| 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 |
| 3.27.1.0a |
$3$ |
$27$ |
$27$ |
$1$ |
$0$ |
$[\ ]$ |
$[ ]$ |
$\langle \rangle$ |
$( )$ |
$x$ |
$27$ |
$0$ |
$1$ |
$1/27$ |
$0$ |
$0\%$ |
$0$ |
$0$ |
| 3.9.3.27a |
$3$ |
$27$ |
$9$ |
$3$ |
$27$ |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
$\langle\frac{1}{3}\rangle$ |
$(\frac{1}{2})$ |
$x^3 + 3 a_{1} x + 3$ |
$9$ |
$0$ |
$19682$ |
$19682/9$ |
$0$ |
$0\%$ |
$1$ |
$0$ |
| 3.9.3.36a |
$3$ |
$27$ |
$9$ |
$3$ |
$36$ |
$[2]$ |
$[1]$ |
$\langle\frac{2}{3}\rangle$ |
$(1)$ |
$x^3 + 3 a_{2} x^2 + 9 c_{3} + 3$ |
$27$ |
$0$ |
$19682$ |
$19682/9$ |
$0$ |
$0\%$ |
$1$ |
$0$ |
| 3.9.3.45a |
$3$ |
$27$ |
$9$ |
$3$ |
$45$ |
$[\frac{5}{2}]$ |
$[\frac{3}{2}]$ |
$\langle1\rangle$ |
$(\frac{3}{2})$ |
$x^3 + 9 b_{4} x + 3$ |
$9$ |
$0$ |
$19683$ |
$2187$ |
$0$ |
$0\%$ |
$1$ |
$0$ |
| 3.3.9.27a |
$3$ |
$27$ |
$3$ |
$9$ |
$27$ |
$[\frac{9}{8}, \frac{9}{8}]$ |
$[\frac{1}{8}, \frac{1}{8}]$ |
$\langle\frac{1}{12}, \frac{1}{9}\rangle$ |
$(\frac{1}{8}, \frac{1}{8})$ |
$x^9 + 3 a_{1} x + 3$ |
$3$ |
$0$ |
$26$ |
$26/3$ |
$0$ |
$0\%$ |
$1$ |
$0$ |
| 3.3.9.30a |
$3$ |
$27$ |
$3$ |
$9$ |
$30$ |
$[\frac{5}{4}, \frac{5}{4}]$ |
$[\frac{1}{4}, \frac{1}{4}]$ |
$\langle\frac{1}{6}, \frac{2}{9}\rangle$ |
$(\frac{1}{4}, \frac{1}{4})$ |
$x^9 + 3 a_{2} x^2 + 3$ |
$3$ |
$0$ |
$26$ |
$26/3$ |
$0$ |
$0\%$ |
$1$ |
$0$ |
| 3.3.9.36a |
$3$ |
$27$ |
$3$ |
$9$ |
$36$ |
$[\frac{3}{2}, \frac{3}{2}]$ |
$[\frac{1}{2}, \frac{1}{2}]$ |
$\langle\frac{1}{3}, \frac{4}{9}\rangle$ |
$(\frac{1}{2}, \frac{1}{2})$ |
$x^9 + 3 a_{4} x^4 + 3 b_{3} x^3 + 3$ |
$3$ |
$0$ |
$702$ |
$234$ |
$0$ |
$0\%$ |
$1$ |
$0$ |
| 3.3.9.39a |
$3$ |
$27$ |
$3$ |
$9$ |
$39$ |
$[\frac{13}{8}, \frac{13}{8}]$ |
$[\frac{5}{8}, \frac{5}{8}]$ |
$\langle\frac{5}{12}, \frac{5}{9}\rangle$ |
$(\frac{5}{8}, \frac{5}{8})$ |
$x^9 + 3 a_{5} x^5 + 3$ |
$3$ |
$0$ |
$26$ |
$26/3$ |
$0$ |
$0\%$ |
$1$ |
$0$ |
| 3.3.9.39b |
$3$ |
$27$ |
$3$ |
$9$ |
$39$ |
$[\frac{3}{2}, \frac{5}{3}]$ |
$[\frac{1}{2}, \frac{2}{3}]$ |
$\langle\frac{1}{3}, \frac{5}{9}\rangle$ |
$(\frac{1}{2}, 1)$ |
$x^9 + 3 c_{6} x^6 + 3 a_{5} x^5 + 3 a_{3} x^3 + 3$ |
$9$ |
$0$ |
$676$ |
$676/3$ |
$0$ |
$0\%$ |
$2$ |
$0$ |
| 3.3.9.45a |
$3$ |
$27$ |
$3$ |
$9$ |
$45$ |
$[\frac{15}{8}, \frac{15}{8}]$ |
$[\frac{7}{8}, \frac{7}{8}]$ |
$\langle\frac{7}{12}, \frac{7}{9}\rangle$ |
$(\frac{7}{8}, \frac{7}{8})$ |
$x^9 + 3 a_{7} x^7 + 3 b_{6} x^6 + 3$ |
$3$ |
$0$ |
$702$ |
$234$ |
$0$ |
$0\%$ |
$1$ |
$0$ |
| 3.3.9.45b |
$3$ |
$27$ |
$3$ |
$9$ |
$45$ |
$[\frac{3}{2}, 2]$ |
$[\frac{1}{2}, 1]$ |
$\langle\frac{1}{3}, \frac{7}{9}\rangle$ |
$(\frac{1}{2}, 2)$ |
$x^9 + 3 b_{8} x^8 + 3 a_{7} x^7 + 3 a_{3} x^3 + 9 c_{9} + 3$ |
$9$ |
$0$ |
$18252$ |
$6084$ |
$0$ |
$0\%$ |
$2$ |
$0$ |
| 3.3.9.48a |
$3$ |
$27$ |
$3$ |
$9$ |
$48$ |
$[2, 2]$ |
$[1, 1]$ |
$\langle\frac{2}{3}, \frac{8}{9}\rangle$ |
$(1, 1)$ |
$x^9 + 3 a_{8} x^8 + 3 b_{6} x^6 + 9 c_{9} + 3$ |
$27$ |
$0$ |
$702$ |
$234$ |
$0$ |
$0\%$ |
$1$ |
$0$ |
| 3.3.9.48b |
$3$ |
$27$ |
$3$ |
$9$ |
$48$ |
$[\frac{3}{2}, \frac{13}{6}]$ |
$[\frac{1}{2}, \frac{7}{6}]$ |
$\langle\frac{1}{3}, \frac{8}{9}\rangle$ |
$(\frac{1}{2}, \frac{5}{2})$ |
$x^9 + 3 a_{8} x^8 + 3 a_{3} x^3 + 9 b_{10} x + 3$ |
$3$ |
$0$ |
$18252$ |
$6084$ |
$0$ |
$0\%$ |
$2$ |
$0$ |
| 3.3.9.54a |
$3$ |
$27$ |
$3$ |
$9$ |
$54$ |
$[\frac{9}{4}, \frac{9}{4}]$ |
$[\frac{5}{4}, \frac{5}{4}]$ |
$\langle\frac{5}{6}, \frac{10}{9}\rangle$ |
$(\frac{5}{4}, \frac{5}{4})$ |
$x^9 + 9 b_{11} x^2 + 9 a_{10} x + 3$ |
$3$ |
$0$ |
$702$ |
$234$ |
$0$ |
$0\%$ |
$1$ |
$0$ |
| 3.3.9.54b |
$3$ |
$27$ |
$3$ |
$9$ |
$54$ |
$[\frac{3}{2}, \frac{5}{2}]$ |
$[\frac{1}{2}, \frac{3}{2}]$ |
$\langle\frac{1}{3}, \frac{10}{9}\rangle$ |
$(\frac{1}{2}, \frac{7}{2})$ |
$x^9 + 9 b_{13} x^4 + 3 a_{3} x^3 + 9 b_{11} x^2 + 9 a_{10} x + 3$ |
$3$ |
$0$ |
$492804$ |
$164268$ |
$0$ |
$0\%$ |
$2$ |
$0$ |
| 3.3.9.54c |
$3$ |
$27$ |
$3$ |
$9$ |
$54$ |
$[2, \frac{7}{3}]$ |
$[1, \frac{4}{3}]$ |
$\langle\frac{2}{3}, \frac{10}{9}\rangle$ |
$(1, 2)$ |
$x^9 + 3 a_{6} x^6 + 9 c_{12} x^3 + 9 b_{11} x^2 + 9 a_{10} x + 9 c_{9} + 3$ |
$27$ |
$0$ |
$18252$ |
$6084$ |
$0$ |
$0\%$ |
$2$ |
$0$ |
| 3.3.9.57a |
$3$ |
$27$ |
$3$ |
$9$ |
$57$ |
$[\frac{19}{8}, \frac{19}{8}]$ |
$[\frac{11}{8}, \frac{11}{8}]$ |
$\langle\frac{11}{12}, \frac{11}{9}\rangle$ |
$(\frac{11}{8}, \frac{11}{8})$ |
$x^9 + 9 b_{12} x^3 + 9 a_{11} x^2 + 3$ |
$3$ |
$0$ |
$702$ |
$234$ |
$0$ |
$0\%$ |
$1$ |
$0$ |
| 3.3.9.57b |
$3$ |
$27$ |
$3$ |
$9$ |
$57$ |
$[\frac{3}{2}, \frac{8}{3}]$ |
$[\frac{1}{2}, \frac{5}{3}]$ |
$\langle\frac{1}{3}, \frac{11}{9}\rangle$ |
$(\frac{1}{2}, 4)$ |
$x^9 + 9 c_{15} x^6 + 9 b_{14} x^5 + 9 b_{13} x^4 + 3 a_{3} x^3 + 9 a_{11} x^2 + 3$ |
$9$ |
$0$ |
$492804$ |
$164268$ |
$0$ |
$0\%$ |
$2$ |
$0$ |
| 3.3.9.57c |
$3$ |
$27$ |
$3$ |
$9$ |
$57$ |
$[2, \frac{5}{2}]$ |
$[1, \frac{3}{2}]$ |
$\langle\frac{2}{3}, \frac{11}{9}\rangle$ |
$(1, \frac{5}{2})$ |
$x^9 + 3 a_{6} x^6 + 9 b_{13} x^4 + 9 a_{11} x^2 + 9 c_{9} + 3$ |
$9$ |
$0$ |
$18252$ |
$6084$ |
$0$ |
$0\%$ |
$2$ |
$0$ |
| 3.3.9.60a |
$3$ |
$27$ |
$3$ |
$9$ |
$60$ |
$[\frac{3}{2}, \frac{17}{6}]$ |
$[\frac{1}{2}, \frac{11}{6}]$ |
$\langle\frac{1}{3}, \frac{4}{3}\rangle$ |
$(\frac{1}{2}, \frac{9}{2})$ |
$x^9 + 9 b_{16} x^7 + 9 b_{14} x^5 + 9 b_{13} x^4 + 3 a_{3} x^3 + 3$ |
$3$ |
$0$ |
$511758$ |
$170586$ |
$0$ |
$0\%$ |
$2$ |
$0$ |
| 3.3.9.63a |
$3$ |
$27$ |
$3$ |
$9$ |
$63$ |
$[2, \frac{17}{6}]$ |
$[1, \frac{11}{6}]$ |
$\langle\frac{2}{3}, \frac{13}{9}\rangle$ |
$(1, \frac{7}{2})$ |
$x^9 + 9 b_{16} x^7 + 3 a_{6} x^6 + 9 b_{14} x^5 + 9 a_{13} x^4 + 9 c_{9} + 3$ |
$9$ |
$0$ |
$492804$ |
$164268$ |
$0$ |
$0\%$ |
$2$ |
$0$ |
| 3.3.9.63b |
$3$ |
$27$ |
$3$ |
$9$ |
$63$ |
$[\frac{5}{2}, \frac{8}{3}]$ |
$[\frac{3}{2}, \frac{5}{3}]$ |
$\langle1, \frac{13}{9}\rangle$ |
$(\frac{3}{2}, 2)$ |
$x^9 + 9 c_{15} x^6 + 9 b_{14} x^5 + 9 a_{13} x^4 + 9 b_{12} x^3 + 3$ |
$9$ |
$0$ |
$18954$ |
$6318$ |
$0$ |
$0\%$ |
$2$ |
$0$ |
| 3.3.9.66a |
$3$ |
$27$ |
$3$ |
$9$ |
$66$ |
$[2, 3]$ |
$[1, 2]$ |
$\langle\frac{2}{3}, \frac{14}{9}\rangle$ |
$(1, 4)$ |
$x^9 + 9 b_{17} x^8 + 9 b_{16} x^7 + 3 a_{6} x^6 + 9 a_{14} x^5 + 9 c_{9} + 27 c_{18} + 3$ |
$27$ |
$0$ |
$492804$ |
$164268$ |
$0$ |
$0\%$ |
$2$ |
$0$ |
| 3.3.9.66b |
$3$ |
$27$ |
$3$ |
$9$ |
$66$ |
$[\frac{5}{2}, \frac{17}{6}]$ |
$[\frac{3}{2}, \frac{11}{6}]$ |
$\langle1, \frac{14}{9}\rangle$ |
$(\frac{3}{2}, \frac{5}{2})$ |
$x^9 + 9 b_{16} x^7 + 9 a_{14} x^5 + 9 b_{12} x^3 + 3$ |
$3$ |
$0$ |
$18954$ |
$6318$ |
$0$ |
$0\%$ |
$2$ |
$0$ |
| 3.3.9.69a |
$3$ |
$27$ |
$3$ |
$9$ |
$69$ |
$[2, \frac{19}{6}]$ |
$[1, \frac{13}{6}]$ |
$\langle\frac{2}{3}, \frac{5}{3}\rangle$ |
$(1, \frac{9}{2})$ |
$x^9 + 9 b_{17} x^8 + 9 b_{16} x^7 + 3 a_{6} x^6 + 27 b_{19} x + 9 c_{9} + 3$ |
$9$ |
$0$ |
$511758$ |
$170586$ |
$0$ |
$0\%$ |
$2$ |
$0$ |
| 3.3.9.72a |
$3$ |
$27$ |
$3$ |
$9$ |
$72$ |
$[\frac{5}{2}, \frac{19}{6}]$ |
$[\frac{3}{2}, \frac{13}{6}]$ |
$\langle1, \frac{16}{9}\rangle$ |
$(\frac{3}{2}, \frac{7}{2})$ |
$x^9 + 9 b_{17} x^8 + 9 a_{16} x^7 + 9 b_{12} x^3 + 27 b_{19} x + 3$ |
$3$ |
$0$ |
$511758$ |
$170586$ |
$0$ |
$0\%$ |
$2$ |
$0$ |
| 3.3.9.75a |
$3$ |
$27$ |
$3$ |
$9$ |
$75$ |
$[\frac{5}{2}, \frac{10}{3}]$ |
$[\frac{3}{2}, \frac{7}{3}]$ |
$\langle1, \frac{17}{9}\rangle$ |
$(\frac{3}{2}, 4)$ |
$x^9 + 9 a_{17} x^8 + (9 b_{12} + 27 c_{21}) x^3 + 27 b_{20} x^2 + 27 b_{19} x + 3$ |
$9$ |
$0$ |
$511758$ |
$170586$ |
$0$ |
$0\%$ |
$2$ |
$0$ |
| 3.3.9.78a |
$3$ |
$27$ |
$3$ |
$9$ |
$78$ |
$[\frac{5}{2}, \frac{7}{2}]$ |
$[\frac{3}{2}, \frac{5}{2}]$ |
$\langle1, 2\rangle$ |
$(\frac{3}{2}, \frac{9}{2})$ |
$x^9 + 27 b_{22} x^4 + 9 b_{12} x^3 + 27 b_{20} x^2 + 27 b_{19} x + 3$ |
$3$ |
$0$ |
$531441$ |
$177147$ |
$0$ |
$0\%$ |
$2$ |
$0$ |
| 3.1.27.27a |
$3$ |
$27$ |
$1$ |
$27$ |
$27$ |
$[\frac{27}{26}, \frac{27}{26}, \frac{27}{26}]$ |
$[\frac{1}{26}, \frac{1}{26}, \frac{1}{26}]$ |
$\langle\frac{1}{39}, \frac{4}{117}, \frac{1}{27}\rangle$ |
$(\frac{1}{26}, \frac{1}{26}, \frac{1}{26})$ |
$x^{27} + 3 a_{1} x + 3$ |
$1$ |
$0$ |
$2$ |
$2$ |
$0$ |
$0\%$ |
$1$ |
$0$ |
| 3.1.27.28a |
$3$ |
$27$ |
$1$ |
$27$ |
$28$ |
$[\frac{14}{13}, \frac{14}{13}, \frac{14}{13}]$ |
$[\frac{1}{13}, \frac{1}{13}, \frac{1}{13}]$ |
$\langle\frac{2}{39}, \frac{8}{117}, \frac{2}{27}\rangle$ |
$(\frac{1}{13}, \frac{1}{13}, \frac{1}{13})$ |
$x^{27} + 3 a_{2} x^2 + 3$ |
$1$ |
$0$ |
$2$ |
$2$ |
$0$ |
$0\%$ |
$1$ |
$0$ |
| 3.1.27.30a |
$3$ |
$27$ |
$1$ |
$27$ |
$30$ |
$[\frac{15}{13}, \frac{15}{13}, \frac{15}{13}]$ |
$[\frac{2}{13}, \frac{2}{13}, \frac{2}{13}]$ |
$\langle\frac{4}{39}, \frac{16}{117}, \frac{4}{27}\rangle$ |
$(\frac{2}{13}, \frac{2}{13}, \frac{2}{13})$ |
$x^{27} + 3 a_{4} x^4 + 3$ |
$1$ |
$0$ |
$2$ |
$2$ |
$0$ |
$0\%$ |
$1$ |
$0$ |
| 3.1.27.30b |
$3$ |
$27$ |
$1$ |
$27$ |
$30$ |
$[\frac{9}{8}, \frac{9}{8}, \frac{7}{6}]$ |
$[\frac{1}{8}, \frac{1}{8}, \frac{1}{6}]$ |
$\langle\frac{1}{12}, \frac{1}{9}, \frac{4}{27}\rangle$ |
$(\frac{1}{8}, \frac{1}{8}, \frac{1}{2})$ |
$x^{27} + 3 a_{4} x^4 + 3 a_{3} x^3 + 3$ |
$1$ |
$0$ |
$4$ |
$4$ |
$0$ |
$0\%$ |
$2$ |
$0$ |
| 3.1.27.31a |
$3$ |
$27$ |
$1$ |
$27$ |
$31$ |
$[\frac{31}{26}, \frac{31}{26}, \frac{31}{26}]$ |
$[\frac{5}{26}, \frac{5}{26}, \frac{5}{26}]$ |
$\langle\frac{5}{39}, \frac{20}{117}, \frac{5}{27}\rangle$ |
$(\frac{5}{26}, \frac{5}{26}, \frac{5}{26})$ |
$x^{27} + 3 a_{5} x^5 + 3$ |
$1$ |
$0$ |
$2$ |
$2$ |
$0$ |
$0\%$ |
$1$ |
$0$ |
| 3.1.27.31b |
$3$ |
$27$ |
$1$ |
$27$ |
$31$ |
$[\frac{9}{8}, \frac{9}{8}, \frac{11}{9}]$ |
$[\frac{1}{8}, \frac{1}{8}, \frac{2}{9}]$ |
$\langle\frac{1}{12}, \frac{1}{9}, \frac{5}{27}\rangle$ |
$(\frac{1}{8}, \frac{1}{8}, 1)$ |
$x^{27} + 3 c_{6} x^6 + 3 a_{5} x^5 + 3 a_{3} x^3 + 3$ |
$3$ |
$0$ |
$4$ |
$4$ |
$0$ |
$0\%$ |
$2$ |
$0$ |
| 3.1.27.33a |
$3$ |
$27$ |
$1$ |
$27$ |
$33$ |
$[\frac{33}{26}, \frac{33}{26}, \frac{33}{26}]$ |
$[\frac{7}{26}, \frac{7}{26}, \frac{7}{26}]$ |
$\langle\frac{7}{39}, \frac{28}{117}, \frac{7}{27}\rangle$ |
$(\frac{7}{26}, \frac{7}{26}, \frac{7}{26})$ |
$x^{27} + 3 a_{7} x^7 + 3$ |
$1$ |
$0$ |
$2$ |
$2$ |
$0$ |
$0\%$ |
$1$ |
$0$ |
| 3.1.27.33b |
$3$ |
$27$ |
$1$ |
$27$ |
$33$ |
$[\frac{9}{8}, \frac{9}{8}, \frac{4}{3}]$ |
$[\frac{1}{8}, \frac{1}{8}, \frac{1}{3}]$ |
$\langle\frac{1}{12}, \frac{1}{9}, \frac{7}{27}\rangle$ |
$(\frac{1}{8}, \frac{1}{8}, 2)$ |
$x^{27} + 3 c_{9} x^9 + 3 b_{8} x^8 + 3 a_{7} x^7 + 3 a_{3} x^3 + 3$ |
$3$ |
$0$ |
$12$ |
$12$ |
$0$ |
$0\%$ |
$2$ |
$0$ |
| 3.1.27.33c |
$3$ |
$27$ |
$1$ |
$27$ |
$33$ |
$[\frac{5}{4}, \frac{5}{4}, \frac{23}{18}]$ |
$[\frac{1}{4}, \frac{1}{4}, \frac{5}{18}]$ |
$\langle\frac{1}{6}, \frac{2}{9}, \frac{7}{27}\rangle$ |
$(\frac{1}{4}, \frac{1}{4}, \frac{1}{2})$ |
$x^{27} + 3 a_{7} x^7 + 3 a_{6} x^6 + 3$ |
$1$ |
$0$ |
$4$ |
$4$ |
$0$ |
$0\%$ |
$2$ |
$0$ |
| 3.1.27.34a |
$3$ |
$27$ |
$1$ |
$27$ |
$34$ |
$[\frac{17}{13}, \frac{17}{13}, \frac{17}{13}]$ |
$[\frac{4}{13}, \frac{4}{13}, \frac{4}{13}]$ |
$\langle\frac{8}{39}, \frac{32}{117}, \frac{8}{27}\rangle$ |
$(\frac{4}{13}, \frac{4}{13}, \frac{4}{13})$ |
$x^{27} + 3 a_{8} x^8 + 3$ |
$1$ |
$0$ |
$2$ |
$2$ |
$0$ |
$0\%$ |
$1$ |
$0$ |
| 3.1.27.34b |
$3$ |
$27$ |
$1$ |
$27$ |
$34$ |
$[\frac{9}{8}, \frac{9}{8}, \frac{25}{18}]$ |
$[\frac{1}{8}, \frac{1}{8}, \frac{7}{18}]$ |
$\langle\frac{1}{12}, \frac{1}{9}, \frac{8}{27}\rangle$ |
$(\frac{1}{8}, \frac{1}{8}, \frac{5}{2})$ |
$x^{27} + 3 b_{10} x^{10} + 3 a_{8} x^8 + 3 a_{3} x^3 + 3$ |
$1$ |
$0$ |
$12$ |
$12$ |
$0$ |
$0\%$ |
$2$ |
$0$ |
| 3.1.27.34c |
$3$ |
$27$ |
$1$ |
$27$ |
$34$ |
$[\frac{5}{4}, \frac{5}{4}, \frac{4}{3}]$ |
$[\frac{1}{4}, \frac{1}{4}, \frac{1}{3}]$ |
$\langle\frac{1}{6}, \frac{2}{9}, \frac{8}{27}\rangle$ |
$(\frac{1}{4}, \frac{1}{4}, 1)$ |
$x^{27} + 3 c_{9} x^9 + 3 a_{8} x^8 + 3 a_{6} x^6 + 3$ |
$3$ |
$0$ |
$4$ |
$4$ |
$0$ |
$0\%$ |
$2$ |
$0$ |
| 3.1.27.36a |
$3$ |
$27$ |
$1$ |
$27$ |
$36$ |
$[\frac{18}{13}, \frac{18}{13}, \frac{18}{13}]$ |
$[\frac{5}{13}, \frac{5}{13}, \frac{5}{13}]$ |
$\langle\frac{10}{39}, \frac{40}{117}, \frac{10}{27}\rangle$ |
$(\frac{5}{13}, \frac{5}{13}, \frac{5}{13})$ |
$x^{27} + 3 a_{10} x^{10} + 3 b_{9} x^9 + 3$ |
$1$ |
$0$ |
$6$ |
$6$ |
$0$ |
$0\%$ |
$1$ |
$0$ |
| 3.1.27.36b |
$3$ |
$27$ |
$1$ |
$27$ |
$36$ |
$[\frac{9}{8}, \frac{9}{8}, \frac{3}{2}]$ |
$[\frac{1}{8}, \frac{1}{8}, \frac{1}{2}]$ |
$\langle\frac{1}{12}, \frac{1}{9}, \frac{10}{27}\rangle$ |
$(\frac{1}{8}, \frac{1}{8}, \frac{7}{2})$ |
$x^{27} + 3 b_{13} x^{13} + 3 b_{11} x^{11} + 3 a_{10} x^{10} + 3 a_{3} x^3 + 3$ |
$1$ |
$0$ |
$36$ |
$36$ |
$0$ |
$0\%$ |
$2$ |
$0$ |
| 3.1.27.36c |
$3$ |
$27$ |
$1$ |
$27$ |
$36$ |
$[\frac{5}{4}, \frac{5}{4}, \frac{13}{9}]$ |
$[\frac{1}{4}, \frac{1}{4}, \frac{4}{9}]$ |
$\langle\frac{1}{6}, \frac{2}{9}, \frac{10}{27}\rangle$ |
$(\frac{1}{4}, \frac{1}{4}, 2)$ |
$x^{27} + 3 c_{12} x^{12} + 3 b_{11} x^{11} + 3 a_{10} x^{10} + 3 a_{6} x^6 + 3$ |
$3$ |
$0$ |
$12$ |
$12$ |
$0$ |
$0\%$ |
$2$ |
$0$ |
| 3.1.27.37a |
$3$ |
$27$ |
$1$ |
$27$ |
$37$ |
$[\frac{37}{26}, \frac{37}{26}, \frac{37}{26}]$ |
$[\frac{11}{26}, \frac{11}{26}, \frac{11}{26}]$ |
$\langle\frac{11}{39}, \frac{44}{117}, \frac{11}{27}\rangle$ |
$(\frac{11}{26}, \frac{11}{26}, \frac{11}{26})$ |
$x^{27} + 3 a_{11} x^{11} + 3 b_{9} x^9 + 3$ |
$1$ |
$0$ |
$6$ |
$6$ |
$0$ |
$0\%$ |
$1$ |
$0$ |
| 3.1.27.37b |
$3$ |
$27$ |
$1$ |
$27$ |
$37$ |
$[\frac{9}{8}, \frac{9}{8}, \frac{14}{9}]$ |
$[\frac{1}{8}, \frac{1}{8}, \frac{5}{9}]$ |
$\langle\frac{1}{12}, \frac{1}{9}, \frac{11}{27}\rangle$ |
$(\frac{1}{8}, \frac{1}{8}, 4)$ |
$x^{27} + 3 c_{15} x^{15} + 3 b_{14} x^{14} + 3 b_{13} x^{13} + 3 a_{11} x^{11} + 3 a_{3} x^3 + 3$ |
$3$ |
$0$ |
$36$ |
$36$ |
$0$ |
$0\%$ |
$2$ |
$0$ |
| 3.1.27.37c |
$3$ |
$27$ |
$1$ |
$27$ |
$37$ |
$[\frac{5}{4}, \frac{5}{4}, \frac{3}{2}]$ |
$[\frac{1}{4}, \frac{1}{4}, \frac{1}{2}]$ |
$\langle\frac{1}{6}, \frac{2}{9}, \frac{11}{27}\rangle$ |
$(\frac{1}{4}, \frac{1}{4}, \frac{5}{2})$ |
$x^{27} + 3 b_{13} x^{13} + 3 a_{11} x^{11} + 3 a_{6} x^6 + 3$ |
$1$ |
$0$ |
$12$ |
$12$ |
$0$ |
$0\%$ |
$2$ |
$0$ |
| 3.1.27.39a |
$3$ |
$27$ |
$1$ |
$27$ |
$39$ |
$[\frac{3}{2}, \frac{3}{2}, \frac{3}{2}]$ |
$[\frac{1}{2}, \frac{1}{2}, \frac{1}{2}]$ |
$\langle\frac{1}{3}, \frac{4}{9}, \frac{13}{27}\rangle$ |
$(\frac{1}{2}, \frac{1}{2}, \frac{1}{2})$ |
$x^{27} + 3 a_{13} x^{13} + 3 b_{12} x^{12} + 3 b_{9} x^9 + 3$ |
$1$ |
$0$ |
$18$ |
$18$ |
$0$ |
$0\%$ |
$1$ |
$0$ |
| 3.1.27.39b |
$3$ |
$27$ |
$1$ |
$27$ |
$39$ |
$[\frac{9}{8}, \frac{9}{8}, \frac{5}{3}]$ |
$[\frac{1}{8}, \frac{1}{8}, \frac{2}{3}]$ |
$\langle\frac{1}{12}, \frac{1}{9}, \frac{13}{27}\rangle$ |
$(\frac{1}{8}, \frac{1}{8}, 5)$ |
$x^{27} + 3 c_{18} x^{18} + 3 b_{17} x^{17} + 3 b_{16} x^{16} + 3 b_{14} x^{14} + 3 a_{13} x^{13} + 3 a_{3} x^3 + 3$ |
$3$ |
$0$ |
$108$ |
$108$ |
$0$ |
$0\%$ |
$2$ |
$0$ |
| 3.1.27.39c |
$3$ |
$27$ |
$1$ |
$27$ |
$39$ |
$[\frac{5}{4}, \frac{5}{4}, \frac{29}{18}]$ |
$[\frac{1}{4}, \frac{1}{4}, \frac{11}{18}]$ |
$\langle\frac{1}{6}, \frac{2}{9}, \frac{13}{27}\rangle$ |
$(\frac{1}{4}, \frac{1}{4}, \frac{7}{2})$ |
$x^{27} + 3 b_{16} x^{16} + 3 b_{14} x^{14} + 3 a_{13} x^{13} + 3 a_{6} x^6 + 3$ |
$1$ |
$0$ |
$36$ |
$36$ |
$0$ |
$0\%$ |
$2$ |
$0$ |
| 3.1.27.40a |
$3$ |
$27$ |
$1$ |
$27$ |
$40$ |
$[\frac{20}{13}, \frac{20}{13}, \frac{20}{13}]$ |
$[\frac{7}{13}, \frac{7}{13}, \frac{7}{13}]$ |
$\langle\frac{14}{39}, \frac{56}{117}, \frac{14}{27}\rangle$ |
$(\frac{7}{13}, \frac{7}{13}, \frac{7}{13})$ |
$x^{27} + 3 a_{14} x^{14} + 3$ |
$1$ |
$0$ |
$2$ |
$2$ |
$0$ |
$0\%$ |
$1$ |
$0$ |
