LMFDB - p-adic families search results

The results below are complete, since the LMFDB contains all families of p-adic fields of degree at most 47 and residue characteristic at most 199

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Residue characteristic $p$	Degree $n$	Ramification index $e$	Residue field degree $f$	Discriminant exponent $c$

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Label	$p$	$n$	$f$	$e$	$c$	Abs. Artin slopes	Swan slopes	Means	Rams	Generic poly	Ambiguity	Field count	Mass	Mass (absolute)	Mass stored	Mass found	Wild segments	Num. Packets
2.32.1.0a	$2$	$32$	$32$	$1$	$0$	$[\ ]$	$[ ]$	$\langle \rangle$	$( )$	$x$	$32$	$0$	$1$	$1/32$	$0$	$0\%$	$0$	$0$
2.16.2.32a	$2$	$32$	$16$	$2$	$32$	$[2]$	$[1]$	$\langle\frac{1}{2}\rangle$	$(1)$	$x^2 + 2 a_{1} x + 4 c_{2} + 2$	$32$	$0$	$65535$	$65535/16$	$0$	$0\%$	$1$	$0$
2.16.2.48a	$2$	$32$	$16$	$2$	$48$	$[3]$	$[2]$	$\langle1\rangle$	$(2)$	$x^2 + 4 b_{3} x + 8 c_{4} + 2$	$32$	$0$	$65536$	$4096$	$0$	$0\%$	$1$	$0$
2.8.4.32a	$2$	$32$	$8$	$4$	$32$	$[\frac{4}{3}, \frac{4}{3}]$	$[\frac{1}{3}, \frac{1}{3}]$	$\langle\frac{1}{6}, \frac{1}{4}\rangle$	$(\frac{1}{3}, \frac{1}{3})$	$x^4 + 2 a_{1} x + 2$	$8$	$0$	$255$	$255/8$	$0$	$0\%$	$1$	$0$
2.8.4.48a	$2$	$32$	$8$	$4$	$48$	$[2, 2]$	$[1, 1]$	$\langle\frac{1}{2}, \frac{3}{4}\rangle$	$(1, 1)$	$x^4 + 2 a_{3} x^3 + 2 b_{2} x^2 + 4 c_{4} + 2$	$32$	$0$	$65280$	$8160$	$0$	$0\%$	$1$	$0$
2.8.4.64a	$2$	$32$	$8$	$4$	$64$	$[\frac{8}{3}, \frac{8}{3}]$	$[\frac{5}{3}, \frac{5}{3}]$	$\langle\frac{5}{6}, \frac{5}{4}\rangle$	$(\frac{5}{3}, \frac{5}{3})$	$x^4 + 4 b_{6} x^2 + 4 a_{5} x + 2$	$8$	$0$	$65280$	$8160$	$0$	$0\%$	$1$	$0$
2.8.4.64b	$2$	$32$	$8$	$4$	$64$	$[2, 3]$	$[1, 2]$	$\langle\frac{1}{2}, \frac{5}{4}\rangle$	$(1, 3)$	$x^4 + 4 b_{7} x^3 + 2 a_{2} x^2 + 4 a_{5} x + 4 c_{4} + 8 c_{8} + 2$	$32$	$0$	$16646400$	$2080800$	$0$	$0\%$	$2$	$0$
2.8.4.72a	$2$	$32$	$8$	$4$	$72$	$[2, \frac{7}{2}]$	$[1, \frac{5}{2}]$	$\langle\frac{1}{2}, \frac{3}{2}\rangle$	$(1, 4)$	$x^4 + 4 b_{7} x^3 + (2 a_{2} + 8 c_{10}) x^2 + 8 b_{9} x + 4 c_{4} + 2$	$32$	$0$	$16711680$	$2088960$	$0$	$0\%$	$2$	$0$
2.8.4.80a	$2$	$32$	$8$	$4$	$80$	$[3, \frac{7}{2}]$	$[2, \frac{5}{2}]$	$\langle1, \frac{7}{4}\rangle$	$(2, 3)$	$x^4 + 4 a_{7} x^3 + (4 b_{6} + 8 c_{10}) x^2 + 8 b_{9} x + 8 c_{8} + 2$	$32$	$0$	$16711680$	$2088960$	$0$	$0\%$	$2$	$0$
2.8.4.88a	$2$	$32$	$8$	$4$	$88$	$[3, 4]$	$[2, 3]$	$\langle1, 2\rangle$	$(2, 4)$	$x^4 + 8 b_{11} x^3 + 4 b_{6} x^2 + 8 b_{9} x + 8 c_{8} + 16 c_{12} + 2$	$32$	$0$	$16777216$	$2097152$	$0$	$0\%$	$2$	$0$
2.4.8.32a	$2$	$32$	$4$	$8$	$32$	$[\frac{8}{7}, \frac{8}{7}, \frac{8}{7}]$	$[\frac{1}{7}, \frac{1}{7}, \frac{1}{7}]$	$\langle\frac{1}{14}, \frac{3}{28}, \frac{1}{8}\rangle$	$(\frac{1}{7}, \frac{1}{7}, \frac{1}{7})$	$x^8 + 2 a_{1} x + 2$	$4$	$0$	$15$	$15/4$	$0$	$0\%$	$1$	$0$
2.4.8.40a	$2$	$32$	$4$	$8$	$40$	$[\frac{10}{7}, \frac{10}{7}, \frac{10}{7}]$	$[\frac{3}{7}, \frac{3}{7}, \frac{3}{7}]$	$\langle\frac{3}{14}, \frac{9}{28}, \frac{3}{8}\rangle$	$(\frac{3}{7}, \frac{3}{7}, \frac{3}{7})$	$x^8 + 2 a_{3} x^3 + 2$	$4$	$0$	$15$	$15/4$	$0$	$0\%$	$1$	$0$
2.4.8.40b	$2$	$32$	$4$	$8$	$40$	$[\frac{4}{3}, \frac{4}{3}, \frac{3}{2}]$	$[\frac{1}{3}, \frac{1}{3}, \frac{1}{2}]$	$\langle\frac{1}{6}, \frac{1}{4}, \frac{3}{8}\rangle$	$(\frac{1}{3}, \frac{1}{3}, 1)$	$x^8 + 2 c_{4} x^4 + 2 a_{3} x^3 + 2 a_{2} x^2 + 2$	$8$	$0$	$225$	$225/4$	$0$	$0\%$	$2$	$0$
2.4.8.48a	$2$	$32$	$4$	$8$	$48$	$[\frac{12}{7}, \frac{12}{7}, \frac{12}{7}]$	$[\frac{5}{7}, \frac{5}{7}, \frac{5}{7}]$	$\langle\frac{5}{14}, \frac{15}{28}, \frac{5}{8}\rangle$	$(\frac{5}{7}, \frac{5}{7}, \frac{5}{7})$	$x^8 + 2 a_{5} x^5 + 2 b_{4} x^4 + 2$	$4$	$0$	$240$	$60$	$0$	$0\%$	$1$	$0$
2.4.8.48b	$2$	$32$	$4$	$8$	$48$	$[\frac{4}{3}, \frac{4}{3}, 2]$	$[\frac{1}{3}, \frac{1}{3}, 1]$	$\langle\frac{1}{6}, \frac{1}{4}, \frac{5}{8}\rangle$	$(\frac{1}{3}, \frac{1}{3}, 3)$	$x^8 + 2 b_{7} x^7 + 2 a_{5} x^5 + 2 a_{2} x^2 + 4 c_{8} + 2$	$8$	$0$	$3600$	$900$	$0$	$0\%$	$2$	$0$
2.4.8.56a	$2$	$32$	$4$	$8$	$56$	$[2, 2, 2]$	$[1, 1, 1]$	$\langle\frac{1}{2}, \frac{3}{4}, \frac{7}{8}\rangle$	$(1, 1, 1)$	$x^8 + 2 a_{7} x^7 + 2 b_{6} x^6 + 2 b_{4} x^4 + 4 c_{8} + 2$	$32$	$0$	$3840$	$960$	$0$	$0\%$	$1$	$0$
2.4.8.56b	$2$	$32$	$4$	$8$	$56$	$[\frac{4}{3}, \frac{4}{3}, \frac{5}{2}]$	$[\frac{1}{3}, \frac{1}{3}, \frac{3}{2}]$	$\langle\frac{1}{6}, \frac{1}{4}, \frac{7}{8}\rangle$	$(\frac{1}{3}, \frac{1}{3}, 5)$	$x^8 + 2 a_{7} x^7 + 4 c_{12} x^4 + 4 b_{11} x^3 + 2 a_{2} x^2 + 4 b_{9} x + 2$	$8$	$0$	$57600$	$14400$	$0$	$0\%$	$2$	$0$
2.4.8.64a	$2$	$32$	$4$	$8$	$64$	$[\frac{16}{7}, \frac{16}{7}, \frac{16}{7}]$	$[\frac{9}{7}, \frac{9}{7}, \frac{9}{7}]$	$\langle\frac{9}{14}, \frac{27}{28}, \frac{9}{8}\rangle$	$(\frac{9}{7}, \frac{9}{7}, \frac{9}{7})$	$x^8 + 4 b_{10} x^2 + 4 a_{9} x + 2$	$4$	$0$	$240$	$60$	$0$	$0\%$	$1$	$0$
2.4.8.64b	$2$	$32$	$4$	$8$	$64$	$[\frac{4}{3}, \frac{4}{3}, 3]$	$[\frac{1}{3}, \frac{1}{3}, 2]$	$\langle\frac{1}{6}, \frac{1}{4}, \frac{9}{8}\rangle$	$(\frac{1}{3}, \frac{1}{3}, 7)$	$x^8 + 4 b_{15} x^7 + 4 b_{13} x^5 + 4 b_{11} x^3 + 2 a_{2} x^2 + 4 a_{9} x + 8 c_{16} + 2$	$8$	$0$	$921600$	$230400$	$0$	$0\%$	$2$	$0$
2.4.8.64c	$2$	$32$	$4$	$8$	$64$	$[2, 2, \frac{5}{2}]$	$[1, 1, \frac{3}{2}]$	$\langle\frac{1}{2}, \frac{3}{4}, \frac{9}{8}\rangle$	$(1, 1, 3)$	$x^8 + 2 a_{6} x^6 + (2 b_{4} + 4 c_{12}) x^4 + 4 b_{11} x^3 + 4 a_{9} x + 4 c_{8} + 2$	$32$	$0$	$57600$	$14400$	$0$	$0\%$	$2$	$0$
2.4.8.64d	$2$	$32$	$4$	$8$	$64$	$[2, \frac{7}{3}, \frac{7}{3}]$	$[1, \frac{4}{3}, \frac{4}{3}]$	$\langle\frac{1}{2}, \frac{11}{12}, \frac{9}{8}\rangle$	$(1, \frac{5}{3}, \frac{5}{3})$	$x^8 + 2 a_{4} x^4 + 4 b_{10} x^2 + 4 a_{9} x + 4 c_{8} + 2$	$8$	$0$	$3600$	$900$	$0$	$0\%$	$2$	$0$
2.4.8.68a	$2$	$32$	$4$	$8$	$68$	$[\frac{4}{3}, \frac{4}{3}, \frac{13}{4}]$	$[\frac{1}{3}, \frac{1}{3}, \frac{9}{4}]$	$\langle\frac{1}{6}, \frac{1}{4}, \frac{5}{4}\rangle$	$(\frac{1}{3}, \frac{1}{3}, 8)$	$x^8 + 4 b_{15} x^7 + 4 b_{13} x^5 + 4 b_{11} x^3 + (2 a_{2} + 8 c_{18}) x^2 + 8 b_{17} x + 2$	$8$	$0$	$983040$	$245760$	$0$	$0\%$	$2$	$0$
2.4.8.72a	$2$	$32$	$4$	$8$	$72$	$[\frac{18}{7}, \frac{18}{7}, \frac{18}{7}]$	$[\frac{11}{7}, \frac{11}{7}, \frac{11}{7}]$	$\langle\frac{11}{14}, \frac{33}{28}, \frac{11}{8}\rangle$	$(\frac{11}{7}, \frac{11}{7}, \frac{11}{7})$	$x^8 + 4 b_{12} x^4 + 4 a_{11} x^3 + 4 b_{10} x^2 + 2$	$4$	$0$	$3840$	$960$	$0$	$0\%$	$1$	$0$
2.4.8.72b	$2$	$32$	$4$	$8$	$72$	$[2, 2, 3]$	$[1, 1, 2]$	$\langle\frac{1}{2}, \frac{3}{4}, \frac{11}{8}\rangle$	$(1, 1, 5)$	$x^8 + 4 b_{15} x^7 + 2 a_{6} x^6 + 4 b_{13} x^5 + 2 b_{4} x^4 + 4 a_{11} x^3 + 4 c_{8} + 8 c_{16} + 2$	$32$	$0$	$921600$	$230400$	$0$	$0\%$	$2$	$0$
2.4.8.72c	$2$	$32$	$4$	$8$	$72$	$[2, \frac{8}{3}, \frac{8}{3}]$	$[1, \frac{5}{3}, \frac{5}{3}]$	$\langle\frac{1}{2}, \frac{13}{12}, \frac{11}{8}\rangle$	$(1, \frac{7}{3}, \frac{7}{3})$	$x^8 + 4 b_{13} x^5 + 2 a_{4} x^4 + 4 a_{11} x^3 + 4 b_{10} x^2 + 4 c_{8} + 2$	$8$	$0$	$57600$	$14400$	$0$	$0\%$	$2$	$0$
2.4.8.80a	$2$	$32$	$4$	$8$	$80$	$[\frac{20}{7}, \frac{20}{7}, \frac{20}{7}]$	$[\frac{13}{7}, \frac{13}{7}, \frac{13}{7}]$	$\langle\frac{13}{14}, \frac{39}{28}, \frac{13}{8}\rangle$	$(\frac{13}{7}, \frac{13}{7}, \frac{13}{7})$	$x^8 + 4 b_{14} x^6 + 4 a_{13} x^5 + 4 b_{12} x^4 + 2$	$4$	$0$	$3840$	$960$	$0$	$0\%$	$1$	$0$
2.4.8.80b	$2$	$32$	$4$	$8$	$80$	$[2, 2, \frac{7}{2}]$	$[1, 1, \frac{5}{2}]$	$\langle\frac{1}{2}, \frac{3}{4}, \frac{13}{8}\rangle$	$(1, 1, 7)$	$x^8 + 4 b_{15} x^7 + 2 a_{6} x^6 + 4 a_{13} x^5 + (2 b_{4} + 8 c_{20}) x^4 + 8 b_{19} x^3 + 8 b_{17} x + 4 c_{8} + 2$	$32$	$0$	$14745600$	$3686400$	$0$	$0\%$	$2$	$0$
2.4.8.80c	$2$	$32$	$4$	$8$	$80$	$[\frac{8}{3}, \frac{8}{3}, 3]$	$[\frac{5}{3}, \frac{5}{3}, 2]$	$\langle\frac{5}{6}, \frac{5}{4}, \frac{13}{8}\rangle$	$(\frac{5}{3}, \frac{5}{3}, 3)$	$x^8 + 4 b_{15} x^7 + 4 a_{13} x^5 + 4 b_{12} x^4 + 4 a_{10} x^2 + 8 c_{16} + 2$	$8$	$0$	$57600$	$14400$	$0$	$0\%$	$2$	$0$
2.4.8.80d	$2$	$32$	$4$	$8$	$80$	$[2, 3, 3]$	$[1, 2, 2]$	$\langle\frac{1}{2}, \frac{5}{4}, \frac{13}{8}\rangle$	$(1, 3, 3)$	$x^8 + 4 b_{15} x^7 + 4 b_{14} x^6 + 4 a_{13} x^5 + 2 a_{4} x^4 + 4 b_{10} x^2 + 4 c_{8} + 8 c_{16} + 2$	$32$	$0$	$921600$	$230400$	$0$	$0\%$	$2$	$0$
2.4.8.84a	$2$	$32$	$4$	$8$	$84$	$[2, 2, \frac{15}{4}]$	$[1, 1, \frac{11}{4}]$	$\langle\frac{1}{2}, \frac{3}{4}, \frac{7}{4}\rangle$	$(1, 1, 8)$	$x^8 + 4 b_{15} x^7 + (2 a_{6} + 8 c_{22}) x^6 + 8 b_{21} x^5 + 2 b_{4} x^4 + 8 b_{19} x^3 + 8 b_{17} x + 4 c_{8} + 2$	$32$	$0$	$15728640$	$3932160$	$0$	$0\%$	$2$	$0$
2.4.8.88a	$2$	$32$	$4$	$8$	$88$	$[\frac{8}{3}, \frac{8}{3}, \frac{7}{2}]$	$[\frac{5}{3}, \frac{5}{3}, \frac{5}{2}]$	$\langle\frac{5}{6}, \frac{5}{4}, \frac{15}{8}\rangle$	$(\frac{5}{3}, \frac{5}{3}, 5)$	$x^8 + 4 a_{15} x^7 + (4 b_{12} + 8 c_{20}) x^4 + 8 b_{19} x^3 + 4 a_{10} x^2 + 8 b_{17} x + 2$	$8$	$0$	$921600$	$230400$	$0$	$0\%$	$2$	$0$
2.4.8.88b	$2$	$32$	$4$	$8$	$88$	$[2, \frac{10}{3}, \frac{10}{3}]$	$[1, \frac{7}{3}, \frac{7}{3}]$	$\langle\frac{1}{2}, \frac{17}{12}, \frac{15}{8}\rangle$	$(1, \frac{11}{3}, \frac{11}{3})$	$x^8 + 4 a_{15} x^7 + 4 b_{14} x^6 + 2 a_{4} x^4 + 8 b_{18} x^2 + 8 b_{17} x + 4 c_{8} + 2$	$8$	$0$	$921600$	$230400$	$0$	$0\%$	$2$	$0$
2.4.8.88c	$2$	$32$	$4$	$8$	$88$	$[3, \frac{19}{6}, \frac{19}{6}]$	$[2, \frac{13}{6}, \frac{13}{6}]$	$\langle1, \frac{19}{12}, \frac{15}{8}\rangle$	$(2, \frac{7}{3}, \frac{7}{3})$	$x^8 + 4 a_{15} x^7 + 4 b_{14} x^6 + 4 b_{12} x^4 + 8 b_{17} x + 8 c_{16} + 2$	$8$	$0$	$61440$	$15360$	$0$	$0\%$	$2$	$0$
2.4.8.88d	$2$	$32$	$4$	$8$	$88$	$[2, 3, \frac{7}{2}]$	$[1, 2, \frac{5}{2}]$	$\langle\frac{1}{2}, \frac{5}{4}, \frac{15}{8}\rangle$	$(1, 3, 5)$	$x^8 + 4 a_{15} x^7 + 4 b_{14} x^6 + (2 a_{4} + 8 c_{20}) x^4 + 8 b_{19} x^3 + 4 a_{10} x^2 + 8 b_{17} x + 4 c_{8} + 8 c_{16} + 2$	$32$	$0$	$13824000$	$3456000$	$0$	$0\%$	$3$	$0$
2.4.8.96a	$2$	$32$	$4$	$8$	$96$	$[\frac{8}{3}, \frac{8}{3}, 4]$	$[\frac{5}{3}, \frac{5}{3}, 3]$	$\langle\frac{5}{6}, \frac{5}{4}, \frac{17}{8}\rangle$	$(\frac{5}{3}, \frac{5}{3}, 7)$	$x^8 + 8 b_{23} x^7 + 8 b_{21} x^5 + 4 b_{12} x^4 + 8 b_{19} x^3 + 4 a_{10} x^2 + 8 a_{17} x + 16 c_{24} + 2$	$8$	$0$	$14745600$	$3686400$	$0$	$0\%$	$2$	$0$
2.4.8.96b	$2$	$32$	$4$	$8$	$96$	$[3, \frac{7}{2}, \frac{7}{2}]$	$[2, \frac{5}{2}, \frac{5}{2}]$	$\langle1, \frac{7}{4}, \frac{17}{8}\rangle$	$(2, 3, 3)$	$x^8 + 4 b_{14} x^6 + (4 b_{12} + 8 c_{20}) x^4 + 8 b_{19} x^3 + 8 b_{18} x^2 + 8 a_{17} x + 8 c_{16} + 2$	$32$	$0$	$983040$	$245760$	$0$	$0\%$	$2$	$0$
2.4.8.96c	$2$	$32$	$4$	$8$	$96$	$[2, 3, 4]$	$[1, 2, 3]$	$\langle\frac{1}{2}, \frac{5}{4}, \frac{17}{8}\rangle$	$(1, 3, 7)$	$x^8 + 8 b_{23} x^7 + 4 b_{14} x^6 + 8 b_{21} x^5 + 2 a_{4} x^4 + 8 b_{19} x^3 + 4 a_{10} x^2 + 8 a_{17} x + 4 c_{8} + 8 c_{16} + 16 c_{24} + 2$	$32$	$0$	$221184000$	$55296000$	$0$	$0\%$	$3$	$0$
2.4.8.96d	$2$	$32$	$4$	$8$	$96$	$[2, \frac{7}{2}, \frac{15}{4}]$	$[1, \frac{5}{2}, \frac{11}{4}]$	$\langle\frac{1}{2}, \frac{3}{2}, \frac{17}{8}\rangle$	$(1, 4, 5)$	$x^8 + (4 b_{14} + 8 c_{22}) x^6 + 8 b_{21} x^5 + (2 a_{4} + 8 c_{20}) x^4 + 8 b_{19} x^3 + 8 b_{18} x^2 + 8 a_{17} x + 4 c_{8} + 2$	$32$	$0$	$14745600$	$3686400$	$0$	$0\%$	$3$	$0$
2.4.8.100a	$2$	$32$	$4$	$8$	$100$	$[\frac{8}{3}, \frac{8}{3}, \frac{17}{4}]$	$[\frac{5}{3}, \frac{5}{3}, \frac{13}{4}]$	$\langle\frac{5}{6}, \frac{5}{4}, \frac{9}{4}\rangle$	$(\frac{5}{3}, \frac{5}{3}, 8)$	$x^8 + 8 b_{23} x^7 + 8 b_{21} x^5 + 4 b_{12} x^4 + 8 b_{19} x^3 + (4 a_{10} + 16 c_{26}) x^2 + 16 b_{25} x + 2$	$8$	$0$	$15728640$	$3932160$	$0$	$0\%$	$2$	$0$
2.4.8.100b	$2$	$32$	$4$	$8$	$100$	$[2, 3, \frac{17}{4}]$	$[1, 2, \frac{13}{4}]$	$\langle\frac{1}{2}, \frac{5}{4}, \frac{9}{4}\rangle$	$(1, 3, 8)$	$x^8 + 8 b_{23} x^7 + 4 b_{14} x^6 + 8 b_{21} x^5 + 2 a_{4} x^4 + 8 b_{19} x^3 + (4 a_{10} + 16 c_{26}) x^2 + 16 b_{25} x + 4 c_{8} + 8 c_{16} + 2$	$32$	$0$	$235929600$	$58982400$	$0$	$0\%$	$3$	$0$
2.4.8.104a	$2$	$32$	$4$	$8$	$104$	$[3, \frac{23}{6}, \frac{23}{6}]$	$[2, \frac{17}{6}, \frac{17}{6}]$	$\langle1, \frac{23}{12}, \frac{19}{8}\rangle$	$(2, \frac{11}{3}, \frac{11}{3})$	$x^8 + 8 b_{22} x^6 + 8 b_{21} x^5 + 4 b_{12} x^4 + 8 a_{19} x^3 + 8 b_{18} x^2 + 8 c_{16} + 2$	$8$	$0$	$983040$	$245760$	$0$	$0\%$	$2$	$0$
2.4.8.104b	$2$	$32$	$4$	$8$	$104$	$[2, \frac{7}{2}, \frac{17}{4}]$	$[1, \frac{5}{2}, \frac{13}{4}]$	$\langle\frac{1}{2}, \frac{3}{2}, \frac{19}{8}\rangle$	$(1, 4, 7)$	$x^8 + 8 b_{23} x^7 + 4 b_{14} x^6 + 8 b_{21} x^5 + (2 a_{4} + 8 c_{20}) x^4 + 8 a_{19} x^3 + (8 b_{18} + 16 c_{26}) x^2 + 16 b_{25} x + 4 c_{8} + 2$	$32$	$0$	$235929600$	$58982400$	$0$	$0\%$	$3$	$0$
2.4.8.104c	$2$	$32$	$4$	$8$	$104$	$[3, \frac{7}{2}, 4]$	$[2, \frac{5}{2}, 3]$	$\langle1, \frac{7}{4}, \frac{19}{8}\rangle$	$(2, 3, 5)$	$x^8 + 8 b_{23} x^7 + 4 a_{14} x^6 + 8 b_{21} x^5 + (4 b_{12} + 8 c_{20}) x^4 + 8 a_{19} x^3 + 8 b_{18} x^2 + 8 c_{16} + 16 c_{24} + 2$	$32$	$0$	$14745600$	$3686400$	$0$	$0\%$	$3$	$0$
2.4.8.108a	$2$	$32$	$4$	$8$	$108$	$[2, \frac{7}{2}, \frac{9}{2}]$	$[1, \frac{5}{2}, \frac{7}{2}]$	$\langle\frac{1}{2}, \frac{3}{2}, \frac{5}{2}\rangle$	$(1, 4, 8)$	$x^8 + 8 b_{23} x^7 + 4 b_{14} x^6 + 8 b_{21} x^5 + (2 a_{4} + 8 c_{20} + 16 c_{28}) x^4 + 16 b_{27} x^3 + 8 b_{18} x^2 + 16 b_{25} x + 4 c_{8} + 2$	$32$	$0$	$251658240$	$62914560$	$0$	$0\%$	$3$	$0$
2.4.8.112a	$2$	$32$	$4$	$8$	$112$	$[3, \frac{7}{2}, \frac{9}{2}]$	$[2, \frac{5}{2}, \frac{7}{2}]$	$\langle1, \frac{7}{4}, \frac{21}{8}\rangle$	$(2, 3, 7)$	$x^8 + 8 b_{23} x^7 + 4 a_{14} x^6 + 8 a_{21} x^5 + (4 b_{12} + 8 c_{20} + 16 c_{28}) x^4 + 16 b_{27} x^3 + 8 b_{18} x^2 + 16 b_{25} x + 8 c_{16} + 2$	$32$	$0$	$235929600$	$58982400$	$0$	$0\%$	$3$	$0$
2.4.8.112b	$2$	$32$	$4$	$8$	$112$	$[3, 4, \frac{17}{4}]$	$[2, 3, \frac{13}{4}]$	$\langle1, 2, \frac{21}{8}\rangle$	$(2, 4, 5)$	$x^8 + 8 b_{23} x^7 + 8 b_{22} x^6 + 8 a_{21} x^5 + 4 b_{12} x^4 + (8 b_{18} + 16 c_{26}) x^2 + 16 b_{25} x + 8 c_{16} + 16 c_{24} + 2$	$32$	$0$	$15728640$	$3932160$	$0$	$0\%$	$3$	$0$
2.4.8.116a	$2$	$32$	$4$	$8$	$116$	$[3, \frac{7}{2}, \frac{19}{4}]$	$[2, \frac{5}{2}, \frac{15}{4}]$	$\langle1, \frac{7}{4}, \frac{11}{4}\rangle$	$(2, 3, 8)$	$x^8 + 8 b_{23} x^7 + (4 a_{14} + 16 c_{30}) x^6 + 16 b_{29} x^5 + (4 b_{12} + 8 c_{20}) x^4 + 16 b_{27} x^3 + 8 b_{18} x^2 + 16 b_{25} x + 8 c_{16} + 2$	$32$	$0$	$251658240$	$62914560$	$0$	$0\%$	$3$	$0$
2.4.8.120a	$2$	$32$	$4$	$8$	$120$	$[3, 4, \frac{19}{4}]$	$[2, 3, \frac{15}{4}]$	$\langle1, 2, \frac{23}{8}\rangle$	$(2, 4, 7)$	$x^8 + 8 a_{23} x^7 + (8 b_{22} + 16 c_{30}) x^6 + 16 b_{29} x^5 + 4 b_{12} x^4 + 16 b_{27} x^3 + 8 b_{18} x^2 + 16 b_{25} x + 8 c_{16} + 16 c_{24} + 2$	$32$	$0$	$251658240$	$62914560$	$0$	$0\%$	$3$	$0$
2.4.8.124a	$2$	$32$	$4$	$8$	$124$	$[3, 4, 5]$	$[2, 3, 4]$	$\langle1, 2, 3\rangle$	$(2, 4, 8)$	$x^8 + 16 b_{31} x^7 + 8 b_{22} x^6 + 16 b_{29} x^5 + 4 b_{12} x^4 + 16 b_{27} x^3 + 8 b_{18} x^2 + 16 b_{25} x + 8 c_{16} + 16 c_{24} + 32 c_{32} + 2$	$32$	$0$	$268435456$	$67108864$	$0$	$0\%$	$3$	$0$
2.2.16.32a	$2$	$32$	$2$	$16$	$32$	$[\frac{16}{15}, \frac{16}{15}, \frac{16}{15}, \frac{16}{15}]$	$[\frac{1}{15}, \frac{1}{15}, \frac{1}{15}, \frac{1}{15}]$	$\langle\frac{1}{30}, \frac{1}{20}, \frac{7}{120}, \frac{1}{16}\rangle$	$(\frac{1}{15}, \frac{1}{15}, \frac{1}{15}, \frac{1}{15})$	$x^{16} + 2 a_{1} x + 2$	$2$	$0$	$3$	$3/2$	$0$	$0\%$	$1$	$0$

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This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.