^{10} - 55935 x^{9} - 77193 x^{8} + 33291 x^{7} + 582984 x^{6} + 438777 x^{5} + 3456918 x^{4} + 1635066 x^{3} + 3636738 x^{2} - 8018757$ $3$ $3$ $5$ $20$ $C_7^3:C_6$ (as 15T44) $[2]$ $[2, 2, 2, 2, 2]^{10}$ $t^{5} + 2 t + 1$ $x^{3} + \left(3 t^{4} + 6 t^{2} + 3 t + 6\right) x^{2} + 9 t^{4} + 9 t^{3} + 18 t + 3$
3.15.20.22 $x^{15} - 9 x^{14} + 720 x^{13} + 1185 x^{12} + 12312 x^{11} + 2673 x^{10} + 119025 x^{9} + 76059 x^{8} + 544077 x^{7} + 269271 x^{6} + 897156 x^{5} - 200718 x^{4} + 583119 x^{3} - 1163484 x^{2} - 1000674$ $3$ $3$ $5$ $20$ $C_7^3:C_6$ (as 15T44) $[2]$ $[2, 2, 2, 2, 2]^{10}$ $t^{5} + 2 t + 1$ $x^{3} + \left(3 t^{4} + 6 t^{3} + 6 t^{2} + 6 t + 3\right) x^{2} + 9 t^{4} + 9 t^{3} + 9 t + 3$
3.15.20.23 $x^{15} + 6 x^{14} + 81 x^{13} + 1887 x^{12} + 12060 x^{11} + 34182 x^{10} + 145593 x^{9} + 446472 x^{8} + 538974 x^{7} + 2789910 x^{6} + 930123 x^{5} + 7395705 x^{4} + 1208601 x^{3} + 9607977 x^{2} + 7056234$ $3$ $3$ $5$ $20$ $C_7^3:C_6$ (as 15T44) $[2]$ $[2, 2, 2, 2, 2]^{10}$ $t^{5} + 2 t + 1$ $x^{3} + \left(3 t^{4} + 3 t^{3} + 3 t^{2} + 6\right) x^{2} + 9 t^{3} + 21$
3.15.20.25 $x^{15} - 48 x^{14} + 1422 x^{13} - 11379 x^{12} + 37548 x^{11} + 5346 x^{10} - 142146 x^{9} + 202257 x^{8} - 13608 x^{7} - 338472 x^{6} + 279855 x^{5} - 291114 x^{4} + 240975 x^{3} + 633987 x^{2} + 656343$ $3$ $3$ $5$ $20$ $C_7^3:C_6$ (as 15T44) $[2]$ $[2, 2, 2, 2, 2]^{10}$ $t^{5} + 2 t + 1$ $x^{3} + \left(6 t^{4} + 6 t^{3} + 6 t^{2} + 3 t\right) x^{2} + 9 t^{3} + 9 t^{2} + 3$
3.15.20.29 $x^{15} + 144 x^{13} + 1059 x^{12} + 10719 x^{11} - 6561 x^{10} + 163359 x^{9} + 4374 x^{8} + 1167615 x^{7} + 1900044 x^{6} + 4064175 x^{5} + 15095646 x^{4} + 5310198 x^{3} + 46605699 x^{2} + 54370521$ $3$ $3$ $5$ $20$ $C_7^3:C_6$ (as 15T44) $[2]$ $[2, 2, 2, 2, 2]^{10}$ $t^{5} + 2 t + 1$ $x^{3} + \left(6 t^{3} + 3 t\right) x^{2} + 9 t^{4} + 18 t^{3} + 9 t^{2} + 21$
3.15.20.3 $x^{15} + 15 x^{14} + 234 x^{13} + 1203 x^{12} + 7443 x^{11} + 486 x^{10} + 25443 x^{9} - 15957 x^{8} + 41796 x^{7} - 50274 x^{6} + 35154 x^{5} - 73872 x^{4} + 13527 x^{3} - 56376 x^{2} - 19440$ $3$ $3$ $5$ $20$ $C_7^3:C_6$ (as 15T44) $[2]$ $[2, 2, 2, 2, 2]^{10}$ $t^{5} + 2 t + 1$ $x^{3} + \left(3 t^{3} + 6 t + 3\right) x^{2} + 9 t + 3$
3.15.20.32 $x^{15} - 24 x^{14} + 297 x^{13} - 507 x^{12} + 63 x^{11} + 4779 x^{10} - 11682 x^{9} + 15714 x^{8} - 28188 x^{7} + 50328 x^{6} - 51435 x^{5} + 112266 x^{4} - 15147 x^{3} + 147501 x^{2} + 152604$ $3$ $3$ $5$ $20$ $C_7^3:C_6$ (as 15T44) $[2]$ $[2, 2, 2, 2, 2]^{10}$ $t^{5} + 2 t + 1$ $x^{3} + \left(3 t^{4} + 3 t^{3} + 3 t^{2}\right) x^{2} + 9 t^{4} + 9 t^{2} + 9 t + 21$
3.15.20.43 $x^{15} - 24 x^{14} + 261 x^{13} - 1443 x^{12} + 4059 x^{11} - 4050 x^{10} + 6651 x^{9} - 2511 x^{8} - 3645 x^{7} + 17766 x^{6} + 8343 x^{5} - 11178 x^{4} + 79137 x^{3} - 70470 x^{2} + 138024$ $3$ $3$ $5$ $20$ $C_7^3:C_6$ (as 15T44) $[2]$ $[2, 2, 2, 2, 2]^{10}$ $t^{5} + 2 t + 1$ $x^{3} + \left(3 t^{4} + 3 t\right) x^{2} + 9 t^{3} + 3$
3.15.20.47 $x^{15} - 9 x^{14} + 369 x^{13} + 150 x^{12} - 486 x^{11} - 2430 x^{10} - 8982 x^{9} + 39366 x^{8} + 62208 x^{7} + 497934 x^{6} + 288441 x^{5} + 1624698 x^{4} + 376569 x^{3} + 2388204 x^{2} + 1235898$ $3$ $3$ $5$ $20$ $C_7^3:C_6$ (as 15T44) $[2]$ $[2, 2, 2, 2, 2]^{10}$ $t^{5} + 2 t + 1$ $x^{3} + \left(3 t^{4} + 3 t^{3} + 6 t^{2} + 3 t + 3\right) x^{2} + 18 t^{2} + 9 t + 3$
3.15.20.5 $x^{15} + 30 x^{14} + 396 x^{13} + 1635 x^{12} + 3303 x^{11} + 12393 x^{10} + 29331 x^{9} + 58968 x^{8} + 92097 x^{7} + 319329 x^{6} + 237249 x^{5} + 820611 x^{4} + 580689 x^{3} + 2432916 x^{2} + 4094307$ $3$ $3$ $5$ $20$ $C_7^3:C_6$ (as 15T44) $[2]$ $[2, 2, 2, 2, 2]^{10}$ $t^{5} + 2 t + 1$ $x^{3} + \left(3 t^{2} + 6 t + 6\right) x^{2} + 18 t^{4} + 9 t^{3} + 9 t^{2} + 21$
3.15.20.75 $x^{15} + 6 x^{14} + 351 x^{13} + 3300 x^{12} + 10602 x^{11} + 37908 x^{10} + 132255 x^{9} + 270297 x^{8} + 691821 x^{7} + 1554012 x^{6} + 1636524 x^{5} + 5551335 x^{4} + 1444311 x^{3} + 10058499 x^{2} + 6897312$ $3$ $3$ $5$ $20$ $C_7^3:C_6$ (as 15T44) $[2]$ $[2, 2, 2, 2, 2]^{10}$ $t^{5} + 2 t + 1$ $x^{3} + \left(3 t^{4} + 3 t^{3} + 6 t^{2} + 3 t + 6\right) x^{2} + 9 t^{3} + 18 t^{2} + 9 t + 12$
3.15.20.8 $x^{15} + 36 x^{13} - 57 x^{12} + 1026 x^{11} - 729 x^{10} + 11619 x^{9} + 13851 x^{8} + 85050 x^{7} + 227475 x^{6} + 224532 x^{5} + 671652 x^{4} + 968031 x^{3} + 1350837 x^{2} + 2809080$ $3$ $3$ $5$ $20$ $C_7^3:C_6$ (as 15T44) $[2]$ $[2, 2, 2, 2, 2]^{10}$ $t^{5} + 2 t + 1$ $x^{3} + 3 t^{2} x^{2} + 9 t^{4} + 18 t^{3} + 18 t^{2} + 3$
3.15.20.9 $x^{15} + 30 x^{14} + 360 x^{13} + 2193 x^{12} + 10998 x^{11} + 39852 x^{10} + 112410 x^{9} + 260658 x^{8} + 512244 x^{7} + 1469934 x^{6} + 582066 x^{5} + 4686984 x^{4} + 3252231 x^{3} + 12108204 x^{2} + 44321256$ $3$ $3$ $5$ $20$ $C_7^3:C_6$ (as 15T44) $[2]$ $[2, 2, 2, 2, 2]^{10}$ $t^{5} + 2 t + 1$ $x^{3} + \left(6 t + 6\right) x^{2} + 9 t^{4} + 18 t^{3} + 21$
3.15.25.1 $x^{15} - 144 x^{14} + 8928 x^{13} - 268815 x^{12} + 3293595 x^{11} - 2677644 x^{10} + 27392778 x^{9} + 95260860 x^{8} + 89837829 x^{7} + 94301280 x^{6} + 184425093 x^{5} + 168206301 x^{4} + 29757699 x^{3} - 27476010 x^{2} - 6703884 x + 3121821$ $3$ $3$ $5$ $25$ $C_7^3:C_6$ (as 15T44) $[5/2]$ $[3/2, 3/2, 3/2, 3/2, 5/2]_{2}^{5}$ $t^{5} + 2 t + 1$ $x^{3} + \left(18 t^{4} + 9 t^{2} + 9 t\right) x^{2} + \left(9 t^{4} + 9 t^{2} + 18 t + 18\right) x + 18 t^{2} + 18 t + 21$
3.15.25.10 $x^{15} - 144 x^{14} + 8190 x^{13} - 204105 x^{12} + 1735884 x^{11} + 2426463 x^{10} + 17777808 x^{9} - 23327757 x^{8} + 46949544 x^{7} - 13219416 x^{6} + 25554852 x^{5} + 13774698 x^{4} + 10060605 x^{3} - 840537 x^{2} + 545292 x - 837378$ $3$ $3$ $5$ $25$ $C_7^3:C_6$ (as 15T44) $[5/2]$ $[3/2, 3/2, 3/2, 3/2, 5/2]_{2}^{5}$ $t^{5} + 2 t + 1$ $x^{3} + \left(18 t^{4} + 9 t^{2}\right) x^{2} + \left(18 t + 18\right) x + 9 t^{2} + 18 t + 3$
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